|\^/| Maple 11 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2007 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > display_poles := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles, array_complex_poles,array_poles,array_real_poles,array_x ; > local rad_given; > if (glob_type_given_pole = 4) then # if number 1 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[1,1],2.0) + expt(array_given_rad_poles[1,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[1,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 2 > omniout_str(ALWAYS,"NO POLE (given) for Equation 1"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 1"); > fi;# end if 2; > if (array_poles[1,1] <> glob_large_float) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4, array_poles[1,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1"); > fi;# end if 2; > if ((array_real_poles[1,1] > 0.0) and (array_real_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4, array_real_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1"); > fi;# end if 2; > if ((array_complex_poles[1,1] > 0.0) and (array_complex_poles[1,1] <> glob_large_float)) then # if number 2 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4, array_complex_poles[1,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[1,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1"); > fi;# end if 2 > ; > if (glob_type_given_pole = 4) then # if number 2 > rad_given := sqrt(expt(array_x[1] - array_given_rad_poles[2,1],2.0) + expt(array_given_rad_poles[2,2],2.0)) ; > omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4, rad_given,4," "); > omniout_float(ALWAYS,"Order of pole (given) ",4, array_given_ord_poles[2,1],4," "); > elif > (glob_type_given_pole = 3) then # if number 3 > omniout_str(ALWAYS,"NO POLE (given) for Equation 2"); > else > omniout_str(ALWAYS,"NO INFO (given) for Equation 2"); > fi;# end if 3; > if (array_poles[2,1] <> glob_large_float) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4, array_poles[2,1],4," "); > omniout_str(ALWAYS,"Order of pole (ratio test) Not computed"); > else > omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2"); > fi;# end if 3; > if ((array_real_poles[2,1] > 0.0) and (array_real_poles[2,1] <> glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4, array_real_poles[2,1],4," "); > omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_real_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2"); > fi;# end if 3; > if ((array_complex_poles[2,1] > 0.0) and (array_complex_poles[2,1] <> glob_large_float)) then # if number 3 > omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4, array_complex_poles[2,1],4," "); > omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_complex_poles[2,2],4," "); > else > omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2"); > fi;# end if 3 > ; > end; display_poles := proc() local rad_given; global ALWAYS, glob_display_flag, glob_large_float, array_pole, glob_type_given_pole, array_given_rad_poles, array_given_ord_poles, array_complex_poles, array_poles, array_real_poles, array_x; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[1, 1], 2.0) + expt(array_given_rad_poles[1, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 1 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[1, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 1") else omniout_str(ALWAYS, "NO INFO (given) for Equation 1") end if; if array_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 1 ", 4, array_poles[1, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1") end if; if 0. < array_real_poles[1, 1] and array_real_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 1 ", 4, array_real_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 1") end if; if 0. < array_complex_poles[1, 1] and array_complex_poles[1, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 1 ", 4, array_complex_poles[1, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[1, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 1") end if; if glob_type_given_pole = 4 then rad_given := sqrt( expt(array_x[1] - array_given_rad_poles[2, 1], 2.0) + expt(array_given_rad_poles[2, 2], 2.0)); omniout_float(ALWAYS, "Radius of convergence (given) for eq 2 ", 4, rad_given, 4, " "); omniout_float(ALWAYS, "Order of pole (given) ", 4, array_given_ord_poles[2, 1], 4, " ") elif glob_type_given_pole = 3 then omniout_str(ALWAYS, "NO POLE (given) for Equation 2") else omniout_str(ALWAYS, "NO INFO (given) for Equation 2") end if; if array_poles[2, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (ratio test) for eq 2 ", 4, array_poles[2, 1], 4, " "); omniout_str(ALWAYS, "Order of pole (ratio test) \ Not computed") else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2") end if; if 0. < array_real_poles[2, 1] and array_real_poles[2, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (three term test) for eq 2 ", 4, array_real_poles[2, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (three term test) ", 4, array_real_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO REAL POLE (three term test) for Equation 2") end if; if 0. < array_complex_poles[2, 1] and array_complex_poles[2, 1] <> glob_large_float then omniout_float(ALWAYS, "Radius of convergence (six term test) for eq 2 ", 4, array_complex_poles[2, 1], 4, " "); omniout_float(ALWAYS, "Order of pole (six term test) ", 4, array_complex_poles[2, 2], 4, " ") else omniout_str(ALWAYS, "NO COMPLEX POLE (six term test) for Equation 2") end if end proc > # End Function number 3 > # Begin Function number 4 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 3 > ret := 1.0; > else > ret := -1.0; > fi;# end if 3; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 4 > # Begin Function number 5 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y1[1]) < min_size) then # if number 3 > min_size := omniabs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (omniabs(array_y2[1]) < min_size) then # if number 3 > min_size := omniabs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > if (min_size < 1.0) then # if number 3 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 3; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y1[1]) < min_size then min_size := omniabs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if omniabs(array_y2[1]) < min_size then min_size := omniabs(array_y2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 5 > # Begin Function number 6 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp; > max_estimated_step_error := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > est_tmp := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > est_tmp := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3); > if (est_tmp >= max_estimated_step_error) then # if number 3 > max_estimated_step_error := est_tmp; > fi;# end if 3; > omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,""); > max_estimated_step_error; > end; test_suggested_h := proc() local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; max_estimated_step_error := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); est_tmp := omniabs(array_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; est_tmp := omniabs(array_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[no_terms]*hn_div_ho_3); if max_estimated_step_error <= est_tmp then max_estimated_step_error := est_tmp end if; omniout_float(ALWAYS, "max_estimated_step_error", 32, max_estimated_step_error, 32, ""); max_estimated_step_error end proc > # End Function number 6 > # Begin Function number 7 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 3 > ret := true; > else > ret := false; > fi;# end if 3; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 7 > # Begin Function number 8 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 3 > if (iter >= 0) then # if number 4 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 5 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 6 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 5; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 5; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 5 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 6 > glob_good_digits := -trunc(log10(relerr)) + 3; > else > glob_good_digits := Digits; > fi;# end if 6; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 5; > if (glob_iter = 1) then # if number 5 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 5; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 4; > #BOTTOM DISPLAY ALOT > fi;# end if 3; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 3 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 8 > # Begin Function number 9 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 4 > glob_normmax := tmp; > fi;# end if 4 > fi;# end if 3; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 4 > glob_normmax := tmp; > fi;# end if 4 > fi;# end if 3; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 3 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 4 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 4 > fi;# end if 3; > if ( not glob_reached_optimal_h) then # if number 3 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 3; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 9 > # Begin Function number 10 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 3 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 3; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 10 > # Begin Function number 11 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; > #TOP CHECK FOR POLE > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > #TOP radius ratio test in Henrici1 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y1_higher[1,n]) = 0.0) or (omniabs(array_y1_higher[1,n+1]) = 0.0)) then # if number 3 > found_sing := 0; > else > tmp_rad := omniabs(array_y1_higher[1,n] * glob_h / array_y1_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 4 > if (tmp_rad < rad_c) then # if number 5 > rad_c := tmp_rad; > fi;# end if 5; > elif > (cnt = 0) then # if number 5 > if (tmp_rad < rad_c) then # if number 6 > rad_c := tmp_rad; > fi;# end if 6; > elif > (cnt > 0) then # if number 6 > found_sing := 0; > fi;# end if 6 > fi;# end if 5; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 5 > if (rad_c < array_pole[1]) then # if number 6 > array_pole[1] := rad_c; > array_poles[1,1] := rad_c; > fi;# end if 6; > fi;# end if 5; > #BOTTOM radius ratio test in Henrici1 > tmp_rad := glob_large_float; > prev_tmp_rad := glob_large_float; > tmp_ratio := glob_large_float; > rad_c := glob_large_float; > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > #TOP radius ratio test in Henrici2 > found_sing := 1; > n := glob_max_terms - 1 - 10; > cnt := 0; > while ((cnt < 5) and (found_sing = 1)) do # do number 1 > if ((omniabs(array_y2_higher[1,n]) = 0.0) or (omniabs(array_y2_higher[1,n+1]) = 0.0)) then # if number 5 > found_sing := 0; > else > tmp_rad := omniabs(array_y2_higher[1,n] * glob_h / array_y2_higher[1,n + 1]); > tmp_ratio := tmp_rad / prev_tmp_rad; > if ((cnt > 0 ) and (tmp_ratio < 2.0) and (tmp_ratio > 0.5)) then # if number 6 > if (tmp_rad < rad_c) then # if number 7 > rad_c := tmp_rad; > fi;# end if 7; > elif > (cnt = 0) then # if number 7 > if (tmp_rad < rad_c) then # if number 8 > rad_c := tmp_rad; > fi;# end if 8; > elif > (cnt > 0) then # if number 8 > found_sing := 0; > fi;# end if 8 > fi;# end if 7; > prev_tmp_rad := tmp_rad;; > cnt := cnt + 1; > n := n + 1; > od;# end do number 1; > if (found_sing = 1) then # if number 7 > if (rad_c < array_pole[1]) then # if number 8 > array_pole[1] := rad_c; > array_poles[2,1] := rad_c; > fi;# end if 8; > fi;# end if 7; > #BOTTOM radius ratio test in Henrici2 > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) = 0.0) or (omniabs(array_y1_higher[1,m-1]) = 0.0) or (omniabs(array_y1_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 7 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 8 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[1,1] := rcs; > array_real_poles[1,2] := ord_no; > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 8 > else > array_real_poles[1,1] := glob_large_float; > array_real_poles[1,2] := glob_large_float; > fi;# end if 7; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) = 0.0) or (omniabs(array_y2_higher[1,m-1]) = 0.0) or (omniabs(array_y2_higher[1,m-2]) = 0.0))) do # do number 1 > m := m - 1; > od;# end do number 1; > if (m > 10) then # if number 7 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > 0.0) then # if number 8 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_poles[2,1] := rcs; > array_real_poles[2,2] := ord_no; > else > array_real_poles[2,1] := glob_large_float; > array_real_poles[2,2] := glob_large_float; > fi;# end if 8 > else > array_real_poles[2,1] := glob_large_float; > array_real_poles[2,2] := glob_large_float; > fi;# end if 7; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y1_higher[1,n]) <> 0.0) then # if number 7 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 7; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 7 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 10 > if (rcs > 0.0) then # if number 11 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 11 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 10 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 9 > fi;# end if 8; > array_complex_poles[1,1] := rad_c; > array_complex_poles[1,2] := ord_no; > fi;# end if 7; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 1 > if (omniabs(array_y2_higher[1,n]) <> 0.0) then # if number 7 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 7; > n := n - 1; > od;# end do number 1; > m := n + cnt; > if (m <= 10) then # if number 7 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) = 0.0) or (omniabs(dr1) = 0.0)) then # if number 8 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) <> 0.0) then # if number 9 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) <> 0.0) then # if number 10 > if (rcs > 0.0) then # if number 11 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 11 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 10 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 9 > fi;# end if 8; > array_complex_poles[2,1] := rad_c; > array_complex_poles[2,2] := ord_no; > fi;# end if 7; > #BOTTOM RADII COMPLEX EQ = 2 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 7 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 1 > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 1; > glob_h := h_new; > fi;# end if 7; > #BOTTOM ADJUST ALL SERIES > ; > if (reached_interval()) then # if number 7 > display_poles(); > fi;# end if 7 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ratio, prev_tmp_rad; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y1_higher[1, n]) = 0. or omniabs(array_y1_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y1_higher[1, n]*glob_h/array_y1_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[1, 1] := rad_c end if end if; tmp_rad := glob_large_float; prev_tmp_rad := glob_large_float; tmp_ratio := glob_large_float; rad_c := glob_large_float; array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found_sing := 1; n := glob_max_terms - 11; cnt := 0; while cnt < 5 and found_sing = 1 do if omniabs(array_y2_higher[1, n]) = 0. or omniabs(array_y2_higher[1, n + 1]) = 0. then found_sing := 0 else tmp_rad := omniabs( array_y2_higher[1, n]*glob_h/array_y2_higher[1, n + 1]); tmp_ratio := tmp_rad/prev_tmp_rad; if 0 < cnt and tmp_ratio < 2.0 and 0.5 < tmp_ratio then if tmp_rad < rad_c then rad_c := tmp_rad end if elif cnt = 0 then if tmp_rad < rad_c then rad_c := tmp_rad end if elif 0 < cnt then found_sing := 0 end if end if; prev_tmp_rad := tmp_rad; cnt := cnt + 1; n := n + 1 end do; if found_sing = 1 then if rad_c < array_pole[1] then array_pole[1] := rad_c; array_poles[2, 1] := rad_c end if end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) = 0. or omniabs(array_y1_higher[1, m - 1]) = 0. or omniabs(array_y1_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[1, 1] := rcs; array_real_poles[1, 2] := ord_no else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if else array_real_poles[1, 1] := glob_large_float; array_real_poles[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y2_higher[1, m]) = 0. or omniabs(array_y2_higher[1, m - 1]) = 0. or omniabs(array_y2_higher[1, m - 2]) = 0.) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if 0. < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_poles[2, 1] := rcs; array_real_poles[2, 2] := ord_no else array_real_poles[2, 1] := glob_large_float; array_real_poles[2, 2] := glob_large_float end if else array_real_poles[2, 1] := glob_large_float; array_real_poles[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y1_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[1, 1] := rad_c; array_complex_poles[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if omniabs(array_y2_higher[1, n]) <> 0. then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) = 0. or omniabs(dr1) = 0. then rad_c := glob_large_float; ord_no := glob_large_float else if omniabs(nr1*dr2 - nr2*dr1) <> 0. then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if omniabs(rcs) <> 0. then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_poles[2, 1] := rad_c; array_complex_poles[2, 2] := ord_no end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_poles() end if end proc > # End Function number 11 > # Begin Function number 12 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 7 > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 1; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 8 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 8; > iii := iii + 1; > od;# end do number 1 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 1 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 8 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 8; > iii := iii + 1; > od;# end do number 1 > #BOTTOM GET NORMS > ; > fi;# end if 7; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 12 > # Begin Function number 13 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_y2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y1_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp5[1] := array_y1[1] - array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y2_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp5[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y1_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp5[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y1_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp5[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y1_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp5[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y1_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp5[kkk] := array_y1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d < glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 1 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y2_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 1 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; array_tmp1[1] := array_m1[1]*array_y2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_y1[1] - array_const_1D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y2, 1); array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := array_y1[2]; if not array_y2_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y2, 1); array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := array_y1[3]; if not array_y2_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y2, 1); array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := array_y1[4]; if not array_y2_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y2, 1); array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := array_y1[5]; if not array_y2_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y1_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; array_tmp5[kkk] := array_y1[kkk]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y2_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 13 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s ", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s ", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s ", prelabel, value, postlabel) else printf("%-30s = %-32d %s ", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, " ") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf(" = %d Years %d Days %d Hours %d Mi\ nutes %d Seconds ", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf(" = %d Days %d Hours %d Minutes %d\ Seconds ", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf(" = %d Hours %d Minutes %d Second\ s ", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds ", minutes_int, sec_int) else printf(" = %d Seconds ", sec_int) end if else printf(" Unknown ") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,m,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_int(ALWAYS,"m",4, m ,4," "); > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, m, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_int(ALWAYS, "m", 4, m, 4, " "); omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > elif > (pole = 4) then # if number 9 > fprintf(file,"Yes"); > else > fprintf(file,"No"); > fi;# end if 9 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") elif pole = 4 then fprintf(file, "Yes") else fprintf(file, "No") end if; fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, " ") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 9 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 9; > if (glob_max_iter < 2) then # if number 9 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 9; > if (errflag) then # if number 9 > quit; > fi;# end if 9 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 9 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 10 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 10 > fi;# end if 9; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 9 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 9; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 9 > if (array_fact_1[nnn] = 0) then # if number 10 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 10; > else > ret := factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 9 > if (array_fact_2[mmm,nnn] = 0) then # if number 10 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 10; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 9; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(1.0 + cos(x)); > end; exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > return(1.0 + sin(x)); > end; exact_soln_y2 := proc(x) return 1.0 + sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > glob_yes_pole, > glob_no_pole, > glob_not_given, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_estimated_step_error, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_min_h, > glob_type_given_pole, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_real_pole, > array_complex_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_type_real_pole, > array_type_complex_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_given_rad_poles, > array_given_ord_poles, > array_real_poles, > array_complex_poles, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > glob_yes_pole := 4; > glob_no_pole := 3; > glob_not_given := 0; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_estimated_step_error := 0.0; > glob_ratio_of_radius := 0.1; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_min_h := 0.000001; > glob_type_given_pole := 0; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 1.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=64;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.01;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 0.0; > glob_smallish_float := 0.0; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=64; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y1_init:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(4 + 1),[]); > array_real_pole:= Array(0..(4 + 1),[]); > array_complex_pole:= Array(0..(4 + 1),[]); > array_1st_rel_error:= Array(0..(3 + 1),[]); > array_last_rel_error:= Array(0..(3 + 1),[]); > array_type_pole:= Array(0..(3 + 1),[]); > array_type_real_pole:= Array(0..(3 + 1),[]); > array_type_complex_pole:= Array(0..(3 + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_given_rad_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_given_ord_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_real_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_complex_poles := Array(0..(3+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 4) do # do number 1 > array_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_real_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= 3) do # do number 1 > array_type_complex_pole[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=2) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_rad_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_given_ord_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_real_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=3) do # do number 1 > term := 1; > while (term <= 3) do # do number 2 > array_complex_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > ord := 1; > while (ord <=max_terms) do # do number 1 > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := ord + 1; > od;# end do number 1; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_1D0[1] := 1.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 1 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 1 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 2 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 2; > iiif := iiif + 1; > od;# end do number 1; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_look_poles := true; > glob_max_iter := 1000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.01; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := false; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > found_h := false; > glob_h := glob_min_h; > if (glob_max_h < glob_h) then # if number 7 > glob_h := glob_max_h; > fi;# end if 7; > if (glob_display_interval < glob_h) then # if number 7 > glob_h := glob_display_interval; > fi;# end if 7; > best_h := glob_h; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > estimated_step_error := 0.0; > while ((opt_iter <= 100) and ( not found_h)) do # do number 1 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > if (glob_subiter_method = 1 ) then # if number 7 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 8 > subiter := 1; > while (subiter <= 2) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 2 + glob_max_terms) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 8; > estimated_step_error := test_suggested_h(); > omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,""); > if (((estimated_step_error > est_needed_step_err) and (opt_iter = 1)) or (glob_h >= glob_max_h )) then # if number 8 > found_h := true; > glob_h := glob_max_h; > best_h := glob_h; > elif > ((estimated_step_error > est_needed_step_err) and ( not found_h)) then # if number 9 > glob_h := glob_h/2.0; > best_h := glob_h; > found_h := true; > else > glob_h := glob_h*2.0; > best_h := glob_h; > fi;# end if 9; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > od;# end do number 1; > if (( not found_h) and (opt_iter = 1)) then # if number 9 > omniout_str(ALWAYS,"Beginning glob_h too large."); > found_h := false; > fi;# end if 9; > if (opt_iter > 100) then # if number 9 > glob_h := glob_max_h; > found_h := false; > fi;# end if 9; > if (glob_display_interval < glob_h) then # if number 9 > glob_h := glob_display_interval; > fi;# end if 9; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 9 > html_log_file := fopen("entry.html",WRITE,TEXT); > fi;# end if 9; > #BEGIN SOLUTION CODE > if (found_h) then # if number 9 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 1 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 1; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 1 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 2 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 2; > r_order := r_order + 1; > od;# end do number 1 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and ((glob_check_sign * array_x[1]) < (glob_check_sign * x_end )) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 1 > #left paren 0001C > if (reached_interval()) then # if number 10 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 10; > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if (glob_subiter_method = 1 ) then # if number 10 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 11 > subiter := 1; > while (subiter <= 2) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 2 + glob_max_terms) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > fi;# end if 11; > display_alot(current_iter); > if (glob_look_poles) then # if number 11 > #left paren 0004C > check_for_pole(); > fi;# end if 11;#was right paren 0004C > if (reached_interval()) then # if number 11 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 11; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y2; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 2; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 2; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 2 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 3 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 3; > term_no := term_no - 1; > od;# end do number 2; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 1;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 11 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 11; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 11 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 11; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 1.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 11 > logstart(html_log_file); > logitem_str(html_log_file,"2013-05-26T02:58:59-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest2") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 12 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 12; > log_revs(html_log_file," 189 ") > ; > logitem_str(html_log_file,"mtest2 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest2 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 - 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 12 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 12; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 11; > if (glob_html_log) then # if number 11 > fclose(html_log_file); > fi;# end if 11 > ; > ;; > fi;# end if 10 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, estimated_step_error, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, glob_yes_pole, glob_no_pole, glob_not_given, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_min_h, glob_type_given_pole, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_real_pole, array_complex_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_type_real_pole, array_type_complex_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_given_rad_poles, array_given_ord_poles, array_real_poles, array_complex_poles, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; glob_yes_pole := 4; glob_no_pole := 3; glob_not_given := 0; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_estimated_step_error := 0.; glob_ratio_of_radius := 0.1; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_min_h := 0.1*10^(-5); glob_type_given_pole := 0; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.; glob_smallish_float := 0.; glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest2postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=64;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.01;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.; glob_smallish_float := 0.; glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 64; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y1_init := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 5, []); array_real_pole := Array(0 .. 5, []); array_complex_pole := Array(0 .. 5, []); array_1st_rel_error := Array(0 .. 4, []); array_last_rel_error := Array(0 .. 4, []); array_type_pole := Array(0 .. 4, []); array_type_real_pole := Array(0 .. 4, []); array_type_complex_pole := Array(0 .. 4, []); array_y1 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 4, 0 .. 4, []); array_given_rad_poles := Array(0 .. 4, 0 .. 4, []); array_given_ord_poles := Array(0 .. 4, 0 .. 4, []); array_real_poles := Array(0 .. 4, 0 .. 4, []); array_complex_poles := Array(0 .. 4, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 4 do array_real_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 4 do array_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_type_pole[term] := 0.; term := term + 1 end do ; term := 1; while term <= 3 do array_type_real_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= 3 do array_type_complex_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_given_rad_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_given_ord_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_real_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= 3 do array_complex_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.01; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := false; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); found_h := false; glob_h := glob_min_h; if glob_max_h < glob_h then glob_h := glob_max_h end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; best_h := glob_h; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer); omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); estimated_step_error := 0.; while opt_iter <= 100 and not found_h do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; estimated_step_error := test_suggested_h(); omniout_float(ALWAYS, "estimated_step_error", 32, estimated_step_error, 32, ""); if est_needed_step_err < estimated_step_error and opt_iter = 1 or glob_max_h <= glob_h then found_h := true; glob_h := glob_max_h; best_h := glob_h elif est_needed_step_err < estimated_step_error and not found_h then glob_h := glob_h/2.0; best_h := glob_h; found_h := true else glob_h := glob_h*2.0; best_h := glob_h end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1 end do; if not found_h and opt_iter = 1 then omniout_str(ALWAYS, "Beginning glob_h too large."); found_h := false end if; if 100 < opt_iter then glob_h := glob_max_h; found_h := false end if; if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT) end if; if found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-05-26T02:58:59-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest2"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 189 "); logitem_str(html_log_file, "mtest2 diffeq.mxt"); logitem_str(html_log_file, "mtest2 maple results") ; logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 13 > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; ! #BEGIN FIRST INPUT BLOCK Digits:=64; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.01; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(1.0 + cos(x)); end; exact_soln_y2 := proc(x) return(1.0 + sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 9.9 estimated_steps = 9900000 step_error = 1.0101010101010101010101010101010e-17 est_needed_step_err = 1.0101010101010101010101010101010e-17 opt_iter = 1 bytes used=4000176, alloc=3276200, time=0.17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.4672086055323049562331277806885e-183 estimated_step_error = 2.4672086055323049562331277806885e-183 best_h = 2.0e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.6557156646065677204134289038211e-175 estimated_step_error = 1.6557156646065677204134289038211e-175 best_h = 4.00e-06 opt_iter = 3 bytes used=8001416, alloc=4586680, time=0.38 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.1111319694584368636820923174826e-167 estimated_step_error = 1.1111319694584368636820923174826e-167 best_h = 8.000e-06 opt_iter = 4 bytes used=12002188, alloc=4586680, time=0.59 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.4566803670241957246681619817534e-160 estimated_step_error = 7.4566803670241957246681619817534e-160 best_h = 1.60000e-05 opt_iter = 5 bytes used=16003096, alloc=4586680, time=0.79 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.0040934120378230048946847695108e-152 estimated_step_error = 5.0040934120378230048946847695108e-152 best_h = 3.200000e-05 opt_iter = 6 bytes used=20004020, alloc=4586680, time=1.00 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.3581901424816281269073121711211e-144 estimated_step_error = 3.3581901424816281269073121711211e-144 best_h = 6.4000000e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.2536431215809227087580736291233e-136 estimated_step_error = 2.2536431215809227087580736291233e-136 best_h = 0.000128 opt_iter = 8 bytes used=24004848, alloc=4586680, time=1.20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.5123941176543087498746423194481e-128 estimated_step_error = 1.5123941176543087498746423194481e-128 best_h = 0.000256 opt_iter = 9 bytes used=28005744, alloc=4586680, time=1.40 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.0149502701580566739311213784161e-120 estimated_step_error = 1.0149502701580566739311213784161e-120 best_h = 0.000512 opt_iter = 10 bytes used=32006408, alloc=4586680, time=1.60 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.8112127244081165253087202414265e-113 estimated_step_error = 6.8112127244081165253087202414265e-113 best_h = 0.001024 opt_iter = 11 bytes used=36007600, alloc=4586680, time=1.80 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.5709231343600303584753702483547e-105 estimated_step_error = 4.5709231343600303584753702483547e-105 best_h = 0.002048 opt_iter = 12 bytes used=40008448, alloc=4586680, time=2.00 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.0674887502340254951354356814935e-97 estimated_step_error = 3.0674887502340254951354356814935e-97 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.0585490116180929098885606683401e-89 estimated_step_error = 2.0585490116180929098885606683401e-89 best_h = 0.008192 opt_iter = 14 bytes used=44009252, alloc=4586680, time=2.20 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3814583197402461309888420940035e-81 estimated_step_error = 1.3814583197402461309888420940035e-81 best_h = 0.016384 opt_iter = 15 bytes used=48010588, alloc=4586680, time=2.40 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.2706681184281159182706538798651e-74 estimated_step_error = 9.2706681184281159182706538798651e-74 best_h = 0.032768 opt_iter = 16 bytes used=52011776, alloc=4586680, time=2.60 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.2212490020161221570851682852212e-66 estimated_step_error = 6.2212490020161221570851682852212e-66 best_h = 0.065536 opt_iter = 17 bytes used=56012620, alloc=4586680, time=2.81 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.1747508750792467142506979498164e-58 estimated_step_error = 4.1747508750792467142506979498164e-58 best_h = 0.131072 opt_iter = 18 bytes used=60013704, alloc=4586680, time=3.01 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.8012747543996062244493916551861e-50 estimated_step_error = 2.8012747543996062244493916551861e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09579 Order of pole (three term test) = -1.134 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=64014656, alloc=4586680, time=3.21 x[1] = 0.11 y1[1] (analytic) = 1.9939560979566968503578396114198 y1[1] (numeric) = 1.9939560979566968503578396114198 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1097783008371748086649494900835 y2[1] (numeric) = 1.1097783008371748086649494900835 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1052 Order of pole (three term test) = -1.184 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=68015432, alloc=4652204, time=3.42 x[1] = 0.12 y1[1] (analytic) = 1.9928086358538662522480981678576 y1[1] (numeric) = 1.9928086358538662522480981678576 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.119712207288919359967350614271 y2[1] (numeric) = 1.119712207288919359967350614271 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1146 Order of pole (three term test) = -1.239 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=72016628, alloc=4652204, time=3.63 x[1] = 0.13 y1[1] (analytic) = 1.9915618937147880395945121711518 y1[1] (numeric) = 1.9915618937147880395945121711518 absolute error = 1e-63 relative error = 5.0211846448554824157110355498792e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1296341426196948595412058107083 y2[1] (numeric) = 1.1296341426196948595412058107083 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1239 Order of pole (three term test) = -1.299 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y1[1] (analytic) = 1.9902159962126371718989482270114 y1[1] (numeric) = 1.9902159962126371718989482270114 absolute error = 1e-63 relative error = 5.0245802561279320882102203714577e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1395431146442364817179883517054 y2[1] (numeric) = 1.1395431146442364817179883517054 absolute error = 1e-63 relative error = 8.7754468185453288747766003261556e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1332 Order of pole (three term test) = -1.364 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=76017384, alloc=4652204, time=3.84 x[1] = 0.15 y1[1] (analytic) = 1.9887710779360422867349809986543 y1[1] (numeric) = 1.9887710779360422867349809986543 absolute error = 1e-63 relative error = 5.0282308059196314117533356413880e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1494381324735992214977254386876 y2[1] (numeric) = 1.1494381324735992214977254386876 absolute error = 1e-63 relative error = 8.6999027763938257948745204743366e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1425 Order of pole (three term test) = -1.433 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=80018088, alloc=4652204, time=4.05 x[1] = 0.16 y1[1] (analytic) = 1.9872272833756269490409525240183 y1[1] (numeric) = 1.9872272833756269490409525240183 absolute error = 1e-63 relative error = 5.0321370301505636686694704794452e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.159318206614245963311463159686 y2[1] (numeric) = 1.159318206614245963311463159686 absolute error = 1e-63 relative error = 8.6257594704776525046338123046310e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1517 Order of pole (three term test) = -1.507 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=84018796, alloc=4652204, time=4.26 x[1] = 0.17 y1[1] (analytic) = 1.9855847669095607091719299902125 y1[1] (numeric) = 1.9855847669095607091719299902125 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1691823490669960101576243766709 y2[1] (numeric) = 1.1691823490669960101576243766709 absolute error = 1e-63 relative error = 8.5529857750418229057076547011106e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1608 Order of pole (three term test) = -1.585 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=88019672, alloc=4652204, time=4.47 x[1] = 0.18 y1[1] (analytic) = 1.9838436927881214145927160246115 y1[1] (numeric) = 1.9838436927881214145927160246115 absolute error = 1e-63 relative error = 5.0407197080864074714095761345368e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1790295734258241783418027396992 y2[1] (numeric) = 1.1790295734258241783418027396992 absolute error = 1e-63 relative error = 8.4815514601077358374588506352998e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1698 Order of pole (three term test) = -1.668 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.19 y1[1] (analytic) = 1.9820042351172703189678775041899 y1[1] (numeric) = 1.9820042351172703189678775041899 absolute error = 1e-63 relative error = 5.0453978971484511380378270067106e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1888588949765005779928511529813 y2[1] (numeric) = 1.1888588949765005779928511529813 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1788 Order of pole (three term test) = -1.755 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=92020596, alloc=4652204, time=4.68 x[1] = 0.2 y1[1] (analytic) = 1.9800665778412416311241965167482 y1[1] (numeric) = 1.9800665778412416311241965167482 absolute error = 1e-63 relative error = 5.0503352321124744441427458016855e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1986693307950612154594126271184 y2[1] (numeric) = 1.1986693307950612154594126271184 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1877 Order of pole (three term test) = -1.847 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=96022092, alloc=4652204, time=4.89 x[1] = 0.21 y1[1] (analytic) = 1.9780309147241482449161385680993 y1[1] (numeric) = 1.9780309147241482449161385680993 absolute error = 1e-63 relative error = 5.0555327146616298321218548967033e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2084598998460995706087124262276 y2[1] (numeric) = 1.2084598998460995706087124262276 absolute error = 1e-63 relative error = 8.2749953070627542800285284189374e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1966 Order of pole (three term test) = -1.943 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=100022884, alloc=4652204, time=5.10 x[1] = 0.22 y1[1] (analytic) = 1.9758974493306054894060229810447 y1[1] (numeric) = 1.9758974493306054894060229810447 absolute error = 1e-63 relative error = 5.0609914008380343129064224226209e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.218229623080869319951791005457 y2[1] (numeric) = 1.218229623080869319951791005457 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2054 Order of pole (three term test) = -2.044 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.23 y1[1] (analytic) = 1.9736663950053748369677306480716 y1[1] (numeric) = 1.9736663950053748369677306480716 absolute error = 1e-63 relative error = 5.0667124015012513028472330778856e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2279775235351883954046172123601 y2[1] (numeric) = 1.2279775235351883954046172123601 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.214 Order of pole (three term test) = -2.149 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=104023740, alloc=4652204, time=5.31 x[1] = 0.24 y1[1] (analytic) = 1.9713379748520296049261752469634 y1[1] (numeric) = 1.9713379748520296049261752469634 absolute error = 1e-63 relative error = 5.0726968828115883892711953865451e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2377026264271345883607920844898 y2[1] (numeric) = 1.2377026264271345883607920844898 absolute error = 1e-63 relative error = 8.0794851578096049324790437368210e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2226 Order of pole (three term test) = -2.259 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=108024448, alloc=4652204, time=5.52 x[1] = 0.25 y1[1] (analytic) = 1.9689124217106447841445954494942 y1[1] (numeric) = 1.9689124217106447841445954494942 absolute error = 2e-63 relative error = 1.0157892133477148162823768328465e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2474039592545229295968487048494 y2[1] (numeric) = 1.2474039592545229295968487048494 absolute error = 1e-63 relative error = 8.0166492384521756598648137763580e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2311 Order of pole (three term test) = -2.373 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=112025292, alloc=4652204, time=5.73 x[1] = 0.26 y1[1] (analytic) = 1.9663899781345132255582176464501 y1[1] (numeric) = 1.9663899781345132255582176464501 absolute error = 2e-63 relative error = 1.0170922463189993136027761953899e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2570805518921550973533884643652 y2[1] (numeric) = 1.2570805518921550973533884643652 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2395 Order of pole (three term test) = -2.491 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=116026316, alloc=4652204, time=5.94 x[1] = 0.27 y1[1] (analytic) = 1.9637708963658905130162327094922 y1[1] (numeric) = 1.9637708963658905130162327094922 absolute error = 2e-63 relative error = 1.0184487425193815822387289203730e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2667314366888311287322865210205 y2[1] (numeric) = 1.2667314366888311287322865210205 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2479 Order of pole (three term test) = -2.613 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.28 y1[1] (analytic) = 1.9610554383107709479245900535965 y1[1] (numeric) = 1.9610554383107709479245900535965 absolute error = 2e-63 relative error = 1.0198589804900035966671716237316e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2763556485641137333196695584578 y2[1] (numeric) = 1.2763556485641137333196695584578 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2561 Order of pole (three term test) = -2.739 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=120027016, alloc=4652204, time=6.15 x[1] = 0.29 y1[1] (analytic) = 1.9582438755126971680701247779319 y1[1] (numeric) = 1.9582438755126971680701247779319 absolute error = 2e-63 relative error = 1.0213232503925847651838292289105e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2859522251048355326839402055044 y2[1] (numeric) = 1.2859522251048355326839402055044 absolute error = 1e-63 relative error = 7.7763386576703993762228663985884e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2642 Order of pole (three term test) = -2.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=124027680, alloc=4652204, time=6.37 x[1] = 0.3 y1[1] (analytic) = 1.955336489125606019642310227568 y1[1] (numeric) = 1.955336489125606019642310227568 absolute error = 2e-63 relative error = 1.0228418541375284006057458660780e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.295520206661339575105320745685 y2[1] (numeric) = 1.295520206661339575105320745685 absolute error = 1e-63 relative error = 7.7189070062988900384443781475275e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2722 Order of pole (three term test) = -3.004 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=128028520, alloc=4652204, time=6.58 x[1] = 0.31 y1[1] (analytic) = 1.9523335698857133978428054362022 y1[1] (numeric) = 1.9523335698857133978428054362022 absolute error = 2e-63 relative error = 1.0244151055175867931257817440931e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.305058636443443501565643323959 y2[1] (numeric) = 1.305058636443443501565643323959 absolute error = 1e-63 relative error = 7.6624909569213548956184351464994e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2801 Order of pole (three term test) = -3.143 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.32 y1[1] (analytic) = 1.9492354180824408675753072737661 y1[1] (numeric) = 1.9492354180824408675753072737661 absolute error = 2e-63 relative error = 1.0260433303471874928122818774541e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3145665606161177666617575434171 y2[1] (numeric) = 1.3145665606161177666617575434171 absolute error = 2e-63 relative error = 1.5214140233892985911200315312248e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2879 Order of pole (three term test) = -3.285 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=132029264, alloc=4652204, time=6.78 x[1] = 0.33 y1[1] (analytic) = 1.9460423435283869715294105783662 y1[1] (numeric) = 1.9460423435283869715294105783662 absolute error = 2e-63 relative error = 1.0277268666075281350616725445343e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3240430283948683467001956961702 y2[1] (numeric) = 1.3240430283948683467001956961702 absolute error = 2e-63 relative error = 1.5105249278979939004455728596918e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2956 Order of pole (three term test) = -3.431 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=136030128, alloc=4652204, time=7.00 x[1] = 0.34 y1[1] (analytic) = 1.9427546655283462285026440600266 y1[1] (numeric) = 1.9427546655283462285026440600266 absolute error = 2e-63 relative error = 1.0294660645975519957886314289830e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3334870921408143967817714870308 y2[1] (numeric) = 1.3334870921408143967817714870308 absolute error = 2e-63 relative error = 1.4998270412870278911587530301459e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3031 Order of pole (three term test) = -3.581 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=140031812, alloc=4652204, time=7.20 x[1] = 0.35 y1[1] (analytic) = 1.9393727128473789200350323573037 y1[1] (numeric) = 1.9393727128473789200350323573037 absolute error = 2e-63 relative error = 1.0312612870909214506215850713097e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3428978074554513491896349069176 y2[1] (numeric) = 1.3428978074554513491896349069176 absolute error = 2e-63 relative error = 1.4893166024223679025311041078695e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3106 Order of pole (three term test) = -3.735 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=144032892, alloc=4652204, time=7.42 x[1] = 0.36 y1[1] (analytic) = 1.9358968236779348583509123681247 y1[1] (numeric) = 1.9358968236779348583509123681247 absolute error = 2e-63 relative error = 1.0331129094991116404338563250505e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3522742332750899768499134359207 y2[1] (numeric) = 1.3522742332750899768499134359207 absolute error = 2e-63 relative error = 1.4789899495135501032851987062370e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3179 Order of pole (three term test) = -3.893 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.37 y1[1] (analytic) = 1.9323273456060344232038129044909 y1[1] (numeric) = 1.9323273456060344232038129044909 absolute error = 2e-63 relative error = 1.0350213200407519209978648165456e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3616154319649619780372924691272 y2[1] (numeric) = 1.3616154319649619780372924691272 absolute error = 3e-63 relative error = 2.2032652756224035342138577028514e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.325 Order of pole (three term test) = -4.054 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=148033620, alloc=4652204, time=7.62 x[1] = 0.38 y1[1] (analytic) = 1.9286646355765102494925308077246 y1[1] (numeric) = 1.9286646355765102494925308077246 absolute error = 2e-63 relative error = 1.0369869199173481044712361719667e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3709204694129826718454854663492 y2[1] (numeric) = 1.3709204694129826718454854663492 absolute error = 3e-63 relative error = 2.1883107495539667077660402456053e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3321 Order of pole (three term test) = -4.219 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=152034524, alloc=4717728, time=7.84 x[1] = 0.39 y1[1] (analytic) = 1.9249090598573130414506767528811 y1[1] (numeric) = 1.9249090598573130414506767528811 absolute error = 2e-63 relative error = 1.0390101234955240921477781782336e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3801884151231614282311820978472 y2[1] (numeric) = 1.3801884151231614282311820978472 absolute error = 3e-63 relative error = 2.1736162737841081757625165280629e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.339 Order of pole (three term test) = -4.387 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=156035360, alloc=4717728, time=8.05 x[1] = 0.4 y1[1] (analytic) = 1.9210609940028850827985267320518 y1[1] (numeric) = 1.9210609940028850827985267320518 absolute error = 2e-63 relative error = 1.0410913584959272590539665982747e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3894183423086504916663117567957 y2[1] (numeric) = 1.3894183423086504916663117567957 absolute error = 3e-63 relative error = 2.1591769078096487269562799734596e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3458 Order of pole (three term test) = -4.559 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.41 y1[1] (analytic) = 1.917120822816605105475642058277 y1[1] (numeric) = 1.917120822816605105475642058277 absolute error = 2e-63 relative error = 1.0432310661889478894613496025689e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3986093279844228935937976400511 y2[1] (numeric) = 1.3986093279844228935937976400511 absolute error = 3e-63 relative error = 2.1449878389724372722099303120905e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3524 Order of pole (three term test) = -4.734 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=160036076, alloc=4717728, time=8.26 x[1] = 0.42 y1[1] (analytic) = 1.9130889403123082724360887896657 y1[1] (numeric) = 1.9130889403123082724360887896657 absolute error = 2e-63 relative error = 1.0454297015974090864488178763314e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4077604530595701859727871580863 y2[1] (numeric) = 1.4077604530595701859727871580863 absolute error = 3e-63 relative error = 2.1310443786653618192289435896370e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3589 Order of pole (three term test) = -4.912 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=164036852, alloc=4717728, time=8.47 x[1] = 0.43 y1[1] (analytic) = 1.9089657496748851224759104776634 y1[1] (numeric) = 1.9089657496748851224759104776634 absolute error = 2e-63 relative error = 1.0476877337063898968472555724709e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4168708024292107662169186726246 y2[1] (numeric) = 1.4168708024292107662169186726246 absolute error = 3e-63 relative error = 2.1173419586715529166330801579148e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3653 Order of pole (three term test) = -5.093 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=168037664, alloc=4717728, time=8.68 x[1] = 0.44 y1[1] (analytic) = 1.9047516632199634171655373889984 y1[1] (numeric) = 1.9047516632199634171655373889984 absolute error = 2e-63 relative error = 1.0500056456803509141406868692400e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4259394650659996027697207507799 y2[1] (numeric) = 1.4259394650659996027697207507799 absolute error = 3e-63 relative error = 2.1038761276315085446489287824607e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3715 Order of pole (three term test) = -5.278 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=172038472, alloc=4717728, time=8.89 x[1] = 0.45 y1[1] (analytic) = 1.9004471023526769216688406114864 y1[1] (numeric) = 1.9004471023526769216688406114864 absolute error = 2e-63 relative error = 1.0523839350877383554554287495668e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4349655341112302104208442462319 y2[1] (numeric) = 1.4349655341112302104208442462319 absolute error = 3e-63 relative error = 2.0906425476331039108511438031133e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3776 Order of pole (three term test) = -5.466 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.46 y1[1] (analytic) = 1.8960524975255252425363899035004 y1[1] (numeric) = 1.8960524975255252425363899035004 absolute error = 2e-63 relative error = 1.0548231141332495642983950217470e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4439481069655197652415136439289 y2[1] (numeric) = 1.4439481069655197652415136439289 absolute error = 3e-63 relative error = 2.0776369909196725801655318740957e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3835 Order of pole (three term test) = -5.657 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=176039840, alloc=4717728, time=9.10 x[1] = 0.47 y1[1] (analytic) = 1.8915682881953289364540192765334 y1[1] (numeric) = 1.8915682881953289364540192765334 absolute error = 1e-63 relative error = 5.2866185494897503913377495700579e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4528862853790682907032748003964 y2[1] (numeric) = 1.4528862853790682907032748003964 absolute error = 3e-63 relative error = 2.0648553367115574478447327143951e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3892 Order of pole (three term test) = -5.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=180041028, alloc=4717728, time=9.31 x[1] = 0.48 y1[1] (analytic) = 1.8869949227792841943999548311587 y1[1] (numeric) = 1.8869949227792841943999548311587 absolute error = 2e-63 relative error = 1.0598862645874398310359626801090e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4617791755414828891366429425886 y2[1] (numeric) = 1.4617791755414828891366429425886 absolute error = 3e-63 relative error = 2.0522935681367318352779055472654e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3949 Order of pole (three term test) = -6.047 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=184041692, alloc=4717728, time=9.52 x[1] = 0.49 y1[1] (analytic) = 1.8823328586101214957054681591367 y1[1] (numeric) = 1.8823328586101214957054681591367 absolute error = 1e-63 relative error = 5.3125566789413687071833591327688e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.470625888171158036181358337188 y2[1] (numeric) = 1.470625888171158036181358337188 absolute error = 3e-63 relative error = 2.0399477692662830003845548414891e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4003 Order of pole (three term test) = -6.246 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (analytic) = 1.8775825618903727161162815826038 y1[1] (numeric) = 1.8775825618903727161162815826038 absolute error = 2e-63 relative error = 1.0651994967328498908487019298619e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4794255386042030002732879352156 y2[1] (numeric) = 1.4794255386042030002732879352156 absolute error = 3e-63 relative error = 2.0278141222507331243186658844985e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4056 Order of pole (three term test) = -6.448 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=188043324, alloc=4717728, time=9.73 x[1] = 0.51 y1[1] (analytic) = 1.8727445076457512631058084735755 y1[1] (numeric) = 1.8727445076457512631058084735755 absolute error = 1e-63 relative error = 5.3397566828649335759938166413281e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4881772468829074945001302376746 y2[1] (numeric) = 1.4881772468829074945001302376746 absolute error = 2e-63 relative error = 1.3439259363688979012428704319126e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4107 Order of pole (three term test) = -6.653 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=192044056, alloc=4717728, time=9.94 x[1] = 0.52 y1[1] (analytic) = 1.8678191796776499003878475719885 y1[1] (numeric) = 1.8678191796776499003878475719885 absolute error = 1e-63 relative error = 5.3538373033120957608058782225345e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4968801378437367143344589425478 y2[1] (numeric) = 1.4968801378437367143344589425478 absolute error = 2e-63 relative error = 1.3361123241844934559451623257491e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4157 Order of pole (three term test) = -6.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=196045072, alloc=4717728, time=10.15 x[1] = 0.53 y1[1] (analytic) = 1.8628070705147610118066950185642 y1[1] (numeric) = 1.8628070705147610118066950185642 absolute error = 2e-63 relative error = 1.0736484908484525005190792269169e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5055333412048469618136610224661 y2[1] (numeric) = 1.5055333412048469618136610224661 absolute error = 2e-63 relative error = 1.3284328850528422535436688681208e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4205 Order of pole (three term test) = -7.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=200046012, alloc=4717728, time=10.37 x[1] = 0.54 y1[1] (analytic) = 1.8577086813638241425379687789178 y1[1] (numeric) = 1.8577086813638241425379687789178 absolute error = 2e-63 relative error = 1.0765950657730218806758766578607e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5141359916531131046772806829582 y2[1] (numeric) = 1.5141359916531131046772806829582 absolute error = 2e-63 relative error = 1.3208853174518539592632826995508e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4251 Order of pole (three term test) = -7.281 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.55 y1[1] (analytic) = 1.8525245220595057428049817976178 y1[1] (numeric) = 1.8525245220595057428049817976178 absolute error = 3e-63 relative error = 1.6194117617751219706707057230078e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5226872289306591677883781077573 y2[1] (numeric) = 1.5226872289306591677883781077573 absolute error = 2e-63 relative error = 1.3134673766224100386001291625475e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4295 Order of pole (three term test) = -7.496 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=204047324, alloc=4717728, time=10.57 x[1] = 0.56 y1[1] (analytic) = 1.8472551110134161260945255038663 y1[1] (numeric) = 1.8472551110134161260945255038663 absolute error = 2e-63 relative error = 1.0826874902529229099584834949339e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.531186197920883403851869441112 y2[1] (numeric) = 1.531186197920883403851869441112 absolute error = 2e-63 relative error = 1.3061768730123704185584278128487e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4338 Order of pole (three term test) = -7.712 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=208048552, alloc=4717728, time=10.78 x[1] = 0.57 y1[1] (analytic) = 1.841900975162268740133756363916 y1[1] (numeric) = 1.841900975162268740133756363916 absolute error = 2e-63 relative error = 1.0858347039117034891643604791244e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5396320487339692409944634930788 y2[1] (numeric) = 1.5396320487339692409944634930788 absolute error = 2e-63 relative error = 1.2990116707719800529642780620819e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4379 Order of pole (three term test) = -7.931 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=212050060, alloc=4717728, time=10.99 x[1] = 0.58 y1[1] (analytic) = 1.83646264991518693465788732805 y1[1] (numeric) = 1.83646264991518693465788732805 absolute error = 2e-63 relative error = 1.0890501911881331673290929365453e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5480239367918735561826960595765 y2[1] (numeric) = 1.5480239367918735561826960595765 absolute error = 3e-63 relative error = 1.9379545294481706612613473985738e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4418 Order of pole (three term test) = -8.151 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.59 y1[1] (analytic) = 1.8309406791001634952479965224907 y1[1] (numeric) = 1.8309406791001634952479965224907 absolute error = 1e-63 relative error = 5.4616733978047902132895212575370e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5563610229127837757225433788758 y2[1] (numeric) = 1.5563610229127837757225433788758 absolute error = 2e-63 relative error = 1.2850488868302101599991556595291e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4456 Order of pole (three term test) = -8.373 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=216050772, alloc=4717728, time=11.21 x[1] = 0.6 y1[1] (analytic) = 1.8253356149096782972409524989554 y1[1] (numeric) = 1.8253356149096782972409524989554 absolute error = 1e-63 relative error = 5.4784445766127356489621396798198e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5646424733950353572009454456587 y2[1] (numeric) = 1.5646424733950353572009454456587 absolute error = 3e-63 relative error = 1.9173709336232307994808196421010e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4492 Order of pole (three term test) = -8.598 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=220051980, alloc=4717728, time=11.42 x[1] = 0.61 y1[1] (analytic) = 1.8196480178454795179007465786548 y1[1] (numeric) = 1.8196480178454795179007465786548 absolute error = 2e-63 relative error = 1.0991136639535721315725263428320e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5728674601004812611909760321627 y2[1] (numeric) = 1.5728674601004812611909760321627 absolute error = 2e-63 relative error = 1.2715629579317711552779454373119e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4526 Order of pole (three term test) = -8.824 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=224052680, alloc=4717728, time=11.63 x[1] = 0.62 y1[1] (analytic) = 1.8138784566625339286839996543607 y1[1] (numeric) = 1.8138784566625339286839996543607 absolute error = 2e-63 relative error = 1.1026097105094475286557172642480e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5810351605373050758429632275822 y2[1] (numeric) = 1.5810351605373050758429632275822 absolute error = 3e-63 relative error = 1.8974910077145080380050596318682e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4558 Order of pole (three term test) = -9.051 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=228053392, alloc=4717728, time=11.84 x[1] = 0.63 y1[1] (analytic) = 1.8080275083121518725237089657771 y1[1] (numeric) = 1.8080275083121518725237089657771 absolute error = 2e-63 relative error = 1.1061778600188778265263196803500e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5891447579422695131181120907946 y2[1] (numeric) = 1.5891447579422695131181120907946 absolute error = 3e-63 relative error = 1.8878078821998568793560236713126e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.58 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.85 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4588 Order of pole (three term test) = -9.281 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.64 y1[1] (analytic) = 1.8020957578842926135861107792603 y1[1] (numeric) = 1.8020957578842926135861107792603 absolute error = 1e-63 relative error = 5.5490946894743599099478432799465e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5971954413623920518835462392079 y2[1] (numeric) = 1.5971954413623920518835462392079 absolute error = 3e-63 relative error = 1.8782923631694249097683450580593e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4617 Order of pole (three term test) = -9.511 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=232054768, alloc=4717728, time=12.05 x[1] = 0.65 y1[1] (analytic) = 1.7960837985490558289176045706799 y1[1] (numeric) = 1.7960837985490558289176045706799 absolute error = 2e-63 relative error = 1.1135337903585987259748653798338e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6051864057360395603725216786059 y2[1] (numeric) = 1.6051864057360395603725216786059 absolute error = 3e-63 relative error = 1.8689418183954684600175006748137e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4643 Order of pole (three term test) = -9.743 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=236055720, alloc=4717728, time=12.27 x[1] = 0.66 y1[1] (analytic) = 1.7899922314973650927838170912302 y1[1] (numeric) = 1.7899922314973650927838170912302 absolute error = 2e-63 relative error = 1.1173232848764707296363091532342e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6131168519734337886151454793963 y2[1] (numeric) = 1.6131168519734337886151454793963 absolute error = 4e-63 relative error = 2.4796715719053658979097023508972e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4668 Order of pole (three term test) = -9.977 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=240056932, alloc=4717728, time=12.48 x[1] = 0.67 y1[1] (analytic) = 1.7838216658808492853029421448381 y1[1] (numeric) = 1.7838216658808492853029421448381 absolute error = 2e-63 relative error = 1.1211883106108603507225653945891e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6209859870365596803574439141266 y2[1] (numeric) = 1.6209859870365596803574439141266 absolute error = 4e-63 relative error = 2.4676339166340887638831083318351e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.05 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4691 Order of pole (three term test) = -10.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.68 y1[1] (analytic) = 1.7775727187509279371823940840443 y1[1] (numeric) = 1.7775727187509279371823940840443 absolute error = 2e-63 relative error = 1.1251297788848650725519883317058e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6287930240184685137041781874202 y2[1] (numeric) = 1.6287930240184685137041781874202 absolute error = 4e-63 relative error = 2.4558061957629337867416766127147e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4712 Order of pole (three term test) = -10.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=244057872, alloc=4717728, time=12.69 x[1] = 0.69 y1[1] (analytic) = 1.7712460149971066019735393154978 y1[1] (numeric) = 1.7712460149971066019735393154978 absolute error = 1e-63 relative error = 5.6457431183077836773546196134198e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6365371822219679402374292070087 y2[1] (numeric) = 1.6365371822219679402374292070087 absolute error = 4e-63 relative error = 2.4441852244194652463306224128026e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4731 Order of pole (three term test) = -10.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=248058776, alloc=4717728, time=12.90 x[1] = 0.7 y1[1] (analytic) = 1.7648421872844884262558599901919 y1[1] (numeric) = 1.7648421872844884262558599901919 absolute error = 2e-63 relative error = 1.1332458020381652884961903425722e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6442176872376910536726143513987 y2[1] (numeric) = 1.6442176872376910536726143513987 absolute error = 4e-63 relative error = 2.4327678938426070075304109808511e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.85 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4749 Order of pole (three term test) = -10.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=252060088, alloc=4717728, time=13.11 x[1] = 0.71 y1[1] (analytic) = 1.7583618759905081665414579441396 y1[1] (numeric) = 1.7583618759905081665414579441396 absolute error = 2e-63 relative error = 1.1374222947556650864249365164370e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6518337710215366812101279728528 y2[1] (numeric) = 1.6518337710215366812101279728528 absolute error = 4e-63 relative error = 2.4215511694777233274212709492360e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.33 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4764 Order of pole (three term test) = -11.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=256061056, alloc=4717728, time=13.32 x[1] = 0.72 y1[1] (analytic) = 1.7518057291408949794454869622519 y1[1] (numeric) = 1.7518057291408949794454869622519 absolute error = 1e-63 relative error = 5.7083955336212487798204503837468e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6593846719714731536180038326482 y2[1] (numeric) = 1.6593846719714731536180038326482 absolute error = 4e-63 relative error = 2.4105320891313891072301790131004e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4777 Order of pole (three term test) = -11.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.73 y1[1] (analytic) = 1.7451744023448703887901321585503 y1[1] (numeric) = 1.7451744023448703887901321585503 absolute error = 1e-63 relative error = 5.7300863378260019292174571738852e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6668696350036978737325941307615 y2[1] (numeric) = 1.6668696350036978737325941307615 absolute error = 4e-63 relative error = 2.3997077611838109845369017811264e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4789 Order of pole (three term test) = -11.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=260062008, alloc=4717728, time=13.53 x[1] = 0.74 y1[1] (analytic) = 1.7384685587295879097914245606988 y1[1] (numeric) = 1.7384685587295879097914245606988 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6742879116281450674838811576082 y2[1] (numeric) = 1.6742879116281450674838811576082 absolute error = 4e-63 relative error = 2.3890753628569406154985665266923e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4799 Order of pole (three term test) = -11.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=264062740, alloc=4717728, time=13.74 x[1] = 0.75 y1[1] (analytic) = 1.7316888688738208863118387530001 y1[1] (numeric) = 1.7316888688738208863118387530001 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6816387600233341667332419527799 y2[1] (numeric) = 1.6816387600233341667332419527799 absolute error = 4e-63 relative error = 2.3786321385363980318117452389586e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.63 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4806 Order of pole (three term test) = -12.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=268063468, alloc=4717728, time=13.95 x[1] = 0.76 y1[1] (analytic) = 1.724836010740905172339688366667 y1[1] (numeric) = 1.724836010740905172339688366667 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6889214451105513391477556387697 y2[1] (numeric) = 1.6889214451105513391477556387697 absolute error = 4e-63 relative error = 2.3683753981453962342993563621979e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.01 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.06 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4812 Order of pole (three term test) = -12.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.77 y1[1] (analytic) = 1.7179106696109433633712905653243 y1[1] (numeric) = 1.7179106696109433633712905653243 absolute error = 1e-63 relative error = 5.8210244437591788121453662605430e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6961352386273567470198837344522 y2[1] (numeric) = 1.6961352386273567470198837344522 absolute error = 4e-63 relative error = 2.3583025155689283576713641688268e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4816 Order of pole (three term test) = -12.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=272064784, alloc=4717728, time=14.16 x[1] = 0.78 y1[1] (analytic) = 1.7109135380122773572162650237646 y1[1] (numeric) = 1.7109135380122773572162650237646 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7032794192004101843678973251179 y2[1] (numeric) = 1.7032794192004101843678973251179 absolute error = 4e-63 relative error = 2.3484109271265459546558310381225e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.21 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.8 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -12.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=276065464, alloc=4717728, time=14.37 x[1] = 0.79 y1[1] (analytic) = 1.703845315652236096912780861085 y1[1] (numeric) = 1.703845315652236096912780861085 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7103532724176078098140288749692 y2[1] (numeric) = 1.7103532724176078098140288749692 absolute error = 3e-63 relative error = 1.7540235975690910053446831558070e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -13.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=280066244, alloc=4717728, time=14.58 x[1] = 0.8 y1[1] (analytic) = 1.6967067093471654209207499816423 y1[1] (numeric) = 1.6967067093471654209207499816423 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7173560908995227616271746105814 y2[1] (numeric) = 1.7173560908995227616271746105814 absolute error = 3e-63 relative error = 1.7468712609442864811736572666541e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4816 Order of pole (three term test) = -13.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=284067316, alloc=4717728, time=14.80 x[1] = 0.81 y1[1] (analytic) = 1.6894984329517470175496392406801 y1[1] (numeric) = 1.6894984329517470175496392406801 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7242871743701425109281768525145 y2[1] (numeric) = 1.7242871743701425109281768525145 absolute error = 3e-63 relative error = 1.7398493966620479980921298643277e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4812 Order of pole (three term test) = -13.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.82 y1[1] (analytic) = 1.6822212072876135516665579784369 y1[1] (numeric) = 1.6822212072876135516665579784369 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7311458297268958793813133646877 y2[1] (numeric) = 1.7311458297268958793813133646877 absolute error = 3e-63 relative error = 1.7329562584991915412741808720444e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4806 Order of pole (three term test) = -13.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=288068156, alloc=4717728, time=15.01 x[1] = 0.83 y1[1] (analytic) = 1.6748757600712671021124629178645 y1[1] (numeric) = 1.6748757600712671021124629178645 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7379313711099627187285802261381 y2[1] (numeric) = 1.7379313711099627187285802261381 absolute error = 3e-63 relative error = 1.7261901418374151892566788287739e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4799 Order of pole (three term test) = -14.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=292068900, alloc=4717728, time=15.22 x[1] = 0.84 y1[1] (analytic) = 1.6674628258413081179226710368709 y1[1] (numeric) = 1.6674628258413081179226710368709 absolute error = 1e-63 relative error = 5.9971351954755342001502602934721e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7446431199708593212565726706296 y2[1] (numeric) = 1.7446431199708593212565726706296 absolute error = 4e-63 relative error = 2.2927325102837145178016633112267e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4789 Order of pole (three term test) = -14.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=296070020, alloc=4717728, time=15.43 x[1] = 0.85 y1[1] (analytic) = 1.6599831458849821703954160294615 y1[1] (numeric) = 1.6599831458849821703954160294615 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7512804051402927027120715242355 y2[1] (numeric) = 1.7512804051402927027120715242355 absolute error = 4e-63 relative error = 2.2840431425255200148397261438241e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.69 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4778 Order of pole (three term test) = -14.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.86 y1[1] (analytic) = 1.6524374681640518462720306642239 y1[1] (numeric) = 1.6524374681640518462720306642239 absolute error = 1e-63 relative error = 6.0516662159146908088972971737922e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7578425628952769722945887295286 y2[1] (numeric) = 1.7578425628952769722945887295286 absolute error = 4e-63 relative error = 2.2755166386526385366592950065839e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.36 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4764 Order of pole (three term test) = -14.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=300071080, alloc=4717728, time=15.64 x[1] = 0.87 y1[1] (analytic) = 1.6448265472400011947776638054828 y1[1] (numeric) = 1.6448265472400011947776638054828 absolute error = 1e-63 relative error = 6.0796684104958529208545021706575e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7643289370255050781448028237229 y2[1] (numeric) = 1.7643289370255050781448028237229 absolute error = 4e-63 relative error = 2.2671509354393001933888010742549e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.03 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4749 Order of pole (three term test) = -15.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=304071888, alloc=4717728, time=15.85 x[1] = 0.88 y1[1] (analytic) = 1.6371511441985802080154986057221 y1[1] (numeric) = 1.6371511441985802080154986057221 absolute error = 1e-63 relative error = 6.1081715243189776179311592162596e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.770738878898969291209645130756 y2[1] (numeric) = 1.770738878898969291209645130756 absolute error = 3e-63 relative error = 1.6942080143772384163768237507404e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.71 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4732 Order of pole (three term test) = -15.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=308072676, alloc=4717728, time=16.06 x[1] = 0.89 y1[1] (analytic) = 1.6294120265736968802035530573803 y1[1] (numeric) = 1.6294120265736968802035530573803 absolute error = 1e-63 relative error = 6.1371831291977448468527348948594e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7770717475268238654903337129732 y2[1] (numeric) = 1.7770717475268238654903337129732 absolute error = 4e-63 relative error = 2.2508939245513621695428056430029e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.39 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4712 Order of pole (three term test) = -15.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=312073904, alloc=4717728, time=16.27 x[1] = 0.9 y1[1] (analytic) = 1.6216099682706644564847161514071 y1[1] (numeric) = 1.6216099682706644564847161514071 absolute error = 2e-63 relative error = 1.2333421964178368350698866458395e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7833269096274833884613823157135 y2[1] (numeric) = 1.7833269096274833884613823157135 absolute error = 4e-63 relative error = 2.2429987336621047724498351638413e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4691 Order of pole (three term test) = -15.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.91 y1[1] (analytic) = 1.6137457494888115465211782261747 y1[1] (numeric) = 1.6137457494888115465211782261747 absolute error = 2e-63 relative error = 1.2393526059687796184498878045927e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7895037396899504118789575178715 y2[1] (numeric) = 1.7895037396899504118789575178715 absolute error = 4e-63 relative error = 2.2352565749278849679304067104333e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4668 Order of pole (three term test) = -15.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=316074916, alloc=4717728, time=16.48 x[1] = 0.92 y1[1] (analytic) = 1.6058201566434628417974047066744 y1[1] (numeric) = 1.6058201566434628417974047066744 absolute error = 2e-63 relative error = 1.2454694828220767875399382800796e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7956016200363660302682761024816 y2[1] (numeric) = 1.7956016200363660302682761024816 absolute error = 5e-63 relative error = 2.7845820276653213343043348785655e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4644 Order of pole (three term test) = -16.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=320075876, alloc=4717728, time=16.69 x[1] = 0.93 y1[1] (analytic) = 1.597833982287298238494907084433 y1[1] (numeric) = 1.597833982287298238494907084433 absolute error = 2e-63 relative error = 1.2516944952797920756527907831158e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8016199408837771520843192159107 y2[1] (numeric) = 1.8016199408837771520843192159107 absolute error = 5e-63 relative error = 2.7752801168193502799048493367323e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4617 Order of pole (three term test) = -16.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=324076752, alloc=4717728, time=16.91 x[1] = 0.94 y1[1] (analytic) = 1.589788025031098229960989815224 y1[1] (numeric) = 1.589788025031098229960989815224 absolute error = 2e-63 relative error = 1.2580293526622063428193425676008e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8075581004051142868702197986341 y2[1] (numeric) = 1.8075581004051142868702197986341 absolute error = 5e-63 relative error = 2.7661628131783912918607235777903e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.88 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4589 Order of pole (three term test) = -16.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.95 y1[1] (analytic) = 1.5816830894638834941661809737605 y1[1] (numeric) = 1.5816830894638834941661809737605 absolute error = 2e-63 relative error = 1.2644758063879322064650124534699e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8134155047893737506854221021026 y2[1] (numeric) = 1.8134155047893737506854221021026 absolute error = 5e-63 relative error = 2.7572279970004693389413559113807e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4558 Order of pole (three term test) = -16.88 NO COMPLEX POLE (six term test) for Equation 2 bytes used=328077492, alloc=4717728, time=17.12 TOP MAIN SOLVE Loop x[1] = 0.96 y1[1] (analytic) = 1.5735199860724566621250508003519 y1[1] (numeric) = 1.5735199860724566621250508003519 absolute error = 2e-63 relative error = 1.2710356510895343653297020475909e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8191915683009982716332221464304 y2[1] (numeric) = 1.8191915683009982716332221464304 absolute error = 6e-63 relative error = 3.2981683207797591528248804525188e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4526 Order of pole (three term test) = -17.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=332078220, alloc=4717728, time=17.33 x[1] = 0.97 y1[1] (analytic) = 1.5652995311603543130365277548499 y1[1] (numeric) = 1.5652995311603543130365277548499 absolute error = 2e-63 relative error = 1.2777107257659515482921316588081e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8248857133384500574766200378563 y2[1] (numeric) = 1.8248857133384500574766200378563 absolute error = 6e-63 relative error = 3.2878771290414600318041140668199e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4492 Order of pole (three term test) = -17.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=336079144, alloc=4717728, time=17.54 x[1] = 0.98 y1[1] (analytic) = 1.5570225467662173008766582673599 y1[1] (numeric) = 1.5570225467662173008766582673599 absolute error = 2e-63 relative error = 1.2845029149730704307483639366537e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8304973704919704680845332877191 y2[1] (numeric) = 1.8304973704919704680845332877191 absolute error = 6e-63 relative error = 3.2777976612921439763050385756450e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4457 Order of pole (three term test) = -17.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=340080124, alloc=4717728, time=17.75 x[1] = 0.99 y1[1] (analytic) = 1.5486898605815875753431264086536 y1[1] (numeric) = 1.5486898605815875753431264086536 absolute error = 2e-63 relative error = 1.2914141500538587988858994933764e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8360259786005205167892594115471 y2[1] (numeric) = 1.8360259786005205167892594115471 absolute error = 6e-63 relative error = 3.2679276164563845942139056185213e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4419 Order of pole (three term test) = -17.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1 y1[1] (analytic) = 1.540302305868139717400936607443 y1[1] (numeric) = 1.540302305868139717400936607443 absolute error = 2e-63 relative error = 1.2984464104095248368837664988544e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8414709848078965066525023216303 y2[1] (numeric) = 1.8414709848078965066525023216303 absolute error = 6e-63 relative error = 3.2582647511146769662190167635487e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.438 Order of pole (three term test) = -18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=344080800, alloc=4717728, time=17.96 x[1] = 1.01 y1[1] (analytic) = 1.5318607213743554662067313557792 y1[1] (numeric) = 1.5318607213743554662067313557792 absolute error = 2e-63 relative error = 1.3056017248132318013964077817385e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.846831844618015190123098784782 y2[1] (numeric) = 1.846831844618015190123098784782 absolute error = 6e-63 relative error = 3.2488068783766260418600614006206e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4339 Order of pole (three term test) = -18.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=348082216, alloc=4717728, time=18.18 x[1] = 1.02 y1[1] (analytic) = 1.5233659512516495698896138080338 y1[1] (numeric) = 1.5233659512516495698896138080338 absolute error = 2e-63 relative error = 1.3128821727679626770830986927370e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8521080219493629236165499854554 y2[1] (numeric) = 1.8521080219493629236165499854554 absolute error = 6e-63 relative error = 3.2395518667884920134138466338583e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4296 Order of pole (three term test) = -18.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=352083008, alloc=4717728, time=18.39 x[1] = 1.03 y1[1] (analytic) = 1.5148188449699553475335022998374 y1[1] (numeric) = 1.5148188449699553475335022998374 absolute error = 2e-63 relative error = 1.3202898859101978301419954888288e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8572989891886033721462743852944 y2[1] (numeric) = 1.8572989891886033721462743852944 absolute error = 6e-63 relative error = 3.2304976392741240282462252067411e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4252 Order of pole (three term test) = -18.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.04 y1[1] (analytic) = 1.5062202572327784037344734209922 y1[1] (numeric) = 1.5062202572327784037344734209922 absolute error = 2e-63 relative error = 1.3278270494611403563077827214457e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8624042272433384032807916921162 y2[1] (numeric) = 1.8624042272433384032807916921162 absolute error = 6e-63 relative error = 3.2216421721083490313067748674392e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4205 Order of pole (three term test) = -18.86 NO COMPLEX POLE (six term test) for Equation 2 bytes used=356083744, alloc=4717728, time=18.61 TOP MAIN SOLVE Loop x[1] = 1.05 y1[1] (analytic) = 1.4975710478917269902908495728121 y1[1] (numeric) = 1.4975710478917269902908495728121 absolute error = 2e-63 relative error = 1.3354959037272989274234396530284e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8674232255940168943814094850003 y2[1] (numeric) = 1.8674232255940168943814094850003 absolute error = 7e-63 relative error = 3.7484807429089027798980785065746e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4158 Order of pole (three term test) = -19.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=360084584, alloc=4717728, time=18.82 x[1] = 1.06 y1[1] (analytic) = 1.4888720818605275619186375399564 y1[1] (numeric) = 1.4888720818605275619186375399564 absolute error = 2e-63 relative error = 1.3432987456523166582740481496900e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8723554823449862622829459219974 y2[1] (numeric) = 1.8723554823449862622829459219974 absolute error = 7e-63 relative error = 3.7386062988599897649183766821830e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4108 Order of pole (three term test) = -19.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=364085452, alloc=4717728, time=19.03 x[1] = 1.07 y1[1] (analytic) = 1.4801242290285341243650930681759 y1[1] (numeric) = 1.4801242290285341243650930681759 absolute error = 2e-63 relative error = 1.3512379304220170351974605718951e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8772005042746816103070632577768 y2[1] (numeric) = 1.8772005042746816103070632577768 absolute error = 7e-63 relative error = 3.7289570208722488606049199034892e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4057 Order of pole (three term test) = -19.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=368086172, alloc=4717728, time=19.24 x[1] = 1.08 y1[1] (analytic) = 1.471328364173740023913524788526 y1[1] (numeric) = 1.471328364173740023913524788526 absolute error = 2e-63 relative error = 1.3593158731247244736031450166152e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8819578068849474737353349876248 y2[1] (numeric) = 1.8819578068849474737353349876248 absolute error = 7e-63 relative error = 3.7195307856484486070138809555319e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4004 Order of pole (three term test) = -19.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.09 y1[1] (analytic) = 1.4624853668753008770278970738751 y1[1] (numeric) = 1.4624853668753008770278970738751 absolute error = 2e-63 relative error = 1.3675350504690078184058136885998e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.886626914449487231608600628636 y2[1] (numeric) = 1.886626914449487231608600628636 absolute error = 7e-63 relative error = 3.7103255266781676213523514696047e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.395 Order of pole (three term test) = -19.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=372086844, alloc=4717728, time=19.45 x[1] = 1.1 y1[1] (analytic) = 1.4535961214255773877713700517847 y1[1] (numeric) = 1.4535961214255773877713700517847 absolute error = 2e-63 relative error = 1.3758980025610902976743740015516e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8912073600614353399518025778717 y2[1] (numeric) = 1.8912073600614353399518025778717 absolute error = 7e-63 relative error = 3.7013392332465367340409222611034e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3894 Order of pole (three term test) = -20.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=376088076, alloc=4717728, time=19.66 x[1] = 1.11 y1[1] (analytic) = 1.4446615167417068486437375119336 y1[1] (numeric) = 1.4446615167417068486437375119336 absolute error = 2e-63 relative error = 1.3844073347442693271740424613815e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8956986856800476292406259593394 y2[1] (numeric) = 1.8956986856800476292406259593394 absolute error = 7e-63 relative error = 3.6925699494742628679171392439037e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3836 Order of pole (three term test) = -20.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=380088888, alloc=4717728, time=19.87 x[1] = 1.12 y1[1] (analytic) = 1.4356824462767121676139887939611 y1[1] (numeric) = 1.4356824462767121676139887939611 absolute error = 2e-63 relative error = 1.3930657195027943979804297604077e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9001004421765049971191032473391 y2[1] (numeric) = 1.9001004421765049971191032473391 absolute error = 7e-63 relative error = 3.6840157733881274506494734253782e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3777 Order of pole (three term test) = -20.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=384090224, alloc=4717728, time=20.09 x[1] = 1.13 y1[1] (analytic) = 1.4266598079301573103712158356535 y1[1] (numeric) = 1.4266598079301573103712158356535 absolute error = 2e-63 relative error = 1.4018758984327613323163809928104e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9044121893788259160370815224114 y2[1] (numeric) = 1.9044121893788259160370815224114 absolute error = 7e-63 relative error = 3.6756748560211820328846403857160e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3717 Order of pole (three term test) = -20.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.14 y1[1] (analytic) = 1.4175945039583580921751867408226 y1[1] (numeric) = 1.4175945039583580921751867408226 absolute error = 2e-63 relative error = 1.4108406842826967518564790674677e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9086334961158832645942155781022 y2[1] (numeric) = 1.9086334961158832645942155781022 absolute error = 7e-63 relative error = 3.6675454005418926515254374957299e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3655 Order of pole (three term test) = -20.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=388091344, alloc=4717728, time=20.30 x[1] = 1.15 y1[1] (analytic) = 1.4084874408841572981525767188099 y1[1] (numeric) = 1.4084874408841572981525767188099 absolute error = 2e-63 relative error = 1.4199629630666279729823385061214e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9127639402605210809440330497537 y2[1] (numeric) = 1.9127639402605210809440330497537 absolute error = 6e-63 relative error = 3.1368219954955820335072147995743e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3591 Order of pole (three term test) = -21.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=392092100, alloc=4717728, time=20.51 x[1] = 1.16 y1[1] (analytic) = 1.399339529406273154451639623394 y1[1] (numeric) = 1.399339529406273154451639623394 absolute error = 1e-63 relative error = 7.1462284812628052419472603003279e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9168031087717669266186616668743 y2[1] (numeric) = 1.9168031087717669266186616668743 absolute error = 6e-63 relative error = 3.1302119516305614955341979356139e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3526 Order of pole (three term test) = -21.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=396093232, alloc=4717728, time=20.72 x[1] = 1.17 y1[1] (analytic) = 1.3901516843082302153326619350505 y1[1] (numeric) = 1.3901516843082302153326619350505 absolute error = 2e-63 relative error = 1.4386919230294236573160021116968e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.920750597736135639573013008962 y2[1] (numeric) = 1.920750597736135639573013008962 absolute error = 7e-63 relative error = 3.6444086016427363074063562662136e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.346 Order of pole (three term test) = -21.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.18 y1[1] (analytic) = 1.3809248243668817730295994667128 y1[1] (numeric) = 1.3809248243668817730295994667128 absolute error = 1e-63 relative error = 7.2415238132783518590352837949841e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9246060124080203461075380258748 y2[1] (numeric) = 1.9246060124080203461075380258748 absolute error = 7e-63 relative error = 3.6371080391886388428364436604749e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3392 Order of pole (three term test) = -21.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=400094004, alloc=4717728, time=20.93 x[1] = 1.19 y1[1] (analytic) = 1.3716598722605329380656795583505 y1[1] (numeric) = 1.3716598722605329380656795583505 absolute error = 1e-63 relative error = 7.2904370844644794030990521946104e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9283689672491666926020211116027 y2[1] (numeric) = 1.9283689672491666926020211116027 absolute error = 7e-63 relative error = 3.6300107079536518167735414536791e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3323 Order of pole (three term test) = -21.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=404094820, alloc=4717728, time=21.15 x[1] = 1.2 y1[1] (analytic) = 1.3623577544766735776383733556231 y1[1] (numeric) = 1.3623577544766735776383733556231 absolute error = 1e-63 relative error = 7.3402158626397872317740364448208e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9320390859672263496701344354948 y2[1] (numeric) = 1.9320390859672263496701344354948 absolute error = 7e-63 relative error = 3.6231151071644224011454912058230e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3253 Order of pole (three term test) = -21.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=408095640, alloc=4717728, time=21.36 x[1] = 1.21 y1[1] (analytic) = 1.3530194012193303387030107136648 y1[1] (numeric) = 1.3530194012193303387030107136648 absolute error = 1e-63 relative error = 7.3908770199363582074053793168680e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9356160015533859334164648885436 y2[1] (numeric) = 1.9356160015533859334164648885436 absolute error = 7e-63 relative error = 3.6164197828403486951992418383993e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3181 Order of pole (three term test) = -22.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=412096900, alloc=4717728, time=21.57 x[1] = 1.22 y1[1] (analytic) = 1.3436457463160470204755229744352 y1[1] (numeric) = 1.3436457463160470204755229744352 absolute error = 1e-63 relative error = 7.4424378802356135937019274632379e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9390993563190675809352452718884 y2[1] (numeric) = 1.9390993563190675809352452718884 absolute error = 7e-63 relative error = 3.6099233271305312612618645636724e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3108 Order of pole (three term test) = -22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.23 y1[1] (analytic) = 1.3342377271245025982395472454977 y1[1] (numeric) = 1.3342377271245025982395472454977 absolute error = 1e-63 relative error = 7.4949162332200065688716271307286e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9424888019316975100238235653892 y2[1] (numeric) = 1.9424888019316975100238235653892 absolute error = 7e-63 relative error = 3.6036243776740889124229759653462e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3034 Order of pole (three term test) = -22.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=416098372, alloc=4717728, time=21.78 x[1] = 1.24 y1[1] (analytic) = 1.3247962844387762365776934156974 y1[1] (numeric) = 1.3247962844387762365776934156974 absolute error = 1e-63 relative error = 7.5483303489459153835038413637013e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9457839994495389862847059630818 y2[1] (numeric) = 1.9457839994495389862847059630818 absolute error = 7e-63 relative error = 3.5975216169833318580825665228144e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2959 Order of pole (three term test) = -22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=420099100, alloc=4717728, time=21.99 x[1] = 1.25 y1[1] (analytic) = 1.315322362395268665447538552438 y1[1] (numeric) = 1.315322362395268665447538552438 absolute error = 1e-63 relative error = 7.6026989929597892104060790066535e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.948984619355586214348490847036 y2[1] (numeric) = 1.948984619355586214348490847036 absolute error = 7e-63 relative error = 3.5916137718493055257231874255241e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2882 Order of pole (three term test) = -22.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=424100316, alloc=4717728, time=22.21 x[1] = 1.26 y1[1] (analytic) = 1.3058169083782893268863424891765 y1[1] (numeric) = 1.3058169083782893268863424891765 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9520903415905157638568162214254 y2[1] (numeric) = 1.9520903415905157638568162214254 absolute error = 7e-63 relative error = 3.5858996127692379945297377638671e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2804 Order of pole (three term test) = -22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.27 y1[1] (analytic) = 1.296280872925318733551137016088 y1[1] (numeric) = 1.296280872925318733551137016088 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9551008555846922350901817421829 y2[1] (numeric) = 1.9551008555846922350901817421829 absolute error = 7e-63 relative error = 3.5803779533954430253479725766801e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2725 Order of pole (three term test) = -22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=428101164, alloc=4717728, time=22.41 x[1] = 1.28 y1[1] (analytic) = 1.2867152096319555127793868935926 y1[1] (numeric) = 1.2867152096319555127793868935926 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9580158602892249637007538591603 y2[1] (numeric) = 1.9580158602892249637007538591603 absolute error = 6e-63 relative error = 3.0643265571473564380330401348300e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2645 Order of pole (three term test) = -23.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=432101968, alloc=4717728, time=22.62 x[1] = 1.29 y1[1] (analytic) = 1.2771208750565576413866060900612 y1[1] (numeric) = 1.2771208750565576413866060900612 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9608350642060726589055612912854 y2[1] (numeric) = 1.9608350642060726589055612912854 absolute error = 7e-63 relative error = 3.5699076009915434930311400530652e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2564 Order of pole (three term test) = -23.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=436102916, alloc=4717728, time=22.84 x[1] = 1.3 y1[1] (analytic) = 1.2674988286245874069979841092929 y1[1] (numeric) = 1.2674988286245874069979841092929 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9635581854171929647013486300396 y2[1] (numeric) = 1.9635581854171929647013486300396 absolute error = 7e-63 relative error = 3.5649567463735357177349704320267e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2482 Order of pole (three term test) = -23.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=440103804, alloc=4717728, time=23.05 x[1] = 1.31 y1[1] (analytic) = 1.2578500325326696613381769786162 y1[1] (numeric) = 1.2578500325326696613381769786162 absolute error = 1e-63 relative error = 7.9500733325618241351132875727626e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9661849516127340291692578059375 y2[1] (numeric) = 1.9661849516127340291692578059375 absolute error = 7e-63 relative error = 3.5601940673273660634899321296923e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2399 Order of pole (three term test) = -23.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.32 y1[1] (analytic) = 1.2481754516523729595739827294274 y1[1] (numeric) = 1.2481754516523729595739827294274 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9687151001182652627358998459728 y2[1] (numeric) = 1.9687151001182652627358998459728 absolute error = 7e-63 relative error = 3.5556185857361960772126246903190e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2315 Order of pole (three term test) = -23.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=444104616, alloc=4717728, time=23.26 x[1] = 1.33 y1[1] (analytic) = 1.2384760534337232075157849860106 y1[1] (numeric) = 1.2384760534337232075157849860106 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9711483779210445623376830377638 y2[1] (numeric) = 1.9711483779210445623376830377638 absolute error = 7e-63 relative error = 3.5512293637594383413052722820045e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.223 Order of pole (three term test) = -23.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=448105292, alloc=4717728, time=23.47 x[1] = 1.34 y1[1] (analytic) = 1.2287528078084594652326394923001 y1[1] (numeric) = 1.2287528078084594652326394923001 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9734845416953193747878703480896 y2[1] (numeric) = 1.9734845416953193747878703480896 absolute error = 7e-63 relative error = 3.5470255034207964665302238738176e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2145 Order of pole (three term test) = -23.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=452106128, alloc=4717728, time=23.69 x[1] = 1.35 y1[1] (analytic) = 1.2190066870930415814200221730106 y1[1] (numeric) = 1.2190066870930415814200221730106 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9757233578266590692611135392652 y2[1] (numeric) = 1.9757233578266590692611135392652 absolute error = 7e-63 relative error = 3.5430061462148021954997148260026e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2058 Order of pole (three term test) = -23.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.36 y1[1] (analytic) = 1.2092386658914193576759752523919 y1[1] (numeric) = 1.2092386658914193576759752523919 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9778646024353161856784924394266 y2[1] (numeric) = 1.9778646024353161856784924394266 absolute error = 7e-63 relative error = 3.5391704727315514236320581551835e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 bytes used=456106944, alloc=4717728, time=23.90 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.197 Order of pole (three term test) = -23.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.37 y1[1] (analytic) = 1.1994497209975729656881983896453 y1[1] (numeric) = 1.1994497209975729656881983896453 absolute error = 1e-63 relative error = 8.3371564684537823697670409228291e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9799080613986142228876885048919 y2[1] (numeric) = 1.9799080613986142228876885048919 absolute error = 7e-63 relative error = 3.5355177022993555853764849836938e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1882 Order of pole (three term test) = -24.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=460107944, alloc=4717728, time=24.11 x[1] = 1.38 y1[1] (analytic) = 1.1896408312978343632091500735982 y1[1] (numeric) = 1.1896408312978343632091500735982 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.981853530372359727878131085206 y2[1] (numeric) = 1.981853530372359727878131085206 absolute error = 7e-63 relative error = 3.5320470926450391647913300445723e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1793 Order of pole (three term test) = -24.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=464109616, alloc=4717728, time=24.33 x[1] = 1.39 y1[1] (analytic) = 1.1798129776729994765961632178041 y1[1] (numeric) = 1.1798129776729994765961632178041 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9837008148112765448400382244429 y2[1] (numeric) = 1.9837008148112765448400382244429 absolute error = 7e-63 relative error = 3.5287579395716280888754412587327e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1703 Order of pole (three term test) = -24.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=468110328, alloc=4717728, time=24.54 x[1] = 1.4 y1[1] (analytic) = 1.1699671429002409386167480352036 y1[1] (numeric) = 1.1699671429002409386167480352036 absolute error = 1e-63 relative error = 8.5472485793155863828236215107456e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9854497299884601806594745788061 y2[1] (numeric) = 1.9854497299884601806594745788061 absolute error = 7e-63 relative error = 3.5256495766531874665860100704788e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1613 Order of pole (three term test) = -24.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.41 y1[1] (analytic) = 1.1601043115548311901635625493609 y1[1] (numeric) = 1.1601043115548311901635625493609 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9871001010138503414290888619422 y2[1] (numeric) = 1.9871001010138503414290888619422 absolute error = 7e-63 relative error = 3.5227213749465805629272827945491e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1522 Order of pole (three term test) = -24.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=472110972, alloc=4717728, time=24.75 x[1] = 1.42 y1[1] (analytic) = 1.1502254699116857734869821029759 y1[1] (numeric) = 1.1502254699116857734869821029759 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9886517628517197927362734733357 y2[1] (numeric) = 1.9886517628517197927362734733357 absolute error = 7e-63 relative error = 3.5199727427199340621071723310795e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.143 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=476112320, alloc=4717728, time=24.96 x[1] = 1.43 y1[1] (analytic) = 1.1403316058467366625338976245749 y1[1] (numeric) = 1.1403316058467366625338976245749 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9901045603371777948572914954818 y2[1] (numeric) = 1.9901045603371777948572914954818 absolute error = 7e-63 relative error = 3.5174031251976075923476729647418e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1338 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=480113804, alloc=4717728, time=25.17 x[1] = 1.44 y1[1] (analytic) = 1.1304237087381454929775201561292 y1[1] (numeric) = 1.1304237087381454929775201561292 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.991458348191686462527604463958 y2[1] (numeric) = 1.991458348191686462527604463958 absolute error = 7e-63 relative error = 3.5150120043214781729140895464402e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1245 Order of pole (three term test) = -24.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=484115104, alloc=4717728, time=25.38 x[1] = 1.45 y1[1] (analytic) = 1.120502769367366570532866627248 y1[1] (numeric) = 1.120502769367366570532866627248 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.992712991037588497665354134323 y2[1] (numeric) = 1.992712991037588497665354134323 absolute error = 7e-63 relative error = 3.5127988985283627163365083233107e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1152 Order of pole (three term test) = -24.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.46 y1[1] (analytic) = 1.1105697798200695511746481091234 y1[1] (numeric) = 1.1105697798200695511746481091234 absolute error = 1e-63 relative error = 9.0043869207571660918496856319543e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.99386836341164484228683230125 y2[1] (numeric) = 1.99386836341164484228683230125 absolute error = 7e-63 relative error = 3.5107633625434139903244090419372e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1058 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=488115916, alloc=4717728, time=25.59 x[1] = 1.47 y1[1] (analytic) = 1.1006257333869317009069746014624 y1[1] (numeric) = 1.1006257333869317009069746014624 absolute error = 1e-63 relative error = 9.0857406806464690431127404880792e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9949243497775808978599284627356 y2[1] (numeric) = 1.9949243497775808978599284627356 absolute error = 7e-63 relative error = 3.5089049871893375288869834451719e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09641 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=492116796, alloc=4717728, time=25.81 x[1] = 1.48 y1[1] (analytic) = 1.0906716244643096557762265406478 y1[1] (numeric) = 1.0906716244643096557762265406478 absolute error = 1e-63 relative error = 9.1686624788754029971031479664534e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9958808445376400564840751325627 y2[1] (numeric) = 1.9958808445376400564840751325627 absolute error = 7e-63 relative error = 3.5072233992112888947321209175871e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08695 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=496118092, alloc=4783252, time=26.02 x[1] = 1.49 y1[1] (analytic) = 1.0807084484548006148683184845637 y1[1] (numeric) = 1.0807084484548006148683184845637 absolute error = 1e-63 relative error = 9.2531894372603662245462113142181e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9967377520431433885532007170437 y2[1] (numeric) = 1.9967377520431433885532007170437 absolute error = 7e-63 relative error = 3.5057182611173224489134435858866e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07747 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.5 y1[1] (analytic) = 1.0707372016677029100881898514343 y1[1] (numeric) = 1.0707372016677029100881898514343 absolute error = 1e-63 relative error = 9.3393598209016390280655430800658e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9974949866040544309417233711415 y2[1] (numeric) = 1.9974949866040544309417233711415 absolute error = 7e-63 relative error = 3.5043892710342743924600322342379e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06795 Order of pole (three term test) = -24.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=500119316, alloc=4783252, time=26.23 x[1] = 1.51 y1[1] (analytic) = 1.0607588812193859065815955149162 y1[1] (numeric) = 1.0607588812193859065815955149162 absolute error = 2e-63 relative error = 1.8854426160457104505460527049495e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9981524724975481192427378648367 y2[1] (numeric) = 1.9981524724975481192427378648367 absolute error = 7e-63 relative error = 3.5032361625789743216581147222816e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0584 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=504120012, alloc=4783252, time=26.44 x[1] = 1.52 y1[1] (analytic) = 1.0507744849335791967261292701527 y1[1] (numeric) = 1.0507744849335791967261292701527 absolute error = 2e-63 relative error = 1.9033579789734069969172736881246e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9987101439755830071723123941168 y2[1] (numeric) = 1.9987101439755830071723123941168 absolute error = 7e-63 relative error = 3.5022587047446908968479511565357e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04883 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=508120704, alloc=4783252, time=26.66 x[1] = 1.53 y1[1] (analytic) = 1.0407850112415910586889890070761 y1[1] (numeric) = 1.0407850112415910586889890070761 absolute error = 2e-63 relative error = 1.9216264438840503565027755280618e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.999167945271476015924265068709 y2[1] (numeric) = 1.999167945271476015924265068709 absolute error = 7e-63 relative error = 3.5014567018027284769530845183077e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03924 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=512121524, alloc=4783252, time=26.87 x[1] = 1.54 y1[1] (analytic) = 1.0307914590824661576224768070764 y1[1] (numeric) = 1.0307914590824661576224768070764 absolute error = 2e-63 relative error = 1.9402566662516307170263734648064e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.99952583060547905600596353844 y2[1] (numeric) = 1.99952583060547905600596353844 absolute error = 7e-63 relative error = 3.5008299932191027312051947550516e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02964 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.55 y1[1] (analytic) = 1.0207948278030924736439127746956 y1[1] (numeric) = 1.0207948278030924736439127746956 absolute error = 2e-63 relative error = 1.9592575760834405038747057926026e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9997837641893569638976113476345 y2[1] (numeric) = 1.9997837641893569638976113476345 absolute error = 8e-63 relative error = 4.0004325183842677922859062475749e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02002 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=516122304, alloc=4783252, time=27.08 x[1] = 1.56 y1[1] (analytic) = 1.0107961170582674458239206637609 y1[1] (numeric) = 1.0107961170582674458239206637609 absolute error = 3e-63 relative error = 2.9679575825151935089528063740599e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9999417202299662957451700234135 y2[1] (numeric) = 1.9999417202299662957451700234135 absolute error = 8e-63 relative error = 4.0001165629366979811154428504490e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0104 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=520123424, alloc=4783252, time=27.29 x[1] = 1.57 y1[1] (analytic) = 1.0007963267107333254854085336454 y1[1] (numeric) = 1.0007963267107333254854085336454 absolute error = 3e-63 relative error = 2.9976129207627572768570066594626e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9999996829318346202105299238233 y2[1] (numeric) = 1.9999996829318346202105299238233 absolute error = 8e-63 relative error = 4.0000006341364312918163752439218e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0007668 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=524124092, alloc=4783252, time=27.51 x[1] = 1.58 y1[1] (analytic) = 0.99079645673119173519461094301727 y1[1] (numeric) = 0.99079645673119173519461094301727 absolute error = 3.5e-63 relative error = 3.5325116235751419526302379451603e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9999576464987400525517942322517 y2[1] (numeric) = 1.9999576464987400525517942322517 absolute error = 8e-63 relative error = 4.0000847087963769519363443713385e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.008874 Order of pole (three term test) = -0.8949 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.59 y1[1] (analytic) = 0.9807975070983074319049726537566 y1[1] (numeric) = 0.9807975070983074319049726537566 absolute error = 3.6e-63 relative error = 3.6704824124712669158299371358500e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9998156151342908719815843437455 y2[1] (numeric) = 1.9998156151342908719815843437455 absolute error = 8e-63 relative error = 4.0003688037323315855291277708955e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01851 Order of pole (three term test) = -0.9018 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=528124888, alloc=4783252, time=27.72 TOP MAIN SOLVE Loop x[1] = 1.6 y1[1] (analytic) = 0.9708004776987112737942295370535 y1[1] (numeric) = 0.9708004776987112737942295370535 absolute error = 3.6e-63 relative error = 3.7082800046965602740765802907448e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9995736030415051643421138255462 y2[1] (numeric) = 1.9995736030415051643421138255462 absolute error = 8e-63 relative error = 4.0008529757701266972226707016307e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02814 Order of pole (three term test) = -0.9135 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=532125784, alloc=4783252, time=27.93 x[1] = 1.61 y1[1] (analytic) = 0.96080636822701239041467239039898 y1[1] (numeric) = 0.96080636822701239041467239039898 absolute error = 3.7e-63 relative error = 3.8509320112309983345219346460795e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9992316344213905321324131478443 y2[1] (numeric) = 1.9992316344213905321324131478443 absolute error = 8e-63 relative error = 4.0015373217697845104384333539557e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03776 Order of pole (three term test) = -0.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=536126496, alloc=4783252, time=28.15 x[1] = 1.62 y1[1] (analytic) = 0.95081617808582955485625572528767 y1[1] (numeric) = 0.95081617808582955485625572528767 absolute error = 3.7e-63 relative error = 3.8913936103283293299780619023621e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9987897434705240139155188912468 y2[1] (numeric) = 1.9987897434705240139155188912468 absolute error = 8e-63 relative error = 4.0024219786666997846476597091736e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04737 Order of pole (three term test) = -0.9513 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=540127240, alloc=4783252, time=28.36 x[1] = 1.63 y1[1] (analytic) = 0.9408309062858517547020283025802 y1[1] (numeric) = 0.9408309062858517547020283025802 absolute error = 3.7e-63 relative error = 3.9326939360512807576430903440025e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9982479743776324551116699849331 y2[1] (numeric) = 1.9982479743776324551116699849331 absolute error = 8e-63 relative error = 4.0035071235298776666665858212064e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05696 Order of pole (three term test) = -0.9775 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.64 y1[1] (analytic) = 0.93085155134593795563550729254339 y1[1] (numeric) = 0.93085155134593795563550729254339 absolute error = 3.8e-63 relative error = 4.0822835762646574408539572634704e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9976063813191736721375819743679 y2[1] (numeric) = 1.9976063813191736721375819743679 absolute error = 8e-63 relative error = 4.0047929736372700946300221012326e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06652 Order of pole (three term test) = -1.008 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=544128052, alloc=4783252, time=28.57 x[1] = 1.65 y1[1] (analytic) = 0.92087911119326604764038540265872 y1[1] (numeric) = 0.92087911119326604764038540265872 absolute error = 3.9e-63 relative error = 4.2350835767644013109686417967926e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9968650284539188517717030402022 y2[1] (numeric) = 1.9968650284539188517717030402022 absolute error = 7e-63 relative error = 3.5054948132472325613181882075811e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07606 Order of pole (three term test) = -1.044 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=548128728, alloc=4783252, time=28.78 x[1] = 1.66 y1[1] (analytic) = 0.91091458306354095881474206834938 y1[1] (numeric) = 0.91091458306354095881474206834938 absolute error = 4.0e-63 relative error = 4.3911910890123267549723763438759e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.996023989916536727501000590613 y2[1] (numeric) = 1.996023989916536727501000590613 absolute error = 7e-63 relative error = 3.5069718777742262253476211444643e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08556 Order of pole (three term test) = -1.085 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=552129916, alloc=4783252, time=28.99 x[1] = 1.67 y1[1] (analytic) = 0.90095896340127191590521765755139 y1[1] (numeric) = 0.90095896340127191590521765755139 absolute error = 4.1e-63 relative error = 4.5507067097948713118445136812227e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9950833498101801744262972465342 y2[1] (numeric) = 1.9950833498101801744262972465342 absolute error = 7e-63 relative error = 3.5086253417262023916794959746074e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09503 Order of pole (three term test) = -1.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.68 y1[1] (analytic) = 0.89101324776012882375199526582718 y1[1] (numeric) = 0.89101324776012882375199526582718 absolute error = 4.2e-63 relative error = 4.7137346280295588486540677644038e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9940432021980759640604878691936 y2[1] (numeric) = 1.9940432021980759640604878691936 absolute error = 7e-63 relative error = 3.5104555369130177628089706990992e-61 % Correct digits = 64 h = 0.01 bytes used=556130692, alloc=4783252, time=29.21 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1045 Order of pole (three term test) = -1.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.69 y1[1] (analytic) = 0.88107843070338772792360953016691 y1[1] (numeric) = 0.88107843070338772792360953016691 absolute error = 4.2e-63 relative error = 4.7668855048999794892679590205801e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9929036510941185200371492939456 y2[1] (numeric) = 1.9929036510941185200371492939456 absolute error = 6e-63 relative error = 3.0106824264715238989336603016991e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1139 Order of pole (three term test) = -1.235 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=560131356, alloc=4783252, time=29.41 x[1] = 1.7 y1[1] (analytic) = 0.87115550570447531591235714266513 y1[1] (numeric) = 0.87115550570447531591235714266513 absolute error = 4.3e-63 relative error = 4.9359729369129440396906043256506e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9916648104524686153461333986479 y2[1] (numeric) = 1.9916648104524686153461333986479 absolute error = 6e-63 relative error = 3.0125551089276480017787666966715e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1232 Order of pole (three term test) = -1.294 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=564132444, alloc=4783252, time=29.63 x[1] = 1.71 y1[1] (analytic) = 0.86124546504762240235731021694889 y1[1] (numeric) = 0.86124546504762240235731021694889 absolute error = 4.3e-63 relative error = 4.9927693956127041283925567628602e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9903268041561580512177522238611 y2[1] (numeric) = 1.9903268041561580512177522238611 absolute error = 6e-63 relative error = 3.0145803128767234413940842938017e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1325 Order of pole (three term test) = -1.358 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=568133264, alloc=4783252, time=29.84 x[1] = 1.72 y1[1] (analytic) = 0.85134929972863633286362171966881 y1[1] (numeric) = 0.85134929972863633286362171966881 absolute error = 4.4e-63 relative error = 5.1682664229623254864635102582586e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9888897660047014571781706570855 y2[1] (numeric) = 1.9888897660047014571781706570855 absolute error = 5e-63 relative error = 2.5139653717682112601595174976708e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1417 Order of pole (three term test) = -1.427 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.73 y1[1] (analytic) = 0.84146799935580222909505164865743 y1[1] (numeric) = 0.84146799935580222909505164865743 absolute error = 4.5e-63 relative error = 5.3477969494324666821277551076568e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9873538397007164510856776762221 y2[1] (numeric) = 1.9873538397007164510856776762221 absolute error = 5e-63 relative error = 2.5159082897653343713084995835276e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1509 Order of pole (three term test) = -1.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=572134040, alloc=4783252, time=30.05 x[1] = 1.74 y1[1] (analytic) = 0.83160255205092298493262268465491 y1[1] (numeric) = 0.83160255205092298493262268465491 absolute error = 4.5e-63 relative error = 5.4112388050060283699873191776570e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9857191788355534971206826956655 y2[1] (numeric) = 1.9857191788355534971206826956655 absolute error = 5e-63 relative error = 2.5179794068021502993051121087842e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1601 Order of pole (three term test) = -1.578 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=576134960, alloc=4783252, time=30.26 x[1] = 1.75 y1[1] (analytic) = 0.82175394435050790961732305605737 y1[1] (numeric) = 0.82175394435050790961732305605737 absolute error = 4.6e-63 relative error = 5.5977826837639526960662185485546e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.983985946873936898731662936968 y2[1] (numeric) = 1.983985946873936898731662936968 absolute error = 5e-63 relative error = 2.5201791413282130462124736332584e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1691 Order of pole (three term test) = -1.661 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=580135648, alloc=4783252, time=30.48 x[1] = 1.76 y1[1] (analytic) = 0.8119231611071198989301998234959 y1[1] (numeric) = 0.8119231611071198989301998234959 absolute error = 4.6e-63 relative error = 5.6655607579017021097525549698803e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.982154317137618462424968099456 y2[1] (numeric) = 1.982154317137618462424968099456 absolute error = 5e-63 relative error = 2.5225079383427523196573065771557e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1781 Order of pole (three term test) = -1.748 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=584136592, alloc=4783252, time=30.69 x[1] = 1.77 y1[1] (analytic) = 0.80211118539089099961051415826961 y1[1] (numeric) = 0.80211118539089099961051415826961 absolute error = 4.6e-63 relative error = 5.7348657938965064764576867455820e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9802244727880454670184814488984 y2[1] (numeric) = 1.9802244727880454670184814488984 absolute error = 5e-63 relative error = 2.5249662695867399505997038216284e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.187 Order of pole (three term test) = -1.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.78 y1[1] (analytic) = 0.79231899839121621537344670968737 y1[1] (numeric) = 0.79231899839121621537344670968737 absolute error = 4.7e-63 relative error = 5.9319541870676226460579378234021e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9781966068080446715477686473056 y2[1] (numeric) = 1.9781966068080446715477686473056 absolute error = 5e-63 relative error = 2.5275546337468657784943005619619e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1959 Order of pole (three term test) = -1.936 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=588137472, alloc=4783252, time=30.90 x[1] = 1.79 y1[1] (analytic) = 0.78254757931863538506482973553539 y1[1] (numeric) = 0.78254757931863538506482973553539 absolute error = 4.8e-63 relative error = 6.1338123417100883300845289748481e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9760709219825241934086604331086 y2[1] (numeric) = 1.9760709219825241934086604331086 absolute error = 5e-63 relative error = 2.5302735566715750555938666458981e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2047 Order of pole (three term test) = -2.036 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=592138912, alloc=4783252, time=31.11 x[1] = 1.8 y1[1] (analytic) = 0.77279790530691294468332569346942 y1[1] (numeric) = 0.77279790530691294468332569346942 absolute error = 4.8e-63 relative error = 6.2111969598231548661516562351643e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9738476308781951865323731788434 y2[1] (numeric) = 1.9738476308781951865323731788434 absolute error = 5e-63 relative error = 2.5331235915993287967044712316726e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2133 Order of pole (three term test) = -2.141 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=596139716, alloc=4783252, time=31.32 x[1] = 1.81 y1[1] (analytic) = 0.76307095131532536521225014915802 y1[1] (numeric) = 0.76307095131532536521225014915802 absolute error = 4.9e-63 relative error = 6.4214212211246435041755094469069e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9715269558223153474084512690904 y2[1] (numeric) = 1.9715269558223153474084512690904 absolute error = 5e-63 relative error = 2.5361053193992580604680486553166e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2219 Order of pole (three term test) = -2.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.82 y1[1] (analytic) = 0.75336769003116603743582895516913 y1[1] (numeric) = 0.75336769003116603743582895516913 absolute error = 4.9e-63 relative error = 6.5041281499572832737106131870216e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9691091288804563745872153184981 y2[1] (numeric) = 1.9691091288804563745872153184981 absolute error = 4e-63 relative error = 2.0313754790595143238206005052467e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2305 Order of pole (three term test) = -2.363 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=600140432, alloc=4783252, time=31.53 x[1] = 1.83 y1[1] (analytic) = 0.74368909177247735317016241638147 y1[1] (numeric) = 0.74368909177247735317016241638147 absolute error = 4.9e-63 relative error = 6.5887748713935628063580447612017e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9665943918332976048972389297428 y2[1] (numeric) = 1.9665943918332976048972389297428 absolute error = 4e-63 relative error = 2.0339730534221253792632316702739e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2389 Order of pole (three term test) = -2.481 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=604141568, alloc=4783252, time=31.75 x[1] = 1.84 y1[1] (analytic) = 0.7340361243910197096197170167184 y1[1] (numeric) = 0.7340361243910197096197170167184 absolute error = 4.9e-63 relative error = 6.6754207826831406787356070773028e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9639829961524481469948936717271 y2[1] (numeric) = 1.9639829961524481469948936717271 absolute error = 4e-63 relative error = 2.0366775108726614899069575991695e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2472 Order of pole (three term test) = -2.603 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=608142240, alloc=4783252, time=31.96 x[1] = 1.85 y1[1] (analytic) = 0.7244097531754871398780501645252 y1[1] (numeric) = 0.7244097531754871398780501645252 absolute error = 4.9e-63 relative error = 6.7641275928721277099601255224206e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9612752029752999300124591686361 y2[1] (numeric) = 1.9612752029752999300124591686361 absolute error = 4e-63 relative error = 2.0394894066533382521347186879782e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2554 Order of pole (three term test) = -2.729 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=612143028, alloc=4783252, time=32.17 x[1] = 1.86 y1[1] (analytic) = 0.71481094075497924792906451171088 y1[1] (numeric) = 0.71481094075497924792906451171088 absolute error = 4.9e-63 relative error = 6.8549594314052438591572497511380e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9584712830789141819789777659032 y2[1] (numeric) = 1.9584712830789141819789777659032 absolute error = 3e-63 relative error = 1.5318069894206963996010683884395e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2636 Order of pole (three term test) = -2.859 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.87 y1[1] (analytic) = 0.70524064700273910087485193519011 y1[1] (numeric) = 0.70524064700273910087485193519011 absolute error = 4.9e-63 relative error = 6.9479829627304065101459315105464e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9555715168529439493442504921726 y2[1] (numeric) = 1.9555715168529439493442504921726 absolute error = 3e-63 relative error = 1.5340783879015739975727742248052e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2716 Order of pole (three term test) = -2.993 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=616143848, alloc=4783252, time=32.38 x[1] = 1.88 y1[1] (analytic) = 0.69569982894016670452068624047776 y1[1] (numeric) = 0.69569982894016670452068624047776 absolute error = 5.0e-63 relative error = 7.1870076604978184534851416211174e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9525761942715953653314574258151 y2[1] (numeric) = 1.9525761942715953653314574258151 absolute error = 3e-63 relative error = 1.5364317196948844218996088375185e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2795 Order of pole (three term test) = -3.131 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=620145008, alloc=4783252, time=32.60 x[1] = 1.89 y1[1] (analytic) = 0.68618944064111766088961758444877 y1[1] (numeric) = 0.68618944064111766088961758444877 absolute error = 5.1e-63 relative error = 7.4323498700810511400181025003410e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9494856148646304709682016721383 y2[1] (numeric) = 1.9494856148646304709682016721383 absolute error = 2e-63 relative error = 1.0259116480522874628264821518867e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2873 Order of pole (three term test) = -3.273 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=624146088, alloc=4783252, time=32.81 x[1] = 1.9 y1[1] (analytic) = 0.67671043313649657772116630491969 y1[1] (numeric) = 0.67671043313649657772116630491969 absolute error = 5.0e-63 relative error = 7.3886846650574246863411364071032e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.946300087687414488489709611635 y2[1] (numeric) = 1.946300087687414488489709611635 absolute error = 2e-63 relative error = 1.0275907670416803606181490885369e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.295 Order of pole (three term test) = -3.419 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.91 y1[1] (analytic) = 0.66726375431915477053366106060247 y1[1] (numeric) = 0.66726375431915477053366106060247 absolute error = 5.1e-63 relative error = 7.6431545501880366835891849325530e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9430199312900105423618865769482 y2[1] (numeric) = 1.9430199312900105423618865769482 absolute error = 2e-63 relative error = 1.0293255194104772916242601689465e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3025 Order of pole (three term test) = -3.569 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=628147320, alloc=4783252, time=33.02 TOP MAIN SOLVE Loop x[1] = 1.92 y1[1] (analytic) = 0.65785034884910176740076339684095 y1[1] (numeric) = 0.65785034884910176740076339684095 absolute error = 5.1e-63 relative error = 7.7525230607878601703952462471591e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.939645473685324918426371339687 y2[1] (numeric) = 1.939645473685324918426371339687 absolute error = 2e-63 relative error = 1.0311162669330501556435735647905e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.31 Order of pole (three term test) = -3.723 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=632148076, alloc=4783252, time=33.24 x[1] = 1.93 y1[1] (analytic) = 0.64847115805904009521271093528813 y1[1] (numeric) = 0.64847115805904009521271093528813 absolute error = 5.1e-63 relative error = 7.8646520151566558897139294366726e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9361770523163060466151293727488 y2[1] (numeric) = 1.9361770523163060466151293727488 absolute error = 2e-63 relative error = 1.0329633840083687944185628728597e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3173 Order of pole (three term test) = -3.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=636148744, alloc=4783252, time=33.45 x[1] = 1.94 y1[1] (analytic) = 0.63912711986023279386493231415927 y1[1] (numeric) = 0.63912711986023279386493231415927 absolute error = 5.1e-63 relative error = 7.9796332240060334815738784802095e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9326150140222004873089793388657 y2[1] (numeric) = 1.9326150140222004873089793388657 absolute error = 3e-63 relative error = 1.5523008867432601679374818716986e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3245 Order of pole (three term test) = -4.041 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=640149488, alloc=4783252, time=33.67 x[1] = 1.95 y1[1] (analytic) = 0.62981916864871307154417154086931 y1[1] (numeric) = 0.62981916864871307154417154086931 absolute error = 5.2e-63 relative error = 8.2563381028187531275854542979935e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9289597150038692957132970350915 y2[1] (numeric) = 1.9289597150038692957132970350915 absolute error = 2e-63 relative error = 1.0368282885555171922020502309869e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3315 Order of pole (three term test) = -4.205 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.96 y1[1] (analytic) = 0.62054823521184548006843478455255 y1[1] (numeric) = 0.62054823521184548006843478455255 absolute error = 5.2e-63 relative error = 8.3796870330713311555156802603665e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.92521152078816823258555628949 y2[1] (numeric) = 1.92521152078816823258555628949 absolute error = 3e-63 relative error = 1.5582703342497248430987418613528e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3385 Order of pole (three term test) = -4.373 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=644150336, alloc=4783252, time=33.87 x[1] = 1.97 y1[1] (analytic) = 0.61131524663524795408536018612069 y1[1] (numeric) = 0.61131524663524795408536018612069 absolute error = 5.3e-63 relative error = 8.6698312027580405972445469623524e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9213708061913953832639509971532 y2[1] (numeric) = 1.9213708061913953832639509971532 absolute error = 2e-63 relative error = 1.0409234873118874952852244284339e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3453 Order of pole (three term test) = -4.545 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=648151032, alloc=4783252, time=34.09 x[1] = 1.98 y1[1] (analytic) = 0.60212112621008402184752614009281 y1[1] (numeric) = 0.60212112621008402184752614009281 absolute error = 5.3e-63 relative error = 8.8022156494651794283516316159777e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.917437955281809840204735217402 y2[1] (numeric) = 1.917437955281809840204735217402 absolute error = 3e-63 relative error = 1.5645877832636747648046754747626e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3519 Order of pole (three term test) = -4.719 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=652152396, alloc=4783252, time=34.30 x[1] = 1.99 y1[1] (analytic) = 0.59296679334073445826636428386971 y1[1] (numeric) = 0.59296679334073445826636428386971 absolute error = 5.3e-63 relative error = 8.9381059100125347572785412561887e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9134133613412251971287932710576 y2[1] (numeric) = 1.9134133613412251971287932710576 absolute error = 2e-63 relative error = 1.0452524480115896542952443510556e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3584 Order of pole (three term test) = -4.898 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=656153156, alloc=4783252, time=34.51 x[1] = 2 y1[1] (analytic) = 0.58385316345285761300243177049924 y1[1] (numeric) = 0.58385316345285761300243177049924 absolute error = 5.3e-63 relative error = 9.0776248751591133664954491738840e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9092974268256816953960198659117 y2[1] (numeric) = 1.9092974268256816953960198659117 absolute error = 2e-63 relative error = 1.0475057326846748133100283768061e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3648 Order of pole (three term test) = -5.079 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.01 y1[1] (analytic) = 0.57478114790184760748261765983457 y1[1] (numeric) = 0.57478114790184760748261765983457 absolute error = 5.3e-63 relative error = 9.2209008930561749805669183972543e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9050905633252009553600997102737 y2[1] (numeric) = 1.9050905633252009553600997102737 absolute error = 3e-63 relative error = 1.5747282873333391534555748591616e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.371 Order of pole (three term test) = -5.263 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=660154176, alloc=4783252, time=34.73 x[1] = 2.02 y1[1] (analytic) = 0.5657516538816995549482971259098 y1[1] (numeric) = 0.5657516538816995549482971259098 absolute error = 5.3e-63 relative error = 9.3680680624368914722800405442350e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9007931915226273171970135245537 y2[1] (numeric) = 1.9007931915226273171970135245537 absolute error = 2e-63 relative error = 1.0521923210372524688200032422639e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3771 Order of pole (three term test) = -5.451 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=664155644, alloc=4783252, time=34.94 x[1] = 2.03 y1[1] (analytic) = 0.5567655843342909169364832683039 y1[1] (numeric) = 0.5567655843342909169364832683039 absolute error = 5.4e-63 relative error = 9.6988753470756088741531163037910e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8964057411515599070388888319676 y2[1] (numeric) = 1.8964057411515599070388888319676 absolute error = 3e-63 relative error = 1.5819399482403493359302101185576e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.383 Order of pole (three term test) = -5.641 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=668156432, alloc=4783252, time=35.15 x[1] = 2.04 y1[1] (analytic) = 0.54782383785908806798272979470864 y1[1] (numeric) = 0.54782383785908806798272979470864 absolute error = 5.4e-63 relative error = 9.8571833257628244112328323711866e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8919286509533796351715256485842 y2[1] (numeric) = 1.8919286509533796351715256485842 absolute error = 3e-63 relative error = 1.5856834762179015926133685921299e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3888 Order of pole (three term test) = -5.835 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.05 y1[1] (analytic) = 0.5389273086232870978140700058326 y1[1] (numeric) = 0.5389273086232870978140700058326 absolute error = 5.5e-63 relative error = 1.0205457975492067135317802628524e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8873623686333754235599666046803 y2[1] (numeric) = 1.8873623686333754235599666046803 absolute error = 3e-63 relative error = 1.5895198769763948025602945222711e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3944 Order of pole (three term test) = -6.031 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=672158132, alloc=4783252, time=35.36 x[1] = 2.06 y1[1] (analytic) = 0.5300768862723978368768903735121 y1[1] (numeric) = 0.5300768862723978368768903735121 absolute error = 5.5e-63 relative error = 1.0375853281732491935715312450161e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8827073508159740500427975851999 y2[1] (numeric) = 1.8827073508159740500427975851999 absolute error = 2e-63 relative error = 1.0622999900293536192841255089695e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3999 Order of pole (three term test) = -6.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=676159132, alloc=4783252, time=35.58 x[1] = 2.07 y1[1] (analytic) = 0.52127345584128004672267286098827 y1[1] (numeric) = 0.52127345584128004672267286098827 absolute error = 5.6e-63 relative error = 1.0742921852719690477632235271204e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8779640629990780861734511204438 y2[1] (numeric) = 1.8779640629990780861734511204438 absolute error = 2e-63 relative error = 1.0649831055904405890913391735797e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4052 Order of pole (three term test) = -6.432 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=680160500, alloc=4783252, time=35.80 x[1] = 2.08 y1[1] (analytic) = 0.51251789766564067155843115022765 y1[1] (numeric) = 0.51251789766564067155843115022765 absolute error = 5.5e-63 relative error = 1.0731332554532800230552597426901e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8731329795075164948766768050246 y2[1] (numeric) = 1.8731329795075164948766768050246 absolute error = 2e-63 relative error = 1.0677298525414033019184784801202e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4103 Order of pole (three term test) = -6.636 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=684161652, alloc=4783252, time=36.01 x[1] = 2.09 y1[1] (analytic) = 0.50381108729400100116293368812955 y1[1] (numeric) = 0.50381108729400100116293368812955 absolute error = 5.5e-63 relative error = 1.0916790318253660656236416421027e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8682145834456125428216220587275 y2[1] (numeric) = 1.8682145834456125428216220587275 absolute error = 2e-63 relative error = 1.0705408349352091404535081101385e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4153 Order of pole (three term test) = -6.843 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.1 y1[1] (analytic) = 0.49515389540014254837906147628083 y1[1] (numeric) = 0.49515389540014254837906147628083 absolute error = 5.6e-63 relative error = 1.1309615156060807661156278215892e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.863209366648873770680759313269 y2[1] (numeric) = 1.863209366648873770680759313269 absolute error = 1e-63 relative error = 5.3670833664741466195688589559232e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4201 Order of pole (three term test) = -7.053 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=688162368, alloc=4783252, time=36.22 x[1] = 2.11 y1[1] (analytic) = 0.48654718769604039652158984292831 y1[1] (numeric) = 0.48654718769604039652158984292831 absolute error = 5.6e-63 relative error = 1.1509674994768392839987337850326e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8581178296348088522373755083107 y2[1] (numeric) = 1.8581178296348088522373755083107 absolute error = 2e-63 relative error = 1.0763580049135400714699908513894e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4247 Order of pole (three term test) = -7.265 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=692163184, alloc=4783252, time=36.44 x[1] = 2.12 y1[1] (analytic) = 0.47799182484529272329309811701611 y1[1] (numeric) = 0.47799182484529272329309811701611 absolute error = 5.6e-63 relative error = 1.1715681542906097162369496086887e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8529404815528762606147273336542 y2[1] (numeric) = 1.8529404815528762606147273336542 absolute error = 1e-63 relative error = 5.3968274208243293468159819123349e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4292 Order of pole (three term test) = -7.479 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=696163956, alloc=4783252, time=36.65 x[1] = 2.13 y1[1] (analytic) = 0.46948866237705515818347379039028 y1[1] (numeric) = 0.46948866237705515818347379039028 absolute error = 5.6e-63 relative error = 1.1927870572309017495647256670424e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8476778401335697467185299963159 y2[1] (numeric) = 1.8476778401335697467185299963159 absolute error = 2e-63 relative error = 1.0824397828224312049823291963519e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4335 Order of pole (three term test) = -7.695 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.14 y1[1] (analytic) = 0.4610385506004885798455500879914 y1[1] (numeric) = 0.4610385506004885798455500879914 absolute error = 5.6e-63 relative error = 1.2146489686613346450046163915088e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8423304316366457213025066370689 y2[1] (numeric) = 1.8423304316366457213025066370689 absolute error = 1e-63 relative error = 5.4279079519499863413845924845851e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4376 Order of pole (three term test) = -7.913 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=700164860, alloc=4783252, time=36.86 x[1] = 2.15 y1[1] (analytic) = 0.45264233451972890859584611773597 y1[1] (numeric) = 0.45264233451972890859584611773597 absolute error = 5.5e-63 relative error = 1.2150874057849037795542428479975e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8368987907984977178756481370438 y2[1] (numeric) = 1.8368987907984977178756481370438 absolute error = 1e-63 relative error = 5.4439580722098531640546833609282e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4415 Order of pole (three term test) = -8.133 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=704165560, alloc=4783252, time=37.07 x[1] = 2.16 y1[1] (analytic) = 0.44430085374938739699030125601663 y1[1] (numeric) = 0.44430085374938739699030125601663 absolute error = 5.5e-63 relative error = 1.2378999395536460664041126813432e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8313834607786831989610381203463 y2[1] (numeric) = 1.8313834607786831989610381203463 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4453 Order of pole (three term test) = -8.356 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=708166264, alloc=4783252, time=37.29 x[1] = 2.17 y1[1] (analytic) = 0.43601494243058986837553000558349 y1[1] (numeric) = 0.43601494243058986837553000558349 absolute error = 5.5e-63 relative error = 1.2614246588293373720871881891887e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8257849931056080529810564239434 y2[1] (numeric) = 1.8257849931056080529810564239434 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4489 Order of pole (three term test) = -8.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=712167380, alloc=4783252, time=37.50 x[1] = 2.18 y1[1] (analytic) = 0.42778542914756329942177513233751 y1[1] (numeric) = 0.42778542914756329942177513233751 absolute error = 5.5e-63 relative error = 1.2856912894297742695997858922121e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8201039476213742132740097460839 y2[1] (numeric) = 1.8201039476213742132740097460839 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4523 Order of pole (three term test) = -8.806 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.19 y1[1] (analytic) = 0.41961313684477808790979483620305 y1[1] (numeric) = 0.41961313684477808790979483620305 absolute error = 5.5e-63 relative error = 1.3107311275706179615097750170375e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.814340892425795914434327645905 y2[1] (numeric) = 1.814340892425795914434327645905 absolute error = 1e-63 relative error = 5.5116433971952635456861645933305e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4555 Order of pole (three term test) = -9.033 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=716168948, alloc=4783252, time=37.71 x[1] = 2.2 y1[1] (analytic) = 0.41149888274465429147585738734507 y1[1] (numeric) = 0.41149888274465429147585738734507 absolute error = 5.5e-63 relative error = 1.3365771404567560804948840144753e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8084964038195901843040369104161 y2[1] (numeric) = 1.8084964038195901843040369104161 absolute error = 1e-63 relative error = 5.5294552861038301567256314290128e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4586 Order of pole (three term test) = -9.262 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=720169684, alloc=4783252, time=37.92 x[1] = 2.21 y1[1] (analytic) = 0.40344347826584006662239082248137 y1[1] (numeric) = 0.40344347826584006662239082248137 absolute error = 5.5e-63 relative error = 1.3632640744723844256031060701646e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.802571066246747252518974042556 y2[1] (numeric) = 1.802571066246747252518974042556 absolute error = 1e-63 relative error = 5.5476314844116870858691896016498e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.12 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4615 Order of pole (three term test) = -9.493 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=724170596, alloc=4783252, time=38.14 x[1] = 2.22 y1[1] (analytic) = 0.39544772894207048008228556249985 y1[1] (numeric) = 0.39544772894207048008228556249985 absolute error = 5.5e-63 relative error = 1.3908285716329655074148578475296e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7965654722360866385208567496092 y2[1] (numeric) = 1.7965654722360866385208567496092 absolute error = 1e-63 relative error = 5.5661762148604290709750739383975e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.42 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4641 Order of pole (three term test) = -9.725 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.23 y1[1] (analytic) = 0.38751243434161480658809608931437 y1[1] (numeric) = 0.38751243434161480658809608931437 absolute error = 5.5e-63 relative error = 1.4193092950280478734014155923465e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7904802223420047633777101271885 y2[1] (numeric) = 1.7904802223420047633777101271885 absolute error = 1e-63 relative error = 5.5850938062413689785812703547247e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.72 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4666 Order of pole (three term test) = -9.958 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=728171468, alloc=4783252, time=38.35 TOP MAIN SOLVE Loop x[1] = 2.24 y1[1] (analytic) = 0.37963838798732036824923773368956 y1[1] (numeric) = 0.37963838798732036824923773368956 absolute error = 5.4e-63 relative error = 1.4224062083469693452650462730837e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7843159250844200106020886706045 y2[1] (numeric) = 1.7843159250844200106020886706045 absolute error = 1e-63 relative error = 5.6043886956436133623004795320692e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4689 Order of pole (three term test) = -10.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=732172476, alloc=4783252, time=38.56 x[1] = 2.25 y1[1] (analytic) = 0.3718263772772609110866109426036 y1[1] (numeric) = 0.3718263772772609110866109426036 absolute error = 5.5e-63 relative error = 1.4791850003419198502411526971053e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7780731968879212414109666755878 y2[1] (numeric) = 1.7780731968879212414109666755878 absolute error = 1e-63 relative error = 5.6240654307722171190821043758261e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4711 Order of pole (three term test) = -10.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=736173168, alloc=4783252, time=38.77 x[1] = 2.26 y1[1] (analytic) = 0.36407718340599745382087343125516 y1[1] (numeric) = 0.36407718340599745382087343125516 absolute error = 5.5e-63 relative error = 1.5106686852899330420422441886633e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7717526620201258495250616377403 y2[1] (numeric) = 1.7717526620201258495250616377403 absolute error = 1e-63 relative error = 5.6441286723385812616549226848790e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.473 Order of pole (three term test) = -10.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=740173864, alloc=4783252, time=38.98 x[1] = 2.27 y1[1] (analytic) = 0.3563915812864594827638656518757 y1[1] (numeric) = 0.3563915812864594827638656518757 absolute error = 5.6e-63 relative error = 1.5713053545725724673194465012849e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7653549525292535196507426019347 y2[1] (numeric) = 1.7653549525292535196507426019347 absolute error = 1e-63 relative error = 5.6645831965253407043347446034605e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4747 Order of pole (three term test) = -10.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.28 y1[1] (analytic) = 0.3487703394724543046286016495393 y1[1] (numeric) = 0.3487703394724543046286016495393 absolute error = 5.5e-63 relative error = 1.5769689613856590767245556249137e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7588807081809219322166535763009 y2[1] (numeric) = 1.7588807081809219322166535763009 absolute error = 1e-63 relative error = 5.6854338975280751750499960730519e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = -11.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=744174952, alloc=4783252, time=39.19 x[1] = 2.29 y1[1] (analytic) = 0.34121422008181230625796898181105 y1[1] (numeric) = 0.34121422008181230625796898181105 absolute error = 5.5e-63 relative error = 1.6118906177712274451063426395539e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7523305763941707347419082779737 y2[1] (numeric) = 1.7523305763941707347419082779737 absolute error = 1e-63 relative error = 5.7066857901762660729518730860283e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4776 Order of pole (three term test) = -11.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=748175616, alloc=4783252, time=39.41 x[1] = 2.3 y1[1] (analytic) = 0.33372397872017580668211942883398 y1[1] (numeric) = 0.33372397872017580668211942883398 absolute error = 5.6e-63 relative error = 1.6780334519191213318347935078453e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7457052121767201773854062116435 y2[1] (numeric) = 1.7457052121767201773854062116435 absolute error = 2e-63 relative error = 1.1456688025272030899982595398474e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4788 Order of pole (three term test) = -11.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=752176452, alloc=4783252, time=39.62 x[1] = 2.31 y1[1] (analytic) = 0.32630036440543912255583567652897 y1[1] (numeric) = 0.32630036440543912255583567652897 absolute error = 5.6e-63 relative error = 1.7162101581479733174893844671213e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7390052780594708867587641920983 y2[1] (numeric) = 1.7390052780594708867587641920983 absolute error = 2e-63 relative error = 1.1500827658394280952087812218684e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4798 Order of pole (three term test) = -11.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=756177272, alloc=4783252, time=39.83 x[1] = 2.32 y1[1] (analytic) = 0.31894411949284740290636383399177 y1[1] (numeric) = 0.31894411949284740290636383399177 absolute error = 5.6e-63 relative error = 1.7557934627873221635583658418973e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7322314440302513279708986777247 y2[1] (numeric) = 1.7322314440302513279708986777247 absolute error = 1e-63 relative error = 5.7729006331473579286921492026411e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4806 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.33 y1[1] (analytic) = 0.311655979600761723245819572184 y1[1] (numeric) = 0.311655979600761723245819572184 absolute error = 5.6e-63 relative error = 1.7968530580333241751680930437250e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7253843874668195801028441924754 y2[1] (numeric) = 1.7253843874668195801028441924754 absolute error = 1e-63 relative error = 5.7958099497363786177046107865009e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4812 Order of pole (three term test) = -12.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=760178344, alloc=4783252, time=40.04 x[1] = 2.34 y1[1] (analytic) = 0.30443667353709786247689442793865 y1[1] (numeric) = 0.30443667353709786247689442793865 absolute error = 5.7e-63 relative error = 1.8723105642216304146237143207234e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.718464793069126124879428686794 y2[1] (numeric) = 1.718464793069126124879428686794 absolute error = 1e-63 relative error = 5.8191474392328414070824568526825e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.39 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -12.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=764179332, alloc=4783252, time=40.25 x[1] = 2.35 y1[1] (analytic) = 0.29728692322644611865287088774108 y1[1] (numeric) = 0.29728692322644611865287088774108 absolute error = 5.7e-63 relative error = 1.9173396320759991255217993203138e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7114733527908444222024911820132 y2[1] (numeric) = 1.7114733527908444222024911820132 absolute error = 1e-63 relative error = 5.8429189000771308407099791936325e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.77 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=768180392, alloc=4783252, time=40.47 x[1] = 2.36 y1[1] (analytic) = 0.2902074436378794515496369653549 y1[1] (numeric) = 0.2902074436378794515496369653549 absolute error = 5.6e-63 relative error = 1.9296541569718226167973807332896e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7044107657701761194310307129327 y2[1] (numeric) = 1.7044107657701761194310307129327 absolute error = 1e-63 relative error = 5.8671302721332415280843951046881e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.86 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.37 y1[1] (analytic) = 0.28319894271345717117528339117765 y1[1] (numeric) = 0.28319894271345717117528339117765 absolute error = 5.6e-63 relative error = 1.9774085123142999473010532185220e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6972777382599378138296964202892 y2[1] (numeric) = 1.6972777382599378138296964202892 absolute error = 1e-63 relative error = 5.8917876400429766323243923406338e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.46 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4816 Order of pole (three term test) = -13.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.48 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=772181116, alloc=4783252, time=40.68 x[1] = 2.38 y1[1] (analytic) = 0.27626212129743132178885239263247 y1[1] (numeric) = 0.27626212129743132178885239263247 absolute error = 5.6e-63 relative error = 2.0270603779122102391002806259789e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6900749835569363594511131070202 y2[1] (numeric) = 1.6900749835569363594511131070202 absolute error = 2e-63 relative error = 1.1833794473371794526768408186209e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=776182060, alloc=4783252, time=40.89 x[1] = 2.39 y1[1] (analytic) = 0.26939767306616284073084170738194 y1[1] (numeric) = 0.26939767306616284073084170738194 absolute error = 5.6e-63 relative error = 2.0787113475269942372077509898234e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.682803221930639780862500311013 y2[1] (numeric) = 1.682803221930639780862500311013 absolute error = 1e-63 relative error = 5.9424654467485745672071818273848e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.69 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4807 Order of pole (three term test) = -13.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=780183200, alloc=4783252, time=41.10 x[1] = 2.4 y1[1] (analytic) = 0.26260628445875450039117777266522 y1[1] (numeric) = 0.26260628445875450039117777266522 absolute error = 5.7e-63 relative error = 2.1705497306540103310689016431889e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6754631805511509265657715253413 y2[1] (numeric) = 1.6754631805511509265657715253413 absolute error = 1e-63 relative error = 5.9684988104068370815749986399566e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4799 Order of pole (three term test) = -14.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=784184140, alloc=4783252, time=41.31 x[1] = 2.41 y1[1] (analytic) = 0.25588863460840756996265560443205 y1[1] (numeric) = 0.25588863460840756996265560443205 absolute error = 5.7e-63 relative error = 2.2275315231263963017578039106272e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6680555934164910646857498006547 y2[1] (numeric) = 1.6680555934164910646857498006547 absolute error = 2e-63 relative error = 1.1990008054249705561159210582795e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.96 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = -14.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.42 y1[1] (analytic) = 0.24924539527450906125646743108926 y1[1] (numeric) = 0.24924539527450906125646743108926 absolute error = 5.7e-63 relative error = 2.2869028307312335730463988485844e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6605812012792006925063341065602 y2[1] (numeric) = 1.6605812012792006925063341065602 absolute error = 2e-63 relative error = 1.2043975919150076890966614461712e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.6 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4779 Order of pole (three term test) = -14.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.72 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=788184880, alloc=4783252, time=41.52 x[1] = 2.43 y1[1] (analytic) = 0.2426772307754563497986447558221 y1[1] (numeric) = 0.2426772307754563497986447558221 absolute error = 5.7e-63 relative error = 2.3487988476653084394370121227541e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6530407515722648997124970471899 y2[1] (numeric) = 1.6530407515722648997124970471899 absolute error = 2e-63 relative error = 1.2098915275365897778349891334245e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4765 Order of pole (three term test) = -14.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.38 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=792186084, alloc=4783252, time=41.74 x[1] = 2.44 y1[1] (analytic) = 0.2361847979222258886893249074626 y1[1] (numeric) = 0.2361847979222258886893249074626 absolute error = 5.8e-63 relative error = 2.4557041990102606507295877326566e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6454349983343706927400610729825 y2[1] (numeric) = 1.6454349983343706927400610729825 absolute error = 2e-63 relative error = 1.2154840525602930899436952389789e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.475 Order of pole (three term test) = -14.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.06 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=796186976, alloc=4783252, time=41.95 x[1] = 2.45 y1[1] (analytic) = 0.22976874595269265829809693266351 y1[1] (numeric) = 0.22976874595269265829809693266351 absolute error = 5.8e-63 relative error = 2.5242771709230499202670927943196e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6377647021345037544385328556338 y2[1] (numeric) = 1.6377647021345037544385328556338 absolute error = 1e-63 relative error = 6.1058832120187773981101872107211e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4733 Order of pole (three term test) = -15.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.73 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.46 y1[1] (analytic) = 0.2234297164667069197957236853138 y1[1] (numeric) = 0.2234297164667069197957236853138 absolute error = 5.8e-63 relative error = 2.5958946248156087507090214414568e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6300306299958921793081937186159 y2[1] (numeric) = 1.6300306299958921793081937186159 absolute error = 1e-63 relative error = 6.1348540426048318370418742023058e-62 % Correct digits = 64 h = 0.01 bytes used=800188612, alloc=4783252, time=42.17 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4714 Order of pole (three term test) = -15.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.47 y1[1] (analytic) = 0.21716834336193476479278441593845 y1[1] (numeric) = 0.21716834336193476479278441593845 absolute error = 5.9e-63 relative error = 2.7167863919130264591590190796650e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6222335553193047898745424048558 y2[1] (numeric) = 1.6222335553193047898745424048558 absolute error = 1e-63 relative error = 6.1643404966011176812438993960884e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4693 Order of pole (three term test) = -15.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=804189924, alloc=4783252, time=42.38 x[1] = 2.48 y1[1] (analytic) = 0.21098525277046887697680796640967 y1[1] (numeric) = 0.21098525277046887697680796640967 absolute error = 5.8e-63 relative error = 2.7490072997233732383393569141035e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6143742578057117043045348806656 y2[1] (numeric) = 1.6143742578057117043045348806656 absolute error = 1e-63 relative error = 6.1943505055588478063216065453407e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.57 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.467 Order of pole (three term test) = -15.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=808190836, alloc=4783252, time=42.59 x[1] = 2.49 y1[1] (analytic) = 0.20488106299621584461890866742843 y1[1] (numeric) = 0.20488106299621584461890866742843 absolute error = 5.9e-63 relative error = 2.8797195376270441655427433200156e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6064535233783148891434102397918 y2[1] (numeric) = 1.6064535233783148891434102397918 absolute error = 2e-63 relative error = 1.2449784390861621708001213306392e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4646 Order of pole (three term test) = -16.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=812191648, alloc=4783252, time=42.81 x[1] = 2.5 y1[1] (analytic) = 0.19885638445306628516649720953265 y1[1] (numeric) = 0.19885638445306628516649720953265 absolute error = 5.9e-63 relative error = 2.9669653384412744621497926822297e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5984721441039564940518547021862 y2[1] (numeric) = 1.5984721441039564940518547021862 absolute error = 1e-63 relative error = 6.2559738916223809323680023061472e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4619 Order of pole (three term test) = -16.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.19 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.51 y1[1] (analytic) = 0.19291181960385396485808249212159 y1[1] (numeric) = 0.19291181960385396485808249212159 absolute error = 6.0e-63 relative error = 3.1102293329258156323477369492172e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5904309181139128276445371550241 y2[1] (numeric) = 1.5904309181139128276445371550241 absolute error = 1e-63 relative error = 6.2876041242074000193085289702263e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4591 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.9 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=816192536, alloc=4783252, time=43.01 x[1] = 2.52 y1[1] (analytic) = 0.18704796290011001739733573954815 y1[1] (numeric) = 0.18704796290011001739733573954815 absolute error = 5.9e-63 relative error = 3.1542711871985480751444917363250e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5823306495240818949664275822971 y2[1] (numeric) = 1.5823306495240818949664275822971 absolute error = 1e-63 relative error = 6.3197916333148847608647696410310e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4561 Order of pole (three term test) = -16.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=820193432, alloc=4783252, time=43.22 x[1] = 2.53 y1[1] (analytic) = 0.18126540072261828621434482744501 y1[1] (numeric) = 0.18126540072261828621434482744501 absolute error = 5.9e-63 relative error = 3.2548958469070917080800246489712e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5741721483545724777866405874022 y2[1] (numeric) = 1.5741721483545724777866405874022 absolute error = 1e-63 relative error = 6.3525453746927570759199622077066e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4529 Order of pole (three term test) = -17.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=824194320, alloc=4783252, time=43.44 x[1] = 2.54 y1[1] (analytic) = 0.17556471132277773473029564419343 y1[1] (numeric) = 0.17556471132277773473029564419343 absolute error = 5.9e-63 relative error = 3.3605842287706567367462005995320e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.565956230448702798734765747982 y2[1] (numeric) = 1.565956230448702798734765747982 absolute error = 1e-63 relative error = 6.3858745254550570855095175873893e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4495 Order of pole (three term test) = -17.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=828195900, alloc=4783252, time=43.65 x[1] = 2.55 y1[1] (analytic) = 0.16994646476477778833568952416771 y1[1] (numeric) = 0.16994646476477778833568952416771 absolute error = 5.9e-63 relative error = 3.4716815134496419433480149952548e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5576837173914168693457702817662 y2[1] (numeric) = 1.5576837173914168693457702817662 absolute error = 1e-63 relative error = 6.4197884900193679609315766945900e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = -17.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.56 y1[1] (analytic) = 0.16441122286859239049971187661756 y1[1] (numeric) = 0.16441122286859239049971187661756 absolute error = 6.0e-63 relative error = 3.6493859088899124509964849982391e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5493554364271266803106833831373 y2[1] (numeric) = 1.5493554364271266803106833831373 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4422 Order of pole (three term test) = -17.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=832196900, alloc=4783252, time=43.86 x[1] = 2.57 y1[1] (analytic) = 0.15895953915379847355763627843287 y1[1] (numeric) = 0.15895953915379847355763627843287 absolute error = 6.0e-63 relative error = 3.7745454169911796013247425418155e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5409722203769884496455725487458 y2[1] (numeric) = 1.5409722203769884496455725487458 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4383 Order of pole (three term test) = -17.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=836197964, alloc=4783252, time=44.07 x[1] = 2.58 y1[1] (analytic) = 0.15359195878422446228236750543077 y1[1] (numeric) = 0.15359195878422446228236750543077 absolute error = 6.0e-63 relative error = 3.9064545093986158633145409615120e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5325349075556212010850587644716 y2[1] (numeric) = 1.5325349075556212010850587644716 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4342 Order of pole (three term test) = -18.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=840198624, alloc=4783252, time=44.28 x[1] = 2.59 y1[1] (analytic) = 0.14830901851343434534364025459169 y1[1] (numeric) = 0.14830901851343434534364025459169 absolute error = 6.0e-63 relative error = 4.0456069766630538300735108341022e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5240443416872760007731302488759 y2[1] (numeric) = 1.5240443416872760007731302488759 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.43 Order of pole (three term test) = -18.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.6 y1[1] (analytic) = 0.1431112466310527662022978483548 y1[1] (numeric) = 0.1431112466310527662022978483548 absolute error = 6.1e-63 relative error = 4.2624183239253547270180490655914e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5155013718214642352577269352094 y2[1] (numeric) = 1.5155013718214642352577269352094 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4255 Order of pole (three term test) = -18.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=844199372, alloc=4783252, time=44.49 x[1] = 2.61 y1[1] (analytic) = 0.13799916290993650088583255127735 y1[1] (numeric) = 0.13799916290993650088583255127735 absolute error = 6.0e-63 relative error = 4.3478524604644363402520747513489e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5069068522480533678909866995555 y2[1] (numeric) = 1.5069068522480533678909866995555 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4209 Order of pole (three term test) = -18.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=848200196, alloc=4783252, time=44.71 x[1] = 2.62 y1[1] (analytic) = 0.13297327855419760545338632325165 y1[1] (numeric) = 0.13297327855419760545338632325165 absolute error = 6.0e-63 relative error = 4.5121847526339691703093458321892e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4982616424118386639887600099976 y2[1] (numeric) = 1.4982616424118386639887600099976 absolute error = 1e-63 relative error = 6.6744016645199699610008033416117e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4161 Order of pole (three term test) = -19.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=852201736, alloc=4783252, time=44.92 x[1] = 2.63 y1[1] (analytic) = 0.12803409614808343079215160980507 y1[1] (numeric) = 0.12803409614808343079215160980507 absolute error = 6.1e-63 relative error = 4.7643558891881255944059640129370e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4895666068265994275056870536116 y2[1] (numeric) = 1.4895666068265994275056870536116 absolute error = 1e-63 relative error = 6.7133620975192154204027839981551e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4112 Order of pole (three term test) = -19.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=856202620, alloc=4783252, time=45.13 x[1] = 2.64 y1[1] (analytic) = 0.12318210960571861670109268373401 y1[1] (numeric) = 0.12318210960571861670109268373401 absolute error = 6.0e-63 relative error = 4.8708371850464359081352360341224e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4808226149886483435305502695329 y2[1] (numeric) = 1.4808226149886483435305502695329 absolute error = 1e-63 relative error = 6.7530032961285223035000128588588e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4061 Order of pole (three term test) = -19.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.65 y1[1] (analytic) = 0.11841780412171409102069763394619 y1[1] (numeric) = 0.11841780412171409102069763394619 absolute error = 6.0e-63 relative error = 5.0668056585756171841182049860794e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4720305412898825715956107783974 y2[1] (numeric) = 1.4720305412898825715956107783974 absolute error = 1e-63 relative error = 6.7933373116276463929622807634632e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4008 Order of pole (three term test) = -19.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=860204084, alloc=4783252, time=45.34 x[1] = 2.66 y1[1] (analytic) = 0.11374165612264801286768899611741 y1[1] (numeric) = 0.11374165612264801286768899611741 absolute error = 6.0e-63 relative error = 5.2751122188076632953996578079533e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4631912649303452846181405937963 y2[1] (numeric) = 1.4631912649303452846181405937963 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3954 Order of pole (three term test) = -19.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=864205240, alloc=4783252, time=45.56 x[1] = 2.67 y1[1] (analytic) = 0.10915413321942351183993714157026 y1[1] (numeric) = 0.10915413321942351183993714157026 absolute error = 6.1e-63 relative error = 5.5884278680841845129290272610297e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4543056698303063972473913211913 y2[1] (numeric) = 1.4543056698303063972473913211913 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3898 Order of pole (three term test) = -20.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=868206040, alloc=4783252, time=45.78 x[1] = 2.68 y1[1] (analytic) = 0.10465569416050798737795418137934 y1[1] (numeric) = 0.10465569416050798737795418137934 absolute error = 6.0e-63 relative error = 5.7330850921479155294960357277233e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4453746445418712754708988319295 y2[1] (numeric) = 1.4453746445418712754708988319295 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3841 Order of pole (three term test) = -20.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.69 y1[1] (analytic) = 0.10024678878605864431406511567113 y1[1] (numeric) = 0.10024678878605864431406511567113 absolute error = 6.0e-63 relative error = 5.9852291256978618361805417014665e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.436399082160126266535504118761 y2[1] (numeric) = 1.436399082160126266535504118761 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3782 Order of pole (three term test) = -20.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=872206744, alloc=4783252, time=45.99 TOP MAIN SOLVE Loop x[1] = 2.7 y1[1] (analytic) = 0.09592785798293885201747271805667 y1[1] (numeric) = 0.09592785798293885201747271805667 absolute error = 5.99e-63 relative error = 6.2442757776008561880466341927583e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4273798802338299345560530858579 y2[1] (numeric) = 1.4273798802338299345560530858579 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3722 Order of pole (three term test) = -20.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=876207596, alloc=4783252, time=46.20 x[1] = 2.71 y1[1] (analytic) = 0.091699333640629825461815406283923 y1[1] (numeric) = 0.091699333640629825461815406283923 absolute error = 6.05e-63 relative error = 6.5976488157591003492020430809984e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4183179406756589326137906811086 y2[1] (numeric) = 1.4183179406756589326137906811086 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.366 Order of pole (three term test) = -20.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=880208908, alloc=4783252, time=46.42 x[1] = 2.72 y1[1] (analytic) = 0.087561638608042037010371200012937 y1[1] (numeric) = 0.087561638608042037010371200012937 absolute error = 6.01e-63 relative error = 6.8637363296762422443669787552228e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4092141696720174866824446740074 y2[1] (numeric) = 1.4092141696720174866824446740074 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3596 Order of pole (three term test) = -21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=884209676, alloc=4783252, time=46.63 x[1] = 2.73 y1[1] (analytic) = 0.083515186651230677741738875107214 y1[1] (numeric) = 0.083515186651230677741738875107214 absolute error = 5.99e-63 relative error = 7.1723482161573203009105010459109e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4000694775924195103584479578945 y2[1] (numeric) = 1.4000694775924195103584479578945 absolute error = 1e-63 relative error = 7.1425026829355283900967676110504e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3532 Order of pole (three term test) = -21.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.74 y1[1] (analytic) = 0.079560382412019396734626748220724 y1[1] (numeric) = 0.079560382412019396734626748220724 absolute error = 5.94e-63 relative error = 7.4660274623097192893693398392843e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3908847788984524121083117016403 y2[1] (numeric) = 1.3908847788984524121083117016403 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3465 Order of pole (three term test) = -21.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=888210408, alloc=4783252, time=46.84 x[1] = 2.75 y1[1] (analytic) = 0.075697621367536455903340510473287 y1[1] (numeric) = 0.075697621367536455903340510473287 absolute error = 5.99e-63 relative error = 7.9130623813350897384483607412393e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3816609920523316985765613723778 y2[1] (numeric) = 1.3816609920523316985765613723778 absolute error = 1e-63 relative error = 7.2376654313341435597607314864692e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3398 Order of pole (three term test) = -21.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=892211268, alloc=4783252, time=47.05 x[1] = 2.76 y1[1] (analytic) = 0.071927289790667346734766802859897 y1[1] (numeric) = 0.071927289790667346734766802859897 absolute error = 5.94e-63 relative error = 8.2583398002168604148059969205415e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3723990394250555184177005924498 y2[1] (numeric) = 1.3723990394250555184177005924498 absolute error = 1e-63 relative error = 7.2865104920135611559264296092513e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3329 Order of pole (three term test) = -21.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=896212116, alloc=4783252, time=47.27 x[1] = 2.77 y1[1] (analytic) = 0.068249764711427823632222792170926 y1[1] (numeric) = 0.068249764711427823632222792170926 absolute error = 5.99e-63 relative error = 8.7765870334158487038603700214690e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3630998472041683311212820091725 y2[1] (numeric) = 1.3630998472041683311212820091725 absolute error = 1e-63 relative error = 7.3362197351212645686264814474797e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3258 Order of pole (three term test) = -21.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.78 bytes used=900213512, alloc=4783252, time=47.48 y1[1] (analytic) = 0.064665413879261216530648330882405 y1[1] (numeric) = 0.064665413879261216530648330882405 absolute error = 5.91e-63 relative error = 9.1393523144145381971917006958334e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3537643453011429243863393172273 y2[1] (numeric) = 1.3537643453011429243863393172273 absolute error = 1e-63 relative error = 7.3868099974043225636108880988956e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3187 Order of pole (three term test) = -22.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.79 y1[1] (analytic) = 0.061174595726263793020460380375909 y1[1] (numeric) = 0.061174595726263793020460380375909 absolute error = 5.97e-63 relative error = 9.7589529266589477474521883241979e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3443934672583900417662615955623 y2[1] (numeric) = 1.3443934672583900417662615955623 absolute error = 1e-63 relative error = 7.4382985662619392383536878462157e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3114 Order of pole (three term test) = -22.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=904214368, alloc=4783252, time=47.70 x[1] = 2.8 y1[1] (analytic) = 0.057777659331341847413211882633846 y1[1] (numeric) = 0.057777659331341847413211882633846 absolute error = 5.89e-63 relative error = 1.0194251667798063943652911693634e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3349881501559049195438537527124 y2[1] (numeric) = 1.3349881501559049195438537527124 absolute error = 1e-63 relative error = 7.4907031937565607014942380243117e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.304 Order of pole (three term test) = -22.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=908215212, alloc=4783252, time=47.91 x[1] = 2.81 y1[1] (analytic) = 0.054474944385304101010279521641165 y1[1] (numeric) = 0.054474944385304101010279521641165 absolute error = 5.97e-63 relative error = 1.0959166764400677530221291250954e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3255493345175600681051012812063 y2[1] (numeric) = 1.3255493345175600681051012812063 absolute error = 1e-63 relative error = 7.5440421111444691436647174241085e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2965 Order of pole (three term test) = -22.48 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=912216264, alloc=4783252, time=48.12 x[1] = 2.82 y1[1] (analytic) = 0.051266781156892904305463936239962 y1[1] (numeric) = 0.051266781156892904305463936239962 absolute error = 5.88e-63 relative error = 1.1469415218414632580454803654865e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3160779642170536684554128560246 y2[1] (numeric) = 1.3160779642170536684554128560246 absolute error = 1e-63 relative error = 7.5983340439478353894932854601517e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2888 Order of pole (three term test) = -22.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.83 y1[1] (analytic) = 0.04815349045975763797297488727547 y1[1] (numeric) = 0.04815349045975763797297488727547 absolute error = 5.86e-63 relative error = 1.2169418964337095430733072271372e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3065749863835229889603130778681 y2[1] (numeric) = 1.3065749863835229889603130778681 absolute error = 1e-63 relative error = 7.6535982275912552419343862107572e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.281 Order of pole (three term test) = -22.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=916217660, alloc=4783252, time=48.33 x[1] = 2.84 y1[1] (analytic) = 0.045135383620373615273180506413763 y1[1] (numeric) = 0.045135383620373615273180506413763 absolute error = 5.94e-63 relative error = 1.3160406589119471653601946099322e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2970413513068322608902560680973 y2[1] (numeric) = 1.2970413513068322608902560680973 absolute error = 1e-63 relative error = 7.7098544236269055820285983146568e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2732 Order of pole (three term test) = -22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=920218380, alloc=4783252, time=48.55 x[1] = 2.85 y1[1] (analytic) = 0.042212762446909693959145892825075 y1[1] (numeric) = 0.042212762446909693959145892825075 absolute error = 5.87e-63 relative error = 1.3905747124184548939427610003610e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2874780123425444839030789266917 y2[1] (numeric) = 1.2874780123425444839030789266917 absolute error = 1e-63 relative error = 7.7671229365736266121798592981736e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2652 Order of pole (three term test) = -23.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=924219148, alloc=4783252, time=48.76 x[1] = 2.86 y1[1] (analytic) = 0.039385919199047710896826833607233 y1[1] (numeric) = 0.039385919199047710896826833607233 absolute error = 5.87e-63 relative error = 1.4903803489603277550495340804264e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2778859258165866642043569097532 y2[1] (numeric) = 1.2778859258165866642043569097532 absolute error = 1e-63 relative error = 7.8254246313964703885954037633078e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = -23.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=928220196, alloc=4783252, time=48.97 x[1] = 2.87 y1[1] (analytic) = 0.036655136558756757430306241262063 y1[1] (numeric) = 0.036655136558756757430306241262063 absolute error = 5.86e-63 relative error = 1.5986845365059950187591222794077e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2682660509296180187823989209871 y2[1] (numeric) = 1.2682660509296180187823989209871 absolute error = 1e-63 relative error = 7.8847809516545566706525756944805e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2489 Order of pole (three term test) = -23.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.88 y1[1] (analytic) = 0.034020687602025218040182095234475 y1[1] (numeric) = 0.034020687602025218040182095234475 absolute error = 5.86e-63 relative error = 1.7224813526846999909156947051421e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2586193496611107088177669201177 y2[1] (numeric) = 1.2586193496611107088177669201177 absolute error = 1e-63 relative error = 7.9452139383464491626141189354785e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2406 Order of pole (three term test) = -23.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=932221040, alloc=4783252, time=49.19 x[1] = 2.89 y1[1] (analytic) = 0.031482835771553399067684492790717 y1[1] (numeric) = 0.031482835771553399067684492790717 absolute error = 5.82e-63 relative error = 1.8486263569874203088840354785917e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2489467866731526941140458405805 y2[1] (numeric) = 1.2489467866731526941140458405805 absolute error = 1e-63 relative error = 8.0067462494837127440852444379963e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2322 Order of pole (three term test) = -23.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=936221776, alloc=4783252, time=49.40 x[1] = 2.9 y1[1] (analytic) = 0.029041834850409478218893330654468 y1[1] (numeric) = 0.029041834850409478218893330654468 absolute error = 5.76e-63 relative error = 1.9833457595461763019746457815059e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2392493292139823281842569187396 y2[1] (numeric) = 1.2392493292139823281842569187396 absolute error = 1e-63 relative error = 8.0694011804248398736554020254220e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2237 Order of pole (three term test) = -23.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=940222484, alloc=4783252, time=49.61 x[1] = 2.91 y1[1] (analytic) = 0.026697928936651409232152893397248 y1[1] (numeric) = 0.026697928936651409232152893397248 absolute error = 5.80e-63 relative error = 2.1724531568580411610247974079318e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.229527947021264340453018223827 y2[1] (numeric) = 1.229527947021264340453018223827 absolute error = 1e-63 relative error = 8.1332026850033469057313643118625e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2151 Order of pole (three term test) = -23.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.92 y1[1] (analytic) = 0.024451352418917319497068264841735 y1[1] (numeric) = 0.024451352418917319497068264841735 absolute error = 5.74e-63 relative error = 2.3475184119301002007671356901307e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2197836122251168778956290930646 y2[1] (numeric) = 1.2197836122251168778956290930646 absolute error = 1e-63 relative error = 8.1981753974855438130589479735715e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2065 Order of pole (three term test) = -23.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=944223420, alloc=4783252, time=49.82 x[1] = 2.93 y1[1] (analytic) = 0.022302329952986841564980395323675 y1[1] (numeric) = 0.022302329952986841564980395323675 absolute error = 5.79e-63 relative error = 2.5961413055072184168878092100371e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2100172992508993033291040342591 y2[1] (numeric) = 1.2100172992508993033291040342591 absolute error = 2e-63 relative error = 1.6528689310790558678599057049813e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1977 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=948224324, alloc=4783252, time=50.03 x[1] = 2.94 y1[1] (analytic) = 0.020251076439315722398236618671679 y1[1] (numeric) = 0.020251076439315722398236618671679 absolute error = 5.74e-63 relative error = 2.8344172307089236499383983854573e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2002299847217704714943170944231 y2[1] (numeric) = 1.2002299847217704714943170944231 absolute error = 2e-63 relative error = 1.6663473046489727757461410596202e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1889 Order of pole (three term test) = -24.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=952225008, alloc=4783252, time=50.25 x[1] = 2.95 y1[1] (analytic) = 0.018297797001545956878610595298032 y1[1] (numeric) = 0.018297797001545956878610595298032 absolute error = 5.72e-63 relative error = 3.1260593827315521641387192864676e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1904226473610272270204473140574 y2[1] (numeric) = 1.1904226473610272270204473140574 absolute error = 3e-63 relative error = 2.5201133451640142286525338036620e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.18 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=956225792, alloc=4783252, time=50.46 x[1] = 2.96 y1[1] (analytic) = 0.016442686965993594543612677023842 y1[1] (numeric) = 0.016442686965993594543612677023842 absolute error = 5.73e-63 relative error = 3.4848318963017788037313726397153e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1805962678942328903405445088013 y2[1] (numeric) = 1.1805962678942328903405445088013 absolute error = 2e-63 relative error = 1.6940592261631439850894137849017e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1711 Order of pole (three term test) = -24.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.97 y1[1] (analytic) = 0.014685931842116270752923625193857 y1[1] (numeric) = 0.014685931842116270752923625193857 absolute error = 5.66e-63 relative error = 3.8540285089491353778186333129219e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.170751828951145518628064498668 y2[1] (numeric) = 1.170751828951145518628064498668 absolute error = 2e-63 relative error = 1.7083039723215826849614839948675e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.162 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=960226884, alloc=4783252, time=50.68 x[1] = 2.98 y1[1] (analytic) = 0.013027707303962415515558035604598 y1[1] (numeric) = 0.013027707303962415515558035604598 absolute error = 5.61e-63 relative error = 4.3062066633118952483752492923215e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1608903149674557488465539545413 y2[1] (numeric) = 1.1608903149674557488465539545413 absolute error = 2e-63 relative error = 1.7228156477953455448828846248518e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1529 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=964228216, alloc=4783252, time=50.89 x[1] = 2.99 y1[1] (analytic) = 0.01146817917260399504141581278916 y1[1] (numeric) = 0.01146817917260399504141581278916 absolute error = 5.61e-63 relative error = 4.8917966100508513317736123913211e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1510127120863440490462950356105 y2[1] (numeric) = 1.1510127120863440490462950356105 absolute error = 3e-63 relative error = 2.6064004059191944315529243141445e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1438 Order of pole (three term test) = -24.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=968228912, alloc=4783252, time=51.10 x[1] = 3 y1[1] (analytic) = 0.010007503399554542728427205268739 y1[1] (numeric) = 0.010007503399554542728427205268739 absolute error = 5.64e-63 relative error = 5.6357712556470872931953173182588e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1411200080598672221007448028081 y2[1] (numeric) = 1.1411200080598672221007448028081 absolute error = 3e-63 relative error = 2.6289960554636154528328783203420e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1345 Order of pole (three term test) = -24.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.01 y1[1] (analytic) = 0.0086458260511741377683744258175829 y1[1] (numeric) = 0.0086458260511741377683744258175829 absolute error = 5.606e-63 relative error = 6.4840536541198197843145032628996e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1312131921501840231502181246849 y2[1] (numeric) = 1.1312131921501840231502181246849 absolute error = 3e-63 bytes used=972230092, alloc=4783252, time=51.31 relative error = 2.6520199912959545544553436322262e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1253 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.02 y1[1] (analytic) = 0.007383283294062890860533466736964 y1[1] (numeric) = 0.007383283294062890860533466736964 absolute error = 5.581e-63 relative error = 7.5589677081574827644815126682608e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1212932550306297681087579963391 y2[1] (numeric) = 1.1212932550306297681087579963391 absolute error = 3e-63 relative error = 2.6754820708504579425038196999236e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1159 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=976230988, alloc=4783252, time=51.52 x[1] = 3.03 y1[1] (analytic) = 0.0062200013814443976723926912915734 y1[1] (numeric) = 0.0062200013814443976723926912915734 absolute error = 5.488e-63 relative error = 8.8231491658054686608023011756636e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1113611886866498256909050329173 y2[1] (numeric) = 1.1113611886866498256909050329173 absolute error = 3e-63 relative error = 2.6993924482330065371596013246168e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1066 Order of pole (three term test) = -24.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=980231796, alloc=4783252, time=51.73 x[1] = 3.04 y1[1] (analytic) = 0.0051560966405405216907550451568149 y1[1] (numeric) = 0.0051560966405405216907550451568149 absolute error = 5.469e-63 relative error = 1.0606860928476849029217587640831e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1014179863166018995266083126088 y2[1] (numeric) = 1.1014179863166018995266083126088 absolute error = 3e-63 relative error = 2.7237615848572604555021187058227e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09716 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=984232860, alloc=4783252, time=51.95 x[1] = 3.05 y1[1] (analytic) = 0.004191675460938768974417798435083 y1[1] (numeric) = 0.004191675460938768974417798435083 absolute error = 5.422e-63 relative error = 1.2935161728350236229965258735486e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0914646422324370200534015886964 y2[1] (numeric) = 1.0914646422324370200534015886964 absolute error = 3e-63 relative error = 2.7486002605305867032605781720218e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08771 Order of pole (three term test) = -24.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.06 y1[1] (analytic) = 0.0033268342839534180612607282068477 y1[1] (numeric) = 0.0033268342839534180612607282068477 absolute error = 5.423e-63 relative error = 1.6300781875902816090717410954860e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0815021517602691780038900888357 y2[1] (numeric) = 1.0815021517602691780038900888357 absolute error = 3e-63 relative error = 2.7739195850116015509009725259660e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07822 Order of pole (three term test) = -24.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=988233780, alloc=4783252, time=52.15 x[1] = 3.07 y1[1] (analytic) = 0.0025616595929814689078863372732293 y1[1] (numeric) = 0.0025616595929814689078863372732293 absolute error = 5.435e-63 relative error = 2.1216714410029408184946738275986e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0715315111408435424423407903189 y2[1] (numeric) = 1.0715315111408435424423407903189 absolute error = 3e-63 relative error = 2.7997310100623592082651729507190e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06871 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=992234820, alloc=4783252, time=52.37 x[1] = 3.08 y1[1] (analytic) = 0.0018962279048543752588814626402055 y1[1] (numeric) = 0.0018962279048543752588814626402055 absolute error = 5.372e-63 relative error = 2.8329927991501389929007080494806e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0615537174299132164456296371357 y2[1] (numeric) = 1.0615537174299132164456296371357 absolute error = 3e-63 relative error = 2.8260463420194922903538701742815e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05916 Order of pole (three term test) = -24.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=996235624, alloc=4783252, time=52.58 x[1] = 3.09 y1[1] (analytic) = 0.0013306057621864252652564819142417 y1[1] (numeric) = 0.0013306057621864252652564819142417 absolute error = 5.364e-63 relative error = 4.0312466340037341405572193804969e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0515697683985344926699585105746 y2[1] (numeric) = 1.0515697683985344926699585105746 absolute error = 3e-63 relative error = 2.8528777549099621997668042292424e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04959 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1000236832, alloc=4783252, time=52.79 x[1] = 3.1 y1[1] (analytic) = 0.00086484972672053550762394545853374 y1[1] (numeric) = 0.00086484972672053550762394545853374 absolute error = 5.3688e-63 relative error = 6.2077836578132551213849760633907e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0415806624332905791946982715967 y2[1] (numeric) = 1.0415806624332905791946982715967 absolute error = 3e-63 relative error = 2.8802378041385143281647803944122e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04001 Order of pole (three term test) = -25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.11 y1[1] (analytic) = 0.00049900637367212383916916328316572 y1[1] (numeric) = 0.00049900637367212383916916328316572 absolute error = 5.3302e-63 relative error = 1.0681627091805947316993569013734e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0315873984364537731876268727034 y2[1] (numeric) = 1.0315873984364537731876268727034 absolute error = 3e-63 relative error = 2.9081394407754596941264645635299e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0304 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1004237772, alloc=4783252, time=53.00 x[1] = 3.12 y1[1] (analytic) = 0.00023311228707162665641502602440867 y1[1] (numeric) = 0.00023311228707162665641502602440867 absolute error = 5.2232e-63 relative error = 2.2406369332197005481459452108483e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0215909757260960660909981042019 y2[1] (numeric) = 1.0215909757260960660909981042019 absolute error = 3e-63 relative error = 2.9365960264750275201658139150552e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02079 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1008238556, alloc=4783252, time=53.22 x[1] = 3.13 y1[1] (analytic) = 6.7194056106126342172760860792849e-05 y1[1] (numeric) = 6.7194056106126342172760860792849e-05 absolute error = 5.23650e-63 relative error = 7.7931000202301644161278787028134e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0115923939361581691846814831183 y2[1] (numeric) = 1.0115923939361581691846814831183 absolute error = 3e-63 relative error = 2.9656213490562590137750149477089e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01116 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1012239416, alloc=4783252, time=53.43 x[1] = 3.14 y1[1] (analytic) = 1.2682724604547148856936549500161e-06 y1[1] (numeric) = 1.2682724604547148856936549500161e-06 absolute error = 5.158590e-63 relative error = 4.0674146611608092533063174299263e-55 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0015926529164869525405414363244 y2[1] (numeric) = 1.0015926529164869525405414363244 absolute error = 3e-63 relative error = 2.9952296387802484758995449833356e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.001534 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.15 y1[1] (analytic) = 3.5341528658038371805343205274808e-05 y1[1] (numeric) = 3.5341528658038371805343205274808e-05 absolute error = 5.15005e-63 relative error = 1.4572233277828602665114729308335e-56 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.99159275263285129354085848342893 y2[1] (numeric) = 0.99159275263285129354085848342893 absolute error = 3.4e-63 relative error = 3.4288269967407571367411476307534e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.008107 Order of pole (three term test) = -0.8946 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1016240152, alloc=4783252, time=53.65 x[1] = 3.16 y1[1] (analytic) = 0.00016941041740165184008290572604826 y1[1] (numeric) = 0.00016941041740165184008290572604826 absolute error = 5.1058e-63 relative error = 3.0138642465502925927689247350406e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.98159369306694633329262072881263 y2[1] (numeric) = 0.98159369306694633329262072881263 absolute error = 3.4e-63 relative error = 3.4637549365021381688695991947324e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01775 Order of pole (three term test) = -0.901 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1020241036, alloc=4783252, time=53.86 x[1] = 3.17 y1[1] (analytic) = 0.00040346153191414445991164986472299 y1[1] (numeric) = 0.00040346153191414445991164986472299 absolute error = 5.0551e-63 relative error = 1.2529323368245455987418150910258e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.97159647411639614042871472510327 y2[1] (numeric) = 0.97159647411639614042871472510327 absolute error = 3.5e-63 relative error = 3.6023185481225861513406024557822e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02738 Order of pole (three term test) = -0.9124 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1024241824, alloc=4783252, time=54.07 x[1] = 3.18 y1[1] (analytic) = 0.00073747146727910692731584613969177 y1[1] (numeric) = 0.00073747146727910692731584613969177 absolute error = 5.0449e-63 relative error = 6.8408070330003470746599651757221e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.96160209549476478194630475327388 y2[1] (numeric) = 0.96160209549476478194630475327388 absolute error = 3.6e-63 relative error = 3.7437522410428226436002701328752e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.037 Order of pole (three term test) = -0.9285 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1028242540, alloc=4783252, time=54.29 x[1] = 3.19 y1[1] (analytic) = 0.0011714068227813434310491703005194 y1[1] (numeric) = 0.0011714068227813434310491703005194 absolute error = 5.027e-63 relative error = 4.2914211375891460228145769763867e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.95161155663158579989199285154883 y2[1] (numeric) = 0.95161155663158579989199285154883 absolute error = 3.6e-63 relative error = 3.7830562007284781474706478439596e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04661 Order of pole (three term test) = -0.9495 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.2 y1[1] (analytic) = 0.0017052242052469153383392777164173 y1[1] (numeric) = 0.0017052242052469153383392777164173 absolute error = 4.944e-63 relative error = 2.8993254873977771540742858403410e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.9416258565724200908627825853809 y2[1] (numeric) = 0.9416258565724200908627825853809 absolute error = 3.7e-63 relative error = 3.9293738316280340907138817627055e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05619 Order of pole (three term test) = -0.9752 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1032243420, alloc=4783252, time=54.50 x[1] = 3.21 y1[1] (analytic) = 0.00233887023338242242789333479576 y1[1] (numeric) = 0.00233887023338242242789333479576 absolute error = 4.924e-63 relative error = 2.1052899514134309414510535139261e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.93164599387895218245161163932314 y2[1] (numeric) = 0.93164599387895218245161163932314 absolute error = 3.7e-63 relative error = 3.9714655827530314494764980522226e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06576 Order of pole (three term test) = -1.006 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1036244160, alloc=4783252, time=54.71 x[1] = 3.22 y1[1] (analytic) = 0.0030722815431130877456572625241352 y1[1] (numeric) = 0.0030722815431130877456572625241352 absolute error = 4.966e-63 relative error = 1.6163883193361378367853394379746e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.92167296652913489692655585208396 y2[1] (numeric) = 0.92167296652913489692655585208396 absolute error = 3.7e-63 relative error = 4.0144391062413131224476728151400e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0753 Order of pole (three term test) = -1.041 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1040244896, alloc=4783252, time=54.93 x[1] = 3.23 y1[1] (analytic) = 0.0039053847939191122792915054150527 y1[1] (numeric) = 0.0039053847939191122792915054150527 absolute error = 4.917e-63 relative error = 1.2590308662173380032548879859620e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.91170777181739238759412427147028 y2[1] (numeric) = 0.91170777181739238759412427147028 absolute error = 3.8e-63 relative error = 4.1680022014346817814627790012013e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08481 Order of pole (three term test) = -1.081 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.24 y1[1] (analytic) = 0.0048380966761696658211761562575268 y1[1] (numeric) = 0.0048380966761696658211761562575268 absolute error = 4.870e-63 relative error = 1.0065941889891278746191827014864e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.90175140625489152745984504056236 y2[1] (numeric) = 0.90175140625489152745984504056236 absolute error = 3.8e-63 relative error = 4.2140217066940526294358889203876e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09428 Order of pole (three term test) = -1.126 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1044245732, alloc=4783252, time=55.14 TOP MAIN SOLVE Loop x[1] = 3.25 y1[1] (analytic) = 0.0058703239194537806269707748284005 y1[1] (numeric) = 0.0058703239194537806269707748284005 absolute error = 4.826e-63 relative error = 8.2210114232487660928382022073868e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.89180486546989162296416915743917 y2[1] (numeric) = 0.89180486546989162296416915743917 absolute error = 3.9e-63 relative error = 4.3731539835736280460707807075185e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1037 Order of pole (three term test) = -1.176 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1048246576, alloc=4783252, time=55.35 x[1] = 3.26 y1[1] (analytic) = 0.0070019633019073147873054328283443 y1[1] (numeric) = 0.0070019633019073147873054328283443 absolute error = 4.788e-63 relative error = 6.8380821114783085012697317345295e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.88186914410818241773927688966392 y2[1] (numeric) = 0.88186914410818241773927688966392 absolute error = 4.0e-63 relative error = 4.5358203387931486457795502189857e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1131 Order of pole (three term test) = -1.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1052247236, alloc=4783252, time=55.56 x[1] = 3.27 y1[1] (analytic) = 0.0082329016605350526240382595052596 y1[1] (numeric) = 0.0082329016605350526240382595052596 absolute error = 4.697e-63 relative error = 5.7051574203969588714442702979986e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.87194523573362034250344310924638 y2[1] (numeric) = 0.87194523573362034250344310924638 absolute error = 4.1e-63 relative error = 4.7021301705380862065196971229628e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1225 Order of pole (three term test) = -1.289 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1056248312, alloc=4783252, time=55.77 x[1] = 3.28 y1[1] (analytic) = 0.0095630159025269099096415838682884 y1[1] (numeric) = 0.0095630159025269099096415838682884 absolute error = 4.640e-63 relative error = 4.8520258120389999449568935731995e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.86203413272877295738508592941475 y2[1] (numeric) = 0.86203413272877295738508592941475 absolute error = 4.1e-63 relative error = 4.7561921788658546526277401656278e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1318 Order of pole (three term test) = -1.353 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.29 y1[1] (analytic) = 0.010992173017567112298624874460517 y1[1] (numeric) = 0.010992173017567112298624874460517 absolute error = 4.67e-63 relative error = 4.2484775235402971046565494496560e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.85213682619568152214947021625736 y2[1] (numeric) = 0.85213682619568152214947021625736 absolute error = 4.1e-63 relative error = 4.8114338847485641862294803692272e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.141 Order of pole (three term test) = -1.421 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1060249132, alloc=4783252, time=55.98 x[1] = 3.3 y1[1] (analytic) = 0.012520230091135116063408948897147 y1[1] (numeric) = 0.012520230091135116063408948897147 absolute error = 4.65e-63 relative error = 3.7139892527154180390876930606919e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.84225430585675161798834572239752 y2[1] (numeric) = 0.84225430585675161798834572239752 absolute error = 4.2e-63 relative error = 4.9866174275330150442771640522455e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1502 Order of pole (three term test) = -1.494 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1064250024, alloc=4783252, time=56.20 x[1] = 3.31 y1[1] (analytic) = 0.014147034318796941053661929414471 y1[1] (numeric) = 0.014147034318796941053661929414471 absolute error = 4.53e-63 relative error = 3.2020845485481437966188341235648e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.83238755995578173172775000568302 y2[1] (numeric) = 0.83238755995578173172775000568302 absolute error = 4.3e-63 relative error = 5.1658628827038519302295407078664e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1593 Order of pole (three term test) = -1.572 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1068250828, alloc=4783252, time=56.41 x[1] = 3.32 y1[1] (analytic) = 0.015872423021485486757710415268806 y1[1] (numeric) = 0.015872423021485486757710415268806 absolute error = 4.53e-63 relative error = 2.8540065961372299032274637398697e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.82253757515913969951307944769159 y2[1] (numeric) = 0.82253757515913969951307944769159 absolute error = 4.3e-63 relative error = 5.2277247020211343679749267165639e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1684 Order of pole (three term test) = -1.654 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1072251600, alloc=4783252, time=56.63 x[1] = 3.33 y1[1] (analytic) = 0.017696223661768303447153285140733 y1[1] (numeric) = 0.017696223661768303447153285140733 absolute error = 4.46e-63 relative error = 2.5203117259619515956705892620325e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.81270533645709689224470717586405 y2[1] (numeric) = 0.81270533645709689224470717586405 absolute error = 4.4e-63 relative error = 5.4140163754569835139075044768475e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1774 Order of pole (three term test) = -1.741 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.34 y1[1] (analytic) = 0.019618253861101191641120098930087 y1[1] (numeric) = 0.019618253861101191641120098930087 absolute error = 4.42e-63 relative error = 2.2530037745937808491588811062266e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.80289182706533000926338308940728 y2[1] (numeric) = 0.80289182706533000926338308940728 absolute error = 4.4e-63 relative error = 5.4801902967209792224602085855056e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1863 Order of pole (three term test) = -1.832 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1076252596, alloc=4783252, time=56.84 x[1] = 3.35 y1[1] (analytic) = 0.021638321418065904544605624728466 y1[1] (numeric) = 0.021638321418065904544605624728466 absolute error = 4.43e-63 relative error = 2.0472937407711203838787775135399e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.79309802832660033002396588397449 y2[1] (numeric) = 0.79309802832660033002396588397449 absolute error = 4.5e-63 relative error = 5.6739518184086134981130800210702e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1952 Order of pole (three term test) = -1.928 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1080253412, alloc=4783252, time=57.05 x[1] = 3.36 y1[1] (analytic) = 0.023756224327590129705834692221679 y1[1] (numeric) = 0.023756224327590129705834692221679 absolute error = 4.30e-63 relative error = 1.8100519428948324974871314858949e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.78332491961262025575038601809447 y2[1] (numeric) = 0.78332491961262025575038601809447 absolute error = 4.5e-63 relative error = 5.7447425548843727602729431021063e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.204 Order of pole (three term test) = -2.028 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1084254204, alloc=4783252, time=57.26 x[1] = 3.37 y1[1] (analytic) = 0.025971750801147827910508234029151 y1[1] (numeric) = 0.025971750801147827910508234029151 absolute error = 4.28e-63 relative error = 1.6479443502941836127492790336513e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.77357347822611695433589651569143 y2[1] (numeric) = 0.77357347822611695433589651569143 absolute error = 4.5e-63 relative error = 5.8171591020919692142646408306585e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2127 Order of pole (three term test) = -2.132 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.38 y1[1] (analytic) = 0.028284679287937909295874650009428 y1[1] (numeric) = 0.028284679287937909295874650009428 absolute error = 4.20e-63 relative error = 1.4849028186757992509987160536610e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.76384467930310290204250822241037 y2[1] (numeric) = 0.76384467930310290204250822241037 absolute error = 4.5e-63 relative error = 5.8912500432752834758245523190851e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2213 Order of pole (three term test) = -2.241 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1088255184, alloc=4783252, time=57.47 x[1] = 3.39 y1[1] (analytic) = 0.030694778497039128834663925327525 y1[1] (numeric) = 0.030694778497039128834663925327525 absolute error = 4.17e-63 relative error = 1.3585372510188484915627146594934e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.75413949571536309486399862844206 y2[1] (numeric) = 0.75413949571536309486399862844206 absolute error = 4.5e-63 relative error = 5.9670658088678691144681818294129e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2298 Order of pole (three term test) = -2.354 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1092256136, alloc=4783252, time=57.68 x[1] = 3.4 y1[1] (analytic) = 0.033201807420538985717798460234306 y1[1] (numeric) = 0.033201807420538985717798460234306 absolute error = 4.16e-63 relative error = 1.2529438374570477273856513394572e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.74445889797316868075009757063626 y2[1] (numeric) = 0.74445889797316868075009757063626 absolute error = 4.5e-63 relative error = 6.0446587612177162384846023855965e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2382 Order of pole (three term test) = -2.472 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1096256996, alloc=4783252, time=57.90 x[1] = 3.41 y1[1] (analytic) = 0.035805515357634313765216359047038 y1[1] (numeric) = 0.035805515357634313765216359047038 absolute error = 4.13e-63 relative error = 1.1534535835467083545158700465553e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.73480385412822674124755569242589 y2[1] (numeric) = 0.73480385412822674124755569242589 absolute error = 4.6e-63 relative error = 6.2601740235255737857367261824398e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2465 Order of pole (three term test) = -2.593 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1100257988, alloc=4783252, time=58.11 x[1] = 3.42 y1[1] (analytic) = 0.038505641939701152825849854398592 y1[1] (numeric) = 0.038505641939701152825849854398592 absolute error = 4.11e-63 relative error = 1.0673760500957637668285725312611e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.7251753296768759274990566423338 y2[1] (numeric) = 0.7251753296768759274990566423338 absolute error = 4.6e-63 relative error = 6.3432935619164965923419833910518e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2548 Order of pole (three term test) = -2.719 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.43 y1[1] (analytic) = 0.041301917156331394200510358774443 y1[1] (numeric) = 0.041301917156331394200510358774443 absolute error = 4.06e-63 relative error = 9.8300521610959181529548679749134e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.71557428746353763095570308540863 y2[1] (numeric) = 0.71557428746353763095570308540863 absolute error = 4.7e-63 relative error = 6.5681510394397595611465216209394e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2629 Order of pole (three term test) = -2.849 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1104258924, alloc=4783252, time=58.32 x[1] = 3.44 y1[1] (analytic) = 0.044194061382333596444834987027515 y1[1] (numeric) = 0.044194061382333596444834987027515 absolute error = 3.98e-63 relative error = 9.0057348781956244163843410476124e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.70600168758443234360554818943968 y2[1] (numeric) = 0.70600168758443234360554818943968 absolute error = 4.7e-63 relative error = 6.6572078830022857935007229792542e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2709 Order of pole (three term test) = -2.982 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1108260400, alloc=4783252, time=58.54 x[1] = 3.45 y1[1] (analytic) = 0.047181785405695271493214860052253 y1[1] (numeric) = 0.047181785405695271493214860052253 absolute error = 3.94e-63 relative error = 8.3506801748210361121982312495271e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.69645848729157083600191363378011 y2[1] (numeric) = 0.69645848729157083600191363378011 absolute error = 4.8e-63 relative error = 6.8920116382909271732208727705618e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2789 Order of pole (three term test) = -3.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1112261816, alloc=4783252, time=58.75 x[1] = 3.46 y1[1] (analytic) = 0.05026479045650384489839462421797 y1[1] (numeric) = 0.05026479045650384489839462421797 absolute error = 3.92e-63 relative error = 7.7986995755848907065565989540712e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.68694564089702975389368422402507 y2[1] (numeric) = 0.68694564089702975389368422402507 absolute error = 4.9e-63 relative error = 7.1330243738084790835049611581477e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2867 Order of pole (three term test) = -3.262 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.47 y1[1] (analytic) = 0.053442768236823398114819946473319 y1[1] (numeric) = 0.053442768236823398114819946473319 absolute error = 3.83e-63 relative error = 7.1665449346260372561412180584218e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.67746409967752120581814601284274 y2[1] (numeric) = 0.67746409967752120581814601284274 absolute error = 5.0e-63 relative error = 7.3804648871874442015772053823607e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2944 Order of pole (three term test) = -3.408 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1116262624, alloc=4783252, time=58.96 TOP MAIN SOLVE Loop x[1] = 3.48 y1[1] (analytic) = 0.056715400951524205176401852617717 y1[1] (numeric) = 0.056715400951524205176401852617717 absolute error = 3.83e-63 relative error = 6.7530158224105267182662535914491e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.66801481177926588461808356455725 y2[1] (numeric) = 0.66801481177926588461808356455725 absolute error = 5.0e-63 relative error = 7.4848639758187949108774187845967e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3019 Order of pole (three term test) = -3.557 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1120263504, alloc=4783252, time=59.18 x[1] = 3.49 y1[1] (analytic) = 0.060082361340061980840721327233228 y1[1] (numeric) = 0.060082361340061980840721327233228 absolute error = 3.72e-63 relative error = 6.1915009946847113310047961536147e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.6585987221231792354917125192625 y2[1] (numeric) = 0.6585987221231792354917125192625 absolute error = 5.0e-63 relative error = 7.5918762549084303977326787909048e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3094 Order of pole (three term test) = -3.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1124264504, alloc=4783252, time=59.39 x[1] = 3.5 y1[1] (analytic) = 0.06354331270920366230134237332824 y1[1] (numeric) = 0.06354331270920366230134237332824 absolute error = 3.74e-63 relative error = 5.8857491694138500943201307489801e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.64921677231038015187963119995636 y2[1] (numeric) = 0.64921677231038015187963119995636 absolute error = 5.0e-63 relative error = 7.7015878413097744124514873526199e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3167 Order of pole (three term test) = -3.867 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1128265372, alloc=4783252, time=59.61 x[1] = 3.51 y1[1] (analytic) = 0.067097908966696451917333694242418 y1[1] (numeric) = 0.067097908966696451917333694242418 absolute error = 3.62e-63 relative error = 5.3951010631296424999888171373410e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.63986990052803164824046007658263 y2[1] (numeric) = 0.63986990052803164824046007658263 absolute error = 5.0e-63 relative error = 7.8140884512209653800015436432356e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3239 Order of pole (three term test) = -4.028 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.52 y1[1] (analytic) = 0.070745794655876754083783487727762 y1[1] (numeric) = 0.070745794655876754083783487727762 absolute error = 3.55e-63 relative error = 5.0179661098839695791225696586931e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.63055904145552292556942567856704 y2[1] (numeric) = 0.63055904145552292556942567856704 absolute error = 5.1e-63 relative error = 8.0880610136485265063050751704621e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.331 Order of pole (three term test) = -4.192 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1132266088, alloc=4783252, time=59.82 x[1] = 3.53 y1[1] (analytic) = 0.074486604991215545378460985315985 y1[1] (numeric) = 0.074486604991215545378460985315985 absolute error = 3.55e-63 relative error = 4.7659575844793347492349585692401e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.62128512617100221137515574599336 y2[1] (numeric) = 0.62128512617100221137515574599336 absolute error = 5.1e-63 relative error = 8.2087913989369810183809517680610e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3379 Order of pole (three term test) = -4.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1136267724, alloc=4783252, time=60.03 x[1] = 3.54 y1[1] (analytic) = 0.078319965894796623477231113870234 y1[1] (numeric) = 0.078319965894796623477231113870234 absolute error = 3.53e-63 relative error = 4.5071521159006583467425334421966e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.61204908205826972075279889951549 y2[1] (numeric) = 0.61204908205826972075279889951549 absolute error = 5.2e-63 relative error = 8.4960506476258998804628589761641e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3447 Order of pole (three term test) = -4.531 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1140268656, alloc=4783252, time=60.25 x[1] = 3.55 y1[1] (analytic) = 0.082245494033724087043729177289527 y1[1] (numeric) = 0.082245494033724087043729177289527 absolute error = 3.49e-63 relative error = 4.2433935633834897521273939675432e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.60285183271404004917977257656305 y2[1] (numeric) = 0.60285183271404004917977257656305 absolute error = 5.2e-63 relative error = 8.6256683944869015764924520236139e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3514 Order of pole (three term test) = -4.705 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1144269628, alloc=4783252, time=60.46 x[1] = 3.56 y1[1] (analytic) = 0.086262796858455305876479386896339 y1[1] (numeric) = 0.086262796858455305876479386896339 absolute error = 3.36e-63 relative error = 3.8950742641851399197325209670881e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.59369429785558327071757857731409 y2[1] (numeric) = 0.59369429785558327071757857731409 absolute error = 5.2e-63 relative error = 8.7587164282735037810376135497297e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3579 Order of pole (three term test) = -4.883 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.57 y1[1] (analytic) = 0.090371472642055548048386563963263 y1[1] (numeric) = 0.090371472642055548048386563963263 absolute error = 3.36e-63 relative error = 3.7179874375936416983315037858228e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.58457739322875397743290054393371 y2[1] (numeric) = 0.58457739322875397743290054393371 absolute error = 5.2e-63 relative error = 8.8953149065159988741068120332325e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3643 Order of pole (three term test) = -5.064 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1148270364, alloc=4783252, time=60.67 x[1] = 3.58 y1[1] (analytic) = 0.094571110520370338608599145450982 y1[1] (numeric) = 0.094571110520370338608599145450982 absolute error = 3.29e-63 relative error = 3.4788636634348749579574821997224e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.57550203051641745705739905165624 y2[1] (numeric) = 0.57550203051641745705739905165624 absolute error = 5.3e-63 relative error = 9.2093506520630875187558948249018e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3705 Order of pole (three term test) = -5.249 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1152271300, alloc=4783252, time=60.88 x[1] = 3.59 y1[1] (analytic) = 0.098861290533111532644350160652166 y1[1] (numeric) = 0.098861290533111532644350160652166 absolute error = 3.21e-63 relative error = 3.2469735957218536186305682785992e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.56646911724728216619212706795597 y2[1] (numeric) = 0.56646911724728216619212706795597 absolute error = 5.4e-63 relative error = 9.5327350345962896171609795562906e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3766 Order of pole (three term test) = -5.436 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1156272132, alloc=4783252, time=61.10 x[1] = 3.6 y1[1] (analytic) = 0.10324158366585299412970827473406 y1[1] (numeric) = 0.10324158366585299412970827473406 absolute error = 3.2e-63 relative error = 3.0995262629416594419772758537806e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.55747955670514761573327265250731 y2[1] (numeric) = 0.55747955670514761573327265250731 absolute error = 5.4e-63 relative error = 9.6864538529725387107577483208285e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3826 Order of pole (three term test) = -5.626 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.61 y1[1] (analytic) = 0.10771155189293168102835030646159 y1[1] (numeric) = 0.10771155189293168102835030646159 absolute error = 3.1e-63 relative error = 2.8780571308465478141481901564330e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.54853424783857674365505981360747 y2[1] (numeric) = 0.54853424783857674365505981360747 absolute error = 5.4e-63 relative error = 9.8444172287837128555890989011514e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3883 Order of pole (three term test) = -5.819 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1160272868, alloc=4783252, time=61.31 x[1] = 3.62 y1[1] (analytic) = 0.112270748221249846577595727932 y1[1] (numeric) = 0.112270748221249846577595727932 absolute error = 3.1e-63 relative error = 2.7611822750934984886961538515729e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.53963408517100180783725645920515 y2[1] (numeric) = 0.53963408517100180783725645920515 absolute error = 5.4e-63 relative error = 1.0006780795339905916739371739795e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.394 Order of pole (three term test) = -6.015 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1164273596, alloc=4783252, time=61.52 x[1] = 3.63 y1[1] (analytic) = 0.11691871673497397657007645560199 y1[1] (numeric) = 0.11691871673497397657007645560199 absolute error = 3.1e-63 relative error = 2.6514146635965384802912185551979e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.53077995871127278827309518546809 y2[1] (numeric) = 0.53077995871127278827309518546809 absolute error = 5.5e-63 relative error = 1.0362109400953895011221714304471e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3994 Order of pole (three term test) = -6.214 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1168274432, alloc=4783252, time=61.73 x[1] = 3.64 y1[1] (analytic) = 0.12165499264112599277656275586591 y1[1] (numeric) = 0.12165499264112599277656275586591 absolute error = 3.1e-63 relative error = 2.5481897065620566116792258247819e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.52197275386465724374284336112709 y2[1] (numeric) = 0.52197275386465724374284336112709 absolute error = 5.5e-63 relative error = 1.0536948450428314206263232798160e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4048 Order of pole (three term test) = -6.416 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1172275508, alloc=4783252, time=61.95 x[1] = 3.65 y1[1] (analytic) = 0.12647910231606216342759552547173 y1[1] (numeric) = 0.12647910231606216342759552547173 absolute error = 3.0e-63 relative error = 2.3719333431883602086757183946347e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.51321335134430052289318861170468 y2[1] (numeric) = 0.51321335134430052289318861170468 absolute error = 5.5e-63 relative error = 1.0716790562040938420077298870891e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4099 Order of pole (three term test) = -6.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.66 y1[1] (analytic) = 0.13139056335283507290160907984007 y1[1] (numeric) = 0.13139056335283507290160907984007 absolute error = 3.0e-63 relative error = 2.2832689985077742338125571840425e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.50450262708315518362754885358965 y2[1] (numeric) = 0.50450262708315518362754885358965 absolute error = 5.6e-63 relative error = 1.1100041306775938803707496793502e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4149 Order of pole (three term test) = -6.827 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1176276456, alloc=4783252, time=62.16 x[1] = 3.67 y1[1] (analytic) = 0.13638888460943391446204381352019 y1[1] (numeric) = 0.13638888460943391446204381352019 absolute error = 2.9e-63 relative error = 2.1262729791393933182135862525947e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.49584145214638842779197594108609 y2[1] (numeric) = 0.49584145214638842779197594108609 absolute error = 5.6e-63 relative error = 1.1293932719337670351989456019436e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4197 Order of pole (three term test) = -7.036 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1180277540, alloc=4783252, time=62.37 x[1] = 3.68 y1[1] (analytic) = 0.14147356625789828205437513146384 y1[1] (numeric) = 0.14147356625789828205437513146384 absolute error = 2.9e-63 relative error = 2.0498528995257422064849305436989e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.48723069264427631034019077495596 y2[1] (numeric) = 0.48723069264427631034019077495596 absolute error = 5.7e-63 relative error = 1.1698770389577098681390520111541e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4244 Order of pole (three term test) = -7.248 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1184278272, alloc=4783252, time=62.58 x[1] = 3.69 y1[1] (analytic) = 0.14664409983430054982480697162784 y1[1] (numeric) = 0.14664409983430054982480697162784 absolute error = 2.8e-63 relative error = 1.9093846961206348862321581402887e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.47867120964559343348424545187534 y2[1] (numeric) = 0.47867120964559343348424545187534 absolute error = 5.7e-63 relative error = 1.1907964977087844873142796446173e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4288 Order of pole (three term test) = -7.461 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.7 y1[1] (analytic) = 0.1518999682895918411643298936456 y1[1] (numeric) = 0.1518999682895918411643298936456 absolute error = 2.8e-63 relative error = 1.8433183571585087042181577414427e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.47016385909150678678922237429879 y2[1] (numeric) = 0.47016385909150678678922237429879 absolute error = 5.7e-63 relative error = 1.2123432904889917559611478896054e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4331 Order of pole (three term test) = -7.677 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1188279124, alloc=4783252, time=62.79 x[1] = 3.71 y1[1] (analytic) = 0.15724064604130650272361082739025 y1[1] (numeric) = 0.15724064604130650272361082739025 absolute error = 2.7e-63 relative error = 1.7171132706302418524149514062617e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.46170949170998234375620595674963 y2[1] (numeric) = 0.46170949170998234375620595674963 absolute error = 5.7e-63 relative error = 1.2345425212918064256698320259111e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4373 Order of pole (three term test) = -7.896 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1192280064, alloc=4783252, time=63.01 x[1] = 3.72 y1[1] (analytic) = 0.16266559902611991299439991051033 y1[1] (numeric) = 0.16266559902611991299439991051033 absolute error = 2.6e-63 relative error = 1.5983711464293730890359032565180e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.45330895293071297416254103294378 y2[1] (numeric) = 0.45330895293071297416254103294378 absolute error = 5.8e-63 relative error = 1.2794805755549491732562419375244e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4412 Order of pole (three term test) = -8.116 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1196280996, alloc=4783252, time=63.22 x[1] = 3.73 y1[1] (analytic) = 0.16817428475325436972039430207837 y1[1] (numeric) = 0.16817428475325436972039430207837 absolute error = 2.5e-63 relative error = 1.4865530741920530551719222822849e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.44496308280057617929725076783427 y2[1] (numeric) = 0.44496308280057617929725076783427 absolute error = 5.8e-63 relative error = 1.3034789231266287928327246643968e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.445 Order of pole (three term test) = -8.338 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1200282336, alloc=4783252, time=63.43 x[1] = 3.74 y1[1] (analytic) = 0.17376615235872771559332264379747 y1[1] (numeric) = 0.17376615235872771559332264379747 absolute error = 2.4e-63 relative error = 1.3811665663433536400217658304970e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.43667271589963010424763888032052 y2[1] (numeric) = 0.43667271589963010424763888032052 absolute error = 5.9e-63 relative error = 1.3511263207376858598161483571860e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4486 Order of pole (three term test) = -8.562 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.75 y1[1] (analytic) = 0.17944064266043927741688759770929 y1[1] (numeric) = 0.17944064266043927741688759770929 absolute error = 2.4e-63 relative error = 1.3374896369166429455942148381823e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.42843868125765622756584442664971 y2[1] (numeric) = 0.42843868125765622756584442664971 absolute error = 5.9e-63 relative error = 1.3770932126578537333795223913967e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.452 Order of pole (three term test) = -8.788 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1204283136, alloc=4783252, time=63.64 x[1] = 3.76 y1[1] (analytic) = 0.18519718821408761019055486243691 y1[1] (numeric) = 0.18519718821408761019055486243691 absolute error = 2.4e-63 relative error = 1.2959160034468797647962271081071e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.42026180227125707397683496224605 y2[1] (numeric) = 0.42026180227125707397683496224605 absolute error = 6.0e-63 relative error = 1.4276814993829282012799402273599e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4553 Order of pole (three term test) = -9.015 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1208284552, alloc=4783252, time=63.86 x[1] = 3.77 y1[1] (analytic) = 0.19103521336991445438537825380378 y1[1] (numeric) = 0.19103521336991445438537825380378 absolute error = 2.3e-63 relative error = 1.2039665145641781950782365028585e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.41214289662151724028748227352559 y2[1] (numeric) = 0.41214289662151724028748227352559 absolute error = 6.0e-63 relative error = 1.4558057530978081590905559978410e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.53 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = -9.244 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1212285776, alloc=4783252, time=64.07 x[1] = 3.78 y1[1] (analytic) = 0.19695413433026923206341974076229 y1[1] (numeric) = 0.19695413433026923206341974076229 absolute error = 2.2e-63 relative error = 1.1170113323495181119619826231527e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.40408277619223596832551418909979 y2[1] (numeric) = 0.40408277619223596832551418909979 absolute error = 6.0e-63 relative error = 1.4848442827826928250133220934105e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4612 Order of pole (three term test) = -9.474 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.79 y1[1] (analytic) = 0.20295335920798832543912274815984 y1[1] (numeric) = 0.20295335920798832543912274815984 absolute error = 2.2e-63 relative error = 1.0839928979669764044848685257565e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.39608224698873944158290927976732 y2[1] (numeric) = 0.39608224698873944158290927976732 absolute error = 6.1e-63 relative error = 1.5400841735210167291420417796466e-60 % Correct digits = 64 h = 0.01 bytes used=1216288144, alloc=4783252, time=64.28 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.4 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4639 Order of pole (three term test) = -9.706 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.8 y1[1] (analytic) = 0.20903228808558330000343182564927 y1[1] (numeric) = 0.20903228808558330000343182564927 absolute error = 2.1e-63 relative error = 1.0046294853454433477922205257451e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.38814210905728092426641391388112 y2[1] (numeric) = 0.38814210905728092426641391388112 absolute error = 6.1e-63 relative error = 1.5715893374248087835918516791368e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.47 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.7 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4664 Order of pole (three term test) = -9.939 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1220288920, alloc=4783252, time=64.49 x[1] = 3.81 y1[1] (analytic) = 0.21519031307523215343766962563504 y1[1] (numeric) = 0.21519031307523215343766962563504 absolute error = 2.0e-63 relative error = 9.2940986581528181693058265395836e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.38026315640503680267411028948219 y2[1] (numeric) = 0.38026315640503680267411028948219 absolute error = 6.1e-63 relative error = 1.6041522554192952089802409313263e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4688 Order of pole (three term test) = -10.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1224289796, alloc=4783252, time=64.71 x[1] = 3.82 y1[1] (analytic) = 0.2214268183795675912422723433438 y1[1] (numeric) = 0.2214268183795675912422723433438 absolute error = 1.9e-63 relative error = 8.5807130947572908692656681994085e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.37244617692070652922722804311009 y2[1] (numeric) = 0.37244617692070652922722804311009 absolute error = 6.2e-63 relative error = 1.6646700608555245468844107654675e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.12 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.31 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4709 Order of pole (three term test) = -10.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1228290688, alloc=4783252, time=64.92 x[1] = 3.83 y1[1] (analytic) = 0.22774118035325625030347747297652 y1[1] (numeric) = 0.22774118035325625030347747297652 absolute error = 1.8e-63 relative error = 7.9037089261062291030264653647063e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.36469195229572440909662976137772 y2[1] (numeric) = 0.36469195229572440909662976137772 absolute error = 6.2e-63 relative error = 1.7000649345210922060952127629309e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.45 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4728 Order of pole (three term test) = -10.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.84 y1[1] (analytic) = 0.23413276756536271252692305975232 y1[1] (numeric) = 0.23413276756536271252692305975232 absolute error = 1.8e-63 relative error = 7.6879456844821817446060488830067e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.35700125794609110817965112113726 y2[1] (numeric) = 0.35700125794609110817965112113726 absolute error = 6.2e-63 relative error = 1.7366885583737157464554544825618e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4746 Order of pole (three term test) = -10.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1232291860, alloc=4783252, time=65.13 x[1] = 3.85 y1[1] (analytic) = 0.24060094086249207218876492604721 y1[1] (numeric) = 0.24060094086249207218876492604721 absolute error = 1.7e-63 relative error = 7.0656415303528747441425327341401e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.349374862934832699211357781338 y2[1] (numeric) = 0.349374862934832699211357781338 absolute error = 6.2e-63 relative error = 1.7745981917297976132285060678790e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4762 Order of pole (three term test) = -11.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1236292556, alloc=4783252, time=65.34 x[1] = 3.86 y1[1] (analytic) = 0.24714505343270474280019539063516 y1[1] (numeric) = 0.24714505343270474280019539063516 absolute error = 1.7e-63 relative error = 6.8785515889877759513526216123046e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.3418135298950950000409906547043 y2[1] (numeric) = 0.3418135298950950000409906547043 absolute error = 6.2e-63 relative error = 1.8138544726134228898872436263505e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4775 Order of pole (three term test) = -11.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1240293240, alloc=4783252, time=65.55 x[1] = 3.87 y1[1] (analytic) = 0.25376445087019711205793919067272 y1[1] (numeric) = 0.25376445087019711205793919067272 absolute error = 1.6e-63 relative error = 6.3050596508429581073448997136456e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.33431801495388089457568407689649 y2[1] (numeric) = 0.33431801495388089457568407689649 absolute error = 6.2e-63 relative error = 1.8545216598200036571194528651561e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4787 Order of pole (three term test) = -11.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1244294464, alloc=4783252, time=65.77 x[1] = 3.88 y1[1] (analytic) = 0.26045847124074157686913192295872 y1[1] (numeric) = 0.26045847124074157686913192295872 absolute error = 1.5e-63 relative error = 5.7590754981186658477870392882790e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.32688906765643826259581048063146 y2[1] (numeric) = 0.32688906765643826259581048063146 absolute error = 6.2e-63 relative error = 1.8966678954574966619627831907867e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4797 Order of pole (three term test) = -11.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.89 y1[1] (analytic) = 0.26722644514787941450161169736831 y1[1] (numeric) = 0.26722644514787941450161169736831 absolute error = 1.4e-63 relative error = 5.2390024468770648263621836287303e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.31952743089130607958596019184132 y2[1] (numeric) = 0.31952743089130607958596019184132 absolute error = 6.3e-63 relative error = 1.9716617075493203609294366295355e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.64 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4805 Order of pole (three term test) = -12.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1248295228, alloc=4783252, time=65.97 x[1] = 3.9 y1[1] (analytic) = 0.27406769579985987062766951538565 y1[1] (numeric) = 0.27406769579985987062766951538565 absolute error = 1.3e-63 relative error = 4.7433536309559642861311179178766e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.31223384081602618190911187462131 y2[1] (numeric) = 0.31223384081602618190911187462131 absolute error = 6.2e-63 relative error = 1.9856912318652711237532159234692e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4811 Order of pole (three term test) = -12.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1252296800, alloc=4783252, time=66.19 x[1] = 3.91 y1[1] (analytic) = 0.28098153907731877040823638612561 y1[1] (numeric) = 0.28098153907731877040823638612561 absolute error = 1.3e-63 relative error = 4.6266384769224073537476207867193e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.30500902678352812608556955192351 y2[1] (numeric) = 0.30500902678352812608556955192351 absolute error = 6.3e-63 relative error = 2.0655126395558299055804405298047e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4815 Order of pole (three term test) = -12.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1256297808, alloc=4783252, time=66.40 x[1] = 3.92 y1[1] (analytic) = 0.28796728360168988481279741570741 y1[1] (numeric) = 0.28796728360168988481279741570741 absolute error = 1.2e-63 relative error = 4.1671400479639695199046763986486e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.29785371126919450362939256217935 y2[1] (numeric) = 0.29785371126919450362939256217935 absolute error = 6.3e-63 relative error = 2.1151322819362758090788394764300e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -12.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.93 y1[1] (analytic) = 0.29502423080434221109541016047305 y1[1] (numeric) = 0.29502423080434221109541016047305 absolute error = 1.2e-63 relative error = 4.0674625156325912845476529544472e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.29076860979861400485005610714845 y2[1] (numeric) = 0.29076860979861400485005610714845 absolute error = 6.3e-63 relative error = 2.1666712938385517428187768975970e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -13.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1260298572, alloc=4783252, time=66.61 x[1] = 3.94 y1[1] (analytic) = 0.30215167499643625375639385056441 y1[1] (numeric) = 0.30215167499643625375639385056441 absolute error = 1.1e-63 relative error = 3.6405556911540338694762793465040e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.28375443087602945625275664545921 y2[1] (numeric) = 0.28375443087602945625275664545921 absolute error = 6.3e-63 relative error = 2.2202296473574471745488023440413e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4816 Order of pole (three term test) = -13.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1264299236, alloc=4783252, time=66.82 x[1] = 3.95 y1[1] (analytic) = 0.30934890343949232041980668835977 y1[1] (numeric) = 0.30934890343949232041980668835977 absolute error = 1.1e-63 relative error = 3.5558555009235924616210980524441e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.27681187591348798667399566455718 y2[1] (numeric) = 0.27681187591348798667399566455718 absolute error = 6.2e-63 relative error = 2.2397882964882929912776710228231e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4813 Order of pole (three term test) = -13.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1268300464, alloc=4783252, time=67.04 x[1] = 3.96 y1[1] (analytic) = 0.31661519641666377585593019124849 y1[1] (numeric) = 0.31661519641666377585593019124849 absolute error = 1.0e-63 relative error = 3.1584080970137824863096410435952e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.26994163916070040707678694126831 y2[1] (numeric) = 0.26994163916070040707678694126831 absolute error = 6.2e-63 relative error = 2.2967927509357104776029681191328e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4807 Order of pole (three term test) = -13.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1272301948, alloc=4783252, time=67.25 x[1] = 3.97 y1[1] (analytic) = 0.32394982730470812688275251068066 y1[1] (numeric) = 0.32394982730470812688275251068066 absolute error = 1.0e-63 relative error = 3.0868977715471882692294612148878e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.26314440763561681800905744824866 y2[1] (numeric) = 0.26314440763561681800905744824866 absolute error = 6.2e-63 relative error = 2.3561207535085859674371487207997e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.48 Order of pole (three term test) = -14.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.98 y1[1] (analytic) = 0.33135206264664874109793628332516 y1[1] (numeric) = 0.33135206264664874109793628332516 absolute error = 9e-64 relative error = 2.7161442509556760792969350636038e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.2564208610557253871066425986234 y2[1] (numeric) = 0.2564208610557253871066425986234 absolute error = 6.2e-63 relative error = 2.4179000002081015807183188564578e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.09 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4791 Order of pole (three term test) = -14.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1276302688, alloc=4783252, time=67.46 x[1] = 3.99 y1[1] (analytic) = 0.33882116222511993332994904798987 y1[1] (numeric) = 0.33882116222511993332994904798987 absolute error = 9e-64 relative error = 2.6562685579893649007643574426834e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.24977167177008116670587470137992 y2[1] (numeric) = 0.24977167177008116670587470137992 absolute error = 6.3e-63 relative error = 2.5223036525131845736266770448164e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.478 Order of pole (three term test) = -14.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1280303404, alloc=4783252, time=67.67 x[1] = 4 y1[1] (analytic) = 0.34635637913638808536083181690225 y1[1] (numeric) = 0.34635637913638808536083181690225 absolute error = 8e-64 relative error = 2.3097596816167670449651070417293e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.24319750469207174862736090548817 y2[1] (numeric) = 0.24319750469207174862736090548817 absolute error = 6.3e-63 relative error = 2.5904871055222551095120701455973e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.41 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4766 Order of pole (three term test) = -14.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1284304068, alloc=4783252, time=67.88 x[1] = 4.01 y1[1] (analytic) = 0.35395695986504139687031758531497 y1[1] (numeric) = 0.35395695986504139687031758531497 absolute error = 8e-64 relative error = 2.2601618013247381250925351112688e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.2366990172329264795094438207023 y2[1] (numeric) = 0.2366990172329264795094438207023 absolute error = 6.3e-63 relative error = 2.6616080090439962267322895112772e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4751 Order of pole (three term test) = -14.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.02 y1[1] (analytic) = 0.36162214435934079868844661923465 y1[1] (numeric) = 0.36162214435934079868844661923465 absolute error = 7e-64 relative error = 1.9357221644712555306899856487553e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.23027685923597588571440266645551 y2[1] (numeric) = 0.23027685923597588571440266645551 absolute error = 6.3e-63 relative error = 2.7358372095669777713183614170062e-60 % Correct digits = 64 h = 0.01 bytes used=1288305132, alloc=4783252, time=68.10 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.76 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4734 Order of pole (three term test) = -15.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.03 y1[1] (analytic) = 0.36935116610722449332814547814755 y1[1] (numeric) = 0.36935116610722449332814547814755 absolute error = 6e-64 relative error = 1.6244703010517015534292677729658e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.2239316729116678818101206987675 y2[1] (numeric) = 0.2239316729116678818101206987675 absolute error = 6.4e-63 relative error = 2.8580146420486685112643648753713e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4716 Order of pole (three term test) = -15.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1292306164, alloc=4783252, time=68.31 x[1] = 4.04 y1[1] (analytic) = 0.37714325221295852240705342082732 y1[1] (numeric) = 0.37714325221295852240705342082732 absolute error = 5e-64 relative error = 1.3257561869824172841045958422601e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.21766409277334726095221776933351 y2[1] (numeric) = 0.21766409277334726095221776933351 absolute error = 6.4e-63 relative error = 2.9403104198101678180824661177740e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4695 Order of pole (three term test) = -15.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1296307420, alloc=4783252, time=68.51 x[1] = 4.05 y1[1] (analytic) = 0.38499762347442569596572927151763 y1[1] (numeric) = 0.38499762347442569596572927151763 absolute error = 4e-64 relative error = 1.0389674522927824501406234962001e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.21147474557380488916409289058062 y2[1] (numeric) = 0.21147474557380488916409289058062 absolute error = 6.3e-63 relative error = 2.9790791249829374797359501611379e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.82 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4672 Order of pole (three term test) = -15.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1300308544, alloc=4783252, time=68.73 x[1] = 4.06 y1[1] (analytic) = 0.39291349446104515485371415221066 y1[1] (numeric) = 0.39291349446104515485371415221066 absolute error = 4e-64 relative error = 1.0180357906736578796202913743453e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.20536425024260294854257330725366 y2[1] (numeric) = 0.20536425024260294854257330725366 absolute error = 6.4e-63 relative error = 3.1164138804292801874174990785338e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4648 Order of pole (three term test) = -16.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.07 y1[1] (analytic) = 0.40089007359231477429214422696039 y1[1] (numeric) = 0.40089007359231477429214422696039 absolute error = 3e-64 relative error = 7.4833481735216284980222168406078e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.19933321782418249681262071972431 y2[1] (numeric) = 0.19933321782418249681262071972431 absolute error = 6.3e-63 relative error = 3.1605369485164169427075376873284e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.22 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4621 Order of pole (three term test) = -16.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1304309296, alloc=4783252, time=68.94 x[1] = 4.08 y1[1] (analytic) = 0.40892656321696855443800898175208 y1[1] (numeric) = 0.40892656321696855443800898175208 absolute error = 3e-64 relative error = 7.3362805693017741425786040038751e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.19338225141675953242356232661989 y2[1] (numeric) = 0.19338225141675953242356232661989 absolute error = 6.3e-63 relative error = 3.2577963871269773406960201406051e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4593 Order of pole (three term test) = -16.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1308310072, alloc=4783252, time=69.15 x[1] = 4.09 y1[1] (analytic) = 0.41702215969274108227696288635572 y1[1] (numeric) = 0.41702215969274108227696288635572 absolute error = 2e-64 relative error = 4.7959082113851829037795929101827e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.18751194611201567552941728764728 y2[1] (numeric) = 0.18751194611201567552941728764728 absolute error = 6.3e-63 relative error = 3.3597859393110415929118237722911e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4563 Order of pole (three term test) = -16.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1312310976, alloc=4783252, time=69.36 x[1] = 4.1 y1[1] (analytic) = 0.42517605346673108846497132034021 y1[1] (numeric) = 0.42517605346673108846497132034021 absolute error = 1e-64 relative error = 2.3519668895892966332899622621527e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.18172288893558949573496297564155 y2[1] (numeric) = 0.18172288893558949573496297564155 absolute error = 6.3e-63 relative error = 3.4668169964175477693063492237949e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4531 Order of pole (three term test) = -17.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1316311648, alloc=4783252, time=69.58 x[1] = 4.11 y1[1] (analytic) = 0.43338742915635606283007600612553 y1[1] (numeric) = 0.43338742915635606283007600612553 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.17601565878837443742517601630396 y2[1] (numeric) = 0.17601565878837443742517601630396 absolute error = 6.3e-63 relative error = 3.5792270093279367231300107190303e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4498 Order of pole (three term test) = -17.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.12 y1[1] (analytic) = 0.4416554656308898331401917272407 y1[1] (numeric) = 0.4416554656308898331401917272407 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.17039082638862921283659693902778 y2[1] (numeric) = 0.17039082638862921283659693902778 absolute error = 6.3e-63 relative error = 3.6973821499233138615057719394618e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4462 Order of pole (three term test) = -17.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1320312560, alloc=4783252, time=69.79 x[1] = 4.13 y1[1] (analytic) = 0.44997933609357495344700530792948 y1[1] (numeric) = 0.44997933609357495344700530792948 absolute error = 1e-64 relative error = 2.2223242708906217635897397192983e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.16484895421490645178307012404365 y2[1] (numeric) = 0.16484895421490645178307012404365 absolute error = 6.2e-63 relative error = 3.7610187031683125839690441984854e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4425 Order of pole (three term test) = -17.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1324314164, alloc=4783252, time=70.00 x[1] = 4.14 y1[1] (analytic) = 0.45835820816430169083556922640269 y1[1] (numeric) = 0.45835820816430169083556922640269 absolute error = 2e-64 relative error = 4.3633995516517205597253265131229e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.15939059644980531512332717185912 y2[1] (numeric) = 0.15939059644980531512332717185912 absolute error = 6.2e-63 relative error = 3.8898154207939617019701373828031e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4386 Order of pole (three term test) = -17.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1328314964, alloc=4783252, time=70.21 x[1] = 4.15 y1[1] (analytic) = 0.46679124396284534274981382833728 y1[1] (numeric) = 0.46679124396284534274981382833728 absolute error = 3e-64 relative error = 6.4268557707538910549032104267013e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.15401629892455369666219427078778 y2[1] (numeric) = 0.15401629892455369666219427078778 absolute error = 6.2e-63 relative error = 4.0255479733590580143659768591490e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4345 Order of pole (three term test) = -18.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.16 y1[1] (analytic) = 0.47527760019265356123160978929078 y1[1] (numeric) = 0.47527760019265356123160978929078 absolute error = 3e-64 relative error = 6.3121005466783020088269131955044e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.14872659906442555521905209735327 y2[1] (numeric) = 0.14872659906442555521905209735327 absolute error = 6.2e-63 relative error = 4.1687230387849298138783288265344e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4303 Order of pole (three term test) = -18.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1332315656, alloc=4783252, time=70.42 x[1] = 4.17 y1[1] (analytic) = 0.48381642822517530541077945724221 y1[1] (numeric) = 0.48381642822517530541077945724221 absolute error = 3e-64 relative error = 6.2006989117859299494028660709900e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.14352202583499883508485599858706 y2[1] (numeric) = 0.14352202583499883508485599858706 absolute error = 6.1e-63 relative error = 4.2502187134767108072164611891232e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4259 Order of pole (three term test) = -18.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1336316576, alloc=4783252, time=70.64 x[1] = 4.18 y1[1] (analytic) = 0.49240687418472298942108196695328 y1[1] (numeric) = 0.49240687418472298942108196695328 absolute error = 4e-64 relative error = 8.1233634413061179583939073332217e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.13840309968925934903088583719909 y2[1] (numeric) = 0.13840309968925934903088583719909 absolute error = 6.2e-63 relative error = 4.4796684567904555056127587007683e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4213 Order of pole (three term test) = -18.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1340317260, alloc=4783252, time=70.85 x[1] = 4.19 y1[1] (analytic) = 0.50104807903385933959809874850755 y1[1] (numeric) = 0.50104807903385933959809874850755 absolute error = 5e-64 relative error = 9.9790822661992779832040705030699e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.13337033251555591343684467407746 y2[1] (numeric) = 0.13337033251555591343684467407746 absolute error = 6.2e-63 relative error = 4.6487100114838888136412452511956e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4165 Order of pole (three term test) = -19.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1344318164, alloc=4783252, time=71.07 x[1] = 4.2 y1[1] (analytic) = 0.50973917865930042234445511862287 y1[1] (numeric) = 0.50973917865930042234445511862287 absolute error = 6e-64 relative error = 1.1770725600847489968802358022421e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.12842422758641193998142290209118 y2[1] (numeric) = 0.12842422758641193998142290209118 absolute error = 6.2e-63 relative error = 4.8277494959650413338816788384022e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4116 Order of pole (three term test) = -19.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.21 y1[1] (analytic) = 0.51847930395832625243117705051315 y1[1] (numeric) = 0.51847930395832625243117705051315 absolute error = 6e-64 relative error = 1.1572303762547600676824988070562e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.1235652795081986026935019100478 y2[1] (numeric) = 0.1235652795081986026935019100478 absolute error = 6.2e-63 relative error = 5.0175907218245944824100744789223e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4065 Order of pole (three term test) = -19.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1348318952, alloc=4783252, time=71.28 x[1] = 4.22 y1[1] (analytic) = 0.52726758092569034074636158684479 y1[1] (numeric) = 0.52726758092569034074636158684479 absolute error = 7e-64 relative error = 1.3275991646803967671830278395018e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.11879397417167461300535326877877 y2[1] (numeric) = 0.11879397417167461300535326877877 absolute error = 6.2e-63 relative error = 5.2191199454612874819257499812404e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4013 Order of pole (three term test) = -19.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1352319620, alloc=4783252, time=71.49 x[1] = 4.23 y1[1] (analytic) = 0.53610313074101949060881041045516 y1[1] (numeric) = 0.53610313074101949060881041045516 absolute error = 8e-64 relative error = 1.4922501924102057053076523640419e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.11411078870339754878911140270074 y2[1] (numeric) = 0.11411078870339754878911140270074 absolute error = 6.2e-63 relative error = 5.4333162275438732729594128098019e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3959 Order of pole (three term test) = -19.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1356320600, alloc=4783252, time=71.70 x[1] = 4.24 y1[1] (analytic) = 0.54498506985669510273982813029406 y1[1] (numeric) = 0.54498506985669510273982813029406 absolute error = 9e-64 relative error = 1.6514213870788364389662696204037e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.10951619141801159620312567541779 y2[1] (numeric) = 0.10951619141801159620312567541779 absolute error = 6.2e-63 relative error = 5.6612633435500534641165332823046e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3903 Order of pole (three term test) = -20.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.25 y1[1] (analytic) = 0.55391251008620720083592227945516 y1[1] (numeric) = 0.55391251008620720083592227945516 absolute error = 1.0e-63 relative error = 1.8053392580795237067344147473851e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.10501064177141647553424717156172 y2[1] (numeric) = 0.10501064177141647553424717156172 absolute error = 6.2e-63 relative error = 5.9041635165852476708329163097911e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3846 Order of pole (three term test) = -20.24 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1360321304, alloc=4783252, time=71.91 TOP MAIN SOLVE Loop x[1] = 4.26 y1[1] (analytic) = 0.56288455869297234241347586451402 y1[1] (numeric) = 0.56288455869297234241347586451402 absolute error = 1.1e-63 relative error = 1.9542195340270462916396196973982e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.10059459031482223410444018114688 y2[1] (numeric) = 0.10059459031482223410444018114688 absolute error = 6.1e-63 relative error = 6.0639443740556573139246044464301e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3787 Order of pole (three term test) = -20.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1364322100, alloc=4783252, time=72.12 x[1] = 4.27 y1[1] (analytic) = 0.57190031847960653320832267790571 y1[1] (numeric) = 0.57190031847960653320832267790571 absolute error = 1.1e-63 relative error = 1.9234121130135811264694240158134e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.096268478649694500724140180338675 y2[1] (numeric) = 0.096268478649694500724140180338675 absolute error = 6.15e-63 relative error = 6.3883839095233447595182694362555e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3727 Order of pole (three term test) = -20.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1368323028, alloc=4783252, time=72.34 x[1] = 4.28 y1[1] (analytic) = 0.58095888787764421791317926316396 y1[1] (numeric) = 0.58095888787764421791317926316396 absolute error = 1.2e-63 relative error = 2.0655506354052579077418983326605e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.092032739383594707129367476700577 y2[1] (numeric) = 0.092032739383594707129367476700577 absolute error = 6.16e-63 relative error = 6.6932702875712190234979424992496e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3665 Order of pole (three term test) = -20.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1372324452, alloc=4783252, time=72.55 x[1] = 4.29 y1[1] (analytic) = 0.59005936103769437542862536622075 y1[1] (numeric) = 0.59005936103769437542862536622075 absolute error = 1.3e-63 relative error = 2.2031681655109831433329860739019e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.087887796086919692343653114751977 y2[1] (numeric) = 0.087887796086919692343653114751977 absolute error = 6.07e-63 relative error = 6.9065334099365313569492086983539e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3601 Order of pole (three term test) = -20.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.3 y1[1] (analytic) = 0.59920082792002470309323760366397 y1[1] (numeric) = 0.59920082792002470309323760366397 absolute error = 1.4e-63 relative error = 2.3364453698432771727739441107214e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.083834063250545015968290639715365 y2[1] (numeric) = 0.083834063250545015968290639715365 absolute error = 6.06e-63 relative error = 7.2285652931901796670624794302972e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3537 Order of pole (three term test) = -21.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1376325160, alloc=4783252, time=72.76 x[1] = 4.31 y1[1] (analytic) = 0.60838237438556483154993990315575 y1[1] (numeric) = 0.60838237438556483154993990315575 absolute error = 1.5e-63 relative error = 2.4655546629123230182816593484867e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.079871946244376216034287573009006 y2[1] (numeric) = 0.079871946244376216034287573009006 absolute error = 6.11e-63 relative error = 7.6497447317808474181807262550036e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3471 Order of pole (three term test) = -21.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1380326128, alloc=4783252, time=72.97 x[1] = 4.32 y1[1] (analytic) = 0.61760308228731947000291984056992 y1[1] (numeric) = 0.61760308228731947000291984056992 absolute error = 1.6e-63 relative error = 2.5906606457894145617206673208597e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.076001841276812156255690901016019 y2[1] (numeric) = 0.076001841276812156255690901016019 absolute error = 6.10e-63 relative error = 8.0261213380116942963943722366155e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3403 Order of pole (three term test) = -21.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1384326860, alloc=4783252, time=73.19 x[1] = 4.33 y1[1] (analytic) = 0.62686202956218234062676254933714 y1[1] (numeric) = 0.62686202956218234062676254933714 absolute error = 1.6e-63 relative error = 2.5523957817599575252057764581654e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.072224135355124516315780813227023 y2[1] (numeric) = 0.072224135355124516315780813227023 absolute error = 6.08e-63 relative error = 8.4182385432581104515076608353245e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3334 Order of pole (three term test) = -21.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1388327700, alloc=4783252, time=73.40 x[1] = 4.34 y1[1] (analytic) = 0.63615829032314172081087264557633 y1[1] (numeric) = 0.63615829032314172081087264557633 absolute error = 1.6e-63 relative error = 2.5150973025711370194364342207439e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.068539206246757387204087089011161 y2[1] (numeric) = 0.068539206246757387204087089011161 absolute error = 6.00e-63 relative error = 8.7541136359218662660353750698755e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3264 Order of pole (three term test) = -21.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.35 y1[1] (analytic) = 0.64549093495186837276179742256413 y1[1] (numeric) = 0.64549093495186837276179742256413 absolute error = 1.7e-63 relative error = 2.6336543364884931634216364227649e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.064947422441550841612444201658582 y2[1] (numeric) = 0.064947422441550841612444201658582 absolute error = 6.03e-63 relative error = 9.2844331203854518166918507698084e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3193 Order of pole (three term test) = -22.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1392328504, alloc=4783252, time=73.61 x[1] = 4.36 y1[1] (analytic) = 0.65485903019167660174764743303657 y1[1] (numeric) = 0.65485903019167660174764743303657 absolute error = 1.8e-63 relative error = 2.7486831776193751947392295544138e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.06144914311489225700156528111504 y2[1] (numeric) = 0.06144914311489225700156528111504 absolute error = 6.02e-63 relative error = 9.7967191971161065701562022688198e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.312 Order of pole (three term test) = -22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1396329292, alloc=4783252, time=73.82 x[1] = 4.37 y1[1] (analytic) = 0.66426163924084914695625730757717 y1[1] (numeric) = 0.66426163924084914695625730757717 absolute error = 1.9e-63 relative error = 2.8603187174430445725028940524414e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.058044718091799076175121149591737 y2[1] (numeric) = 0.058044718091799076175121149591737 absolute error = 5.96e-63 relative error = 1.0267945466759130295628082993075e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3046 Order of pole (three term test) = -22.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1400330384, alloc=4783252, time=74.04 x[1] = 4.38 y1[1] (analytic) = 0.67369782184631657255577147615592 y1[1] (numeric) = 0.67369782184631657255577147615592 absolute error = 2.0e-63 relative error = 2.9686900196869546317829203850419e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.054734487811936597055336089061836 y2[1] (numeric) = 0.054734487811936597055336089061836 absolute error = 5.96e-63 relative error = 1.0888929883619432200394632040880e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2971 Order of pole (three term test) = -22.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.39 y1[1] (analytic) = 0.68316663439768179109661463324426 y1[1] (numeric) = 0.68316663439768179109661463324426 absolute error = 2.0e-63 relative error = 2.9275434415255257923808111430098e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.051518783295574289851971036385868 y2[1] (numeric) = 0.051518783295574289851971036385868 absolute error = 5.91e-63 relative error = 1.1471544205718261393894567507376e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2894 Order of pole (three term test) = -22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1404331380, alloc=4783252, time=74.25 x[1] = 4.4 y1[1] (analytic) = 0.69266713002158031688086025778229 y1[1] (numeric) = 0.69266713002158031688086025778229 absolute error = 2.1e-63 relative error = 3.0317592808750339777379471558933e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.048397926110484045964607666619612 y2[1] (numeric) = 0.048397926110484045964607666619612 absolute error = 5.87e-63 relative error = 1.2128618872221531043174626214454e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2817 Order of pole (three term test) = -22.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1408332116, alloc=4783252, time=74.47 x[1] = 4.41 y1[1] (analytic) = 0.70219835867636681335229353350936 y1[1] (numeric) = 0.70219835867636681335229353350936 absolute error = 2.1e-63 relative error = 2.9906079586378811000154584443216e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.045372228339783668765758435463846 y2[1] (numeric) = 0.045372228339783668765758435463846 absolute error = 5.86e-63 relative error = 1.2915389467133101405531174895237e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2738 Order of pole (three term test) = -22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1412332964, alloc=4783252, time=74.68 x[1] = 4.42 y1[1] (analytic) = 0.71175936724711846593133485650678 y1[1] (numeric) = 0.71175936724711846593133485650678 absolute error = 2.1e-63 relative error = 2.9504353530634925128022563790430e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.042441992550728821888927268161108 y2[1] (numeric) = 0.042441992550728821888927268161108 absolute error = 5.87e-63 relative error = 1.3830641888417180956642130859917e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2658 Order of pole (three term test) = -23.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1416333988, alloc=4783252, time=74.89 x[1] = 4.43 y1[1] (analytic) = 0.72134919964094568003670965106636 y1[1] (numeric) = 0.72134919964094568003670965106636 absolute error = 2.2e-63 relative error = 3.0498404948602679602036828031338e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.039607511764456555800785465699523 y2[1] (numeric) = 0.039607511764456555800785465699523 absolute error = 5.89e-63 relative error = 1.4870916494394974607056906762811e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2577 Order of pole (three term test) = -23.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.44 y1[1] (analytic) = 0.73096689688260057330348764383661 y1[1] (numeric) = 0.73096689688260057330348764383661 absolute error = 2.3e-63 relative error = 3.1465173181014780334652570755474e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.036869069426683438279591966922158 y2[1] (numeric) = 0.036869069426683438279591966922158 absolute error = 5.83e-63 relative error = 1.5812712635976172979972361074679e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2495 Order of pole (three term test) = -23.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1420335024, alloc=4783252, time=75.10 x[1] = 4.45 y1[1] (analytic) = 0.74061149721037370122794327025554 y1[1] (numeric) = 0.74061149721037370122794327025554 absolute error = 2.3e-63 relative error = 3.1055418511099290515925192315933e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.034226939379361218962391981308307 y2[1] (numeric) = 0.034226939379361218962391981308307 absolute error = 5.83e-63 relative error = 1.7033366423395365579950201140481e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2413 Order of pole (three term test) = -23.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1424335840, alloc=4783252, time=75.31 x[1] = 4.46 y1[1] (analytic) = 0.75028203617226942664658639888734 y1[1] (numeric) = 0.75028203617226942664658639888734 absolute error = 2.4e-63 relative error = 3.1987970980141460536932522573070e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.031681385833292862370919071753561 y2[1] (numeric) = 0.031681385833292862370919071753561 absolute error = 5.74e-63 relative error = 1.8117894306151324933975762186805e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2329 Order of pole (three term test) = -23.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1428336484, alloc=4783252, time=75.52 x[1] = 4.47 y1[1] (analytic) = 0.75997754672245031559256134466984 y1[1] (numeric) = 0.75997754672245031559256134466984 absolute error = 2.5e-63 relative error = 3.2895708705891798629255162677856e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.029232663341711687790078200728413 y2[1] (numeric) = 0.029232663341711687790078200728413 absolute error = 5.71e-63 relative error = 1.9532944820161080021765100072491e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2244 Order of pole (three term test) = -23.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.48 y1[1] (analytic) = 0.76969705931794091517019859315115 y1[1] (numeric) = 0.76969705931794091517019859315115 absolute error = 2.5e-63 relative error = 3.2480311178729838616704138016814e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.026881016774826258063004581467315 y2[1] (numeric) = 0.026881016774826258063004581467315 absolute error = 5.73e-63 relative error = 2.1316157971249341277018164116019e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2158 Order of pole (three term test) = -23.76 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1432337292, alloc=4783252, time=75.74 TOP MAIN SOLVE Loop x[1] = 4.49 y1[1] (analytic) = 0.7794396020155812431505179934839 y1[1] (numeric) = 0.7794396020155812431505179934839 absolute error = 2.6e-63 relative error = 3.3357299183625842776430226060619e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.024626681295333562792606306340817 y2[1] (numeric) = 0.024626681295333562792606306340817 absolute error = 5.72e-63 relative error = 2.3226840561273133989244664305975e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2072 Order of pole (three term test) = -23.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1436338216, alloc=4783252, time=75.95 x[1] = 4.5 y1[1] (analytic) = 0.78920420056922029401951817520617 y1[1] (numeric) = 0.78920420056922029401951817520617 absolute error = 2.7e-63 relative error = 3.4211678017585332896009664055515e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.02246988233490294461086498550137 y2[1] (numeric) = 0.02246988233490294461086498550137 absolute error = 5.68e-63 relative error = 2.5278281013412943330413796840642e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1984 Order of pole (three term test) = -23.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1440339440, alloc=4783252, time=76.16 x[1] = 4.51 y1[1] (analytic) = 0.79898987852713984220964167825923 y1[1] (numeric) = 0.79898987852713984220964167825923 absolute error = 2.7e-63 relative error = 3.3792668374938459639650393562122e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.020410835571633120103670802952336 y2[1] (numeric) = 0.020410835571633120103670802952336 absolute error = 5.61e-63 relative error = 2.7485400978864141577324156757266e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1896 Order of pole (three term test) = -24.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1444340432, alloc=4783252, time=76.37 x[1] = 4.52 y1[1] (analytic) = 0.80879565732969880021527888180112 y1[1] (numeric) = 0.80879565732969880021527888180112 absolute error = 2.7e-63 relative error = 3.3382968559874049024703343260710e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.018449746908484549670313753257891 y2[1] (numeric) = 0.018449746908484549670313753257891 absolute error = 5.66e-63 relative error = 3.0677927605592876694046017951584e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1807 Order of pole (three term test) = -24.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.53 y1[1] (analytic) = 0.8186205564071883672378692086186 y1[1] (numeric) = 0.8186205564071883672378692086186 absolute error = 2.8e-63 relative error = 3.4203880883333911285165305659228e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.016586812452689313062672144563041 y2[1] (numeric) = 0.016586812452689313062672144563041 absolute error = 5.58e-63 relative error = 3.3641183415534931547191419310095e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1718 Order of pole (three term test) = -24.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1448341472, alloc=4783252, time=76.58 x[1] = 4.54 y1[1] (analytic) = 0.8284635932778881829272807804022 y1[1] (numeric) = 0.8284635932778881829272807804022 absolute error = 2.9e-63 relative error = 3.5004555704444392671236147693030e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.014822218496140549599386069217458 y2[1] (numeric) = 0.014822218496140549599386069217458 absolute error = 5.61e-63 relative error = 3.7848585226703731119324156319535e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1627 Order of pole (three term test) = -24.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1452342152, alloc=4783252, time=76.79 x[1] = 4.55 y1[1] (analytic) = 0.83832378364631368068580757499206 y1[1] (numeric) = 0.83832378364631368068580757499206 absolute error = 3.0e-63 relative error = 3.5785695915144059747115839226684e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.013156141496763424094652345974906 y2[1] (numeric) = 0.013156141496763424094652345974906 absolute error = 5.55e-63 relative error = 4.2185621075642654400270109483863e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1536 Order of pole (three term test) = -24.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1456342872, alloc=4783252, time=77.01 x[1] = 4.56 y1[1] (analytic) = 0.8482001415016448158813262073901 y1[1] (numeric) = 0.8482001415016448158813262073901 absolute error = 3.1e-63 relative error = 3.6547977868900043452269188818632e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.011588748060869481389523910961909 y2[1] (numeric) = 0.011588748060869481389523910961909 absolute error = 5.46e-63 relative error = 4.7114666496514954377880790995815e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1445 Order of pole (three term test) = -24.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.57 bytes used=1460347288, alloc=4783252, time=77.22 y1[1] (analytic) = 0.85809167921632632617881468562541 y1[1] (numeric) = 0.85809167921632632617881468562541 absolute error = 3.2e-63 relative error = 3.7292052556930513335850620174197e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.010120194926496154035555871934926 y2[1] (numeric) = 0.010120194926496154035555871934926 absolute error = 5.46e-63 relative error = 5.3951529981946489108073888389419e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1353 Order of pole (three term test) = -24.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.58 y1[1] (analytic) = 0.8679974076448296640463665993177 y1[1] (numeric) = 0.8679974076448296640463665993177 absolute error = 3.2e-63 relative error = 3.6866469551823680533554788225694e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0087506289477330891661461639026889 y2[1] (numeric) = 0.0087506289477330891661461639026889 absolute error = 5.442e-63 relative error = 6.2189815526457531555180166310044e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.126 Order of pole (three term test) = -24.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1464348044, alloc=4783252, time=77.43 x[1] = 4.59 y1[1] (analytic) = 0.8779163362225667253247514756035 y1[1] (numeric) = 0.8779163362225667253247514756035 absolute error = 3.2e-63 relative error = 3.6449942528336157596220910374978e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0074801870800368619098223213121856 y2[1] (numeric) = 0.0074801870800368619098223213121856 absolute error = 5.453e-63 relative error = 7.2899246257529804262374109224907e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1167 Order of pole (three term test) = -24.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1468349668, alloc=4783252, time=77.64 x[1] = 4.6 y1[1] (analytic) = 0.88784747306494548257009217877081 y1[1] (numeric) = 0.88784747306494548257009217877081 absolute error = 3.3e-63 relative error = 3.7168546401422342976619321695229e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0063089963665355438618953400911705 y2[1] (numeric) = 0.0063089963665355438618953400911705 absolute error = 5.354e-63 relative error = 8.4862943152082356373405004021685e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1073 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1472350536, alloc=4783252, time=77.86 x[1] = 4.61 y1[1] (analytic) = 0.89778982506655761768887117182731 y1[1] (numeric) = 0.89778982506655761768887117182731 absolute error = 3.3e-63 relative error = 3.6756932500937562017019912696893e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0052371739253244961462206425968638 y2[1] (numeric) = 0.0052371739253244961462206425968638 absolute error = 5.307e-63 relative error = 1.0133327775000669695845872405532e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09791 Order of pole (three term test) = -24.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.62 y1[1] (analytic) = 0.90774239800048823518465822438418 y1[1] (numeric) = 0.90774239800048823518465822438418 absolute error = 3.4e-63 relative error = 3.7455560162104175371643021829072e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0042648269377546574771731655485343 y2[1] (numeric) = 0.0042648269377546574771731655485343 absolute error = 5.332e-63 relative error = 1.2502265807782547220989495976129e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08846 Order of pole (three term test) = -24.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1476351328, alloc=4783252, time=78.06 x[1] = 4.63 y1[1] (analytic) = 0.91770419661773772512799271259738 y1[1] (numeric) = 0.91770419661773772512799271259738 absolute error = 3.5e-63 relative error = 3.8138650917141841795604218596364e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0033920526377144983832706460192959 y2[1] (numeric) = 0.0033920526377144983832706460192959 absolute error = 5.294e-63 relative error = 1.5607069127226156998165620864847e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07898 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1480352024, alloc=4783252, time=78.28 x[1] = 4.64 y1[1] (analytic) = 0.92767422474674583374597479923988 y1[1] (numeric) = 0.92767422474674583374597479923988 absolute error = 3.5e-63 relative error = 3.7728761957954546116076860897300e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.002618938301906713388091068117169 y2[1] (numeric) = 0.002618938301906713388091068117169 absolute error = 5.209e-63 relative error = 1.9889739274146308769605037923778e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06947 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1484352828, alloc=4783252, time=78.49 x[1] = 4.65 y1[1] (analytic) = 0.93765148539300798930744298382293 y1[1] (numeric) = 0.93765148539300798930744298382293 absolute error = 3.6e-63 relative error = 3.8393796160746155453468224874407e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0019455612411206234711634491039746 y2[1] (numeric) = 0.0019455612411206234711634491039746 absolute error = 5.216e-63 relative error = 2.6809744611254884442871598837684e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05992 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1488354164, alloc=4783252, time=78.70 x[1] = 4.66 y1[1] (analytic) = 0.94763498083877392175416283320404 y1[1] (numeric) = 0.94763498083877392175416283320404 absolute error = 3.6e-63 relative error = 3.7989310998350395032035529348120e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0013719887925011615613129021674769 y2[1] (numeric) = 0.0013719887925011615613129021674769 absolute error = 5.163e-63 relative error = 3.7631502736897385189299531369586e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05036 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.67 y1[1] (analytic) = 0.95762371274281860629914567989472 y1[1] (numeric) = 0.95762371274281860629914567989472 absolute error = 3.6e-63 relative error = 3.7593054057620473769544583167194e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.00089827831281521415746815072661771 y2[1] (numeric) = 0.00089827831281521415746815072661771 absolute error = 5.1419e-63 relative error = 5.7241724826743602291649771159318e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04077 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1492355404, alloc=4783252, time=78.91 x[1] = 4.68 y1[1] (analytic) = 0.96761668224027555398087963205543 y1[1] (numeric) = 0.96761668224027555398087963205543 absolute error = 3.7e-63 relative error = 3.8238282451203415177126670788071e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.00052447717271599243715805024032733 y2[1] (numeric) = 0.00052447717271599243715805024032733 absolute error = 5.1108e-63 relative error = 9.7445613763013650308993454870347e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03117 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1496356288, alloc=4783252, time=79.12 x[1] = 4.69 y1[1] (analytic) = 0.97761289004252246592761160355799 y1[1] (numeric) = 0.97761289004252246592761160355799 absolute error = 3.7e-63 relative error = 3.7847291475862843663779062026540e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.00025062275200600641080659305708347 y2[1] (numeric) = 0.00025062275200600641080659305708347 absolute error = 5.0776e-63 relative error = 2.0259932345959996973524501268529e-57 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02155 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1500357132, alloc=4783252, time=79.34 x[1] = 4.7 y1[1] (analytic) = 0.98761133653710926284949170367289 y1[1] (numeric) = 0.98761133653710926284949170367289 absolute error = 3.8e-63 relative error = 3.8476674572449238962048535958092e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 7.6742435899115820463458425028554e-05 y2[1] (numeric) = 7.6742435899115820463458425028554e-05 absolute error = 5.05740e-63 relative error = 6.5900957413553617444967783550810e-57 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01193 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.71 y1[1] (analytic) = 0.9976110218877184970389038522753 y1[1] (numeric) = 0.9976110218877184970389038522753 absolute error = 3.8e-63 relative error = 3.8090998561839180008390339330634e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 2.8536122820315747652874064262784e-06 y2[1] (numeric) = 2.8536122820315747652874064262784e-06 absolute error = 5.028030e-63 relative error = 1.7619877905839366754845766999887e-55 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0023 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1504357768, alloc=4783252, time=79.55 x[1] = 4.72 y1[1] (analytic) = 1.0076109461341481509210826531746 y1[1] (numeric) = 1.0076109461341481509210826531746 absolute error = 3e-63 relative error = 2.9773396284646905713322794085100e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 2.8963669975541567702112038360479e-05 y2[1] (numeric) = 2.8963669975541567702112038360479e-05 absolute error = 4.93429e-63 relative error = 1.7036135283155662298345586918143e-56 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.007339 Order of pole (three term test) = -0.8943 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1508358908, alloc=4783252, time=79.76 x[1] = 4.73 y1[1] (analytic) = 1.0176101092923068239584801849428 y1[1] (numeric) = 1.0176101092923068239584801849428 absolute error = 4e-63 relative error = 3.9307785599553302034417673470662e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.00015506999799563475715808844231872 y2[1] (numeric) = 0.00015506999799563475715808844231872 absolute error = 4.8842e-63 relative error = 3.1496743813316428465257358670914e-57 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01698 Order of pole (three term test) = -0.9004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1512360236, alloc=4783252, time=79.97 x[1] = 4.74 y1[1] (analytic) = 1.027607511454211308473521317219 y1[1] (numeric) = 1.027607511454211308473521317219 absolute error = 4e-63 relative error = 3.8925367471666580595752066480661e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.00038115998581459739020295192722966 y2[1] (numeric) = 0.00038115998581459739020295192722966 absolute error = 4.8550e-63 relative error = 1.2737433573002475203551922020477e-57 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02661 Order of pole (three term test) = -0.9113 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1516361268, alloc=4783252, time=80.19 x[1] = 4.75 y1[1] (analytic) = 1.0376021528879765547154963123733 y1[1] (numeric) = 1.0376021528879765547154963123733 absolute error = 4e-63 relative error = 3.8550421169296235063376193148237e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.00070721102462205526572924440292074 y2[1] (numeric) = 0.00070721102462205526572924440292074 absolute error = 4.8490e-63 relative error = 6.8565107601247903866599652829648e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03623 Order of pole (three term test) = -0.927 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.76 y1[1] (analytic) = 1.0475930341377880262584087164105 y1[1] (numeric) = 1.0475930341377880262584087164105 absolute error = 4e-63 relative error = 3.8182766300008512651522407536324e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0011331905095858359312599154305637 y2[1] (numeric) = 0.0011331905095858359312599154305637 absolute error = 4.788e-63 relative error = 4.2252383509194247548132345393355e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04584 Order of pole (three term test) = -0.9476 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1520362144, alloc=4783252, time=80.40 x[1] = 4.77 y1[1] (analytic) = 1.0575791561238464485775487727873 y1[1] (numeric) = 1.0575791561238464485775487727873 absolute error = 4e-63 relative error = 3.7822228027455423281346723107062e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0016590558431124247295906617005143 y2[1] (numeric) = 0.0016590558431124247295906617005143 absolute error = 4.726e-63 relative error = 2.8486081524139184739636945326938e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05543 Order of pole (three term test) = -0.973 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1524362968, alloc=4783252, time=80.61 x[1] = 4.78 y1[1] (analytic) = 1.0675595202422749564132217146596 y1[1] (numeric) = 1.0675595202422749564132217146596 absolute error = 4e-63 relative error = 3.7468636868998449506310026169620e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0022847544391066886523793783523275 y2[1] (numeric) = 0.0022847544391066886523793783523275 absolute error = 4.685e-63 relative error = 2.0505485927983483103743358410152e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.065 Order of pole (three term test) = -1.003 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1528364328, alloc=4783252, time=80.83 x[1] = 4.79 y1[1] (analytic) = 1.0775331284649786492901502413476 y1[1] (numeric) = 1.0775331284649786492901502413476 absolute error = 4e-63 relative error = 3.7121828501906757454238376321981e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.003010223728230442031847121237262 y2[1] (numeric) = 0.003010223728230442031847121237262 absolute error = 4.730e-63 relative error = 1.5713117784705415494299547803502e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07454 Order of pole (three term test) = -1.038 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.8 y1[1] (analytic) = 1.0874989834394465693202152576495 y1[1] (numeric) = 1.0874989834394465693202152576495 absolute error = 4e-63 relative error = 3.6781643577717656510041120214024e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0038353911641593282184035334963654 y2[1] (numeric) = 0.0038353911641593282184035334963654 absolute error = 4.612e-63 relative error = 1.2024849103001193183081414648758e-58 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08405 Order of pole (three term test) = -1.078 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1532365160, alloc=4783252, time=81.04 TOP MAIN SOLVE Loop x[1] = 4.81 y1[1] (analytic) = 1.0974560885884861211739226395384 y1[1] (numeric) = 1.0974560885884861211739226395384 absolute error = 4e-63 relative error = 3.6447927544369229007899929081408e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0047601742308373915612430245959728 y2[1] (numeric) = 0.0047601742308373915612430245959728 absolute error = 4.563e-63 relative error = 9.5857835842224929902765702844710e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09353 Order of pole (three term test) = -1.122 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1536366228, alloc=4783252, time=81.25 x[1] = 4.82 y1[1] (analytic) = 1.1074034482098799608617106191698 y1[1] (numeric) = 1.1074034482098799608617106191698 absolute error = 4e-63 relative error = 3.6120530475735907657611268381449e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0057844804507286142407590987016601 y2[1] (numeric) = 0.0057844804507286142407590987016601 absolute error = 4.563e-63 relative error = 7.8883488999003249557972407441402e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.103 Order of pole (three term test) = -1.172 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1540367108, alloc=4783252, time=81.47 x[1] = 4.83 y1[1] (analytic) = 1.1173400675759553877192667889538 y1[1] (numeric) = 1.1173400675759553877192667889538 absolute error = 4e-63 relative error = 3.5799306908217403349947728534110e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0069082073940645928059698487305991 y2[1] (numeric) = 0.0069082073940645928059698487305991 absolute error = 4.481e-63 relative error = 6.4864873684162904244136842793645e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1124 Order of pole (three term test) = -1.226 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1544367892, alloc=4783252, time=81.68 x[1] = 4.84 y1[1] (analytic) = 1.1272649530330562827406304097327 y1[1] (numeric) = 1.1272649530330562827406304097327 absolute error = 5e-63 relative error = 4.4355144605062323621209495972153e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.008131242689087429657007244959484 y2[1] (numeric) = 0.008131242689087429657007244959484 absolute error = 4.525e-63 relative error = 5.5649550419553905765142636881865e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1217 Order of pole (three term test) = -1.284 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.85 y1[1] (analytic) = 1.1371771121009076461481397184653 y1[1] (numeric) = 1.1371771121009076461481397184653 absolute error = 5e-63 relative error = 4.3968524751281873902806729849141e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.0094534640332868151920576837088197 y2[1] (numeric) = 0.0094534640332868151920576837088197 absolute error = 4.457e-63 relative error = 4.7146738849445580689818953683145e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.131 Order of pole (three term test) = -1.348 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1548368552, alloc=4783252, time=81.89 x[1] = 4.86 y1[1] (analytic) = 1.1470755535718627978282707459854 y1[1] (numeric) = 1.1470755535718627978282707459854 absolute error = 4e-63 relative error = 3.4871286268323433330747658802123e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.010874739205630176919903305957091 y2[1] (numeric) = 0.010874739205630176919903305957091 absolute error = 4.34e-63 relative error = 3.9909003038464154818212854810115e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1403 Order of pole (three term test) = -1.416 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1552369292, alloc=4783252, time=82.10 x[1] = 4.87 y1[1] (analytic) = 1.156959287610023315996029785628 y1[1] (numeric) = 1.156959287610023315996029785628 absolute error = 4e-63 relative error = 3.4573385968169706603069524330727e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.012394926079784672533344588707492 y2[1] (numeric) = 0.012394926079784672533344588707492 absolute error = 4.39e-63 relative error = 3.5417718280384162448512978281708e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1495 Order of pole (three term test) = -1.488 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1556370312, alloc=4783252, time=82.32 x[1] = 4.88 y1[1] (analytic) = 1.1668273258502218021766327470316 y1[1] (numeric) = 1.1668273258502218021766327470316 absolute error = 4e-63 relative error = 3.4280993523059251210472885374115e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.014013872638329704755215157681578 y2[1] (numeric) = 0.014013872638329704755215157681578 absolute error = 4.28e-63 relative error = 3.0541165247168448869429253179896e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1586 Order of pole (three term test) = -1.566 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1560371020, alloc=4783252, time=82.53 x[1] = 4.89 y1[1] (analytic) = 1.1766786814968575743104585897138 y1[1] (numeric) = 1.1766786814968575743104585897138 absolute error = 5e-63 relative error = 4.2492483960357642863617610448280e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.015731416987958536717347942751101 y2[1] (numeric) = 0.015731416987958536717347942751101 absolute error = 4.29e-63 relative error = 2.7270270715497145840622019473206e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1677 Order of pole (three term test) = -1.648 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.9 y1[1] (analytic) = 1.1865123694225754044943291441219 y1[1] (numeric) = 1.1865123694225754044943291441219 absolute error = 5e-63 relative error = 4.2140310786926605670891027960233e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.017547387375667487723622750081671 y2[1] (numeric) = 0.017547387375667487723622750081671 absolute error = 4.21e-63 relative error = 2.3992175643411731388589232311431e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1767 Order of pole (three term test) = -1.734 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1564372184, alloc=4783252, time=82.74 x[1] = 4.91 y1[1] (analytic) = 1.1963274062667774335675731995194 y1[1] (numeric) = 1.1963274062667774335675731995194 absolute error = 5e-63 relative error = 4.1794578756687071617795244809446e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.01946160220593109049100989773031 y2[1] (numeric) = 0.01946160220593109049100989773031 absolute error = 4.18e-63 relative error = 2.1478190519823229581980537588426e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1856 Order of pole (three term test) = -1.825 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1568372868, alloc=4783252, time=82.95 x[1] = 4.92 y1[1] (analytic) = 1.2061228105339584114335092408118 y1[1] (numeric) = 1.2061228105339584114335092408118 absolute error = 5e-63 relative error = 4.1455148317661511482865452331361e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.021473870058861492367198393658874 y2[1] (numeric) = 0.021473870058861492367198393658874 absolute error = 4.10e-63 relative error = 1.9092972010921141541419067077560e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1945 Order of pole (three term test) = -1.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1572374296, alloc=4783252, time=83.17 x[1] = 4.93 y1[1] (analytic) = 1.2158976026918544296742604464858 y1[1] (numeric) = 1.2158976026918544296742604464858 absolute error = 6e-63 relative error = 4.9346260628499513231470339245466e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.023583989709350284599819677250865 y2[1] (numeric) = 0.023583989709350284599819677250865 absolute error = 4.07e-63 relative error = 1.7257470216696954459786408332783e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2033 Order of pole (three term test) = -2.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.94 y1[1] (analytic) = 1.2256508052693953316674308040397 y1[1] (numeric) = 1.2256508052693953316674308040397 absolute error = 5e-63 relative error = 4.0794653571014552363451182351083e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.025791750147190845490291473176844 y2[1] (numeric) = 0.025791750147190845490291473176844 absolute error = 3.98e-63 relative error = 1.5431290925534531067644108467782e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.212 Order of pole (three term test) = -2.124 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1576375332, alloc=4783252, time=83.37 x[1] = 4.95 y1[1] (analytic) = 1.2353814429544510050452574116347 y1[1] (numeric) = 1.2353814429544510050452574116347 absolute error = 5e-63 relative error = 4.0473329339012517022132666369228e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.028096930598179185214734936622646 y2[1] (numeric) = 0.028096930598179185214734936622646 absolute error = 3.93e-63 relative error = 1.3987292975890692838040321072638e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2206 Order of pole (three term test) = -2.232 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1580376304, alloc=4783252, time=83.59 x[1] = 4.96 y1[1] (analytic) = 1.2450885426913617819484480229353 y1[1] (numeric) = 1.2450885426913617819484480229353 absolute error = 6e-63 relative error = 4.8189343924332514910852705673233e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.030499300546191182245066976903265 y2[1] (numeric) = 0.030499300546191182245066976903265 absolute error = 3.89e-63 relative error = 1.2754390855975847955817996880021e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2291 Order of pole (three term test) = -2.345 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1584377060, alloc=4783252, time=83.80 x[1] = 4.97 y1[1] (analytic) = 1.2547711337782431941159535140125 y1[1] (numeric) = 1.2547711337782431941159535140125 absolute error = 6e-63 relative error = 4.7817485105298774559121332554294e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.032998619756234003665023285922095 y2[1] (numeric) = 0.032998619756234003665023285922095 absolute error = 3.85e-63 relative error = 1.1667154652044709086317460394923e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2375 Order of pole (three term test) = -2.462 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1588377852, alloc=4783252, time=84.01 x[1] = 4.98 y1[1] (analytic) = 1.2644282479640553524162533206808 y1[1] (numeric) = 1.2644282479640553524162533206808 absolute error = 6e-63 relative error = 4.7452277419940759967034484307054e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.035594638298469404258289922071078 y2[1] (numeric) = 0.035594638298469404258289922071078 absolute error = 3.78e-63 relative error = 1.0619576938256295730934780517507e-59 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2459 Order of pole (three term test) = -2.583 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.99 y1[1] (analytic) = 1.2740589195454272439630915976969 y1[1] (numeric) = 1.2740589195454272439630915976969 absolute error = 6e-63 relative error = 4.7093583412459025053139247812776e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.038287096573206502058853985588893 y2[1] (numeric) = 0.038287096573206502058853985588893 absolute error = 3.76e-63 relative error = 9.8205409564309100392081362301257e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2541 Order of pole (three term test) = -2.709 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1592378788, alloc=4783252, time=84.22 x[1] = 5 y1[1] (analytic) = 1.2836621854632262644666391715136 y1[1] (numeric) = 1.2836621854632262644666391715136 absolute error = 6e-63 relative error = 4.6741269377151759276910596514521e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.041075725336861531106845593844006 y2[1] (numeric) = 0.041075725336861531106845593844006 absolute error = 3.68e-63 relative error = 8.9590627306526278299428380701732e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2623 Order of pole (three term test) = -2.838 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1596379472, alloc=4783252, time=84.43 x[1] = 5.01 y1[1] (analytic) = 1.2932370853988633289473205124347 y1[1] (numeric) = 1.2932370853988633289473205124347 absolute error = 7e-63 relative error = 5.4127739445710706367727333201472e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.043960245728881975456228627531302 y2[1] (numeric) = 0.043960245728881975456228627531302 absolute error = 3.58e-63 relative error = 8.1437215389538469842895933707646e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2703 Order of pole (three term test) = -2.972 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1600380344, alloc=4783252, time=84.64 x[1] = 5.02 y1[1] (analytic) = 1.3027826618703239303814883348922 y1[1] (numeric) = 1.3027826618703239303814883348922 absolute error = 7e-63 relative error = 5.3731141846411556934549832434758e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.046940369299632392043376182258299 y2[1] (numeric) = 0.046940369299632392043376182258299 absolute error = 3.51e-63 relative error = 7.4775721886523124357433967858729e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2782 Order of pole (three term test) = -3.109 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.03 y1[1] (analytic) = 1.3122979603279155432531068738344 y1[1] (numeric) = 1.3122979603279155432531068738344 absolute error = 7e-63 relative error = 5.3341544463353793881794638706536e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.050015798039239133857481976239102 y2[1] (numeric) = 0.050015798039239133857481976239102 absolute error = 3.47e-63 relative error = 6.9378079247634202729847259116013e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.286 Order of pole (three term test) = -3.251 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1604381156, alloc=4783252, time=84.85 TOP MAIN SOLVE Loop x[1] = 5.04 y1[1] (analytic) = 1.3217820292497217973508779058945 y1[1] (numeric) = 1.3217820292497217973508779058945 absolute error = 7e-63 relative error = 5.2958807466715097405710614882499e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.053186224407391088964527862139932 y2[1] (numeric) = 0.053186224407391088964527862139932 absolute error = 3.39e-63 relative error = 6.3738308890542425653764657031193e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2937 Order of pole (three term test) = -3.396 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1608381932, alloc=4783252, time=85.07 x[1] = 5.05 y1[1] (analytic) = 1.3312339202367538764729746824182 y1[1] (numeric) = 1.3312339202367538764729746824182 absolute error = 7e-63 relative error = 5.2582794755974081178565771126887e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.056451331364093455335738912731992 y2[1] (numeric) = 0.056451331364093455335738912731992 absolute error = 3.29e-63 relative error = 5.8280290659232243716431474720186e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3013 Order of pole (three term test) = -3.545 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1612382740, alloc=4783252, time=85.28 x[1] = 5.06 y1[1] (analytic) = 1.3406526881077896269788058689017 y1[1] (numeric) = 1.3406526881077896269788058689017 absolute error = 7e-63 relative error = 5.2213373844644795811561300209267e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.059810792401371476128671295106488 y2[1] (numeric) = 0.059810792401371476128671295106488 absolute error = 3.23e-63 relative error = 5.4003631624280826420981184120770e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3088 Order of pole (three term test) = -3.698 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1616383932, alloc=4783252, time=85.49 x[1] = 5.07 y1[1] (analytic) = 1.3500373909938908923559866414642 y1[1] (numeric) = 1.3500373909938908923559866414642 absolute error = 7e-63 relative error = 5.1850415749201097328124828993135e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.063264271575920965073824515999517 y2[1] (numeric) = 0.063264271575920965073824515999517 absolute error = 3.16e-63 relative error = 4.9949203891612159572240923341416e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3161 Order of pole (three term test) = -3.855 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.08 y1[1] (analytic) = 1.359387090432589622147824426171 y1[1] (numeric) = 1.359387090432589622147824426171 absolute error = 8e-63 relative error = 5.8850051293735678001372513419147e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.06681142354270235694144805746205 y2[1] (numeric) = 0.06681142354270235694144805746205 absolute error = 3.05e-63 relative error = 4.5650875827403976892192282862871e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3233 Order of pole (three term test) = -4.015 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1620385344, alloc=4783252, time=85.70 x[1] = 5.09 y1[1] (analytic) = 1.3687008514617333367089146951106 y1[1] (numeric) = 1.3687008514617333367089146951106 absolute error = 8e-63 relative error = 5.8449587369338076779420585227312e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.070451893589474923711490670950491 y2[1] (numeric) = 0.070451893589474923711490670950491 absolute error = 3.04e-63 relative error = 4.3150011236236766815752794967820e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3304 Order of pole (three term test) = -4.179 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1624386020, alloc=4783252, time=85.91 x[1] = 5.1 y1[1] (analytic) = 1.377977742712980563320575552929 y1[1] (numeric) = 1.377977742712980563320575552929 absolute error = 8e-63 relative error = 5.8056090109623219276535122883397e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.074185317672267703053853752455137 y2[1] (numeric) = 0.074185317672267703053853752455137 absolute error = 2.96e-63 relative error = 3.9900078517915692981299841050271e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3374 Order of pole (three term test) = -4.346 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1628387188, alloc=4783252, time=86.12 x[1] = 5.11 y1[1] (analytic) = 1.3872168365049368942004221740824 y1[1] (numeric) = 1.3872168365049368942004221740824 absolute error = 8e-63 relative error = 5.7669426938010849423977607512655e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.078011322451783592055659781865728 y2[1] (numeric) = 0.078011322451783592055659781865728 absolute error = 2.89e-63 relative error = 3.7045904481188874129547850155333e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3442 Order of pole (three term test) = -4.517 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.12 bytes used=1632388204, alloc=4783252, time=86.34 y1[1] (analytic) = 1.3964172089359223528778932563282 y1[1] (numeric) = 1.3964172089359223528778932563282 absolute error = 8e-63 relative error = 5.7289468711833222874532638654495e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.081929525330732965816499743380584 y2[1] (numeric) = 0.081929525330732965816499743380584 absolute error = 2.74e-63 relative error = 3.3443376962568411695912389053311e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3509 Order of pole (three term test) = -4.691 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.13 y1[1] (analytic) = 1.4055779399763607922763978187695 y1[1] (numeric) = 1.4055779399763607922763978187695 absolute error = 9e-63 relative error = 6.4030600822828531780683678351675e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.085939534492093087580911247342328 y2[1] (numeric) = 0.085939534492093087580911247342328 absolute error = 2.68e-63 relative error = 3.1184716275680720849214502619976e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3574 Order of pole (three term test) = -4.869 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1636389240, alloc=4783252, time=86.55 x[1] = 5.14 y1[1] (analytic) = 1.4146981135607820856392650382033 y1[1] (numeric) = 1.4146981135607820856392650382033 absolute error = 8e-63 relative error = 5.6549167086001647999899973050705e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.090040948938289484498956841189151 y2[1] (numeric) = 0.090040948938289484498956841189151 absolute error = 2.60e-63 relative error = 2.8875750762932734805585171592380e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3638 Order of pole (three term test) = -5.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1640389952, alloc=4783252, time=86.76 x[1] = 5.15 y1[1] (analytic) = 1.4237768176794279101570727656681 y1[1] (numeric) = 1.4237768176794279101570727656681 absolute error = 8e-63 relative error = 5.6188581669976657149965207055302e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.094233358531295370909977489320687 y2[1] (numeric) = 0.094233358531295370909977489320687 absolute error = 2.50e-63 relative error = 2.6529883249037945129833813704004e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.37 Order of pole (three term test) = -5.234 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1644390888, alloc=4783252, time=86.97 x[1] = 5.16 y1[1] (analytic) = 1.4328131444694519627943298888998 y1[1] (numeric) = 1.4328131444694519627943298888998 absolute error = 8e-63 relative error = 5.5834216979927786904562622053152e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.098516344033645109240608921213243 y2[1] (numeric) = 0.098516344033645109240608921213243 absolute error = 2.45e-63 relative error = 2.4868969956531078631085726898717e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3761 Order of pole (three term test) = -5.421 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.17 y1[1] (analytic) = 1.4418061903057054883699297989835 y1[1] (numeric) = 1.4418061903057054883699297989835 absolute error = 8e-63 relative error = 5.5485959581736597779755008274587e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.10288947715035760720514881630516 y2[1] (numeric) = 0.10288947715035760720514881630516 absolute error = 2.3e-63 relative error = 2.2354083854842545660161394642357e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3821 Order of pole (three term test) = -5.611 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1648391620, alloc=4783252, time=87.18 x[1] = 5.18 y1[1] (analytic) = 1.4507550558910990414142212704052 y1[1] (numeric) = 1.4507550558910990414142212704052 absolute error = 8e-63 relative error = 5.5143698913984830304598651360916e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.10735232057176545900349083681378 y2[1] (numeric) = 0.10735232057176545900349083681378 absolute error = 2.3e-63 relative error = 2.1424781390379360541814991237059e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3879 Order of pole (three term test) = -5.804 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1652392460, alloc=4783252, time=87.40 x[1] = 5.19 y1[1] (analytic) = 1.4596588463465314457018122646263 y1[1] (numeric) = 1.4596588463465314457018122646263 absolute error = 8e-63 relative error = 5.4807327205419846212786624276761e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.1119044280172455476381965471094 y2[1] (numeric) = 0.1119044280172455476381965471094 absolute error = 2.2e-63 relative error = 1.9659633126054304664111804278891e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3935 Order of pole (three term test) = -6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1656393132, alloc=4783252, time=87.61 x[1] = 5.2 y1[1] (analytic) = 1.4685166713003769586390939266086 y1[1] (numeric) = 1.4685166713003769586390939266086 absolute error = 8e-63 relative error = 5.4476739395242754247140901894985e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.1165453442798467353269155595782 y2[1] (numeric) = 0.1165453442798467353269155595782 absolute error = 2.1e-63 relative error = 1.8018737796659770920518827868036e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.399 Order of pole (three term test) = -6.198 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1660394088, alloc=4783252, time=87.83 x[1] = 5.21 y1[1] (analytic) = 1.4773276449775216918646184103044 y1[1] (numeric) = 1.4773276449775216918646184103044 absolute error = 8e-63 relative error = 5.4151833056110746231605921027741e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.12127460527181017927830228300415 y2[1] (numeric) = 0.12127460527181017927830228300415 absolute error = 2.1e-63 relative error = 1.7316073676705151169434704763777e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4043 Order of pole (three term test) = -6.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.22 y1[1] (analytic) = 1.4860908862879403844944672651737 y1[1] (numeric) = 1.4860908862879403844944672651737 absolute error = 8e-63 relative error = 5.3832508319749864111682343079404e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.12609173807097772083778515183022 y2[1] (numeric) = 0.12609173807097772083778515183022 absolute error = 2.0e-63 relative error = 1.5861467456925601190180443830834e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4095 Order of pole (three term test) = -6.604 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1664395156, alloc=4783252, time=88.04 x[1] = 5.23 y1[1] (analytic) = 1.4948055189148046714090995785478 y1[1] (numeric) = 1.4948055189148046714090995785478 absolute error = 7e-63 relative error = 4.6828834329444028449714214630752e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.13099626096808370720294728808506 y2[1] (numeric) = 0.13099626096808370720294728808506 absolute error = 2.0e-63 relative error = 1.5267611344168712983129283111116e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4145 Order of pole (three term test) = -6.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1668396036, alloc=4783252, time=88.25 x[1] = 5.24 y1[1] (analytic) = 1.5034706714021140358282745011865 y1[1] (numeric) = 1.5034706714021140358282745011865 absolute error = 8e-63 relative error = 5.3210216548749307179724809089120e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.13598768351492551656575677797294 y2[1] (numeric) = 0.13598768351492551656575677797294 absolute error = 1.9e-63 relative error = 1.3971853559748761131294968029082e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4193 Order of pole (three term test) = -7.019 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1672396800, alloc=4783252, time=88.46 x[1] = 5.25 y1[1] (analytic) = 1.5120854772418406831518162141691 y1[1] (numeric) = 1.5120854772418406831518162141691 absolute error = 8e-63 relative error = 5.2907061938010347015161580161482e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.14106550657340796966927431057729 y2[1] (numeric) = 0.14106550657340796966927431057729 absolute error = 1.8e-63 relative error = 1.2760029320585980064909585016655e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.424 Order of pole (three term test) = -7.231 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.26 y1[1] (analytic) = 1.5206490749605796216514577467554 y1[1] (numeric) = 1.5206490749605796216514577467554 absolute error = 8e-63 relative error = 5.2609113645811984046680438443276e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.14622922236545672337855271464404 y2[1] (numeric) = 0.14622922236545672337855271464404 absolute error = 1.8e-63 relative error = 1.2309441101324002041731760755223e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4285 Order of pole (three term test) = -7.444 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1676397564, alloc=4783252, time=88.68 x[1] = 5.27 y1[1] (analytic) = 1.5291606082056952850779026207164 y1[1] (numeric) = 1.5291606082056952850779026207164 absolute error = 8e-63 relative error = 5.2316283568062451120406445640596e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.1514783145237956549679656594851 y2[1] (numeric) = 0.1514783145237956549679656594851 absolute error = 1.7e-63 relative error = 1.1222728516252059461805780832102e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4328 Order of pole (three term test) = -7.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1680398252, alloc=4783252, time=88.89 x[1] = 5.28 y1[1] (analytic) = 1.5376192258309560825926322278478 y1[1] (numeric) = 1.5376192258309560825926322278478 absolute error = 7e-63 relative error = 4.5524925042590298405176317144076e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.15681225814358315942885113299026 y2[1] (numeric) = 0.15681225814358315942885113299026 absolute error = 1.6e-63 relative error = 1.0203283971173862255520241458817e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.437 Order of pole (three term test) = -7.878 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1684399216, alloc=4783252, time=89.11 x[1] = 5.29 y1[1] (analytic) = 1.5460240819816483126408276469977 y1[1] (numeric) = 1.5460240819816483126408276469977 absolute error = 8e-63 relative error = 5.1745636392324721718838888355674e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.16223051983490219621076903672188 y2[1] (numeric) = 0.16223051983490219621076903672188 absolute error = 1.5e-63 relative error = 9.2461024074046683760418939074607e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4409 Order of pole (three term test) = -8.098 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1688400140, alloc=4783252, time=89.32 x[1] = 5.3 y1[1] (analytic) = 1.5543743361791609294449466335608 y1[1] (numeric) = 1.5543743361791609294449466335608 absolute error = 8e-63 relative error = 5.1467653664849885512427091842180e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.16773255777609883643544033214541 y2[1] (numeric) = 0.16773255777609883643544033214541 absolute error = 1.5e-63 relative error = 8.9428076450268232197087544497593e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4447 Order of pole (three term test) = -8.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.31 y1[1] (analytic) = 1.562669153405032703712793494195 y1[1] (numeric) = 1.562669153405032703712793494195 absolute error = 9e-63 relative error = 5.7593765003866203304702211155888e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.17331782176796397677309498526352 y2[1] (numeric) = 0.17331782176796397677309498526352 absolute error = 1.4e-63 relative error = 8.0776459438447411475357302681939e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4483 Order of pole (three term test) = -8.544 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1692401000, alloc=4783252, time=89.53 x[1] = 5.32 y1[1] (analytic) = 1.5709077041844533729140501068966 y1[1] (numeric) = 1.5709077041844533729140501068966 absolute error = 9e-63 relative error = 5.7291717241099194147717551956479e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.17898575328875280185499235258526 y2[1] (numeric) = 0.17898575328875280185499235258526 absolute error = 1.4e-63 relative error = 7.8218515958720939984423761520675e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4518 Order of pole (three term test) = -8.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1696402408, alloc=4783252, time=89.74 x[1] = 5.33 y1[1] (analytic) = 1.5790891646692104310798244932856 y1[1] (numeric) = 1.5790891646692104310798244932856 absolute error = 9e-63 relative error = 5.6994881615094428388477684422672e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.18473578555003649332172215557053 y2[1] (numeric) = 0.18473578555003649332172215557053 absolute error = 1.3e-63 relative error = 7.0370772838048171748751818277299e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.455 Order of pole (three term test) = -8.997 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1700403308, alloc=4783252, time=89.95 x[1] = 5.34 y1[1] (analytic) = 1.5872127167200732635153590826657 y1[1] (numeric) = 1.5872127167200732635153590826657 absolute error = 8e-63 relative error = 5.0402821976702381389472344773816e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.19056734355338060038292414918256 y2[1] (numeric) = 0.19056734355338060038292414918256 absolute error = 1.2e-63 relative error = 6.2969865540675025316741955618823e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4581 Order of pole (three term test) = -9.226 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.35 y1[1] (analytic) = 1.5952775479886063880810806137854 y1[1] (numeric) = 1.5952775479886063880810806137854 absolute error = 8e-63 relative error = 5.0148013491989148840094161317716e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.19647984414784440409860233060843 y2[1] (numeric) = 0.19647984414784440409860233060843 absolute error = 1.1e-63 relative error = 5.5985386428354828626950162273526e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.461 Order of pole (three term test) = -9.456 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1704404444, alloc=4783252, time=90.16 TOP MAIN SOLVE Loop x[1] = 5.36 y1[1] (analytic) = 1.6032828519984036217860410431167 y1[1] (numeric) = 1.6032828519984036217860410431167 absolute error = 8e-63 relative error = 4.9897620934624488502287316235724e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.20247269608829552549352153390762 y2[1] (numeric) = 0.20247269608829552549352153390762 absolute error = 1.0e-63 relative error = 4.9389375422941664901002495347434e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.37 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4637 Order of pole (three term test) = -9.688 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1708405172, alloc=4783252, time=90.37 x[1] = 5.37 y1[1] (analytic) = 1.611227828225735049344785028739 y1[1] (numeric) = 1.611227828225735049344785028739 absolute error = 8e-63 relative error = 4.9651575400168609288069362046054e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.20854530009453394609247031570643 y2[1] (numeric) = 0.20854530009453394609247031570643 absolute error = 1.0e-63 relative error = 4.7951212496598977118055038187866e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4662 Order of pole (three term test) = -9.921 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1712406004, alloc=4783252, time=90.58 x[1] = 5.38 y1[1] (analytic) = 1.6191116821795987290679938861927 y1[1] (numeric) = 1.6191116821795987290679938861927 absolute error = 7e-63 relative error = 4.3233583433706152064099121223011e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.21469704891121952852360645852928 y2[1] (numeric) = 0.21469704891121952852360645852928 absolute error = 9e-64 relative error = 4.1919532875003027604319552805117e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.98 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4686 Order of pole (three term test) = -10.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1716407292, alloc=4783252, time=90.79 x[1] = 5.39 y1[1] (analytic) = 1.6269336254811691309830264844484 y1[1] (numeric) = 1.6269336254811691309830264844484 absolute error = 7e-63 relative error = 4.3025725760199558802560714011735e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.2209273273685970444877641912544 y2[1] (numeric) = 0.2209273273685970444877641912544 absolute error = 8e-64 relative error = 3.6211002483421761159820892099865e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.29 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4707 Order of pole (three term test) = -10.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.4 y1[1] (analytic) = 1.6346928759426343624067518389807 y1[1] (numeric) = 1.6346928759426343624067518389807 absolute error = 8e-63 relative error = 4.8938856452695159787001668441201e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.22723551244401263764153021726577 y2[1] (numeric) = 0.22723551244401263764153021726577 absolute error = 7e-64 relative error = 3.0805044179547830011600914928889e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4727 Order of pole (three term test) = -10.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1720408572, alloc=4783252, time=91.00 x[1] = 5.41 y1[1] (analytic) = 1.6423886576454142973138135876736 y1[1] (numeric) = 1.6423886576454142973138135876736 absolute error = 8e-63 relative error = 4.8709542426267599887882753699364e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.23362097332421556979906379088919 y2[1] (numeric) = 0.23362097332421556979906379088919 absolute error = 7e-64 relative error = 2.9963063248972549976533901079166e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.93 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4745 Order of pole (three term test) = -10.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1724409424, alloc=4783252, time=91.22 x[1] = 5.42 y1[1] (analytic) = 1.6500202010177517877525710803082 y1[1] (numeric) = 1.6500202010177517877525710803082 absolute error = 8e-63 relative error = 4.8484254890125019625653022030870e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.24008307146843902032995860887945 y2[1] (numeric) = 0.24008307146843902032995860887945 absolute error = 6e-64 relative error = 2.4991349716170019427292009938223e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.25 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.476 Order of pole (three term test) = -11.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1728410224, alloc=4783252, time=91.43 x[1] = 5.43 y1[1] (analytic) = 1.6575867429116691982522346148438 y1[1] (numeric) = 1.6575867429116691982522346148438 absolute error = 8e-63 relative error = 4.8262934257952800047040834153507e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.24662116067225363072577388837689 y2[1] (numeric) = 0.24662116067225363072577388837689 absolute error = 5e-64 relative error = 2.0274010495979837393941000336111e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4774 Order of pole (three term test) = -11.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1732411176, alloc=4783252, time=91.64 x[1] = 5.44 y1[1] (analytic) = 1.6650875266792825676318843385363 y1[1] (numeric) = 1.6650875266792825676318843385363 absolute error = 9e-63 relative error = 5.4051212658765635051389286314872e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.25323458713218740903398908799371 y2[1] (numeric) = 0.25323458713218740903398908799371 absolute error = 4e-64 relative error = 1.5795630625732876344914303789767e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4786 Order of pole (three term test) = -11.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.45 y1[1] (analytic) = 1.6725218022484657668587868348645 y1[1] (numeric) = 1.6725218022484657668587868348645 absolute error = 8e-63 relative error = 4.7831962424915161001729517317491e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.25992268951110553222278861742014 y2[1] (numeric) = 0.25992268951110553222278861742014 absolute error = 3e-64 relative error = 1.1541893497804165841582450275957e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.27 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4796 Order of pole (three term test) = -11.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1736412044, alloc=4783252, time=91.85 x[1] = 5.46 y1[1] (analytic) = 1.6798888261978570866032768193071 y1[1] (numeric) = 1.6798888261978570866032768193071 absolute error = 9e-63 relative error = 5.3574973889016041202879373660478e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.2666847990043435085509230441066 y2[1] (numeric) = 0.2666847990043435085509230441066 absolute error = 3e-64 relative error = 1.1249235094015009273842421791853e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4805 Order of pole (three term test) = -12.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1740412740, alloc=4783252, time=92.07 x[1] = 5.47 y1[1] (analytic) = 1.6871878618312007538939537370804 y1[1] (numeric) = 1.6871878618312007538939537370804 absolute error = 9e-63 relative error = 5.3343200265984542739545880696046e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.27352023940658708668152059583978 y2[1] (numeric) = 0.27352023940658708668152059583978 absolute error = 1e-64 relative error = 3.6560365776570659514864515040821e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.97 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4811 Order of pole (three term test) = -12.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1744413432, alloc=4783252, time=92.28 x[1] = 5.48 y1[1] (analytic) = 1.6944181792510159437834788005517 y1[1] (numeric) = 1.6944181792510159437834788005517 absolute error = 9e-63 relative error = 5.3115577430704102001745204237476e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.2804283271794922236046706498801 y2[1] (numeric) = 0.2804283271794922236046706498801 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.34 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -12.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.49 y1[1] (analytic) = 1.7015790554315859191851965250435 y1[1] (numeric) = 1.7015790554315859191851965250435 absolute error = 9e-63 relative error = 5.2892047367833013858510872596733e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.28740837152003834942833673574752 y2[1] (numeric) = 0.28740837152003834942833673574752 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1748414828, alloc=4783252, time=92.49 x[1] = 5.5 y1[1] (analytic) = 1.7086697742912600000274211813258 y1[1] (numeric) = 1.7086697742912600000274211813258 absolute error = 9e-63 relative error = 5.2672553441364142772753195631350e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.29445967442960809376808082447793 y2[1] (numeric) = 0.29445967442960809376808082447793 absolute error = 2e-64 relative error = 6.7921015122840155580297391494076e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -13.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.92 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1752415484, alloc=4783252, time=92.70 x[1] = 5.51 y1[1] (analytic) = 1.7156896267640611315887241762732 y1[1] (numeric) = 1.7156896267640611315887241762732 absolute error = 9e-63 relative error = 5.2457040362100793154261276957590e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.30158153078378656582052617869171 y2[1] (numeric) = 0.30158153078378656582052617869171 absolute error = 2e-64 relative error = 6.6317058435314591426290658952509e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.47 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -13.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1756416652, alloc=4783252, time=92.92 x[1] = 5.52 y1[1] (analytic) = 1.7226379108705918913170616076532 y1[1] (numeric) = 1.7226379108705918913170616076532 absolute error = 9e-63 relative error = 5.2245454156129381393618862668913e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.30877322840287320825071729003055 y2[1] (numeric) = 0.30877322840287320825071729003055 absolute error = 3e-64 relative error = 9.7158682296307664192552222317314e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.13 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4813 Order of pole (three term test) = -13.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1760417552, alloc=4783252, time=93.13 x[1] = 5.53 y1[1] (analytic) = 1.7295139317882318435911482223455 y1[1] (numeric) = 1.7295139317882318435911482223455 absolute error = 9e-63 relative error = 5.2037742134256445362621522520511e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.31603404812309917376674785034254 y2[1] (numeric) = 0.31603404812309917376674785034254 absolute error = 4e-64 relative error = 1.2656864106116662740272311512809e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.75 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4808 Order of pole (three term test) = -13.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.54 y1[1] (analytic) = 1.7363170019206192227470992412368 y1[1] (numeric) = 1.7363170019206192227470992412368 absolute error = 8e-63 relative error = 4.6074535877670011129417085277252e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.32336326386854310270334690980483 y2[1] (numeric) = 0.32336326386854310270334690980483 absolute error = 5e-64 relative error = 1.5462486184060321886931890583214e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4801 Order of pole (three term test) = -13.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1764418488, alloc=4783252, time=93.34 x[1] = 5.55 y1[1] (analytic) = 1.7430464409664099962599385961293 y1[1] (numeric) = 1.7430464409664099962599385961293 absolute error = 8e-63 relative error = 4.5896654340228028835948017608374e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.33076014272373811009659447825526 y2[1] (numeric) = 0.33076014272373811009659447825526 absolute error = 6e-64 relative error = 1.8140033289958397072027501648868e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.01 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4792 Order of pole (three term test) = -14.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1768419188, alloc=4783252, time=93.55 x[1] = 5.56 y1[1] (analytic) = 1.7497015759873074322309544561574 y1[1] (numeric) = 1.7497015759873074322309544561574 absolute error = 8e-63 relative error = 4.5722082609920636336026433588662e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.33822394500696272161156471904958 y2[1] (numeric) = 0.33822394500696272161156471904958 absolute error = 7e-64 relative error = 2.0696346616901701327296812663913e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.478 Order of pole (three term test) = -14.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.77 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1772419944, alloc=4783252, time=93.76 x[1] = 5.57 y1[1] (analytic) = 1.7562817414753553682808444254304 y1[1] (numeric) = 1.7562817414753553682808444254304 absolute error = 8e-63 relative error = 4.5550778164325966804102749853966e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.3457539243442084292903795474788 y2[1] (numeric) = 0.3457539243442084292903795474788 absolute error = 7e-64 relative error = 2.0245612579168557734439019112515e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4767 Order of pole (three term test) = -14.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.44 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.58 y1[1] (analytic) = 1.7627862794194884525778386345335 y1[1] (numeric) = 1.7627862794194884525778386345335 absolute error = 8e-63 relative error = 4.5382699499082317064781797228823e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.35334932774381647042673725271193 y2[1] (numeric) = 0.35334932774381647042673725271193 absolute error = 9e-64 relative error = 2.5470545132960134431943269842401e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4753 Order of pole (three term test) = -14.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.11 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1776420732, alloc=4783252, time=93.98 TOP MAIN SOLVE Loop x[1] = 5.59 y1[1] (analytic) = 1.7692145393713327020321562629051 y1[1] (numeric) = 1.7692145393713327020321562629051 absolute error = 8e-63 relative error = 4.5217806105316631630363649724701e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.36100939567177636595122579880666 y2[1] (numeric) = 0.36100939567177636595122579880666 absolute error = 1.0e-63 relative error = 2.7700110079937727698334594651288e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.61 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4736 Order of pole (three term test) = -15.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1780422096, alloc=4783252, time=94.19 x[1] = 5.6 y1[1] (analytic) = 1.7755658785102497976558096621573 y1[1] (numeric) = 1.7755658785102497976558096621573 absolute error = 8e-63 relative error = 4.5056058447756538433469429789379e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.36873336212767868853633084628333 y2[1] (numeric) = 0.36873336212767868853633084628333 absolute error = 1.1e-63 relative error = 2.9831854477521098141652387122011e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4717 Order of pole (three term test) = -15.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1784422940, alloc=4783252, time=94.40 x[1] = 5.61 y1[1] (analytic) = 1.7818396617076186127124234987124 y1[1] (numeric) = 1.7818396617076186127124234987124 absolute error = 8e-63 relative error = 4.4897417943504711000170809651842e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.37652045472131446520762175590142 y2[1] (numeric) = 0.37652045472131446520762175590142 absolute error = 1.2e-63 relative error = 3.1870778465095408802675875448385e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4697 Order of pole (three term test) = -15.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1788423852, alloc=4783252, time=94.61 x[1] = 5.62 y1[1] (analytic) = 1.788035261590347545557821695409 y1[1] (numeric) = 1.788035261590347545557821695409 absolute error = 8e-63 relative error = 4.4741846941455121826251410366109e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.38436989474991355458468707877178 y2[1] (numeric) = 0.38436989474991355458468707877178 absolute error = 1.2e-63 relative error = 3.1219926856674559628848674953839e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.62 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4674 Order of pole (three term test) = -15.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.63 y1[1] (analytic) = 1.7941520586036113059910248809931 y1[1] (numeric) = 1.7941520586036113059910248809931 absolute error = 8e-63 relative error = 4.4589308702331510599838303111051e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.39228089727601427497846053907225 y2[1] (numeric) = 0.39228089727601427497846053907225 absolute error = 1.3e-63 relative error = 3.3139518366230869164677701667194e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.3 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.465 Order of pole (three term test) = -16.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.54 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1792424676, alloc=4783252, time=94.83 x[1] = 5.64 y1[1] (analytic) = 1.8001894410728058814893037287734 y1[1] (numeric) = 1.8001894410728058814893037287734 absolute error = 8e-63 relative error = 4.4439767379329120041632517464525e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.4002526712059564964470189172122 y2[1] (numeric) = 0.4002526712059564964470189172122 absolute error = 1.4e-63 relative error = 3.4977905226261621091201372695354e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.99 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4624 Order of pole (three term test) = -16.36 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.24 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1796425432, alloc=4783252, time=95.05 x[1] = 5.65 y1[1] (analytic) = 1.8061468052647154878822936455404 y1[1] (numeric) = 1.8061468052647154878822936455404 absolute error = 9e-63 relative error = 4.9829836499259134431214573938373e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.40828441936899034756605694566804 y2[1] (numeric) = 0.40828441936899034756605694566804 absolute error = 1.5e-63 relative error = 3.6739094828018966430719846914341e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4596 Order of pole (three term test) = -16.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1800426336, alloc=4783252, time=95.26 x[1] = 5.66 y1[1] (analytic) = 1.8120235554478853878210756882658 y1[1] (numeric) = 1.8120235554478853878210756882658 absolute error = 9e-63 relative error = 4.9668228500348786147945786157444e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.4163753385969926261092858725629 y2[1] (numeric) = 0.4163753385969926261092858725629 absolute error = 1.6e-63 relative error = 3.8426867580373944746071341311487e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4566 Order of pole (three term test) = -16.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1804427140, alloc=4783252, time=95.47 x[1] = 5.67 y1[1] (analytic) = 1.8178191039521945398106873148475 y1[1] (numeric) = 1.8178191039521945398106873148475 absolute error = 9e-63 relative error = 4.9509876865265270337625526462421e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.42452461980478294206411777393379 y2[1] (numeric) = 0.42452461980478294206411777393379 absolute error = 1.7e-63 relative error = 4.0044791766888399627769509066227e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4534 Order of pole (three term test) = -17.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.68 y1[1] (analytic) = 1.8235328712276221205908034265397 y1[1] (numeric) = 1.8235328712276221205908034265397 absolute error = 9e-63 relative error = 4.9354745077565299487396007343170e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.43273144807103156143526394233455 y2[1] (numeric) = 0.43273144807103156143526394233455 absolute error = 1.8e-63 relative error = 4.1596237297376534360256574944563e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4501 Order of pole (three term test) = -17.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1808428292, alloc=4783252, time=95.68 x[1] = 5.69 y1[1] (analytic) = 1.8291642859022020442613215727059 y1[1] (numeric) = 1.8291642859022020442613215727059 absolute error = 9e-63 relative error = 4.9202797525433389647217008418441e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.44099500271975086011928997036201 y2[1] (numeric) = 0.44099500271975086011928997036201 absolute error = 1.9e-63 relative error = 4.3084388446175574475448434083369e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4465 Order of pole (three term test) = -17.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1812429452, alloc=4783252, time=95.90 x[1] = 5.7 y1[1] (analytic) = 1.8347127848391596827492340309974 y1[1] (numeric) = 1.8347127848391596827492340309974 absolute error = 9e-63 relative error = 4.9053999483570318522283780802707e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.44931445740236223877264939212753 y2[1] (numeric) = 0.44931445740236223877264939212753 absolute error = 2.0e-63 relative error = 4.4512255660827644278289609624904e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4428 Order of pole (three term test) = -17.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1816430408, alloc=4783252, time=96.11 x[1] = 5.71 y1[1] (analytic) = 1.840177813193225073992353850756 y1[1] (numeric) = 1.840177813193225073992353850756 absolute error = 9e-63 relative error = 4.8908317095631500699087658488398e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.45768898018033029205009794707004 y2[1] (numeric) = 0.45768898018033029205009794707004 absolute error = 2.1e-63 relative error = 4.5882686517219535721193701658978e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4389 Order of pole (three term test) = -17.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.72 y1[1] (analytic) = 1.8455588244661169865660040040995 y1[1] (numeric) = 1.8455588244661169865660040040995 absolute error = 9e-63 relative error = 4.8765717357199485708580535081230e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.46611773360835596886542620284383 y2[1] (numeric) = 0.46611773360835596886542620284383 absolute error = 2.2e-63 relative error = 4.7198375890338817695996894169664e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4349 Order of pole (three term test) = -18.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1820431212, alloc=4783252, time=96.32 x[1] = 5.73 y1[1] (analytic) = 1.8508552805611922923924435421742 y1[1] (numeric) = 1.8508552805611922923924435421742 absolute error = 9e-63 relative error = 4.8626168099275362714532359335984e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.47459987481812040442781186647779 y2[1] (numeric) = 0.47459987481812040442781186647779 absolute error = 2.3e-63 relative error = 4.8461875403600193318796332883392e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4306 Order of pole (three term test) = -18.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1824431936, alloc=4783252, time=96.54 x[1] = 5.74 y1[1] (analytic) = 1.8560666518372551826413008060802 y1[1] (numeric) = 1.8560666518372551826413008060802 absolute error = 9e-63 relative error = 4.8489637972274412306820134796954e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.48313455560257104974037444265051 y2[1] (numeric) = 0.48313455560257104974037444265051 absolute error = 2.4e-63 relative error = 4.9675602214101453015223923616058e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4262 Order of pole (three term test) = -18.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1828432868, alloc=4783252, time=96.75 x[1] = 5.75 y1[1] (analytic) = 1.8611924171615208459442645129289 y1[1] (numeric) = 1.8611924171615208459442645129289 absolute error = 9e-63 relative error = 4.8356096430511882102720436334727e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.49172092250074167001822059073657 y2[1] (numeric) = 0.49172092250074167001822059073657 absolute error = 2.4e-63 relative error = 4.8808173298673904690765438753185e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4217 Order of pole (three term test) = -18.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1832434012, alloc=4783252, time=96.96 x[1] = 5.76 y1[1] (analytic) = 1.8662320639617283126003474993147 y1[1] (numeric) = 1.8662320639617283126003474993147 absolute error = 9e-63 relative error = 4.8225513717165279497454290474614e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.50035811688309773009682147249262 y2[1] (numeric) = 0.50035811688309773009682147249262 absolute error = 2.5e-63 relative error = 4.9964213942872700561885479017481e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4169 Order of pole (three term test) = -19.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.77 y1[1] (analytic) = 1.8711850882773972535307298212406 y1[1] (numeric) = 1.8711850882773972535307298212406 absolute error = 9e-63 relative error = 4.8097860849700072801985681942338e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.50904527503739863236330217008544 y2[1] (numeric) = 0.50904527503739863236330217008544 absolute error = 2.6e-63 relative error = 5.1076006938852005244343743674315e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.412 Order of pole (three term test) = -19.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1836434888, alloc=4783252, time=97.17 x[1] = 5.78 y1[1] (analytic) = 1.8760509948102236083459995829373 y1[1] (numeric) = 1.8760509948102236083459995829373 absolute error = 9e-63 relative error = 4.7973109605746171967676377084859e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.51778152825506822105840167195699 y2[1] (numeric) = 0.51778152825506822105840167195699 absolute error = 2.7e-63 relative error = 5.2145545035162646033522258861685e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4069 Order of pole (three term test) = -19.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1840435628, alloc=4783252, time=97.39 x[1] = 5.79 y1[1] (analytic) = 1.8808292969736090030049809872269 y1[1] (numeric) = 1.8808292969736090030049809872269 absolute error = 1.0e-62 relative error = 5.3168036121570025438366731729951e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.52656600291806491597064841086205 y2[1] (numeric) = 0.52656600291806491597064841086205 absolute error = 2.8e-63 relative error = 5.3174720443083514428373241408589e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4017 Order of pole (three term test) = -19.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1844436296, alloc=4783252, time=97.60 x[1] = 5.8 y1[1] (analytic) = 1.8855195169413190041646581017615 y1[1] (numeric) = 1.8855195169413190041646581017615 absolute error = 9e-63 relative error = 4.7732202818031595689272627606328e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.53539782058624278858177347329741 y2[1] (numeric) = 0.53539782058624278858177347329741 absolute error = 2.9e-63 relative error = 5.4165330684846579119170936370433e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3963 Order of pole (three term test) = -19.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.81 y1[1] (analytic) = 1.8901211856952653444363077588889 y1[1] (numeric) = 1.8901211856952653444363077588889 absolute error = 9e-63 relative error = 4.7615994509311977886119438759723e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.54427609808519484462854759312049 y2[1] (numeric) = 0.54427609808519484462854759312049 absolute error = 3.0e-63 relative error = 5.5119084055945697982471115917976e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3907 Order of pole (three term test) = -20.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1848437060, alloc=4783252, time=97.81 x[1] = 5.82 y1[1] (analytic) = 1.8946338430724073403651343641758 y1[1] (numeric) = 1.8946338430724073403651343641758 absolute error = 9e-63 relative error = 4.7502582268905699240923222774744e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.55319994759456972882598823711744 y2[1] (numeric) = 0.55319994759456972882598823711744 absolute error = 3.1e-63 relative error = 5.6037604730070114326284084696085e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.385 Order of pole (three term test) = -20.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1852437848, alloc=4783252, time=98.03 x[1] = 5.83 y1[1] (analytic) = 1.8990570378107678130306930348074 y1[1] (numeric) = 1.8990570378107678130306930348074 absolute error = 1.0e-62 relative error = 5.2657712753735906559532738483371e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.56216847673685302015506147042438 y2[1] (numeric) = 0.56216847673685302015506147042438 absolute error = 3.2e-63 relative error = 5.6922437532866090465947427334198e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3792 Order of pole (three term test) = -20.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1856438748, alloc=4783252, time=98.25 x[1] = 5.84 y1[1] (analytic) = 1.903390327594558909714387498229 y1[1] (numeric) = 1.903390327594558909714387498229 absolute error = 1.0e-62 relative error = 5.2537831337189076868416007999943e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.57118078866660423965933399774091 y2[1] (numeric) = 0.57118078866660423965933399774091 absolute error = 3.3e-63 relative error = 5.7775052408602554604629525389552e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3731 Order of pole (three term test) = -20.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1860439876, alloc=4783252, time=98.46 x[1] = 5.85 y1[1] (analytic) = 1.90763327909841331408948072728 y1[1] (numeric) = 1.90763327909841331408948072728 absolute error = 1.0e-62 relative error = 5.2420976869968453689582750386638e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.58023598216014064712415964041523 y2[1] (numeric) = 0.58023598216014064712415964041523 absolute error = 3.4e-63 relative error = 5.8596848601878438392775816871964e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.367 Order of pole (three term test) = -20.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.86 y1[1] (analytic) = 1.9117854680307164218494585297175 y1[1] (numeric) = 1.9117854680307164218494585297175 absolute error = 1.0e-62 relative error = 5.2307124241825920347489552300374e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.5893331517056588583334685788649 y2[1] (numeric) = 0.5893331517056588583334685788649 absolute error = 3.5e-63 relative error = 5.9389158574742241443604220303983e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3607 Order of pole (three term test) = -20.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1864440896, alloc=4783252, time=98.67 x[1] = 5.87 y1[1] (analytic) = 1.9158464791760351485932932817607 y1[1] (numeric) = 1.9158464791760351485932932817607 absolute error = 1.0e-62 relative error = 5.2196249066369803600317103433371e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.59847138759378527081753477878537 y2[1] (numeric) = 0.59847138759378527081753477878537 absolute error = 3.5e-63 relative error = 5.8482328020260148240721031005191e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3542 Order of pole (three term test) = -21.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1868442068, alloc=4783252, time=98.89 x[1] = 5.88 y1[1] (analytic) = 1.9198159064366391271221765013287 y1[1] (numeric) = 1.9198159064366391271221765013287 absolute error = 1.0e-62 relative error = 5.2088327669713659551814502842531e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.60764977600854624312460526099845 y2[1] (numeric) = 0.60764977600854624312460526099845 absolute error = 3.6e-63 relative error = 5.9244652794035886871435866267666e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3476 Order of pole (three term test) = -21.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1872442724, alloc=4783252, time=99.10 x[1] = 5.89 y1[1] (analytic) = 1.9236933528731101420625914701266 y1[1] (numeric) = 1.9236933528731101420625914701266 absolute error = 1.0e-62 relative error = 5.1983337079501858764872704781611e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.6168673991187489306742722820455 y2[1] (numeric) = 0.6168673991187489306742722820455 absolute error = 3.7e-63 relative error = 5.9980475630350798709596898225998e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3409 Order of pole (three term test) = -21.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.9 y1[1] (analytic) = 1.9274784307440357409061046800325 y1[1] (numeric) = 1.9274784307440357409061046800325 absolute error = 9e-63 relative error = 4.6693129512872755098828793096911e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.62612333516976364018515353101662 y2[1] (numeric) = 0.62612333516976364018515353101662 absolute error = 3.8e-63 relative error = 6.0690918011699546116030294086530e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.334 Order of pole (three term test) = -21.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1876443576, alloc=4783252, time=99.31 TOP MAIN SOLVE Loop x[1] = 5.91 y1[1] (analytic) = 1.9311707615447830521378500235795 y1[1] (numeric) = 1.9311707615447830521378500235795 absolute error = 9e-63 relative error = 4.6603853886026710736111836779499e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.63541665857569852451792261500197 y2[1] (numeric) = 0.63541665857569852451792261500197 absolute error = 3.9e-63 relative error = 6.1377049961861910925371552615308e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.327 Order of pole (three term test) = -21.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1880444532, alloc=4783252, time=99.53 x[1] = 5.92 y1[1] (analytic) = 1.9347699760453489331042042875189 y1[1] (numeric) = 1.9347699760453489331042042875189 absolute error = 1.0e-62 relative error = 5.1685730726708417380791825934553e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.64474644001195740054101751977893 y2[1] (numeric) = 0.64474644001195740054101751977893 absolute error = 4.0e-63 relative error = 6.2039892766617159069025310275776e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3198 Order of pole (three term test) = -21.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1884445844, alloc=4783252, time=99.74 x[1] = 5.93 y1[1] (analytic) = 1.938275714327282662636408866662 y1[1] (numeric) = 1.938275714327282662636408866662 absolute error = 9e-63 relative error = 4.6433022575034583927818949785062e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.65411174650817143431437173267238 y2[1] (numeric) = 0.65411174650817143431437173267238 absolute error = 4.2e-63 relative error = 6.4209212300814901570195760979300e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3126 Order of pole (three term test) = -22.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1888446528, alloc=4783252, time=99.96 x[1] = 5.94 y1[1] (analytic) = 1.9416876258196774861916441437897 y1[1] (numeric) = 1.9416876258196774861916441437897 absolute error = 9e-63 relative error = 4.6351430993956494707272123093800e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.66351164154149540050009246731935 y2[1] (numeric) = 0.66351164154149540050009246731935 absolute error = 4.2e-63 relative error = 6.3299567589234768673462725738835e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3052 Order of pole (three term test) = -22.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.95 y1[1] (analytic) = 1.9450053693342274143870352824965 y1[1] (numeric) = 1.9450053693342274143870352824965 absolute error = 9e-63 relative error = 4.6272365834551332186860877611477e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.67294518513025918645189154620177 y2[1] (numeric) = 0.67294518513025918645189154620177 absolute error = 4.3e-63 relative error = 6.3898220761735102908646296009876e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2977 Order of pole (three term test) = -22.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1892447548, alloc=4783252, time=100.17 x[1] = 5.96 y1[1] (analytic) = 1.9482286130993457692759499337911 y1[1] (numeric) = 1.9482286130993457692759499337911 absolute error = 9e-63 relative error = 4.6195810591665220379064899205795e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.68241143392796517591090265779117 y2[1] (numeric) = 0.68241143392796517591090265779117 absolute error = 4.5e-63 relative error = 6.5942623119574173571646469520339e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.29 Order of pole (three term test) = -22.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1896448412, alloc=4783252, time=100.38 x[1] = 5.97 y1[1] (analytic) = 1.9513570347933420665403922538039 y1[1] (numeric) = 1.9513570347933420665403922538039 absolute error = 9e-63 relative error = 4.6121749323814247761584805712246e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.69190944131762211264784629855594 y2[1] (numeric) = 0.69190944131762211264784629855594 absolute error = 4.5e-63 relative error = 6.5037412864760548230103622917305e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2823 Order of pole (three term test) = -22.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1900449500, alloc=4783252, time=100.59 x[1] = 5.98 y1[1] (analytic) = 1.9543903215766539159389213028699 y1[1] (numeric) = 1.9543903215766539159389213028699 absolute error = 9e-63 relative error = 4.6050166646033543815286248172595e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.70143825750640601074378947433419 y2[1] (numeric) = 0.70143825750640601074378947433419 absolute error = 4.6e-63 relative error = 6.5579542472531727778404164965030e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2744 Order of pole (three term test) = -22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 5.99 y1[1] (analytic) = 1.9573281701231307168469088616542 y1[1] (numeric) = 1.9573281701231307168469088616542 absolute error = 1.0e-62 relative error = 5.1090053025553321059706116952282e-61 % Correct digits = 64 bytes used=1904451032, alloc=4783252, time=100.81 h = 0.01 y2[1] (analytic) = 0.71099692962063864549735591405603 y2[1] (numeric) = 0.71099692962063864549735591405603 absolute error = 4.7e-63 relative error = 6.6104364227110574375803280524384e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2665 Order of pole (three term test) = -23.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6 y1[1] (analytic) = 1.9601702866503660205456522979229 y1[1] (numeric) = 1.9601702866503660205456522979229 absolute error = 1.0e-62 relative error = 5.1015975847121346886927851693976e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.72058450180107412718844455338811 y2[1] (numeric) = 0.72058450180107412718844455338811 absolute error = 4.8e-63 relative error = 6.6612590029380020737432868762754e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2584 Order of pole (three term test) = -23.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1908452440, alloc=4783252, time=101.02 x[1] = 6.01 y1[1] (analytic) = 1.9629163869490755260493904569901 y1[1] (numeric) = 1.9629163869490755260493904569901 absolute error = 1.0e-62 relative error = 5.0944605009604174857161493669980e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.73020001529848402912048512990378 y2[1] (numeric) = 0.73020001529848402912048512990378 absolute error = 4.9e-63 relative error = 6.7104901360444725091113199258718e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2502 Order of pole (three term test) = -23.28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1912453492, alloc=4783252, time=101.23 x[1] = 6.02 y1[1] (analytic) = 1.9655661964115177716951214558362 y1[1] (numeric) = 1.9655661964115177716951214558362 absolute error = 1.0e-62 relative error = 5.0875925818508354309447609093762e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.73984250856953151150808067207442 y2[1] (numeric) = 0.73984250856953151150808067207442 absolute error = 5.0e-63 relative error = 6.7581950781219439503883411932527e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2419 Order of pole (three term test) = -23.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1916454416, alloc=4783252, time=101.45 x[1] = 6.03 y1[1] (analytic) = 1.9681194500589546804497472298303 y1[1] (numeric) = 1.9681194500589546804497472298303 absolute error = 9e-63 relative error = 4.5728931746141762605718830112174e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.74951101737292485387754295475596 y2[1] (numeric) = 0.74951101737292485387754295475596 absolute error = 5.1e-63 relative error = 6.8044363348730557406848920907736e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2335 Order of pole (three term test) = -23.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.04 y1[1] (analytic) = 1.9705758925681492129028978290782 y1[1] (numeric) = 1.9705758925681492129028978290782 absolute error = 9e-63 relative error = 4.5671927855926256372214647697052e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.75920457486584078070720854419957 y2[1] (numeric) = 0.75920457486584078070720854419957 absolute error = 5.1e-63 relative error = 6.7175569916727941234517124111960e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2251 Order of pole (three term test) = -23.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1920455088, alloc=4783252, time=101.65 x[1] = 6.05 y1[1] (analytic) = 1.9729352782968974782022174858561 y1[1] (numeric) = 1.9729352782968974782022174858561 absolute error = 9e-63 relative error = 4.5617309898625237988536344401480e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.76892221170060793805532390450696 y2[1] (numeric) = 0.76892221170060793805532390450696 absolute error = 5.2e-63 relative error = 6.7627126917029449750222267169733e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2165 Order of pole (three term test) = -23.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1924456132, alloc=4783252, time=101.86 x[1] = 6.06 y1[1] (analytic) = 1.9751973713085927497412956127139 y1[1] (numeric) = 1.9751973713085927497412956127139 absolute error = 9e-63 relative error = 4.5565066715522147568771463022637e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.77866295612164085290840607231132 y2[1] (numeric) = 0.77866295612164085290840607231132 absolute error = 5.3e-63 relative error = 6.8065392842086695544744595149413e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2079 Order of pole (three term test) = -23.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1928456852, alloc=4848776, time=102.06 x[1] = 6.07 y1[1] (analytic) = 1.9773619453958189292191438829885 y1[1] (numeric) = 1.9773619453958189292191438829885 absolute error = 8e-63 relative error = 4.0457944579279328498567918747431e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.78842583406261468193492209381295 y2[1] (numeric) = 0.78842583406261468193492209381295 absolute error = 5.5e-63 relative error = 6.9759256513190366034365564404297e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1991 Order of pole (three term test) = -23.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1932458216, alloc=4848776, time=102.28 x[1] = 6.08 y1[1] (analytic) = 1.9794287841029710997444746005297 y1[1] (numeric) = 1.9794287841029710997444746005297 absolute error = 9e-63 relative error = 4.5467662551338419247862174734445e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.79820986924387103225039054359125 y2[1] (numeric) = 0.79820986924387103225039054359125 absolute error = 5.6e-63 relative error = 7.0156987726859016050918948664997e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1903 Order of pole (three term test) = -24.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.09 y1[1] (analytic) = 1.9813976807479009059483203288902 y1[1] (numeric) = 1.9813976807479009059483203288902 absolute error = 8e-63 relative error = 4.0375539336355283080874425794074e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.80801408327004511369299986177423 y2[1] (numeric) = 0.80801408327004511369299986177423 absolute error = 5.6e-63 relative error = 6.9305722708900270778448182090005e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1814 Order of pole (three term test) = -24.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1936458948, alloc=4848776, time=102.48 x[1] = 6.1 y1[1] (analytic) = 1.983268438442584596585021274648 y1[1] (numeric) = 1.983268438442584596585021274648 absolute error = 8e-63 relative error = 4.0337454299843632191880307759244e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.81783749572790445997587163677534 y2[1] (numeric) = 0.81783749572790445997587163677534 absolute error = 5.8e-63 relative error = 7.0918734226507843175717253836919e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1725 Order of pole (three term test) = -24.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1940460308, alloc=4848776, time=102.69 x[1] = 6.11 y1[1] (analytic) = 1.9850408701128116628345436375483 y1[1] (numeric) = 1.9850408701128116628345436375483 absolute error = 8e-63 relative error = 4.0301437216984619491955348220709e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.82767912428438943492538560312259 y2[1] (numeric) = 0.82767912428438943492538560312259 absolute error = 5.8e-63 relative error = 7.0075465598032019394562349133227e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1635 Order of pole (three term test) = -24.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1944461176, alloc=4848776, time=102.90 x[1] = 6.12 y1[1] (analytic) = 1.9867147985168921034587058395238 y1[1] (numeric) = 1.9867147985168921034587058395238 absolute error = 8e-63 relative error = 4.0267480797808028985868540111585e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.83753798478484571983664267141119 y2[1] (numeric) = 0.83753798478484571983664267141119 absolute error = 5.9e-63 relative error = 7.0444566183056700322117985732006e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1544 Order of pole (three term test) = -24.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.13 y1[1] (analytic) = 1.9882900562633804461003863456359 y1[1] (numeric) = 1.9882900562633804461003863456359 absolute error = 7e-63 relative error = 3.5206130906046936210446328872211e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.84741309135143895877919057733864 y2[1] (numeric) = 0.84741309135143895877919057733864 absolute error = 6.0e-63 relative error = 7.0803720891676446914999105747519e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1452 Order of pole (three term test) = -24.48 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1948462064, alloc=4848776, time=103.11 x[1] = 6.14 y1[1] (analytic) = 1.9897664858278147523383531246708 y1[1] (numeric) = 1.9897664858278147523383531246708 absolute error = 7e-63 relative error = 3.5180007552935273588300234206111e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.85730345648174172047049350830549 y2[1] (numeric) = 0.85730345648174172047049350830549 absolute error = 6.1e-63 relative error = 7.1153334958353964689895348432235e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.136 Order of pole (three term test) = -24.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1952463144, alloc=4848776, time=103.31 x[1] = 6.15 y1[1] (analytic) = 1.9911439395684689326111583908272 y1[1] (numeric) = 1.9911439395684689326111583908272 absolute error = 7e-63 relative error = 3.5155670370656761238376259782825e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.86720809114748291810311388832781 y2[1] (numeric) = 0.86720809114748291810311388832781 absolute error = 6.1e-63 relative error = 7.0340672120903853991227061332791e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1267 Order of pole (three term test) = -24.61 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1956464004, alloc=4848776, time=103.52 x[1] = 6.16 y1[1] (analytic) = 1.9924222797411167957917331223665 y1[1] (numeric) = 1.9924222797411167957917331223665 absolute error = 6e-63 relative error = 3.0114098105646577195187701665902e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.87712600489344981226591451196916 y2[1] (numeric) = 0.87712600489344981226591451196916 absolute error = 6.1e-63 relative error = 6.9545310091917826386094931125835e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1174 Order of pole (three term test) = -24.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1960464716, alloc=4848776, time=103.73 x[1] = 6.17 y1[1] (analytic) = 1.9936013785128063570200272314103 y1[1] (numeric) = 1.9936013785128063570200272314103 absolute error = 6e-63 relative error = 3.0096287375542951952714783185829e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.88705620593653270684140696811863 y2[1] (numeric) = 0.88705620593653270684140696811863 absolute error = 6.1e-63 relative error = 6.8766781170983027269583856796076e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1081 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.18 y1[1] (analytic) = 1.9946811179746430263743906724648 y1[1] (numeric) = 1.9946811179746430263743906724648 absolute error = 6e-63 relative error = 3.0079995974957004463204338355044e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.89699770126490243349219359023036 y2[1] (numeric) = 0.89699770126490243349219359023036 absolute error = 6.2e-63 relative error = 6.9119463642516165021277204677058e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09866 Order of pole (three term test) = -24.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1964465536, alloc=4848776, time=103.94 x[1] = 6.19 y1[1] (analytic) = 1.9956613901535804000734809732792 y1[1] (numeric) = 1.9956613901535804000734809732792 absolute error = 6e-63 relative error = 3.0065220631132504591459373685639e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.90694949673731070707070191707552 y2[1] (numeric) = 0.90694949673731070707070191707552 absolute error = 6.3e-63 relative error = 6.9463625291858285921982225113784e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08922 Order of pole (three term test) = -24.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1968466196, alloc=4848776, time=104.15 x[1] = 6.2 y1[1] (analytic) = 1.9965420970232174751394026238693 y1[1] (numeric) = 1.9965420970232174751394026238693 absolute error = 6e-63 relative error = 3.0051958378167004110740042755987e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.91691059718250342199942071090163 y2[1] (numeric) = 0.91691059718250342199942071090163 absolute error = 6.3e-63 relative error = 6.8708988851898255912957367061879e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07974 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1972467064, alloc=4848776, time=104.35 x[1] = 6.21 y1[1] (analytic) = 1.9973231505136012078096096586582 y1[1] (numeric) = 1.9973231505136012078096096586582 absolute error = 6e-63 relative error = 3.0040206555745029856645479979420e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.92688000649873694837484364690016 y2[1] (numeric) = 0.92688000649873694837484364690016 absolute error = 6.3e-63 relative error = 6.7969963272787295334300116469397e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07022 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.22 y1[1] (analytic) = 1.9980044725200334354498990129263 y1[1] (numeric) = 1.9980044725200334354498990129263 absolute error = 6e-63 relative error = 3.0029962808002871814654061722655e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.93685672775338747624844024993293 y2[1] (numeric) = 0.93685672775338747624844024993293 absolute error = 6.4e-63 relative error = 6.8313540484972612189431217801980e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06068 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1976467784, alloc=4848776, time=104.56 TOP MAIN SOLVE Loop x[1] = 6.23 y1[1] (analytic) = 1.9985859949108812812836424313629 y1[1] (numeric) = 1.9985859949108812812836424313629 absolute error = 6e-63 relative error = 3.0021225082524133825750103296523e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.9468397632826434472332334916325 y2[1] (numeric) = 0.9468397632826434472332334916325 absolute error = 6.4e-63 relative error = 6.7593274471400926889063407119755e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05112 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1980468768, alloc=4848776, time=104.77 x[1] = 6.24 y1[1] (analytic) = 1.9990676595343902609032926544429 y1[1] (numeric) = 1.9990676595343902609032926544429 absolute error = 6e-63 relative error = 3.0013991629465311250068495300833e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.95682811479127110427590013953252 y2[1] (numeric) = 0.95682811479127110427590013953252 absolute error = 6.5e-63 relative error = 6.7932786458913297610438690659816e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04153 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1984469472, alloc=4848776, time=104.98 x[1] = 6.25 y1[1] (analytic) = 1.999449418224499409259190301842 y1[1] (numeric) = 1.999449418224499409259190301842 absolute error = 6e-63 relative error = 3.0008261000810755759975112600967e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.96682078345244318312255432921071 y2[1] (numeric) = 0.96682078345244318312255432921071 absolute error = 6.5e-63 relative error = 6.7230660648284746163610135630738e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03193 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1988470184, alloc=4848776, time=105.19 x[1] = 6.26 y1[1] (analytic) = 1.999731232805657846617818495209 y1[1] (numeric) = 1.999731232805657846617818495209 absolute error = 6e-63 relative error = 3.0004032049756482549621539097585e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.97681677000762076269225808000719 y2[1] (numeric) = 0.97681677000762076269225808000719 absolute error = 6.6e-63 relative error = 6.7566407566369988142165396629654e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02232 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.27 y1[1] (analytic) = 1.999913075096642301836923186416 y1[1] (numeric) = 1.999913075096642301836923186416 absolute error = 6e-63 relative error = 3.0001303930222369754782557168545e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.9868150748664782862564560011288 y2[1] (numeric) = 0.9868150748664782862564560011288 absolute error = 6.6e-63 relative error = 6.6881831947014162526725730242359e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0127 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1992471436, alloc=4848776, time=105.39 x[1] = 6.28 y1[1] (analytic) = 1.9999949269133752112083529380473 y1[1] (numeric) = 1.9999949269133752112083529380473 absolute error = 6e-63 relative error = 3.0000076096492393880753075162014e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.99681469820686176100548681808265 y2[1] (numeric) = 0.99681469820686176100548681808265 absolute error = 6.7e-63 relative error = 6.7214097184285271736698264092353e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.003067 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1996472252, alloc=4848776, time=105.61 x[1] = 6.29 y1[1] (analytic) = 1.9999767800707431110610822800232 y1[1] (numeric) = 1.9999767800707431110610822800232 absolute error = 5e-63 relative error = 2.5000290252485532202083427808432e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0068146400747701402655132902638 y2[1] (numeric) = 1.0068146400747701402655132902638 absolute error = 6e-63 relative error = 5.9593889095160710568717386524102e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.006571 Order of pole (three term test) = -0.894 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2000473104, alloc=4848776, time=105.82 x[1] = 6.3 y1[1] (analytic) = 1.9998586363834151422866736621397 y1[1] (numeric) = 1.9998586363834151422866736621397 absolute error = 5e-63 relative error = 2.5001767170114089945631747089485e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0168139004843498903109663674941 y2[1] (numeric) = 1.0168139004843498903109663674941 absolute error = 7e-63 relative error = 6.8842489236876234568965976011603e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01621 Order of pole (three term test) = -0.8997 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.31 bytes used=2004475136, alloc=4848776, time=106.03 y1[1] (analytic) = 1.9996405076656615849374075411613 y1[1] (numeric) = 1.9996405076656615849374075411613 absolute error = 5e-63 relative error = 2.5004494462041555645401210370467e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0268114795178927423991508690108 y2[1] (numeric) = 1.0268114795178927423991508690108 absolute error = 7e-63 relative error = 6.8172202391880458465228237872211e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02584 Order of pole (three term test) = -0.9102 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.32 y1[1] (analytic) = 1.9993224157301724410434695687937 y1[1] (numeric) = 1.9993224157301724410434695687937 absolute error = 5e-63 relative error = 2.5008472673848105914906888150686e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0368063774258266303351404065955 y2[1] (numeric) = 1.0368063774258266303351404065955 absolute error = 7e-63 relative error = 6.7515016809402116452291008865434e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03547 Order of pole (three term test) = -0.9256 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2008475980, alloc=4848776, time=106.23 x[1] = 6.33 y1[1] (analytic) = 1.9989043923858761837899286507793 y1[1] (numeric) = 1.9989043923858761837899286507793 absolute error = 5e-63 relative error = 2.5013702601513823627474242584929e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0467975947266898145565305659031 y2[1] (numeric) = 1.0467975947266898145565305659031 absolute error = 7e-63 relative error = 6.6870616012712964308208614930798e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04508 Order of pole (three term test) = -0.9458 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2012476788, alloc=4848776, time=106.44 x[1] = 6.34 y1[1] (analytic) = 1.9983864794347588911767704763508 y1[1] (numeric) = 1.9983864794347588911767704763508 absolute error = 5e-63 relative error = 2.5020185291757196674626970221840e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0567841323070781954089533630368 y2[1] (numeric) = 1.0567841323070781954089533630368 absolute error = 7e-63 relative error = 6.6238693277104904147273338156042e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05467 Order of pole (three term test) = -0.9708 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2016478112, alloc=4848776, time=106.65 x[1] = 6.35 y1[1] (analytic) = 1.9977687286676840822459698015753 y1[1] (numeric) = 1.9977687286676840822459698015753 absolute error = 5e-63 relative error = 2.5027922042480412097301979604919e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0667649915215558209643145750232 y2[1] (numeric) = 1.0667649915215558209643145750232 absolute error = 7e-63 relative error = 6.5618951274504333632756547844822e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06424 Order of pole (three term test) = -1.001 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.36 y1[1] (analytic) = 1.9970512018592136738884953211603 y1[1] (numeric) = 1.9970512018592136738884953211603 absolute error = 5e-63 relative error = 2.5036914403321770813571703009514e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0767391742925185984142305994414 y2[1] (numeric) = 1.0767391742925185984142305994414 absolute error = 7e-63 relative error = 6.5011101733151062672912180478946e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07378 Order of pole (three term test) = -1.035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2020478948, alloc=4848776, time=106.86 x[1] = 6.37 y1[1] (analytic) = 1.9962339707614305761312505732947 y1[1] (numeric) = 1.9962339707614305761312505732947 absolute error = 5e-63 relative error = 2.5047164176315626645094097957003e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0867056832100012227507449816142 y2[1] (numeric) = 1.0867056832100012227507449816142 absolute error = 7e-63 relative error = 6.4414865111617162273767268779834e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08329 Order of pole (three term test) = -1.075 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2024480156, alloc=4848776, time=107.07 x[1] = 6.38 y1[1] (analytic) = 1.9953171170967635436392743633319 y1[1] (numeric) = 1.9953171170967635436392743633319 absolute error = 5e-63 relative error = 2.5058673416660332274042564396660e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0966635216314173421246287010364 y2[1] (numeric) = 1.0966635216314173421246287010364 absolute error = 7e-63 relative error = 6.3829970286480104241396306789362e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09277 Order of pole (three term test) = -1.119 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2028481308, alloc=4848776, time=107.28 x[1] = 6.39 y1[1] (analytic) = 1.9943007325498150009420712157889 y1[1] (numeric) = 1.9943007325498150009420712157889 absolute error = 4e-63 relative error = 2.0057155546875803385153253431429e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1066116937812229859478449144211 y2[1] (numeric) = 1.1066116937812229859478449144211 absolute error = 7e-63 relative error = 6.3256154253001227138572185692237e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1022 Order of pole (three term test) = -1.168 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2032482008, alloc=4848776, time=107.49 x[1] = 6.4 y1[1] (analytic) = 1.9931849187581926585947390986722 y1[1] (numeric) = 1.9931849187581926585947390986722 absolute error = 5e-63 relative error = 2.5085479791383999116155245045140e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1165492048504932894804204887989 y2[1] (numeric) = 1.1165492048504932894804204887989 absolute error = 7e-63 relative error = 6.2693161838195073900482675298314e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1116 Order of pole (three term test) = -1.221 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.41 y1[1] (analytic) = 1.9919697873023458371046380129593 y1[1] (numeric) = 1.9919697873023458371046380129593 absolute error = 5e-63 relative error = 2.5100782310415074061751451971544e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1264750610964025573122459647381 y2[1] (numeric) = 1.1264750610964025573122459647381 absolute error = 7e-63 relative error = 6.2140745425707629782735628578234e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.121 Order of pole (three term test) = -1.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2036482664, alloc=4848776, time=107.70 x[1] = 6.42 y1[1] (analytic) = 1.9906554596944075149827370785494 y1[1] (numeric) = 1.9906554596944075149827370785494 absolute error = 5e-63 relative error = 2.5117355068403286097743053993064e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1363882699415977178163555462574 y2[1] (numeric) = 1.1363882699415977178163555462574 absolute error = 8e-63 relative error = 7.0398473933659515457662653983223e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1303 Order of pole (three term test) = -1.343 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2040483476, alloc=4848776, time=107.91 x[1] = 6.43 y1[1] (analytic) = 1.989242067366043216705536719677 y1[1] (numeric) = 1.989242067366043216705536719677 absolute error = 4e-63 relative error = 2.0108161121368214068188196306627e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1462878400734552313110527254404 y2[1] (numeric) = 1.1462878400734552313110527254404 absolute error = 8e-63 relative error = 6.9790498689119412429147823417842e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1395 Order of pole (three term test) = -1.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2044484188, alloc=4848776, time=108.11 x[1] = 6.44 y1[1] (analytic) = 1.9877297516553079556886438646254 y1[1] (numeric) = 1.9877297516553079556886438646254 absolute error = 4e-63 relative error = 2.0123459925419678751334884350700e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1561727815432115263227791436111 y2[1] (numeric) = 1.1561727815432115263227791436111 absolute error = 9e-63 relative error = 7.7843036470614477599605198470208e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1487 Order of pole (three term test) = -1.483 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.45 y1[1] (analytic) = 1.9861186637925125465667502912062 y1[1] (numeric) = 1.9861186637925125465667502912062 absolute error = 4e-63 relative error = 2.0139783553324864380900969747703e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1660421058649570509887088237076 y2[1] (numeric) = 1.1660421058649570509887088237076 absolute error = 9e-63 relative error = 7.7184176752553032459424329681034e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1579 Order of pole (three term test) = -1.559 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2048484924, alloc=4848776, time=108.32 x[1] = 6.46 y1[1] (analytic) = 1.9844089648851007001370080863308 y1[1] (numeric) = 1.9844089648851007001370080863308 absolute error = 4e-63 relative error = 2.0157135302155844036645593584617e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1758948261144840402764222822845 y2[1] (numeric) = 1.1758948261144840402764222822845 absolute error = 9e-63 relative error = 7.6537457263408081923137095252245e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.167 Order of pole (three term test) = -1.641 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2052485668, alloc=4848776, time=108.52 x[1] = 6.47 y1[1] (analytic) = 1.9826008259015384132437055032545 y1[1] (numeric) = 1.9826008259015384132437055032545 absolute error = 4e-63 relative error = 2.0175518681028993772327509655872e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1857299570279781143263114185045 y2[1] (numeric) = 1.1857299570279781143263114185045 absolute error = 1.0e-62 relative error = 8.4336234744923823479358954877477e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.176 Order of pole (three term test) = -1.727 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2056487120, alloc=4848776, time=108.73 x[1] = 6.48 y1[1] (analytic) = 1.9806944276542172646518292852309 y1[1] (numeric) = 1.9806944276542172646518292852309 absolute error = 4e-63 relative error = 2.0194937412618934624841830736464e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1955465151005438388391236641071 y2[1] (numeric) = 1.1955465151005438388391236641071 absolute error = 1.0e-62 relative error = 8.3643755167142230146165190715056e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1849 Order of pole (three term test) = -1.817 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2060487816, alloc=4848776, time=108.95 x[1] = 6.49 y1[1] (analytic) = 1.9786899607813733265656788933949 y1[1] (numeric) = 1.9786899607813733265656788933949 absolute error = 4e-63 relative error = 2.0215395434767470706373373855130e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.205343518684554395034710999914 y2[1] (numeric) = 1.205343518684554395034710999914 absolute error = 9e-63 relative error = 7.4667510634828027032727984579699e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1938 Order of pole (three term test) = -1.912 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.5 y1[1] (analytic) = 1.9765876257280234998863132539441 y1[1] (numeric) = 1.9765876257280234998863132539441 absolute error = 3e-63 relative error = 1.5177672676641541564757371626233e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2151199880878155242969457490747 y2[1] (numeric) = 1.2151199880878155242969457490747 absolute error = 9e-63 relative error = 7.4066759564731798877994636165576e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2026 Order of pole (three term test) = -2.012 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2064488616, alloc=4848776, time=109.15 x[1] = 6.51 y1[1] (analytic) = 1.9743876327259211795584179456101 y1[1] (numeric) = 1.9743876327259211795584179456101 absolute error = 3e-63 relative error = 1.5194584641203794369370887992056e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2248749456715339311921416700011 y2[1] (numeric) = 1.2248749456715339311921416700011 absolute error = 9e-63 relative error = 7.3476888655484561413259355771695e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2113 Order of pole (three term test) = -2.115 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2068489480, alloc=4848776, time=109.36 x[1] = 6.52 y1[1] (analytic) = 1.9720902017725332544233545841722 y1[1] (numeric) = 1.9720902017725332544233545841722 absolute error = 3e-63 relative error = 1.5212285915236390982241826836864e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2346074159480803481023185705953 y2[1] (numeric) = 1.2346074159480803481023185705953 absolute error = 1.0e-62 relative error = 8.0997407522623659020033995603057e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2199 Order of pole (three term test) = -2.223 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2072490208, alloc=4848776, time=109.57 x[1] = 6.53 y1[1] (analytic) = 1.9696955626090405438608879906796 y1[1] (numeric) = 1.9696955626090405438608879906796 absolute error = 3e-63 relative error = 1.5230780111146860266765184590499e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2443164256785374852483160662742 y2[1] (numeric) = 1.2443164256785374852483160662742 absolute error = 1.0e-62 relative error = 8.0365410225513222365951612934665e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2284 Order of pole (three term test) = -2.336 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.54 y1[1] (analytic) = 1.9672039546973638711575940623119 y1[1] (numeric) = 1.9672039546973638711575940623119 absolute error = 3e-63 relative error = 1.5250071009853791420927654474248e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2540010039700231113890438578016 y2[1] (numeric) = 1.2540010039700231113890438578016 absolute error = 1.0e-62 relative error = 7.9744752742152110406332444362640e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2369 Order of pole (three term test) = -2.453 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2076490904, alloc=4848776, time=109.78 TOP MAIN SOLVE Loop x[1] = 6.55 y1[1] (analytic) = 1.9646156271962180709754666300476 y1[1] (numeric) = 1.9646156271962180709754666300476 absolute error = 3e-63 relative error = 1.5270162562441899052712697406268e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2636601823727785329699009008071 y2[1] (numeric) = 1.2636601823727785329699009008071 absolute error = 1.0e-62 relative error = 7.9135198999646960950638259948951e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2452 Order of pole (three term test) = -2.573 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2080491840, alloc=4848776, time=109.99 x[1] = 6.56 y1[1] (analytic) = 1.9619308389361963255000215151936 y1[1] (numeric) = 1.9619308389361963255000215151936 absolute error = 3e-63 relative error = 1.5291058891895845133967295878129e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2732929949770127629533554213434 y2[1] (numeric) = 1.2732929949770127629533554213434 absolute error = 1.0e-62 relative error = 7.8536519398510739147066435140732e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2535 Order of pole (three term test) = -2.698 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2084492672, alloc=4848776, time=110.20 x[1] = 6.57 y1[1] (analytic) = 1.9591498583938873208135199903714 y1[1] (numeric) = 1.9591498583938873208135199903714 absolute error = 3e-63 relative error = 1.5312764294914134280394257699717e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2828984785094926949955059244941 y2[1] (numeric) = 1.2828984785094926949955059244941 absolute error = 1.0e-62 relative error = 7.7948490605572153037144041365452e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2616 Order of pole (three term test) = -2.828 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2088493976, alloc=4848776, time=110.41 x[1] = 6.58 y1[1] (analytic) = 1.9562729636650278117561053581557 y1[1] (numeric) = 1.9562729636650278117561053581557 absolute error = 3e-63 relative error = 1.5335283243804463979453693537674e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2924756724298696240316970834387 y2[1] (numeric) = 1.2924756724298696240316970834387 absolute error = 1.0e-62 relative error = 7.7370895354648193566077120447095e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2697 Order of pole (three term test) = -2.961 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.59 y1[1] (analytic) = 1.9533004424366932799959937456649 y1[1] (numeric) = 1.9533004424366932799959937456649 absolute error = 3e-63 relative error = 1.5358620388461978183666020555377e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.302023619026732480699403780303 y2[1] (numeric) = 1.302023619026732480699403780303 absolute error = 1.0e-62 relative error = 7.6803522254650321611163746150942e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2776 Order of pole (three term test) = -3.098 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2092494916, alloc=4848776, time=110.62 x[1] = 6.6 y1[1] (analytic) = 1.9502325919585294662197377216682 y1[1] (numeric) = 1.9502325919585294662197377216682 absolute error = 3e-63 relative error = 1.5382780558431941189086031668030e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3115413635133781743549851055926 y2[1] (numeric) = 1.3115413635133781743549851055926 absolute error = 1.0e-62 relative error = 7.6246165604810500132304654335020e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2854 Order of pole (three term test) = -3.239 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2096495816, alloc=4848776, time=110.82 x[1] = 6.61 y1[1] (analytic) = 1.9470697190130276532653700665807 y1[1] (numeric) = 1.9470697190130276532653700665807 absolute error = 2e-63 relative error = 1.0271845843372279343612560788600e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.321027954123289467729814993965 y2[1] (numeric) = 1.321027954123289467729814993965 absolute error = 1.1e-62 relative error = 8.3268487738400933541536489389905e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2931 Order of pole (three term test) = -3.384 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2100497032, alloc=4848776, time=111.03 x[1] = 6.62 y1[1] (analytic) = 1.9438121398848466726453438661522 y1[1] (numeric) = 1.9438121398848466726453438661522 absolute error = 3e-63 relative error = 1.5433590203720627686267385638226e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3304824422053108355178885136054 y2[1] (numeric) = 1.3304824422053108355178885136054 absolute error = 1.0e-62 relative error = 7.5160706242952954807309474847693e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3007 Order of pole (three term test) = -3.533 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2104497836, alloc=4848776, time=111.24 x[1] = 6.63 y1[1] (analytic) = 1.9404601803291847022330517254913 y1[1] (numeric) = 1.9404601803291847022330517254913 absolute error = 2e-63 relative error = 1.0306833504105787979625170703049e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3399038823185127893883579996919 y2[1] (numeric) = 1.3399038823185127893883579996919 absolute error = 1.0e-62 relative error = 7.4632219011832584379584893433556e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3082 Order of pole (three term test) = -3.686 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.64 y1[1] (analytic) = 1.9370141755392040179067987040978 y1[1] (numeric) = 1.9370141755392040179067987040978 absolute error = 2e-63 relative error = 1.0325169661927036250377238268722e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3492913323267351830695511189999 y2[1] (numeric) = 1.3492913323267351830695511189999 absolute error = 1.1e-62 relative error = 8.1524276755202004447306656381132e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3155 Order of pole (three term test) = -3.842 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2108498580, alloc=4848776, time=111.45 x[1] = 6.65 y1[1] (analytic) = 1.9334744701125119566489186248007 y1[1] (numeric) = 1.9334744701125119566489186248007 absolute error = 2e-63 relative error = 1.0344072450481421753077588258766e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3586438534928000432527482887922 y2[1] (numeric) = 1.3586438534928000432527482887922 absolute error = 1.0e-62 relative error = 7.3602806020812677249436516226206e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3228 Order of pole (three term test) = -4.002 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2112500112, alloc=4848776, time=111.66 x[1] = 6.66 y1[1] (analytic) = 1.9298414180167014429757914073278 y1[1] (numeric) = 1.9298414180167014429757914073278 absolute error = 2e-63 relative error = 1.0363545840234896352567719961663e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3679605105723845051111395029691 y2[1] (numeric) = 1.3679605105723845051111395029691 absolute error = 1.0e-62 relative error = 7.3101525392833028173564651674616e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3299 Order of pole (three term test) = -4.166 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2116501292, alloc=4848776, time=111.87 x[1] = 6.67 y1[1] (analytic) = 1.9261153825539545246174022925197 y1[1] (numeric) = 1.9261153825539545246174022925197 absolute error = 2e-63 relative error = 1.0383593932716934794294502789363e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3772403719075444652186358553043 y2[1] (numeric) = 1.3772403719075444652186358553043 absolute error = 1.0e-62 relative error = 7.2608966480916594003181956896358e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3368 Order of pole (three term test) = -4.333 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.68 y1[1] (analytic) = 1.9222967363247124570633780459879 y1[1] (numeric) = 1.9222967363247124570633780459879 absolute error = 2e-63 relative error = 1.0404220962388202196621023177089e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3864825095198795995811799962591 y2[1] (numeric) = 1.3864825095198795995811799962591 absolute error = 1.0e-62 relative error = 7.2124963216902509805112433140572e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3437 Order of pole (three term test) = -4.503 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2120502204, alloc=4848776, time=112.08 x[1] = 6.69 y1[1] (analytic) = 1.9183858611904159699367707089691 y1[1] (numeric) = 1.9183858611904159699367707089691 absolute error = 2e-63 relative error = 1.0425431298575876747077686807610e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3956859992033304303563896485654 y2[1] (numeric) = 1.3956859992033304303563896485654 absolute error = 1.0e-62 relative error = 7.1649353835376194849895976534820e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3503 Order of pole (three term test) = -4.677 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2124503496, alloc=4848776, time=112.29 x[1] = 6.7 y1[1] (analytic) = 1.9143831482353194411379018434767 y1[1] (numeric) = 1.9143831482353194411379018434767 absolute error = 2e-63 relative error = 1.0447229447478172120317894418131e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4048499206165981616321928483868 y2[1] (numeric) = 1.4048499206165981616321928483868 absolute error = 1.1e-62 relative error = 7.8300178820325699761519871836835e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3569 Order of pole (three term test) = -4.855 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2128504276, alloc=4848776, time=112.50 x[1] = 6.71 y1[1] (analytic) = 1.9102889977273827973090314718501 y1[1] (numeric) = 1.9102889977273827973090314718501 absolute error = 1e-63 relative error = 5.2348100271198333448246358296598e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4139733573751780423578933216319 y2[1] (numeric) = 1.4139733573751780423578933216319 absolute error = 1.1e-62 relative error = 7.7794959449729602937871165062305e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3633 Order of pole (three term test) = -5.035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2132505264, alloc=4848776, time=112.71 x[1] = 6.72 y1[1] (analytic) = 1.9061038190782450513972152694962 y1[1] (numeric) = 1.9061038190782450513972152694962 absolute error = 1e-63 relative error = 5.2463039525495555798932830348906e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4230553971429970531680671023396 y2[1] (numeric) = 1.4230553971429970531680671023396 absolute error = 1.1e-62 relative error = 7.7298466539561247361920025399857e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3696 Order of pole (three term test) = -5.219 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.73 y1[1] (analytic) = 1.9018280308022834799282384509219 y1[1] (numeric) = 1.9018280308022834799282384509219 absolute error = 2e-63 relative error = 1.0516197929611452897461600234911e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.432095131723646753406972487949 y2[1] (numeric) = 1.432095131723646753406972487949 absolute error = 1.1e-62 relative error = 7.6810539721342228558427655914439e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3757 Order of pole (three term test) = -5.406 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2136505968, alloc=4848776, time=112.92 x[1] = 6.74 y1[1] (analytic) = 1.8974620604747625340397817171234 y1[1] (numeric) = 1.8974620604747625340397817171234 absolute error = 1e-63 relative error = 5.2701976014729420370251442054659e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4410916571512021651447980095527 y2[1] (numeric) = 1.4410916571512021651447980095527 absolute error = 1.1e-62 relative error = 7.6331022703615988042248813827387e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3816 Order of pole (three term test) = -5.596 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2140507216, alloc=4848776, time=113.13 x[1] = 6.75 y1[1] (analytic) = 1.8930063446890766693478401565171 y1[1] (numeric) = 1.8930063446890766693478401565171 absolute error = 1e-63 relative error = 5.2826024741308959298644708035083e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4500440737806176123730289434098 y2[1] (numeric) = 1.4500440737806176123730289434098 absolute error = 1.1e-62 relative error = 7.5859763154097270539628014023094e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3874 Order of pole (three term test) = -5.788 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2144508364, alloc=4848776, time=113.34 x[1] = 6.76 y1[1] (analytic) = 1.8884613290130913703277776011807 y1[1] (numeric) = 1.8884613290130913703277776011807 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4589514863776904758703424419645 y2[1] (numeric) = 1.4589514863776904758703424419645 absolute error = 1.1e-62 relative error = 7.5396612585871424591996591888787e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3931 Order of pole (three term test) = -5.984 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.77 y1[1] (analytic) = 1.883827467944586735071195974561 y1[1] (numeric) = 1.883827467944586735071195974561 absolute error = 1e-63 relative error = 5.3083417511216332618988728679588e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4678130042085838674385142406797 y2[1] (numeric) = 1.4678130042085838674385142406797 absolute error = 1.1e-62 relative error = 7.4941426247487058972766102827517e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3986 Order of pole (three term test) = -6.182 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2148509216, alloc=4848776, time=113.55 x[1] = 6.78 y1[1] (analytic) = 1.8791052248658080760230137214455 y1[1] (numeric) = 1.8791052248658080760230137214455 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4766277411288992713155153298713 y2[1] (numeric) = 1.4766277411288992713155153298713 absolute error = 1.1e-62 relative error = 7.4494063016792374862882508487033e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4039 Order of pole (three term test) = -6.384 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2152510080, alloc=4848776, time=113.76 x[1] = 6.79 y1[1] (analytic) = 1.8742950719971280816008052392169 y1[1] (numeric) = 1.8742950719971280816008052392169 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4853948156722902455758842356298 y2[1] (numeric) = 1.4853948156722902455758842356298 absolute error = 1.2e-62 relative error = 8.0786602143678517825972829604160e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4091 Order of pole (three term test) = -6.587 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2156510816, alloc=4848776, time=113.97 x[1] = 6.8 y1[1] (analytic) = 1.8693974903498251724416246398463 y1[1] (numeric) = 1.8693974903498251724416246398463 absolute error = 1e-63 relative error = 5.3493171204208015791782507038975e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4941133511386083222220793776203 y2[1] (numeric) = 1.4941133511386083222220793776203 absolute error = 1.2e-62 relative error = 8.0315191553942312673814756509545e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4141 Order of pole (three term test) = -6.794 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2160511936, alloc=4848776, time=114.18 x[1] = 6.81 y1[1] (analytic) = 1.864412969677982774401337921625 y1[1] (numeric) = 1.864412969677982774401337921625 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.502782475681572291450257040417 y2[1] (numeric) = 1.502782475681572291450257040417 absolute error = 1.2e-62 relative error = 7.9851876064481769960838295596651e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4189 Order of pole (three term test) = -7.003 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.82 y1[1] (analytic) = 1.8593420084295143183390798118649 y1[1] (numeric) = 1.8593420084295143183390798118649 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5114013223959521032351058739392 y2[1] (numeric) = 1.5114013223959521032351058739392 absolute error = 1.2e-62 relative error = 7.9396516479004894181637661295472e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4236 Order of pole (three term test) = -7.214 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2164512624, alloc=4848776, time=114.38 x[1] = 6.83 y1[1] (analytic) = 1.8541851136963188641460444707435 y1[1] (numeric) = 1.8541851136963188641460444707435 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.519969029404258667916232448682 y2[1] (numeric) = 1.519969029404258667916232448682 absolute error = 1.2e-62 relative error = 7.8948977037402642833395774351649e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4281 Order of pole (three term test) = -7.427 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2168513580, alloc=4848776, time=114.59 x[1] = 6.84 y1[1] (analytic) = 1.8489428011635723334146703357036 y1[1] (numeric) = 1.8489428011635723334146703357036 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.52848473994293088687828048687 y2[1] (numeric) = 1.52848473994293088687828048687 absolute error = 1.3e-62 relative error = 8.5051552431497495138152958505930e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4325 Order of pole (three term test) = -7.643 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2172514396, alloc=4848776, time=114.80 x[1] = 6.85 y1[1] (analytic) = 1.8436155950581594215826950226731 y1[1] (numeric) = 1.8436155950581594215826950226731 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5369476024480112946935380437703 y2[1] (numeric) = 1.5369476024480112946935380437703 absolute error = 1.3e-62 relative error = 8.4583234843490621125547120716719e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4366 Order of pole (three term test) = -7.861 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.86 y1[1] (analytic) = 1.8382040280962513463178926153105 y1[1] (numeric) = 1.8382040280962513463178926153105 absolute error = 1e-63 relative error = 5.4400925289868768419384095953337e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5453567706403017452342145089099 y2[1] (numeric) = 1.5453567706403017452342145089099 absolute error = 1.3e-62 relative error = 8.4122969187326183593883626526185e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4406 Order of pole (three term test) = -8.081 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2176515160, alloc=4848776, time=115.00 TOP MAIN SOLVE Loop x[1] = 6.87 y1[1] (analytic) = 1.8327086414300346743249698044871 y1[1] (numeric) = 1.8327086414300346743249698044871 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.553711403609990626256739034717 y2[1] (numeric) = 1.553711403609990626256739034717 absolute error = 1.3e-62 relative error = 8.3670622290568144018239704670302e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4444 Order of pole (three term test) = -8.302 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2180516092, alloc=4848776, time=115.21 x[1] = 6.88 y1[1] (analytic) = 1.8271299845935965536475476920373 y1[1] (numeric) = 1.8271299845935965536475476920373 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5620106659007431398071444064856 y2[1] (numeric) = 1.5620106659007431398071444064856 absolute error = 1.4e-62 relative error = 8.9628069165115547764433424990882e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4481 Order of pole (three term test) = -8.526 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2184516760, alloc=4848776, time=115.42 x[1] = 6.89 y1[1] (analytic) = 1.8214686154479717628969035711689 y1[1] (numeric) = 1.8214686154479717628969035711689 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5702537275932462394895708153654 y2[1] (numeric) = 1.5702537275932462394895708153654 absolute error = 1.4e-62 relative error = 8.9157565774150593296086534259459e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4515 Order of pole (three term test) = -8.752 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2188517684, alloc=4848776, time=115.63 x[1] = 6.9 y1[1] (analytic) = 1.8157251001253570726567558363581 y1[1] (numeric) = 1.8157251001253570726567558363581 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5784397643881998701737832329889 y2[1] (numeric) = 1.5784397643881998701737832329889 absolute error = 1.4e-62 relative error = 8.8695180619872259121777506331035e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4548 Order of pole (three term test) = -8.979 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.91 y1[1] (analytic) = 1.8099000129724984975814636670357 y1[1] (numeric) = 1.8099000129724984975814636670357 absolute error = 1e-63 relative error = 5.5251670967041152213488743667067e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5865679576887462110868907718869 y2[1] (numeric) = 1.5865679576887462110868907718869 absolute error = 1.3e-62 relative error = 8.1937870590415309948380280778790e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4579 Order of pole (three term test) = -9.207 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2192518380, alloc=4848776, time=115.84 x[1] = 6.92 y1[1] (analytic) = 1.8039939364932571004152545324359 y1[1] (numeric) = 1.8039939364932571004152545324359 absolute error = 1e-63 relative error = 5.5432558822446893616743182364585e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5946374946823286794336496667012 y2[1] (numeric) = 1.5946374946823286794336496667012 absolute error = 1.3e-62 relative error = 8.1523230473078517623353504494812e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.79 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.05 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4608 Order of pole (three term test) = -9.438 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2196519584, alloc=4848776, time=116.05 x[1] = 6.93 y1[1] (analytic) = 1.7980074612903590913042159244115 y1[1] (numeric) = 1.7980074612903590913042159244115 absolute error = 2e-63 relative error = 1.1123424363126273261738972590534e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6026475684219725087132034548561 y2[1] (numeric) = 1.6026475684219725087132034548561 absolute error = 1.3e-62 relative error = 8.1115775271791616266531319419481e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.1 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.35 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4635 Order of pole (three term test) = -9.669 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2200520980, alloc=4848776, time=116.26 x[1] = 6.94 y1[1] (analytic) = 1.7919411860063360473425786969406 y1[1] (numeric) = 1.7919411860063360473425786969406 absolute error = 2e-63 relative error = 1.1161080595827815782426298062847e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6105973779069787737421622721598 y2[1] (numeric) = 1.6105973779069787737421622721598 absolute error = 1.3e-62 relative error = 8.0715392799744297619311820667991e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.42 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = -9.902 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.95 y1[1] (analytic) = 1.7857957172636611582821210643353 y1[1] (numeric) = 1.7857957172636611582821210643353 absolute error = 2e-63 relative error = 1.1199489284611790612246748864688e-61 % Correct digits = 64 bytes used=2204521892, alloc=4848776, time=116.47 h = 0.01 y2[1] (analytic) = 1.6184861281630237930487637521055 y2[1] (numeric) = 1.6184861281630237930487637521055 absolute error = 1.3e-62 relative error = 8.0321973563993133714665554617829e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4684 Order of pole (three term test) = -10.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 6.96 y1[1] (analytic) = 1.7795716696040874847302360221301 y1[1] (numeric) = 1.7795716696040874847302360221301 absolute error = 2e-63 relative error = 1.1238659471607303087525777448871e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6263130303216558987646253922822 y2[1] (numeric) = 1.6263130303216558987646253922822 absolute error = 1.3e-62 relative error = 7.9935410696603902650441422941521e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.07 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.26 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4706 Order of pole (three term test) = -10.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2208523180, alloc=4848776, time=116.67 x[1] = 6.97 y1[1] (analytic) = 1.7732696654271942949602911009115 y1[1] (numeric) = 1.7732696654271942949602911009115 absolute error = 2e-63 relative error = 1.1278600423800655408953628380105e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6340773016991816244033463000763 y2[1] (numeric) = 1.6340773016991816244033463000763 absolute error = 1.2e-62 relative error = 7.3435938358129693724433464307539e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.4 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.58 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4725 Order of pole (three term test) = -10.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2212524552, alloc=4848776, time=116.88 x[1] = 6.98 y1[1] (analytic) = 1.7668903349281476256493882018266 y1[1] (numeric) = 1.7668903349281476256493882018266 absolute error = 2e-63 relative error = 1.1319321637929113543837152159994e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6417781658749334219729187281771 y2[1] (numeric) = 1.6417781658749334219729187281771 absolute error = 1.2e-62 relative error = 7.3091482451315107569235661529435e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.74 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.9 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4743 Order of pole (three term test) = -10.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2216525780, alloc=4848776, time=117.09 x[1] = 6.99 y1[1] (analytic) = 1.7604343160346812904355837112889 y1[1] (numeric) = 1.7604343160346812904355837112889 absolute error = 2e-63 relative error = 1.1360832845527189585012697855709e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6494148527689110817154610389165 y2[1] (numeric) = 1.6494148527689110817154610389165 absolute error = 1.2e-62 relative error = 7.2753073490609841776913230842010e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.08 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.23 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4759 Order of pole (three term test) = -11.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7 y1[1] (analytic) = 1.7539022543433046381411975217192 y1[1] (numeric) = 1.7539022543433046381411975217192 absolute error = 2e-63 relative error = 1.1403144018130241692011552807951e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6569865987187890903969990915936 y2[1] (numeric) = 1.6569865987187890903969990915936 absolute error = 1.2e-62 relative error = 7.2420621924634810498815377179356e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.43 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4773 Order of pole (three term test) = -11.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2220526972, alloc=4848776, time=117.30 x[1] = 7.01 y1[1] (analytic) = 1.7472948030547434398332286031403 y1[1] (numeric) = 1.7472948030547434398332286031403 absolute error = 2e-63 relative error = 1.1446265372640378682713734056146e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6644926465562822274756396593097 y2[1] (numeric) = 1.6644926465562822274756396593097 absolute error = 1.2e-62 relative error = 7.2094040336117752156236203348513e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.78 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.89 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4785 Order of pole (three term test) = -11.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2224527712, alloc=4848776, time=117.50 x[1] = 7.02 y1[1] (analytic) = 1.7406126229086203605783720026158 y1[1] (numeric) = 1.7406126229086203605783720026158 absolute error = 2e-63 relative error = 1.1490207376859848848158780167122e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6719322456828617626521568426536 y2[1] (numeric) = 1.6719322456828617626521568426536 absolute error = 1.2e-62 relative error = 7.1773243389410673461737538043872e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.15 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4796 Order of pole (three term test) = -11.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2228529388, alloc=4848776, time=117.71 x[1] = 7.03 y1[1] (analytic) = 1.7338563821173815477910290110704 y1[1] (numeric) = 1.7338563821173815477910290110704 absolute error = 2e-63 relative error = 1.1534980755197292981567840744097e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6793046521448146832463330425656 y2[1] (numeric) = 1.6793046521448146832463330425656 absolute error = 1.1e-62 relative error = 6.5503302131336059712327716718662e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.51 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.59 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4804 Order of pole (three term test) = -12.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2232530260, alloc=4848776, time=117.92 x[1] = 7.04 y1[1] (analytic) = 1.7270267562994759434604147036375 y1[1] (numeric) = 1.7270267562994759434604147036375 absolute error = 2e-63 relative error = 1.1580596494552450314764859193670e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6866091287076384455388660059318 y2[1] (numeric) = 1.6866091287076384455388660059318 absolute error = 1.1e-62 relative error = 6.5219616168144023110097309325955e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.94 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.481 Order of pole (three term test) = -12.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.05 y1[1] (analytic) = 1.7201244284117940022698564219134 y1[1] (numeric) = 1.7201244284117940022698564219134 absolute error = 2e-63 relative error = 1.1627065850385123429463172761815e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6938449449297638106657031726717 y2[1] (numeric) = 1.6938449449297638106657031726717 absolute error = 1.2e-62 relative error = 7.0844737211159469130807306725239e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.27 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.31 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4815 Order of pole (three term test) = -12.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2236530916, alloc=4848776, time=118.12 x[1] = 7.06 y1[1] (analytic) = 1.7131500886813725716801703877066 y1[1] (numeric) = 1.7131500886813725716801703877066 absolute error = 2e-63 relative error = 1.1674400352974434665335592324637e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7010113772355983928426493826761 y2[1] (numeric) = 1.7010113772355983928426493826761 absolute error = 1.2e-62 relative error = 7.0546265360681013987111319669571e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.33 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4817 Order of pole (three term test) = -12.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2240531668, alloc=4848776, time=118.33 x[1] = 7.07 y1[1] (analytic) = 1.7061044345363727634321957003992 y1[1] (numeric) = 1.7061044345363727634321957003992 absolute error = 2e-63 relative error = 1.1722611813874642510160168681551e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7081077089878836156262949024486 y2[1] (numeric) = 1.7081077089878836156262949024486 absolute error = 1.2e-62 relative error = 7.0253180972471809471903702836896e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.95 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = -13.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2244533348, alloc=4848776, time=118.54 x[1] = 7.08 y1[1] (analytic) = 1.6989881705363377186238172158325 y1[1] (numeric) = 1.6989881705363377186238172158325 absolute error = 3e-63 relative error = 1.7657568498861048570383562112350e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7151332305593578405759349412061 y2[1] (numeric) = 1.7151332305593578405759349412061 absolute error = 1.2e-62 relative error = 6.9965410186160464772325447935919e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.57 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4817 Order of pole (three term test) = -13.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.09 y1[1] (analytic) = 1.6918020083017372405268512690559 y1[1] (numeric) = 1.6918020083017372405268512690559 absolute error = 2e-63 relative error = 1.1821714303363652555616451058383e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7220872394037185020633335393084 y2[1] (numeric) = 1.7220872394037185020633335393084 absolute error = 1.2e-62 relative error = 6.9682880898386200575199689642326e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4814 Order of pole (three term test) = -13.49 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2248534184, alloc=4848776, time=118.75 TOP MAIN SOLVE Loop x[1] = 7.1 y1[1] (analytic) = 1.6845466664428063406217999420893 y1[1] (numeric) = 1.6845466664428063406217999420893 absolute error = 2e-63 relative error = 1.1872630422422933321748562384215e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7289690401258761520759857678532 y2[1] (numeric) = 1.7289690401258761520759857678532 absolute error = 1.2e-62 relative error = 6.9405522721947351854801789547746e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.84 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4808 Order of pole (three term test) = -13.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2252535700, alloc=4848776, time=118.95 x[1] = 7.11 y1[1] (analytic) = 1.6772228704876848139365693873049 y1[1] (numeric) = 1.6772228704876848139365693873049 absolute error = 2e-63 relative error = 1.1924473695129506113101862710630e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.735777944551493389667942755402 y2[1] (numeric) = 1.735777944551493389667942755402 absolute error = 1.2e-62 relative error = 6.9133266946197272496868943228237e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4801 Order of pole (three term test) = -13.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2256536916, alloc=4848776, time=119.16 x[1] = 7.12 y1[1] (analytic) = 1.6698313528098650296717348469898 y1[1] (numeric) = 1.6698313528098650296717348469898 absolute error = 2e-63 relative error = 1.1977257443600830202313872106256e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7425132717958017212232033740469 y2[1] (numeric) = 1.7425132717958017212232033740469 absolute error = 1.1e-62 relative error = 6.3127209290426837839940289048506e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.14 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = -14.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2260538476, alloc=4848776, time=119.37 x[1] = 7.13 y1[1] (analytic) = 1.6623728525549551922728298696433 y1[1] (numeric) = 1.6623728525549551922728298696433 absolute error = 2e-63 relative error = 1.2030995314475537815160201286274e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7491743483316894699029934380455 y2[1] (numeric) = 1.7491743483316894699029934380455 absolute error = 1.1e-62 relative error = 6.2886812915427631437111086434975e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.8 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4781 Order of pole (three term test) = -14.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.14 y1[1] (analytic) = 1.6548481155667653965625220817479 y1[1] (numeric) = 1.6548481155667653965625220817479 absolute error = 2e-63 relative error = 1.2085701286942725083485817634342e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7557605080570539255427274225094 y2[1] (numeric) = 1.7557605080570539255427274225094 absolute error = 1.1e-62 relative error = 6.2650913661184546609468979226744e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.46 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4769 Order of pole (three term test) = -14.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2264539236, alloc=4848776, time=119.58 x[1] = 7.15 y1[1] (analytic) = 1.6472578943127238682655675486971 y1[1] (numeric) = 1.6472578943127238682655675486971 absolute error = 2e-63 relative error = 1.2141389681027746620001541644640e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7622710923614109998397896104677 y2[1] (numeric) = 1.7622710923614109998397896104677 absolute error = 1.1e-62 relative error = 6.2419454348877739290702722632435e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.13 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4754 Order of pole (three term test) = -14.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2268540348, alloc=4848776, time=119.78 x[1] = 7.16 y1[1] (analytic) = 1.6396029478086308482403383037247 y1[1] (numeric) = 1.6396029478086308482403383037247 absolute error = 3e-63 relative error = 1.8297112749215124579336990808531e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.768705450191755725922123751153 y2[1] (numeric) = 1.768705450191755725922123751153 absolute error = 1.1e-62 relative error = 6.2192379170920887468999485658574e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.81 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4737 Order of pole (three term test) = -15.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2272541192, alloc=4848776, time=120.00 x[1] = 7.17 y1[1] (analytic) = 1.6318840415427576449657950046255 y1[1] (numeric) = 1.6318840415427576449657950046255 absolute error = 3e-63 relative error = 1.8383659154873816460863845216008e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7750629381176670163025579372399 y2[1] (numeric) = 1.7750629381176670163025579372399 absolute error = 1.1e-62 relative error = 6.1969633660791478992488606585285e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4719 Order of pole (three term test) = -15.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.18 y1[1] (analytic) = 1.6241019473992984453154054422433 y1[1] (numeric) = 1.6241019473992984453154054422433 absolute error = 3e-63 relative error = 1.8471746830942171272543289209991e-61 % Correct digits = 64 h = 0.01 bytes used=2276542220, alloc=4848776, time=120.20 y2[1] (analytic) = 1.7813429203956501687973230526633 y2[1] (numeric) = 1.7813429203956501687973230526633 absolute error = 1.0e-62 relative error = 5.6137422421612801729968010398996e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.18 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4698 Order of pole (three term test) = -15.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.19 y1[1] (analytic) = 1.6162574435811825383731415638198 y1[1] (numeric) = 1.6162574435811825383731415638198 absolute error = 3e-63 relative error = 1.8561399434936701950052948390031e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7875447690327106862117915153751 y2[1] (numeric) = 1.7875447690327106862117915153751 absolute error = 1.0e-62 relative error = 5.5942654825989467216601216357490e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4676 Order of pole (three term test) = -15.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2280543664, alloc=4848776, time=120.41 x[1] = 7.2 y1[1] (analytic) = 1.6083513145322546710048504790937 y1[1] (numeric) = 1.6083513145322546710048504790937 absolute error = 3e-63 relative error = 1.8652641204029907978536052110640e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7936678638491530524644457476436 y2[1] (numeric) = 1.7936678638491530524644457476436 absolute error = 1.0e-62 relative error = 5.5751681799886431493476533290595e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.56 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4652 Order of pole (three term test) = -16.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2284544352, alloc=4848776, time=120.62 x[1] = 7.21 y1[1] (analytic) = 1.600384350858831317084592824522 y1[1] (numeric) = 1.600384350858831317084592824522 absolute error = 3e-63 relative error = 1.8745496970087704336632842443938e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7997115925405981853237961160432 y2[1] (numeric) = 1.7997115925405981853237961160432 absolute error = 1.0e-62 relative error = 5.5564458446829826606542366982492e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.26 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4626 Order of pole (three term test) = -16.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2288545416, alloc=4848776, time=120.83 x[1] = 7.22 y1[1] (analytic) = 1.5923573492506407046836562940431 y1[1] (numeric) = 1.5923573492506407046836562940431 absolute error = 3e-63 relative error = 1.8839992175197309360346335056680e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8056753507392133640646556876854 y2[1] (numeric) = 1.8056753507392133640646556876854 absolute error = 1.0e-62 relative error = 5.5380940964311036490975823505852e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 13.97 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4598 Order of pole (three term test) = -16.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.23 y1[1] (analytic) = 1.5842711124011545071536423439622 y1[1] (numeric) = 1.5842711124011545071536423439622 absolute error = 3e-63 relative error = 1.8936152887703273933677187359809e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8115585420741485091020309448447 y2[1] (numeric) = 1.8115585420741485091020309448447 absolute error = 1.0e-62 relative error = 5.5201086620973754722988537532323e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4568 Order of pole (three term test) = -16.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2292546412, alloc=4848776, time=121.04 x[1] = 7.24 y1[1] (analytic) = 1.5761264489273191648681277271593 y1[1] (numeric) = 1.5761264489273191648681277271593 absolute error = 3e-63 relative error = 1.9034005818770069658803831763116e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8173605782311727700250284673932 y2[1] (numeric) = 1.8173605782311727700250284673932 absolute error = 9e-63 relative error = 4.9522368361041766213428970856101e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4537 Order of pole (three term test) = -17.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2296547112, alloc=4848776, time=121.25 x[1] = 7.25 y1[1] (analytic) = 1.5679241732886948644238363482182 y1[1] (numeric) = 1.5679241732886948644238363482182 absolute error = 3e-63 relative error = 1.9133578339490422663021192306244e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8230808790115054584216711834121 y2[1] (numeric) = 1.8230808790115054584216711834121 absolute error = 9e-63 relative error = 4.9366981485099548480931534148810e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4503 Order of pole (three term test) = -17.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2300548084, alloc=4848776, time=121.46 x[1] = 7.26 y1[1] (analytic) = 1.5596651057060102613360173629058 y1[1] (numeric) = 1.5596651057060102613360173629058 absolute error = 3e-63 relative error = 1.9234898498559384185401981650425e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.82871887238983544245036732029 y2[1] (numeric) = 1.82871887238983544245036732029 absolute error = 9e-63 relative error = 4.9214781647867378612148648932379e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4468 Order of pole (three term test) = -17.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2304549044, alloc=4848776, time=121.67 x[1] = 7.27 y1[1] (analytic) = 1.5513500720791410906878891460087 y1[1] (numeric) = 1.5513500720791410906878891460087 absolute error = 4e-63 relative error = 2.5783993387379961162649450302467e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8342739945715232012669242437267 y2[1] (numeric) = 1.8342739945715232012669242437267 absolute error = 9e-63 relative error = 4.9065734054101077006758572261733e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4431 Order of pole (three term test) = -17.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.28 y1[1] (analytic) = 1.5429799039045208678047332531733 y1[1] (numeric) = 1.5429799039045208678047332531733 absolute error = 3e-63 relative error = 1.9442897424707088714923807273225e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8397456900489798191493327030497 y2[1] (numeric) = 1.8397456900489798191493327030497 absolute error = 9e-63 relative error = 4.8919804778889802323227247664305e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4393 Order of pole (three term test) = -17.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2308549844, alloc=4848776, time=121.87 x[1] = 7.29 y1[1] (analytic) = 1.5345554381919919378137467806639 y1[1] (numeric) = 1.5345554381919919378137467806639 absolute error = 3e-63 relative error = 1.9549635844597376827152897819351e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8451334116572172814678913429188 y2[1] (numeric) = 1.8451334116572172814678913429188 absolute error = 1.0e-62 relative error = 5.4196623056207312225760454425609e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4352 Order of pole (three term test) = -18.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2312550924, alloc=4848776, time=122.08 x[1] = 7.3 y1[1] (analytic) = 1.5260775173811051889154065767377 y1[1] (numeric) = 1.5260775173811051889154065767377 absolute error = 3e-63 relative error = 1.9658241248113572893553767512474e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8504366206285645175173662279669 y2[1] (numeric) = 1.8504366206285645175173662279669 absolute error = 9e-63 relative error = 4.8637169734258934452224192076734e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.431 Order of pole (three term test) = -18.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2316551664, alloc=4848776, time=122.29 x[1] = 7.31 y1[1] (analytic) = 1.5175469892568767993252681617755 y1[1] (numeric) = 1.5175469892568767993252681617755 absolute error = 4e-63 relative error = 2.6358327144510684596369859293902e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8556547866465437186524987147974 y2[1] (numeric) = 1.8556547866465437186524987147974 absolute error = 9e-63 relative error = 4.8500400315644900788021961000484e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4266 Order of pole (three term test) = -18.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.32 y1[1] (analytic) = 1.5089647068650104421413027004031 y1[1] (numeric) = 1.5089647068650104421413027004031 absolute error = 3e-63 relative error = 1.9881180695290941481089386640300e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8607873878989015441399449026743 y2[1] (numeric) = 1.8607873878989015441399449026743 absolute error = 9e-63 relative error = 4.8366621885600285887041564226182e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.422 Order of pole (three term test) = -18.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2320552424, alloc=4848776, time=122.50 x[1] = 7.33 y1[1] (analytic) = 1.5003315284265934258456373647886 y1[1] (numeric) = 1.5003315284265934258456373647886 absolute error = 4e-63 relative error = 2.6660774130333871800129318122596e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8658339111297899116502539931945 y2[1] (numeric) = 1.8658339111297899116502539931945 absolute error = 9e-63 relative error = 4.8235804625023496627476231686647e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4173 Order of pole (three term test) = -19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2324553772, alloc=4848776, time=122.72 x[1] = 7.34 y1[1] (analytic) = 1.4916483172522753007555626024528 y1[1] (numeric) = 1.4916483172522753007555626024528 absolute error = 4e-63 relative error = 2.6815972328975578843263523297670e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8707938516910911543543202082359 y2[1] (numeric) = 1.8707938516910911543543202082359 absolute error = 9e-63 relative error = 4.8107919490244808585220229826781e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4124 Order of pole (three term test) = -19.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2328554584, alloc=4848776, time=122.93 x[1] = 7.35 y1[1] (analytic) = 1.4829159416559375134916436182999 y1[1] (numeric) = 1.4829159416559375134916436182999 absolute error = 3e-63 relative error = 2.0230411689080435921858025802924e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8756667135928824121513694426684 y2[1] (numeric) = 1.8756667135928824121513694426684 absolute error = 9e-63 relative error = 4.7982938198867401800793917772863e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4073 Order of pole (three term test) = -19.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2332556144, alloc=4848776, time=123.13 x[1] = 7.36 y1[1] (analytic) = 1.4741352748678627424255475449175 y1[1] (numeric) = 1.4741352748678627424255475449175 absolute error = 3e-63 relative error = 2.0350913862154959928544593673868e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8804520095530342106314113723386 y2[1] (numeric) = 1.8804520095530342106314113723386 absolute error = 9e-63 relative error = 4.7860833216047962371690221329891e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4021 Order of pole (three term test) = -19.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.37 y1[1] (analytic) = 1.4653071949474125971016828724969 y1[1] (numeric) = 1.4653071949474125971016828724969 absolute error = 4e-63 relative error = 2.7298030159085878582822533051551e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8851492610459382679555927834817 y2[1] (numeric) = 1.8851492610459382679555927834817 absolute error = 9e-63 relative error = 4.7741577741205095276061409054612e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3967 Order of pole (three term test) = -19.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2336556968, alloc=4848776, time=123.34 x[1] = 7.38 y1[1] (analytic) = 1.4564325846952224137899406331777 y1[1] (numeric) = 1.4564325846952224137899406331777 absolute error = 4e-63 relative error = 2.7464367675054814628985238272663e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8897579983503596569143704586037 y2[1] (numeric) = 1.8897579983503596569143704586037 absolute error = 9e-63 relative error = 4.7625145695144225707228551653148e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3912 Order of pole (three term test) = -20.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2340558336, alloc=4848776, time=123.56 x[1] = 7.39 y1[1] (analytic) = 1.447512331564921927616811305895 y1[1] (numeric) = 1.447512331564921927616811305895 absolute error = 4e-63 relative error = 2.7633616051308902012574093504971e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8942777605964085369871744703402 y2[1] (numeric) = 1.8942777605964085369871744703402 absolute error = 9e-63 relative error = 4.7511511707588082970698225343362e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3855 Order of pole (three term test) = -20.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2344559064, alloc=4848776, time=123.76 x[1] = 7.4 y1[1] (analytic) = 1.4385473275743906491340984687003 y1[1] (numeric) = 1.4385473275743906491340984687003 absolute error = 4e-63 relative error = 2.7805828305590805376290833686805e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8987080958116267592694988965346 y2[1] (numeric) = 1.8987080958116267592694988965346 absolute error = 8e-63 relative error = 4.2133912093424234056508902641402e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3796 Order of pole (three term test) = -20.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.41 y1[1] (analytic) = 1.4295384692165568197136187208456 y1[1] (numeric) = 1.4295384692165568197136187208456 absolute error = 4e-63 relative error = 2.7981058825175631484597901172432e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9030485609661847356453326235512 y2[1] (numeric) = 1.9030485609661847356453326235512 absolute error = 8e-63 relative error = 4.2037813243916228035620350404590e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3736 Order of pole (three term test) = -20.59 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2348559972, alloc=4848776, time=123.97 TOP MAIN SOLVE Loop x[1] = 7.42 y1[1] (analytic) = 1.4204866573697488657980144485792 y1[1] (numeric) = 1.4204866573697488657980144485792 absolute error = 4e-63 relative error = 2.8159363407232699770851559366021e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.907298722017184052555676926842 y2[1] (numeric) = 1.907298722017184052555676926842 absolute error = 8e-63 relative error = 4.1944137578717063564123115066842e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3675 Order of pole (three term test) = -20.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2352560772, alloc=4848776, time=124.18 x[1] = 7.43 y1[1] (analytic) = 1.4113927972076083167875474809437 y1[1] (numeric) = 1.4113927972076083167875474809437 absolute error = 4e-63 relative error = 2.8340799300618943403028291283864e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9114581539520613991386916987506 y2[1] (numeric) = 1.9114581539520613991386916987506 absolute error = 8e-63 relative error = 4.1852864963114629496811357870510e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3612 Order of pole (three term test) = -20.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2356561460, alloc=4848776, time=124.39 x[1] = 7.44 y1[1] (analytic) = 1.4022577981085731951960126380232 y1[1] (numeric) = 1.4022577981085731951960126380232 absolute error = 4e-63 relative error = 2.8525425249161569245467311355244e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.915526440831089469384826128484 y2[1] (numeric) = 1.915526440831089469384826128484 absolute error = 8e-63 relative error = 4.1763975842218288293577459503270e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3547 Order of pole (three term test) = -21.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2360562224, alloc=4848776, time=124.60 x[1] = 7.45 y1[1] (analytic) = 1.3930825735649409306613253235169 y1[1] (numeric) = 1.3930825735649409306613253235169 absolute error = 4e-63 relative error = 2.8713301536490242712709564501959e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9195031758289705882521356215873 y2[1] (numeric) = 1.9195031758289705882521356215873 absolute error = 8e-63 relative error = 4.1677451231853585621435941998362e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3481 Order of pole (three term test) = -21.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.46 y1[1] (analytic) = 1.3838680410915198914436014504911 y1[1] (numeric) = 1.3838680410915198914436014504911 absolute error = 4e-63 relative error = 2.8904490032481835607326235118702e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9233879612755189024138346667882 y2[1] (numeric) = 1.9233879612755189024138346667882 absolute error = 7e-63 relative error = 3.6394113621039106504424520203923e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3414 Order of pole (three term test) = -21.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2364563352, alloc=4848776, time=124.80 x[1] = 7.47 y1[1] (analytic) = 1.3746151221338786681814564223101 y1[1] (numeric) = 1.3746151221338786681814564223101 absolute error = 4e-63 relative error = 2.9099054241383689195893765919359e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9271804086954270674529126075413 y2[1] (numeric) = 1.9271804086954270674529126075413 absolute error = 8e-63 relative error = 4.1511422407077434988975361552448e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3345 Order of pole (three term test) = -21.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2368564368, alloc=4848776, time=125.01 x[1] = 7.48 y1[1] (analytic) = 1.3653247419762022849016888635084 y1[1] (numeric) = 1.3653247419762022849016888635084 absolute error = 5e-63 relative error = 3.6621324189605511330861915869382e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9308801388471134548682316522293 y2[1] (numeric) = 1.9308801388471134548682316522293 absolute error = 8e-63 relative error = 4.1431883000136021105033719322312e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3275 Order of pole (three term test) = -21.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2372565568, alloc=4848776, time=125.22 x[1] = 7.49 y1[1] (analytic) = 1.3559978296487645515844618973593 y1[1] (numeric) = 1.3559978296487645515844618973593 absolute error = 4e-63 relative error = 2.9498572287804431268983044841769e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9344867817606459942037790778139 y2[1] (numeric) = 1.9344867817606459942037790778139 absolute error = 8e-63 relative error = 4.1354637702506875124436206599643e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3204 Order of pole (three term test) = -21.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.5 y1[1] (analytic) = 1.3466353178350258109716193361719 y1[1] (numeric) = 1.3466353178350258109716193361719 absolute error = 5e-63 relative error = 3.7129577204602487552087167596485e-61 % Correct digits = 64 h = 0.01 bytes used=2376568804, alloc=4848776, time=125.42 y2[1] (analytic) = 1.937999976774738857948463798149 y2[1] (numeric) = 1.937999976774738857948463798149 absolute error = 8e-63 relative error = 4.1279670257343199992040020821354e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3132 Order of pole (three term test) = -22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.51 y1[1] (analytic) = 1.3372381427783653697660376664312 y1[1] (numeric) = 1.3372381427783653697660376664312 absolute error = 5e-63 relative error = 3.7390497922917106905624265951741e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9414193725728182895687977852796 y2[1] (numeric) = 1.9414193725728182895687977852796 absolute error = 8e-63 relative error = 4.1206964929984172853141300023513e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3058 Order of pole (three term test) = -22.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2380570212, alloc=4848776, time=125.63 x[1] = 7.52 y1[1] (analytic) = 1.3278072441884579409011711786587 y1[1] (numeric) = 1.3278072441884579409011711786587 absolute error = 5e-63 relative error = 3.7656068091840757381029468754693e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9447446272181539681217138320954 y2[1] (numeric) = 1.9447446272181539681217138320954 absolute error = 8e-63 relative error = 4.1136506500822901037988473654778e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2983 Order of pole (three term test) = -22.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2384570940, alloc=4848776, time=125.83 x[1] = 7.53 y1[1] (analytic) = 1.3183435651473034591585439161043 y1[1] (numeric) = 1.3183435651473034591585439161043 absolute error = 6e-63 relative error = 4.5511656889906369367441796778007e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9479754081880523963403344141535 y2[1] (numeric) = 1.9479754081880523963403344141535 absolute error = 8e-63 relative error = 4.1068280258431789958112989480699e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2906 Order of pole (three term test) = -22.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2388571632, alloc=4848776, time=126.04 x[1] = 7.54 y1[1] (analytic) = 1.3088480520149196670733184671152 y1[1] (numeric) = 1.3088480520149196670733184671152 absolute error = 6e-63 relative error = 4.5841837719536946709835051265027e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.951111392407108892882377468875 y2[1] (numeric) = 1.951111392407108892882377468875 absolute error = 7e-63 relative error = 3.5876987993822425048851646414231e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2829 Order of pole (three term test) = -22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.55 y1[1] (analytic) = 1.2993216543347069017907617945243 y1[1] (numeric) = 1.2993216543347069017907617945243 absolute error = 6e-63 relative error = 4.6177942005224153757048018379399e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.954152266279514863569684152709 y2[1] (numeric) = 1.954152266279514863569684152709 absolute error = 7e-63 relative error = 3.5821159490950053475504963116981e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2751 Order of pole (three term test) = -22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2392572424, alloc=4848776, time=126.25 x[1] = 7.56 y1[1] (analytic) = 1.2897653247384945463160600407277 y1[1] (numeric) = 1.2897653247384945463160600407277 absolute error = 6e-63 relative error = 4.6520090786411285670529682212835e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9570977257204171209186672597821 y2[1] (numeric) = 1.9570977257204171209186672597821 absolute error = 7e-63 relative error = 3.5767248145072909973436830888727e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2671 Order of pole (three term test) = -23.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2396573148, alloc=4848776, time=126.45 x[1] = 7.57 y1[1] (analytic) = 1.2801800188512786404332296334417 y1[1] (numeric) = 1.2801800188512786404332296334417 absolute error = 6e-63 relative error = 4.6868408439805787520183605871059e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9599474761863261160558599363545 y2[1] (numeric) = 1.9599474761863261160558599363545 absolute error = 7e-63 relative error = 3.5715242806509431951670885917670e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.259 Order of pole (three term test) = -23.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2400573864, alloc=4848776, time=126.66 x[1] = 7.58 y1[1] (analytic) = 1.270566695195660177452647741408 y1[1] (numeric) = 1.270566695195660177452647741408 absolute error = 6e-63 relative error = 4.7223022787292826829203056943534e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9627012327045700422207132450103 y2[1] (numeric) = 1.9627012327045700422207132450103 absolute error = 6e-63 relative error = 3.0570113780038231332452974980229e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2509 Order of pole (three term test) = -23.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2404575212, alloc=4848776, time=126.88 x[1] = 7.59 y1[1] (analytic) = 1.2609263150959936428778928397435 y1[1] (numeric) = 1.2609263150959936428778928397435 absolute error = 5e-63 relative error = 3.9653387673326118873796439473620e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9653587199017918644698373032588 y2[1] (numeric) = 1.9653587199017918644698373032588 absolute error = 6e-63 relative error = 3.0528777974434191008592812429848e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2426 Order of pole (three term test) = -23.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.6 y1[1] (analytic) = 1.2512598425822553800581527493518 y1[1] (numeric) = 1.2512598425822553800581527493518 absolute error = 5e-63 relative error = 3.9959725628862014391210231882770e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9679196720314864259034630180288 y2[1] (numeric) = 1.9679196720314864259034630180288 absolute error = 6e-63 relative error = 3.0489049351319258933010279374237e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2342 Order of pole (three term test) = -23.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2408575916, alloc=4848776, time=127.08 x[1] = 7.61 y1[1] (analytic) = 1.2415682442936413959095254813347 y1[1] (numeric) = 1.2415682442936413959095254813347 absolute error = 5e-63 relative error = 4.0271648562054054034472077690614e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9703838330005748767264492819134 y2[1] (numeric) = 1.9703838330005748767264492819134 absolute error = 6e-63 relative error = 3.0450919762485939192604800639450e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2257 Order of pole (three term test) = -23.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2412577612, alloc=4848776, time=127.29 x[1] = 7.62 y1[1] (analytic) = 1.2318524893819042468443058622056 y1[1] (numeric) = 1.2318524893819042468443058622056 absolute error = 5e-63 relative error = 4.0589275445705401607506758432562e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9727509563950137687230748141779 y2[1] (numeric) = 1.9727509563950137687230748141779 absolute error = 6e-63 relative error = 3.0414381402528085039643687908925e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2172 Order of pole (three term test) = -23.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2416578880, alloc=4848776, time=127.50 x[1] = 7.63 y1[1] (analytic) = 1.2221135494144386711391126846887 y1[1] (numeric) = 1.2221135494144386711391126846887 absolute error = 5e-63 relative error = 4.0912728628167907755244893064891e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9750208055044362542575080082731 y2[1] (numeric) = 1.9750208055044362542575080082731 absolute error = 6e-63 relative error = 3.0379426805418141271572448181974e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2086 Order of pole (three term test) = -23.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.64 y1[1] (analytic) = 1.2123523982771256590978578675718 y1[1] (numeric) = 1.2123523982771256590978578675718 absolute error = 5e-63 relative error = 4.1242133946412787519803477380049e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9771931533458229257005890029222 y2[1] (numeric) = 1.9771931533458229257005890029222 absolute error = 6e-63 relative error = 3.0346048841241177718294985007315e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1998 Order of pole (three term test) = -23.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2420579736, alloc=4848776, time=127.70 x[1] = 7.65 y1[1] (analytic) = 1.2025700120769446765215783227058 y1[1] (numeric) = 1.2025700120769446765215783227058 absolute error = 5e-63 relative error = 4.1577620843584467673931620302621e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9792677826861999282187069323438 y2[1] (numeric) = 1.9792677826861999282187069323438 absolute error = 6e-63 relative error = 3.0314240713083243729916720739020e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.191 Order of pole (three term test) = -24.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2424580512, alloc=4848776, time=127.91 x[1] = 7.66 y1[1] (analytic) = 1.1927673690443637801816273360472 y1[1] (numeric) = 1.1927673690443637801816273360472 absolute error = 5e-63 relative error = 4.1919322491241207313440369845348e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9812444860643620761324084988271 y2[1] (numeric) = 1.9812444860643620761324084988271 absolute error = 5e-63 relative error = 2.5236663295059747591229589117296e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1822 Order of pole (three term test) = -24.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2428581576, alloc=4848776, time=128.12 x[1] = 7.67 y1[1] (analytic) = 1.1829454494355173862033368443022 y1[1] (numeric) = 1.1829454494355173862033368443022 absolute error = 5e-63 relative error = 4.2267375916496571194952493704904e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9831230658116188005512045434252 y2[1] (numeric) = 1.9831230658116188005512045434252 absolute error = 5e-63 relative error = 2.5212757020471068137395855471859e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1732 Order of pole (three term test) = -24.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2432582376, alloc=4848776, time=128.33 x[1] = 7.68 y1[1] (analytic) = 1.173105235434181473501793986326 y1[1] (numeric) = 1.173105235434181473501793986326 absolute error = 4e-63 relative error = 3.4097537707429530680941223448840e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9849033340715608537070993661777 y2[1] (numeric) = 1.9849033340715608537070993661777 absolute error = 6e-63 relative error = 3.0228172309491846610766719574282e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1642 Order of pole (three term test) = -24.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.69 y1[1] (analytic) = 1.1632477110535560246677012934441 y1[1] (numeric) = 1.1632477110535560246677012934441 absolute error = 5e-63 relative error = 4.2983106285001746888892885120697e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9865851128188457933328816416347 y2[1] (numeric) = 1.9865851128188457933328816416347 absolute error = 6e-63 relative error = 3.0202582115831714078938631003974e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1551 Order of pole (three term test) = -24.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2436583264, alloc=4848776, time=128.54 x[1] = 7.7 y1[1] (analytic) = 1.1533738620378645259773842395721 y1[1] (numeric) = 1.1533738620378645259773842395721 absolute error = 5e-63 relative error = 4.3351077777726275532102945132067e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9881682338770003685523936187237 y2[1] (numeric) = 1.9881682338770003685523936187237 absolute error = 6e-63 relative error = 3.0178532670244820135311376953155e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.146 Order of pole (three term test) = -24.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2440583968, alloc=4848776, time=128.75 x[1] = 7.71 y1[1] (analytic) = 1.1434846757637803664949450070563 y1[1] (numeric) = 1.1434846757637803664949450070563 absolute error = 5e-63 relative error = 4.3725990439358487245902366955261e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9896525389352380270590248501636 y2[1] (numeric) = 1.9896525389352380270590248501636 absolute error = 6e-63 relative error = 3.0156019116839859089613793260304e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1367 Order of pole (three term test) = -24.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2444585044, alloc=4848776, time=128.95 x[1] = 7.72 y1[1] (analytic) = 1.1335811411416899935445078592584 y1[1] (numeric) = 1.1335811411416899935445078592584 absolute error = 5e-63 relative error = 4.4108002669877107091396095549034e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9910378795642898618457271446539 y2[1] (numeric) = 1.9910378795642898618457271446539 absolute error = 5e-63 relative error = 2.5112530762569813211169402952083e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1275 Order of pole (three term test) = -24.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.73 y1[1] (analytic) = 1.1236642485168026981547284658423 y1[1] (numeric) = 1.1236642485168026981547284658423 absolute error = 4e-63 relative error = 3.5597822083241140461157576695284e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9923241172312474144050701519763 y2[1] (numeric) = 1.9923241172312474144050701519763 absolute error = 6e-63 relative error = 3.0115581837850055783214154591527e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1182 Order of pole (three term test) = -24.67 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2448585852, alloc=4848776, time=129.16 TOP MAIN SOLVE Loop x[1] = 7.74 y1[1] (analytic) = 1.1137349895701169194146144923951 y1[1] (numeric) = 1.1137349895701169194146144923951 absolute error = 4e-63 relative error = 3.5915186623919691223573417845484e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9935111233134158501313865368873 y2[1] (numeric) = 1.9935111233134158501313865368873 absolute error = 5e-63 relative error = 2.5081374974670306637586602709478e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1088 Order of pole (three term test) = -24.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2452587280, alloc=4848776, time=129.37 x[1] = 7.75 y1[1] (analytic) = 1.1037943572192529710276940677138 y1[1] (numeric) = 1.1037943572192529710276940677138 absolute error = 4e-63 relative error = 3.6238634251374934121356528794203e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9945987791111761206190108016398 y2[1] (numeric) = 1.9945987791111761206190108016398 absolute error = 5e-63 relative error = 2.5067698087271851565596751159675e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09941 Order of pole (three term test) = -24.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2456588284, alloc=4848776, time=129.58 x[1] = 7.76 y1[1] (analytic) = 1.0938433455191621067092375928365 y1[1] (numeric) = 1.0938433455191621067092375928365 absolute error = 4e-63 relative error = 3.6568307668421313430462771357173e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9955869758598548266511003661026 y2[1] (numeric) = 1.9955869758598548266511003661026 absolute error = 5e-63 relative error = 2.5055284788304499953783513875035e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08997 Order of pole (three term test) = -24.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2460589480, alloc=4848776, time=129.79 x[1] = 7.77 y1[1] (analytic) = 1.083882949562721853437250999942 y1[1] (numeric) = 1.083882949562721853437250999942 absolute error = 4e-63 relative error = 3.6904353939821147192047513149969e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9964756147406005949026315428916 y2[1] (numeric) = 1.9964756147406005949026315428916 absolute error = 5e-63 relative error = 2.5044132585860024688531800758806e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08049 Order of pole (three term test) = -24.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.78 y1[1] (analytic) = 1.073914165381227552941078415626 y1[1] (numeric) = 1.073914165381227552941078415626 absolute error = 4e-63 relative error = 3.7246924651376067900710827633945e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9972646068902658807289637249532 y2[1] (numeric) = 1.9972646068902658807289637249532 absolute error = 5e-63 relative error = 2.5034239242766048872824864737195e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07098 Order of pole (three term test) = -24.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2464590592, alloc=4848776, time=129.99 x[1] = 7.79 y1[1] (analytic) = 1.0639379898447900621905419292717 y1[1] (numeric) = 1.0639379898447900621905419292717 absolute error = 3e-63 relative error = 2.8197132056894100673062355726186e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9979538734102932088679277373902 y2[1] (numeric) = 1.9979538734102932088679277373902 absolute error = 5e-63 relative error = 2.5025602775631329669507391440519e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06144 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2468591304, alloc=4848776, time=130.20 x[1] = 7.8 y1[1] (analytic) = 1.0539554205626495730325679129525 y1[1] (numeric) = 1.0539554205626495730325679129525 absolute error = 4e-63 relative error = 3.7952269346122981042961844919662e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9985433453746049634387733205961 y2[1] (numeric) = 1.9985433453746049634387733205961 absolute error = 5e-63 relative error = 2.5018221454000063264537888717150e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05188 Order of pole (three term test) = -24.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2472592164, alloc=4848776, time=130.42 x[1] = 7.81 y1[1] (analytic) = 1.043967455783415519510264690171 y1[1] (numeric) = 1.043967455783415519510264690171 absolute error = 4e-63 relative error = 3.8315370635747590434385199067926e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9990329638364959382655506530315 y2[1] (numeric) = 1.9990329638364959382655506530315 absolute error = 5e-63 relative error = 2.5012093799614591512418912720130e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0423 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.82 bytes used=2476593432, alloc=4848776, time=130.63 y1[1] (analytic) = 1.0339750942952425487905865122099 y1[1] (numeric) = 1.0339750942952425487905865122099 absolute error = 4e-63 relative error = 3.8685651347592662318530425394860e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9994226798345279582756373482821 y2[1] (numeric) = 1.9994226798345279582756373482821 absolute error = 5e-63 relative error = 2.5007218585785970736931639353964e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.0327 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.83 y1[1] (analytic) = 1.0239793353259525380203046620934 y1[1] (numeric) = 1.0239793353259525380203046620934 absolute error = 4e-63 relative error = 3.9063288310664220613124090005152e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9997124543974259825161832418216 y2[1] (numeric) = 1.9997124543974259825161832418216 absolute error = 5e-63 relative error = 2.5003594836871942467544187138666e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02308 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2480594492, alloc=4848776, time=130.83 x[1] = 7.84 y1[1] (analytic) = 1.0139811784431126448253687138652 y1[1] (numeric) = 1.0139811784431126448253687138652 absolute error = 5e-63 relative error = 4.9310579982136373034571918845104e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9999022585479751991822513952502 y2[1] (numeric) = 1.9999022585479751991822513952502 absolute error = 5e-63 relative error = 2.5001221827861924684660119282346e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01346 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2484595264, alloc=4848776, time=131.04 x[1] = 7.85 y1[1] (analytic) = 1.0039816234540793835653399973692 y1[1] (numeric) = 1.0039816234540793835653399973692 absolute error = 5e-63 relative error = 4.9801708349980496577216742925009e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9999920733059187229504000722697 y2[1] (numeric) = 1.9999920733059187229504000722697 absolute error = 5e-63 relative error = 2.5000099084068720513657871124991e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.003834 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2488596132, alloc=4848776, time=131.25 x[1] = 7.86 y1[1] (analytic) = 0.99398167030601872285197549971847 y1[1] (numeric) = 0.99398167030601872285197549971847 absolute error = 5.0e-63 relative error = 5.0302738464590016251616813247818e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9999818896898556048503870679297 y2[1] (numeric) = 1.9999818896898556048503870679297 absolute error = 4e-63 relative error = 2.0000181104741375468961237075655e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.005803 Order of pole (three term test) = -0.8937 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.87 y1[1] (analytic) = 0.98398231898591220223889403738305 y1[1] (numeric) = 0.98398231898591220223889403738305 absolute error = 5.1e-63 relative error = 5.1830199604155868343342765076584e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9998717087181389648755908903309 y2[1] (numeric) = 1.9998717087181389648755908903309 absolute error = 5e-63 relative error = 2.5001603743896443064801090016890e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01544 Order of pole (three term test) = -0.8991 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2492596888, alloc=4848776, time=131.46 x[1] = 7.88 y1[1] (analytic) = 0.97398456942055906738732777394789 y1[1] (numeric) = 0.97398456942055906738732777394789 absolute error = 5.1e-63 relative error = 5.2362225851628036552101358947237e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9996615414087741575196361940153 y2[1] (numeric) = 1.9996615414087741575196361940153 absolute error = 4e-63 relative error = 2.0003385158780294351912422511682e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02508 Order of pole (three term test) = -0.9092 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2496597664, alloc=4848776, time=131.67 x[1] = 7.89 y1[1] (analytic) = 0.96398942137658442341111123213176 y1[1] (numeric) = 0.96398942137658442341111123213176 absolute error = 5.2e-63 relative error = 5.3942500661203930879182367389730e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9993514087783169804225849407293 y2[1] (numeric) = 1.9993514087783169804225849407293 absolute error = 4e-63 relative error = 2.0006488016252023795473823663153e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0347 Order of pole (three term test) = -0.9242 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2500598628, alloc=4848776, time=131.88 x[1] = 7.9 y1[1] (analytic) = 0.95399787436046340550224704004151 y1[1] (numeric) = 0.95399787436046340550224704004151 absolute error = 5.2e-63 relative error = 5.4507458976110942268407011315033e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9989413418397720363049105120439 y2[1] (numeric) = 1.9989413418397720363049105120439 absolute error = 4e-63 relative error = 2.0010592188355598299828991236667e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04431 Order of pole (three term test) = -0.944 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2504599636, alloc=4848776, time=132.09 x[1] = 7.91 y1[1] (analytic) = 0.94401092751857136433667294165175 y1[1] (numeric) = 0.94401092751857136433667294165175 absolute error = 5.3e-63 relative error = 5.6143417893811764304166848450949e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.998431381599491458351310017202 y2[1] (numeric) = 1.998431381599491458351310017202 absolute error = 4e-63 relative error = 2.0015698496480305079048845588943e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0539 Order of pole (three term test) = -0.9686 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.92 y1[1] (analytic) = 0.93402957953727006115839826028491 y1[1] (numeric) = 0.93402957953727006115839826028491 absolute error = 5.3e-63 relative error = 5.6743384964592730622440734628230e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.997821579053074309169232028065 y2[1] (numeric) = 1.997821579053074309169232028065 absolute error = 4e-63 relative error = 2.0021807962930886118959281917629e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.06348 Order of pole (three term test) = -0.9981 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2508601848, alloc=4848776, time=132.29 x[1] = 7.93 y1[1] (analytic) = 0.92405482854303986383924017488675 y1[1] (numeric) = 0.92405482854303986383924017488675 absolute error = 5.3e-63 relative error = 5.7355903960336710369963259903409e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9971119951802670633788067322389 y2[1] (numeric) = 1.9971119951802670633788067322389 absolute error = 4e-63 relative error = 2.0028921811362634714144775536490e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07302 Order of pole (three term test) = -1.032 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2512602524, alloc=4848776, time=132.50 x[1] = 7.94 y1[1] (analytic) = 0.91408767200266793061133094292942 y1[1] (numeric) = 0.91408767200266793061133094292942 absolute error = 5.3e-63 relative error = 5.7981309258752709543317774251957e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9963027009388656837816699276909 y2[1] (numeric) = 1.9963027009388656837816699276909 absolute error = 3e-63 relative error = 1.5027781100476862562666240063815e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08254 Order of pole (three term test) = -1.071 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2516603276, alloc=4848776, time=132.71 x[1] = 7.95 y1[1] (analytic) = 0.90412910662350236257084658291809 y1[1] (numeric) = 0.90412910662350236257084658291809 absolute error = 5.3e-63 relative error = 5.8619946655550235948810867324404e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9953937772576199008959823902 y2[1] (numeric) = 1.9953937772576199008959823902 absolute error = 3e-63 relative error = 1.5034626419067348345204221367742e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09202 Order of pole (three term test) = -1.115 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 7.96 y1[1] (analytic) = 0.89418012825378229945458538112409 y1[1] (numeric) = 0.89418012825378229945458538112409 absolute error = 5.3e-63 relative error = 5.9272173833142679089993313711318e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9943853150281404054237780310308 y2[1] (numeric) = 1.9943853150281404054237780310308 absolute error = 3e-63 relative error = 1.5042228687677990442008221858471e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1015 Order of pole (three term test) = -1.164 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2520604248, alloc=4848776, time=132.92 x[1] = 7.97 y1[1] (analytic) = 0.8842417317830539255967605880346 y1[1] (numeric) = 0.8842417317830539255967605880346 absolute error = 5.3e-63 relative error = 5.9938360851988596363832023320553e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.993277415095809762924650126215 y2[1] (numeric) = 1.993277415095809762924650126215 absolute error = 3e-63 relative error = 1.5050589432659581202639894998979e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1109 Order of pole (three term test) = -1.217 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2524604952, alloc=4848776, time=133.12 x[1] = 7.98 y1[1] (analytic) = 0.87431491104268234438242524016836 y1[1] (numeric) = 0.87431491104268234438242524016836 absolute error = 5.4e-63 relative error = 6.1762643319900814991191540668600e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9920701882496979595967340362938 y2[1] (numeric) = 1.9920701882496979595967340362938 absolute error = 3e-63 relative error = 1.5059710333981274889440303989367e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1202 Order of pole (three term test) = -1.275 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2528605660, alloc=4848776, time=133.33 x[1] = 7.99 y1[1] (analytic) = 0.86440065870646926992717726984173 y1[1] (numeric) = 0.86440065870646926992717726984173 absolute error = 5.4e-63 relative error = 6.2471030599176309998831075251061e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9907637552114835876020046344143 y2[1] (numeric) = 1.9907637552114835876020046344143 absolute error = 3e-63 relative error = 1.5069593225949117383279571621265e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1295 Order of pole (three term test) = -1.337 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2532606568, alloc=4848776, time=133.54 x[1] = 8 y1[1] (analytic) = 0.85449996619138647413115861816881 y1[1] (numeric) = 0.85449996619138647413115861816881 absolute error = 5.4e-63 relative error = 6.3194853290263746886492647701796e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9893582466233817778081235982453 y2[1] (numeric) = 1.9893582466233817778081235982453 absolute error = 3e-63 relative error = 1.5080240097991507316445759034883e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1388 Order of pole (three term test) = -1.405 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.01 y1[1] (analytic) = 0.84461382355843491567992109966912 y1[1] (numeric) = 0.84461382355843491567992109966912 absolute error = 5.5e-63 relative error = 6.5118517440645233441593587950102e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.987853803035080087143502358473 y2[1] (numeric) = 1.987853803035080087143502358473 absolute error = 3e-63 relative error = 1.5091653095512167045551048533533e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.148 Order of pole (three term test) = -1.477 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2536607544, alloc=4848776, time=133.74 x[1] = 8.02 y1[1] (analytic) = 0.83474321941363946499664181478805 y1[1] (numeric) = 0.83474321941363946499664181478805 absolute error = 5.5e-63 relative error = 6.5888525621848634043663916933931e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9862505748896836469659584733293 y2[1] (numeric) = 1.9862505748896836469659584733293 absolute error = 3e-63 relative error = 1.5103834520811252598965544704122e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1572 Order of pole (three term test) = -1.553 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2540608252, alloc=4848776, time=133.95 x[1] = 8.03 y1[1] (analytic) = 0.82488914080918912559068876792971 y1[1] (numeric) = 0.82488914080918912559068876792971 absolute error = 5.6e-63 relative error = 6.7887910301578029291168704518637e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9845487225086709779184162261999 y2[1] (numeric) = 1.9845487225086709779184162261999 absolute error = 3e-63 relative error = 1.5116786834075283165623729395227e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1662 Order of pole (three term test) = -1.634 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2544608988, alloc=4848776, time=134.16 x[1] = 8.04 y1[1] (analytic) = 0.81505257314473263769801896017425 y1[1] (numeric) = 0.81505257314473263769801896017425 absolute error = 5.6e-63 relative error = 6.8707224349877393971410343424153e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9827484160758619756776290970863 y2[1] (numeric) = 1.9827484160758619756776290970863 absolute error = 3e-63 relative error = 1.5130512654436622894782365392339e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1753 Order of pole (three term test) = -1.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.05 y1[1] (analytic) = 0.80523450006883933457079152741579 y1[1] (numeric) = 0.80523450006883933457079152741579 absolute error = 5.7e-63 relative error = 7.0786832897903755399122232109410e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9808498356203996707839892683332 y2[1] (numeric) = 1.9808498356203996707839892683332 absolute error = 3e-63 relative error = 1.5145014761103300810378114452011e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1842 Order of pole (three term test) = -1.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2548609772, alloc=4848776, time=134.37 TOP MAIN SOLVE Loop x[1] = 8.06 y1[1] (analytic) = 0.79543590338063510524845128323445 y1[1] (numeric) = 0.79543590338063510524845128323445 absolute error = 5.6e-63 relative error = 7.0401649915471140827748154741312e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9788531709987474643622593641338 y2[1] (numeric) = 1.9788531709987474643622593641338 absolute error = 3e-63 relative error = 1.5160296094560008571316652068877e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1931 Order of pole (three term test) = -1.905 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2552610504, alloc=4848776, time=134.57 x[1] = 8.07 y1[1] (analytic) = 0.7856577629316233001320358003571 y1[1] (numeric) = 0.7856577629316233001320358003571 absolute error = 5.6e-63 relative error = 7.1277854865253516866673856733554e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9767586218757036399946520970817 y2[1] (numeric) = 1.9767586218757036399946520970817 absolute error = 2e-63 relative error = 1.0117573171894113796031390447308e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2019 Order of pole (three term test) = -2.004 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2556611188, alloc=4848776, time=134.79 x[1] = 8.08 y1[1] (analytic) = 0.77590105652770039718933296069646 y1[1] (numeric) = 0.77590105652770039718933296069646 absolute error = 5.7e-63 relative error = 7.3462975105467002816058782584357e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9745663977044350502792493264352 y2[1] (numeric) = 1.9745663977044350502792493264352 absolute error = 2e-63 relative error = 1.0128806011918025174276154302466e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2106 Order of pole (three term test) = -2.107 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2560612312, alloc=4848776, time=135.00 x[1] = 8.09 y1[1] (analytic) = 0.76616675983137622714261511889606 y1[1] (numeric) = 0.76616675983137622714261511889606 absolute error = 5.7e-63 relative error = 7.4396336396197860280305117510471e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9722767177055319746884661471167 y2[1] (numeric) = 1.9722767177055319746884661471167 absolute error = 2e-63 relative error = 1.0140564871275873425986522709975e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2192 Order of pole (three term test) = -2.215 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.1 y1[1] (analytic) = 0.75645584626420853553494823189785 y1[1] (numeric) = 0.75645584626420853553494823189785 absolute error = 5.7e-63 relative error = 7.5351390674679932897657929029671e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9698898108450862432243199360999 y2[1] (numeric) = 1.9698898108450862432243199360999 absolute error = 2e-63 relative error = 1.0152852149339238583656078096818e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2278 Order of pole (three term test) = -2.327 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2564613004, alloc=4848776, time=135.20 x[1] = 8.11 y1[1] (analytic) = 0.74676928690946163813756506302267 y1[1] (numeric) = 0.74676928690946163813756506302267 absolute error = 5.8e-63 relative error = 7.7667896921732835213125394599866e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.967405915811794818039870659888 y2[1] (numeric) = 1.967405915811794818039870659888 absolute error = 2e-63 relative error = 1.0165670357734774565669327980965e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2362 Order of pole (three term test) = -2.443 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2568613664, alloc=4848776, time=135.41 x[1] = 8.12 y1[1] (analytic) = 0.73710805041499890375164420647488 y1[1] (numeric) = 0.73710805041499890375164420647488 absolute error = 5.8e-63 relative error = 7.8685885966576329729601973792484e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9648252809930911226495900140035 y2[1] (numeric) = 1.9648252809930911226495900140035 absolute error = 2e-63 relative error = 1.0179022121443441268192926308958e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2446 Order of pole (three term test) = -2.564 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2572614760, alloc=4848776, time=135.62 x[1] = 8.13 y1[1] (analytic) = 0.72747310289641877507529209311262 y1[1] (numeric) = 0.72747310289641877507529209311262 absolute error = 5.9e-63 relative error = 8.1102654881799406317435524578551e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9621481644503065055758478648868 y2[1] (numeric) = 1.9621481644503065055758478648868 absolute error = 2e-63 relative error = 1.0192910179952173191349911870845e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2528 Order of pole (three term test) = -2.688 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2576615420, alloc=4848776, time=135.83 x[1] = 8.14 y1[1] (analytic) = 0.71786540784044401395292156573867 y1[1] (numeric) = 0.71786540784044401395292156573867 absolute error = 5.9e-63 relative error = 8.2188108461013355705309617022213e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.95937483389286432226445263426 y2[1] (numeric) = 1.95937483389286432226445263426 absolute error = 2e-63 relative error = 1.0207337388458858816285037553581e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.261 Order of pole (three term test) = -2.817 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.15 y1[1] (analytic) = 0.70828592600857383200199339212464 y1[1] (numeric) = 0.70828592600857383200199339212464 absolute error = 5.9e-63 relative error = 8.3299692727885436521766267032316e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9565055666515092158395492118634 y2[1] (numeric) = 1.9565055666515092158395492118634 absolute error = 2e-63 relative error = 1.0222306719131548315435382679511e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.269 Order of pole (three term test) = -2.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2580616280, alloc=4848776, time=136.04 x[1] = 8.16 y1[1] (analytic) = 0.69873561534100854132376841810555 y1[1] (numeric) = 0.69873561534100854132376841810555 absolute error = 5.9e-63 relative error = 8.4438232007403603824026292200893e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9535406496505742737474900484332 y2[1] (numeric) = 1.9535406496505742737474900484332 absolute error = 1e-63 relative error = 5.1189106312114258103268783267092e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.277 Order of pole (three term test) = -3.087 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2584617396, alloc=4848776, time=136.25 x[1] = 8.17 y1[1] (analytic) = 0.6892154308608563327529367613304 y1[1] (numeric) = 0.6892154308608563327529367613304 absolute error = 6.0e-63 relative error = 8.7055508790709624647388791054932e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9504803793792888335509044160486 y2[1] (numeric) = 1.9504803793792888335509044160486 absolute error = 1e-63 relative error = 5.1269421142202672246488602528338e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2848 Order of pole (three term test) = -3.228 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2588618160, alloc=4848776, time=136.46 x[1] = 8.18 y1[1] (analytic) = 0.67972632457863176088847166404938 y1[1] (numeric) = 0.67972632457863176088847166404938 absolute error = 6.0e-63 relative error = 8.8270819932116826517976723046844e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9473250618621298070684763467843 y2[1] (numeric) = 1.9473250618621298070684763467843 absolute error = 1e-63 relative error = 5.1352494741876833277041043365337e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2925 Order of pole (three term test) = -3.373 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.19 y1[1] (analytic) = 0.67026924539705548597762058902613 y1[1] (numeric) = 0.67026924539705548597762058902613 absolute error = 5.9e-63 relative error = 8.8024328141520886299825498223851e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9440750126282194877033101243501 y2[1] (numeric) = 1.9440750126282194877033101243501 absolute error = 1e-63 relative error = 5.1438344379936626460445329282536e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3001 Order of pole (three term test) = -3.521 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2592619128, alloc=4848776, time=136.66 x[1] = 8.2 y1[1] (analytic) = 0.66084513901616479259951187548036 y1[1] (numeric) = 0.66084513901616479259951187548036 absolute error = 5.9e-63 relative error = 8.9279615626493718568509572624138e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9407305566797729011536487499456 y2[1] (numeric) = 1.9407305566797729011536487499456 absolute error = 1e-63 relative error = 5.1526987945756520523606370279498e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3076 Order of pole (three term test) = -3.673 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2596620804, alloc=4848776, time=136.87 x[1] = 8.21 y1[1] (analytic) = 0.65145494783874437401743429021275 y1[1] (numeric) = 0.65145494783874437401743429021275 absolute error = 6.0e-63 relative error = 9.2101533957267434113085733236719e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9372920284595978547445805237238 y2[1] (numeric) = 1.9372920284595978547445805237238 absolute error = 1e-63 relative error = 5.1618443957317659437539092630106e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.315 Order of pole (three term test) = -3.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2600621764, alloc=4848776, time=137.08 x[1] = 8.22 y1[1] (analytic) = 0.64209961087608683904254682894266 y1[1] (numeric) = 0.64209961087608683904254682894266 absolute error = 6.0e-63 relative error = 9.3443445508611081690450564001393e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9337597718176509353487173692576 y2[1] (numeric) = 1.9337597718176509353487173692576 absolute error = 1e-63 relative error = 5.1712731569549771476097422710048e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3222 Order of pole (three term test) = -3.989 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2604622740, alloc=4848776, time=137.29 x[1] = 8.23 y1[1] (analytic) = 0.63278006365409236527979974770724 y1[1] (numeric) = 0.63278006365409236527979974770724 absolute error = 6.0e-63 relative error = 9.4819675028192496143399523274392e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9301341399766528002681829243461 y2[1] (numeric) = 1.9301341399766528002681829243461 absolute error = 1e-63 relative error = 5.1809870582989436887832390953910e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3293 Order of pole (three term test) = -4.153 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.24 y1[1] (analytic) = 0.62349723811971688871249220409109 y1[1] (numeric) = 0.62349723811971688871249220409109 absolute error = 6.0e-63 relative error = 9.6231380560629650331784812980004e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9264154954967661995201683705964 y2[1] (numeric) = 1.9264154954967661995201683705964 absolute error = 1e-63 relative error = 5.1909881452761531838264816968861e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3363 Order of pole (three term test) = -4.319 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2608623432, alloc=4848776, time=137.50 x[1] = 8.25 y1[1] (analytic) = 0.61425206254777818472854847037505 y1[1] (numeric) = 0.61425206254777818472854847037505 absolute error = 6.0e-63 relative error = 9.7679769687925204027472419322993e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9226042102393402616943925628889 y2[1] (numeric) = 1.9226042102393402616943925628889 absolute error = 1e-63 relative error = 5.2012785297890950917739083579671e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3431 Order of pole (three term test) = -4.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2612624292, alloc=4848776, time=137.71 x[1] = 8.26 y1[1] (analytic) = 0.60504546144812915990274875070963 y1[1] (numeric) = 0.60504546144812915990274875070963 absolute error = 6.0e-63 relative error = 9.9166102091559658818561328434480e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9187006653297246689236677183023 y2[1] (numeric) = 1.9187006653297246689236677183023 absolute error = 1e-63 relative error = 5.2118603910952003855535004470991e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3498 Order of pole (three term test) = -4.663 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2616624968, alloc=4848776, time=137.92 x[1] = 8.27 y1[1] (analytic) = 0.59587835547320763712838104690138 y1[1] (numeric) = 0.59587835547320763712838104690138 absolute error = 6.0e-63 relative error = 1.0069169227056740838016632969197e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9147052511191574395190855236994 y2[1] (numeric) = 1.9147052511191574395190855236994 absolute error = 1e-63 relative error = 5.2227359768063184539308233475707e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3564 Order of pole (three term test) = -4.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.28 y1[1] (analytic) = 0.58675166132597187904275931870762 y1[1] (numeric) = 0.58675166132597187904275931870762 absolute error = 6.1e-63 relative error = 1.0396221096698564393437981144190e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9106183671457301294598000680928 y2[1] (numeric) = 1.9106183671457301294598000680928 absolute error = 1e-63 relative error = 5.2339076039235322431607251828502e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3628 Order of pole (three term test) = -5.021 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2620625720, alloc=4848776, time=138.12 TOP MAIN SOLVE Loop x[1] = 8.29 y1[1] (analytic) = 0.57766629166823105611754524541246 y1[1] (numeric) = 0.57766629166823105611754524541246 absolute error = 6.1e-63 relative error = 1.0559729878618900667157838617165e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.9064404220944343561847297311685 y2[1] (numeric) = 1.9064404220944343561847297311685 absolute error = 1e-63 relative error = 5.2453776599081448440568210515547e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3691 Order of pole (three term test) = -5.204 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2624626476, alloc=4848776, time=138.34 x[1] = 8.3 y1[1] (analytic) = 0.56862315502937982629067353455349 y1[1] (numeric) = 0.56862315502937982629067353455349 absolute error = 6.1e-63 relative error = 1.0727667253868377905886017378288e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.902171833756293640000504405253 y2[1] (numeric) = 1.902171833756293640000504405253 absolute error = 1e-63 relative error = 5.2571486037897039696183511181892e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3752 Order of pole (three term test) = -5.391 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2628627156, alloc=4848776, time=138.55 x[1] = 8.31 y1[1] (analytic) = 0.55962315571554615260586332180965 y1[1] (numeric) = 0.55962315571554615260586332180965 absolute error = 6.1e-63 relative error = 1.0900192277069753043865016043739e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8978130289865846498874605706974 y2[1] (numeric) = 1.8978130289865846498874605706974 absolute error = 1e-63 relative error = 5.2692229673119650981843501278805e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3812 Order of pole (three term test) = -5.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2632627932, alloc=4848776, time=138.75 x[1] = 8.32 y1[1] (analytic) = 0.55066719371916144400224181130983 y1[1] (numeric) = 0.55066719371916144400224181130983 absolute error = 6.1e-63 relative error = 1.1077471237756322608385101511792e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8933644436621520315442881127292 y2[1] (numeric) = 1.8933644436621520315442881127292 absolute error = 1e-63 relative error = 5.2816033561177295268006230303096e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.387 Order of pole (three term test) = -5.773 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.33 y1[1] (analytic) = 0.54175616462896206216464322918317 y1[1] (numeric) = 0.54175616462896206216464322918317 absolute error = 6.1e-63 relative error = 1.1259678058629508586328512231492e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8888265226378210861529535570277 y2[1] (numeric) = 1.8888265226378210861529535570277 absolute error = 1e-63 relative error = 5.2942924509735302406499564825221e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3926 Order of pole (three term test) = -5.968 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2636628588, alloc=4848776, time=138.96 x[1] = 8.34 y1[1] (analytic) = 0.53289095954043119420889956615966 y1[1] (numeric) = 0.53289095954043119420889956615966 absolute error = 6.1e-63 relative error = 1.1446994719633978578280292203655e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8841997197019126585597005850824 y2[1] (numeric) = 1.8841997197019126585597005850824 absolute error = 1e-63 relative error = 5.3072930090351764107617969067656e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3981 Order of pole (three term test) = -6.167 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2640629312, alloc=4848776, time=139.17 x[1] = 8.35 y1[1] (analytic) = 0.52407246496669004694022305615659 y1[1] (numeric) = 0.52407246496669004694022305615659 absolute error = 6.1e-63 relative error = 1.1639611709780850477780453863856e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8794844975308646833462389263335 y2[1] (numeric) = 1.8794844975308646833462389263335 absolute error = 1e-63 relative error = 5.3206078651552065398360521724259e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4035 Order of pole (three term test) = -6.367 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2644630204, alloc=4848776, time=139.38 x[1] = 8.36 y1[1] (analytic) = 0.51530156274984727349099746200915 y1[1] (numeric) = 0.51530156274984727349099746200915 absolute error = 6.2e-63 relative error = 1.2031789631908772186675334041289e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8746813276429649265986992559849 y2[1] (numeric) = 1.8746813276429649265986992559849 absolute error = 1e-63 relative error = 5.3342399332333408433575199229826e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4087 Order of pole (three term test) = -6.571 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.37 y1[1] (analytic) = 0.5065791299728154973214391576657 y1[1] (numeric) = 0.5065791299728154973214391576657 absolute error = 6.1e-63 relative error = 1.2041554100989797309084550010400e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8697906903511995500616212829926 y2[1] (numeric) = 1.8697906903511995500616212829926 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 bytes used=2648630888, alloc=4848776, time=139.59 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4137 Order of pole (three term test) = -6.777 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.38 y1[1] (analytic) = 0.49790603887160375185724195569388 y1[1] (numeric) = 0.49790603887160375185724195569388 absolute error = 6.1e-63 relative error = 1.2251307523452275140720711036351e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.86481307471522221278126689719 y2[1] (numeric) = 1.86481307471522221278126689719 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4186 Order of pole (three term test) = -6.986 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2652632336, alloc=4848776, time=139.80 x[1] = 8.39 y1[1] (analytic) = 0.48928315674809460644715252561116 y1[1] (numeric) = 0.48928315674809460644715252561116 absolute error = 6.1e-63 relative error = 1.2467218451871948599751462590133e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8597489784924485132880684290261 y2[1] (numeric) = 1.8597489784924485132880684290261 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4233 Order of pole (three term test) = -7.197 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2656633176, alloc=4848776, time=140.01 x[1] = 8.4 y1[1] (analytic) = 0.48071134588331470085519515941454 y1[1] (numeric) = 0.48071134588331470085519515941454 absolute error = 6.2e-63 relative error = 1.2897552872623386790579303051678e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8545989080882806628332392814224 y2[1] (numeric) = 1.8545989080882806628332392814224 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4278 Order of pole (three term test) = -7.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2660633944, alloc=4848776, time=140.22 x[1] = 8.41 y1[1] (analytic) = 0.47219146345120736116182234815788 y1[1] (numeric) = 0.47219146345120736116182234815788 absolute error = 6.2e-63 relative error = 1.3130267020679971222285497181914e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8493633785054673671707439719806 y2[1] (numeric) = 1.8493633785054673671707439719806 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4321 Order of pole (three term test) = -7.626 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.42 y1[1] (analytic) = 0.46372436143291591974054514062359 y1[1] (numeric) = 0.46372436143291591974054514062359 absolute error = 6.1e-63 relative error = 1.3154366057351180477831323457146e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8440429132926039808542494306898 y2[1] (numeric) = 1.8440429132926039808542494306898 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4363 Order of pole (three term test) = -7.843 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2664635156, alloc=4848776, time=140.43 x[1] = 8.43 y1[1] (analytic) = 0.45531088653158631090661529246805 y1[1] (numeric) = 0.45531088653158631090661529246805 absolute error = 6.1e-63 relative error = 1.3397439377010864233937451767535e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8386380444917780839907114629715 y2[1] (numeric) = 1.8386380444917780839907114629715 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4403 Order of pole (three term test) = -8.063 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2668636260, alloc=4848776, time=140.63 x[1] = 8.44 y1[1] (analytic) = 0.44695188008769746190719673732551 y1[1] (numeric) = 0.44695188008769746190719673732551 absolute error = 6.1e-63 relative error = 1.3648001656919095842225743939260e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8331493125853657168492924788063 y2[1] (numeric) = 1.8331493125853657168492924788063 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4441 Order of pole (three term test) = -8.285 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2672636988, alloc=4848776, time=140.85 x[1] = 8.45 y1[1] (analytic) = 0.43864817799492794614336959040814 y1[1] (numeric) = 0.43864817799492794614336959040814 absolute error = 6.2e-63 relative error = 1.4134334327661769302818169837220e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8275772664419835926578132727978 y2[1] (numeric) = 1.8275772664419835926578132727978 absolute error = 1e-63 relative error = 5.4717248805947815829525503016178e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4478 Order of pole (three term test) = -8.508 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2676638016, alloc=4848776, time=141.06 x[1] = 8.46 y1[1] (analytic) = 0.43040061061656731188853359559002 y1[1] (numeric) = 0.43040061061656731188853359559002 absolute error = 6.2e-63 relative error = 1.4405184024061291198041936861568e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.821922463261602693320419537459 y2[1] (numeric) = 1.821922463261602693320419537459 absolute error = 1e-63 relative error = 5.4887077807350900759550916784442e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4512 Order of pole (three term test) = -8.734 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.47 y1[1] (analytic) = 0.42221000270248044530068218175304 y1[1] (numeric) = 0.42221000270248044530068218175304 absolute error = 6.2e-63 relative error = 1.4684635513879490484291567312657e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8161854685198287366511528252971 y2[1] (numeric) = 1.8161854685198287366511528252971 absolute error = 1e-63 relative error = 5.5060455957451804002762446663009e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4545 Order of pole (three term test) = -8.961 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2680638868, alloc=4848776, time=141.26 x[1] = 8.48 y1[1] (analytic) = 0.41407717330663327122304976748636 y1[1] (numeric) = 0.41407717330663327122304976748636 absolute error = 6.2e-63 relative error = 1.4973054299249583072334082074927e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.810366855911355087030269813403 y2[1] (numeric) = 1.810366855911355087030269813403 absolute error = 1e-63 relative error = 5.5237423107627041402291206236722e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4576 Order of pole (three term test) = -9.189 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2684639580, alloc=4848776, time=141.47 x[1] = 8.49 y1[1] (analytic) = 0.40600293570518803913432389583803 y1[1] (numeric) = 0.40600293570518803913432389583803 absolute error = 6.2e-63 relative error = 1.5270825540291221001344932626931e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.8044672072925937641451218212426 y2[1] (numeric) = 1.8044672072925937641451218212426 absolute error = 1e-63 relative error = 5.5418020120209939005867274520417e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.03 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4606 Order of pole (three term test) = -9.419 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2688640420, alloc=4848776, time=141.68 x[1] = 8.5 y1[1] (analytic) = 0.397988097315176384651573477043 y1[1] (numeric) = 0.397988097315176384651573477043 absolute error = 6.1e-63 relative error = 1.5327091541557492109388883507652e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7984871126234902866669131603391 y2[1] (numeric) = 1.7984871126234902866669131603391 absolute error = 2e-63 relative error = 1.1120457777885095343512874607727e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.32 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4633 Order of pole (three term test) = -9.651 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.51 y1[1] (analytic) = 0.39003345961375829921197062356349 y1[1] (numeric) = 0.39003345961375829921197062356349 absolute error = 6.2e-63 relative error = 1.5896072111709918242081078178941e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7924271699085281693304831713681 y2[1] (numeric) = 1.7924271699085281693304831713681 absolute error = 2e-63 relative error = 1.1158054472595752757596574258110e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.63 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4659 Order of pole (three term test) = -9.884 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2692641164, alloc=4848776, time=141.89 x[1] = 8.52 y1[1] (analytic) = 0.38213981805807508196905393760653 y1[1] (numeric) = 0.38213981805807508196905393760653 absolute error = 6.2e-63 relative error = 1.6224428094163600110707195046227e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7862879851369289729182412152366 y2[1] (numeric) = 1.7862879851369289729182412152366 absolute error = 2e-63 relative error = 1.1196402912863397023164106907546e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.93 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4682 Order of pole (three term test) = -10.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2696642204, alloc=4848776, time=142.10 x[1] = 8.53 y1[1] (analytic) = 0.37430796200570428854155464066714 y1[1] (numeric) = 0.37430796200570428854155464066714 absolute error = 6.2e-63 relative error = 1.6563900930072961498267938394453e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7800701722220538870934230990784 y2[1] (numeric) = 1.7800701722220538870934230990784 absolute error = 1e-63 relative error = 5.6177560615585414291118667295314e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4704 Order of pole (three term test) = -10.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2700643980, alloc=4848776, time=142.31 x[1] = 8.54 y1[1] (analytic) = 0.36653867463572463105362334073292 y1[1] (numeric) = 0.36653867463572463105362334073292 absolute error = 6.1e-63 relative error = 1.6642172905935052216192150876893e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7737743529400129058738870988791 y2[1] (numeric) = 1.7737743529400129058738870988791 absolute error = 1e-63 relative error = 5.6376956761298876335587558712645e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.55 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4724 Order of pole (three term test) = -10.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2704644856, alloc=4848776, time=142.52 x[1] = 8.55 y1[1] (analytic) = 0.35883273287039872291067438377066 y1[1] (numeric) = 0.35883273287039872291067438377066 absolute error = 6.1e-63 relative error = 1.6999563978471175876732408994926e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7674011568674877347777433492199 y2[1] (numeric) = 1.7674011568674877347777433492199 absolute error = 1e-63 relative error = 5.6580250392750861567069740918783e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4742 Order of pole (three term test) = -10.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.56 y1[1] (analytic) = 0.35119090729748149997110604325389 y1[1] (numeric) = 0.35119090729748149997110604325389 absolute error = 6.1e-63 relative error = 1.7369470203375464815768804584018e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7609512213187746472982879658692 y2[1] (numeric) = 1.7609512213187746472982879658692 absolute error = 1e-63 relative error = 5.6787490073183343379484757827473e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.2 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4758 Order of pole (three term test) = -11.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2708645716, alloc=4848776, time=142.73 x[1] = 8.57 y1[1] (analytic) = 0.34361396209316208720703660916504 y1[1] (numeric) = 0.34361396209316208720703660916504 absolute error = 6.0e-63 relative error = 1.7461455766961106007318052819557e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.754425191282053586370130296421 y2[1] (numeric) = 1.754425191282053586370130296421 absolute error = 1e-63 relative error = 5.6998725563741238503580034901276e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4772 Order of pole (three term test) = -11.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2712646964, alloc=4848776, time=142.94 x[1] = 8.58 y1[1] (analytic) = 0.33610265494564681660317540579733 y1[1] (numeric) = 0.33610265494564681660317540579733 absolute error = 6.0e-63 relative error = 1.7851688797192917488666864870032e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7478237193548898838632577811713 y2[1] (numeric) = 1.7478237193548898838632577811713 absolute error = 1e-63 relative error = 5.7214007850236370089378616349995e-62 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.87 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4785 Order of pole (three term test) = -11.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2716647624, alloc=4848776, time=143.15 x[1] = 8.59 y1[1] (analytic) = 0.32865773697939103792835824510594 y1[1] (numeric) = 0.32865773697939103792835824510594 absolute error = 6.0e-63 relative error = 1.8256074100504862718976203753958e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7411474656789750478793406298218 y2[1] (numeric) = 1.7411474656789750478793406298218 absolute error = 2e-63 relative error = 1.1486677834149350679831064105705e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.21 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4795 Order of pole (three term test) = -11.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.6 y1[1] (analytic) = 0.32127995267998729913553021483952 y1[1] (numeric) = 0.32127995267998729913553021483952 absolute error = 6.0e-63 relative error = 1.8675301555389401125188149317393e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7343970978741131437171641875635 y2[1] (numeric) = 1.7343970978741131437171641875635 absolute error = 2e-63 relative error = 1.1531384608815604554818088651748e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.56 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4803 Order of pole (three term test) = -12.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2720648560, alloc=4848776, time=143.35 TOP MAIN SOLVE Loop x[1] = 8.61 y1[1] (analytic) = 0.31397003981971740750954282881698 y1[1] (numeric) = 0.31397003981971740750954282881698 absolute error = 5.9e-63 relative error = 1.8791601910130656763960605205864e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7275732909714593698140812814806 y2[1] (numeric) = 1.7275732909714593698140812814806 absolute error = 2e-63 relative error = 1.1576932859822971736045100632146e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.92 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.481 Order of pole (three term test) = -12.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2724649608, alloc=4848776, time=143.56 x[1] = 8.62 y1[1] (analytic) = 0.30672872938377581629461101739017 y1[1] (numeric) = 0.30672872938377581629461101739017 absolute error = 5.9e-63 relative error = 1.9235237637678148413607658241301e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7206767273460175047502560674387 y2[1] (numeric) = 1.7206767273460175047502560674387 absolute error = 2e-63 relative error = 1.1623333821018271396874654346258e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.28 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4815 Order of pole (three term test) = -12.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2728650460, alloc=4848776, time=143.77 x[1] = 8.63 y1[1] (analytic) = 0.29955674549717171440128690618464 y1[1] (numeric) = 0.29955674549717171440128690618464 absolute error = 5.9e-63 relative error = 1.9695767458709105435447685328582e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7137080966484029755147470130818 y2[1] (numeric) = 1.7137080966484029755147470130818 absolute error = 2e-63 relative error = 1.1670599000562082238068689866437e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.65 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -12.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2732651256, alloc=4848776, time=143.97 x[1] = 8.64 y1[1] (analytic) = 0.29245480535231712892306496354556 y1[1] (numeric) = 0.29245480535231712892306496354556 absolute error = 5.9e-63 relative error = 2.0174057297134625824814608658938e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.7066680957358783706697384884108 y2[1] (numeric) = 1.7066680957358783706697384884108 absolute error = 2e-63 relative error = 1.1718740187368670863104847903672e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.02 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = -12.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.98 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.65 y1[1] (analytic) = 0.28542361913730828159202380941506 y1[1] (numeric) = 0.28542361913730828159202380941506 absolute error = 5.9e-63 relative error = 2.0671029320673340930625661611184e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6995574286026682948041343266528 y2[1] (numeric) = 1.6995574286026682948041343266528 absolute error = 2e-63 relative error = 1.1767769457748466530341073726831e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4817 Order of pole (three term test) = -13.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.6 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2736652600, alloc=4848776, time=144.18 x[1] = 8.66 y1[1] (analytic) = 0.27846388996490737097809378439138 y1[1] (numeric) = 0.27846388996490737097809378439138 absolute error = 5.9e-63 relative error = 2.1187666381962598152967436233347e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6923768063095605327329972350144 y2[1] (numeric) = 1.6923768063095605327329972350144 absolute error = 2e-63 relative error = 1.1817699182259832238247621401914e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 19.19 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4814 Order of pole (three term test) = -13.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 18.23 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2740653700, alloc=4848776, time=144.38 x[1] = 8.67 y1[1] (analytic) = 0.27157631380223188219454870131795 y1[1] (numeric) = 0.27157631380223188219454870131795 absolute error = 5.9e-63 relative error = 2.1725016874249628767374823139129e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6851269469128005632677486104297 y2[1] (numeric) = 1.6851269469128005632677486104297 absolute error = 2e-63 relative error = 1.1868542032777148498172593318813e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.81 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4809 Order of pole (three term test) = -13.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.87 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2744654428, alloc=4848776, time=144.59 x[1] = 8.68 y1[1] (analytic) = 0.26476157940115845512015918362236 y1[1] (numeric) = 0.26476157940115845512015918362236 absolute error = 5.9e-63 relative error = 2.2284200046489769332285122366982e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6778085753922865330464973659755 y2[1] (numeric) = 1.6778085753922865330464973659755 absolute error = 2e-63 relative error = 1.1920310989782503959953929806835e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.44 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4802 Order of pole (three term test) = -13.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2748655224, alloc=4848776, time=144.80 x[1] = 8.69 y1[1] (analytic) = 0.2580203682294482706931887919121 y1[1] (numeric) = 0.2580203682294482706931887919121 absolute error = 5.9e-63 relative error = 2.2866411828206296291538456073515e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6704224235790718708672774127254 y2[1] (numeric) = 1.6704224235790718708672774127254 absolute error = 2e-63 relative error = 1.1973019349888576828048187832702e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 18.07 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4793 Order of pole (three term test) = -14.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 17.17 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.7 y1[1] (analytic) = 0.25135335440260084268120821911072 y1[1] (numeric) = 0.25135335440260084268120821911072 absolute error = 5.9e-63 relative error = 2.3472931220761741298758565193167e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6629692300821827922023461866156 y2[1] (numeric) = 1.6629692300821827922023461866156 absolute error = 2e-63 relative error = 1.2026680733600593317283773220652e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.71 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4782 Order of pole (three term test) = -14.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2752656604, alloc=4848776, time=145.01 x[1] = 8.71 y1[1] (analytic) = 0.24476120461644302949076225515113 y1[1] (numeric) = 0.24476120461644302949076225515113 absolute error = 5.8e-63 relative error = 2.3696565838891759846655507817143e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6554497402147580120821075808528 y2[1] (numeric) = 1.6554497402147580120821075808528 absolute error = 2e-63 relative error = 1.2081309093325564855727913648178e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.477 Order of pole (three term test) = -14.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.49 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2756657404, alloc=4848776, time=145.22 x[1] = 8.72 y1[1] (analytic) = 0.23824457808046000705953291829004 y1[1] (numeric) = 0.23824457808046000705953291829004 absolute error = 5.8e-63 relative error = 2.4344730305011276385884289576032e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.647864705919518052315820857473 y2[1] (numeric) = 1.647864705919518052315820857473 absolute error = 3e-63 relative error = 1.8205378082456002481069538476631e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 17.01 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4755 Order of pole (three term test) = -14.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 16.16 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2760658908, alloc=4848776, time=145.43 x[1] = 8.73 y1[1] (analytic) = 0.23180412645187486967815219933192 y1[1] (numeric) = 0.23180412645187486967815219933192 absolute error = 5.8e-63 relative error = 2.5021124898758628857075112816317e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6402148856935715960562647635402 y2[1] (numeric) = 1.6402148856935715960562647635402 absolute error = 3e-63 relative error = 1.8290286389709465949861215340725e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.67 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4739 Order of pole (three term test) = -15.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.83 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.74 y1[1] (analytic) = 0.22544049377048345072664875461818 y1[1] (numeric) = 0.22544049377048345072664875461818 absolute error = 5.8e-63 relative error = 2.5727409938628267692027330909304e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6325010445125664090102392232487 y2[1] (numeric) = 1.6325010445125664090102392232487 absolute error = 3e-63 relative error = 1.8376711059904666868075777949683e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16.33 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.472 Order of pole (three term test) = -15.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.52 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2764659800, alloc=4848776, time=145.63 x[1] = 8.75 y1[1] (analytic) = 0.21915431639425087978915076807331 y1[1] (numeric) = 0.21915431639425087978915076807331 absolute error = 5.7e-63 relative error = 2.6009070201227071387763326096702e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6247239537541924121395762007922 y2[1] (numeric) = 1.6247239537541924121395762007922 absolute error = 3e-63 relative error = 1.8464675141078616273700156931128e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 16 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.47 Order of pole (three term test) = -15.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 15.2 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2768660564, alloc=4848776, time=145.84 x[1] = 8.76 y1[1] (analytic) = 0.2129462229356763164374641551822 y1[1] (numeric) = 0.2129462229356763164374641551822 absolute error = 5.7e-63 relative error = 2.6767321445855241651784882847871e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6168843911210445554816424059899 y2[1] (numeric) = 1.6168843911210445554816424059899 absolute error = 3e-63 relative error = 1.8554202245220459201594703271791e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.68 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4678 Order of pole (three term test) = -15.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.89 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2772661256, alloc=4848776, time=146.05 x[1] = 8.77 y1[1] (analytic) = 0.20681683419893222415711853932893 y1[1] (numeric) = 0.20681683419893222415711853932893 absolute error = 5.6e-63 relative error = 2.7077099510253079160382707702903e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6089831405628532067376710681854 y2[1] (numeric) = 1.6089831405628532067376710681854 absolute error = 3e-63 relative error = 1.8645316562798429188008702946527e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.36 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4654 Order of pole (three term test) = -16.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.59 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2776661928, alloc=4848776, time=146.26 x[1] = 8.78 y1[1] (analytic) = 0.20076676311778447043610463211708 y1[1] (numeric) = 0.20076676311778447043610463211708 absolute error = 5.6e-63 relative error = 2.7893063139712176010170425255761e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.6010209921980898315252561517565 y2[1] (numeric) = 1.6010209921980898315252561517565 absolute error = 3e-63 relative error = 1.8738042877758959604716851669953e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 15.04 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.4628 Order of pole (three term test) = -16.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 14.29 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.79 y1[1] (analytic) = 0.19479661469429946095456106645153 y1[1] (numeric) = 0.19479661469429946095456106645153 absolute error = 5.5e-63 relative error = 2.8234576913111787810369183083636e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5929987422349558046616553817875 y2[1] (numeric) = 1.5929987422349558046616553817875 absolute error = 3e-63 relative error = 1.8832406583014876453412970611916e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 Radius of convergence (ratio test) for eq 1 = 14.73 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 1 = 0.46 Order of pole (three term test) = -16.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.99 Order of pole (ratio test) Not computed NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2780662860, alloc=4848776, time=146.46 x[1] = 8.8 y1[1] (analytic) = 0.18890698593834443711091449578068 y1[1] (numeric) = 0.18890698593834443711091449578068 absolute error = 5.5e-63 relative error = 2.9114857625197052984144840119642e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5849171928917622535309313118124 y2[1] (numeric) = 1.5849171928917622535309313118124 absolute error = 4e-63 relative error = 2.5237911595253730506194238863723e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4571 Order of pole (three term test) = -16.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2784663600, alloc=4848776, time=146.68 x[1] = 8.81 y1[1] (analytic) = 0.18309846580788698680430409481551 y1[1] (numeric) = 0.18309846580788698680430409481551 absolute error = 5.5e-63 relative error = 3.0038482167135050279195086457515e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.576777152316708895484243810161 y2[1] (numeric) = 1.576777152316708895484243810161 absolute error = 4e-63 relative error = 2.5368201169854131059271840875591e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4539 Order of pole (three term test) = -17.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2788664264, alloc=4848776, time=146.88 x[1] = 8.82 y1[1] (analytic) = 0.17737163515009973847246197742839 y1[1] (numeric) = 0.17737163515009973847246197742839 absolute error = 5.5e-63 relative error = 3.1008340174265497690076616471254e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5685794345070698913227031896634 y2[1] (numeric) = 1.5685794345070698913227031896634 absolute error = 4e-63 relative error = 2.5500780591688748328143825225925e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4506 Order of pole (three term test) = -17.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.83 y1[1] (analytic) = 0.17172706664327612786656648565256 y1[1] (numeric) = 0.17172706664327612786656648565256 absolute error = 5.4e-63 relative error = 3.1445246841706498216528457491053e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5603248592277947962100907977845 y2[1] (numeric) = 1.5603248592277947962100907977845 absolute error = 5e-63 relative error = 3.2044608982737744632154970027393e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4471 Order of pole (three term test) = -17.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2792665056, alloc=4848776, time=147.10 TOP MAIN SOLVE Loop x[1] = 8.84 y1[1] (analytic) = 0.1661653247395630459379874981106 y1[1] (numeric) = 0.1661653247395630459379874981106 absolute error = 5.3e-63 relative error = 3.1895944646134099702027003104053e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5520142519295327478525234803321 y2[1] (numeric) = 1.5520142519295327478525234803321 absolute error = 5e-63 relative error = 3.2216199005800229609344468279950e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4434 Order of pole (three term test) = -17.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2796666044, alloc=4848776, time=147.30 x[1] = 8.85 y1[1] (analytic) = 0.16068696560851609452441244898895 y1[1] (numeric) = 0.16068696560851609452441244898895 absolute error = 5.2e-63 relative error = 3.2361056668832945977905446128995e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5436484436660880894579310034853 y2[1] (numeric) = 1.5436484436660880894579310034853 absolute error = 5e-63 relative error = 3.2390794811578012499528778657290e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4396 Order of pole (three term test) = -17.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2800667056, alloc=4848776, time=147.51 x[1] = 8.86 y1[1] (analytic) = 0.15529253708148309426274731481916 y1[1] (numeric) = 0.15529253708148309426274731481916 absolute error = 5.2e-63 relative error = 3.3485189293233860712916862131875e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.535228271011315681844263734824 y2[1] (numeric) = 1.535228271011315681844263734824 absolute error = 5e-63 relative error = 3.2568446623942782916509735197626e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4355 Order of pole (three term test) = -18.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2804668244, alloc=4848776, time=147.72 x[1] = 8.87 y1[1] (analytic) = 0.14998257859682140633165435671775 y1[1] (numeric) = 0.14998257859682140633165435671775 absolute error = 5.1e-63 relative error = 3.4003949310070634683538750177793e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5267545759754642150959660868594 y2[1] (numeric) = 1.5267545759754642150959660868594 absolute error = 5e-63 relative error = 3.2749205921360557606911941824039e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4313 Order of pole (three term test) = -18.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.88 y1[1] (analytic) = 0.14475762114595454624590028460325 y1[1] (numeric) = 0.14475762114595454624590028460325 absolute error = 5.1e-63 relative error = 3.5231305679290147811482732093398e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5182282059209758853678364011496 y2[1] (numeric) = 1.5182282059209758853678364011496 absolute error = 5e-63 relative error = 3.2933125471522501197989876501942e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.427 Order of pole (three term test) = -18.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2808669572, alloc=4848776, time=147.93 x[1] = 8.89 y1[1] (analytic) = 0.13961818722027348399618273657824 y1[1] (numeric) = 0.13961818722027348399618273657824 absolute error = 5.0e-63 relative error = 3.5811953295966923555516347301109e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5096500134777508567984261849018 y2[1] (numeric) = 1.5096500134777508567984261849018 absolute error = 5e-63 relative error = 3.3120259367146951900804205220862e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4224 Order of pole (three term test) = -18.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2812670644, alloc=4848776, time=148.15 x[1] = 8.9 y1[1] (analytic) = 0.13456479075888794036017232177465 y1[1] (numeric) = 0.13456479075888794036017232177465 absolute error = 4.9e-63 relative error = 3.6413685722439674161235953108424e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.5010208564578849820161746471113 y2[1] (numeric) = 1.5010208564578849820161746471113 absolute error = 5e-63 relative error = 3.3310663062997139090019880364425e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4177 Order of pole (three term test) = -18.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2816671704, alloc=4848776, time=148.36 x[1] = 8.91 y1[1] (analytic) = 0.12959793709723290421159868118538 y1[1] (numeric) = 0.12959793709723290421159868118538 absolute error = 4.8e-63 relative error = 3.7037626581962674315803825007556e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.492341597769889307395176258041 y2[1] (numeric) = 1.492341597769889307395176258041 absolute error = 5e-63 relative error = 3.3504393414161011126513599647418e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4128 Order of pole (three term test) = -19.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2820673004, alloc=4848776, time=148.57 x[1] = 8.92 y1[1] (analytic) = 0.12471812291653551013282189839333 y1[1] (numeric) = 0.12471812291653551013282189839333 absolute error = 4.8e-63 relative error = 3.8486788349214333158247000928149e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4836131053323999410385722479477 y2[1] (numeric) = 1.4836131053323999410385722479477 absolute error = 5e-63 relative error = 3.3701508715641616343103007303253e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4078 Order of pole (three term test) = -19.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.93 y1[1] (analytic) = 0.11992583619414732960101720810331 y1[1] (numeric) = 0.11992583619414732960101720810331 absolute error = 4.8e-63 relative error = 4.0024736556594062680147170064973e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.474836251987386912430859502249 y2[1] (numeric) = 1.474836251987386912430859502249 absolute error = 4e-63 relative error = 2.7121654994646882201446929094721e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4025 Order of pole (three term test) = -19.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2824673888, alloc=4848776, time=148.77 x[1] = 8.94 y1[1] (analytic) = 0.1152215561547470424774647646268 y1[1] (numeric) = 0.1152215561547470424774647646268 absolute error = 4.7e-63 relative error = 4.0790978327768084853979298289262e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4660119154128707028008259130412 y2[1] (numeric) = 1.4660119154128707028008259130412 absolute error = 5e-63 relative error = 3.4106134796263628018907972098060e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3972 Order of pole (three term test) = -19.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2828674772, alloc=4848776, time=148.98 x[1] = 8.95 y1[1] (analytic) = 0.11060575322241836849213123646506 y1[1] (numeric) = 0.11060575322241836849213123646506 absolute error = 4.7e-63 relative error = 4.2493268777336713097076858033154e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4571409780351551744693399111853 y2[1] (numeric) = 1.4571409780351551744693399111853 absolute error = 5e-63 relative error = 3.4313769740674806166947163206650e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3916 Order of pole (three term test) = -20 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2832675688, alloc=4848776, time=149.19 x[1] = 8.96 y1[1] (analytic) = 0.10607888897360805089045984485144 y1[1] (numeric) = 0.10607888897360805089045984485144 absolute error = 4.6e-63 relative error = 4.3363953417201223249757495027312e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4482243269405856758159204182652 y2[1] (numeric) = 1.4482243269405856758159204182652 absolute error = 4e-63 relative error = 2.7620030444110213764404270902682e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3859 Order of pole (three term test) = -20.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 8.97 y1[1] (analytic) = 0.10164141609096859640480261762689 y1[1] (numeric) = 0.10164141609096859640480261762689 absolute error = 4.6e-63 relative error = 4.5257141989078756202694467295928e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4392628537868411459800558940076 y2[1] (numeric) = 1.4392628537868411459800558940076 absolute error = 4e-63 relative error = 2.7792004702098781376050350230490e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3801 Order of pole (three term test) = -20.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2836676888, alloc=4848776, time=149.40 x[1] = 8.98 y1[1] (analytic) = 0.097293778318090387238033460080346 y1[1] (numeric) = 0.097293778318090387238033460080346 absolute error = 4.53e-63 relative error = 4.6560017282808218966499616932728e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4302574547137690900128793475898 y2[1] (numeric) = 1.4302574547137690900128793475898 absolute error = 4e-63 relative error = 2.7966992843260528791391443508449e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3741 Order of pole (three term test) = -20.57 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2840677556, alloc=4848776, time=149.61 x[1] = 8.99 y1[1] (analytic) = 0.093036410415127691810420567177367 y1[1] (numeric) = 0.093036410415127691810420567177367 absolute error = 4.50e-63 relative error = 4.8368160163542824945542641936373e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4212090302537723409073802056387 y2[1] (numeric) = 1.4212090302537723409073802056387 absolute error = 4e-63 relative error = 2.8145050550978813184659793169937e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.368 Order of pole (three term test) = -20.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2844678784, alloc=4848776, time=149.81 x[1] = 9 y1[1] (analytic) = 0.088869738115323011631705288818835 y1[1] (numeric) = 0.088869738115323011631705288818835 absolute error = 4.45e-63 relative error = 5.0073288099773599130359529233717e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4121184852417565697562725663524 y2[1] (numeric) = 1.4121184852417565697562725663524 absolute error = 5e-63 relative error = 3.5407793696178358045765648864313e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3617 Order of pole (three term test) = -20.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2848679872, alloc=4848776, time=150.02 x[1] = 9.01 y1[1] (analytic) = 0.084794178082434111827470650068928 y1[1] (numeric) = 0.084794178082434111827470650068928 absolute error = 4.41e-63 relative error = 5.2008287593904654686655600669229e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.4029867287246475492114605615293 y2[1] (numeric) = 1.4029867287246475492114605615293 absolute error = 5e-63 relative error = 3.5638255855385985687117320633540e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3552 Order of pole (three term test) = -21.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.02 y1[1] (analytic) = 0.080810137869067992581269533196919 y1[1] (numeric) = 0.080810137869067992581269533196919 absolute error = 4.35e-63 relative error = 5.3829879699599748340701544173951e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3938146738704872184433528508576 y2[1] (numeric) = 1.3938146738704872184433528508576 absolute error = 4e-63 relative error = 2.8698219892407867047602948350208e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3487 Order of pole (three term test) = -21.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2852681288, alloc=4848776, time=150.23 x[1] = 9.03 y1[1] (analytic) = 0.076918015875925968060646733988494 y1[1] (numeric) = 0.076918015875925968060646733988494 absolute error = 4.34e-63 relative error = 5.6423712319890277519832891396691e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3846032378771176399177772903271 y2[1] (numeric) = 1.3846032378771176399177772903271 absolute error = 4e-63 relative error = 2.8889142323058734598603244988234e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3419 Order of pole (three term test) = -21.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2856681980, alloc=4848776, time=150.44 x[1] = 9.04 y1[1] (analytic) = 0.07311820131196392828519996910056 y1[1] (numeric) = 0.07311820131196392828519996910056 absolute error = 4.25e-63 relative error = 5.8125062210804082295404512239037e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3753533418804619795187216342643 y2[1] (numeric) = 1.3753533418804619795187216342643 absolute error = 4e-63 relative error = 2.9083435348555379662109802892884e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3351 Order of pole (three term test) = -21.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2860682828, alloc=4848776, time=150.65 x[1] = 9.05 y1[1] (analytic) = 0.069411074155471767877293357247927 y1[1] (numeric) = 0.069411074155471767877293357247927 absolute error = 4.25e-63 relative error = 6.1229422706822738482107049425383e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3660659108624116818424557351316 y2[1] (numeric) = 1.3660659108624116818424557351316 absolute error = 4e-63 relative error = 2.9281164021395996983778823463499e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3281 Order of pole (three term test) = -21.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.06 y1[1] (analytic) = 0.065797005116075873720114601611839 y1[1] (numeric) = 0.065797005116075873720114601611839 absolute error = 4.17e-63 relative error = 6.3376744771946519101585286033412e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3567418735583290518687453974845 y2[1] (numeric) = 1.3567418735583290518687453974845 absolute error = 3e-63 relative error = 2.2111796344369436080589975463545e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.321 Order of pole (three term test) = -21.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2864683680, alloc=4848776, time=150.86 x[1] = 9.07 y1[1] (analytic) = 0.0622763555976684712426455796823 y1[1] (numeric) = 0.0622763555976684712426455796823 absolute error = 4.17e-63 relative error = 6.6959602243585978852814153306004e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3473821623641744926739098396967 y2[1] (numeric) = 1.3473821623641744926739098396967 absolute error = 4e-63 relative error = 2.9687197231269772450343624020585e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3137 Order of pole (three term test) = -22.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2868684868, alloc=4848776, time=151.07 x[1] = 9.08 y1[1] (analytic) = 0.058849477662267536366025735019854 y1[1] (numeric) = 0.058849477662267536366025735019854 absolute error = 4.12e-63 relative error = 7.0009117559961224301194877458778e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3379877132432676863845577471149 y2[1] (numeric) = 1.3379877132432676863845577471149 absolute error = 4e-63 relative error = 2.9895640747731856519907639287428e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3064 Order of pole (three term test) = -22.28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2872685812, alloc=4848776, time=151.28 x[1] = 9.09 y1[1] (analytic) = 0.055516713994810887089996994941924 y1[1] (numeric) = 0.055516713994810887089996994941924 absolute error = 4.07e-63 relative error = 7.3311255424455063784422968653707e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3285594656326920421762077861611 y2[1] (numeric) = 1.3285594656326920421762077861611 absolute error = 4e-63 relative error = 3.0107797983247242763462297682175e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2989 Order of pole (three term test) = -22.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2876686720, alloc=4848776, time=151.48 x[1] = 9.1 y1[1] (analytic) = 0.052278397868887975280933410424631 y1[1] (numeric) = 0.052278397868887975280933410424631 absolute error = 4.02e-63 relative error = 7.6896006072756687169502962830505e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3190983623493517707939976839854 y2[1] (numeric) = 1.3190983623493517707939976839854 absolute error = 4e-63 relative error = 3.0323743203470331210042991301934e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2913 Order of pole (three term test) = -22.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.11 y1[1] (analytic) = 0.04913485311341280545371997026879 y1[1] (numeric) = 0.04913485311341280545371997026879 absolute error = 4.06e-63 relative error = 8.2629737197519033801236068237260e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3096053494956909798097442924788 y2[1] (numeric) = 1.3096053494956909798097442924788 absolute error = 4e-63 relative error = 3.0543552693491508057739797745048e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2835 Order of pole (three term test) = -22.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2880688404, alloc=4848776, time=151.69 x[1] = 9.12 y1[1] (analytic) = 0.04608639408024131322782992654193 y1[1] (numeric) = 0.04608639408024131322782992654193 absolute error = 3.99e-63 relative error = 8.6576528271076831848081909215438e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.3000813763650842176272617719129 y2[1] (numeric) = 1.3000813763650842176272617719129 absolute error = 4e-63 relative error = 3.0767304821977037990096578811225e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2757 Order of pole (three term test) = -22.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2884689528, alloc=4848776, time=151.90 x[1] = 9.13 y1[1] (analytic) = 0.043133325612736441692769595562116 y1[1] (numeric) = 0.043133325612736441692769595562116 absolute error = 3.89e-63 relative error = 9.0185487549129710422711090629914e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.290527395346907927102696411862 y2[1] (numeric) = 1.290527395346907927102696411862 absolute error = 4e-63 relative error = 3.0995080107731894377526722969930e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2677 Order of pole (three term test) = -23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2888690296, alloc=4848776, time=152.11 x[1] = 9.14 y1[1] (analytic) = 0.040275943015284059149058407567067 y1[1] (numeric) = 0.040275943015284059149058407567067 absolute error = 3.88e-63 relative error = 9.6335422823684195287823787104251e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.280944361831302301555409197633 y2[1] (numeric) = 1.280944361831302301555409197633 absolute error = 4e-63 relative error = 3.1226961288790087589172917376389e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2597 Order of pole (three term test) = -23.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.15 y1[1] (analytic) = 0.037514532023762766607566789858955 y1[1] (numeric) = 0.037514532023762766607566789858955 absolute error = 3.84e-63 relative error = 1.0236033325879249382342174599913e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2713332341136330669044401785046 y2[1] (numeric) = 1.2713332341136330669044401785046 absolute error = 4e-63 relative error = 3.1463033394142167938722199311234e-61 % Correct digits = 64 h = 0.01 bytes used=2892691104, alloc=4848776, time=152.32 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2515 Order of pole (three term test) = -23.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.16 y1[1] (analytic) = 0.034849368776970548041853537914185 y1[1] (numeric) = 0.034849368776970548041853537914185 absolute error = 3.79e-63 relative error = 1.0875376321032648273158536766847e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2616949732986627436727260751701 y2[1] (numeric) = 1.2616949732986627436727260751701 absolute error = 3e-63 relative error = 2.3777537863661231615176457407368e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2432 Order of pole (three term test) = -23.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2896691768, alloc=4848776, time=152.53 x[1] = 9.17 y1[1] (analytic) = 0.032280719789011120704666395301587 y1[1] (numeric) = 0.032280719789011120704666395301587 absolute error = 3.78e-63 relative error = 1.1709776066662470016295615342159e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2520305432044409716530136891507 y2[1] (numeric) = 1.2520305432044409716530136891507 absolute error = 3e-63 relative error = 2.3961076798668300680127872843525e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2349 Order of pole (three term test) = -23.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2900693040, alloc=4848776, time=152.74 x[1] = 9.18 y1[1] (analytic) = 0.029808841922642746850562894319242 y1[1] (numeric) = 0.029808841922642746850562894319242 absolute error = 3.75e-63 relative error = 1.2580159973110214066695469814763e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2423409102659235081229113936966 y2[1] (numeric) = 1.2423409102659235081229113936966 absolute error = 4e-63 relative error = 3.2197281494527927888130350525350e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2264 Order of pole (three term test) = -23.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2904694344, alloc=4848776, time=152.94 x[1] = 9.19 y1[1] (analytic) = 0.027433982363592171961269945732327 y1[1] (numeric) = 0.027433982363592171961269945732327 absolute error = 3.68e-63 relative error = 1.3414020433590981280726913645632e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2326270434383295376289399672643 y2[1] (numeric) = 1.2326270434383295376289399672643 absolute error = 3e-63 relative error = 2.4338262055582550484805911109812e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2179 Order of pole (three term test) = -23.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.2 y1[1] (analytic) = 0.025156378595836258058554661524196 y1[1] (numeric) = 0.025156378595836258058554661524196 absolute error = 3.66e-63 relative error = 1.4548993950209441366744319213862e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2228899141002469575280690577583 y2[1] (numeric) = 1.2228899141002469575280690577583 absolute error = 4e-63 relative error = 3.2709403797340487172224357249045e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2092 Order of pole (three term test) = -23.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2908694996, alloc=4848776, time=153.15 x[1] = 9.21 y1[1] (analytic) = 0.022976258377853783920676553334472 y1[1] (numeric) = 0.022976258377853783920676553334472 absolute error = 3.63e-63 relative error = 1.5798917039942684078878389634650e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2131304959564953286774397976603 y2[1] (numeric) = 1.2131304959564953286774397976603 absolute error = 4e-63 relative error = 3.2972545108151711765721229103612e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2005 Order of pole (three term test) = -23.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2912696200, alloc=4848776, time=153.36 x[1] = 9.22 y1[1] (analytic) = 0.020893839719849787002609360845137 y1[1] (numeric) = 0.020893839719849787002609360845137 absolute error = 3.58e-63 relative error = 1.7134236923426240635786269875020e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.2033497649407562048962573265169 y2[1] (numeric) = 1.2033497649407562048962573265169 absolute error = 4e-63 relative error = 3.3240543327790732512461756946221e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1917 Order of pole (three term test) = -24.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2916697272, alloc=4848776, time=153.57 x[1] = 9.23 y1[1] (analytic) = 0.018909330861954724606860836130891 y1[1] (numeric) = 0.018909330861954724606860836130891 absolute error = 3.60e-63 relative error = 1.9038219946974132272326259396975e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1935486991179805780857659098894 y2[1] (numeric) = 1.1935486991179805780857659098894 absolute error = 4e-63 relative error = 3.3513504752306765604075937861716e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1829 Order of pole (three term test) = -24.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2920698152, alloc=4848776, time=153.78 x[1] = 9.24 y1[1] (analytic) = 0.017022930253400634370606096862142 y1[1] (numeric) = 0.017022930253400634370606096862142 absolute error = 3.55e-63 relative error = 2.0854223962357033638276900388078e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1837282785865831981814677992768 y2[1] (numeric) = 1.1837282785865831981814677992768 absolute error = 5e-63 relative error = 4.2239423442432169308873158485030e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1739 Order of pole (three term test) = -24.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.25 y1[1] (analytic) = 0.015234826532676376435732693275154 y1[1] (numeric) = 0.015234826532676376435732693275154 absolute error = 3.49e-63 relative error = 2.2908038975793278316792279772483e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1738894853804335484240861494355 y2[1] (numeric) = 1.1738894853804335484240861494355 absolute error = 4e-63 relative error = 3.4074757886630885824398876419233e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1649 Order of pole (three term test) = -24.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2924699172, alloc=4848776, time=153.99 x[1] = 9.26 y1[1] (analytic) = 0.013545198508663941761043141335247 y1[1] (numeric) = 0.013545198508663941761043141335247 absolute error = 3.46e-63 relative error = 2.5544106996932333227949642256750e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1640333033706532767700709817761 y2[1] (numeric) = 1.1640333033706532767700709817761 absolute error = 4e-63 relative error = 3.4363277995718253441006706460086e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1558 Order of pole (three term test) = -24.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2928700184, alloc=4848776, time=154.20 x[1] = 9.27 y1[1] (analytic) = 0.011954215142757712930064011165613 y1[1] (numeric) = 0.011954215142757712930064011165613 absolute error = 3.35e-63 relative error = 2.8023587997992061319983124875241e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1541607181672299036166719422002 y2[1] (numeric) = 1.1541607181672299036166719422002 absolute error = 4e-63 relative error = 3.4657218332225613589701078983601e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1467 Order of pole (three term test) = -24.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2932700948, alloc=4848776, time=154.40 x[1] = 9.28 y1[1] (analytic) = 0.010462035531968465513480223508068 y1[1] (numeric) = 0.010462035531968465513480223508068 absolute error = 3.35e-63 relative error = 3.2020537396986710138894725792742e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1442727170204566443888170425023 y2[1] (numeric) = 1.1442727170204566443888170425023 absolute error = 4e-63 relative error = 3.4956701671743959953993351737345e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1375 Order of pole (three term test) = -24.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.29 y1[1] (analytic) = 0.0090688088930137995719783588546681 y1[1] (numeric) = 0.0090688088930137995719783588546681 absolute error = 3.308e-63 relative error = 3.6476675592406999185579963902229e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.13437028872220820292340549006 y2[1] (numeric) = 1.13437028872220820292340549006 absolute error = 5e-63 relative error = 4.4077318047814559246464025567564e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1282 Order of pole (three term test) = -24.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2936701864, alloc=4848776, time=154.61 x[1] = 9.3 y1[1] (analytic) = 0.0077746745473965922430907653648447 y1[1] (numeric) = 0.0077746745473965922430907653648447 absolute error = 3.280e-63 relative error = 4.2188261129185561378158785652416e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1244544235070624079894062785863 y2[1] (numeric) = 1.1244544235070624079894062785863 absolute error = 5e-63 relative error = 4.4466008541328809940886600628778e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = -24.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2940703136, alloc=4848776, time=154.82 x[1] = 9.31 y1[1] (analytic) = 0.0065797619074729635543471997616135 y1[1] (numeric) = 0.0065797619074729635543471997616135 absolute error = 3.241e-63 relative error = 4.9257101481423435069366447407925e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1145261129532775806977121685111 y2[1] (numeric) = 1.1145261129532775806977121685111 absolute error = 5e-63 relative error = 4.4862116211444986219375460310234e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1096 Order of pole (three term test) = -24.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2944704404, alloc=4848776, time=155.03 x[1] = 9.32 y1[1] (analytic) = 0.0054841904635111486545426962537714 y1[1] (numeric) = 0.0054841904635111486545426962537714 absolute error = 3.121e-63 relative error = 5.6909037364137041664229545540956e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.1045863498836355349814894861648 y2[1] (numeric) = 1.1045863498836355349814894861648 absolute error = 6e-63 relative error = 5.4318976516703106681265066093862e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1002 Order of pole (three term test) = -24.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2948705296, alloc=4848776, time=155.23 x[1] = 9.33 y1[1] (analytic) = 0.0044880697717425705651142995040825 y1[1] (numeric) = 0.0044880697717425705651142995040825 absolute error = 3.119e-63 relative error = 6.9495354542783643214522243403233e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0946361282661601267643451492879 y2[1] (numeric) = 1.0946361282661601267643451492879 absolute error = 6e-63 relative error = 5.4812734981656877589355199566022e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09072 Order of pole (three term test) = -24.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.34 y1[1] (analytic) = 0.0035914994434063083343941177877119 y1[1] (numeric) = 0.0035914994434063083343941177877119 absolute error = 3.031e-63 relative error = 8.4393720443550721166924624534929e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0846764431147212798786598355838 y2[1] (numeric) = 1.0846764431147212798786598355838 absolute error = 6e-63 relative error = 5.5316034916095318644818129616767e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.08125 Order of pole (three term test) = -24.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2952706164, alloc=4848776, time=155.44 x[1] = 9.35 y1[1] (analytic) = 0.0027945691347880561387936915961134 y1[1] (numeric) = 0.0027945691347880561387936915961134 absolute error = 3.023e-63 relative error = 1.0817409962660552906928840749210e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0747082903895344282486657586974 y2[1] (numeric) = 1.0747082903895344282486657586974 absolute error = 5e-63 relative error = 4.6524252624753831436547334210840e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.07174 Order of pole (three term test) = -24.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2956707252, alloc=4848776, time=155.65 x[1] = 9.36 y1[1] (analytic) = 0.0020973585382545694267087195033409 y1[1] (numeric) = 0.0020973585382545694267087195033409 absolute error = 2.906e-63 relative error = 1.3855523254590440172194145005433e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0647326668975653243111338887167 y2[1] (numeric) = 1.0647326668975653243111338887167 absolute error = 6e-63 relative error = 5.6352173522419423071135790983231e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.0622 Order of pole (three term test) = -24.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2960708704, alloc=4848776, time=155.86 x[1] = 9.37 y1[1] (analytic) = 0.0014999373742844946530584808463874 y1[1] (numeric) = 0.0014999373742844946530584808463874 absolute error = 2.899e-63 relative error = 1.9327473597908653154385650490905e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.054750570192850173109832832146 y2[1] (numeric) = 1.054750570192850173109832832146 absolute error = 6e-63 relative error = 5.6885487143211142286459784775072e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.05264 Order of pole (three term test) = -24.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.38 y1[1] (analytic) = 0.0010023653844963795148455481926131 y1[1] (numeric) = 0.0010023653844963795148455481926131 absolute error = 2.844e-63 relative error = 2.8372887212470098638907740050576e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0447629984767410599672836474296 y2[1] (numeric) = 1.0447629984767410599672836474296 absolute error = 6e-63 relative error = 5.7429292660134100714041871216787e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.04306 Order of pole (three term test) = -24.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=2964709404, alloc=4848776, time=156.07 TOP MAIN SOLVE Loop x[1] = 9.39 y1[1] (analytic) = 0.00060469232567456088090226151925041 y1[1] (numeric) = 0.00060469232567456088090226151925041 absolute error = 2.7311e-63 relative error = 4.5165117598496687528990615453596e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0347709504980866471079148873655 y2[1] (numeric) = 1.0347709504980866471079148873655 absolute error = 6e-63 relative error = 5.7983846542192762842230294984246e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.03346 Order of pole (three term test) = -25.01 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2968710132, alloc=4848776, time=156.28 x[1] = 9.4 y1[1] (analytic) = 0.00030695796479352782205257932708477 y1[1] (numeric) = 0.00030695796479352782205257932708477 absolute error = 2.6862e-63 relative error = 8.7510353471585118419151641867003e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0247754254533581210797730773676 y2[1] (numeric) = 1.0247754254533581210797730773676 absolute error = 6e-63 relative error = 5.8549413373623931275099533806254e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.02385 Order of pole (three term test) = -25.02 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2972711484, alloc=4848776, time=156.49 x[1] = 9.41 y1[1] (analytic) = 0.00010919207504125730123994018285572 y1[1] (numeric) = 0.00010919207504125730123994018285572 absolute error = 2.6649e-63 relative error = 2.4405617339839819817175568600461e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0147774228867303782968183588059 y2[1] (numeric) = 1.0147774228867303782968183588059 absolute error = 6e-63 relative error = 5.9126266161222242525988157685505e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.01423 Order of pole (three term test) = -25.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2976712160, alloc=4848776, time=156.70 x[1] = 9.42 y1[1] (analytic) = 1.1414432841920186738246025601479e-05 y1[1] (numeric) = 1.1414432841920186738246025601479e-05 absolute error = 2.57139e-63 relative error = 2.2527531902911694033377370324582e-56 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 1.0047779425901284404999856666986 y2[1] (numeric) = 1.0047779425901284404999856666986 absolute error = 6e-63 relative error = 5.9714686655373118341325367825612e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.004601 Order of pole (three term test) = -25.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.43 y1[1] (analytic) = 1.3634815878255315363576086538077e-05 y1[1] (numeric) = 1.3634815878255315363576086538077e-05 absolute error = 2.54730e-63 relative error = 1.8682320485621017239875683224181e-56 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.99477798450324909541217095950362 y2[1] (numeric) = 0.99477798450324909541217095950362 absolute error = 5.6e-63 relative error = 5.6293967973129280211694920885696e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.005035 Order of pole (three term test) = -0.8935 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2980713080, alloc=4848776, time=156.90 x[1] = 9.44 y1[1] (analytic) = 0.00011585300211380936663229413048657 y1[1] (numeric) = 0.00011585300211380936663229413048657 absolute error = 2.4749e-63 relative error = 2.1362415775542501616399888171170e-57 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.98477854861356776033976198064944 y2[1] (numeric) = 0.98477854861356776033976198064944 absolute error = 5.6e-63 relative error = 5.6865576609929479819473498898189e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.01468 Order of pole (three term test) = -0.8985 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2984714036, alloc=4848776, time=157.11 x[1] = 9.45 y1[1] (analytic) = 0.00031805876981514032306333581925136 y1[1] (numeric) = 0.00031805876981514032306333581925136 absolute error = 2.3992e-63 relative error = 7.5432600125896374716426708303989e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.97478063485634056795102606282269 y2[1] (numeric) = 0.97478063485634056795102606282269 absolute error = 5.6e-63 relative error = 5.7448822840282485978106349738732e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.02431 Order of pole (three term test) = -0.9082 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2988714944, alloc=4848776, time=157.32 x[1] = 9.46 y1[1] (analytic) = 0.00062023189857398229629714879012246 y1[1] (numeric) = 0.00062023189857398229629714879012246 absolute error = 2.2900e-63 relative error = 3.6921674058768923136895716041644e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.9647852430146116739394458188179 y2[1] (numeric) = 0.9647852430146116739394458188179 absolute error = 5.7e-63 relative error = 5.9080505649003521206718098368214e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.03394 Order of pole (three term test) = -0.9228 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2992715744, alloc=4848776, time=157.53 x[1] = 9.47 y1[1] (analytic) = 0.0010223421713292695034004747379178 y1[1] (numeric) = 0.0010223421713292695034004747379178 absolute error = 2.289e-63 relative error = 2.2389764055451189549147325043922e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.95479337261923578575790941952403 y2[1] (numeric) = 0.95479337261923578575790941952403 absolute error = 5.7e-63 relative error = 5.9698780526340288348778661475885e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.04355 Order of pole (three term test) = -0.9423 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.48 y1[1] (analytic) = 0.0015243493773888171926443573858882 y1[1] (numeric) = 0.0015243493773888171926443573858882 absolute error = 2.217e-63 relative error = 1.4543909899433165040634853497785e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.94480602284892591008756775834644 y2[1] (numeric) = 0.94480602284892591008756775834644 absolute error = 5.8e-63 relative error = 6.1388262349460250917293672751890e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.05314 Order of pole (three term test) = -0.9665 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=2996716944, alloc=4848776, time=157.74 x[1] = 9.49 y1[1] (analytic) = 0.0021262033164503573531808575892935 y1[1] (numeric) = 0.0021262033164503573531808575892935 absolute error = 2.189e-63 relative error = 1.0295346560057483690394575867344e-58 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.93482419243033631418331835021631 y2[1] (numeric) = 0.93482419243033631418331835021631 absolute error = 5.8e-63 relative error = 6.2043751616240073311412490836092e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.06271 Order of pole (three term test) = -0.9956 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3000717952, alloc=4848776, time=157.95 x[1] = 9.5 y1[1] (analytic) = 0.002827843803621527108398359822012 y1[1] (numeric) = 0.002827843803621527108398359822012 absolute error = 2.066e-63 relative error = 7.3059197872037392726068115216357e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.92484887953819069271651749546599 y2[1] (numeric) = 0.92484887953819069271651749546599 absolute error = 5.8e-63 relative error = 6.2712948334825710367093366573659e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.07226 Order of pole (three term test) = -1.029 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3004718644, alloc=4848776, time=158.16 x[1] = 9.51 y1[1] (analytic) = 0.0036292006754383077982994442322779 y1[1] (numeric) = 0.0036292006754383077982994442322779 absolute error = 2.061e-63 relative error = 5.6789364499693525125698570436074e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.91488108169546552721501018714384 y2[1] (numeric) = 0.91488108169546552721501018714384 absolute error = 5.8e-63 relative error = 6.3396217454309907414842398778769e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.08178 Order of pole (three term test) = -1.068 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.52 y1[1] (analytic) = 0.0045301937968813129120084356644659 y1[1] (numeric) = 0.0045301937968813129120084356644659 absolute error = 2.035e-63 relative error = 4.4920815559831892284276729395105e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.90492179567363861968135350224591 y2[1] (numeric) = 0.90492179567363861968135350224591 absolute error = 5.9e-63 relative error = 6.5199004247742129775924214470359e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09127 Order of pole (three term test) = -1.111 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3008719460, alloc=4848776, time=158.37 x[1] = 9.53 y1[1] (analytic) = 0.0055307330693892232474622660127888 y1[1] (numeric) = 0.0055307330693892232474622660127888 absolute error = 1.959e-63 relative error = 3.5420259401821731926666426088319e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.89497201739301277545274570962751 y2[1] (numeric) = 0.89497201739301277545274570962751 absolute error = 5.9e-63 relative error = 6.5923848850450801519034567496266e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1007 Order of pole (three term test) = -1.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3012720468, alloc=4848776, time=158.58 x[1] = 9.54 y1[1] (analytic) = 0.0066307184398685679614465211942478 y1[1] (numeric) = 0.0066307184398685679614465211942478 absolute error = 1.887e-63 relative error = 2.8458454647297669407355510540212e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.88503274182312460285131178094508 y2[1] (numeric) = 0.88503274182312460285131178094508 absolute error = 5.9e-63 relative error = 6.6664200330558230250273836116456e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1101 Order of pole (three term test) = -1.212 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3016721240, alloc=4848776, time=158.79 x[1] = 9.55 y1[1] (analytic) = 0.0078300399106989505393797949840419 y1[1] (numeric) = 0.0078300399106989505393797949840419 absolute error = 1.825e-63 relative error = 2.3307671746427802085257452996678e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.87510496288324838866178788576117 y2[1] (numeric) = 0.87510496288324838866178788576117 absolute error = 5.9e-63 relative error = 6.7420483830431036104642339537173e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1195 Order of pole (three term test) = -1.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3020721972, alloc=4848776, time=158.99 x[1] = 9.56 y1[1] (analytic) = 0.0091285775507327191705870317939627 y1[1] (numeric) = 0.0091285775507327191705870317939627 absolute error = 1.733e-63 relative error = 1.8984337815708189031217713967462e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.86518967334300499896614394163858 y2[1] (numeric) = 0.86518967334300499896614394163858 absolute error = 6.0e-63 relative error = 6.9348955320012195351476478536397e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1288 Order of pole (three term test) = -1.332 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.57 y1[1] (analytic) = 0.010526201507287981571190692484306 y1[1] (numeric) = 0.010526201507287981571190692484306 absolute error = 1.67e-63 relative error = 1.5865172245123268545996915896407e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.85528786472308574436223511708336 y2[1] (numeric) = 0.85528786472308574436223511708336 absolute error = 6.0e-63 relative error = 7.0151819609209630150334288785171e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1381 Order of pole (three term test) = -1.399 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3024722736, alloc=4848776, time=159.20 x[1] = 9.58 y1[1] (analytic) = 0.01202277201913376496313159979792 y1[1] (numeric) = 0.01202277201913376496313159979792 absolute error = 1.62e-63 relative error = 1.3474430001848444213402947390851e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.84540052719610113709723058563525 y2[1] (numeric) = 0.84540052719610113709723058563525 absolute error = 6.0e-63 relative error = 7.0972276536187037258464619264986e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1473 Order of pole (three term test) = -1.471 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3028723736, alloc=4848776, time=159.41 x[1] = 9.59 y1[1] (analytic) = 0.013618139430466022704142491911221 y1[1] (numeric) = 0.013618139430466022704142491911221 absolute error = 1.62e-63 relative error = 1.1895898175163289642145092125317e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.83552864948756445515748042792753 y2[1] (numeric) = 0.83552864948756445515748042792753 absolute error = 6.0e-63 relative error = 7.1810823048136551911489349969909e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1564 Order of pole (three term test) = -1.547 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3032724460, alloc=4848776, time=159.62 x[1] = 9.6 y1[1] (analytic) = 0.015312144205873089979657920116266 y1[1] (numeric) = 0.015312144205873089979657920116266 absolute error = 1.54e-63 relative error = 1.0057376545665767867311737601641e-59 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.82567321877702001487589827347958 y2[1] (numeric) = 0.82567321877702001487589827347958 absolute error = 6.0e-63 relative error = 7.2667974006558524169573472211539e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1655 Order of pole (three term test) = -1.628 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.61 y1[1] (analytic) = 0.017104616946289092023562471150107 y1[1] (numeric) = 0.017104616946289092023562471150107 absolute error = 1.46e-63 relative error = 8.5357070818049055167180535113029e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.81583522059932603914720611244047 y2[1] (numeric) = 0.81583522059932603914720611244047 absolute error = 6.0e-63 relative error = 7.3544262965164715707036122943233e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1745 Order of pole (three term test) = -1.713 NO COMPLEX POLE (six term test) for Equation 2 bytes used=3036726508, alloc=4848776, time=159.83 TOP MAIN SOLVE Loop x[1] = 9.62 y1[1] (analytic) = 0.018995378405933709540249701884841 y1[1] (numeric) = 0.018995378405933709540249701884841 absolute error = 1.36e-63 relative error = 7.1596362596028515031675741061126e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.80601563874610199288195575052908 y2[1] (numeric) = 0.80601563874610199288195575052908 absolute error = 6.1e-63 relative error = 7.5680913703977440028694724437855e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1835 Order of pole (three term test) = -1.803 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3040727984, alloc=4848776, time=160.03 x[1] = 9.63 y1[1] (analytic) = 0.020984239510236607365566004615135 y1[1] (numeric) = 0.020984239510236607365566004615135 absolute error = 1.36e-63 relative error = 6.4810545044368174373556565003535e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.79621545516735024088365455832705 y2[1] (numeric) = 0.79621545516735024088365455832705 absolute error = 6.0e-63 relative error = 7.5356487506750385376027670427942e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1924 Order of pole (three term test) = -1.897 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3044728852, alloc=4848776, time=160.24 x[1] = 9.64 y1[1] (analytic) = 0.023071001374744733938710282650819 y1[1] (numeric) = 0.023071001374744733938710282650819 absolute error = 1.24e-63 relative error = 5.3747125226969902903156227336772e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.78643564987326186590122612385328 y2[1] (numeric) = 0.78643564987326186590122612385328 absolute error = 6.0e-63 relative error = 7.6293591229834643681480896243285e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2012 Order of pole (three term test) = -1.996 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3048730248, alloc=4848776, time=160.46 x[1] = 9.65 y1[1] (analytic) = 0.025255455325010600870898276620058 y1[1] (numeric) = 0.025255455325010600870898276620058 absolute error = 1.19e-63 relative error = 4.7118532795626819787574641445637e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.77667720083621646619317235015962 y2[1] (numeric) = 0.77667720083621646619317235015962 absolute error = 6.0e-63 relative error = 7.7252171089096554509550846363242e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2099 Order of pole (three term test) = -2.099 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.66 y1[1] (analytic) = 0.027537382917459553799408186112568 y1[1] (numeric) = 0.027537382917459553799408186112568 absolute error = 1.20e-63 relative error = 4.3577125814638065239516548998352e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.76694108389298573254201401859704 y2[1] (numeric) = 0.76694108389298573254201401859704 absolute error = 6.1e-63 relative error = 7.9536748364508748708809643473840e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2185 Order of pole (three term test) = -2.206 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3052731096, alloc=4848776, time=160.66 x[1] = 9.67 y1[1] (analytic) = 0.029916555961233947817311516514547 y1[1] (numeric) = 0.029916555961233947817311516514547 absolute error = 1.06e-63 relative error = 3.5431885988933831192938045506723e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.75722827264715058427981162619756 y2[1] (numeric) = 0.75722827264715058427981162619756 absolute error = 6.0e-63 relative error = 7.9236344134707840909864490346869e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2271 Order of pole (three term test) = -2.318 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3056731768, alloc=4848776, time=160.88 x[1] = 9.68 y1[1] (analytic) = 0.032392736541012043079549596797259 y1[1] (numeric) = 0.032392736541012043079549596797259 absolute error = 1.08e-63 relative error = 3.3340807703375889782024712651179e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.7475397383717416225298451628392 y2[1] (numeric) = 0.7475397383717416225298451628392 absolute error = 6.1e-63 relative error = 8.1601013121881029663727067652381e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2355 Order of pole (three term test) = -2.434 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3060732536, alloc=4848776, time=161.09 x[1] = 9.69 y1[1] (analytic) = 0.034965677040799338714810843560169 y1[1] (numeric) = 0.034965677040799338714810843560169 absolute error = 9.5e-64 relative error = 2.7169501076484299814017592641032e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.73787644991211263653799597502699 y2[1] (numeric) = 0.73787644991211263653799597502699 absolute error = 6.0e-63 relative error = 8.1314426022332750306001765801876e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2439 Order of pole (three term test) = -2.554 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3064733340, alloc=4848776, time=161.30 x[1] = 9.7 y1[1] (analytic) = 0.03763512016868996592964362910856 y1[1] (numeric) = 0.03763512016868996592964362910856 absolute error = 8.9e-64 relative error = 2.3648124305457209027430920885317e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.72823937358905687566225910317516 y2[1] (numeric) = 0.72823937358905687566225910317516 absolute error = 6.0e-63 relative error = 8.2390491610328400120357653083577e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2522 Order of pole (three term test) = -2.678 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.71 y1[1] (analytic) = 0.040400798982595664186128767750693 y1[1] (numeric) = 0.040400798982595664186128767750693 absolute error = 8.2e-64 relative error = 2.0296628300674185548514922606218e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.71862947310217577531245097026894 y2[1] (numeric) = 0.71862947310217577531245097026894 absolute error = 6.1e-63 relative error = 8.4883799347493408456687861475045e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2603 Order of pole (three term test) = -2.807 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3068734232, alloc=4848776, time=161.50 x[1] = 9.72 y1[1] (analytic) = 0.043262436916939767576934595078059 y1[1] (numeric) = 0.043262436916939767576934595078059 absolute error = 8.0e-64 relative error = 1.8491792349467797444370920443490e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.70904770943350979988699265784006 y2[1] (numeric) = 0.70904770943350979988699265784006 absolute error = 6.0e-63 relative error = 8.4620539918162497967746908617108e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2684 Order of pole (three term test) = -2.939 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3072735516, alloc=4848776, time=161.72 x[1] = 9.73 y1[1] (analytic) = 0.046219747810313532021362049216815 y1[1] (numeric) = 0.046219747810313532021362049216815 absolute error = 7.4e-64 relative error = 1.6010472472436889399867874706433e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.69949504075144103954216772773388 y2[1] (numeric) = 0.69949504075144103954216772773388 absolute error = 6.1e-63 relative error = 8.7205764796373694726045771615258e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2763 Order of pole (three term test) = -3.076 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3076736220, alloc=4848776, time=161.92 x[1] = 9.74 y1[1] (analytic) = 0.049272435934092037672707012049341 y1[1] (numeric) = 0.049272435934092037672707012049341 absolute error = 6.4e-64 relative error = 1.2989006690395395990154339722612e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.68997242231487717045409676146381 y2[1] (numeric) = 0.68997242231487717045409676146381 absolute error = 6.1e-63 relative error = 8.8409330615480628780923523207090e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2842 Order of pole (three term test) = -3.216 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.75 y1[1] (analytic) = 0.052420196022006804970545680022781 y1[1] (numeric) = 0.052420196022006804970545680022781 absolute error = 6.1e-64 relative error = 1.1636736340015070009879909889703e-60 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.68048080637772636009755598607246 y2[1] (numeric) = 0.68048080637772636009755598607246 absolute error = 6.1e-63 relative error = 8.9642498992307602494796626087525e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2919 Order of pole (three term test) = -3.361 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3080737376, alloc=4848776, time=162.13 x[1] = 9.76 y1[1] (analytic) = 0.055662713300672167100981500571712 y1[1] (numeric) = 0.055662713300672167100981500571712 absolute error = 5.3e-64 relative error = 9.5216342965013146543525516870006e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.67102114209367266997150812438323 y2[1] (numeric) = 0.67102114209367266997150812438323 absolute error = 6.2e-63 relative error = 9.2396492615049338997944114865671e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2995 Order of pole (three term test) = -3.509 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3084738256, alloc=4848776, time=162.34 x[1] = 9.77 y1[1] (analytic) = 0.058999663521062346253046208382863 y1[1] (numeric) = 0.058999663521062346253046208382863 absolute error = 5.1e-64 relative error = 8.6441170942938447896081197114358e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.66159437542126147815171935000727 y2[1] (numeric) = 0.66159437542126147815171935000727 absolute error = 6.1e-63 relative error = 9.2201509363133651004615518981695e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.307 Order of pole (three term test) = -3.661 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3088739192, alloc=4848776, time=162.55 x[1] = 9.78 y1[1] (analytic) = 0.062430712990936085989860130842391 y1[1] (numeric) = 0.062430712990936085989860130842391 absolute error = 4.1e-64 relative error = 6.5672804355049615587105481636707e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.65220144902930441304911186785548 y2[1] (numeric) = 0.65220144902930441304911186785548 absolute error = 6.1e-63 relative error = 9.3529384350170580943884811747421e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = -3.817 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3092740460, alloc=4848776, time=162.76 x[1] = 9.79 y1[1] (analytic) = 0.065955518608205597298335083542914 y1[1] (numeric) = 0.065955518608205597298335083542914 absolute error = 3.9e-64 relative error = 5.9130760887001755577388797398672e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.64284330220261325780164732579296 y2[1] (numeric) = 0.64284330220261325780164732579296 absolute error = 6.1e-63 relative error = 9.4890931881831817165900648386496e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3216 Order of pole (three term test) = -3.976 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.8 y1[1] (analytic) = 0.069573727895246481450622247910779 y1[1] (numeric) = 0.069573727895246481450622247910779 absolute error = 2.6e-64 relative error = 3.7370428158092719126060835991791e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.63352087074807225183074705127114 y2[1] (numeric) = 0.63352087074807225183074705127114 absolute error = 6.1e-63 relative error = 9.6287277683480513216030744106933e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3287 Order of pole (three term test) = -4.139 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3096741392, alloc=4848776, time=162.97 x[1] = 9.81 y1[1] (analytic) = 0.073284979034145198713610393245203 y1[1] (numeric) = 0.073284979034145198713610393245203 absolute error = 2.4e-64 relative error = 3.2748866570348385353428864345119e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.62423508690105818225382064978751 y2[1] (numeric) = 0.62423508690105818225382064978751 absolute error = 6.1e-63 relative error = 9.7719595197423682110733254688561e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3357 Order of pole (three term test) = -4.306 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3100742876, alloc=4848776, time=163.18 x[1] = 9.82 y1[1] (analytic) = 0.077088900902880558188976286028855 y1[1] (numeric) = 0.077088900902880558188976286028855 absolute error = 2.1e-64 relative error = 2.7241275662311718343785176211783e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.6149868792322176230657787151004 y2[1] (numeric) = 0.6149868792322176230657787151004 absolute error = 6.0e-63 relative error = 9.7563057076774053884490482215789e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3426 Order of pole (three term test) = -4.476 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3104744188, alloc=4848776, time=163.39 x[1] = 9.83 y1[1] (analytic) = 0.08098511311243561066495442249836 y1[1] (numeric) = 0.08098511311243561066495442249836 absolute error = 8e-65 relative error = 9.8783587409370003916060234130704e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.60577717255461064428792612486422 y2[1] (numeric) = 0.60577717255461064428792612486422 absolute error = 6.0e-63 relative error = 9.9046320525706202013980218942958e-61 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3493 Order of pole (three term test) = -4.649 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.84 y1[1] (analytic) = 0.084973226044836233321467381789552 y1[1] (numeric) = 0.084973226044836233321467381789552 absolute error = 2e-65 relative error = 2.3536825575442991853136860376239e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.59660688783123027663594104791333 y2[1] (numeric) = 0.59660688783123027663594104791333 absolute error = 6.0e-63 relative error = 1.0056873499752982668313823223817e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3559 Order of pole (three term test) = -4.826 NO COMPLEX POLE (six term test) for Equation 2 bytes used=3108745056, alloc=4848776, time=163.60 TOP MAIN SOLVE Loop x[1] = 9.85 y1[1] (analytic) = 0.089052840892112602461845001547209 y1[1] (numeric) = 0.089052840892112602461845001547209 absolute error = 0 relative error = 0 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.5874769420829069796834060094069 y2[1] (numeric) = 0.5874769420829069796834060094069 absolute error = 6.1e-63 relative error = 1.0383386245547565350225150790357e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3623 Order of pole (three term test) = -5.006 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3112746340, alloc=4848776, time=163.80 x[1] = 9.86 y1[1] (analytic) = 0.093223549696179658156326989798697 y1[1] (numeric) = 0.093223549696179658156326989798697 absolute error = 4e-65 relative error = 4.2907613076697955319856699559845e-62 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.57838824829660732299732864001849 y2[1] (numeric) = 0.57838824829660732299732864001849 absolute error = 6.1e-63 relative error = 1.0546548997087880553053011862629e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3686 Order of pole (three term test) = -5.189 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3116747192, alloc=4848776, time=164.02 x[1] = 9.87 y1[1] (analytic) = 0.097484935389632572784118232587709 y1[1] (numeric) = 0.097484935389632572784118232587709 absolute error = 1.4e-64 relative error = 1.4361193290064883462680709681955e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.56934171533413605030112104610044 y2[1] (numeric) = 0.56934171533413605030112104610044 absolute error = 6.1e-63 relative error = 1.0714127975709673048944998657852e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3747 Order of pole (three term test) = -5.376 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3120748536, alloc=4848776, time=164.22 x[1] = 9.88 y1[1] (analytic) = 0.10183657183745314396113870230185 y1[1] (numeric) = 0.10183657183745314396113870230185 absolute error = 2e-64 relative error = 1.9639309964128683450202932452911e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.56033824784125065638254014329326 y2[1] (numeric) = 0.56033824784125065638254014329326 absolute error = 6.0e-63 relative error = 1.0707818042254825849016731115816e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3807 Order of pole (three term test) = -5.565 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.89 y1[1] (analytic) = 0.10627802387962294124893040329212 y1[1] (numeric) = 0.10627802387962294124893040329212 absolute error = 2e-64 relative error = 1.8818565936691894246848597886752e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.55137874615719756521316055942936 y2[1] (numeric) = 0.55137874615719756521316055942936 absolute error = 6.0e-63 relative error = 1.0881812260295948381686002720938e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3865 Order of pole (three term test) = -5.757 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3124749412, alloc=4848776, time=164.43 x[1] = 9.9 y1[1] (analytic) = 0.11080884737463894536556130131089 y1[1] (numeric) = 0.11080884737463894536556130131089 absolute error = 3e-64 relative error = 2.7073650444690180290436657249342e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.54246410622467895558618189249464 y2[1] (numeric) = 0.54246410622467895558618189249464 absolute error = 6.0e-63 relative error = 1.1060639646293771621740442102086e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3922 Order of pole (three term test) = -5.953 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3128750512, alloc=4848776, time=164.64 x[1] = 9.91 y1[1] (analytic) = 0.11542858924392732837086805817458 y1[1] (numeric) = 0.11542858924392732837086805817458 absolute error = 5e-64 relative error = 4.3316824997608197435602363947167e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.53359521950025923751497914771223 y2[1] (numeric) = 0.53359521950025923751497914771223 absolute error = 6.0e-63 relative error = 1.1244478549900286371144086907184e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3977 Order of pole (three term test) = -6.151 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3132751348, alloc=4848776, time=164.85 x[1] = 9.92 y1[1] (analytic) = 0.12013678751715093348503040749387 y1[1] (numeric) = 0.12013678751715093348503040749387 absolute error = 5e-64 relative error = 4.1619225079463619242886864196834e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.52477297286522013867009547790727 y2[1] (numeric) = 0.52477297286522013867009547790727 absolute error = 6.0e-63 relative error = 1.1433515653903555079515144501666e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4031 Order of pole (three term test) = -6.351 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.93 y1[1] (analytic) = 0.12493297137840592383025142136221 y1[1] (numeric) = 0.12493297137840592383025142136221 absolute error = 5e-64 relative error = 4.0021460666741385693658529426457e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.51599824853687331527174634753366 y2[1] (numeric) = 0.51599824853687331527174634753366 absolute error = 6.1e-63 relative error = 1.1821745553006645620739196333592e-60 % Correct digits = 64 h = 0.01 bytes used=3136752100, alloc=4848776, time=165.06 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4083 Order of pole (three term test) = -6.555 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.94 y1[1] (analytic) = 0.12981666121330298046916657893683 y1[1] (numeric) = 0.12981666121330298046916657893683 absolute error = 6e-64 relative error = 4.6219028774290716105027684055490e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.50727192398033935610283995871037 y2[1] (numeric) = 0.50727192398033935610283995871037 absolute error = 6.1e-63 relative error = 1.2025108648111227576937954959505e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4133 Order of pole (three term test) = -6.761 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3140752784, alloc=4848776, time=165.27 x[1] = 9.95 y1[1] (analytic) = 0.13478736865692834165941199692317 y1[1] (numeric) = 0.13478736865692834165941199692317 absolute error = 6e-64 relative error = 4.4514556963209830719857479308097e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.4985948718208020016685953856268 y2[1] (numeric) = 0.4985948718208020016685953856268 absolute error = 6.1e-63 relative error = 1.2234381749101456302705916786856e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4182 Order of pole (three term test) = -6.969 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3144753564, alloc=4848776, time=165.48 x[1] = 9.96 y1[1] (analytic) = 0.13984459664267988726039376462704 y1[1] (numeric) = 0.13984459664267988726039376462704 absolute error = 7e-64 relative error = 5.0055562875166777947088234894833e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.48996795975624635300772121520774 y2[1] (numeric) = 0.48996795975624635300772121520774 absolute error = 6.1e-63 relative error = 1.2449793662089012125273568516614e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4229 Order of pole (three term test) = -7.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3148754328, alloc=4848776, time=165.69 x[1] = 9.97 y1[1] (analytic) = 0.14498783945197338472451430799106 y1[1] (numeric) = 0.14498783945197338472451430799106 absolute error = 7e-64 relative error = 4.8279911104673855879884469191708e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.48139205047068979626155565924353 y2[1] (numeric) = 0.48139205047068979626155565924353 absolute error = 6.1e-63 relative error = 1.2671584406172919801121274489409e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4274 Order of pole (three term test) = -7.393 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 9.98 y1[1] (analytic) = 0.15021658276481392608967839356558 y1[1] (numeric) = 0.15021658276481392608967839356558 absolute error = 8e-64 relative error = 5.3256437157308872919038788786055e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.47286800154791431983640390213977 y2[1] (numeric) = 0.47286800154791431983640390213977 absolute error = 6.2e-63 relative error = 1.3111481385301078122063685542733e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4318 Order of pole (three term test) = -7.608 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=3152755232, alloc=4848776, time=165.90 x[1] = 9.99 y1[1] (analytic) = 0.15553030371122749887152224549834 y1[1] (numeric) = 0.15553030371122749887152224549834 absolute error = 8e-64 relative error = 5.1436921352983200170751049764559e-61 % Correct digits = 64 h = 0.01 y2[1] (analytic) = 0.46439666538570885085546695448582 y2[1] (numeric) = 0.46439666538570885085546695448582 absolute error = 6.2e-63 relative error = 1.3350655726286350315730911320105e-60 % Correct digits = 64 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.436 Order of pole (three term test) = -7.826 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 990 Total Elapsed Time = 2 Minutes 46 Seconds Elapsed Time(since restart) = 2 Minutes 43 Seconds Time to Timeout = 13 Seconds Percent Done = 100.1 % > quit bytes used=3155675376, alloc=4848776, time=166.04