|\^/| 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_2, > #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_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_2, 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_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_2, > #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_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_2, 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_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_2, > #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_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_2, 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_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_2, > #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_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_2, 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_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_2, > #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_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_2, 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_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_2, > #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_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_2, 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_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_2, > #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_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 - 2 - 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 - 2 - 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 - 2 - 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_2, 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_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 - 12; 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 - 3; 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 - 3; 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_2, > #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_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_2, 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_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_2, > #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_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 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_tmp2[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 diff $eq_no = 2 i = 1 order_d = 1 > array_tmp4[1] := array_y1_higher[2,1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * expt(glob_h , (2)) * factorial_3(0,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y2_higher[3,1] := 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 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_tmp2[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 diff $eq_no = 2 i = 2 order_d = 1 > array_tmp4[2] := array_y1_higher[2,2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * expt(glob_h , (2)) * factorial_3(1,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[2,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[3,2] := 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 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_tmp2[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 diff $eq_no = 2 i = 3 order_d = 1 > array_tmp4[3] := array_y1_higher[2,3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * expt(glob_h , (2)) * factorial_3(2,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[2,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,3] := 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 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_tmp2[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 diff $eq_no = 2 i = 4 order_d = 1 > array_tmp4[4] := array_y1_higher[2,4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * expt(glob_h , (2)) * factorial_3(3,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[2,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[3,4] := 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 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_tmp2[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 diff $eq_no = 2 i = 5 order_d = 1 > array_tmp4[5] := array_y1_higher[2,5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,7]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * expt(glob_h , (2)) * factorial_3(4,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[2,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[3,5] := 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 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_tmp2[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 diff $eq_no = 2 > array_tmp4[kkk] := array_y1_higher[2,kkk]; > #emit assign $eq_no = 2 > order_d := 2; > 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_tmp4[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_2, 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_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]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[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_tmp4[1] := array_y1_higher[2, 1]; if not array_y2_set_initial[2, 3] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*expt(glob_h, 2)*factorial_3(0, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary; temporary := temporary*1.0/glob_h; array_y2_higher[3, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y2, 1); array_tmp2[2] := array_tmp1[2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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_tmp4[2] := array_y1_higher[2, 2]; if not array_y2_set_initial[2, 4] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*expt(glob_h, 2)*factorial_3(1, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[2, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[3, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y2, 1); array_tmp2[3] := array_tmp1[3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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_tmp4[3] := array_y1_higher[2, 3]; if not array_y2_set_initial[2, 5] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*expt(glob_h, 2)*factorial_3(2, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y2, 1); array_tmp2[4] := array_tmp1[4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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_tmp4[4] := array_y1_higher[2, 4]; if not array_y2_set_initial[2, 6] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*expt(glob_h, 2)*factorial_3(3, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[3, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y2, 1); array_tmp2[5] := array_tmp1[5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[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_tmp4[5] := array_y1_higher[2, 5]; if not array_y2_set_initial[2, 7] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*expt(glob_h, 2)*factorial_3(4, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[3, 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]; order_d := 1; if kkk + order_d < glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp2[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_tmp4[kkk] := array_y1_higher[2, kkk]; order_d := 2; if kkk + order_d < glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp4[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( - cos(x)); > end; exact_soln_y1 := proc(x) return -cos(x) end proc > exact_soln_y2 := proc(x) > return( - sin(x)); > end; exact_soln_y2 := proc(x) return -sin(x) end proc > exact_soln_y2p := proc(x) > return( - cos(x)); > end; exact_soln_y2p := proc(x) return -cos(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_2, > #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_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/mtest5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 ;"); > omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > 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 := 0.5;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > 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,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > 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( - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return( - sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return( - cos(x));"); > omniout_str(ALWAYS,"end;"); > 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:=32; > 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_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..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(3+ 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_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 <=3) 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 <=3) 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 <=3) 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_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_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 1 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 1; > array_const_2[1] := 2; > 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 := 0.5; > x_end := 5.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > glob_max_iter := 20; > #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] := true; > 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 := 2; > #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 <= 3) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 3 + 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 := 2; > #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 <= 3) do # do number 2 > atomall(); > subiter := subiter + 1; > od;# end do number 2; > else > subiter := 1; > while (subiter <= 3 + 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 := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 2 > array_y2_higher_work[3,iii] := array_y2_higher[3,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 := 3; > 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 := 2; > calc_term := 2; > #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 := 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 := 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 := 3; > #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 := 3; > #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 ;"); > omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); > 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,"2013-05-26T03:19:56-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest5") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 ;") > ; > 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,"mtest5 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest5 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 , 2 ) = diff ( y1, x , 1) ;") > ; > 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_2, 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_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/mtest5postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ;"); omniout_str(ALWAYS, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); 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 := 0.5;"); omniout_str(ALWAYS, "x_end := 5.0;"); 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, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "glob_max_iter := 20;"); 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( - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return( - sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return( - cos(x));"); omniout_str(ALWAYS, "end;"); 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 := 32; 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_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 .. 4, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 4, 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_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 <= 3 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 <= 3 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 <= 3 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_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_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; 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 := 0.5; x_end := 5.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); glob_max_iter := 20; 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] := true; 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 := 2; 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 <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + 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 := 2; 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 <= 3 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 3 + 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 := 3; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; 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 := 2; calc_term := 2; 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 := 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 := 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 := 3; 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 := 3; 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 ;"); omniout_str(INFO, "diff ( y2 , x , 2 ) = diff ( y1, x , 1) ;"); 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, "2013-05-26T03:19:56-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest5"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 ;"); 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, "mtest5 diffeq.mxt"); logitem_str(html_log_file, "mtest5 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 , 2 ) = diff ( y1, x , 1) ;"); 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/mtest5postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1, x , 1) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 5.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); glob_max_iter := 20; #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( - cos(x)); end; exact_soln_y2 := proc(x) return( - sin(x)); end; exact_soln_y2p := proc(x) return( - cos(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 = 4.5 estimated_steps = 4500000 step_error = 2.2222222222222222222222222222222e-17 est_needed_step_err = 2.2222222222222222222222222222222e-17 opt_iter = 1 bytes used=4000496, alloc=3276200, time=0.41 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.1760504191201347172640125560893e-183 estimated_step_error = 2.1760504191201347172640125560893e-183 best_h = 2.0e-06 opt_iter = 2 bytes used=8002184, alloc=4521156, time=0.89 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.4603227015650941259925623828007e-175 estimated_step_error = 1.4603227015650941259925623828007e-175 best_h = 4.00e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.8000595592556264960821340759545e-168 estimated_step_error = 9.8000595592556264960821340759545e-168 best_h = 8.000e-06 opt_iter = 4 bytes used=12003840, alloc=4521156, time=1.36 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.5767083754010533133506200318762e-160 estimated_step_error = 6.5767083754010533133506200318762e-160 best_h = 1.60000e-05 opt_iter = 5 bytes used=16004576, alloc=4521156, time=1.83 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.4135539221189055046517224808234e-152 estimated_step_error = 4.4135539221189055046517224808234e-152 best_h = 3.200000e-05 opt_iter = 6 bytes used=20005340, alloc=4521156, time=2.31 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.9618854197278297629265913043536e-144 estimated_step_error = 2.9618854197278297629265913043536e-144 best_h = 6.4000000e-05 opt_iter = 7 bytes used=24006472, alloc=4521156, time=2.78 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.9876870146750669269415596204014e-136 estimated_step_error = 1.9876870146750669269415596204014e-136 best_h = 0.000128 opt_iter = 8 bytes used=28008388, alloc=4521156, time=3.25 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.3339133117490700886825683454309e-128 estimated_step_error = 1.3339133117490700886825683454309e-128 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.9517291104750232104266630304315e-121 estimated_step_error = 8.9517291104750232104266630304315e-121 best_h = 0.000512 opt_iter = 10 bytes used=32009264, alloc=4521156, time=3.71 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.0073881555206778057824142455026e-113 estimated_step_error = 6.0073881555206778057824142455026e-113 best_h = 0.001024 opt_iter = 11 bytes used=36011240, alloc=4521156, time=4.18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.0314690639458288589709402905376e-105 estimated_step_error = 4.0314690639458288589709402905376e-105 best_h = 0.002048 opt_iter = 12 bytes used=40012132, alloc=4521156, time=4.64 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.7054450608346626620567681632845e-97 estimated_step_error = 2.7054450608346626620567681632845e-97 best_h = 0.004096 opt_iter = 13 bytes used=44015044, alloc=4521156, time=5.10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.8155558208048948153888608098124e-89 estimated_step_error = 1.8155558208048948153888608098124e-89 best_h = 0.008192 opt_iter = 14 bytes used=48016136, alloc=4521156, time=5.56 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.2183483761748801207239377571011e-81 estimated_step_error = 1.2183483761748801207239377571011e-81 best_h = 0.016384 opt_iter = 15 bytes used=52017408, alloc=4521156, time=6.02 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 8.1755193361148759155424465667867e-74 estimated_step_error = 8.1755193361148759155424465667867e-74 best_h = 0.032768 opt_iter = 16 bytes used=56018812, alloc=4521156, time=6.48 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.4855871411416643488751115852213e-66 estimated_step_error = 5.4855871411416643488751115852213e-66 best_h = 0.065536 opt_iter = 17 bytes used=60020848, alloc=4521156, time=6.94 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.6800905139569868890031721847892e-58 estimated_step_error = 3.6800905139569868890031721847892e-58 best_h = 0.131072 opt_iter = 18 bytes used=64021752, alloc=4521156, time=7.39 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.4680179083383405292585812506907e-50 estimated_step_error = 2.4680179083383405292585812506907e-50 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.5 y1[1] (analytic) = -0.87758256189037271611628158260383 y1[1] (numeric) = -0.87758256189037271611628158260383 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.47942553860420300027328793521557 y2[1] (numeric) = -0.47942553860420300027328793521557 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=68022532, alloc=4586680, time=7.87 x[1] = 0.51 y1[1] (analytic) = -0.87274450764575126310580847357551 y1[1] (numeric) = -0.87274450764575126310580847357551 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.48817724688290749450013023767457 y2[1] (numeric) = -0.48817724688290749450013023767457 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=72024136, alloc=4586680, time=8.36 x[1] = 0.52 y1[1] (analytic) = -0.86781917967764990038784757198851 y1[1] (numeric) = -0.86781917967764990038784757198851 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.49688013784373671433445894254775 y2[1] (numeric) = -0.49688013784373671433445894254775 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=76026092, alloc=4586680, time=8.85 x[1] = 0.53 y1[1] (analytic) = -0.8628070705147610118066950185642 y1[1] (numeric) = -0.8628070705147610118066950185642 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.50553334120484696181366102246608 y2[1] (numeric) = -0.50553334120484696181366102246608 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=80027116, alloc=4586680, time=9.35 x[1] = 0.54 y1[1] (analytic) = -0.8577086813638241425379687789178 y1[1] (numeric) = -0.85770868136382414253796877891779 absolute error = 1e-32 relative error = 1.1658970250947227087204260706763e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.51413599165311310467728068295824 y2[1] (numeric) = -0.51413599165311310467728068295824 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 0.55 y1[1] (analytic) = -0.85252452205950574280498179761777 y1[1] (numeric) = -0.85252452205950574280498179761777 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.52268722893065916778837810775729 y2[1] (numeric) = -0.52268722893065916778837810775729 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=84029244, alloc=4586680, time=9.83 x[1] = 0.56 y1[1] (analytic) = -0.84725511101341612609452550386632 y1[1] (numeric) = -0.84725511101341612609452550386632 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.53118619792088340385186944111203 y2[1] (numeric) = -0.53118619792088340385186944111203 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=88030916, alloc=4586680, time=10.32 x[1] = 0.57 y1[1] (analytic) = -0.84190097516226874013375636391601 y1[1] (numeric) = -0.84190097516226874013375636391601 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.53963204873396924099446349307883 y2[1] (numeric) = -0.53963204873396924099446349307882 absolute error = 1e-32 relative error = 1.8531145478592311512083539534776e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=92031576, alloc=4586680, time=10.80 x[1] = 0.58 y1[1] (analytic) = -0.83646264991518693465788732805002 y1[1] (numeric) = -0.83646264991518693465788732805002 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.54802393679187355618269605957646 y2[1] (numeric) = -0.54802393679187355618269605957646 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=96032816, alloc=4652204, time=11.29 x[1] = 0.59 y1[1] (analytic) = -0.83094067910016349524799652249068 y1[1] (numeric) = -0.83094067910016349524799652249068 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.55636102291278377572254337887577 y2[1] (numeric) = -0.55636102291278377572254337887577 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=100034540, alloc=4652204, time=11.78 x[1] = 0.6 y1[1] (analytic) = -0.82533561490967829724095249895538 y1[1] (numeric) = -0.82533561490967829724095249895538 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.56464247339503535720094544565866 y2[1] (numeric) = -0.56464247339503535720094544565866 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 0.61 y1[1] (analytic) = -0.81964801784547951790074657865482 y1[1] (numeric) = -0.81964801784547951790074657865483 absolute error = 1e-32 relative error = 1.2200358912946465931687778838392e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.57286746010048126119097603216272 y2[1] (numeric) = -0.57286746010048126119097603216272 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=104036056, alloc=4652204, time=12.26 x[1] = 0.62 y1[1] (analytic) = -0.8138784566625339286839996543607 y1[1] (numeric) = -0.8138784566625339286839996543607 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.58103516053730507584296322758221 y2[1] (numeric) = -0.58103516053730507584296322758221 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=108036964, alloc=4652204, time=12.74 x[1] = 0.63 y1[1] (analytic) = -0.80802750831215187252370896577706 y1[1] (numeric) = -0.80802750831215187252370896577706 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.58914475794226951311811209079462 y2[1] (numeric) = -0.58914475794226951311811209079461 absolute error = 1e-32 relative error = 1.6973757069361725967914220639108e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=112039072, alloc=4652204, time=13.23 x[1] = 0.64 y1[1] (analytic) = -0.80209575788429261358611077926032 y1[1] (numeric) = -0.80209575788429261358611077926033 absolute error = 1e-32 relative error = 1.2467339344091835043765333244264e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.59719544136239205188354623920793 y2[1] (numeric) = -0.59719544136239205188354623920792 absolute error = 1e-32 relative error = 1.6744936929168164811188136616446e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=116041708, alloc=4652204, time=13.72 x[1] = 0.65 y1[1] (analytic) = -0.79608379854905582891760457067991 y1[1] (numeric) = -0.79608379854905582891760457067991 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.60518640573603956037252167860594 y2[1] (numeric) = -0.60518640573603956037252167860593 absolute error = 1e-32 relative error = 1.6523834483423011016172799055209e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=120043556, alloc=4652204, time=14.20 x[1] = 0.66 y1[1] (analytic) = -0.78999223149736509278381709123024 y1[1] (numeric) = -0.78999223149736509278381709123025 absolute error = 1e-32 relative error = 1.2658352324611882697842840177057e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.6131168519734337886151454793963 y2[1] (numeric) = -0.61311685197343378861514547939629 absolute error = 1e-32 relative error = 1.6310104620046062095590933145473e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.67 y1[1] (analytic) = -0.78382166588084928530294214483812 y1[1] (numeric) = -0.78382166588084928530294214483812 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.62098598703655968035744391412659 y2[1] (numeric) = -0.62098598703655968035744391412658 absolute error = 1e-32 relative error = 1.6103422957612188443809399991484e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=124045452, alloc=4652204, time=14.68 x[1] = 0.68 y1[1] (analytic) = -0.77757271875092793718239408404432 y1[1] (numeric) = -0.77757271875092793718239408404432 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.62879302401846851370417818742025 y2[1] (numeric) = -0.62879302401846851370417818742023 absolute error = 2e-32 relative error = 3.1806968646351541844819338546206e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=128046160, alloc=4652204, time=15.18 x[1] = 0.69 y1[1] (analytic) = -0.77124601499710660197353931549777 y1[1] (numeric) = -0.77124601499710660197353931549777 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.63653718222196794023742920700872 y2[1] (numeric) = -0.63653718222196794023742920700871 absolute error = 1e-32 relative error = 1.5710001362517238398235222357594e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=132048412, alloc=4652204, time=15.68 x[1] = 0.7 y1[1] (analytic) = -0.76484218728448842625585999019186 y1[1] (numeric) = -0.76484218728448842625585999019187 absolute error = 1e-32 relative error = 1.3074592597335938698746728353053e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.64421768723769105367261435139872 y2[1] (numeric) = -0.64421768723769105367261435139871 absolute error = 1e-32 relative error = 1.5522703269571039119899736409549e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=136049744, alloc=4652204, time=16.16 x[1] = 0.71 y1[1] (analytic) = -0.75836187599050816654145794413955 y1[1] (numeric) = -0.75836187599050816654145794413956 absolute error = 1e-32 relative error = 1.3186316871399746265297346929438e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.65183377102153668121012797285284 y2[1] (numeric) = -0.65183377102153668121012797285283 absolute error = 1e-32 relative error = 1.5341334623286338698889510906510e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.72 y1[1] (analytic) = -0.75180572914089497944548696225195 y1[1] (numeric) = -0.75180572914089497944548696225195 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.65938467197147315361800383264817 y2[1] (numeric) = -0.65938467197147315361800383264816 absolute error = 1e-32 relative error = 1.5165654321477203357119039156049e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=140050808, alloc=4652204, time=16.65 TOP MAIN SOLVE Loop x[1] = 0.73 y1[1] (analytic) = -0.74517440234487038879013215855033 y1[1] (numeric) = -0.74517440234487038879013215855034 absolute error = 1e-32 relative error = 1.3419677284314378095774142725353e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.66686963500369787373259413076153 y2[1] (numeric) = -0.66686963500369787373259413076152 absolute error = 1e-32 relative error = 1.4995434602363547076596292654967e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=144052716, alloc=4652204, time=17.13 x[1] = 0.74 y1[1] (analytic) = -0.73846855872958790979142456069883 y1[1] (numeric) = -0.73846855872958790979142456069884 absolute error = 1e-32 relative error = 1.3541537932506339212970812949552e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.67428791162814506748388115760817 y2[1] (numeric) = -0.67428791162814506748388115760816 absolute error = 1e-32 relative error = 1.4830460145509444868398300234299e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=148055340, alloc=4652204, time=17.62 x[1] = 0.75 y1[1] (analytic) = -0.73168886887382088631183875300008 y1[1] (numeric) = -0.73168886887382088631183875300009 absolute error = 1e-32 relative error = 1.3667011246722261352150686601568e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.68163876002333416673324195277989 y2[1] (numeric) = -0.68163876002333416673324195277988 absolute error = 1e-32 relative error = 1.4670527244750101169725783295448e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=152057636, alloc=4652204, time=18.11 x[1] = 0.76 y1[1] (analytic) = -0.72483601074090517233968836666701 y1[1] (numeric) = -0.72483601074090517233968836666701 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.68892144511055133914775563876973 y2[1] (numeric) = -0.68892144511055133914775563876971 absolute error = 2e-32 relative error = 2.9030886092957371454415397095206e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=156058688, alloc=4652204, time=18.60 x[1] = 0.77 y1[1] (analytic) = -0.71791066961094336337129056532434 y1[1] (numeric) = -0.71791066961094336337129056532435 absolute error = 1e-32 relative error = 1.3929309624858048638846923337441e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.69613523862735674701988373445221 y2[1] (numeric) = -0.69613523862735674701988373445219 absolute error = 2e-32 relative error = 2.8730049694706029924906087380248e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.78 y1[1] (analytic) = -0.71091353801227735721626502376456 y1[1] (numeric) = -0.71091353801227735721626502376457 absolute error = 1e-32 relative error = 1.4066408171041612210983571067735e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.70327941920041018436789732511792 y2[1] (numeric) = -0.70327941920041018436789732511791 absolute error = 1e-32 relative error = 1.4219099446091351719853706495587e-30 % Correct digits = 32 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 = 18.2 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=160059812, alloc=4652204, time=19.08 x[1] = 0.79 y1[1] (analytic) = -0.70384531565223609691278086108495 y1[1] (numeric) = -0.70384531565223609691278086108496 absolute error = 1e-32 relative error = 1.4207667192802507471305291751001e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.7103532724176078098140288749692 y2[1] (numeric) = -0.71035327241760780981402887496918 absolute error = 2e-32 relative error = 2.8155005089132960296161411393593e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 17.84 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 bytes used=164060508, alloc=4652204, time=19.57 x[1] = 0.8 y1[1] (analytic) = -0.69670670934716542092074998164232 y1[1] (numeric) = -0.69670670934716542092074998164233 absolute error = 1e-32 relative error = 1.4353241996722398004969524081629e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.71735609089952276162717461058139 y2[1] (numeric) = -0.71735609089952276162717461058137 absolute error = 2e-32 relative error = 2.7880156387772723490049644522139e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 17.48 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=168062136, alloc=4652204, time=20.05 x[1] = 0.81 y1[1] (analytic) = -0.6894984329517470175496392406801 y1[1] (numeric) = -0.68949843295174701754963924068011 absolute error = 1e-32 relative error = 1.4503296196323374815898349922412e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.72428717437014251092817685251454 y2[1] (numeric) = -0.72428717437014251092817685251453 absolute error = 1e-32 relative error = 1.3806678281575591497744905002579e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 17.14 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=172063224, alloc=4652204, time=20.54 x[1] = 0.82 y1[1] (analytic) = -0.68222120728761355166655797843693 y1[1] (numeric) = -0.68222120728761355166655797843694 absolute error = 1e-32 relative error = 1.4658002262577216994844494554605e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.73114582972689587938131336468772 y2[1] (numeric) = -0.73114582972689587938131336468771 absolute error = 1e-32 relative error = 1.3677162056351041919994290452163e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.8 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=176064460, alloc=4652204, time=21.04 x[1] = 0.83 y1[1] (analytic) = -0.67487576007126710211246291786445 y1[1] (numeric) = -0.67487576007126710211246291786446 absolute error = 1e-32 relative error = 1.4817542119076845659331474984770e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.73793137110996271872858022613808 y2[1] (numeric) = -0.73793137110996271872858022613807 absolute error = 1e-32 relative error = 1.3551395687323139549321573017265e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.46 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 x[1] = 0.84 y1[1] (analytic) = -0.66746282584130811792267103687086 y1[1] (numeric) = -0.66746282584130811792267103687086 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.74464311997085932125657267062965 y2[1] (numeric) = -0.74464311997085932125657267062963 absolute error = 2e-32 relative error = 2.6858503709512115049324626494095e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.13 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=180067156, alloc=4652204, time=21.52 x[1] = 0.85 y1[1] (analytic) = -0.65998314588498217039541602946147 y1[1] (numeric) = -0.65998314588498217039541602946147 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.75128040514029270271207152423547 y2[1] (numeric) = -0.75128040514029270271207152423545 absolute error = 2e-32 relative error = 2.6621218739579980491485171088475e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.81 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 bytes used=184068444, alloc=4652204, time=22.01 x[1] = 0.86 y1[1] (analytic) = -0.65243746816405184627203066422386 y1[1] (numeric) = -0.65243746816405184627203066422386 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.75784256289527697229458872952865 y2[1] (numeric) = -0.75784256289527697229458872952863 absolute error = 2e-32 relative error = 2.6390705641540635661109487598376e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.5 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=188070640, alloc=4652204, time=22.50 x[1] = 0.87 y1[1] (analytic) = -0.64482654724000119477766380548283 y1[1] (numeric) = -0.64482654724000119477766380548283 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.76432893702550507814480282372285 y2[1] (numeric) = -0.76432893702550507814480282372284 absolute error = 1e-32 relative error = 1.3083372244045115314688242731840e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.19 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 bytes used=192072808, alloc=4652204, time=22.99 x[1] = 0.88 y1[1] (analytic) = -0.63715114419858020801549860572209 y1[1] (numeric) = -0.63715114419858020801549860572209 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.77073887889896929120964513075599 y2[1] (numeric) = -0.77073887889896929120964513075598 absolute error = 1e-32 relative error = 1.2974562817286954688159028980636e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.88 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=196075104, alloc=4652204, time=23.48 x[1] = 0.89 y1[1] (analytic) = -0.62941202657369688020355305738025 y1[1] (numeric) = -0.62941202657369688020355305738025 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.77707174752682386549033371297318 y2[1] (numeric) = -0.77707174752682386549033371297317 absolute error = 1e-32 relative error = 1.2868824573569776297419516230397e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.58 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] = 0.9 y1[1] (analytic) = -0.62160996827066445648471615140713 y1[1] (numeric) = -0.62160996827066445648471615140713 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.78332690962748338846138231571355 y2[1] (numeric) = -0.78332690962748338846138231571354 absolute error = 1e-32 relative error = 1.2766062134588954960156456522320e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.28 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=200078332, alloc=4652204, time=23.97 x[1] = 0.91 y1[1] (analytic) = -0.61374574948881154652117822617468 y1[1] (numeric) = -0.61374574948881154652117822617468 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.78950373968995041187895751787155 y2[1] (numeric) = -0.78950373968995041187895751787154 absolute error = 1e-32 relative error = 1.2666184461554476328851986985698e-30 % Correct digits = 32 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 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=204079996, alloc=4652204, time=24.46 x[1] = 0.92 y1[1] (analytic) = -0.60582015664346284179740470667438 y1[1] (numeric) = -0.60582015664346284179740470667438 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.79560162003636603026827610248162 y2[1] (numeric) = -0.79560162003636603026827610248161 absolute error = 1e-32 relative error = 1.2569104622415061901025446361799e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.71 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=208080752, alloc=4652204, time=24.95 x[1] = 0.93 y1[1] (analytic) = -0.59783398228729823849490708443298 y1[1] (numeric) = -0.59783398228729823849490708443299 absolute error = 1e-32 relative error = 1.6727051817530083924888988545676e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.80161994088377715208431921591065 y2[1] (numeric) = -0.80161994088377715208431921591064 absolute error = 1e-32 relative error = 1.2474739574186627875214517543531e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.42 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=212083464, alloc=4652204, time=25.44 x[1] = 0.94 y1[1] (analytic) = -0.58978802503109822996098981522402 y1[1] (numeric) = -0.58978802503109822996098981522402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.80755810040511428687021979863415 y2[1] (numeric) = -0.80755810040511428687021979863414 absolute error = 1e-32 relative error = 1.2383009959262950555565426520017e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.15 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 x[1] = 0.95 y1[1] (analytic) = -0.58168308946388349416618097376046 y1[1] (numeric) = -0.58168308946388349416618097376046 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.81341550478937375068542210210256 y2[1] (numeric) = -0.81341550478937375068542210210255 absolute error = 1e-32 relative error = 1.2293839914681003518494659282533e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=216086712, alloc=4652204, time=25.93 TOP MAIN SOLVE Loop x[1] = 0.96 y1[1] (analytic) = -0.57351998607245666212505080035186 y1[1] (numeric) = -0.57351998607245666212505080035186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.81919156830099827163322214643043 y2[1] (numeric) = -0.81919156830099827163322214643042 absolute error = 1e-32 relative error = 1.2207156893399160174865568665939e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=220088108, alloc=4652204, time=26.42 x[1] = 0.97 y1[1] (analytic) = -0.56529953116035431303652775484986 y1[1] (numeric) = -0.56529953116035431303652775484986 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.82488571333845005747662003785634 y2[1] (numeric) = -0.82488571333845005747662003785634 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=224089864, alloc=4652204, time=26.92 x[1] = 0.98 y1[1] (analytic) = -0.55702254676621730087665826735994 y1[1] (numeric) = -0.55702254676621730087665826735994 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.83049737049197046808453328771915 y2[1] (numeric) = -0.83049737049197046808453328771914 absolute error = 1e-32 relative error = 1.2040977317093965936477359077356e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=228091204, alloc=4652204, time=27.42 x[1] = 0.99 y1[1] (analytic) = -0.54868986058158757534312640865361 y1[1] (numeric) = -0.54868986058158757534312640865361 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.83602597860052051678925941154711 y2[1] (numeric) = -0.8360259786005205167892594115471 absolute error = 1e-32 relative error = 1.1961350790485799284337371675417e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=232092592, alloc=4717728, time=27.91 x[1] = 1 y1[1] (analytic) = -0.54030230586813971740093660744298 y1[1] (numeric) = -0.54030230586813971740093660744297 absolute error = 1e-32 relative error = 1.8508157176809256179117532413986e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.8414709848078965066525023216303 y2[1] (numeric) = -0.84147098480789650665250232163029 absolute error = 1e-32 relative error = 1.1883951057781212162615994523745e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.01 y1[1] (analytic) = -0.53186072137435546620673135577918 y1[1] (numeric) = -0.53186072137435546620673135577917 absolute error = 1e-32 relative error = 1.8801914858761304160058742988838e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.84683184461801519012309878478201 y2[1] (numeric) = -0.846831844618015190123098784782 absolute error = 1e-32 relative error = 1.1808719834468142374663420640003e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=236093748, alloc=4717728, time=28.39 x[1] = 1.02 y1[1] (analytic) = -0.52336595125164956988961380803381 y1[1] (numeric) = -0.5233659512516495698896138080338 absolute error = 1e-32 relative error = 1.9107089362776886454378422779994e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.85210802194936292361654998545538 y2[1] (numeric) = -0.85210802194936292361654998545537 absolute error = 1e-32 relative error = 1.1735601288112572819824797672248e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=240095740, alloc=4717728, time=28.88 x[1] = 1.03 y1[1] (analytic) = -0.51481884496995534753350229983735 y1[1] (numeric) = -0.51481884496995534753350229983734 absolute error = 1e-32 relative error = 1.9424308371197244332449996487096e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.85729898918860337214627438529442 y2[1] (numeric) = -0.85729898918860337214627438529441 absolute error = 1e-32 relative error = 1.1664541923074667312790368212473e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=244097356, alloc=4717728, time=29.37 x[1] = 1.04 y1[1] (analytic) = -0.50622025723277840373447342099217 y1[1] (numeric) = -0.50622025723277840373447342099216 absolute error = 1e-32 relative error = 1.9754247004385756762283379285025e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.86240422724333840328079169211617 y2[1] (numeric) = -0.86240422724333840328079169211616 absolute error = 1e-32 relative error = 1.1595490471985327900404013996952e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=248098536, alloc=4717728, time=29.86 x[1] = 1.05 y1[1] (analytic) = -0.4975710478917269902908495728121 y1[1] (numeric) = -0.49757104789172699029084957281209 absolute error = 1e-32 relative error = 2.0097632373047619814603684257021e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.86742322559401689438140948500027 y2[1] (numeric) = -0.86742322559401689438140948500026 absolute error = 1e-32 relative error = 1.1528397793536064180769674011258e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=252100960, alloc=4717728, time=30.36 x[1] = 1.06 y1[1] (analytic) = -0.48887208186052756191863753995641 y1[1] (numeric) = -0.4888720818605275619186375399564 absolute error = 1e-32 relative error = 2.0455248665340933506028342705602e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.87235548234498626228294592199742 y2[1] (numeric) = -0.87235548234498626228294592199741 absolute error = 1e-32 relative error = 1.1463216776168946790260800959306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.07 y1[1] (analytic) = -0.48012422902853412436509306817592 y1[1] (numeric) = -0.48012422902853412436509306817591 absolute error = 1e-32 relative error = 2.0827942843529550116983739353760e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.87720050427468161030706325777682 y2[1] (numeric) = -0.87720050427468161030706325777681 absolute error = 1e-32 relative error = 1.1399902247284454927049148925566e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=256103164, alloc=4717728, time=30.84 x[1] = 1.08 y1[1] (analytic) = -0.47132836417374002391352478852603 y1[1] (numeric) = -0.47132836417374002391352478852602 absolute error = 1e-32 relative error = 2.1216631037112423847777714573716e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.88195780688494747373533498762476 y2[1] (numeric) = -0.88195780688494747373533498762474 absolute error = 2e-32 relative error = 2.2676821775226970277154571941427e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=260104324, alloc=4717728, time=31.34 x[1] = 1.09 y1[1] (analytic) = -0.46248536687530087702789707387514 y1[1] (numeric) = -0.46248536687530087702789707387513 absolute error = 1e-32 relative error = 2.1622305733829374458118142722034e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.88662691444948723160860062863605 y2[1] (numeric) = -0.88662691444948723160860062863603 absolute error = 2e-32 relative error = 2.2557402300851805280872224776897e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=264105276, alloc=4717728, time=31.83 x[1] = 1.1 y1[1] (analytic) = -0.45359612142557738777137005178472 y1[1] (numeric) = -0.4535961214255773877713700517847 absolute error = 2e-32 relative error = 4.4092087774347180679720506661284e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.8912073600614353399518025778717 y2[1] (numeric) = -0.89120736006143533995180257787168 absolute error = 2e-32 relative error = 2.2441466370544000988174833006507e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=268107228, alloc=4717728, time=32.32 x[1] = 1.11 y1[1] (analytic) = -0.44466151674170684864373751193357 y1[1] (numeric) = -0.44466151674170684864373751193356 absolute error = 1e-32 relative error = 2.2489016079636949635358455092129e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.89569868568004762924062595933937 y2[1] (numeric) = -0.89569868568004762924062595933935 absolute error = 2e-32 relative error = 2.2328937531950556528878894438313e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=272108180, alloc=4717728, time=32.82 x[1] = 1.12 y1[1] (analytic) = -0.43568244627671216761398879396113 y1[1] (numeric) = -0.43568244627671216761398879396111 absolute error = 2e-32 relative error = 4.5904993811243727864546572322733e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.90010044217650499711910324733915 y2[1] (numeric) = -0.90010044217650499711910324733913 absolute error = 2e-32 relative error = 2.2219742445230467316799051434832e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.13 y1[1] (analytic) = -0.42665980793015731037121583565354 y1[1] (numeric) = -0.42665980793015731037121583565352 absolute error = 2e-32 relative error = 4.6875753535411352140507026782080e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9044121893788259160370815224114 y2[1] (numeric) = -0.90441218937882591603708152241138 absolute error = 2e-32 relative error = 2.2113810754515069216797302583732e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=276109036, alloc=4717728, time=33.31 x[1] = 1.14 y1[1] (analytic) = -0.41759450395835809217518674082258 y1[1] (numeric) = -0.41759450395835809217518674082256 absolute error = 2e-32 relative error = 4.7893350631823378816383682599086e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9086334961158832645942155781022 y2[1] (numeric) = -0.90863349611588326459421557810219 absolute error = 1e-32 relative error = 1.1005537483206146725447225549655e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=280109868, alloc=4717728, time=33.80 x[1] = 1.15 y1[1] (analytic) = -0.40848744088415729815257671880992 y1[1] (numeric) = -0.4084874408841572981525767188099 absolute error = 2e-32 relative error = 4.8961113606603605924931240884617e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.91276394026052108094403304975368 y2[1] (numeric) = -0.91276394026052108094403304975366 absolute error = 2e-32 relative error = 2.1911470335135719826111150008028e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=284110524, alloc=4717728, time=34.30 x[1] = 1.16 y1[1] (analytic) = -0.39933952940627315445163962339401 y1[1] (numeric) = -0.39933952940627315445163962339399 absolute error = 2e-32 relative error = 5.0082695368864286332773691729060e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.91680310877176692661866166687433 y2[1] (numeric) = -0.91680310877176692661866166687432 absolute error = 1e-32 relative error = 1.0907467376934304006864358212757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=288111496, alloc=4717728, time=34.79 x[1] = 1.17 y1[1] (analytic) = -0.3901516843082302153326619350505 y1[1] (numeric) = -0.39015168430823021533266193505049 absolute error = 1e-32 relative error = 2.5631056848391647153358290323670e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.92075059773613563957301300896203 y2[1] (numeric) = -0.92075059773613563957301300896201 absolute error = 2e-32 relative error = 2.1721408652000143041485420121306e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=292112236, alloc=4717728, time=35.28 x[1] = 1.18 y1[1] (analytic) = -0.38092482436688177302959946671276 y1[1] (numeric) = -0.38092482436688177302959946671275 absolute error = 1e-32 relative error = 2.6251898958332672918090036648854e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.92460601240802034610753802587476 y2[1] (numeric) = -0.92460601240802034610753802587474 absolute error = 2e-32 relative error = 2.1630834897896142230973730778543e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.19 y1[1] (analytic) = -0.37165987226053293806567955835047 y1[1] (numeric) = -0.37165987226053293806567955835045 absolute error = 2e-32 relative error = 5.3812642937088548613935325903777e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.92836896724916669260202111160267 y2[1] (numeric) = -0.92836896724916669260202111160265 absolute error = 2e-32 relative error = 2.1543158706889609330084255263453e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=296113660, alloc=4717728, time=35.77 x[1] = 1.2 y1[1] (analytic) = -0.36235775447667357763837335562308 y1[1] (numeric) = -0.36235775447667357763837335562306 absolute error = 2e-32 relative error = 5.5194072026648129137668658784755e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.93203908596722634967013443549483 y2[1] (numeric) = -0.9320390859672263496701344354948 absolute error = 3e-32 relative error = 3.2187491331296916861153507673057e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=300114940, alloc=4717728, time=36.26 x[1] = 1.21 y1[1] (analytic) = -0.35301940121933033870301071366479 y1[1] (numeric) = -0.35301940121933033870301071366477 absolute error = 2e-32 relative error = 5.6654110031686430904777888040839e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.93561600155338593341646488854361 y2[1] (numeric) = -0.93561600155338593341646488854358 absolute error = 3e-32 relative error = 3.2064436638740204488227490204825e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=304115636, alloc=4717728, time=36.75 x[1] = 1.22 y1[1] (analytic) = -0.3436457463160470204755229744352 y1[1] (numeric) = -0.34364574631604702047552297443518 absolute error = 2e-32 relative error = 5.8199469117264239878678497503029e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.93909935631906758093524527188837 y2[1] (numeric) = -0.93909935631906758093524527188835 absolute error = 2e-32 relative error = 2.1297001073872334107089126326436e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=308118104, alloc=4717728, time=37.24 x[1] = 1.23 y1[1] (analytic) = -0.33423772712450259823954724549766 y1[1] (numeric) = -0.33423772712450259823954724549765 absolute error = 1e-32 relative error = 2.9918824801830430638065894219944e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.94248880193169751002382356538924 y2[1] (numeric) = -0.94248880193169751002382356538922 absolute error = 2e-32 relative error = 2.1220411275983952675618352134190e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.24 y1[1] (analytic) = -0.32479628443877623657769341569738 y1[1] (numeric) = -0.32479628443877623657769341569737 absolute error = 1e-32 relative error = 3.0788529546387066657065462901600e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.94578399944953898628470596308179 y2[1] (numeric) = -0.94578399944953898628470596308176 absolute error = 3e-32 relative error = 3.1719716148148485389551099569729e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=312119612, alloc=4717728, time=37.73 TOP MAIN SOLVE Loop x[1] = 1.25 y1[1] (analytic) = -0.31532236239526866544753855243804 y1[1] (numeric) = -0.31532236239526866544753855243803 absolute error = 1e-32 relative error = 3.1713576937701033608479299546555e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.94898461935558621434849084703605 y2[1] (numeric) = -0.94898461935558621434849084703602 absolute error = 3e-32 relative error = 3.1612735747362989631759231890560e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=316120972, alloc=4717728, time=38.23 x[1] = 1.26 y1[1] (analytic) = -0.30581690837828932688634248917648 y1[1] (numeric) = -0.30581690837828932688634248917648 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.95209034159051576385681622142542 y2[1] (numeric) = -0.9520903415905157638568162214254 absolute error = 2e-32 relative error = 2.1006409923861819534960845647385e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=320122464, alloc=4717728, time=38.73 x[1] = 1.27 y1[1] (analytic) = -0.29628087292531873355113701608796 y1[1] (numeric) = -0.29628087292531873355113701608795 absolute error = 1e-32 relative error = 3.3751756909804379950299232532105e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.95510085558469223509018174218289 y2[1] (numeric) = -0.95510085558469223509018174218286 absolute error = 3e-32 relative error = 3.1410295388788699371739444480923e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=324123148, alloc=4717728, time=39.22 x[1] = 1.28 y1[1] (analytic) = -0.28671520963195551277938689359259 y1[1] (numeric) = -0.28671520963195551277938689359258 absolute error = 1e-32 relative error = 3.4877814863175858325385099206348e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.95801586028922496370075385916029 y2[1] (numeric) = -0.95801586028922496370075385916026 absolute error = 3e-32 relative error = 3.1314721648703186153781013544840e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=328124880, alloc=4717728, time=39.71 x[1] = 1.29 y1[1] (analytic) = -0.27712087505655764138660609006118 y1[1] (numeric) = -0.27712087505655764138660609006117 absolute error = 1e-32 relative error = 3.6085336400439333502208771241743e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.96083506420607265890556129128537 y2[1] (numeric) = -0.96083506420607265890556129128535 absolute error = 2e-32 relative error = 2.0815227030172736098408450886038e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.3 y1[1] (analytic) = -0.26749882862458740699798410929287 y1[1] (numeric) = -0.26749882862458740699798410929286 absolute error = 1e-32 relative error = 3.7383341270754411719436683964147e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.96355818541719296470134863003955 y2[1] (numeric) = -0.96355818541719296470134863003953 absolute error = 2e-32 relative error = 2.0756400913496028853066938324360e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=332125876, alloc=4717728, time=40.20 x[1] = 1.31 y1[1] (analytic) = -0.2578500325326696613381769786162 y1[1] (numeric) = -0.25785003253266966133817697861618 absolute error = 2e-32 relative error = 7.7564465684005663928806699624399e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9661849516127340291692578059375 y2[1] (numeric) = -0.96618495161273402916925780593747 absolute error = 3e-32 relative error = 3.1049955756322513352726932282974e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=336127400, alloc=4717728, time=40.69 x[1] = 1.32 y1[1] (analytic) = -0.24817545165237295957398272942735 y1[1] (numeric) = -0.24817545165237295957398272942734 absolute error = 1e-32 relative error = 4.0294073944135738581860237987434e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.96871510011826526273589984597277 y2[1] (numeric) = -0.96871510011826526273589984597275 absolute error = 2e-32 relative error = 2.0645905073182307793178455494037e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=340129332, alloc=4717728, time=41.18 x[1] = 1.33 y1[1] (analytic) = -0.23847605343372320751578498601058 y1[1] (numeric) = -0.23847605343372320751578498601056 absolute error = 2e-32 relative error = 8.3865862890750833359123504948680e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9711483779210445623376830377638 y2[1] (numeric) = -0.97114837792104456233768303776377 absolute error = 3e-32 relative error = 3.0891263046972862465940813612778e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=344131524, alloc=4717728, time=41.68 x[1] = 1.34 y1[1] (analytic) = -0.22875280780845946523263949230014 y1[1] (numeric) = -0.22875280780845946523263949230013 absolute error = 1e-32 relative error = 4.3715310407788541476741032102713e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.97348454169531937478787034808955 y2[1] (numeric) = -0.97348454169531937478787034808953 absolute error = 2e-32 relative error = 2.0544753556302066436267292789820e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=348134556, alloc=4717728, time=42.18 x[1] = 1.35 y1[1] (analytic) = -0.21900668709304158142002217301063 y1[1] (numeric) = -0.21900668709304158142002217301061 absolute error = 2e-32 relative error = 9.1321412443919172973506823621498e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.97572335782665906926111353926522 y2[1] (numeric) = -0.97572335782665906926111353926519 absolute error = 3e-32 relative error = 3.0746419832382052117105986469068e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.36 y1[1] (analytic) = -0.20923866589141935767597525239186 y1[1] (numeric) = -0.20923866589141935767597525239184 absolute error = 2e-32 relative error = 9.5584627797133060877550893995346e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.97786460243531618567849243942663 y2[1] (numeric) = -0.9778646024353161856784924394266 absolute error = 3e-32 relative error = 3.0679093941315296578650955118218e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=352136432, alloc=4717728, time=42.66 x[1] = 1.37 y1[1] (analytic) = -0.19944972099757296568819838964531 y1[1] (numeric) = -0.19944972099757296568819838964529 absolute error = 2e-32 relative error = 1.0027589860726540222418547501368e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.97990806139861422288768850489193 y2[1] (numeric) = -0.9799080613986142228876885048919 absolute error = 3e-32 relative error = 3.0615117052084725025716087432751e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=356138124, alloc=4717728, time=43.16 x[1] = 1.38 y1[1] (analytic) = -0.1896408312978343632091500735982 y1[1] (numeric) = -0.18964083129783436320915007359819 absolute error = 1e-32 relative error = 5.2731260096064537536605461963399e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98185353037235972787813108520605 y2[1] (numeric) = -0.98185353037235972787813108520602 absolute error = 3e-32 relative error = 3.0554455498696176470477246956131e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=360139796, alloc=4717728, time=43.65 x[1] = 1.39 y1[1] (analytic) = -0.17981297767299947659616321780405 y1[1] (numeric) = -0.17981297767299947659616321780404 absolute error = 1e-32 relative error = 5.5613338533248644647924530616214e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98370081481127654484003822444291 y2[1] (numeric) = -0.98370081481127654484003822444288 absolute error = 3e-32 relative error = 3.0497077514117454340774764863295e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=364141632, alloc=4717728, time=44.14 x[1] = 1.4 y1[1] (analytic) = -0.16996714290024093861674803520365 y1[1] (numeric) = -0.16996714290024093861674803520364 absolute error = 1e-32 relative error = 5.8834900848273448269942703098450e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9854497299884601806594745788061 y2[1] (numeric) = -0.98544972998846018065947457880607 absolute error = 3e-32 relative error = 3.0442953188846382027007465438561e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=368144392, alloc=4717728, time=44.64 x[1] = 1.41 y1[1] (analytic) = -0.16010431155483119016356254936092 y1[1] (numeric) = -0.16010431155483119016356254936091 absolute error = 1e-32 relative error = 6.2459279846284984956630466211963e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98710010101385034142908886194224 y2[1] (numeric) = -0.98710010101385034142908886194221 absolute error = 3e-32 relative error = 3.0392054432156379314749133768739e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.42 y1[1] (analytic) = -0.15022546991168577348698210297591 y1[1] (numeric) = -0.1502254699116857734869821029759 absolute error = 1e-32 relative error = 6.6566608218158868242394588307625e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9886517628517197927362734733357 y2[1] (numeric) = -0.98865176285171979273627347333567 absolute error = 3e-32 relative error = 3.0344354935924457800398381194336e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=372146812, alloc=4717728, time=45.12 x[1] = 1.43 y1[1] (analytic) = -0.14033160584673666253389762457492 y1[1] (numeric) = -0.14033160584673666253389762457491 absolute error = 1e-32 relative error = 7.1259784562869696005765449324739e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99010456033717779485729149548183 y2[1] (numeric) = -0.9901045603371777948572914954818 absolute error = 3e-32 relative error = 3.0299830140953567660089132712971e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=376148004, alloc=4717728, time=45.62 x[1] = 1.44 y1[1] (analytic) = -0.13042370873814549297752015612917 y1[1] (numeric) = -0.13042370873814549297752015612916 absolute error = 1e-32 relative error = 7.6673176194346817373660360175223e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99145834819168646252760446395798 y2[1] (numeric) = -0.99145834819168646252760446395795 absolute error = 3e-32 relative error = 3.0258457205707912781319328706012e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=380148672, alloc=4717728, time=46.11 x[1] = 1.45 y1[1] (analytic) = -0.12050276936736657053286662724802 y1[1] (numeric) = -0.12050276936736657053286662724801 absolute error = 1e-32 relative error = 8.2985644666089360283162255101862e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99271299103758849766535413432301 y2[1] (numeric) = -0.99271299103758849766535413432298 absolute error = 3e-32 relative error = 3.0220214977386215669938803278051e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=384150400, alloc=4717728, time=46.61 x[1] = 1.46 y1[1] (analytic) = -0.11056977982006955117464810912337 y1[1] (numeric) = -0.11056977982006955117464810912337 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99386836341164484228683230125003 y2[1] (numeric) = -0.99386836341164484228683230125 absolute error = 3e-32 relative error = 3.0185083965263985238359092642818e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=388151160, alloc=4717728, time=47.09 x[1] = 1.47 y1[1] (analytic) = -0.10062573338693170090697460146241 y1[1] (numeric) = -0.1006257333869317009069746014624 absolute error = 1e-32 relative error = 9.9378157688028373545061746907286e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99492434977758089785992846273557 y2[1] (numeric) = -0.99492434977758089785992846273554 absolute error = 3e-32 relative error = 3.0153046316241645395900158976590e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.48 y1[1] (analytic) = -0.090671624464309655776226540647838 y1[1] (numeric) = -0.090671624464309655776226540647832 absolute error = 6e-33 relative error = 6.6172852151355597158742307192576e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99588084453764005648407513256269 y2[1] (numeric) = -0.99588084453764005648407513256266 absolute error = 3e-32 relative error = 3.0124085792540944600162588667607e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=392152340, alloc=4717728, time=47.58 x[1] = 1.49 y1[1] (analytic) = -0.080708448454800614868318484563714 y1[1] (numeric) = -0.080708448454800614868318484563708 absolute error = 6e-33 relative error = 7.4341659576818618964543522687971e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9967377520431433885532007170437 y2[1] (numeric) = -0.99673775204314338855320071704367 absolute error = 3e-32 relative error = 3.0098187751497409110967395816956e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=396154824, alloc=4717728, time=48.07 x[1] = 1.5 y1[1] (analytic) = -0.070737201667702910088189851434269 y1[1] (numeric) = -0.070737201667702910088189851434263 absolute error = 6e-33 relative error = 8.4820997417819418491539370605113e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99749498660405443094172337114149 y2[1] (numeric) = -0.99749498660405443094172337114146 absolute error = 3e-32 relative error = 3.0075339127401747298625509485262e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=400156208, alloc=4717728, time=48.56 x[1] = 1.51 y1[1] (analytic) = -0.060758881219385906581595514916193 y1[1] (numeric) = -0.060758881219385906581595514916188 absolute error = 5e-33 relative error = 8.2292496169344957538401347130756e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99815247249754811924273786483671 y2[1] (numeric) = -0.99815247249754811924273786483668 absolute error = 3e-32 relative error = 3.0055528415348079570850271345298e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=404157364, alloc=4717728, time=49.06 x[1] = 1.52 y1[1] (analytic) = -0.050774484933579196726129270152727 y1[1] (numeric) = -0.050774484933579196726129270152722 absolute error = 5e-33 relative error = 9.8474657232678299652149632858788e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99871014397558300717231239411685 y2[1] (numeric) = -0.99871014397558300717231239411682 absolute error = 3e-32 relative error = 3.0038745657051677886292664950797e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.53 y1[1] (analytic) = -0.040785011241591058688989007076121 y1[1] (numeric) = -0.040785011241591058688989007076115 absolute error = 6e-33 relative error = 1.4711286860898103781269382278386e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99916794527147601592426506870898 y2[1] (numeric) = -0.99916794527147601592426506870895 absolute error = 3e-32 relative error = 3.0024982428603569134803097180172e-30 % Correct digits = 32 h = 0.01 bytes used=408158316, alloc=4717728, time=49.55 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 1.54 y1[1] (analytic) = -0.030791459082466157622476807076397 y1[1] (numeric) = -0.030791459082466157622476807076391 absolute error = 6e-33 relative error = 1.9485922976013277072731329223155e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99952583060547905600596353844003 y2[1] (numeric) = -0.99952583060547905600596353844001 absolute error = 2e-32 relative error = 2.0009487886755937225918666730081e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=412159772, alloc=4717728, time=50.03 x[1] = 1.55 y1[1] (analytic) = -0.020794827803092473643912774695556 y1[1] (numeric) = -0.020794827803092473643912774695551 absolute error = 5e-33 relative error = 2.4044440508694339918709693984240e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99978376418935696389761134763447 y2[1] (numeric) = -0.99978376418935696389761134763445 absolute error = 2e-32 relative error = 2.0004325651573635306403025905592e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=416161656, alloc=4717728, time=50.54 x[1] = 1.56 y1[1] (analytic) = -0.010796117058267445823920663760906 y1[1] (numeric) = -0.010796117058267445823920663760901 absolute error = 5e-33 relative error = 4.6312947266268312414233422888360e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99994172022996629574517002341348 y2[1] (numeric) = -0.99994172022996629574517002341346 absolute error = 2e-32 relative error = 2.0001165663335265201073221180553e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=420164244, alloc=4717728, time=51.04 x[1] = 1.57 y1[1] (analytic) = -0.00079632671073332548540853364535419 y1[1] (numeric) = -0.0007963267107333254854085336453493 absolute error = 4.89e-33 relative error = 6.1406956894574983586604671771261e-28 % Correct digits = 30 h = 0.01 y2[1] (analytic) = -0.99999968293183462021052992382333 y2[1] (numeric) = -0.9999996829318346202105299238233 absolute error = 3e-32 relative error = 3.0000009512047977361285288765229e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=424165828, alloc=4717728, time=51.53 x[1] = 1.58 y1[1] (analytic) = 0.0092035432688082648053890569827275 y1[1] (numeric) = 0.0092035432688082648053890569827321 absolute error = 4.6e-33 relative error = 4.9980750518008247430707146528410e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99995764649874005255179423225172 y2[1] (numeric) = -0.99995764649874005255179423225169 absolute error = 3e-32 relative error = 3.0001270658854649824820910040972e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.008862 Order of pole (three term test) = -0.8909 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.59 y1[1] (analytic) = 0.019202492901692568095027346243403 y1[1] (numeric) = 0.019202492901692568095027346243408 absolute error = 5e-33 relative error = 2.6038285891303645687127360533955e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99981561513429087198158434374551 y2[1] (numeric) = -0.99981561513429087198158434374548 absolute error = 3e-32 relative error = 3.0005532566092729875425661606254e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.01849 Order of pole (three term test) = -0.8974 NO COMPLEX POLE (six term test) for Equation 2 bytes used=428166576, alloc=4717728, time=52.02 TOP MAIN SOLVE Loop x[1] = 1.6 y1[1] (analytic) = 0.029199522301288726205770462946499 y1[1] (numeric) = 0.029199522301288726205770462946503 absolute error = 4e-33 relative error = 1.3698854244007475682118184593316e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.99957360304150516434211382554623 y2[1] (numeric) = -0.9995736030415051643421138255462 absolute error = 3e-32 relative error = 3.0012797365512576379008119576430e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.02811 Order of pole (three term test) = -0.9087 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=432167632, alloc=4717728, time=52.51 x[1] = 1.61 y1[1] (analytic) = 0.039193631772987609585327609601018 y1[1] (numeric) = 0.039193631772987609585327609601022 absolute error = 4e-33 relative error = 1.0205739603740458230429188084879e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.9992316344213905321324131478443 y2[1] (numeric) = -0.99923163442139053213241314784427 absolute error = 3e-32 relative error = 3.0023068692547581122115856994688e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.03771 Order of pole (three term test) = -0.9245 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=436170244, alloc=4717728, time=53.01 x[1] = 1.62 y1[1] (analytic) = 0.049183821914170445143744274712327 y1[1] (numeric) = 0.04918382191417044514374427471233 absolute error = 3e-33 relative error = 6.0995666526998062618493970535457e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9987897434705240139155188912468 y2[1] (numeric) = -0.99878974347052401391551889124676 absolute error = 4e-32 relative error = 4.0048468921007165020633175294879e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.0473 Order of pole (three term test) = -0.945 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=440171504, alloc=4717728, time=53.51 x[1] = 1.63 y1[1] (analytic) = 0.059169093714148245297971697419802 y1[1] (numeric) = 0.059169093714148245297971697419804 absolute error = 2e-33 relative error = 3.3801430349131223417711167977356e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9982479743776324551116699849331 y2[1] (numeric) = -0.99824797437763245511166998493307 absolute error = 3e-32 relative error = 3.0052653018107846275631705160304e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.05688 Order of pole (three term test) = -0.9701 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=444173828, alloc=4717728, time=54.00 x[1] = 1.64 y1[1] (analytic) = 0.069148448654062044364492707456605 y1[1] (numeric) = 0.069148448654062044364492707456607 absolute error = 2e-33 relative error = 2.8923280838962283068738858110495e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99760638131917367213758197436794 y2[1] (numeric) = -0.99760638131917367213758197436791 absolute error = 3e-32 relative error = 3.0071980855144325146425184256964e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.06643 Order of pole (three term test) = -0.9997 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.65 y1[1] (analytic) = 0.079120888806733952359614597341276 y1[1] (numeric) = 0.079120888806733952359614597341278 absolute error = 2e-33 relative error = 2.5277774683311958314673347138389e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99686502845391885177170304020219 y2[1] (numeric) = -0.99686502845391885177170304020216 absolute error = 3e-32 relative error = 3.0094344915006497260087110451188e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.07595 Order of pole (three term test) = -1.034 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=448175512, alloc=4717728, time=54.49 x[1] = 1.66 y1[1] (analytic) = 0.089085416936459041185257931650621 y1[1] (numeric) = 0.089085416936459041185257931650622 absolute error = 1e-33 relative error = 1.1225181790564653402725400811556e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99602398991653672750100059061296 y2[1] (numeric) = -0.99602398991653672750100059061293 absolute error = 3e-32 relative error = 3.0119756455378041085776170901350e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.08544 Order of pole (three term test) = -1.073 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=452176280, alloc=4717728, time=54.98 x[1] = 1.67 y1[1] (analytic) = 0.099041036598728084094782342448611 y1[1] (numeric) = 0.099041036598728084094782342448612 absolute error = 1e-33 relative error = 1.0096824855050460085000116506600e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99508334981018017442629724653424 y2[1] (numeric) = -0.9950833498101801744262972465342 absolute error = 4e-32 relative error = 4.0197637723141793680983275593241e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.0949 Order of pole (three term test) = -1.116 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=456177008, alloc=4717728, time=55.47 x[1] = 1.68 y1[1] (analytic) = 0.10898675223987117624800473417282 y1[1] (numeric) = 0.10898675223987117624800473417282 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99404320219807596406048786919357 y2[1] (numeric) = -0.99404320219807596406048786919354 absolute error = 3e-32 relative error = 3.0179774816288228092661184002861e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1043 Order of pole (three term test) = -1.164 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=460178944, alloc=4717728, time=55.97 x[1] = 1.69 y1[1] (analytic) = 0.11892156929661227207639046983309 y1[1] (numeric) = 0.11892156929661227207639046983308 absolute error = 1e-32 relative error = 8.4089034976137594341836857769806e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99290365109411852003714929394559 y2[1] (numeric) = -0.99290365109411852003714929394556 absolute error = 3e-32 relative error = 3.0214412009606221357185031229109e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1137 Order of pole (three term test) = -1.217 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=464179624, alloc=4717728, time=56.47 x[1] = 1.7 y1[1] (analytic) = 0.12884449429552468408764285733487 y1[1] (numeric) = 0.12884449429552468408764285733487 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99166481045246861534613339864788 y2[1] (numeric) = -0.99166481045246861534613339864784 absolute error = 4e-32 relative error = 4.0336209955609023711423887391225e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.123 Order of pole (three term test) = -1.274 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.71 y1[1] (analytic) = 0.13875453495237759764268978305111 y1[1] (numeric) = 0.1387545349523775976426897830511 absolute error = 1e-32 relative error = 7.2069716520848367499722646064324e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.99032680415615805121775222386113 y2[1] (numeric) = -0.9903268041561580512177522238611 absolute error = 3e-32 relative error = 3.0293030415916622413029594344818e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1323 Order of pole (three term test) = -1.335 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=468181036, alloc=4717728, time=56.95 x[1] = 1.72 y1[1] (analytic) = 0.14865070027136366713637828033119 y1[1] (numeric) = 0.14865070027136366713637828033118 absolute error = 1e-32 relative error = 6.7271798799096660715465999324522e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98888976600470145717817065708548 y2[1] (numeric) = -0.98888976600470145717817065708544 absolute error = 4e-32 relative error = 4.0449402324798484027477905260024e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1416 Order of pole (three term test) = -1.401 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=472182988, alloc=4717728, time=57.44 x[1] = 1.73 y1[1] (analytic) = 0.15853200064419777090494835134257 y1[1] (numeric) = 0.15853200064419777090494835134256 absolute error = 1e-32 relative error = 6.3078747252067794695968576927849e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98735383970071645108567767622206 y2[1] (numeric) = -0.98735383970071645108567767622203 absolute error = 3e-32 relative error = 3.0384244020455224422402222833601e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1507 Order of pole (three term test) = -1.472 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=476184324, alloc=4717728, time=57.94 x[1] = 1.74 y1[1] (analytic) = 0.16839744794907701506737731534509 y1[1] (numeric) = 0.16839744794907701506737731534508 absolute error = 1e-32 relative error = 5.9383322739095048810312180156736e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98571917883555349712068269566555 y2[1] (numeric) = -0.98571917883555349712068269566552 absolute error = 3e-32 relative error = 3.0434631530086997243606855505693e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1598 Order of pole (three term test) = -1.546 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=480185464, alloc=4717728, time=58.43 x[1] = 1.75 y1[1] (analytic) = 0.17824605564949209038267694394263 y1[1] (numeric) = 0.17824605564949209038267694394262 absolute error = 1e-32 relative error = 5.6102223208037057389553331056725e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98398594687393689873166293696799 y2[1] (numeric) = -0.98398594687393689873166293696796 absolute error = 3e-32 relative error = 3.0488240299882496314164822396665e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1689 Order of pole (three term test) = -1.625 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=484186420, alloc=4717728, time=58.92 x[1] = 1.76 y1[1] (analytic) = 0.1880768388928801010698001765041 y1[1] (numeric) = 0.18807683889288010106980017650408 absolute error = 2e-32 relative error = 1.0633951590068502903522191460181e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.98215431713761846242496809945596 y2[1] (numeric) = -0.98215431713761846242496809945593 absolute error = 3e-32 relative error = 3.0545098134305131359654926896528e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1779 Order of pole (three term test) = -1.709 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.77 y1[1] (analytic) = 0.19788881460910900038948584173039 y1[1] (numeric) = 0.19788881460910900038948584173038 absolute error = 1e-32 relative error = 5.0533427165921741754996416250772e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.98022447278804546701848144889842 y2[1] (numeric) = -0.9802244727880454670184814488984 absolute error = 2e-32 relative error = 2.0403489767108285761786555002274e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1868 Order of pole (three term test) = -1.797 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=488188568, alloc=4717728, time=59.41 x[1] = 1.78 y1[1] (analytic) = 0.20768100160878378462655329031263 y1[1] (numeric) = 0.20768100160878378462655329031261 absolute error = 2e-32 relative error = 9.6301538634115042834193614266641e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9781966068080446715477686473056 y2[1] (numeric) = -0.97819660680804467154776864730557 absolute error = 3e-32 relative error = 3.0668681317442983929187334974028e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1956 Order of pole (three term test) = -1.889 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=492189324, alloc=4717728, time=59.90 x[1] = 1.79 y1[1] (analytic) = 0.21745242068136461493517026446461 y1[1] (numeric) = 0.21745242068136461493517026446459 absolute error = 2e-32 relative error = 9.1974142837003486012585058173159e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.97607092198252419340866043310862 y2[1] (numeric) = -0.97607092198252419340866043310859 absolute error = 3e-32 relative error = 3.0735471495315303691984956558714e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2044 Order of pole (three term test) = -1.985 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=496191712, alloc=4717728, time=60.39 x[1] = 1.8 y1[1] (analytic) = 0.22720209469308705531667430653058 y1[1] (numeric) = 0.22720209469308705531667430653056 absolute error = 2e-32 relative error = 8.8027357437072644438879910467243e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.97384763087819518653237317884336 y2[1] (numeric) = -0.97384763087819518653237317884333 absolute error = 3e-32 relative error = 3.0805640480889843939586028778288e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = -2.086 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=500192536, alloc=4717728, time=60.89 x[1] = 1.81 y1[1] (analytic) = 0.23692904868467463478774985084198 y1[1] (numeric) = 0.23692904868467463478774985084195 absolute error = 3e-32 relative error = 1.2662018509991384007063247977962e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.97152695582231534740845126909038 y2[1] (numeric) = -0.97152695582231534740845126909035 absolute error = 3e-32 relative error = 3.0879225553353317830888532133930e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2216 Order of pole (three term test) = -2.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=504194220, alloc=4717728, time=61.38 x[1] = 1.82 y1[1] (analytic) = 0.24663230996883396256417104483087 y1[1] (numeric) = 0.24663230996883396256417104483084 absolute error = 3e-32 relative error = 1.2163856391642681381308001051063e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.96910912888045637458721531849805 y2[1] (numeric) = -0.96910912888045637458721531849803 absolute error = 2e-32 relative error = 2.0637510682728366751881481993565e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2301 Order of pole (three term test) = -2.299 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.83 y1[1] (analytic) = 0.25631090822752264682983758361853 y1[1] (numeric) = 0.2563109082275226468298375836185 absolute error = 3e-32 relative error = 1.1704535014705473297850042147286e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.96659439183329760489723892974281 y2[1] (numeric) = -0.96659439183329760489723892974279 absolute error = 2e-32 relative error = 2.0691202192955898054828824640410e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2385 Order of pole (three term test) = -2.412 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=508196744, alloc=4717728, time=61.87 x[1] = 1.84 y1[1] (analytic) = 0.2659638756089802903802829832816 y1[1] (numeric) = 0.26596387560898029038028298328157 absolute error = 3e-32 relative error = 1.1279727343162180830575871388935e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = -0.96398299615244814699489367172712 y2[1] (numeric) = -0.9639829961524481469948936717271 absolute error = 2e-32 relative error = 2.0747253924422044041935905298016e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2469 Order of pole (three term test) = -2.529 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=512197584, alloc=4717728, time=62.37 x[1] = 1.85 y1[1] (analytic) = 0.2755902468245128601219498354748 y1[1] (numeric) = 0.27559024682451286012194983547478 absolute error = 2e-32 relative error = 7.2571508717924137937811312151998e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.96127520297529993001245916863613 y2[1] (numeric) = -0.96127520297529993001245916863611 absolute error = 2e-32 relative error = 2.0805696368840903260509773546865e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2551 Order of pole (three term test) = -2.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=516199280, alloc=4717728, time=62.87 x[1] = 1.86 y1[1] (analytic) = 0.28518905924502075207093548828912 y1[1] (numeric) = 0.2851890592450207520709354882891 absolute error = 2e-32 relative error = 7.0128917473012034093643202129961e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9584712830789141819789777659032 y2[1] (numeric) = -0.95847128307891418197897776590318 absolute error = 2e-32 relative error = 2.0866561526761289901266268234546e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2632 Order of pole (three term test) = -2.774 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=520201000, alloc=4717728, time=63.35 x[1] = 1.87 y1[1] (analytic) = 0.29475935299726089912514806480989 y1[1] (numeric) = 0.29475935299726089912514806480987 absolute error = 2e-32 relative error = 6.7851960579469223372137213129011e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.95557151685294394934425049217263 y2[1] (numeric) = -0.95557151685294394934425049217262 absolute error = 1e-32 relative error = 1.0464941476001458678685505995315e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2712 Order of pole (three term test) = -2.903 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.88 y1[1] (analytic) = 0.30430017105983329547931375952224 y1[1] (numeric) = 0.30430017105983329547931375952222 absolute error = 2e-32 relative error = 6.5724576921343504499090039097593e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.95257619427159536533145742581513 y2[1] (numeric) = -0.95257619427159536533145742581511 absolute error = 2e-32 relative error = 2.0995695798689743792995432793856e-30 % Correct digits = 32 h = 0.01 bytes used=524202732, alloc=4717728, time=63.85 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 Radius of convergence (three term test) for eq 2 = 0.2791 Order of pole (three term test) = -3.035 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.89 y1[1] (analytic) = 0.31381055935888233911038241555123 y1[1] (numeric) = 0.31381055935888233911038241555121 absolute error = 2e-32 relative error = 6.3732718366329582156693488786626e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.94948561486463047096820167213832 y2[1] (numeric) = -0.94948561486463047096820167213831 absolute error = 1e-32 relative error = 1.0532018435503853710694052094469e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2869 Order of pole (three term test) = -3.172 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=528203884, alloc=4717728, time=64.33 x[1] = 1.9 y1[1] (analytic) = 0.32328956686350342227883369508031 y1[1] (numeric) = 0.32328956686350342227883369508029 absolute error = 2e-32 relative error = 6.1864044033453854991113860277268e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.94630008768741448848970961163496 y2[1] (numeric) = -0.94630008768741448848970961163495 absolute error = 1e-32 relative error = 1.0567472337911521726622641141563e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2946 Order of pole (three term test) = -3.312 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=532204940, alloc=4717728, time=64.83 x[1] = 1.91 y1[1] (analytic) = 0.33273624568084522946633893939753 y1[1] (numeric) = 0.3327362456808452294663389393975 absolute error = 3e-32 relative error = 9.0161502960442349248329201766593e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.94301993129001054236188657694821 y2[1] (numeric) = -0.94301993129001054236188657694821 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3021 Order of pole (three term test) = -3.455 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=536205712, alloc=4717728, time=65.32 x[1] = 1.92 y1[1] (analytic) = 0.34214965115089823259923660315905 y1[1] (numeric) = 0.34214965115089823259923660315902 absolute error = 3e-32 relative error = 8.7680931133754400524760675860459e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.93964547368532491842637133968703 y2[1] (numeric) = -0.93964547368532491842637133968703 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3095 Order of pole (three term test) = -3.602 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=540207120, alloc=4717728, time=65.82 x[1] = 1.93 y1[1] (analytic) = 0.35152884194095990478728906471187 y1[1] (numeric) = 0.35152884194095990478728906471185 absolute error = 2e-32 relative error = 5.6894335866071117449295365202584e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.93617705231630604661512937274878 y2[1] (numeric) = -0.93617705231630604661512937274878 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3168 Order of pole (three term test) = -3.753 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.94 y1[1] (analytic) = 0.36087288013976720613506768584073 y1[1] (numeric) = 0.3608728801397672061350676858407 absolute error = 3e-32 relative error = 8.3131766477937896741660787069603e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.9326150140222004873089793388657 y2[1] (numeric) = -0.9326150140222004873089793388657 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.324 Order of pole (three term test) = -3.908 NO COMPLEX POLE (six term test) for Equation 2 bytes used=544209032, alloc=4717728, time=66.30 TOP MAIN SOLVE Loop x[1] = 1.95 y1[1] (analytic) = 0.37018083135128692845582845913069 y1[1] (numeric) = 0.37018083135128692845582845913066 absolute error = 3e-32 relative error = 8.1041473407711891297445891378239e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.92895971500386929571329703509148 y2[1] (numeric) = -0.92895971500386929571329703509149 absolute error = 1e-32 relative error = 1.0764729447883913974130191869883e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3311 Order of pole (three term test) = -4.065 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=548210012, alloc=4717728, time=66.80 x[1] = 1.96 y1[1] (analytic) = 0.37945176478815451993156521544745 y1[1] (numeric) = 0.37945176478815451993156521544742 absolute error = 3e-32 relative error = 7.9061432265966155338035230709437e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.92521152078816823258555628949003 y2[1] (numeric) = -0.92521152078816823258555628949003 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.338 Order of pole (three term test) = -4.226 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=552210800, alloc=4717728, time=67.29 x[1] = 1.97 y1[1] (analytic) = 0.38868475336475204591463981387931 y1[1] (numeric) = 0.38868475336475204591463981387928 absolute error = 3e-32 relative error = 7.7183372232373640515944072044727e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.92137080619139538326395099715317 y2[1] (numeric) = -0.92137080619139538326395099715317 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3448 Order of pole (three term test) = -4.391 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=556211676, alloc=4717728, time=67.78 x[1] = 1.98 y1[1] (analytic) = 0.39787887378991597815247385990719 y1[1] (numeric) = 0.39787887378991597815247385990717 absolute error = 2e-32 relative error = 5.0266554264351818499094138133063e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.917437955281809840204735217402 y2[1] (numeric) = -0.917437955281809840204735217402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3514 Order of pole (three term test) = -4.558 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=560213944, alloc=4717728, time=68.29 x[1] = 1.99 y1[1] (analytic) = 0.40703320665926554173363571613029 y1[1] (numeric) = 0.40703320665926554173363571613027 absolute error = 2e-32 relative error = 4.9136040187360787088299364222843e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.91341336134122519712879327105761 y2[1] (numeric) = -0.91341336134122519712879327105762 absolute error = 1e-32 relative error = 1.0947945829603739534239322114247e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3579 Order of pole (three term test) = -4.729 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2 y1[1] (analytic) = 0.41614683654714238699756822950076 y1[1] (numeric) = 0.41614683654714238699756822950074 absolute error = 2e-32 relative error = 4.8059959234447619795092008028402e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.90929742682568169539601986591174 y2[1] (numeric) = -0.90929742682568169539601986591175 absolute error = 1e-32 relative error = 1.0997501702946164667566973970263e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3643 Order of pole (three term test) = -4.903 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=564215684, alloc=4717728, time=68.77 x[1] = 2.01 y1[1] (analytic) = 0.42521885209815239251738234016543 y1[1] (numeric) = 0.42521885209815239251738234016541 absolute error = 2e-32 relative error = 4.7034603243281041454310061394566e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.90509056332520095536009971027372 y2[1] (numeric) = -0.90509056332520095536009971027372 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3705 Order of pole (three term test) = -5.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=568217740, alloc=4717728, time=69.26 x[1] = 2.02 y1[1] (analytic) = 0.4342483461183004450517028740902 y1[1] (numeric) = 0.43424834611830044505170287409018 absolute error = 2e-32 relative error = 4.6056594524257518692344113007603e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.90079319152262731719701352455371 y2[1] (numeric) = -0.90079319152262731719701352455371 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3766 Order of pole (three term test) = -5.259 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=572219152, alloc=4717728, time=69.75 x[1] = 2.03 y1[1] (analytic) = 0.4432344156657090830635167316961 y1[1] (numeric) = 0.44323441566570908306351673169608 absolute error = 2e-32 relative error = 4.5122849880601687891884331490848e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.89640574115155990703888883196757 y2[1] (numeric) = -0.89640574115155990703888883196757 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3825 Order of pole (three term test) = -5.442 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=576220420, alloc=4717728, time=70.25 x[1] = 2.04 y1[1] (analytic) = 0.45217616214091193201727020529136 y1[1] (numeric) = 0.45217616214091193201727020529135 absolute error = 1e-32 relative error = 2.2115274614772138136154039325036e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.8919286509533796351715256485842 y2[1] (numeric) = -0.8919286509533796351715256485842 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3883 Order of pole (three term test) = -5.628 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=580221160, alloc=4717728, time=70.74 x[1] = 2.05 y1[1] (analytic) = 0.4610726913767129021859299941674 y1[1] (numeric) = 0.46107269137671290218592999416739 absolute error = 1e-32 relative error = 2.1688554076237063126612835928559e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.88736236863337542355996660468034 y2[1] (numeric) = -0.88736236863337542355996660468033 absolute error = 1e-32 relative error = 1.1269353258016761656221986601155e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3939 Order of pole (three term test) = -5.816 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.06 y1[1] (analytic) = 0.4699231137276021631231096264879 y1[1] (numeric) = 0.46992311372760216312310962648789 absolute error = 1e-32 relative error = 2.1280076905935397163185023347168e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.8827073508159740500427975851999 y2[1] (numeric) = -0.88270735081597405004279758519989 absolute error = 1e-32 relative error = 1.1328782966128023156341294283346e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3993 Order of pole (three term test) = -6.007 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=584223328, alloc=4717728, time=71.23 x[1] = 2.07 y1[1] (analytic) = 0.47872654415871995327732713901173 y1[1] (numeric) = 0.47872654415871995327732713901172 absolute error = 1e-32 relative error = 2.0888751881459362481795224245323e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.87796406299907808617345112044384 y2[1] (numeric) = -0.87796406299907808617345112044383 absolute error = 1e-32 relative error = 1.1389987838272715938342828503963e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4046 Order of pole (three term test) = -6.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=588224716, alloc=4717728, time=71.72 x[1] = 2.08 y1[1] (analytic) = 0.48748210233435932844156884977235 y1[1] (numeric) = 0.48748210233435932844156884977234 absolute error = 1e-32 relative error = 2.0513573630937316539311885790751e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.87313297950751649487667680502462 y2[1] (numeric) = -0.87313297950751649487667680502461 absolute error = 1e-32 relative error = 1.1453009146029987423503721874535e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4097 Order of pole (three term test) = -6.396 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=592227140, alloc=4717728, time=72.21 x[1] = 2.09 y1[1] (analytic) = 0.49618891270599899883706631187045 y1[1] (numeric) = 0.49618891270599899883706631187044 absolute error = 1e-32 relative error = 2.0153614367286724927354395563966e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.86821458344561254282162205872751 y2[1] (numeric) = -0.8682145834456125428216220587275 absolute error = 1e-32 relative error = 1.1517889921076669803333046944329e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4147 Order of pole (three term test) = -6.595 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=596228280, alloc=4717728, time=72.70 x[1] = 2.1 y1[1] (analytic) = 0.50484610459985745162093852371917 y1[1] (numeric) = 0.50484610459985745162093852371916 absolute error = 1e-32 relative error = 1.9808016559672239571942225812533e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.86320936664887377068075931326902 y2[1] (numeric) = -0.86320936664887377068075931326902 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4195 Order of pole (three term test) = -6.796 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=600229596, alloc=4717728, time=73.20 x[1] = 2.11 y1[1] (analytic) = 0.51345281230395960347841015707169 y1[1] (numeric) = 0.51345281230395960347841015707168 absolute error = 1e-32 relative error = 1.9475986420501066201724483171570e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.85811782963480885223737550831068 y2[1] (numeric) = -0.85811782963480885223737550831068 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4241 Order of pole (three term test) = -6.999 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.12 y1[1] (analytic) = 0.52200817515470727670690188298389 y1[1] (numeric) = 0.52200817515470727670690188298388 absolute error = 1e-32 relative error = 1.9156788104010642135972945821173e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.85294048155287626061472733365415 y2[1] (numeric) = -0.85294048155287626061472733365415 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4286 Order of pole (three term test) = -7.204 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=604231356, alloc=4717728, time=73.69 x[1] = 2.13 y1[1] (analytic) = 0.53051133762294484181652620960972 y1[1] (numeric) = 0.53051133762294484181652620960971 absolute error = 1e-32 relative error = 1.8849738527374114560688554155413e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.8476778401335697467185299963159 y2[1] (numeric) = -0.84767784013356974671852999631589 absolute error = 1e-32 relative error = 1.1796934550541378361417484489905e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4329 Order of pole (three term test) = -7.411 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=608234052, alloc=4717728, time=74.18 x[1] = 2.14 y1[1] (analytic) = 0.5389614493995114201544499120086 y1[1] (numeric) = 0.53896144939951142015444991200859 absolute error = 1e-32 relative error = 1.8554202737768326198782713657620e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.84233043163664572130250663706891 y2[1] (numeric) = -0.8423304316366457213025066370689 absolute error = 1e-32 relative error = 1.1871825621413234937582104236738e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.437 Order of pole (three term test) = -7.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=612235068, alloc=4717728, time=74.67 x[1] = 2.15 y1[1] (analytic) = 0.54735766548027109140415388226403 y1[1] (numeric) = 0.54735766548027109140415388226402 absolute error = 1e-32 relative error = 1.8269589759422925385973718785549e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.83689879079849771787564813704379 y2[1] (numeric) = -0.83689879079849771787564813704378 absolute error = 1e-32 relative error = 1.1948876148403619587406674857067e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4409 Order of pole (three term test) = -7.832 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=616235968, alloc=4717728, time=75.16 x[1] = 2.16 y1[1] (analytic) = 0.55569914625061260300969874398337 y1[1] (numeric) = 0.55569914625061260300969874398336 absolute error = 1e-32 relative error = 1.7995348863627979696802643103276e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.83138346077868319896103812034632 y2[1] (numeric) = -0.83138346077868319896103812034632 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4447 Order of pole (three term test) = -8.045 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.17 y1[1] (analytic) = 0.56398505756941013162446999441651 y1[1] (numeric) = 0.5639850575694101316244699944165 absolute error = 1e-32 relative error = 1.7730966212290635557088100342660e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.82578499310560805298105642394338 y2[1] (numeric) = -0.82578499310560805298105642394338 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4483 Order of pole (three term test) = -8.26 NO COMPLEX POLE (six term test) for Equation 2 bytes used=620237328, alloc=4717728, time=75.66 TOP MAIN SOLVE Loop x[1] = 2.18 y1[1] (analytic) = 0.57221457085243670057822486766249 y1[1] (numeric) = 0.57221457085243670057822486766248 absolute error = 1e-32 relative error = 1.7475961832119809106567839058896e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.82010394762137421327400974608394 y2[1] (numeric) = -0.82010394762137421327400974608394 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4517 Order of pole (three term test) = -8.476 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=624239252, alloc=4717728, time=76.14 x[1] = 2.19 y1[1] (analytic) = 0.58038686315522191209020516379695 y1[1] (numeric) = 0.58038686315522191209020516379694 absolute error = 1e-32 relative error = 1.7229886882063255820227271681440e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.814340892425795914434327645905 y2[1] (numeric) = -0.814340892425795914434327645905 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4549 Order of pole (three term test) = -8.694 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=628240904, alloc=4717728, time=76.64 x[1] = 2.2 y1[1] (analytic) = 0.58850111725534570852414261265493 y1[1] (numeric) = 0.58850111725534570852414261265492 absolute error = 1e-32 relative error = 1.6992321181373532904394435004937e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.80849640381959018430403691041612 y2[1] (numeric) = -0.80849640381959018430403691041612 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.1 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4579 Order of pole (three term test) = -8.914 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=632241692, alloc=4717728, time=77.13 x[1] = 2.21 y1[1] (analytic) = 0.59655652173415993337760917751863 y1[1] (numeric) = 0.59655652173415993337760917751863 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.80257106624674725251897404255597 y2[1] (numeric) = -0.80257106624674725251897404255597 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.38 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4608 Order of pole (three term test) = -9.135 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=636243272, alloc=4717728, time=77.63 x[1] = 2.22 y1[1] (analytic) = 0.60455227105792951991771443750015 y1[1] (numeric) = 0.60455227105792951991771443750015 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.79656547223608663852085674960916 y2[1] (numeric) = -0.79656547223608663852085674960916 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.66 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4635 Order of pole (three term test) = -9.358 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.23 y1[1] (analytic) = 0.61248756565838519341190391068563 y1[1] (numeric) = 0.61248756565838519341190391068563 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.79048022234200476337771012718854 y2[1] (numeric) = -0.79048022234200476337771012718854 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.95 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = -9.581 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=640244448, alloc=4717728, time=78.12 x[1] = 2.24 y1[1] (analytic) = 0.62036161201267963175076226631044 y1[1] (numeric) = 0.62036161201267963175076226631044 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.7843159250844200106020886706045 y2[1] (numeric) = -0.7843159250844200106020886706045 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.24 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4683 Order of pole (three term test) = -9.806 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=644245200, alloc=4717728, time=78.61 x[1] = 2.25 y1[1] (analytic) = 0.6281736227227390889133890573964 y1[1] (numeric) = 0.6281736227227390889133890573964 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.77807319688792124141096667558776 y2[1] (numeric) = -0.77807319688792124141096667558776 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.53 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4704 Order of pole (three term test) = -10.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=648246172, alloc=4717728, time=79.10 x[1] = 2.26 y1[1] (analytic) = 0.63592281659400254617912656874484 y1[1] (numeric) = 0.63592281659400254617912656874484 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.77175266202012584952506163774032 y2[1] (numeric) = -0.77175266202012584952506163774032 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.83 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4723 Order of pole (three term test) = -10.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=652247152, alloc=4717728, time=79.60 x[1] = 2.27 y1[1] (analytic) = 0.6436084187135405172361343481243 y1[1] (numeric) = 0.6436084187135405172361343481243 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.76535495252925351965074260193472 y2[1] (numeric) = -0.76535495252925351965074260193472 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4741 Order of pole (three term test) = -10.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=656248716, alloc=4717728, time=80.10 x[1] = 2.28 y1[1] (analytic) = 0.6512296605275456953713983504607 y1[1] (numeric) = 0.65122966052754569537139835046069 absolute error = 1e-32 relative error = 1.5355565948730340819789574880371e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.75888070818092193221665357630092 y2[1] (numeric) = -0.75888070818092193221665357630092 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.45 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4756 Order of pole (three term test) = -10.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.29 y1[1] (analytic) = 0.65878577991818769374203101818895 y1[1] (numeric) = 0.65878577991818769374203101818894 absolute error = 1e-32 relative error = 1.5179441185330176815715512444306e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.75233057639417073474190827797365 y2[1] (numeric) = -0.75233057639417073474190827797366 absolute error = 1e-32 relative error = 1.3292029213977701045232408598066e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.76 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.477 Order of pole (three term test) = -10.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=660250848, alloc=4717728, time=80.59 x[1] = 2.3 y1[1] (analytic) = 0.66627602127982419331788057116602 y1[1] (numeric) = 0.66627602127982419331788057116601 absolute error = 1e-32 relative error = 1.5008794674602549050021477349038e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.7457052121767201773854062116435 y2[1] (numeric) = -0.74570521217672017738540621164351 absolute error = 1e-32 relative error = 1.3410124854578809564413220294695e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4781 Order of pole (three term test) = -11.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=664252260, alloc=4717728, time=81.08 x[1] = 2.31 y1[1] (analytic) = 0.67369963559456087744416432347103 y1[1] (numeric) = 0.67369963559456087744416432347103 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.73900527805947088675876419209826 y2[1] (numeric) = -0.73900527805947088675876419209827 absolute error = 1e-32 relative error = 1.3531703083716348800224786494875e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.41 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4791 Order of pole (three term test) = -11.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=668252924, alloc=4717728, time=81.57 x[1] = 2.32 y1[1] (analytic) = 0.68105588050715259709363616600823 y1[1] (numeric) = 0.68105588050715259709363616600822 absolute error = 1e-32 relative error = 1.4683082968982569152679736077002e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.73223144403025132797089867772467 y2[1] (numeric) = -0.73223144403025132797089867772469 absolute error = 2e-32 relative error = 2.7313768294241297615197433078798e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.74 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4799 Order of pole (three term test) = -11.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=672253712, alloc=4717728, time=82.07 x[1] = 2.33 y1[1] (analytic) = 0.688344020399238276754180427816 y1[1] (numeric) = 0.68834402039923827675418042781599 absolute error = 1e-32 relative error = 1.4527619480445284079444116906663e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.72538438746681958010284419247542 y2[1] (numeric) = -0.72538438746681958010284419247543 absolute error = 1e-32 relative error = 1.3785794363347003309458045492630e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 17.08 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4805 Order of pole (three term test) = -11.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=676254960, alloc=4717728, time=82.56 x[1] = 2.34 y1[1] (analytic) = 0.69556332646290213752310557206135 y1[1] (numeric) = 0.69556332646290213752310557206134 absolute error = 1e-32 relative error = 1.4376836183776790727046175124394e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.71846479306912612487942868679401 y2[1] (numeric) = -0.71846479306912612487942868679402 absolute error = 1e-32 relative error = 1.3918566499664046076648310495166e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 17.43 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4809 Order of pole (three term test) = -12.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.35 y1[1] (analytic) = 0.70271307677355388134712911225892 y1[1] (numeric) = 0.70271307677355388134712911225891 absolute error = 1e-32 relative error = 1.4230559143589773958804564382109e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.71147335279084442220249118201321 y2[1] (numeric) = -0.71147335279084442220249118201322 absolute error = 1e-32 relative error = 1.4055340176513613990205539733054e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 17.78 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4811 Order of pole (three term test) = -12.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=680257264, alloc=4717728, time=83.04 x[1] = 2.36 y1[1] (analytic) = 0.7097925563621205484503630346451 y1[1] (numeric) = 0.70979255636212054845036303464509 absolute error = 1e-32 relative error = 1.4088623373641326237051151901722e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.7044107657701761194310307129327 y2[1] (numeric) = -0.70441076577017611943103071293271 absolute error = 1e-32 relative error = 1.4196262303098644139793149698341e-30 % Correct digits = 32 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 = 18.14 Order of pole (ratio test) Not computed Radius of convergence (three term test) for eq 2 = 0.4811 Order of pole (three term test) = -12.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=684258320, alloc=4717728, time=83.53 x[1] = 2.37 y1[1] (analytic) = 0.71680105728654282882471660882235 y1[1] (numeric) = 0.71680105728654282882471660882234 absolute error = 1e-32 relative error = 1.3950872279478903715491859949333e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.69727773825993781382969642028923 y2[1] (numeric) = -0.69727773825993781382969642028923 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4809 Order of pole (three term test) = -12.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=688259628, alloc=4717728, time=84.02 x[1] = 2.38 y1[1] (analytic) = 0.72373787870256867821114760736753 y1[1] (numeric) = 0.72373787870256867821114760736752 absolute error = 1e-32 relative error = 1.3817157142482043989095556284519e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.6900749835569363594511131070202 y2[1] (numeric) = -0.6900749835569363594511131070202 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4806 Order of pole (three term test) = -13.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=692262004, alloc=4717728, time=84.51 x[1] = 2.39 y1[1] (analytic) = 0.73060232693383715926915829261806 y1[1] (numeric) = 0.73060232693383715926915829261805 absolute error = 1e-32 relative error = 1.3687336641764614957568409192704e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.68280322193063978086250031101305 y2[1] (numeric) = -0.68280322193063978086250031101305 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.48 Order of pole (three term test) = -13.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=696262648, alloc=4717728, time=85.01 x[1] = 2.4 y1[1] (analytic) = 0.73739371554124549960882222733478 y1[1] (numeric) = 0.73739371554124549960882222733477 absolute error = 1e-32 relative error = 1.3561276410743506504844288442144e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.67546318055115092656577152534128 y2[1] (numeric) = -0.67546318055115092656577152534129 absolute error = 1e-32 relative error = 1.4804655957472619235220928705026e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = -13.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.41 y1[1] (analytic) = 0.74411136539159243003734439556795 y1[1] (numeric) = 0.74411136539159243003734439556794 absolute error = 1e-32 relative error = 1.3438848625484235964925226525405e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.66805559341649106468574980065472 y2[1] (numeric) = -0.66805559341649106468574980065473 absolute error = 1e-32 relative error = 1.4968814120482369301677581370305e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4783 Order of pole (three term test) = -13.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=700265052, alloc=4717728, time=85.30 x[1] = 2.42 y1[1] (analytic) = 0.75075460472549093874353256891074 y1[1] (numeric) = 0.75075460472549093874353256891073 absolute error = 1e-32 relative error = 1.3319931622206222665277112189853e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.66058120127920069250633410656023 y2[1] (numeric) = -0.66058120127920069250633410656024 absolute error = 1e-32 relative error = 1.5138184345293544687938366466739e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4772 Order of pole (three term test) = -13.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=704265952, alloc=4717728, time=85.51 x[1] = 2.43 y1[1] (analytic) = 0.7573227692245436502013552441779 y1[1] (numeric) = 0.75732276922454365020135524417789 absolute error = 1e-32 relative error = 1.3204409541574252711767224633132e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.6530407515722648997124970471899 y2[1] (numeric) = -0.6530407515722648997124970471899 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4758 Order of pole (three term test) = -14.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=708267080, alloc=4717728, time=85.72 x[1] = 2.44 y1[1] (analytic) = 0.7638152020777741113106750925374 y1[1] (numeric) = 0.76381520207777411131067509253739 absolute error = 1e-32 relative error = 1.3092171997621183713699516777911e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.64543499833437069274006107298253 y2[1] (numeric) = -0.64543499833437069274006107298254 absolute error = 1e-32 relative error = 1.5493426953614703268077690437558e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4743 Order of pole (three term test) = -14.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=712267772, alloc=4717728, time=85.93 x[1] = 2.45 y1[1] (analytic) = 0.77023125404730734170190306733649 y1[1] (numeric) = 0.77023125404730734170190306733648 absolute error = 1e-32 relative error = 1.2983113769343100949470174575785e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.63776470213450375443853285563378 y2[1] (numeric) = -0.63776470213450375443853285563379 absolute error = 1e-32 relative error = 1.5679763973345475110466345608186e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4726 Order of pole (three term test) = -14.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.46 y1[1] (analytic) = 0.7765702835332930802042763146862 y1[1] (numeric) = 0.77657028353329308020427631468619 absolute error = 1e-32 relative error = 1.2877134513184447042842961898857e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.63003062999589217930819371861593 y2[1] (numeric) = -0.63003062999589217930819371861594 absolute error = 1e-32 relative error = 1.5872244179723770466630917804731e-30 % Correct digits = 32 h = 0.01 bytes used=716268516, alloc=4717728, time=86.14 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 Radius of convergence (three term test) for eq 2 = 0.4707 Order of pole (three term test) = -14.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.47 y1[1] (analytic) = 0.78283165663806523520721558406155 y1[1] (numeric) = 0.78283165663806523520721558406154 absolute error = 1e-32 relative error = 1.2774138494789314341106192185427e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.62223355531930478987454240485577 y2[1] (numeric) = -0.62223355531930478987454240485578 absolute error = 1e-32 relative error = 1.6071135853270416031045231965001e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4686 Order of pole (three term test) = -15.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=720269720, alloc=4717728, time=86.34 x[1] = 2.48 y1[1] (analytic) = 0.78901474722953112302319203359033 y1[1] (numeric) = 0.78901474722953112302319203359032 absolute error = 1e-32 relative error = 1.2674034338538053541654351058974e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.6143742578057117043045348806656 y2[1] (numeric) = -0.6143742578057117043045348806656 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4664 Order of pole (three term test) = -15.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=724271748, alloc=4717728, time=86.55 x[1] = 2.49 y1[1] (analytic) = 0.79511893700378415538109133257157 y1[1] (numeric) = 0.79511893700378415538109133257156 absolute error = 1e-32 relative error = 1.2576734793517322152968107255541e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.6064535233783148891434102397918 y2[1] (numeric) = -0.6064535233783148891434102397918 absolute error = 0 relative error = 0 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4639 Order of pole (three term test) = -15.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=728273652, alloc=4717728, time=86.76 x[1] = 2.5 y1[1] (analytic) = 0.80114361554693371483350279046735 y1[1] (numeric) = 0.80114361554693371483350279046734 absolute error = 1e-32 relative error = 1.2482156514688178309064332740749e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.59847214410395649405185470218616 y2[1] (numeric) = -0.59847214410395649405185470218617 absolute error = 1e-32 relative error = 1.6709215455586799279466768703960e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4613 Order of pole (three term test) = -15.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=732275112, alloc=4717728, time=86.97 x[1] = 2.51 y1[1] (analytic) = 0.80708818039614603514191750787841 y1[1] (numeric) = 0.8070881803961460351419175078784 absolute error = 1e-32 relative error = 1.2390219858122149092393174395193e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.59043091811391282764453715502405 y2[1] (numeric) = -0.59043091811391282764453715502406 absolute error = 1e-32 relative error = 1.6936782429931427171986606826110e-30 % Correct digits = 32 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 Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = -15.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.52 y1[1] (analytic) = 0.81295203709988998260266426045185 y1[1] (numeric) = 0.81295203709988998260266426045184 absolute error = 1e-32 relative error = 1.2300848689270543568895393433307e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.58233064952408189496642758229713 y2[1] (numeric) = -0.58233064952408189496642758229713 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4554 Order of pole (three term test) = -16.2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=736276280, alloc=4717728, time=87.17 TOP MAIN SOLVE Loop x[1] = 2.53 y1[1] (analytic) = 0.81873459927738171378565517255499 y1[1] (numeric) = 0.81873459927738171378565517255498 absolute error = 1e-32 relative error = 1.2213970203318680090221199219169e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.5741721483545724777866405874022 y2[1] (numeric) = -0.5741721483545724777866405874022 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4522 Order of pole (three term test) = -16.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=740277184, alloc=4717728, time=87.39 x[1] = 2.54 y1[1] (analytic) = 0.82443528867722226526970435580657 y1[1] (numeric) = 0.82443528867722226526970435580655 absolute error = 2e-32 relative error = 2.4259029513510155668659391918379e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.56595623044870279873476574798203 y2[1] (numeric) = -0.56595623044870279873476574798203 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4489 Order of pole (three term test) = -16.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=744278868, alloc=4717728, time=87.60 x[1] = 2.55 y1[1] (analytic) = 0.83005353523522221166431047583229 y1[1] (numeric) = 0.83005353523522221166431047583227 absolute error = 2e-32 relative error = 2.4094831418713686297368098080937e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.55768371739141686934577028176624 y2[1] (numeric) = -0.55768371739141686934577028176624 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4453 Order of pole (three term test) = -16.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=748280016, alloc=4783252, time=87.81 x[1] = 2.56 y1[1] (analytic) = 0.83558877713140760950028812338244 y1[1] (numeric) = 0.83558877713140760950028812338243 absolute error = 1e-32 relative error = 1.1967609275857190065665676649005e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.54935543642712668031068338313728 y2[1] (numeric) = -0.54935543642712668031068338313728 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4416 Order of pole (three term test) = -17.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=752281584, alloc=4783252, time=88.02 x[1] = 2.57 y1[1] (analytic) = 0.84104046084620152644236372156713 y1[1] (numeric) = 0.84104046084620152644236372156711 absolute error = 2e-32 relative error = 2.3780068773239838550906410534134e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.54097222037698844964557254874584 y2[1] (numeric) = -0.54097222037698844964557254874584 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4377 Order of pole (three term test) = -17.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.58 y1[1] (analytic) = 0.84640804121577553771763249456923 y1[1] (numeric) = 0.84640804121577553771763249456922 absolute error = 1e-32 relative error = 1.1814632556699318156810796937003e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.53253490755562120108505876447165 y2[1] (numeric) = -0.53253490755562120108505876447165 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4336 Order of pole (three term test) = -17.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=756282728, alloc=4783252, time=88.22 x[1] = 2.59 y1[1] (analytic) = 0.85169098148656565465635974540831 y1[1] (numeric) = 0.8516909814865656546563597454083 absolute error = 1e-32 relative error = 1.1741347762712851175874594268037e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.52404434168727600077313024887591 y2[1] (numeric) = -0.52404434168727600077313024887592 absolute error = 1e-32 relative error = 1.9082354687396873512105115417111e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4293 Order of pole (three term test) = -17.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=760283664, alloc=4783252, time=88.43 x[1] = 2.6 y1[1] (analytic) = 0.8568887533689472337977021516452 y1[1] (numeric) = 0.85688875336894723379770215164519 absolute error = 1e-32 relative error = 1.1670126326998645031327785253268e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.51550137182146423525772693520937 y2[1] (numeric) = -0.51550137182146423525772693520937 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4249 Order of pole (three term test) = -17.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=764284756, alloc=4783252, time=88.64 x[1] = 2.61 y1[1] (analytic) = 0.86200083709006349911416744872265 y1[1] (numeric) = 0.86200083709006349911416744872264 absolute error = 1e-32 relative error = 1.1600916808570547640068911228112e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.5069068522480533678909866995555 y2[1] (numeric) = -0.5069068522480533678909866995555 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4203 Order of pole (three term test) = -18.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=768285592, alloc=4783252, time=88.85 x[1] = 2.62 y1[1] (analytic) = 0.86702672144580239454661367674835 y1[1] (numeric) = 0.86702672144580239454661367674834 absolute error = 1e-32 relative error = 1.1533669900420822601708712465435e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.49826164241183866398876000999763 y2[1] (numeric) = -0.49826164241183866398876000999764 absolute error = 1e-32 relative error = 2.0069776897926430981025624256600e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4155 Order of pole (three term test) = -18.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=772288216, alloc=4783252, time=89.06 x[1] = 2.63 y1[1] (analytic) = 0.87196590385191656920784839019493 y1[1] (numeric) = 0.87196590385191656920784839019492 absolute error = 1e-32 relative error = 1.1468338332754661110922812227155e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.48956660682659942750568705361163 y2[1] (numeric) = -0.48956660682659942750568705361163 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4106 Order of pole (three term test) = -18.5 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.64 y1[1] (analytic) = 0.87681789039428138329890731626599 y1[1] (numeric) = 0.87681789039428138329890731626598 absolute error = 1e-32 relative error = 1.1404876781771947429276752400430e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.48082261498864834353055026953286 y2[1] (numeric) = -0.48082261498864834353055026953286 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4055 Order of pole (three term test) = -18.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=776289476, alloc=4783252, time=89.26 x[1] = 2.65 y1[1] (analytic) = 0.88158219587828590897930236605381 y1[1] (numeric) = 0.8815821958782859089793023660538 absolute error = 1e-32 relative error = 1.1343241783640367849402194948475e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.47203054128988257159561077839739 y2[1] (numeric) = -0.47203054128988257159561077839739 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.4003 Order of pole (three term test) = -18.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=780290888, alloc=4783252, time=89.47 x[1] = 2.66 y1[1] (analytic) = 0.88625834387735198713231100388259 y1[1] (numeric) = 0.88625834387735198713231100388258 absolute error = 1e-32 relative error = 1.1283391653330245615931625666865e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.46319126493034528461814059379635 y2[1] (numeric) = -0.46319126493034528461814059379635 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3948 Order of pole (three term test) = -19.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=784291956, alloc=4783252, time=89.68 x[1] = 2.67 y1[1] (analytic) = 0.89084586678057648816006285842974 y1[1] (numeric) = 0.89084586678057648816006285842973 absolute error = 1e-32 relative error = 1.1225286408005630636274489176957e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.4543056698303063972473913211913 y2[1] (numeric) = -0.4543056698303063972473913211913 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3893 Order of pole (three term test) = -19.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=788293560, alloc=4783252, time=89.89 x[1] = 2.68 y1[1] (analytic) = 0.89534430583949201262204581862066 y1[1] (numeric) = 0.89534430583949201262204581862065 absolute error = 1e-32 relative error = 1.1168887694688366829380191711037e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.44537464454187127547089883192945 y2[1] (numeric) = -0.44537464454187127547089883192946 absolute error = 1e-32 relative error = 2.2453006974131559390638199730639e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3835 Order of pole (three term test) = -19.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=792294532, alloc=4783252, time=90.09 x[1] = 2.69 y1[1] (analytic) = 0.89975321121394135568593488432887 y1[1] (numeric) = 0.89975321121394135568593488432886 absolute error = 1e-32 relative error = 1.1114158721932276400313009153953e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.43639908216012626653550411876099 y2[1] (numeric) = -0.436399082160126266535504118761 absolute error = 1e-32 relative error = 2.2914805298171405821646122390405e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3777 Order of pole (three term test) = -19.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.7 y1[1] (analytic) = 0.90407214201706114798252728194333 y1[1] (numeric) = 0.90407214201706114798252728194332 absolute error = 1e-32 relative error = 1.1061064195263396963425488606102e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.42737988023382993455605308585788 y2[1] (numeric) = -0.42737988023382993455605308585789 absolute error = 1e-32 relative error = 2.3398387389057146555658140918751e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3716 Order of pole (three term test) = -19.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=796295644, alloc=4783252, time=90.30 x[1] = 2.71 y1[1] (analytic) = 0.90830066635937017453818459371608 y1[1] (numeric) = 0.90830066635937017453818459371607 absolute error = 1e-32 relative error = 1.1009570256159526822865442199961e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.41831794067565893261379068110859 y2[1] (numeric) = -0.4183179406756589326137906811086 absolute error = 1e-32 relative error = 2.3905262068961699674253512918432e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3654 Order of pole (three term test) = -19.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=800297472, alloc=4783252, time=90.51 x[1] = 2.72 y1[1] (analytic) = 0.91243836139195796298962879998706 y1[1] (numeric) = 0.91243836139195796298962879998706 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.40921416967201748668244467400742 y2[1] (numeric) = -0.40921416967201748668244467400743 absolute error = 1e-32 relative error = 2.4437081462782521427127640082373e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3591 Order of pole (three term test) = -20.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=804298568, alloc=4783252, time=90.72 x[1] = 2.73 y1[1] (analytic) = 0.91648481334876932225826112489279 y1[1] (numeric) = 0.91648481334876932225826112489278 absolute error = 1e-32 relative error = 1.0911255543297790357577190842425e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.40006947759241951035844795789445 y2[1] (numeric) = -0.40006947759241951035844795789446 absolute error = 1e-32 relative error = 2.4995658404582772723923773162784e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3526 Order of pole (three term test) = -20.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=808300060, alloc=4783252, time=90.93 x[1] = 2.74 y1[1] (analytic) = 0.92043961758798060326537325177928 y1[1] (numeric) = 0.92043961758798060326537325177927 absolute error = 1e-32 relative error = 1.0864373728507123766068740273868e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.39088477889845241210831170164027 y2[1] (numeric) = -0.39088477889845241210831170164028 absolute error = 1e-32 relative error = 2.5582986444703416206762531667397e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.346 Order of pole (three term test) = -20.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.75 y1[1] (analytic) = 0.92430237863246354409665948952671 y1[1] (numeric) = 0.92430237863246354409665948952671 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.38166099205233169857656137237778 y2[1] (numeric) = -0.38166099205233169857656137237779 absolute error = 1e-32 relative error = 2.6201262922433643431964797278233e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3393 Order of pole (three term test) = -20.67 NO COMPLEX POLE (six term test) for Equation 2 bytes used=812300776, alloc=4783252, time=91.14 TOP MAIN SOLVE Loop x[1] = 2.76 y1[1] (analytic) = 0.9280727102093326532652331971401 y1[1] (numeric) = 0.9280727102093326532652331971401 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.37239903942505551841770059244975 y2[1] (numeric) = -0.37239903942505551841770059244976 absolute error = 1e-32 relative error = 2.6852915666589622993927633959210e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3324 Order of pole (three term test) = -20.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=816301752, alloc=4783252, time=91.35 x[1] = 2.77 y1[1] (analytic) = 0.93175023528857217636777720782907 y1[1] (numeric) = 0.93175023528857217636777720782907 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.36309984720416833112128200917246 y2[1] (numeric) = -0.36309984720416833112128200917247 absolute error = 1e-32 relative error = 2.7540634007419658088380035492556e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3254 Order of pole (three term test) = -20.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=820304172, alloc=4783252, time=91.56 x[1] = 2.78 y1[1] (analytic) = 0.93533458612073878346935166911759 y1[1] (numeric) = 0.93533458612073878346935166911759 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.35376434530114292438633931722734 y2[1] (numeric) = -0.35376434530114292438633931722735 absolute error = 1e-32 relative error = 2.8267404934455650167981703294397e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3182 Order of pole (three term test) = -21.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=824305772, alloc=4783252, time=91.77 x[1] = 2.79 y1[1] (analytic) = 0.93882540427373620697953961962409 y1[1] (numeric) = 0.93882540427373620697953961962409 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.34439346725839004176626159556229 y2[1] (numeric) = -0.3443934672583900417662615955623 absolute error = 1e-32 relative error = 2.9036555424836915477923452310660e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3109 Order of pole (three term test) = -21.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=828306468, alloc=4783252, time=91.98 x[1] = 2.8 y1[1] (analytic) = 0.94222234066865815258678811736615 y1[1] (numeric) = 0.94222234066865815258678811736615 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.33498815015590491954385375271242 y2[1] (numeric) = -0.33498815015590491954385375271243 absolute error = 1e-32 relative error = 2.9851802206573447982399170446714e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.3035 Order of pole (three term test) = -21.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.81 y1[1] (analytic) = 0.94552505561469589898972047835884 y1[1] (numeric) = 0.94552505561469589898972047835883 absolute error = 1e-32 relative error = 1.0576134329405891418234074231371e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.32554933451756006810510128120633 y2[1] (numeric) = -0.32554933451756006810510128120634 absolute error = 1e-32 relative error = 3.0717310526280931270504447516423e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.296 Order of pole (three term test) = -21.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=832307476, alloc=4783252, time=92.18 x[1] = 2.82 y1[1] (analytic) = 0.94873321884310709569453606376004 y1[1] (numeric) = 0.94873321884310709569453606376003 absolute error = 1e-32 relative error = 1.0540370887607456486683317706204e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.31607796421705366845541285602457 y2[1] (numeric) = -0.31607796421705366845541285602458 absolute error = 1e-32 relative error = 3.1637763881359686586138345258726e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2884 Order of pole (three term test) = -21.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=836308136, alloc=4783252, time=92.39 x[1] = 2.83 y1[1] (analytic) = 0.95184650954024236202702511272453 y1[1] (numeric) = 0.95184650954024236202702511272452 absolute error = 1e-32 relative error = 1.0505895540689817435563597689260e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.3065749863835229889603130778681 y2[1] (numeric) = -0.30657498638352298896031307786811 absolute error = 1e-32 relative error = 3.2618447179803754903727107270218e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2806 Order of pole (three term test) = -21.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=840309216, alloc=4783252, time=92.60 x[1] = 2.84 y1[1] (analytic) = 0.95486461637962638472681949358624 y1[1] (numeric) = 0.95486461637962638472681949358623 absolute error = 1e-32 relative error = 1.0472688827778587411748286751844e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.29704135130683226089025606809731 y2[1] (numeric) = -0.29704135130683226089025606809732 absolute error = 1e-32 relative error = 3.3665346444207310506307682570007e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2728 Order of pole (three term test) = -22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=844310004, alloc=4783252, time=92.81 x[1] = 2.85 y1[1] (analytic) = 0.95778723755309030604085410717493 y1[1] (numeric) = 0.95778723755309030604085410717492 absolute error = 1e-32 relative error = 1.0440732145844340857680869364712e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.28747801234254448390307892669172 y2[1] (numeric) = -0.28747801234254448390307892669173 absolute error = 1e-32 relative error = 3.4785269031582484896781683663001e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2648 Order of pole (three term test) = -22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=848310872, alloc=4783252, time=93.02 x[1] = 2.86 y1[1] (analytic) = 0.96061408080095228910317316639277 y1[1] (numeric) = 0.96061408080095228910317316639276 absolute error = 1e-32 relative error = 1.0410007723041161841650780220451e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.27788592581658666420435690975324 y2[1] (numeric) = -0.27788592581658666420435690975324 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2567 Order of pole (three term test) = -22.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.87 y1[1] (analytic) = 0.96334486344124324256969375873794 y1[1] (numeric) = 0.96334486344124324256969375873793 absolute error = 1e-32 relative error = 1.0380498593492448136008015252841e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.26826605092961801878239892098714 y2[1] (numeric) = -0.26826605092961801878239892098714 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2485 Order of pole (three term test) = -22.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=852311536, alloc=4783252, time=93.22 x[1] = 2.88 y1[1] (analytic) = 0.96597931239797478195981790476552 y1[1] (numeric) = 0.96597931239797478195981790476552 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.25861934966111070881776692011768 y2[1] (numeric) = -0.25861934966111070881776692011768 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2402 Order of pole (three term test) = -22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=856312532, alloc=4783252, time=93.44 x[1] = 2.89 y1[1] (analytic) = 0.96851716422844660093231550720928 y1[1] (numeric) = 0.96851716422844660093231550720928 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.24894678667315269411404584058049 y2[1] (numeric) = -0.24894678667315269411404584058049 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2319 Order of pole (three term test) = -22.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=860314768, alloc=4783252, time=93.64 x[1] = 2.9 y1[1] (analytic) = 0.97095816514959052178110666934553 y1[1] (numeric) = 0.97095816514959052178110666934553 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.23924932921398232818425691873958 y2[1] (numeric) = -0.23924932921398232818425691873958 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2234 Order of pole (three term test) = -22.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=864317016, alloc=4783252, time=93.85 x[1] = 2.91 y1[1] (analytic) = 0.97330207106334859076784710660275 y1[1] (numeric) = 0.97330207106334859076784710660275 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.22952794702126434045301822382699 y2[1] (numeric) = -0.229527947021264340453018223827 absolute error = 1e-32 relative error = 4.3567679360080548419401459949694e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2148 Order of pole (three term test) = -22.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=868318304, alloc=4783252, time=94.06 x[1] = 2.92 y1[1] (analytic) = 0.97554864758108268050293173515827 y1[1] (numeric) = 0.97554864758108268050293173515826 absolute error = 1e-32 relative error = 1.0250642061567565716677397753355e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.21978361222511687789562909306458 y2[1] (numeric) = -0.21978361222511687789562909306459 absolute error = 1e-32 relative error = 4.5499297689935772634393913813968e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2062 Order of pole (three term test) = -22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.93 y1[1] (analytic) = 0.97769767004701315843501960467633 y1[1] (numeric) = 0.97769767004701315843501960467632 absolute error = 1e-32 relative error = 1.0228110699618568397721468468929e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.21001729925089930332910403425911 y2[1] (numeric) = -0.21001729925089930332910403425912 absolute error = 1e-32 relative error = 4.7615125209535230985898698723305e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1974 Order of pole (three term test) = -23.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=872319072, alloc=4783252, time=94.27 x[1] = 2.94 y1[1] (analytic) = 0.97974892356068427760176338132832 y1[1] (numeric) = 0.97974892356068427760176338132832 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.20022998472177047149431709442312 y2[1] (numeric) = -0.20022998472177047149431709442313 absolute error = 1e-32 relative error = 4.9942569859831421674745800189863e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1886 Order of pole (three term test) = -23.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=876320132, alloc=4783252, time=94.48 x[1] = 2.95 y1[1] (analytic) = 0.98170220299845404312138940470197 y1[1] (numeric) = 0.98170220299845404312138940470197 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.19042264736102722702044731405738 y2[1] (numeric) = -0.19042264736102722702044731405739 absolute error = 1e-32 relative error = 5.2514761970726838536540501288232e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1798 Order of pole (three term test) = -23.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=880321836, alloc=4783252, time=94.68 x[1] = 2.96 y1[1] (analytic) = 0.98355731303400640545638732297616 y1[1] (numeric) = 0.98355731303400640545638732297616 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.18059626789423289034054450880135 y2[1] (numeric) = -0.18059626789423289034054450880136 absolute error = 1e-32 relative error = 5.5372129870682322915499384819863e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1708 Order of pole (three term test) = -23.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=884323956, alloc=4783252, time=94.89 x[1] = 2.97 y1[1] (analytic) = 0.98531406815788372924707637480614 y1[1] (numeric) = 0.98531406815788372924707637480614 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.17075182895114551862806449866797 y2[1] (numeric) = -0.17075182895114551862806449866798 absolute error = 1e-32 relative error = 5.8564526432458533522652748324000e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1618 Order of pole (three term test) = -23.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 2.98 y1[1] (analytic) = 0.9869722926960375844844419643954 y1[1] (numeric) = 0.9869722926960375844844419643954 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.16089031496745574884655395454133 y2[1] (numeric) = -0.16089031496745574884655395454134 absolute error = 1e-32 relative error = 6.2154145213916450546258508174006e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1527 Order of pole (three term test) = -23.44 NO COMPLEX POLE (six term test) for Equation 2 bytes used=888324836, alloc=4783252, time=95.10 TOP MAIN SOLVE Loop x[1] = 2.99 y1[1] (analytic) = 0.98853182082739600495858418721084 y1[1] (numeric) = 0.98853182082739600495858418721084 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.15101271208634404904629503561052 y2[1] (numeric) = -0.15101271208634404904629503561053 absolute error = 1e-32 relative error = 6.6219590800291914525142806545476e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1435 Order of pole (three term test) = -23.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=892327932, alloc=4783252, time=95.31 x[1] = 3 y1[1] (analytic) = 0.98999249660044545727157279473126 y1[1] (numeric) = 0.98999249660044545727157279473126 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.14112000805986722210074480280811 y2[1] (numeric) = -0.14112000805986722210074480280812 absolute error = 1e-32 relative error = 7.0861673957371859182175322724613e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1343 Order of pole (three term test) = -23.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=896329988, alloc=4783252, time=95.52 x[1] = 3.01 y1[1] (analytic) = 0.99135417394882586223162557418242 y1[1] (numeric) = 0.99135417394882586223162557418242 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.13121319215018402315021812468485 y2[1] (numeric) = -0.13121319215018402315021812468486 absolute error = 1e-32 relative error = 7.6211849099396940900082969487215e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1251 Order of pole (three term test) = -23.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=900331892, alloc=4783252, time=95.73 x[1] = 3.02 y1[1] (analytic) = 0.99261671670593710913946653326304 y1[1] (numeric) = 0.99261671670593710913946653326304 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.12129325503062976810875799633911 y2[1] (numeric) = -0.12129325503062976810875799633912 absolute error = 1e-32 relative error = 8.2444815232922345332773777793007e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1158 Order of pole (three term test) = -23.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=904332608, alloc=4783252, time=95.94 x[1] = 3.03 y1[1] (analytic) = 0.99377999861855560232760730870843 y1[1] (numeric) = 0.99377999861855560232760730870843 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.11136118868664982569090503291726 y2[1] (numeric) = -0.11136118868664982569090503291727 absolute error = 1e-32 relative error = 8.9797892047813759655275720827597e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1064 Order of pole (three term test) = -23.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.04 y1[1] (analytic) = 0.99484390335945947830924495484319 y1[1] (numeric) = 0.99484390335945947830924495484319 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.10141798631660189952660831260879 y2[1] (numeric) = -0.1014179863166018995266083126088 absolute error = 1e-32 relative error = 9.8601839409258929143111130003625e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.09702 Order of pole (three term test) = -23.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=908334932, alloc=4783252, time=96.14 x[1] = 3.05 y1[1] (analytic) = 0.99580832453906123102558220156492 y1[1] (numeric) = 0.99580832453906123102558220156492 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.091464642232437020053401588696418 y2[1] (numeric) = -0.091464642232437020053401588696432 absolute error = 1.4e-32 relative error = 1.5306461227303680527854692922925e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.08758 Order of pole (three term test) = -23.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=912337068, alloc=4783252, time=96.35 x[1] = 3.06 y1[1] (analytic) = 0.99667316571604658193873927179315 y1[1] (numeric) = 0.99667316571604658193873927179316 absolute error = 1e-32 relative error = 1.0033379390540361325077898799425e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.081502151760269178003890088835723 y2[1] (numeric) = -0.081502151760269178003890088835737 absolute error = 1.4e-32 relative error = 1.7177460591690471528306899937744e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.07811 Order of pole (three term test) = -23.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=916337752, alloc=4783252, time=96.56 x[1] = 3.07 y1[1] (analytic) = 0.99743834040701853109211366272677 y1[1] (numeric) = 0.99743834040701853109211366272678 absolute error = 1e-32 relative error = 1.0025682385458896118104345192173e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.071531511140843542442340790318903 y2[1] (numeric) = -0.071531511140843542442340790318917 absolute error = 1.4e-32 relative error = 1.9571793992209100716264011646757e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.0686 Order of pole (three term test) = -23.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=920338444, alloc=4783252, time=96.77 x[1] = 3.08 y1[1] (analytic) = 0.99810377209514562474111853735979 y1[1] (numeric) = 0.9981037720951456247411185373598 absolute error = 1e-32 relative error = 1.0018998304163042625061034377805e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.061553717429913216445629637135705 y2[1] (numeric) = -0.061553717429913216445629637135719 absolute error = 1.4e-32 relative error = 2.2744361485463150792054329356661e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.05907 Order of pole (three term test) = -23.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=924340020, alloc=4783252, time=96.98 x[1] = 3.09 y1[1] (analytic) = 0.99866939423781357473474351808576 y1[1] (numeric) = 0.99866939423781357473474351808576 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.051569768398534492669958510574615 y2[1] (numeric) = -0.051569768398534492669958510574628 absolute error = 1.3e-32 relative error = 2.5208567739795072277317365266868e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.04952 Order of pole (three term test) = -23.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.1 y1[1] (analytic) = 0.99913515027327946449237605454147 y1[1] (numeric) = 0.99913515027327946449237605454147 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.041580662433290579194698271596673 y2[1] (numeric) = -0.041580662433290579194698271596686 absolute error = 1.3e-32 relative error = 3.1264533172977676815935366476197e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.03995 Order of pole (three term test) = -24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=928341168, alloc=4783252, time=97.19 x[1] = 3.11 y1[1] (analytic) = 0.99950099362632787616083083671683 y1[1] (numeric) = 0.99950099362632787616083083671684 absolute error = 1e-32 relative error = 1.0004992555053513850774541731279e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.031587398436453773187626872703365 y2[1] (numeric) = -0.031587398436453773187626872703378 absolute error = 1.3e-32 relative error = 4.1155652708002732215949975315208e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.03036 Order of pole (three term test) = -24.02 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=932342520, alloc=4783252, time=97.40 x[1] = 3.12 y1[1] (analytic) = 0.99976688771292837334358497397559 y1[1] (numeric) = 0.9997668877129283733435849739756 absolute error = 1e-32 relative error = 1.0002331666410805977636579275351e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.021590975726096066090998104201892 y2[1] (numeric) = -0.021590975726096066090998104201905 absolute error = 1.3e-32 relative error = 6.0210340490946269518832671844294e-29 % Correct digits = 31 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.02076 Order of pole (three term test) = -24.03 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=936343384, alloc=4783252, time=97.61 x[1] = 3.13 y1[1] (analytic) = 0.99993280594389387365782723913921 y1[1] (numeric) = 0.99993280594389387365782723913922 absolute error = 1e-32 relative error = 1.0000671985714507066524953955073e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.011592393936158169184681483118307 y2[1] (numeric) = -0.01159239393615816918468148311832 absolute error = 1.3e-32 relative error = 1.1214249680949269913695389085879e-28 % Correct digits = 30 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.01115 Order of pole (three term test) = -24.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=940344988, alloc=4783252, time=97.82 x[1] = 3.14 y1[1] (analytic) = 0.99999873172753954528511430634505 y1[1] (numeric) = 0.99999873172753954528511430634506 absolute error = 1e-32 relative error = 1.0000012682740689717888714570959e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = -0.0015926529164869525405414363244433 y2[1] (numeric) = -0.0015926529164869525405414363244558 absolute error = 1.25e-32 relative error = 7.8485399239228426744706254548376e-28 % Correct digits = 30 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.001531 Order of pole (three term test) = -24.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=944346112, alloc=4783252, time=98.03 x[1] = 3.15 y1[1] (analytic) = 0.99996465847134196162819465679473 y1[1] (numeric) = 0.99996465847134196162819465679474 absolute error = 1e-32 relative error = 1.0000353427777258302239144347070e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.008407247367148706459141516571067 y2[1] (numeric) = 0.0084072473671487064591415165710546 absolute error = 1.24e-32 relative error = 1.4749179438270083881842796911264e-28 % Correct digits = 30 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.16 y1[1] (analytic) = 0.99983058958259834815991709427395 y1[1] (numeric) = 0.99983058958259834815991709427397 absolute error = 2e-32 relative error = 2.0003388782443081202577655560834e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.01840630693305366670737927118737 y2[1] (numeric) = 0.018406306933053666707379271187358 absolute error = 1.2e-32 relative error = 6.5195044522758920605196154816803e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=948347132, alloc=4783252, time=98.23 x[1] = 3.17 y1[1] (analytic) = 0.99959653846808585554008835013528 y1[1] (numeric) = 0.9995965384680858555400883501353 absolute error = 2e-32 relative error = 2.0008072487576486856484747461864e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.028403525883603859571285274896733 y2[1] (numeric) = 0.028403525883603859571285274896721 absolute error = 1.2e-32 relative error = 4.2248275968185649291008109297936e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=952348208, alloc=4783252, time=98.44 x[1] = 3.18 y1[1] (analytic) = 0.99926252853272089307268415386031 y1[1] (numeric) = 0.99926252853272089307268415386033 absolute error = 2e-32 relative error = 2.0014760314656489361062559609102e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.03839790450523521805369524672612 y2[1] (numeric) = 0.038397904505235218053695246726108 absolute error = 1.2e-32 relative error = 3.1251705411069776154664952509576e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=956349916, alloc=4783252, time=98.65 x[1] = 3.19 y1[1] (analytic) = 0.99882859317721865656895082969948 y1[1] (numeric) = 0.9988285931772186565689508296995 absolute error = 2e-32 relative error = 2.0023455612520165505996040115299e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.048388443368414200108007148451169 y2[1] (numeric) = 0.048388443368414200108007148451158 absolute error = 1.1e-32 relative error = 2.2732700691050345608598019668675e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=960351584, alloc=4783252, time=98.86 x[1] = 3.2 y1[1] (analytic) = 0.99829477579475308466166072228358 y1[1] (numeric) = 0.9982947757947530846616607222836 absolute error = 2e-32 relative error = 2.0034162739234799024546068656658e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.058374143427579909137217414619095 y2[1] (numeric) = 0.058374143427579909137217414619084 absolute error = 1.1e-32 relative error = 1.8843959592566549021970197939579e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.21 y1[1] (analytic) = 0.99766112976661757757210666520424 y1[1] (numeric) = 0.99766112976661757757210666520426 absolute error = 2e-32 relative error = 2.0046887067434000426513713834122e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.068354006121047817548388360676863 y2[1] (numeric) = 0.068354006121047817548388360676852 absolute error = 1.1e-32 relative error = 1.6092692475873538374885266650403e-29 % Correct digits = 31 h = 0.01 bytes used=964352404, alloc=4783252, time=99.07 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.22 y1[1] (analytic) = 0.99692771845688691225434273747586 y1[1] (numeric) = 0.99692771845688691225434273747588 absolute error = 2e-32 relative error = 2.0061634990907235999060378923184e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.078327033470865103073444147916042 y2[1] (numeric) = 0.078327033470865103073444147916031 absolute error = 1.1e-32 relative error = 1.4043682637478684113731991349273e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=968353408, alloc=4783252, time=99.28 x[1] = 3.23 y1[1] (analytic) = 0.99609461520608088772070849458495 y1[1] (numeric) = 0.99609461520608088772070849458496 absolute error = 1e-32 relative error = 1.0039206966228917236328623211591e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.088292228182607612405875728529723 y2[1] (numeric) = 0.088292228182607612405875728529713 absolute error = 1.0e-32 relative error = 1.1326025184592482851296365408645e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=972354952, alloc=4783252, time=99.48 x[1] = 3.24 y1[1] (analytic) = 0.99516190332383033417882384374247 y1[1] (numeric) = 0.99516190332383033417882384374249 absolute error = 2e-32 relative error = 2.0097232353047488526139009096253e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.098248593745108472540154959437637 y2[1] (numeric) = 0.098248593745108472540154959437627 absolute error = 1.0e-32 relative error = 1.0178262730094162305888199498389e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=976356744, alloc=4783252, time=99.69 x[1] = 3.25 y1[1] (analytic) = 0.9941296760805462193730292251716 y1[1] (numeric) = 0.99412967608054621937302922517162 absolute error = 2e-32 relative error = 2.0118099762248283515863440190997e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.10819513453010837703583084256083 y2[1] (numeric) = 0.10819513453010837703583084256082 absolute error = 1e-32 relative error = 9.2425597910941321028953286566179e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=980357408, alloc=4783252, time=99.90 x[1] = 3.26 y1[1] (analytic) = 0.99299803669809268521269456717166 y1[1] (numeric) = 0.99299803669809268521269456717168 absolute error = 2e-32 relative error = 2.0141026730026378991846493446658e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.11813085589181758226072311033608 y2[1] (numeric) = 0.11813085589181758226072311033607 absolute error = 1e-32 relative error = 8.4651888149848384458040674739664e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.27 y1[1] (analytic) = 0.99176709833946494737596174049474 y1[1] (numeric) = 0.99176709833946494737596174049476 absolute error = 2e-32 relative error = 2.0166024899884651566227217823812e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.12805476426637965749655689075362 y2[1] (numeric) = 0.12805476426637965749655689075361 absolute error = 1e-32 relative error = 7.8091588839271839286141847664172e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=984358496, alloc=4783252, time=100.11 TOP MAIN SOLVE Loop x[1] = 3.28 y1[1] (analytic) = 0.99043698409747309009035841613171 y1[1] (numeric) = 0.99043698409747309009035841613173 absolute error = 2e-32 relative error = 2.0193107003394892876752512439983e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.13796586727122704261491407058525 y2[1] (numeric) = 0.13796586727122704261491407058524 absolute error = 1e-32 relative error = 7.2481695638103039271032128979851e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=988359848, alloc=4783252, time=100.32 x[1] = 3.29 y1[1] (analytic) = 0.98900782698243288770137512553948 y1[1] (numeric) = 0.9890078269824328877013751255395 absolute error = 2e-32 relative error = 2.0222286876153556653792182312660e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.14786317380431847785052978374264 y2[1] (numeric) = 0.14786317380431847785052978374263 absolute error = 1e-32 relative error = 6.7630091676741358753823081802124e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=992360764, alloc=4783252, time=100.52 x[1] = 3.3 y1[1] (analytic) = 0.98747976990886488393659105110285 y1[1] (numeric) = 0.98747976990886488393659105110287 absolute error = 2e-32 relative error = 2.0253579475198577805975407169415e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.15774569414324838201165427760248 y2[1] (numeric) = 0.15774569414324838201165427760247 absolute error = 1e-32 relative error = 6.3393172500284100361868555679349e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=996362008, alloc=4783252, time=100.74 x[1] = 3.31 y1[1] (analytic) = 0.98585296568120305894633807058553 y1[1] (numeric) = 0.98585296568120305894633807058555 absolute error = 2e-32 relative error = 2.0287000897928458257955360596540e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.16761244004421826827224999431698 y2[1] (numeric) = 0.16761244004421826827224999431696 absolute error = 2e-32 relative error = 1.1932288554909020258741742172114e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1000363624, alloc=4783252, time=100.95 x[1] = 3.32 y1[1] (analytic) = 0.98412757697851451324228958473119 y1[1] (numeric) = 0.98412757697851451324228958473122 absolute error = 3e-32 relative error = 3.0483852603852966119497410512131e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.17746242484086030048692055230841 y2[1] (numeric) = 0.17746242484086030048692055230839 absolute error = 2e-32 relative error = 1.1269991389971725244457202316317e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.33 y1[1] (analytic) = 0.98230377633823169655284671485927 y1[1] (numeric) = 0.98230377633823169655284671485929 absolute error = 2e-32 relative error = 2.0360300430234222211883489835665e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.18729466354290310775529282413595 y2[1] (numeric) = 0.18729466354290310775529282413593 absolute error = 2e-32 relative error = 1.0678360836169072881224613658003e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1004364896, alloc=4783252, time=101.15 x[1] = 3.34 y1[1] (analytic) = 0.98038174613889880835887990106991 y1[1] (numeric) = 0.98038174613889880835887990106994 absolute error = 3e-32 relative error = 3.0600324942963239678707661732179e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.19710817293466999073661691059272 y2[1] (numeric) = 0.1971081729346699907366169105927 absolute error = 2e-32 relative error = 1.0146712691933301183593687562886e-29 % Correct digits = 31 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1008366772, alloc=4783252, time=101.36 x[1] = 3.35 y1[1] (analytic) = 0.97836167858193409545539437527153 y1[1] (numeric) = 0.97836167858193409545539437527156 absolute error = 3e-32 relative error = 3.0663506816296069087620608186982e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.20690197167339966997603411602551 y2[1] (numeric) = 0.20690197167339966997603411602549 absolute error = 2e-32 relative error = 9.6664134412264268803230680025431e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1012369116, alloc=4783252, time=101.57 x[1] = 3.36 y1[1] (analytic) = 0.97624377567240987029416530777832 y1[1] (numeric) = 0.97624377567240987029416530777835 absolute error = 3e-32 relative error = 3.0730029473772393444869677080355e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.21667508038737974424961398190553 y2[1] (numeric) = 0.21667508038737974424961398190551 absolute error = 2e-32 relative error = 9.2304107903148152926906480455249e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1016369876, alloc=4783252, time=101.78 x[1] = 3.37 y1[1] (analytic) = 0.97402824919885217208949176597085 y1[1] (numeric) = 0.97402824919885217208949176597088 absolute error = 3e-32 relative error = 3.0799928056168078761574911558517e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.22642652177388304566410348430857 y2[1] (numeric) = 0.22642652177388304566410348430855 absolute error = 2e-32 relative error = 8.8328875271831699364184321568232e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1020371136, alloc=4783252, time=101.99 x[1] = 3.38 y1[1] (analytic) = 0.97171532071206209070412534999057 y1[1] (numeric) = 0.9717153207120620907041253499906 absolute error = 3e-32 relative error = 3.0873239683013679772491094393227e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.23615532069689709795749177758963 y2[1] (numeric) = 0.23615532069689709795749177758961 absolute error = 2e-32 relative error = 8.4690024941973644260865989969192e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.39 y1[1] (analytic) = 0.96930522150296087116533607467248 y1[1] (numeric) = 0.9693052215029608711653360746725 absolute error = 2e-32 relative error = 2.0633335667983820255708760103271e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.24586050428463690513600137155794 y2[1] (numeric) = 0.24586050428463690513600137155792 absolute error = 2e-32 relative error = 8.1346941259201430733668415489387e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1024371776, alloc=4783252, time=102.19 x[1] = 3.4 y1[1] (analytic) = 0.96679819257946101428220153976569 y1[1] (numeric) = 0.96679819257946101428220153976572 absolute error = 3e-32 relative error = 3.1030260741343187821538765664552e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.25554110202683131924990242936374 y2[1] (numeric) = 0.25554110202683131924990242936372 absolute error = 2e-32 relative error = 7.8265296037973722347871080744204e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1028373468, alloc=4783252, time=102.40 x[1] = 3.41 y1[1] (analytic) = 0.96419448464236568623478364095296 y1[1] (numeric) = 0.96419448464236568623478364095299 absolute error = 3e-32 relative error = 3.1114054765753460646068306985358e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.26519614587177325875244430757411 y2[1] (numeric) = 0.26519614587177325875244430757409 absolute error = 2e-32 relative error = 7.5415877309432438681495770677803e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1032374232, alloc=4783252, time=102.61 x[1] = 3.42 y1[1] (analytic) = 0.96149435806029884717415014560141 y1[1] (numeric) = 0.96149435806029884717415014560144 absolute error = 3e-32 relative error = 3.1201431135302189336775747581903e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.2748246703231240725009433576662 y2[1] (numeric) = 0.27482467032312407250094335766618 absolute error = 2e-32 relative error = 7.2773670487751609857863149091906e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1036375540, alloc=4783252, time=102.82 x[1] = 3.43 y1[1] (analytic) = 0.95869808284366860579948964122556 y1[1] (numeric) = 0.95869808284366860579948964122559 absolute error = 3e-32 relative error = 3.1292437668191301065322891083732e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.28442571253646236904429691459137 y2[1] (numeric) = 0.28442571253646236904429691459135 absolute error = 2e-32 relative error = 7.0317130689919853257458521080857e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1040377244, alloc=4783252, time=103.03 x[1] = 3.44 y1[1] (analytic) = 0.95580593861766640355516501297249 y1[1] (numeric) = 0.95580593861766640355516501297252 absolute error = 3e-32 relative error = 3.1387124507080879516123252767506e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.29399831241556765639445181056032 y2[1] (numeric) = 0.2939983124155676563944518105603 absolute error = 2e-32 relative error = 6.8027601368438908347139897698201e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.45 y1[1] (analytic) = 0.95281821459430472850678513994775 y1[1] (numeric) = 0.95281821459430472850678513994778 absolute error = 3e-32 relative error = 3.1485544189322132551799144753866e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.30354151270842916399808636621989 y2[1] (numeric) = 0.30354151270842916399808636621988 absolute error = 1e-32 relative error = 3.2944423023962567395839057338678e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1044378192, alloc=4783252, time=103.24 x[1] = 3.46 y1[1] (analytic) = 0.94973520954349615510160537578203 y1[1] (numeric) = 0.94973520954349615510160537578206 absolute error = 3e-32 relative error = 3.1587751721261266192765087526678e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.31305435910297024610631577597493 y2[1] (numeric) = 0.31305435910297024610631577597491 absolute error = 2e-32 relative error = 6.3886668300381576996974977141096e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1048379480, alloc=4783252, time=103.45 x[1] = 3.47 y1[1] (analytic) = 0.94655723176317660188518005352668 y1[1] (numeric) = 0.94655723176317660188518005352671 absolute error = 3e-32 relative error = 3.1693804656817449066846084915797e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.32253590032247879418185398715726 y2[1] (numeric) = 0.32253590032247879418185398715725 absolute error = 1e-32 relative error = 3.1004300575538321582027428502563e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1052380336, alloc=4783252, time=103.66 x[1] = 3.48 y1[1] (analytic) = 0.94328459904847579482359814738228 y1[1] (numeric) = 0.94328459904847579482359814738231 absolute error = 3e-32 relative error = 3.1803763180552349187078415428792e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.33198518822073411538191643544275 y2[1] (numeric) = 0.33198518822073411538191643544274 absolute error = 1e-32 relative error = 3.0121825776609905359728894020887e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1056381928, alloc=4783252, time=103.87 x[1] = 3.49 y1[1] (analytic) = 0.93991763865993801915927867276677 y1[1] (numeric) = 0.9399176386599380191592786727668 absolute error = 3e-32 relative error = 3.1917690195464022940556779489570e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.3414012778768207645082874807375 y2[1] (numeric) = 0.34140127787682076450828748073749 absolute error = 1e-32 relative error = 2.9291044433665091494158517668943e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.5 y1[1] (analytic) = 0.93645668729079633769865762667176 y1[1] (numeric) = 0.93645668729079633769865762667179 absolute error = 3e-32 relative error = 3.2035651415754319764399127552571e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.35078322768961984812036880004364 y2[1] (numeric) = 0.35078322768961984812036880004362 absolute error = 2e-32 relative error = 5.7015268750809282632903349024746e-30 % Correct digits = 32 h = 0.01 bytes used=1060383916, alloc=4783252, time=104.08 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.51 y1[1] (analytic) = 0.93290209103330354808266630575758 y1[1] (numeric) = 0.93290209103330354808266630575761 absolute error = 3e-32 relative error = 3.2157715464836528034738979738615e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.36013009947196835175953992341737 y2[1] (numeric) = 0.36013009947196835175953992341736 absolute error = 1e-32 relative error = 2.7767742864765391820343105316800e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1064386772, alloc=4783252, time=104.29 x[1] = 3.52 y1[1] (analytic) = 0.92925420534412324591621651227224 y1[1] (numeric) = 0.92925420534412324591621651227227 absolute error = 3e-32 relative error = 3.2283953978868829510200500241719e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.36944095854447707443057432143296 y2[1] (numeric) = 0.36944095854447707443057432143295 absolute error = 1e-32 relative error = 2.7067924572841042756477628875396e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1068388312, alloc=4783252, time=104.49 x[1] = 3.53 y1[1] (analytic) = 0.92551339500878445462153901468401 y1[1] (numeric) = 0.92551339500878445462153901468405 absolute error = 4e-32 relative error = 4.3219255621492482461819263374475e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.37871487382899778862484425400664 y2[1] (numeric) = 0.37871487382899778862484425400662 absolute error = 2e-32 relative error = 5.2810178268917574299183980839462e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1072390728, alloc=4783252, time=104.70 x[1] = 3.54 y1[1] (analytic) = 0.92168003410520337652276888612977 y1[1] (numeric) = 0.9216800341052033765227688861298 absolute error = 3e-32 relative error = 3.2549256672490432069778069602331e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.38795091794173027924720110048451 y2[1] (numeric) = 0.38795091794173027924720110048449 absolute error = 2e-32 relative error = 5.1552913203839805983861661454303e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1076392416, alloc=4783252, time=104.92 x[1] = 3.55 y1[1] (analytic) = 0.91775450596627591295627082271047 y1[1] (numeric) = 0.91775450596627591295627082271051 absolute error = 4e-32 relative error = 4.3584640271403747487873891249449e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.39714816728595995082022742343695 y2[1] (numeric) = 0.39714816728595995082022742343693 absolute error = 2e-32 relative error = 5.0359038886359336304585698354206e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.56 y1[1] (analytic) = 0.91373720314154469412352061310366 y1[1] (numeric) = 0.9137372031415446941235206131037 absolute error = 4e-32 relative error = 4.3776262871288280315333366313346e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.40630570214441672928242142268591 y2[1] (numeric) = 0.4063057021444167292824214226859 absolute error = 1e-32 relative error = 2.4612009989575814558071788733097e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=1080393428, alloc=4783252, time=105.12 TOP MAIN SOLVE Loop x[1] = 3.57 y1[1] (analytic) = 0.90962852735794445195161343603674 y1[1] (numeric) = 0.90962852735794445195161343603678 absolute error = 4e-32 relative error = 4.3973994654918900298651116988602e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.41542260677124602256709945606629 y2[1] (numeric) = 0.41542260677124602256709945606627 absolute error = 2e-32 relative error = 4.8143744885345330113528478794894e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1084394700, alloc=4783252, time=105.33 x[1] = 3.58 y1[1] (analytic) = 0.90542888947962966139140085454902 y1[1] (numeric) = 0.90542888947962966139140085454906 absolute error = 4e-32 relative error = 4.4177958605881130299232047275343e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.42449796948358254294260094834376 y2[1] (numeric) = 0.42449796948358254294260094834375 absolute error = 1e-32 relative error = 2.3557238712273157186325818437360e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1088395344, alloc=4783252, time=105.54 x[1] = 3.59 y1[1] (analytic) = 0.90113870946688846735564983934783 y1[1] (numeric) = 0.90113870946688846735564983934788 absolute error = 5e-32 relative error = 5.5485353669447716804922396964309e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.43353088275271783380787293204403 y2[1] (numeric) = 0.43353088275271783380787293204402 absolute error = 1e-32 relative error = 2.3066407487523584818720126263562e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1092397672, alloc=4783252, time=105.75 x[1] = 3.6 y1[1] (analytic) = 0.89675841633414700587029172526594 y1[1] (numeric) = 0.89675841633414700587029172526599 absolute error = 5e-32 relative error = 5.5756376621916391017857263551022e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.44252044329485238426672734749269 y2[1] (numeric) = 0.44252044329485238426672734749269 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1096398728, alloc=4783252, time=105.96 x[1] = 3.61 y1[1] (analytic) = 0.89228844810706831897164969353841 y1[1] (numeric) = 0.89228844810706831897164969353847 absolute error = 6e-32 relative error = 6.7242829521424470218226855619390e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.45146575216142325634494018639253 y2[1] (numeric) = 0.45146575216142325634494018639252 absolute error = 1e-32 relative error = 2.2150074401268122907060729334685e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.62 y1[1] (analytic) = 0.887729251778750153422404272068 y1[1] (numeric) = 0.88772925177875015342240427206805 absolute error = 5e-32 relative error = 5.6323479146163768770126261726770e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.46036591482899819216274354079485 y2[1] (numeric) = 0.46036591482899819216274354079484 absolute error = 1e-32 relative error = 2.1721851418375480430853532160604e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1100400896, alloc=4783252, time=106.17 x[1] = 3.63 y1[1] (analytic) = 0.88308128326502602342992354439801 y1[1] (numeric) = 0.88308128326502602342992354439806 absolute error = 5e-32 relative error = 5.6619929498601144327620307950744e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.46922004128872721172690481453191 y2[1] (numeric) = 0.4692200412887272117269048145319 absolute error = 1e-32 relative error = 2.1311962661557877584986803289582e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1104401964, alloc=4783252, time=106.37 x[1] = 3.64 y1[1] (analytic) = 0.87834500735887400722343724413409 y1[1] (numeric) = 0.87834500735887400722343724413414 absolute error = 5e-32 relative error = 5.6925239605273934403660845502851e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.47802724613534275625715663887291 y2[1] (numeric) = 0.4780272461353427562571566388729 absolute error = 1e-32 relative error = 2.0919309685474963425349997549629e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1108404240, alloc=4783252, time=106.58 x[1] = 3.65 y1[1] (analytic) = 0.87352089768393783657240447452827 y1[1] (numeric) = 0.87352089768393783657240447452832 absolute error = 5e-32 relative error = 5.7239615139798609139683912980158e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.48678664865569947710681138829532 y2[1] (numeric) = 0.48678664865569947710681138829531 absolute error = 1e-32 relative error = 2.0542880597928897864245366054038e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1112404960, alloc=4783252, time=106.79 x[1] = 3.66 y1[1] (analytic) = 0.86860943664716492709839092015993 y1[1] (numeric) = 0.86860943664716492709839092015997 absolute error = 4e-32 relative error = 4.6050616436312414376255882253501e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.49549737291684481637245114641035 y2[1] (numeric) = 0.49549737291684481637245114641034 absolute error = 1e-32 relative error = 2.0181741713650248632342090941543e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1116406860, alloc=4783252, time=107.00 x[1] = 3.67 y1[1] (analytic) = 0.86361111539056608553795618647981 y1[1] (numeric) = 0.86361111539056608553795618647985 absolute error = 4e-32 relative error = 4.6317143546618311590046727388390e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.50415854785361157220802405891391 y2[1] (numeric) = 0.5041585478536115722080240589139 absolute error = 1e-32 relative error = 1.9835030155838236188588021195751e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.68 y1[1] (analytic) = 0.85852643374210171794562486853616 y1[1] (numeric) = 0.8585264337421017179456248685362 absolute error = 4e-32 relative error = 4.6591460003916265545546539244775e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.51276930735572368965980922504404 y2[1] (numeric) = 0.51276930735572368965980922504403 absolute error = 1e-32 relative error = 1.9501947282236016043783828662545e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1120409040, alloc=4783252, time=107.21 x[1] = 3.69 y1[1] (analytic) = 0.85335590016569945017519302837216 y1[1] (numeric) = 0.8533559001656994501751930283722 absolute error = 4e-32 relative error = 4.6873760399656279020433582684154e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.52132879035440656651575454812466 y2[1] (numeric) = 0.52132879035440656651575454812465 absolute error = 1e-32 relative error = 1.9181752830496587076247694350921e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1124410788, alloc=4783252, time=107.42 x[1] = 3.7 y1[1] (analytic) = 0.8481000317104081588356701063544 y1[1] (numeric) = 0.84810003171040815883567010635444 absolute error = 4e-32 relative error = 4.7164247735411453608845494722616e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.52983614090849321321077762570121 y2[1] (numeric) = 0.5298361409084932132107776257012 absolute error = 1e-32 relative error = 1.8873759692672752393665846131690e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1128411864, alloc=4783252, time=107.62 x[1] = 3.71 y1[1] (analytic) = 0.84275935395869349727638917260975 y1[1] (numeric) = 0.84275935395869349727638917260978 absolute error = 3e-32 relative error = 3.5597350369451256247924205429640e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.53829050829001765624379404325037 y2[1] (numeric) = 0.53829050829001765624379404325037 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1132412524, alloc=4783252, time=107.83 x[1] = 3.72 y1[1] (analytic) = 0.83733440097388008700560008948967 y1[1] (numeric) = 0.8373344009738800870056000894897 absolute error = 3e-32 relative error = 3.5827979795297845066105551811822e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.54669104706928702583745896705622 y2[1] (numeric) = 0.54669104706928702583745896705622 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.73 y1[1] (analytic) = 0.83182571524674563027960569792163 y1[1] (numeric) = 0.83182571524674563027960569792166 absolute error = 3e-32 relative error = 3.6065247142667449109327873797439e-30 % Correct digits = 32 h = 0.01 bytes used=1136414596, alloc=4783252, time=108.04 y2[1] (analytic) = 0.55503691719942382070274923216573 y2[1] (numeric) = 0.55503691719942382070274923216573 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 3.74 y1[1] (analytic) = 0.82623384764127228440667735620253 y1[1] (numeric) = 0.82623384764127228440667735620257 absolute error = 4e-32 relative error = 4.8412444145433854816585550698792e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.56332728410036989575236111967948 y2[1] (numeric) = 0.56332728410036989575236111967948 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1140415792, alloc=4783252, time=108.25 x[1] = 3.75 y1[1] (analytic) = 0.82055935733956072258311240229071 y1[1] (numeric) = 0.82055935733956072258311240229075 absolute error = 4e-32 relative error = 4.8747235214877153105826287371072e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.57156131874234377243415557335029 y2[1] (numeric) = 0.57156131874234377243415557335029 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1144416596, alloc=4783252, time=108.46 x[1] = 3.76 y1[1] (analytic) = 0.81480281178591238980944513756309 y1[1] (numeric) = 0.81480281178591238980944513756313 absolute error = 4e-32 relative error = 4.9091632259253801189308114356384e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.57973819772874292602316503775395 y2[1] (numeric) = 0.57973819772874292602316503775395 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1148417768, alloc=4783252, time=108.67 x[1] = 3.77 y1[1] (analytic) = 0.80896478663008554561462174619622 y1[1] (numeric) = 0.80896478663008554561462174619625 absolute error = 3e-32 relative error = 3.7084432469516213445706500905239e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.58785710337848275971251772647441 y2[1] (numeric) = 0.58785710337848275971251772647441 absolute error = 0 relative error = 0 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1152419796, alloc=4783252, time=108.88 x[1] = 3.78 y1[1] (analytic) = 0.80304586566973076793658025923771 y1[1] (numeric) = 0.80304586566973076793658025923775 absolute error = 4e-32 relative error = 4.9810355435477489698553701171814e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.59591722380776403167448581090021 y2[1] (numeric) = 0.59591722380776403167448581090021 absolute error = 0 relative error = 0 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.79 y1[1] (analytic) = 0.79704664079201167456087725184016 y1[1] (numeric) = 0.79704664079201167456087725184019 absolute error = 3e-32 relative error = 3.7638951680656367675908407364283e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.60391775301126055841709072023268 y2[1] (numeric) = 0.60391775301126055841709072023269 absolute error = 1e-32 relative error = 1.6558546176425354270845997327108e-30 % Correct digits = 32 h = 0.01 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1156421364, alloc=4783252, time=109.09 TOP MAIN SOLVE Loop x[1] = 3.8 y1[1] (analytic) = 0.79096771191441669999656817435073 y1[1] (numeric) = 0.79096771191441669999656817435076 absolute error = 3e-32 relative error = 3.7928223299266636200212290530847e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.61185789094271907573358608611888 y2[1] (numeric) = 0.61185789094271907573358608611889 absolute error = 1e-32 relative error = 1.6343664350871598385445951448472e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1160422948, alloc=4783252, time=109.30 x[1] = 3.81 y1[1] (analytic) = 0.78480968692476784656233037436496 y1[1] (numeric) = 0.78480968692476784656233037436499 absolute error = 3e-32 relative error = 3.8225827866056667757849837176074e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.61973684359496319732588971051781 y2[1] (numeric) = 0.61973684359496319732588971051781 absolute error = 0 relative error = 0 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1164425252, alloc=4783252, time=109.51 x[1] = 3.82 y1[1] (analytic) = 0.7785731816204324087577276566562 y1[1] (numeric) = 0.77857318162043240875772765665623 absolute error = 3e-32 relative error = 3.8532023332169572830062673734720e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.62755382307929347077277195688991 y2[1] (numeric) = 0.62755382307929347077277195688992 absolute error = 1e-32 relative error = 1.5934888183664953005220038049735e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1168427504, alloc=4783252, time=109.72 x[1] = 3.83 y1[1] (analytic) = 0.77225881964674374969652252702348 y1[1] (numeric) = 0.77225881964674374969652252702352 absolute error = 4e-32 relative error = 5.1796106411963411866775573372135e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.63530804770427559090337023862228 y2[1] (numeric) = 0.63530804770427559090337023862229 absolute error = 1e-32 relative error = 1.5740395602000652112546247382985e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1172428360, alloc=4783252, time=109.93 x[1] = 3.84 y1[1] (analytic) = 0.76586723243463728747307694024768 y1[1] (numeric) = 0.76586723243463728747307694024772 absolute error = 4e-32 relative error = 5.2228373673649483592679319449829e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.64299874205390889182034887886274 y2[1] (numeric) = 0.64299874205390889182034887886275 absolute error = 1e-32 relative error = 1.5552129959161882634687231225976e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.85 y1[1] (analytic) = 0.75939905913750792781123507395279 y1[1] (numeric) = 0.75939905913750792781123507395283 absolute error = 4e-32 relative error = 5.2673228283203618675604036053148e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.650625137065167300788642218662 y2[1] (numeric) = 0.65062513706516730078864221866201 absolute error = 1e-32 relative error = 1.5369833457569576565559634340774e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1176429060, alloc=4783252, time=110.13 x[1] = 3.86 y1[1] (analytic) = 0.75285494656729525719980460936484 y1[1] (numeric) = 0.75285494656729525719980460936488 absolute error = 4e-32 relative error = 5.3131084789152713608170922317323e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.6581864701049049999590093452957 y2[1] (numeric) = 0.65818647010490499995900934529571 absolute error = 1e-32 relative error = 1.5193262782211476891123098907326e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1180429852, alloc=4783252, time=110.34 x[1] = 3.87 y1[1] (analytic) = 0.74623554912980288794206080932728 y1[1] (numeric) = 0.74623554912980288794206080932733 absolute error = 5e-32 relative error = 6.7002972531000155642241600406925e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.66568198504611910542431592310351 y2[1] (numeric) = 0.66568198504611910542431592310352 absolute error = 1e-32 relative error = 1.5022188108796710373507403052542e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1184430596, alloc=4783252, time=110.54 x[1] = 3.88 y1[1] (analytic) = 0.73954152875925842313086807704128 y1[1] (numeric) = 0.73954152875925842313086807704133 absolute error = 5e-32 relative error = 6.7609455393108027747553392791551e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.67311093234356173740418951936854 y2[1] (numeric) = 0.67311093234356173740418951936855 absolute error = 1e-32 relative error = 1.4856392192566428391871432796665e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1188431368, alloc=4783252, time=110.75 x[1] = 3.89 y1[1] (analytic) = 0.73277355485212058549838830263169 y1[1] (numeric) = 0.73277355485212058549838830263173 absolute error = 4e-32 relative error = 5.4587122768195847016188239762821e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.68047256910869392041403980815868 y2[1] (numeric) = 0.6804725691086939204140398081587 absolute error = 2e-32 relative error = 2.9391339060436600981196707933377e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1192432752, alloc=4783252, time=110.96 x[1] = 3.9 y1[1] (analytic) = 0.72593230420014012937233048461435 y1[1] (numeric) = 0.72593230420014012937233048461439 absolute error = 4e-32 relative error = 5.5101556672110802385544401960560e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.68776615918397381809088812537869 y2[1] (numeric) = 0.68776615918397381809088812537871 absolute error = 2e-32 relative error = 2.9079651176396577465695190128444e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 3.91 y1[1] (analytic) = 0.71901846092268122959176361387439 y1[1] (numeric) = 0.71901846092268122959176361387443 absolute error = 4e-32 relative error = 5.5631394983475050241049681273074e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.69499097321647187391443044807649 y2[1] (numeric) = 0.69499097321647187391443044807651 absolute error = 2e-32 relative error = 2.8777352182631173033567307721590e-30 % Correct digits = 32 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 NO REAL POLE (three term test) for Equation 2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1196433844, alloc=4783252, time=111.17 x[1] = 3.92 y1[1] (analytic) = 0.71203271639831011518720258429259 y1[1] (numeric) = 0.71203271639831011518720258429263 absolute error = 4e-32 relative error = 5.6177193938970713546924655947707e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.70214628873080549637060743782065 y2[1] (numeric) = 0.70214628873080549637060743782067 absolute error = 2e-32 relative error = 2.8484092732515689767411345177547e-30 % Correct digits = 32 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 = 18.25 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=1200436140, alloc=4783252, time=111.37 x[1] = 3.93 y1[1] (analytic) = 0.70497576919565778890458983952695 y1[1] (numeric) = 0.70497576919565778890458983952699 absolute error = 4e-32 relative error = 5.6739538786755757696853768695737e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.70923139020138599514994389285155 y2[1] (numeric) = 0.70923139020138599514994389285157 absolute error = 2e-32 relative error = 2.8199541470268267847307086814027e-30 % Correct digits = 32 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 = 17.89 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=1204439096, alloc=4783252, time=111.58 x[1] = 3.94 y1[1] (analytic) = 0.69784832500356374624360614943559 y1[1] (numeric) = 0.69784832500356374624360614943563 absolute error = 4e-32 relative error = 5.7319045653359889437816948699444e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.71624556912397054374724335454079 y2[1] (numeric) = 0.71624556912397054374724335454081 absolute error = 2e-32 relative error = 2.7923383909322757588324056936659e-30 % Correct digits = 32 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 = 17.54 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=1208440812, alloc=4783252, time=111.79 x[1] = 3.95 y1[1] (analytic) = 0.69065109656050767958019331164023 y1[1] (numeric) = 0.69065109656050767958019331164026 absolute error = 3e-32 relative error = 4.3437272668359126283592945040719e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.72318812408651201332600433544282 y2[1] (numeric) = 0.72318812408651201332600433544285 absolute error = 3e-32 relative error = 4.1482982091131827962000111752156e-30 % Correct digits = 32 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 = 17.19 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 bytes used=1212441772, alloc=4783252, time=112.00 x[1] = 3.96 y1[1] (analytic) = 0.68338480358333622414406980875151 y1[1] (numeric) = 0.68338480358333622414406980875154 absolute error = 3e-32 relative error = 4.3899132440017174100431284466408e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.73005836083929959292321305873169 y2[1] (numeric) = 0.73005836083929959292321305873171 absolute error = 2e-32 relative error = 2.7395070137964489284258773417777e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.85 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] = 3.97 y1[1] (analytic) = 0.67605017269529187311724748931934 y1[1] (numeric) = 0.67605017269529187311724748931937 absolute error = 3e-32 relative error = 4.4375404683938371599095772151617e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.73685559236438318199094255175134 y2[1] (numeric) = 0.73685559236438318199094255175136 absolute error = 2e-32 relative error = 2.7142360331181120188580302083677e-30 % Correct digits = 32 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 = 16.51 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 bytes used=1216442920, alloc=4783252, time=112.20 x[1] = 3.98 y1[1] (analytic) = 0.66864793735335125890206371667484 y1[1] (numeric) = 0.66864793735335125890206371667487 absolute error = 3e-32 relative error = 4.4866660501109583217335839694484e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.7435791389442746128933574013766 y2[1] (numeric) = 0.74357913894427461289335740137662 absolute error = 2e-32 relative error = 2.6896935312622913876929294727838e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 16.19 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 bytes used=1220445436, alloc=4783252, time=112.41 x[1] = 3.99 y1[1] (analytic) = 0.66117883777488006667005095201013 y1[1] (numeric) = 0.66117883777488006667005095201016 absolute error = 3e-32 relative error = 4.5373503031284978871857231880547e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.75022832822991883329412529862008 y2[1] (numeric) = 0.75022832822991883329412529862011 absolute error = 3e-32 relative error = 3.9987826200567096759904483175361e-30 % Correct digits = 32 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 = 15.86 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 bytes used=1224446800, alloc=4783252, time=112.61 x[1] = 4 y1[1] (analytic) = 0.65364362086361191463916818309775 y1[1] (numeric) = 0.65364362086361191463916818309778 absolute error = 3e-32 relative error = 4.5896569693991927238885327688121e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.75680249530792825137263909451183 y2[1] (numeric) = 0.75680249530792825137263909451186 absolute error = 3e-32 relative error = 3.9640461264327071330903752691186e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.55 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=1228447480, alloc=4783252, time=112.82 x[1] = 4.01 y1[1] (analytic) = 0.64604304013495860312968241468503 y1[1] (numeric) = 0.64604304013495860312968241468506 absolute error = 3e-32 relative error = 4.6436534621180951277398302543607e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.7633009827670735204905561792977 y2[1] (numeric) = 0.76330098276707352049055617929773 absolute error = 3e-32 relative error = 3.9302975729502897510244952033511e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 15.23 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=1232448648, alloc=4783252, time=113.03 x[1] = 4.02 y1[1] (analytic) = 0.63837785564065920131155338076535 y1[1] (numeric) = 0.63837785564065920131155338076539 absolute error = 4e-32 relative error = 6.2658815067852022503978614369740e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.76972314076402411428559733354449 y2[1] (numeric) = 0.76972314076402411428559733354452 absolute error = 3e-32 relative error = 3.8975052731586216646046771930873e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (ratio test) for eq 2 = 14.93 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] = 4.03 y1[1] (analytic) = 0.63064883389277550667185452185245 y1[1] (numeric) = 0.63064883389277550667185452185248 absolute error = 3e-32 relative error = 4.7570055453556384587875678172840e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.7760683270883321181898793012325 y2[1] (numeric) = 0.77606832708833211818987930123253 absolute error = 3e-32 relative error = 3.8656390104921005467677122484934e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.63 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=1236449432, alloc=4783252, time=113.23 x[1] = 4.04 y1[1] (analytic) = 0.62285674778704147759294657917268 y1[1] (numeric) = 0.62285674778704147759294657917271 absolute error = 3e-32 relative error = 4.8165168165212176594979803302127e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.78233590722665273904778223066649 y2[1] (numeric) = 0.78233590722665273904778223066653 absolute error = 4e-32 relative error = 5.1128932764697309674029135156845e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.33 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=1240450472, alloc=4783252, time=113.44 x[1] = 4.05 y1[1] (analytic) = 0.61500237652557430403427072848237 y1[1] (numeric) = 0.6150023765255743040342707284824 absolute error = 3e-32 relative error = 4.8780299304668585772041615152127e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.78852525442619511083590710941938 y2[1] (numeric) = 0.78852525442619511083590710941942 absolute error = 4e-32 relative error = 5.0727607994125374567271993125513e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 14.04 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=1244452172, alloc=4783252, time=113.65 x[1] = 4.06 y1[1] (analytic) = 0.60708650553895484514628584778934 y1[1] (numeric) = 0.60708650553895484514628584778937 absolute error = 3e-32 relative error = 4.9416351255191907225089079122630e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.79463574975739705145742669274634 y2[1] (numeric) = 0.79463574975739705145742669274638 absolute error = 4e-32 relative error = 5.0337528876862176069820282344369e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.75 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=1248453952, alloc=4783252, time=113.86 x[1] = 4.07 y1[1] (analytic) = 0.59910992640768522570785577303961 y1[1] (numeric) = 0.59910992640768522570785577303964 absolute error = 3e-32 relative error = 5.0074282994913114884796287958635e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.80066678217581750318737928027569 y2[1] (numeric) = 0.80066678217581750318737928027573 absolute error = 4e-32 relative error = 4.9958360819340755087563146388017e-30 % Correct digits = 32 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 Radius of convergence (ratio test) for eq 2 = 13.47 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] = 4.08 y1[1] (analytic) = 0.59107343678303144556199101824792 y1[1] (numeric) = 0.59107343678303144556199101824795 absolute error = 3e-32 relative error = 5.0755114564575270936107778784018e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.80661774858324046757643767338011 y2[1] (numeric) = 0.80661774858324046757643767338015 absolute error = 4e-32 relative error = 4.9589784095696876653662672944968e-30 % Correct digits = 32 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 bytes used=1252454796, alloc=4783252, time=114.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 Radius of convergence (ratio test) for eq 2 = 13.19 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] = 4.09 y1[1] (analytic) = 0.58297784030725891772303711364428 y1[1] (numeric) = 0.58297784030725891772303711364431 absolute error = 3e-32 relative error = 5.1459931966176410749972099668250e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.81248805388798432447058271235272 y2[1] (numeric) = 0.81248805388798432447058271235276 absolute error = 4e-32 relative error = 4.9231493076838147523488210562858e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1256456116, alloc=4783252, time=114.27 x[1] = 4.1 y1[1] (analytic) = 0.57482394653326891153502867965979 y1[1] (numeric) = 0.57482394653326891153502867965982 absolute error = 3e-32 relative error = 5.2189892541757042270342562840468e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.81827711106441050426503702435845 y2[1] (numeric) = 0.8182771110644105042650370243585 absolute error = 5e-32 relative error = 6.1103994385178715953405970226515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1260457868, alloc=4783252, time=114.48 x[1] = 4.11 y1[1] (analytic) = 0.56661257084364393716992399387447 y1[1] (numeric) = 0.5666125708436439371699239938745 absolute error = 3e-32 relative error = 5.2946230888122078398714042348155e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.82398434121162556257482398369604 y2[1] (numeric) = 0.82398434121162556257482398369609 absolute error = 5e-32 relative error = 6.0680764790357100989823430845784e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1264459724, alloc=4783252, time=114.69 x[1] = 4.12 y1[1] (analytic) = 0.5583445343691101668598082727593 y1[1] (numeric) = 0.55834453436911016685980827275932 absolute error = 2e-32 relative error = 3.5820176913880934531311371463441e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.82960917361137078716340306097222 y2[1] (numeric) = 0.82960917361137078716340306097226 absolute error = 4e-32 relative error = 4.8215474553971050858283709615162e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1268460648, alloc=4783252, time=114.90 x[1] = 4.13 y1[1] (analytic) = 0.55002066390642504655299469207052 y1[1] (numeric) = 0.55002066390642504655299469207054 absolute error = 2e-32 relative error = 3.6362270206274645968173257745338e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.83515104578509354821692987595635 y2[1] (numeric) = 0.8351510457850935482169298759564 absolute error = 5e-32 relative error = 5.9869409554527843311485256468253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.14 y1[1] (analytic) = 0.54164179183569830916443077359731 y1[1] (numeric) = 0.54164179183569830916443077359733 absolute error = 2e-32 relative error = 3.6924772610727206540335417561348e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.84060940355019468487667282814088 y2[1] (numeric) = 0.84060940355019468487667282814092 absolute error = 4e-32 relative error = 4.7584525977303690385808762993197e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=1272462392, alloc=4783252, time=115.10 TOP MAIN SOLVE Loop x[1] = 4.15 y1[1] (analytic) = 0.53320875603715465725018617166272 y1[1] (numeric) = 0.53320875603715465725018617166274 absolute error = 2e-32 relative error = 3.7508761387643782103914058422479e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.84598370107544630333780572921222 y2[1] (numeric) = 0.84598370107544630333780572921226 absolute error = 4e-32 relative error = 4.7282234810375773622625658636071e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1276463692, alloc=4783252, time=115.31 x[1] = 4.16 y1[1] (analytic) = 0.52472239980734643876839021070922 y1[1] (numeric) = 0.52472239980734643876839021070924 absolute error = 2e-32 relative error = 3.8115392076540025776076108914687e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.85127340093557444478094790264673 y2[1] (numeric) = 0.85127340093557444478094790264677 absolute error = 4e-32 relative error = 4.6988429282576932819496359093661e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1280465888, alloc=4783252, time=115.52 x[1] = 4.17 y1[1] (analytic) = 0.51618357177482469458922054275779 y1[1] (numeric) = 0.51618357177482469458922054275781 absolute error = 2e-32 relative error = 3.8745905707988361069370766912611e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.85647797416500116491514400141294 y2[1] (numeric) = 0.85647797416500116491514400141298 absolute error = 4e-32 relative error = 4.6702893952406495970139792893957e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1284467440, alloc=4783252, time=115.73 x[1] = 4.18 y1[1] (analytic) = 0.50759312581527701057891803304672 y1[1] (numeric) = 0.50759312581527701057891803304674 absolute error = 2e-32 relative error = 3.9401636828467192723642713130950e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.86159690031074065096911416280091 y2[1] (numeric) = 0.86159690031074065096911416280095 absolute error = 4e-32 relative error = 4.6425422358847546961572918477634e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1288468300, alloc=4783252, time=115.94 x[1] = 4.19 y1[1] (analytic) = 0.49895192096614066040190125149245 y1[1] (numeric) = 0.49895192096614066040190125149246 absolute error = 1e-32 relative error = 2.0042011223519488692871578243948e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.86662966748444408656315532592254 y2[1] (numeric) = 0.86662966748444408656315532592258 absolute error = 4e-32 relative error = 4.6155816608618462611967465927719e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.2 y1[1] (analytic) = 0.49026082134069957765554488137713 y1[1] (numeric) = 0.49026082134069957765554488137715 absolute error = 2e-32 relative error = 4.0794612029789940956405236822714e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.87157577241358806001857709790882 y2[1] (numeric) = 0.87157577241358806001857709790886 absolute error = 4e-32 relative error = 4.5893886987279444837779720315225e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1292470164, alloc=4783252, time=116.15 x[1] = 4.21 y1[1] (analytic) = 0.48152069604167374756882294948685 y1[1] (numeric) = 0.48152069604167374756882294948687 absolute error = 2e-32 relative error = 4.1535078688017757840058343124216e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.8764347204918013973064980899522 y2[1] (numeric) = 0.87643472049180139730649808995224 absolute error = 4e-32 relative error = 4.5639451592646231466542429649931e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1296472304, alloc=4783252, time=116.36 x[1] = 4.22 y1[1] (analytic) = 0.47273241907430965925363841315521 y1[1] (numeric) = 0.47273241907430965925363841315522 absolute error = 1e-32 relative error = 2.1153615864936231532481864793789e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.88120602582832538699464673122123 y2[1] (numeric) = 0.88120602582832538699464673122127 absolute error = 4e-32 relative error = 4.5392335989078576403577651210616e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1300473228, alloc=4783252, time=116.57 x[1] = 4.23 y1[1] (analytic) = 0.46389686925898050939118958954484 y1[1] (numeric) = 0.46389686925898050939118958954485 absolute error = 1e-32 relative error = 2.1556515386650050152561719058495e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.88588921129660245121088859729926 y2[1] (numeric) = 0.8858892112966024512108885972993 absolute error = 4e-32 relative error = 4.5152372881316979404339230878253e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1304474688, alloc=4783252, time=116.78 x[1] = 4.24 y1[1] (analytic) = 0.45501493014330489726017186970594 y1[1] (numeric) = 0.45501493014330489726017186970595 absolute error = 1e-32 relative error = 2.1977300825822451942620043560178e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.89048380858198840379687432458221 y2[1] (numeric) = 0.89048380858198840379687432458225 absolute error = 4e-32 relative error = 4.4919401806638385324850391160610e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1308476220, alloc=4783252, time=116.99 x[1] = 4.25 y1[1] (analytic) = 0.44608748991379279916407772054484 y1[1] (numeric) = 0.44608748991379279916407772054485 absolute error = 1e-32 relative error = 2.2417127191646907170552393918760e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.89498935822858352446575282843828 y2[1] (numeric) = 0.89498935822858352446575282843832 absolute error = 4e-32 relative error = 4.4693268844190944098018437771026e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.26 y1[1] (analytic) = 0.43711544130702765758652413548598 y1[1] (numeric) = 0.43711544130702765758652413548599 absolute error = 1e-32 relative error = 2.2877251762369224974101511493109e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.89940540968517776589555981885312 y2[1] (numeric) = 0.89940540968517776589555981885316 absolute error = 4e-32 relative error = 4.4473826340450130678748540310834e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1312478780, alloc=4783252, time=117.19 x[1] = 4.27 y1[1] (analytic) = 0.42809968152039346679167732209429 y1[1] (numeric) = 0.4280996815203934667916773220943 absolute error = 1e-32 relative error = 2.3359045642092186603069729504190e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.90373152135030549927585981966133 y2[1] (numeric) = 0.90373152135030549927585981966137 absolute error = 4e-32 relative error = 4.4260932649814205041644917624577e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1316480168, alloc=4783252, time=117.40 x[1] = 4.28 y1[1] (analytic) = 0.41904111212235578208682073683604 y1[1] (numeric) = 0.41904111212235578208682073683605 absolute error = 1e-32 relative error = 2.3864006921306806692079899168699e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.90796726061640529287063252329942 y2[1] (numeric) = 0.90796726061640529287063252329947 absolute error = 5e-32 relative error = 5.5068064861783401034805390208186e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1320480920, alloc=4783252, time=117.62 x[1] = 4.29 y1[1] (analytic) = 0.40994063896230562457137463377925 y1[1] (numeric) = 0.40994063896230562457137463377926 absolute error = 1e-32 relative error = 2.4393775706924992473406648051432e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.91211220391308030765634688524802 y2[1] (numeric) = 0.91211220391308030765634688524807 absolute error = 5e-32 relative error = 5.4817817134222609086214205991799e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1324482204, alloc=4783252, time=117.83 x[1] = 4.3 y1[1] (analytic) = 0.40079917207997529690676239633603 y1[1] (numeric) = 0.40079917207997529690676239633605 absolute error = 2e-32 relative error = 4.9900302678292979301779116876909e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.91616593674945498403170936028464 y2[1] (numeric) = 0.91616593674945498403170936028468 absolute error = 4e-32 relative error = 4.3660213063497523133926511091642e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1328482956, alloc=4783252, time=118.03 x[1] = 4.31 y1[1] (analytic) = 0.39161762561443516845006009684425 y1[1] (numeric) = 0.39161762561443516845006009684426 absolute error = 1e-32 relative error = 2.5535112175582825336333077853388e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.92012805375562378396571242699099 y2[1] (numeric) = 0.92012805375562378396571242699104 absolute error = 5e-32 relative error = 5.4340262527501925003561202236560e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.32 y1[1] (analytic) = 0.38239691771268052999708015943008 y1[1] (numeric) = 0.38239691771268052999708015943009 absolute error = 1e-32 relative error = 2.6150838400621327783291715359200e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.92399815872318784374430909898398 y2[1] (numeric) = 0.92399815872318784374430909898403 absolute error = 5e-32 relative error = 5.4112661944144677276888335209132e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1332484664, alloc=4783252, time=118.24 x[1] = 4.33 y1[1] (analytic) = 0.37313797043781765937323745066286 y1[1] (numeric) = 0.37313797043781765937323745066287 absolute error = 1e-32 relative error = 2.6799738413827467775104792430524e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.92777586464487548368421918677298 y2[1] (numeric) = 0.92777586464487548368421918677303 absolute error = 5e-32 relative error = 5.3892326698041974234557391724278e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1336486948, alloc=4783252, time=118.45 x[1] = 4.34 y1[1] (analytic) = 0.36384170967685827918912735442367 y1[1] (numeric) = 0.36384170967685827918912735442368 absolute error = 1e-32 relative error = 2.7484479470155804818466931725000e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.93146079375324261279591291098884 y2[1] (numeric) = 0.93146079375324261279591291098889 absolute error = 5e-32 relative error = 5.3679124591523838771046633103813e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1340488432, alloc=4783252, time=118.66 x[1] = 4.35 y1[1] (analytic) = 0.35450906504813162723820257743587 y1[1] (numeric) = 0.35450906504813162723820257743588 absolute error = 1e-32 relative error = 2.8208023393258792784069342753200e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.93505257755844915838755579834142 y2[1] (numeric) = 0.93505257755844915838755579834147 absolute error = 5e-32 relative error = 5.3472928902625855078319284276965e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1344490880, alloc=4783252, time=118.87 x[1] = 4.36 y1[1] (analytic) = 0.34514096980832339825235256696343 y1[1] (numeric) = 0.34514096980832339825235256696343 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.93855085688510774299843471888496 y2[1] (numeric) = 0.93855085688510774299843471888501 absolute error = 5e-32 relative error = 5.3273618188301037620056795064106e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.37 y1[1] (analytic) = 0.33573836075915085304374269242283 y1[1] (numeric) = 0.33573836075915085304374269242283 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.94195528190820092382487885040826 y2[1] (numeric) = 0.94195528190820092382487885040831 absolute error = 5e-32 relative error = 5.3081076098124999683572217997629e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=1348491964, alloc=4783252, time=119.08 TOP MAIN SOLVE Loop x[1] = 4.38 y1[1] (analytic) = 0.32630217815368342744422852384408 y1[1] (numeric) = 0.32630217815368342744422852384408 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.94526551218806340294466391093816 y2[1] (numeric) = 0.94526551218806340294466391093821 absolute error = 5e-32 relative error = 5.2895191197933338272377404633819e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1352492644, alloc=4783252, time=119.28 x[1] = 4.39 y1[1] (analytic) = 0.31683336560231820890338536675574 y1[1] (numeric) = 0.31683336560231820890338536675574 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.94848121670442571014802896361413 y2[1] (numeric) = 0.94848121670442571014802896361418 absolute error = 5e-32 relative error = 5.2715856802867454083116275412932e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1356494932, alloc=4783252, time=119.49 x[1] = 4.4 y1[1] (analytic) = 0.30733286997841968311913974221771 y1[1] (numeric) = 0.30733286997841968311913974221771 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.95160207388951595403539233338039 y2[1] (numeric) = 0.95160207388951595403539233338044 absolute error = 5e-32 relative error = 5.2542970819339723300267806413692e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1360496220, alloc=4783252, time=119.70 x[1] = 4.41 y1[1] (analytic) = 0.29780164132363318664770646649064 y1[1] (numeric) = 0.29780164132363318664770646649063 absolute error = 1e-32 relative error = 3.3579398540428433181964241724346e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.95462777166021633123424156453615 y2[1] (numeric) = 0.95462777166021633123424156453621 absolute error = 6e-32 relative error = 6.2851722714553488741577422114757e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1364497712, alloc=4783252, time=119.91 x[1] = 4.42 y1[1] (analytic) = 0.28824063275288153406866514349322 y1[1] (numeric) = 0.28824063275288153406866514349321 absolute error = 1e-32 relative error = 3.4693234970009724492882803113689e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.95755800744927117811107273183889 y2[1] (numeric) = 0.95755800744927117811107273183895 absolute error = 6e-32 relative error = 6.2659389335406541416515476414429e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.43 y1[1] (analytic) = 0.27865080035905431996329034893364 y1[1] (numeric) = 0.27865080035905431996329034893364 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96039248823554344419921453430048 y2[1] (numeric) = 0.96039248823554344419921453430053 absolute error = 5e-32 relative error = 5.2062048186009057849067596221068e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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 bytes used=1368499044, alloc=4783252, time=120.11 TOP MAIN SOLVE Loop x[1] = 4.44 y1[1] (analytic) = 0.26903310311739942669651235616339 y1[1] (numeric) = 0.26903310311739942669651235616338 absolute error = 1e-32 relative error = 3.7170147034419946633608241631069e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96313093057331656172040803307784 y2[1] (numeric) = 0.9631309305733165617204080330779 absolute error = 6e-32 relative error = 6.2296826002965347514989885407114e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1372499700, alloc=4783252, time=120.32 x[1] = 4.45 y1[1] (analytic) = 0.25938850278962629877205672974446 y1[1] (numeric) = 0.25938850278962629877205672974445 absolute error = 1e-32 relative error = 3.8552209879982117337591946524116e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96577306062063878103760801869169 y2[1] (numeric) = 0.96577306062063878103760801869175 absolute error = 6e-32 relative error = 6.2126396403562912663802694134309e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1376501744, alloc=4783252, time=120.53 x[1] = 4.46 y1[1] (analytic) = 0.24971796382773057335341360111266 y1[1] (numeric) = 0.24971796382773057335341360111265 absolute error = 1e-32 relative error = 4.0045176753477613806281067805341e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96831861416670713762908092824644 y2[1] (numeric) = 0.9683186141667071376290809282465 absolute error = 6e-32 relative error = 6.1963076122040046770186173204906e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1380502936, alloc=4783252, time=120.74 x[1] = 4.47 y1[1] (analytic) = 0.24002245327754968440743865533016 y1[1] (numeric) = 0.24002245327754968440743865533015 absolute error = 1e-32 relative error = 4.1662768892860667673646637117370e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97076733665828831220992179927159 y2[1] (numeric) = 0.97076733665828831220992179927165 absolute error = 6e-32 relative error = 6.1806776695372166174808263991622e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1384503668, alloc=4783252, time=120.95 x[1] = 4.48 y1[1] (analytic) = 0.23030294068205908482980140684885 y1[1] (numeric) = 0.23030294068205908482980140684884 absolute error = 1e-32 relative error = 4.3421069528614202905886570075463e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97311898322517374193699541853268 y2[1] (numeric) = 0.97311898322517374193699541853275 absolute error = 7e-32 relative error = 7.1933649642720443095871478089705e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.49 y1[1] (analytic) = 0.2205603979844187568494820065161 y1[1] (numeric) = 0.22056039798441875684948200651608 absolute error = 2e-32 relative error = 9.0678109863643235165973944524780e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97537331870466643720739369365918 y2[1] (numeric) = 0.97537331870466643720739369365925 absolute error = 7e-32 relative error = 7.1767392707607290804592711788314e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1388506456, alloc=4783252, time=121.16 x[1] = 4.5 y1[1] (analytic) = 0.21079579943077970598048182479383 y1[1] (numeric) = 0.21079579943077970598048182479381 absolute error = 2e-32 relative error = 9.4878550967366506722573236959487e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97753011766509705538913501449863 y2[1] (numeric) = 0.9775301176650970553891350144987 absolute error = 7e-32 relative error = 7.1609046856991142500208612472957e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1392508936, alloc=4783252, time=121.37 x[1] = 4.51 y1[1] (analytic) = 0.20101012147286015779035832174077 y1[1] (numeric) = 0.20101012147286015779035832174075 absolute error = 2e-32 relative error = 9.9497477308376960681588136420416e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97958916442836687989632919704766 y2[1] (numeric) = 0.97958916442836687989632919704773 absolute error = 7e-32 relative error = 7.1458528270724657794077074953538e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1396509740, alloc=4783252, time=121.58 x[1] = 4.52 y1[1] (analytic) = 0.19120434267030119978472111819888 y1[1] (numeric) = 0.19120434267030119978472111819887 absolute error = 1e-32 relative error = 5.2300067353821923687859766195964e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98155025309151545032968624674211 y2[1] (numeric) = 0.98155025309151545032968624674217 absolute error = 6e-32 relative error = 6.1127792296953197932989379045282e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1400511008, alloc=4783252, time=121.79 x[1] = 4.53 y1[1] (analytic) = 0.1813794435928116327621307913814 y1[1] (numeric) = 0.18137944359281163276213079138139 absolute error = 1e-32 relative error = 5.5133039345128504593960921109290e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98341318754731068693732785543696 y2[1] (numeric) = 0.98341318754731068693732785543702 absolute error = 6e-32 relative error = 6.1011994510306971685084201831205e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1404511664, alloc=4783252, time=122.00 x[1] = 4.54 y1[1] (analytic) = 0.1715364067221118170727192195978 y1[1] (numeric) = 0.17153640672211181707271921959779 absolute error = 1e-32 relative error = 5.8296662446707034023631287904177e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98517778150385945040061393078254 y2[1] (numeric) = 0.9851777815038594504006139307826 absolute error = 6e-32 relative error = 6.0902713323894575670212290206752e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.55 y1[1] (analytic) = 0.16167621635368631931419242500794 y1[1] (numeric) = 0.16167621635368631931419242500793 absolute error = 1e-32 relative error = 6.1852016490315359343761647364504e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98684385850323657590534765402509 y2[1] (numeric) = 0.98684385850323657590534765402515 absolute error = 6e-32 relative error = 6.0799891981901832481803540053891e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1408512512, alloc=4783252, time=122.20 x[1] = 4.56 y1[1] (analytic) = 0.1517998584983551841186737926099 y1[1] (numeric) = 0.15179985849835518411867379260989 absolute error = 1e-32 relative error = 6.5876214239740903601587833413468e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98841125193913051861047608903809 y2[1] (numeric) = 0.98841125193913051861047608903815 absolute error = 6e-32 relative error = 6.0703477304905255350219664978212e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1412513360, alloc=4783252, time=122.41 x[1] = 4.57 y1[1] (analytic) = 0.14190832078367367382118531437459 y1[1] (numeric) = 0.14190832078367367382118531437458 absolute error = 1e-32 relative error = 7.0468031365434098387633243681115e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98987980507350384596444412806507 y2[1] (numeric) = 0.98987980507350384596444412806513 absolute error = 6e-32 relative error = 6.0613419621733449285538145993670e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1416514512, alloc=4783252, time=122.62 x[1] = 4.58 y1[1] (analytic) = 0.1320025923551703359536334006823 y1[1] (numeric) = 0.13200259235517033595363340068229 absolute error = 1e-32 relative error = 7.5756087979648799485203494353145e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.99124937105226691083385383609731 y2[1] (numeric) = 0.99124937105226691083385383609737 absolute error = 6e-32 relative error = 6.0529672706179503839366128228515e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1420515780, alloc=4783252, time=122.83 x[1] = 4.59 y1[1] (analytic) = 0.1220836637774332746752485243965 y1[1] (numeric) = 0.1220836637774332746752485243965 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.99251981291996313809017767868781 y2[1] (numeric) = 0.99251981291996313809017767868787 absolute error = 6e-32 relative error = 6.0452193718412353629041758892717e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1424517404, alloc=4783252, time=123.04 x[1] = 4.6 y1[1] (analytic) = 0.11215252693505451742990782122919 y1[1] (numeric) = 0.11215252693505451742990782122918 absolute error = 1e-32 relative error = 8.9164286113596152761366411596562e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.99369100363346445613810465990883 y2[1] (numeric) = 0.99369100363346445613810465990889 absolute error = 6e-32 relative error = 6.0380943150947315848626379343855e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.61 y1[1] (analytic) = 0.10221017493344238231112882817269 y1[1] (numeric) = 0.10221017493344238231112882817268 absolute error = 1e-32 relative error = 9.7837617502482886281334189202740e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.99476282607467550385377935740314 y2[1] (numeric) = 0.9947628260746755038537793574032 absolute error = 6e-32 relative error = 6.0315884779047705300698592246970e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1428519336, alloc=4783252, time=123.24 x[1] = 4.62 y1[1] (analytic) = 0.09225760199951176481534177561582 y1[1] (numeric) = 0.092257601999511764815341775615812 absolute error = 8e-33 relative error = 8.6713721434493134666528310430633e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.99573517306224534252282683445147 y2[1] (numeric) = 0.99573517306224534252282683445153 absolute error = 6e-32 relative error = 6.0256985615440626090019468163775e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1432520024, alloc=4783252, time=123.45 x[1] = 4.63 y1[1] (analytic) = 0.082295803382262274872007287402623 y1[1] (numeric) = 0.082295803382262274872007287402614 absolute error = 9e-33 relative error = 1.0936159111534751531162479916746e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.9966079473622855016167293539807 y2[1] (numeric) = 0.99660794736228550161672935398077 absolute error = 7e-32 relative error = 7.0238251847447589836211974996759e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1436521696, alloc=4783252, time=123.66 x[1] = 4.64 y1[1] (analytic) = 0.072325775253254166254025200760118 y1[1] (numeric) = 0.072325775253254166254025200760109 absolute error = 9e-33 relative error = 1.2443696550069211219570507968708e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99738106169809328661190893188283 y2[1] (numeric) = 0.9973810616980932866119089318829 absolute error = 7e-32 relative error = 7.0183807060484333241425357927588e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1440523244, alloc=4783252, time=123.88 x[1] = 4.65 y1[1] (analytic) = 0.062348514606992010692557016177074 y1[1] (numeric) = 0.062348514606992010692557016177064 absolute error = 1.0e-32 relative error = 1.6038874483272068491530378967730e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99805443875887937652883655089603 y2[1] (numeric) = 0.99805443875887937652883655089609 absolute error = 6e-32 relative error = 6.0116961229702460321302792321874e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.66 y1[1] (analytic) = 0.052365019161226078245837166795957 y1[1] (numeric) = 0.052365019161226078245837166795946 absolute error = 1.1e-32 relative error = 2.1006389716257377237734581876828e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99862801120749883843868709783252 y2[1] (numeric) = 0.99862801120749883843868709783259 absolute error = 7e-32 relative error = 7.0096171161230451310708612605621e-30 % Correct digits = 32 h = 0.01 bytes used=1444524348, alloc=4783252, time=124.08 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.67 y1[1] (analytic) = 0.042376287257181393700854320105276 y1[1] (numeric) = 0.042376287257181393700854320105265 absolute error = 1.1e-32 relative error = 2.5957913521873863627510073009947e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99910172168718478584253184927338 y2[1] (numeric) = 0.99910172168718478584253184927345 absolute error = 7e-32 relative error = 7.0062936015955292622678557694555e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1448526420, alloc=4783252, time=124.29 x[1] = 4.68 y1[1] (analytic) = 0.032383317759724446019120367944567 y1[1] (numeric) = 0.032383317759724446019120367944555 absolute error = 1.2e-32 relative error = 3.7056116637080825175316674686596e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99947552282728400756284194975967 y2[1] (numeric) = 0.99947552282728400756284194975974 absolute error = 7e-32 relative error = 7.0036732667535734929377917493953e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1452527508, alloc=4783252, time=124.50 x[1] = 4.69 y1[1] (analytic) = 0.022387109957477534072388396442007 y1[1] (numeric) = 0.022387109957477534072388396441995 absolute error = 1.2e-32 relative error = 5.3602273910268045584797562760735e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99974937724799399358919340694292 y2[1] (numeric) = 0.99974937724799399358919340694298 absolute error = 6e-32 relative error = 6.0015041134770949973363608729398e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1456529116, alloc=4783252, time=124.71 x[1] = 4.7 y1[1] (analytic) = 0.012388663462890737150508296327111 y1[1] (numeric) = 0.012388663462890737150508296327098 absolute error = 1.3e-32 relative error = 1.0493464479796769973014688957839e-28 % Correct digits = 30 h = 0.01 y2[1] (analytic) = 0.99992325756410088417953654157497 y2[1] (numeric) = 0.99992325756410088417953654157503 absolute error = 6e-32 relative error = 6.0004604899545155115161830423735e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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=1460529908, alloc=4783252, time=124.92 x[1] = 4.71 y1[1] (analytic) = 0.0023889781122815029610961477246958 y1[1] (numeric) = 0.0023889781122815029610961477246826 absolute error = 1.32e-32 relative error = 5.5253750263094041143425920190249e-28 % Correct digits = 30 h = 0.01 y2[1] (analytic) = 0.99999714638771796842523471259357 y2[1] (numeric) = 0.99999714638771796842523471259363 absolute error = 6e-32 relative error = 6.0000171217225509472095116666056e-30 % Correct digits = 32 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 NO REAL POLE (three term test) for Equation 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] = 4.72 y1[1] (analytic) = -0.0076109461341481509210826531746326 y1[1] (numeric) = -0.0076109461341481509210826531746464 absolute error = 1.38e-32 relative error = 1.8131779882245289335742057384004e-28 % Correct digits = 30 h = 0.01 y2[1] (analytic) = 0.99997103633002445843229788796164 y2[1] (numeric) = 0.9999710363300244584322978879617 absolute error = 6e-32 relative error = 6.0001737870533641090660986277635e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.007329 Order of pole (three term test) = -0.8902 NO COMPLEX POLE (six term test) for Equation 2 bytes used=1464530644, alloc=4783252, time=125.13 TOP MAIN SOLVE Loop x[1] = 4.73 y1[1] (analytic) = -0.017610109292306823958480184942845 y1[1] (numeric) = -0.017610109292306823958480184942859 absolute error = 1.4e-32 relative error = 7.9499790532907475130413165459613e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99984493000200436524284191155768 y2[1] (numeric) = 0.99984493000200436524284191155774 absolute error = 6e-32 relative error = 6.0009305642905764830474544380700e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.01696 Order of pole (three term test) = -0.8961 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1468531912, alloc=4783252, time=125.34 x[1] = 4.74 y1[1] (analytic) = -0.027607511454211308473521317218995 y1[1] (numeric) = -0.02760751145421130847352131721901 absolute error = 1.5e-32 relative error = 5.4333039125523456477223259770513e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99961884001418540260979704807277 y2[1] (numeric) = 0.99961884001418540260979704807283 absolute error = 6e-32 relative error = 6.0022878319448792406953594877485e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.02657 Order of pole (three term test) = -0.9066 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1472533812, alloc=4783252, time=125.54 x[1] = 4.75 y1[1] (analytic) = -0.037602152887976554715496312373334 y1[1] (numeric) = -0.03760215288797655471549631237335 absolute error = 1.6e-32 relative error = 4.2550755132736207669448847940431e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99929278897537794473427075559708 y2[1] (numeric) = 0.99929278897537794473427075559714 absolute error = 6e-32 relative error = 6.0042462691560930331782970071647e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.03618 Order of pole (three term test) = -0.9217 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1476535192, alloc=4783252, time=125.75 x[1] = 4.76 y1[1] (analytic) = -0.047593034137788026258408716410526 y1[1] (numeric) = -0.047593034137788026258408716410543 absolute error = 1.7e-32 relative error = 3.5719512966504274752345865674988e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99886680949041416406874008456944 y2[1] (numeric) = 0.9988668094904141640687400845695 absolute error = 6e-32 relative error = 6.0068068565227266819074279962207e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.04578 Order of pole (three term test) = -0.9414 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1480537228, alloc=4783252, time=125.96 x[1] = 4.77 y1[1] (analytic) = -0.057579156123846448577548772787261 y1[1] (numeric) = -0.057579156123846448577548772787278 absolute error = 1.7e-32 relative error = 2.9524573030273081537218111722566e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99834094415688757527040933829949 y2[1] (numeric) = 0.99834094415688757527040933829955 absolute error = 6e-32 relative error = 6.0099708773009215993994969486846e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.05535 Order of pole (three term test) = -0.9658 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.78 y1[1] (analytic) = -0.067559520242274956413221714659554 y1[1] (numeric) = -0.067559520242274956413221714659572 absolute error = 1.8e-32 relative error = 2.6643173212968747722276302394925e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99771524556089331134762062164767 y2[1] (numeric) = 0.99771524556089331134762062164774 absolute error = 7e-32 relative error = 7.0160299054714311334454905501766e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.06491 Order of pole (three term test) = -0.9947 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1484538344, alloc=4783252, time=126.17 x[1] = 4.79 y1[1] (analytic) = -0.077533128464978649290150241347593 y1[1] (numeric) = -0.077533128464978649290150241347612 absolute error = 1.9e-32 relative error = 2.4505653745910963649682874901239e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99698977627176955796815287876274 y2[1] (numeric) = 0.99698977627176955796815287876281 absolute error = 7e-32 relative error = 7.0211351877412524174098609369303e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.07444 Order of pole (three term test) = -1.028 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1488539608, alloc=4783252, time=126.37 x[1] = 4.8 y1[1] (analytic) = -0.087498983439446569320215257649488 y1[1] (numeric) = -0.087498983439446569320215257649507 absolute error = 1.9e-32 relative error = 2.1714537990202934996762627797288e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99616460883584067178159646650363 y2[1] (numeric) = 0.99616460883584067178159646650371 absolute error = 8e-32 relative error = 8.0308012642098700984750584521554e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.08393 Order of pole (three term test) = -1.066 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1492540716, alloc=4783252, time=126.58 x[1] = 4.81 y1[1] (analytic) = -0.097456088588486121173922639538394 y1[1] (numeric) = -0.097456088588486121173922639538414 absolute error = 2.0e-32 relative error = 2.0522063105211556252161332319848e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99523982576916260843875697540403 y2[1] (numeric) = 0.9952398257691626084387569754041 absolute error = 7e-32 relative error = 7.0334805930722373580952535833995e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.0934 Order of pole (three term test) = -1.109 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1496542348, alloc=4783252, time=126.80 x[1] = 4.82 y1[1] (analytic) = -0.10740344820987996086171061916977 y1[1] (numeric) = -0.10740344820987996086171061916979 absolute error = 2e-32 relative error = 1.8621376066918692590613198706732e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99421551954927138575924090129834 y2[1] (numeric) = 0.99421551954927138575924090129841 absolute error = 7e-32 relative error = 7.0407269473860728911603538749756e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1028 Order of pole (three term test) = -1.156 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1500543312, alloc=4783252, time=127.01 x[1] = 4.83 y1[1] (analytic) = -0.11734006757595538771926678895382 y1[1] (numeric) = -0.11734006757595538771926678895384 absolute error = 2e-32 relative error = 1.7044476292851801834054597978547e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.9930917926059354071940301512694 y2[1] (numeric) = 0.99309179260593540719403015126947 absolute error = 7e-32 relative error = 7.0486938388963613834221295250664e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1122 Order of pole (three term test) = -1.208 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.84 y1[1] (analytic) = -0.12726495303305628274063040973268 y1[1] (numeric) = -0.1272649530330562827406304097327 absolute error = 2e-32 relative error = 1.5715245653534421187727174574801e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99186875731091257034299275504052 y2[1] (numeric) = 0.99186875731091257034299275504058 absolute error = 6e-32 relative error = 6.0491874109098806845344917968352e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1216 Order of pole (three term test) = -1.264 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1504545380, alloc=4783252, time=127.22 x[1] = 4.85 y1[1] (analytic) = -0.13717711210090764614813971846528 y1[1] (numeric) = -0.1371771121009076461481397184653 absolute error = 2e-32 relative error = 1.4579691680116414981777981573388e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.99054653596671318480794231629118 y2[1] (numeric) = 0.99054653596671318480794231629124 absolute error = 6e-32 relative error = 6.0572621094922762562752759695056e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1308 Order of pole (three term test) = -1.325 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1508546896, alloc=4783252, time=127.43 x[1] = 4.86 y1[1] (analytic) = -0.1470755535718627978282707459854 y1[1] (numeric) = -0.14707555357186279782827074598542 absolute error = 2e-32 relative error = 1.3598452981669568373244533066068e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.98912526079436982308009669404291 y2[1] (numeric) = 0.98912526079436982308009669404297 absolute error = 6e-32 relative error = 6.0659657960624520131777365496702e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1401 Order of pole (three term test) = -1.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1512547612, alloc=4783252, time=127.64 x[1] = 4.87 y1[1] (analytic) = -0.15695928761002331599602978562804 y1[1] (numeric) = -0.15695928761002331599602978562805 absolute error = 1e-32 relative error = 6.3710788652696501108340620463256e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.98760507392021532746665541129251 y2[1] (numeric) = 0.98760507392021532746665541129257 absolute error = 6e-32 relative error = 6.0753029307388066891096838899294e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1493 Order of pole (three term test) = -1.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1516548728, alloc=4783252, time=127.85 x[1] = 4.88 y1[1] (analytic) = -0.16682732585022180217663274703162 y1[1] (numeric) = -0.16682732585022180217663274703164 absolute error = 2e-32 relative error = 1.1988443678559035879299005793817e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.98598612736167029524478484231842 y2[1] (numeric) = 0.98598612736167029524478484231848 absolute error = 6e-32 relative error = 6.0852783152791110164030908504765e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1584 Order of pole (three term test) = -1.534 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1520549712, alloc=4783252, time=128.06 x[1] = 4.89 y1[1] (analytic) = -0.17667868149685757431045858971384 y1[1] (numeric) = -0.17667868149685757431045858971386 absolute error = 2e-32 relative error = 1.1319984862098782479514253635421e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.9842685830120414632826520572489 y2[1] (numeric) = 0.98426858301204146328265205724896 absolute error = 6e-32 relative error = 6.0958970991829335661172510667959e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1675 Order of pole (three term test) = -1.613 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.9 y1[1] (analytic) = -0.18651236942257540449432914412192 y1[1] (numeric) = -0.18651236942257540449432914412194 absolute error = 2e-32 relative error = 1.0723149387849235939823868584558e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.98245261262433251227637724991833 y2[1] (numeric) = 0.98245261262433251227637724991839 absolute error = 6e-32 relative error = 6.1071647862717458642179643179974e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1764 Order of pole (three term test) = -1.695 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1524551868, alloc=4783252, time=128.26 x[1] = 4.91 y1[1] (analytic) = -0.1963274062667774335675731995194 y1[1] (numeric) = -0.19632740626677743356757319951942 absolute error = 2e-32 relative error = 1.0187064750818950922164329369779e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.98053839779406890950899010226969 y2[1] (numeric) = 0.98053839779406890950899010226975 absolute error = 6e-32 relative error = 6.1190872417625712486435357518926e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1854 Order of pole (three term test) = -1.782 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1528553668, alloc=4783252, time=128.47 x[1] = 4.92 y1[1] (analytic) = -0.20612281053395841143350924081177 y1[1] (numeric) = -0.2061228105339584114335092408118 absolute error = 3e-32 relative error = 1.4554429915973587410080426737934e-29 % Correct digits = 31 h = 0.01 y2[1] (analytic) = 0.97852612994113850763280160634113 y2[1] (numeric) = 0.97852612994113850763280160634119 absolute error = 6e-32 relative error = 6.1316706998523578395372370828605e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.1942 Order of pole (three term test) = -1.874 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1532554356, alloc=4783252, time=128.68 x[1] = 4.93 y1[1] (analytic) = -0.21589760269185442967426044648577 y1[1] (numeric) = -0.21589760269185442967426044648579 absolute error = 2e-32 relative error = 9.2636508004887528057229078526246e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97641601029064971540018032274914 y2[1] (numeric) = 0.9764160102906497154001803227492 absolute error = 6e-32 relative error = 6.1449217718316399132586550412144e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.203 Order of pole (three term test) = -1.969 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1536555044, alloc=4783252, time=128.89 x[1] = 4.94 y1[1] (analytic) = -0.22565080526939533166743080403972 y1[1] (numeric) = -0.22565080526939533166743080403974 absolute error = 2e-32 relative error = 8.8632522166817939312687887323304e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97420824985280915450970852682316 y2[1] (numeric) = 0.97420824985280915450970852682322 absolute error = 6e-32 relative error = 6.1588474547475100566126551058651e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2117 Order of pole (three term test) = -2.069 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1540555904, alloc=4783252, time=129.10 x[1] = 4.95 y1[1] (analytic) = -0.23538144295445100504525741163474 y1[1] (numeric) = -0.23538144295445100504525741163476 absolute error = 2e-32 relative error = 8.4968465436207850095753093699717e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.97190306940182081478526506337735 y2[1] (numeric) = 0.97190306940182081478526506337742 absolute error = 7e-32 relative error = 7.2023643307437072165889346092849e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2203 Order of pole (three term test) = -2.173 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 4.96 y1[1] (analytic) = -0.24508854269136178194844802293532 y1[1] (numeric) = -0.24508854269136178194844802293534 absolute error = 2e-32 relative error = 8.1603161781356113572270331873118e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96950069945380881775493302309673 y2[1] (numeric) = 0.9695006994538088177549330230968 absolute error = 7e-32 relative error = 7.2202113974168515806274480166017e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2288 Order of pole (three term test) = -2.281 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1544557432, alloc=4783252, time=129.30 x[1] = 4.97 y1[1] (analytic) = -0.25477113377824319411595351401254 y1[1] (numeric) = -0.25477113377824319411595351401256 absolute error = 2e-32 relative error = 7.8501829086368610638002805666221e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96700138024376599633497671407791 y2[1] (numeric) = 0.96700138024376599633497671407797 absolute error = 6e-32 relative error = 6.2047481240280064455944575163143e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2372 Order of pole (three term test) = -2.394 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1548559596, alloc=4783252, time=129.51 x[1] = 4.98 y1[1] (analytic) = -0.26442824796405535241625332068078 y1[1] (numeric) = -0.2644282479640553524162533206808 absolute error = 2e-32 relative error = 7.5634884525342652761140772259340e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96440536170153059574171007792892 y2[1] (numeric) = 0.96440536170153059574171007792899 absolute error = 7e-32 relative error = 7.2583586508163752644110335513589e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2455 Order of pole (three term test) = -2.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop bytes used=1552561024, alloc=4783252, time=129.72 x[1] = 4.99 y1[1] (analytic) = -0.27405891954542724396309159769695 y1[1] (numeric) = -0.27405891954542724396309159769697 absolute error = 2e-32 relative error = 7.2977008130855072016523539894619e-30 % Correct digits = 32 h = 0.01 y2[1] (analytic) = 0.96171290342679349794114601441111 y2[1] (numeric) = 0.96171290342679349794114601441117 absolute error = 6e-32 relative error = 6.2388681472617110558166000535117e-30 % Correct digits = 32 h = 0.01 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 Radius of convergence (three term test) for eq 2 = 0.2538 Order of pole (three term test) = -2.63 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y1 , x , 1 ) = m1 * y2 ; diff ( y2 , x , 2 ) = diff ( y1, x , 1) ; Iterations = 450 Total Elapsed Time = 2 Minutes 9 Seconds Elapsed Time(since restart) = 2 Minutes 2 Seconds Time to Timeout = 50 Seconds Percent Done = 100.2 % > quit bytes used=1554142840, alloc=4783252, time=129.80