|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > 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 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y2[1]) < min_size) then # if number 1 > min_size := omniabs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (omniabs(array_y1[1]) < min_size) then # if number 1 > min_size := omniabs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; 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 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 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 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 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,""); > value3 := 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 (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > value3 := 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 (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 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, ""); value3 := 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_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; value3 := 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_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, 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 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > 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_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 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 3; > 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 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, 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_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)) + 2 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_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)) + 2 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 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > 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 1; > 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; 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_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_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 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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 1 > 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 1; > 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, 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 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; > #TOP CHECK FOR POLE > #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 - 3 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > 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) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > 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) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1; > #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 - 3 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y2_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y2_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > 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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > 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) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y1_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y1_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-5]) <= (glob_small_float)))) then # if number 3 > 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) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > 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) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3; > #BOTTOM RADII COMPLEX EQ = 2 > found_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found_sing := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing ) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 1 > #TOP WHICH RADII EQ = 2 > if (2 <> found_sing and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found_sing := 2; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 2"); > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found_sing := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing ) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 2"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if (array_pole[1] > array_poles[2,1]) then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3; > #BOTTOM WHICH RADIUS EQ = 2 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 3 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > 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; > 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; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 3; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 3 > display_pole(); > fi;# end if 3 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 4; while 10 <= m and ( omniabs(array_y2_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float*glob_small_float) 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 glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y1_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float*glob_small_float) 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 glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 4; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y2_higher[1, n]) 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 elif glob_large_float <= omniabs(array_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) or omniabs(array_y2_higher[1, m]) <= glob_small_float or omniabs(array_y2_higher[1, m - 1]) <= glob_small_float or omniabs(array_y2_higher[1, m - 2]) <= glob_small_float or omniabs(array_y2_higher[1, m - 3]) <= glob_small_float or omniabs(array_y2_higher[1, m - 4]) <= glob_small_float or omniabs(array_y2_higher[1, m - 5]) <= glob_small_float 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) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) 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 glob_small_float < omniabs(rcs) 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_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y1_higher[1, n]) 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 elif glob_large_float <= omniabs(array_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) or omniabs(array_y1_higher[1, m]) <= glob_small_float or omniabs(array_y1_higher[1, m - 1]) <= glob_small_float or omniabs(array_y1_higher[1, m - 2]) <= glob_small_float or omniabs(array_y1_higher[1, m - 3]) <= glob_small_float or omniabs(array_y1_higher[1, m - 4]) <= glob_small_float or omniabs(array_y1_higher[1, m - 5]) <= glob_small_float 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) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) 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 glob_small_float < omniabs(rcs) 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_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found_sing := 0; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found_sing := 2; array_type_pole[2] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 2") end if end if end if; if 2 <> found_sing and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and -1.0*glob_smallish_float < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found_sing := 2; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 2") end if end if end if; if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found_sing := 2; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 2") end if end if; if 2 <> found_sing and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and -1.0*glob_smallish_float < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found_sing := 2; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 2") end if end if end if; if 2 <> found_sing and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found_sing := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 2") end if end if end if; if 2 <> found_sing then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 2") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] 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_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; 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; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, 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_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; 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 end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre cos 1 $eq_no = 1 > array_tmp1[1] := cos(array_x[1]); > array_tmp1_g[1] := sin(array_x[1]); > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp2[1] := (array_m1[1] * (array_tmp1[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (3)) * factorial_3(0,3); > 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; > temporary := temporary / glob_h * (1.0); > array_y2_higher[4,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > # emit pre mult FULL FULL $eq_no = 2 i = 1 > array_tmp5[1] := (array_m1[1] * (array_y2[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre cos ID_LINEAR iii = 2 $eq_no = 1 > array_tmp1[2] := -array_tmp1_g[1] * array_x[2] / 1; > array_tmp1_g[2] := array_tmp1[1] * array_x[2] / 1; > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp2[2] := ats(2,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,5]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (3)) * factorial_3(1,4); > 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; > temporary := temporary / glob_h * (2.0); > array_y2_higher[4,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > # emit pre mult FULL FULL $eq_no = 2 i = 2 > array_tmp5[2] := ats(2,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre cos ID_LINEAR iii = 3 $eq_no = 1 > array_tmp1[3] := -array_tmp1_g[2] * array_x[2] / 2; > array_tmp1_g[3] := array_tmp1[2] * array_x[2] / 2; > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp2[3] := ats(3,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (3)) * factorial_3(2,5); > 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; > temporary := temporary / glob_h * (3.0); > array_y2_higher[4,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > # emit pre mult FULL FULL $eq_no = 2 i = 3 > array_tmp5[3] := ats(3,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre cos ID_LINEAR iii = 4 $eq_no = 1 > array_tmp1[4] := -array_tmp1_g[3] * array_x[2] / 3; > array_tmp1_g[4] := array_tmp1[3] * array_x[2] / 3; > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp2[4] := ats(4,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,7]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (3)) * factorial_3(3,6); > 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; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > # emit pre mult FULL FULL $eq_no = 2 i = 4 > array_tmp5[4] := ats(4,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre cos ID_LINEAR iii = 5 $eq_no = 1 > array_tmp1[5] := -array_tmp1_g[4] * array_x[2] / 4; > array_tmp1_g[5] := array_tmp1[4] * array_x[2] / 4; > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp2[5] := ats(5,array_m1,array_tmp1,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,8]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (3)) * factorial_3(4,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (7.0); > array_y2_higher[2,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[3,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[4,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > # emit pre mult FULL FULL $eq_no = 2 i = 5 > array_tmp5[5] := ats(5,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit cos LINEAR $eq_no = 1 > array_tmp1[kkk] := -array_tmp1_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / (kkk - 1); > #emit mult FULL FULL $eq_no = 1 > array_tmp2[kkk] := ats(kkk,array_m1,array_tmp1,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 3; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_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 2 > 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 2 > fi;# end if 2 > fi;# end if 1; > #emit mult FULL FULL $eq_no = 2 > array_tmp5[kkk] := ats(kkk,array_m1,array_y2,1); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_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 2 > 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 2 > 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := cos(array_x[1]); array_tmp1_g[1] := sin(array_x[1]); array_tmp2[1] := array_m1[1]*array_tmp1[1]; array_tmp3[1] := array_const_0D0[1] + array_tmp2[1]; if not array_y2_set_initial[1, 4] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 3)*factorial_3(0, 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; temporary := temporary*1.0/glob_h; array_y2_higher[4, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_m1[1]*array_y2[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[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_tmp1[2] := -array_tmp1_g[1]*array_x[2]; array_tmp1_g[2] := array_tmp1[1]*array_x[2]; array_tmp2[2] := ats(2, array_m1, array_tmp1, 1); array_tmp3[2] := array_tmp2[2]; if not array_y2_set_initial[1, 5] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 3)*factorial_3(1, 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; temporary := temporary*2.0/glob_h; array_y2_higher[4, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := ats(2, array_m1, array_y2, 1); if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[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_tmp1[3] := -1/2*array_tmp1_g[2]*array_x[2]; array_tmp1_g[3] := 1/2*array_tmp1[2]*array_x[2]; array_tmp2[3] := ats(3, array_m1, array_tmp1, 1); array_tmp3[3] := array_tmp2[3]; if not array_y2_set_initial[1, 6] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 3)*factorial_3(2, 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; temporary := temporary*3.0/glob_h; array_y2_higher[4, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := ats(3, array_m1, array_y2, 1); if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[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_tmp1[4] := -1/3*array_tmp1_g[3]*array_x[2]; array_tmp1_g[4] := 1/3*array_tmp1[3]*array_x[2]; array_tmp2[4] := ats(4, array_m1, array_tmp1, 1); array_tmp3[4] := array_tmp2[4]; if not array_y2_set_initial[1, 7] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 3)*factorial_3(3, 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; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := ats(4, array_m1, array_y2, 1); if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[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_tmp1[5] := -1/4*array_tmp1_g[4]*array_x[2]; array_tmp1_g[5] := 1/4*array_tmp1[4]*array_x[2]; array_tmp2[5] := ats(5, array_m1, array_tmp1, 1); array_tmp3[5] := array_tmp2[5]; if not array_y2_set_initial[1, 8] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 3)*factorial_3(4, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*7.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[4, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := ats(5, array_m1, array_y2, 1); if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[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; while kkk <= glob_max_terms do array_tmp1[kkk] := -array_tmp1_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/(kkk - 1); array_tmp2[kkk] := ats(kkk, array_m1, array_tmp1, 1); array_tmp3[kkk] := array_tmp2[kkk]; order_d := 3; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_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; array_tmp5[kkk] := ats(kkk, array_m1, array_y2, 1); order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_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; kkk := kkk + 1 end do end proc > # End Function number 12 > #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\n", 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 \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", 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\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", 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, "\n") 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 Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") 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,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_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, 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_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 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # End Function number 16 > # Begin Function number 17 > 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 17 > # Begin Function number 18 > 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 18 > # Begin Function number 19 > 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 19 > # Begin Function number 20 > 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 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > 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 22 > # Begin Function number 23 > 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"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > 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") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > 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 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > 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 26 > # Begin Function number 27 > 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 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > 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 27 > # Begin Function number 28 > 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 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > 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 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > 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 30 > # Begin Function number 31 > 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 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > 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 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > 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 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > 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 > exact_soln_y2pp := proc(x) > return( -sin(x)); > end; exact_soln_y2pp := proc(x) return -sin(x) end proc > exact_soln_y1 := proc(x) > return( cos(x)); > end; exact_soln_y1 := 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,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > 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_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_3, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > 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; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > 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_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 := 0.1e-200; > glob_smallish_float := 0.1e-100; > 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/mtest4postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = m1 * cos(x) ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2;"); > 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 := 0.1;"); > 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,"array_y2_init[2 + 1] := exact_soln_y2pp(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:=0.001;"); > 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_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,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return( -sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y1 := 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 := 1.0e-200; > glob_smallish_float := 1.0e-64; > 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_y2_init:= Array(0..(max_terms + 1),[]); > array_y1_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..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y2_higher := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(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_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(2+ 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 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=4) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=4) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=4) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_3[1] := 3; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 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); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > 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_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_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); > if (glob_display_interval < glob_h) then # if number 3 > glob_h := glob_display_interval; > fi;# end if 3; > if (glob_max_h < glob_h) then # if number 3 > glob_h := glob_max_h; > fi;# end if 3; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > 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 := 3; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > 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 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > 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 4; > r_order := r_order + 1; > od;# end do number 3 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > 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 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > 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 4; > r_order := r_order + 1; > od;# end do number 3 > ; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 4) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 4 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 4; > 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,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 4 > best_h := glob_h; > found_h := 1.0; > fi;# end if 4; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 4 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 4; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 4 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 4; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 4 > 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 := 3; > #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 > ; > 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 > ; > 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 2 > #left paren 0001C > if (reached_interval()) then # if number 5 > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > fi;# end if 5; > 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 5 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 6 > subiter := 1; > while (subiter <= 4) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 4 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 6; > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2; > order_diff := 4; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_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 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_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_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > 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 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_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 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 3 ) = m1 * cos(x) ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T16:47:44-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest4") > ; > logitem_str(html_log_file,"diff ( y2 , x , 3 ) = m1 * cos(x) ;") > ; > 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_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"mtest4 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest4 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 ( y1 , x , 1 ) = m1 * y2;") > ; > 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) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 7 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 7; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #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, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, 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_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_3, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, 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; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; 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_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 := 0.1*10^(-200); glob_smallish_float := 0.1*10^(-100); 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/mtest4postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2;"); 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 := 0.1;"); 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, "array_y2_init[2 + 1] := exact_soln_y2pp(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:=0.001;"); 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_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, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return( -sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y1 := 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 := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); 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_y2_init := Array(0 .. max_terms + 1, []); array_y1_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 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 5, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 5, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 5, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 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_poles := Array(0 .. 3, 0 .. 4, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); 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_y1_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 <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[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_x[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_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 4 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 <= 4 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 <= 4 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 <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[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_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[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_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_const_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; 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_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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 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); array_y2_init[3] := exact_soln_y2pp(x_start); glob_max_iter := 20; glob_desired_digits_correct := 10; glob_display_interval := 0.001; 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_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_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); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. 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 := 3; 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; 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; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 4 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 4 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < 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 := 3; 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; 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; 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 <= 4 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 4 + 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 := 4; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; 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 := 3; calc_term := 2; 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 := 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 := 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 := 3; 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 := 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 := 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 := 4; 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 := 4; 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; 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 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 ( y2 , x , 3 ) = m1 * cos(x) ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2;"); 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, "2013-01-28T16:47:44-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest4"); logitem_str(html_log_file, "diff ( y2 , x , 3 ) = m1 * cos(x) ;"); 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_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; 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, " 165 "); logitem_str(html_log_file, "mtest4 diffeq.mxt"); logitem_str(html_log_file, "mtest4 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 ( y1 , x , 1 ) = m1 * y2;"); 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); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; 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 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest4postode.ode################# diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; 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); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; 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_y2 := proc(x) return(sin(x)); end; exact_soln_y2p := proc(x) return( cos(x)); end; exact_soln_y2pp := proc(x) return( -sin(x)); end; exact_soln_y1 := proc(x) return( cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 memory used=3.8MB, alloc=3.1MB, time=0.18 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 4.9 estimated_steps = 4900 step_error = 2.0408163265306122448979591836735e-14 est_needed_step_err = 2.0408163265306122448979591836735e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.4759225582891422933370225621906e-106 value3 = 2.4672040251049429538467757202074e-105 max_value3 = 2.4672040251049429538467757202074e-105 value3 = 2.4672040251049429538467757202074e-105 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.4MB, time=0.41 x[1] = 0.1 y2[1] (analytic) = 0.099833416646828152306814198410622 y2[1] (numeric) = 0.099833416646828152306814198410622 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.99500416527802576609556198780387 y1[1] (numeric) = 0.99500416527802576609556198780387 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.4MB, time=0.64 x[1] = 0.101 y2[1] (analytic) = 0.10082837072956799512975211952319 y2[1] (numeric) = 0.10082837072956799512975211952319 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.99490383437597665937840299982896 y1[1] (numeric) = 0.99490383437597665937840299982896 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.87 memory used=19.0MB, alloc=4.4MB, time=1.10 x[1] = 0.102 y2[1] (analytic) = 0.10182322398394551074864229608065 y2[1] (numeric) = 0.10182322398394551074864229608065 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.99480250857017608533468567645987 y1[1] (numeric) = 0.99480250857017608533468567645986 absolute error = 1e-32 relative error = 1.0052246464851543641113853959517e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.33 x[1] = 0.103 y2[1] (analytic) = 0.10281797541510752769040421050459 y2[1] (numeric) = 0.10281797541510752769040421050459 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.99470018796194984132116719282663 y1[1] (numeric) = 0.99470018796194984132116719282663 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.56 x[1] = 0.104 y2[1] (analytic) = 0.10381262402830269768897075466946 y2[1] (numeric) = 0.10381262402830269768897075466946 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.99459687265361852703737449448465 y1[1] (numeric) = 0.99459687265361852703737449448465 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.79 x[1] = 0.105 y2[1] (analytic) = 0.10480716882888249043655360002678 y2[1] (numeric) = 0.10480716882888249043655360002679 absolute error = 1e-32 relative error = 9.5413320593812526309072352799452e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.99449256274849744220501312460406 y1[1] (numeric) = 0.99449256274849744220501312460406 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.02 x[1] = 0.106 y2[1] (analytic) = 0.10580160882230218823209061801872 y2[1] (numeric) = 0.10580160882230218823209061801873 absolute error = 1e-32 relative error = 9.4516521169308294618670380485659e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.99438725835089648325267611187222 y1[1] (numeric) = 0.99438725835089648325267611187222 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.25 memory used=41.9MB, alloc=4.4MB, time=2.49 x[1] = 0.107 y2[1] (analytic) = 0.10679594301412188052588070241646 y2[1] (numeric) = 0.10679594301412188052588070241648 absolute error = 2e-32 relative error = 1.8727303149854065733057027563251e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99428095956612003900595623439178 y1[1] (numeric) = 0.99428095956612003900595623439178 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.72 x[1] = 0.108 y2[1] (analytic) = 0.10779017041000745835941144903159 y2[1] (numeric) = 0.1077901704100074583594114490316 absolute error = 1e-32 relative error = 9.2772837838204026890097042904989e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.99417366650046688538306596945332 y1[1] (numeric) = 0.99417366650046688538306596945332 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=2.95 x[1] = 0.109 y2[1] (analytic) = 0.10878429001573160869938525305544 y2[1] (numeric) = 0.10878429001573160869938525305546 absolute error = 2e-32 relative error = 1.8385007611951820012922404986594e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99406537926123007909607043355394 y1[1] (numeric) = 0.99406537926123007909607043355393 absolute error = 1e-32 relative error = 1.0059700507256176800023823254121e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=3.18 x[1] = 0.11 y2[1] (analytic) = 0.10977830083717480866494949008345 y2[1] (numeric) = 0.10977830083717480866494949008347 absolute error = 2e-32 relative error = 1.8218536675717332517910891446314e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99395609795669685035783961141985 y1[1] (numeric) = 0.99395609795669685035783961141984 absolute error = 1e-32 relative error = 1.0060806529138739295356804682092e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=3.42 x[1] = 0.111 y2[1] (analytic) = 0.11077220188032631964713655367693 y2[1] (numeric) = 0.11077220188032631964713655367695 absolute error = 2e-32 relative error = 1.8055071272851620555989418706744e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99384582269614849459482716707199 y1[1] (numeric) = 0.99384582269614849459482716707198 absolute error = 1e-32 relative error = 1.0061922857281385794439936053254e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.4MB, time=3.65 x[1] = 0.112 y2[1] (analytic) = 0.11176599215128518131951963010521 y2[1] (numeric) = 0.11176599215128518131951963010523 absolute error = 2e-32 relative error = 1.7894530898923374189964964806201e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99373455358986026316578412414666 y1[1] (numeric) = 0.99373455358986026316578412414665 absolute error = 1e-32 relative error = 1.0063049497348218881188352883004e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=64.8MB, alloc=4.4MB, time=3.88 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=4.12 x[1] = 0.113 y2[1] (analytic) = 0.1127596706562612055390901996952 y2[1] (numeric) = 0.11275967065626120553909019969522 absolute error = 2e-32 relative error = 1.7736837899224087635266901706967e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99362229074910125308651669674845 y1[1] (numeric) = 0.99362229074910125308651669674844 absolute error = 1e-32 relative error = 1.0064186455057188094301217864537e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=4.35 x[1] = 0.114 y2[1] (analytic) = 0.11375323640157597013636336399366 y2[1] (numeric) = 0.11375323640157597013636336399369 absolute error = 3e-32 relative error = 2.6372876015670329842055288886658e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99350903428613429576079854606851 y1[1] (numeric) = 0.9935090342861342957607985460685 absolute error = 1e-32 relative error = 1.0065333736180161216129094911941e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=4.59 x[1] = 0.115 y2[1] (analytic) = 0.1147466883936638125937172087197 y2[1] (numeric) = 0.11474668839366381259371720871972 absolute error = 2e-32 relative error = 1.7429696908886460082358354876600e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99339478431421584471754873184649 y1[1] (numeric) = 0.99339478431421584471754873184648 absolute error = 1e-32 relative error = 1.0066491346542996261800482583824e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=4.82 x[1] = 0.116 y2[1] (analytic) = 0.11574002563907282361097252425083 y2[1] (numeric) = 0.11574002563907282361097252425086 absolute error = 3e-32 relative error = 2.5920160147149873747757779608540e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99327954094759586235438762148898 y1[1] (numeric) = 0.99327954094759586235438762148897 absolute error = 1e-32 relative error = 1.0067659292025614170289689631342e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=5.06 x[1] = 0.117 y2[1] (analytic) = 0.11673324714446584055721931814593 y2[1] (numeric) = 0.11673324714446584055721931814596 absolute error = 3e-32 relative error = 2.5699619203492925282605557316595e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99316330430151770568768401327901 y1[1] (numeric) = 0.993163304301517705687684013279 absolute error = 1e-32 relative error = 1.0068837578562072199125500669319e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=5.29 memory used=91.5MB, alloc=4.5MB, time=5.53 x[1] = 0.118 y2[1] (analytic) = 0.11772635191662144080789666796104 y2[1] (numeric) = 0.11772635191662144080789666796107 absolute error = 3e-32 relative error = 2.5482824798008870739516172767680e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99304607449221801110920772362005 y1[1] (numeric) = 0.99304607449221801110920772362003 absolute error = 2e-32 relative error = 2.0140052424281276048914818951106e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=5.76 x[1] = 0.119 y2[1] (analytic) = 0.11871933896243493496613257736117 y2[1] (numeric) = 0.1187193389624349349661325773612 absolute error = 3e-32 relative error = 2.5269682481547991652855569079698e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99292785163692657814950288165217 y1[1] (numeric) = 0.99292785163692657814950288165216 absolute error = 1e-32 relative error = 1.0071225198803864548213591876719e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=6.00 x[1] = 0.12 y2[1] (analytic) = 0.11971220728891935996735061427097 y2[1] (numeric) = 0.119712207288919359967350614271 absolute error = 3e-32 relative error = 2.5060100953277485493704713765586e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99280863585386625224809816785763 y1[1] (numeric) = 0.99280863585386625224809816785762 absolute error = 1e-32 relative error = 1.0072434544648665414102250278741e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=6.23 x[1] = 0.121 y2[1] (analytic) = 0.12070495590320647206615022654028 y2[1] (numeric) = 0.12070495590320647206615022654031 absolute error = 3e-32 relative error = 2.4853991930585729737566257769192e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9926884272622528065306712264356 y1[1] (numeric) = 0.99268842726225280653067122643559 absolute error = 1e-32 relative error = 1.0073654255826391234225488347859e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=6.46 x[1] = 0.122 y2[1] (analytic) = 0.12169758381254773970446774832719 y2[1] (numeric) = 0.12169758381254773970446774832722 absolute error = 3e-32 relative error = 2.4651270025384696917350998058999e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99256722598229482259328547427195 y1[1] (numeric) = 0.99256722598229482259328547427194 absolute error = 1e-32 relative error = 1.0074884338542906528092467852338e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=6.69 x[1] = 0.123 y2[1] (analytic) = 0.1226900900243153362600252291201 y2[1] (numeric) = 0.12269009002431533626002522912013 absolute error = 3e-32 relative error = 2.4451852626446398247872951751935e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99244503213519357029381852225733 y1[1] (numeric) = 0.99244503213519357029381852225732 absolute error = 1e-32 relative error = 1.0076124799058667375836260944151e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=114.4MB, alloc=4.5MB, time=6.93 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=7.16 x[1] = 0.124 y2[1] (analytic) = 0.12368247354600313267407433703294 y2[1] (numeric) = 0.12368247354600313267407433703296 absolute error = 2e-32 relative error = 1.6170439858288483451141645179909e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99232184584314288655070241751501 y1[1] (numeric) = 0.992321845843142886550702417515 absolute error = 1e-32 relative error = 1.0077375643688799787456540909005e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=7.40 x[1] = 0.125 y2[1] (analytic) = 0.12467473338522768995744270871211 y2[1] (numeric) = 0.12467473338522768995744270871213 absolute error = 2e-32 relative error = 1.6041742746866572385064010529927e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99219766722932905314909690778825 y1[1] (numeric) = 0.99219766722932905314909690778824 absolute error = 1e-32 relative error = 1.0078636878803178789928053359720e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=7.63 x[1] = 0.126 y2[1] (analytic) = 0.12566686854972925157389023989174 y2[1] (numeric) = 0.12566686854972925157389023989176 absolute error = 2e-32 relative error = 1.5915093795852438996711327343762e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9920724964179306735546179218037 y1[1] (numeric) = 0.99207249641793067355461792180369 absolute error = 1e-32 relative error = 1.0079908510826508234032678713900e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=7.87 x[1] = 0.127 y2[1] (analytic) = 0.12665887804737273569978293332346 y2[1] (numeric) = 0.12665887804737273569978293332349 absolute error = 3e-32 relative error = 2.3685666936651255984889845433167e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99194633353411854873474445187208 y1[1] (numeric) = 0.99194633353411854873474445187207 absolute error = 1e-32 relative error = 1.0081190546238401322790836307790e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=8.10 x[1] = 0.128 y2[1] (analytic) = 0.12765076088614872735909204448972 y2[1] (numeric) = 0.12765076088614872735909204448974 absolute error = 2e-32 relative error = 1.5667748363707703165401616468333e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9918191787040555519880280173089 y1[1] (numeric) = 0.99181917870405555198802801730889 absolute error = 1e-32 relative error = 1.0082482991573461863385991383886e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=8.33 memory used=141.1MB, alloc=4.5MB, time=8.57 x[1] = 0.129 y2[1] (analytic) = 0.12864251607417447043272639018397 y2[1] (numeric) = 0.12864251607417447043272639018399 absolute error = 2e-32 relative error = 1.5546959598075744297272131568719e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99169103205489650278122987945538 y1[1] (numeric) = 0.99169103205489650278122987945538 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=8.81 x[1] = 0.13 y2[1] (analytic) = 0.12963414261969485954120581070831 y2[1] (numeric) = 0.12963414261969485954120581070834 absolute error = 3e-32 relative error = 2.3142051464027043651080784631679e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99156189371478803959451217115181 y1[1] (numeric) = 0.99156189371478803959451217115181 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.5MB, time=9.04 x[1] = 0.131 y2[1] (analytic) = 0.13062563953108343179968390309763 y2[1] (numeric) = 0.13062563953108343179968390309766 absolute error = 3e-32 relative error = 2.2966394735132574302657382733344e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99143176381286849177481009546157 y1[1] (numeric) = 0.99143176381286849177481009546157 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.5MB, time=9.27 x[1] = 0.132 y2[1] (analytic) = 0.13161700581684335844432827043014 y2[1] (numeric) = 0.13161700581684335844432827043017 absolute error = 3e-32 relative error = 2.2793407139004240084226567699808e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99130064247926775039751334026303 y1[1] (numeric) = 0.99130064247926775039751334026302 absolute error = 1e-32 relative error = 1.0087757004766736944944587987897e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=9.51 x[1] = 0.133 y2[1] (analytic) = 0.13260824048560843632906666092685 y2[1] (numeric) = 0.13260824048560843632906666092688 absolute error = 3e-32 relative error = 2.2623028471036690624594044292858e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99116852984510713813658584701707 y1[1] (numeric) = 0.99116852984510713813658584701706 absolute error = 1e-32 relative error = 1.0089101599667142196699075397981e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=9.74 memory used=164.0MB, alloc=4.5MB, time=9.98 x[1] = 0.134 y2[1] (analytic) = 0.13359934254614407929170750017626 y2[1] (numeric) = 0.13359934254614407929170750017629 absolute error = 3e-32 relative error = 2.2455200323787712171921533804707e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99103542604249927814325406357971 y1[1] (numeric) = 0.9910354260424992781432540635797 absolute error = 1e-32 relative error = 1.0090456644857782184325006083823e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=10.21 x[1] = 0.135 y2[1] (analytic) = 0.13459031100734830938844345044656 y2[1] (numeric) = 0.13459031100734830938844345044659 absolute error = 3e-32 relative error = 2.2289866020416634361258187411509e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9909013312045479619333948023605 y1[1] (numeric) = 0.99090133120454796193339480236049 absolute error = 1e-32 relative error = 1.0091822147260531177532107153118e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=10.45 x[1] = 0.136 y2[1] (analytic) = 0.13558114487825274799574676266417 y2[1] (numeric) = 0.13558114487825274799574676266421 absolute error = 4e-32 relative error = 2.9502627401412370525616513318783e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99076624546534801628375481642801 y1[1] (numeric) = 0.990766245465348016283754816428 absolute error = 1e-32 relative error = 1.0093198113852930344593646476510e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=10.68 x[1] = 0.137 y2[1] (analytic) = 0.13657184316802360677866531924609 y2[1] (numeric) = 0.13657184316802360677866531924613 absolute error = 4e-32 relative error = 2.9288614015985867859203487897751e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99063016895998516913713519733158 y1[1] (numeric) = 0.99063016895998516913713519733157 absolute error = 1e-32 relative error = 1.0094584551668275603936199092155e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.5MB, time=10.91 x[1] = 0.138 y2[1] (analytic) = 0.13756240488596267852452839957234 y2[1] (numeric) = 0.13756240488596267852452839957238 absolute error = 4e-32 relative error = 2.9077712063233733070646618948586e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99049310182453591451667468944385 y1[1] (numeric) = 0.99049310182453591451667468944384 absolute error = 1e-32 relative error = 1.0095981467795706219166959869415e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=11.15 x[1] = 0.139 y2[1] (analytic) = 0.13855282904150832784107133447554 y2[1] (numeric) = 0.13855282904150832784107133447558 absolute error = 4e-32 relative error = 2.8869854391797807457119937484372e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99035504419606737644936700652949 y1[1] (numeric) = 0.99035504419606737644936700652948 absolute error = 1e-32 relative error = 1.0097388869380294139635406927797e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=186.9MB, alloc=4.5MB, time=11.38 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=11.62 x[1] = 0.14 y2[1] (analytic) = 0.13954311464423648171798835170537 y2[1] (numeric) = 0.13954311464423648171798835170541 absolute error = 4e-32 relative error = 2.8664975768943904047348344728184e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9902159962126371718989482270114 y1[1] (numeric) = 0.99021599621263717189894822701139 absolute error = 1e-32 relative error = 1.0098806763623134088645046107846e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=11.85 x[1] = 0.141 y2[1] (analytic) = 0.14053326070386161995092305089768 y2[1] (numeric) = 0.14053326070386161995092305089772 absolute error = 4e-32 relative error = 2.8463012812525502454663909326840e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.99007595801329327270829133503572 y1[1] (numeric) = 0.99007595801329327270829133503571 absolute error = 1e-32 relative error = 1.0100235157781434401449973833090e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=12.08 x[1] = 0.142 y2[1] (analytic) = 0.14152326623023776542690608414029 y2[1] (numeric) = 0.14152326623023776542690608414033 absolute error = 4e-32 relative error = 2.8263903925822217230896398122439e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98993492973807386655144596492939 y1[1] (numeric) = 0.98993492973807386655144596492938 absolute error = 1e-32 relative error = 1.0101674059168608615190084776355e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=12.32 x[1] = 0.143 y2[1] (analytic) = 0.14251313023335947427024975678031 y2[1] (numeric) = 0.14251313023335947427024975678035 absolute error = 4e-32 relative error = 2.8067589235112316542769556155696e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98979291152800721689546239699913 y1[1] (numeric) = 0.98979291152800721689546239699913 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=12.55 x[1] = 0.144 y2[1] (analytic) = 0.14350285172336282584790940266096 y2[1] (numeric) = 0.143502851723362825847909402661 absolute error = 4e-32 relative error = 2.7874010529846385946826490766625e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98964990352511152197213984283608 y1[1] (numeric) = 0.98964990352511152197213984283608 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=12.78 memory used=213.6MB, alloc=4.5MB, time=13.02 x[1] = 0.145 y2[1] (analytic) = 0.14449242971052641263332152850892 y2[1] (numeric) = 0.14449242971052641263332152850896 absolute error = 4e-32 relative error = 2.7683111205296564740920274489173e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98950590587239477275984004836598 y1[1] (numeric) = 0.98950590587239477275984004836598 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.5MB, time=13.25 x[1] = 0.146 y2[1] (analytic) = 0.14548186320527232992772886371659 y2[1] (numeric) = 0.14548186320527232992772886371663 absolute error = 4e-32 relative error = 2.7494836207562663056441142687637e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98936091871385460997550823281966 y1[1] (numeric) = 0.98936091871385460997550823281966 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.5MB, time=13.49 x[1] = 0.147 y2[1] (analytic) = 0.14647115121816716543800259427676 y2[1] (numeric) = 0.1464711512181671654380025942768 absolute error = 4e-32 relative error = 2.7309131980822927275088846228469e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98921494219447818007704437159081 y1[1] (numeric) = 0.98921494219447818007704437159081 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.5MB, time=13.72 x[1] = 0.148 y2[1] (analytic) = 0.14746029275992298870997220312979 y2[1] (numeric) = 0.14746029275992298870997220312982 absolute error = 3e-32 relative error = 2.0344459812542465978317799765866e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98906797646024199027616882059779 y1[1] (numeric) = 0.98906797646024199027616882059779 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.5MB, time=13.96 x[1] = 0.149 y2[1] (analytic) = 0.14844928684139834041627348367598 y2[1] (numeric) = 0.14844928684139834041627348367601 absolute error = 3e-32 relative error = 2.0208921604353468567672441188698e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98892002165811176256192726927181 y1[1] (numeric) = 0.98892002165811176256192726927181 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.5MB, time=14.19 x[1] = 0.15 y2[1] (analytic) = 0.14943813247359922149772543868764 y2[1] (numeric) = 0.14943813247359922149772543868767 absolute error = 3e-32 relative error = 2.0075197343154705432671799057549e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98877107793604228673498099865434 y1[1] (numeric) = 0.98877107793604228673498099865433 absolute error = 1e-32 relative error = 1.0113564426736640909001707623026e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=236.5MB, alloc=4.5MB, time=14.43 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.5MB, time=14.66 x[1] = 0.151 y2[1] (analytic) = 0.1504268286676800821572469233262 y2[1] (numeric) = 0.15042682866768008215724692332623 absolute error = 3e-32 relative error = 1.9943250991666782599453113627838e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98862114544297727245282941030121 y1[1] (numeric) = 0.9886211454429772724528294103012 absolute error = 1e-32 relative error = 1.0115098231607459068428168850929e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.5MB, time=14.90 x[1] = 0.152 y2[1] (analytic) = 0.15141537443494481070532403843028 y2[1] (numeric) = 0.15141537443494481070532403843032 absolute error = 4e-32 relative error = 2.6417396614625740911382876042344e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98847022432884920028611278075862 y1[1] (numeric) = 0.98847022432884920028611278075861 absolute error = 1e-32 relative error = 1.0116642619953264434243559168126e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.5MB, time=15.13 x[1] = 0.153 y2[1] (analytic) = 0.15240376878684772225603942868975 y2[1] (numeric) = 0.15240376878684772225603942868978 absolute error = 3e-32 relative error = 1.9684552579508760171758263767710e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98831831474457917178614418529584 y1[1] (numeric) = 0.98831831474457917178614418529583 absolute error = 1e-32 relative error = 1.0118197599711989968484884781582e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.5MB, time=15.37 x[1] = 0.154 y2[1] (analytic) = 0.15339201073499454727267478975868 y2[1] (numeric) = 0.15339201073499454727267478975871 absolute error = 3e-32 relative error = 1.9557733063313876918685621005562e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98816541684207675856382052335014 y1[1] (numeric) = 0.98816541684207675856382052335013 absolute error = 1e-32 relative error = 1.0119763178878932375929380206807e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.5MB, time=15.61 x[1] = 0.155 y2[1] (analytic) = 0.15438009929114341996189803878732 y2[1] (numeric) = 0.15438009929114341996189803878736 absolute error = 4e-32 relative error = 2.5910075316485268356306218432037e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98801153077423985038006356676048 y1[1] (numeric) = 0.98801153077423985038006356676047 absolute error = 1e-32 relative error = 1.0121339365506853674070105333455e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.5MB, time=15.84 memory used=263.2MB, alloc=4.6MB, time=16.08 x[1] = 0.156 y2[1] (analytic) = 0.15536803346720586651554675426811 y2[1] (numeric) = 0.15536803346720586651554675426815 absolute error = 4e-32 relative error = 2.5745321677411174259917564016792e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98785665669495450224794294033609 y1[1] (numeric) = 0.98785665669495450224794294033608 absolute error = 1e-32 relative error = 1.0122926167706083547235968765122e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.6MB, time=16.31 x[1] = 0.157 y2[1] (analytic) = 0.15635581227524779319901964349465 y2[1] (numeric) = 0.15635581227524779319901964349469 absolute error = 4e-32 relative error = 2.5582675448984429427799567573079e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98770079475909478054663393262434 y1[1] (numeric) = 0.98770079475909478054663393262434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=16.55 x[1] = 0.158 y2[1] (analytic) = 0.15734343472749047428528794932464 y2[1] (numeric) = 0.15734343472749047428528794932468 absolute error = 4e-32 relative error = 2.5422096618951807505055052777335e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98754394512252260814736402290726 y1[1] (numeric) = 0.98754394512252260814736402290726 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.6MB, time=16.79 x[1] = 0.159 y2[1] (analytic) = 0.15833089983631153983353886231754 y2[1] (numeric) = 0.15833089983631153983353886231758 absolute error = 4e-32 relative error = 2.5263546181669850754475700812186e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98738610794208760855150299846715 y1[1] (numeric) = 0.98738610794208760855150299846715 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.6MB, time=17.02 x[1] = 0.16 y2[1] (analytic) = 0.15931820661424596331146315968599 y2[1] (numeric) = 0.15931820661424596331146315968603 absolute error = 4e-32 relative error = 2.5106986106648320739151935355573e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98722728337562694904095252401834 y1[1] (numeric) = 0.98722728337562694904095252401834 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.6MB, time=17.25 memory used=286.1MB, alloc=4.6MB, time=17.49 x[1] = 0.161 y2[1] (analytic) = 0.16030535407398704906019944885553 y2[1] (numeric) = 0.16030535407398704906019944885557 absolute error = 4e-32 relative error = 2.4952379308265942807815527499195e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98706747158196518284099201290235 y1[1] (numeric) = 0.98706747158196518284099201290235 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.6MB, time=17.72 x[1] = 0.162 y2[1] (analytic) = 0.16129234122838741960094755077078 y2[1] (numeric) = 0.16129234122838741960094755077083 absolute error = 5e-32 relative error = 3.0999612020759737140576118841411e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98690667272091409029573863718748 y1[1] (numeric) = 0.98690667272091409029573863718748 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.6MB, time=17.96 x[1] = 0.163 y2[1] (analytic) = 0.16227916709046000278226371641693 y2[1] (numeric) = 0.16227916709046000278226371641698 absolute error = 5e-32 relative error = 3.0811102186720169758233241157470e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98674488695327251905638030119956 y1[1] (numeric) = 0.98674488695327251905638030119956 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.6MB, time=18.19 x[1] = 0.164 y2[1] (analytic) = 0.1632658306733790187670505293435 y2[1] (numeric) = 0.16326583067337901876705052934355 absolute error = 5e-32 relative error = 3.0624901606036203697306847941525e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98658211444082622328234139023756 y1[1] (numeric) = 0.98658211444082622328234139023756 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.6MB, time=18.42 x[1] = 0.165 y2[1] (analytic) = 0.16425233099048096685825450728289 y2[1] (numeric) = 0.16425233099048096685825450728294 absolute error = 5e-32 relative error = 3.0440968294628151037097848810189e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98641835534634770185554209329493 y1[1] (numeric) = 0.98641835534634770185554209329493 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.6MB, time=18.66 x[1] = 0.166 y2[1] (analytic) = 0.16523866705526561216228457724819 y2[1] (numeric) = 0.16523866705526561216228457724824 absolute error = 5e-32 relative error = 3.0259261280095556579241856402078e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98625360983359603560791308551389 y1[1] (numeric) = 0.98625360983359603560791308551389 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.6MB, time=18.89 memory used=312.8MB, alloc=4.6MB, time=19.13 x[1] = 0.167 y2[1] (analytic) = 0.16622483788139697208916476077408 y2[1] (numeric) = 0.16622483788139697208916476077413 absolute error = 5e-32 relative error = 3.0079740571427407921695119892411e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98608787806731672356232834284434 y1[1] (numeric) = 0.98608787806731672356232834284434 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.6MB, time=19.36 x[1] = 0.168 y2[1] (analytic) = 0.16721084248270430268843456923034 y2[1] (numeric) = 0.16721084248270430268843456923039 absolute error = 5e-32 relative error = 2.9902367129794123791800299871764e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98592116021324151818711984796102 y1[1] (numeric) = 0.98592116021324151818711984796102 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.6MB, time=19.60 x[1] = 0.169 y2[1] (analytic) = 0.16819667987318308481981077338977 y2[1] (numeric) = 0.16819667987318308481981077338982 absolute error = 5e-32 relative error = 2.9727102840376513254963121267443e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98575345643808825966433893291046 y1[1] (numeric) = 0.98575345643808825966433893291046 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.6MB, time=19.83 x[1] = 0.17 y2[1] (analytic) = 0.16918234906699601015762437667085 y2[1] (numeric) = 0.1691823490669960101576243766709 absolute error = 5e-32 relative error = 2.9553910485189006998222702989205e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9855847669095607091719299902125 y1[1] (numeric) = 0.98558476690956070917192999021251 absolute error = 1e-32 relative error = 1.0146260713176810517259565757587e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.6MB, time=20.07 x[1] = 0.171 y2[1] (analytic) = 0.1701678490784739670280467877005 y2[1] (numeric) = 0.17016784907847396702804678770055 absolute error = 5e-32 relative error = 2.9382753716856459492710558963929e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98541509179634838117998327022891 y1[1] (numeric) = 0.98541509179634838117998327022891 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.6MB, time=20.30 memory used=335.6MB, alloc=4.6MB, time=20.54 x[1] = 0.172 y2[1] (analytic) = 0.17115317892211702607811935505273 y2[1] (numeric) = 0.17115317892211702607811935505278 absolute error = 5e-32 relative error = 2.9213597033305713917877497864678e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98524443126812637476123446853214 y1[1] (numeric) = 0.98524443126812637476123446853214 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.6MB, time=20.78 x[1] = 0.173 y2[1] (analytic) = 0.17213833761259542577560059521592 y2[1] (numeric) = 0.17213833761259542577560059521597 absolute error = 5e-32 relative error = 2.9046405753334916325379291744553e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98507278549555520391597979276082 y1[1] (numeric) = 0.98507278549555520391597979276082 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.6MB, time=21.01 x[1] = 0.174 y2[1] (analytic) = 0.17312332416475055773864561402361 y2[1] (numeric) = 0.17312332416475055773864561402366 absolute error = 5e-32 relative error = 2.8881145993025267291643714528634e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98490015465028062691157618403252 y1[1] (numeric) = 0.98490015465028062691157618403252 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.6MB, time=21.24 x[1] = 0.175 y2[1] (analytic) = 0.17410813759359595189433239195141 y2[1] (numeric) = 0.17410813759359595189433239195146 absolute error = 5e-32 relative error = 2.8717784642961513559615079167125e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98472653890493347463669735339954 y1[1] (numeric) = 0.98472653890493347463669735339955 absolute error = 1e-32 relative error = 1.0155103579436900310860316496696e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.6MB, time=21.47 x[1] = 0.176 y2[1] (analytic) = 0.17509277691431826146504977483591 y2[1] (numeric) = 0.17509277691431826146504977483596 absolute error = 5e-32 relative error = 2.8556289346229013874695579649332e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98455193843312947797051727907732 y1[1] (numeric) = 0.98455193843312947797051727907733 absolute error = 1e-32 relative error = 1.0156904485825861288648277975906e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.6MB, time=21.71 x[1] = 0.177 y2[1] (analytic) = 0.17607724114227824778176218370968 y2[1] (numeric) = 0.17607724114227824778176218370973 absolute error = 5e-32 relative error = 2.8396628477156667041145082348994e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98437635340946909416699379524751 y1[1] (numeric) = 0.98437635340946909416699379524752 absolute error = 1e-32 relative error = 1.0158716191590920594909590187708e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=358.5MB, alloc=4.6MB, time=21.94 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.6MB, time=22.18 x[1] = 0.178 y2[1] (analytic) = 0.17706152929301176492316623056969 y2[1] (numeric) = 0.17706152929301176492316623056975 absolute error = 6e-32 relative error = 3.3886525344931644646353271200804e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98419978400953733225442588813777 y1[1] (numeric) = 0.98419978400953733225442588813778 absolute error = 1e-32 relative error = 1.0160538706136411391933024975140e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.6MB, time=22.41 x[1] = 0.179 y2[1] (analytic) = 0.17804564038223074417975460100464 y2[1] (numeric) = 0.17804564038223074417975460100469 absolute error = 5e-32 relative error = 2.8082687052970988950786659401376e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98402223040990357745045929980641 y1[1] (numeric) = 0.98402223040990357745045929980641 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.6MB, time=22.65 x[1] = 0.18 y2[1] (analytic) = 0.17902957342582417834180273969921 y2[1] (numeric) = 0.17902957342582417834180273969926 absolute error = 5e-32 relative error = 2.7928346721284056824311567640715e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98384369278812141459271602461153 y1[1] (numeric) = 0.98384369278812141459271602461154 absolute error = 1e-32 relative error = 1.0164216199486862747130581631310e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.6MB, time=22.88 x[1] = 0.181 y2[1] (analytic) = 0.18001332743985910581029405091082 y2[1] (numeric) = 0.18001332743985910581029405091087 absolute error = 5e-32 relative error = 2.7775721226365624019241711735312e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98366417132272845058522426772069 y1[1] (numeric) = 0.98366417132272845058522426772069 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.6MB, time=23.12 x[1] = 0.182 y2[1] (analytic) = 0.18099690144058159452979950307546 y2[1] (numeric) = 0.18099690144058159452979950307551 absolute error = 5e-32 relative error = 2.7624782304029776531654387248195e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98348366619324613586082641921602 y1[1] (numeric) = 0.98348366619324613586082641921602 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.6MB, time=23.35 memory used=385.2MB, alloc=4.6MB, time=23.59 x[1] = 0.183 y2[1] (analytic) = 0.18198029444441772574232770474512 y2[1] (numeric) = 0.18198029444441772574232770474517 absolute error = 5e-32 relative error = 2.7475502307900435366341437073610e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98330217758017958485974358137227 y1[1] (numeric) = 0.98330217758017958485974358137228 absolute error = 1e-32 relative error = 1.0169813743938941451098394484078e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.6MB, time=23.82 x[1] = 0.184 y2[1] (analytic) = 0.18296350546797457756116169808868 y2[1] (numeric) = 0.18296350546797457756116169808873 absolute error = 5e-32 relative error = 2.7327854192623053316311387016763e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98311970566501739552447617052807 y1[1] (numeric) = 0.98311970566501739552447617052808 absolute error = 1e-32 relative error = 1.0171701312034674033329241399744e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.6MB, time=24.06 x[1] = 0.185 y2[1] (analytic) = 0.18394653352804120836369889620145 y2[1] (numeric) = 0.1839465335280412083636988962015 absolute error = 5e-32 relative error = 2.7181811497620797295929628809550e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98293625063023146781122109863481 y1[1] (numeric) = 0.98293625063023146781122109863481 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.6MB, time=24.29 x[1] = 0.186 y2[1] (analytic) = 0.18492937764158964000231077146534 y2[1] (numeric) = 0.18492937764158964000231077146539 absolute error = 5e-32 relative error = 2.7037348331374724835936761169047e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98275181265927682121798702305087 y1[1] (numeric) = 0.98275181265927682121798702305088 absolute error = 1e-32 relative error = 1.0175509087020154702940004460262e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.6MB, time=24.53 x[1] = 0.187 y2[1] (analytic) = 0.18591203682577584083223908418196 y2[1] (numeric) = 0.18591203682577584083223908418201 absolute error = 5e-32 relative error = 2.6894439356208339985666098852970e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98256639193659141132959013645082 y1[1] (numeric) = 0.98256639193659141132959013645083 absolute error = 1e-32 relative error = 1.0177429313748944538576970335856e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.6MB, time=24.76 x[1] = 0.188 y2[1] (analytic) = 0.18689451009794070855554562366427 y2[1] (numeric) = 0.18689451009794070855554562366432 absolute error = 5e-32 relative error = 2.6753059773557748538193492962713e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98237998864759594537971395183828 y1[1] (numeric) = 0.98237998864759594537971395183828 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 memory used=408.1MB, alloc=4.6MB, time=25.00 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.6MB, time=25.23 x[1] = 0.189 y2[1] (analytic) = 0.18787679647561105288013261791901 y2[1] (numeric) = 0.18787679647561105288013261791905 absolute error = 4e-32 relative error = 2.1290548247767541934683710290399e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98219260297869369683021752058749 y1[1] (numeric) = 0.98219260297869369683021752058749 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.6MB, time=25.47 x[1] = 0.19 y2[1] (analytic) = 0.18885889497650057799285115298131 y2[1] (numeric) = 0.18885889497650057799285115298135 absolute error = 4e-32 relative error = 2.1179833761590704274770212663126e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98200423511727031896787750418991 y1[1] (numeric) = 0.98200423511727031896787750418992 absolute error = 1e-32 relative error = 1.0183255471200494754242006144117e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.6MB, time=25.70 x[1] = 0.191 y2[1] (analytic) = 0.18984080461851086484571512887505 y2[1] (numeric) = 0.1898408046185108648457151288751 absolute error = 5e-32 relative error = 2.6337857185380173453582594735157e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98181488525169365751875050294814 y1[1] (numeric) = 0.98181488525169365751875050294814 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.6MB, time=25.94 x[1] = 0.192 y2[1] (analytic) = 0.19082252441973235325423846606677 y2[1] (numeric) = 0.19082252441973235325423846606682 absolute error = 5e-32 relative error = 2.6202357479571032370847657268204e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98162455357131356228034302723921 y1[1] (numeric) = 0.98162455357131356228034302723921 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.6MB, time=26.17 x[1] = 0.193 y2[1] (analytic) = 0.19180405339844532380691346415776 y2[1] (numeric) = 0.19180405339844532380691346415781 absolute error = 5e-32 relative error = 2.6068270776390837838106857765799e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98143324026646169777177747916177 y1[1] (numeric) = 0.98143324026646169777177747916177 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.6MB, time=26.41 memory used=434.8MB, alloc=4.6MB, time=26.64 x[1] = 0.194 y2[1] (analytic) = 0.1927853905731208795848484034179 y2[1] (numeric) = 0.19278539057312087958484840341795 absolute error = 5e-32 relative error = 2.5935575227644482359339519489016e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98124094552845135290214349438516 y1[1] (numeric) = 0.98124094552845135290214349438516 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.6MB, time=26.88 x[1] = 0.195 y2[1] (analytic) = 0.19376653496242192769058266960535 y2[1] (numeric) = 0.1937665349624219276905826696054 absolute error = 5e-32 relative error = 2.5804249433317646677716829163615e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98104766954957724965722497583334 y1[1] (numeric) = 0.98104766954957724965722497583334 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.6MB, time=27.12 x[1] = 0.196 y2[1] (analytic) = 0.19474748558520416058509787333882 y2[1] (numeric) = 0.19474748558520416058509787333887 absolute error = 5e-32 relative error = 2.5674272430143623954294863762027e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98085341252311535080479413246059 y1[1] (numeric) = 0.98085341252311535080479413246059 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.6MB, time=27.35 x[1] = 0.197 y2[1] (analytic) = 0.19572824146051703723204362709306 y2[1] (numeric) = 0.19572824146051703723204362709311 absolute error = 5e-32 relative error = 2.5545623680518362541269401604753e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98065817464332266661866481780904 y1[1] (numeric) = 0.98065817464332266661866481780903 absolute error = 1e-32 relative error = 1.0197233101775878134712231934977e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.6MB, time=27.59 x[1] = 0.198 y2[1] (analytic) = 0.19670880160760476404819683567353 y2[1] (numeric) = 0.19670880160760476404819683567358 absolute error = 5e-32 relative error = 2.5418283061751416591442963873590e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9804619561054370606216984442784 y1[1] (numeric) = 0.9804619561054370606216984442784 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.6MB, time=27.82 memory used=457.7MB, alloc=4.6MB, time=28.06 x[1] = 0.199 y2[1] (analytic) = 0.1976891650459072756591735497928 y2[1] (numeric) = 0.19768916504590727565917354979285 absolute error = 5e-32 relative error = 2.5292230855640988650413057475668e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98026475710567705434795673008606 y1[1] (numeric) = 0.98026475710567705434795673008605 absolute error = 1e-32 relative error = 1.0201325639336387930542160760853e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.6MB, time=28.29 x[1] = 0.2 y2[1] (analytic) = 0.19866933079506121545941262711839 y2[1] (numeric) = 0.19866933079506121545941262711844 absolute error = 5e-32 relative error = 2.5167447738361721012130481837629e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.98006657784124163112419651674817 y1[1] (numeric) = 0.98006657784124163112419651674816 absolute error = 1e-32 relative error = 1.0203388449411926897924327768492e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.6MB, time=28.52 x[1] = 0.201 y2[1] (analytic) = 0.19964929787490091597545064089029 y2[1] (numeric) = 0.19964929787490091597545064089034 absolute error = 5e-32 relative error = 2.5043914770654344089893772546519e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97986741851031003887090287557097 y1[1] (numeric) = 0.97986741851031003887090287557096 absolute error = 1e-32 relative error = 1.0205462301423364743683220232069e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.6MB, time=28.76 x[1] = 0.202 y2[1] (analytic) = 0.20062906530545937903150767291479 y2[1] (numeric) = 0.20062906530545937903150767291485 absolute error = 6e-32 relative error = 2.9905936065968065693439906962999e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97966727931204159192305770210243 y1[1] (numeric) = 0.97966727931204159192305770210242 absolute error = 1e-32 relative error = 1.0207547206253910946566144738978e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.6MB, time=28.99 x[1] = 0.203 y2[1] (analytic) = 0.20160863210696925571640382543065 y2[1] (numeric) = 0.20160863210696925571640382543071 absolute error = 6e-32 relative error = 2.9760630471499491692462707270234e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97946616044657547187084197775936 y1[1] (numeric) = 0.97946616044657547187084197775935 absolute error = 1e-32 relative error = 1.0209643174850087502316977408038e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.6MB, time=29.23 x[1] = 0.204 y2[1] (analytic) = 0.20258799729986382615082648501258 y2[1] (numeric) = 0.20258799729986382615082648501264 absolute error = 6e-32 relative error = 2.9616759531508696286151854503810e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97926406211503052742047085791098 y1[1] (numeric) = 0.97926406211503052742047085791097 absolute error = 1e-32 relative error = 1.0211750218221872198667318869741e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=480.6MB, alloc=4.6MB, time=29.47 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.6MB, time=29.70 x[1] = 0.205 y2[1] (analytic) = 0.20356715990477797905396857132664 y2[1] (numeric) = 0.2035671599047779790539685713267 absolute error = 6e-32 relative error = 2.9474302253893027866527504965771e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97906098451950507327536172556728 y1[1] (numeric) = 0.97906098451950507327536172556727 absolute error = 1e-32 relative error = 1.0213868347442842820643752835181e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.6MB, time=29.93 x[1] = 0.206 y2[1] (analytic) = 0.20454611894254919110855820418075 y2[1] (numeric) = 0.20454611894254919110855820418081 absolute error = 6e-32 relative error = 2.9333238054177983467961801486221e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9788569278630766880378363294873 y1[1] (numeric) = 0.97885692786307668803783632948729 absolute error = 1e-32 relative error = 1.0215997573650322289777602930288e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.6MB, time=30.17 x[1] = 0.207 y2[1] (analytic) = 0.20552487343421850612330042392233 y2[1] (numeric) = 0.20552487343421850612330042392239 absolute error = 6e-32 relative error = 2.9193546745671127327026468641512e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97865189234980201113155910498837 y1[1] (numeric) = 0.97865189234980201113155910498837 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.6MB, time=30.40 x[1] = 0.208 y2[1] (analytic) = 0.20650342240103151399175180282299 y2[1] (numeric) = 0.20650342240103151399175180282305 absolute error = 6e-32 relative error = 2.9055208529900031070226668496727e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97844587818471653874491475500107 y1[1] (numeric) = 0.97844587818471653874491475500106 absolute error = 1e-32 relative error = 1.0220289361893702539671306987524e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.6MB, time=30.64 x[1] = 0.209 y2[1] (analytic) = 0.20748176486443932944664898865714 y2[1] (numeric) = 0.2074817648644393294466489886572 absolute error = 6e-32 relative error = 2.8918203987324722843572920053212e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97823888557383441879552914797525 y1[1] (numeric) = 0.97823888557383441879552914797525 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.6MB, time=30.87 memory used=507.3MB, alloc=4.6MB, time=31.11 x[1] = 0.21 y2[1] (analytic) = 0.20845989984609957060871242622764 y2[1] (numeric) = 0.2084598998460995706087124262277 absolute error = 6e-32 relative error = 2.8782514068315495085983108012333e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97803091472414824491613856809935 y1[1] (numeric) = 0.97803091472414824491613856809934 absolute error = 1e-32 relative error = 1.0224625673331073524464086165795e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.6MB, time=31.34 x[1] = 0.211 y2[1] (analytic) = 0.20943782636787733732894670811626 y2[1] (numeric) = 0.20943782636787733732894670811632 absolute error = 6e-32 relative error = 2.8648120084387267579237056876084e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97782196584362884946201333194623 y1[1] (numeric) = 0.97782196584362884946201333194622 absolute error = 1e-32 relative error = 1.0226810553772299008291453097415e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.6MB, time=31.58 x[1] = 0.212 y2[1] (analytic) = 0.21041554345184618932345921244009 y2[1] (numeric) = 0.21041554345184618932345921244015 absolute error = 6e-32 relative error = 2.8515003699682034609745210268973e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97761203914122509554014276410505 y1[1] (numeric) = 0.97761203914122509554014276410505 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.6MB, time=31.81 x[1] = 0.213 y2[1] (analytic) = 0.2113930501202891240998188928769 y2[1] (numeric) = 0.21139305012028912409981889287695 absolute error = 5e-32 relative error = 2.3652622435576036036004180859693e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97740113482686366806038950259663 y1[1] (numeric) = 0.97740113482686366806038950259662 absolute error = 1e-32 relative error = 1.0231213821714453843335760579166e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.6MB, time=32.04 x[1] = 0.214 y2[1] (analytic) = 0.21237034539569955467397729468196 y2[1] (numeric) = 0.21237034539569955467397729468202 absolute error = 6e-32 relative error = 2.8252532098210254498225507640244e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97718925311144886380882208290055 y1[1] (numeric) = 0.97718925311144886380882208290055 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.6MB, time=32.28 x[1] = 0.215 y2[1] (analytic) = 0.21334742830078228707677407985706 y2[1] (numeric) = 0.21334742830078228707677407985712 absolute error = 6e-32 relative error = 2.8123141899517331231565278462172e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97697639420686238054343572724421 y1[1] (numeric) = 0.97697639420686238054343572724421 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=530.2MB, alloc=4.6MB, time=32.52 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.6MB, time=32.76 x[1] = 0.216 y2[1] (analytic) = 0.21432429785845449764904955504731 y2[1] (numeric) = 0.21432429785845449764904955504736 absolute error = 5e-32 relative error = 2.3329132767308230338683587696005e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97676255832596310511247224341507 y1[1] (numeric) = 0.97676255832596310511247224341507 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.6MB, time=33.00 x[1] = 0.217 y2[1] (analytic) = 0.21530095309184671012438690713494 y2[1] (numeric) = 0.21530095309184671012438690713499 absolute error = 5e-32 relative error = 2.3223306391342428055785476454432e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97654774568258690059555091475888 y1[1] (numeric) = 0.97654774568258690059555091475888 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.6MB, time=33.23 x[1] = 0.218 y2[1] (analytic) = 0.21627739302430377249850706386915 y2[1] (numeric) = 0.2162773930243037724985070638692 absolute error = 5e-32 relative error = 2.3118458799982549432751464213592e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97633195649154639246782324021503 y1[1] (numeric) = 0.97633195649154639246782324021504 absolute error = 1e-32 relative error = 1.0242417994731062950624582262842e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.6MB, time=33.46 x[1] = 0.219 y2[1] (analytic) = 0.21725361667938583368433931021855 y2[1] (numeric) = 0.21725361667938583368433931021861 absolute error = 6e-32 relative error = 2.7617491905115481427810280168860e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97611519096863075378736536021661 y1[1] (numeric) = 0.97611519096863075378736536021661 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.6MB, time=33.70 x[1] = 0.22 y2[1] (analytic) = 0.21822962308086931995179100545701 y2[1] (numeric) = 0.21822962308086931995179100545707 absolute error = 6e-32 relative error = 2.7493975910761578254322454743429e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9758974493306054894060229810447 y1[1] (numeric) = 0.9758974493306054894060229810447 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.6MB, time=33.93 memory used=556.9MB, alloc=4.6MB, time=34.17 x[1] = 0.221 y2[1] (analytic) = 0.21920541125274791115123996129451 y2[1] (numeric) = 0.21920541125274791115123996129456 absolute error = 5e-32 relative error = 2.2809655890451112630654473036541e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97567873179521221920392458677419 y1[1] (numeric) = 0.97567873179521221920392458677419 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.6MB, time=34.40 x[1] = 0.222 y2[1] (analytic) = 0.22018098021923351671977325764203 y2[1] (numeric) = 0.22018098021923351671977325764208 absolute error = 5e-32 relative error = 2.2708591791268780626947750128358e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97545903858116846034787970427966 y1[1] (numeric) = 0.97545903858116846034787970427966 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.6MB, time=34.63 x[1] = 0.223 y2[1] (analytic) = 0.221156329004757251469196489853 y2[1] (numeric) = 0.22115632900475725146919648985305 absolute error = 5e-32 relative error = 2.2608441831626016711826744745465e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97523836990816740857387996288501 y1[1] (numeric) = 0.97523836990816740857387996288501 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=568.4MB, alloc=4.6MB, time=34.87 x[1] = 0.224 y2[1] (analytic) = 0.22213145663397041115483765951328 y2[1] (numeric) = 0.22213145663397041115483765951333 absolute error = 5e-32 relative error = 2.2509193770961629001610403686333e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97501672599687771849392166613751 y1[1] (numeric) = 0.97501672599687771849392166613752 absolute error = 1e-32 relative error = 1.0256234312058378833097624131908e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.6MB, time=35.11 x[1] = 0.225 y2[1] (analytic) = 0.2231063621317454478241701400572 y2[1] (numeric) = 0.22310636213174544782417014005725 absolute error = 5e-32 relative error = 2.2410835586335608079003891057243e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97479410706894328292736956886549 y1[1] (numeric) = 0.9747941070689432829273695688655 absolute error = 1e-32 relative error = 1.0258576582975526802407957225818e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.6MB, time=35.34 memory used=579.8MB, alloc=4.6MB, time=35.58 x[1] = 0.226 y2[1] (analytic) = 0.22408104452317694494427936866789 y2[1] (numeric) = 0.22408104452317694494427936866794 absolute error = 5e-32 relative error = 2.2313355467614506718371546819434e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9745705133469830112570825281373 y1[1] (numeric) = 0.97457051334698301125708252813731 absolute error = 1e-32 relative error = 1.0260930187244061985416703970041e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.6MB, time=35.82 x[1] = 0.227 y2[1] (analytic) = 0.22505550283358259230719813707651 y2[1] (numeric) = 0.22505550283358259230719813707656 absolute error = 5e-32 relative error = 2.2216741812784078334062357423122e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97434594505459060681052267197768 y1[1] (numeric) = 0.97434594505459060681052267197769 absolute error = 1e-32 relative error = 1.0263295137375175806345868771829e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.6MB, time=36.05 x[1] = 0.228 y2[1] (analytic) = 0.2260297360885041607121355760063 y2[1] (numeric) = 0.22602973608850416071213557600636 absolute error = 6e-32 relative error = 2.6545179868062320502929165659443e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97412040241633434326607070471358 y1[1] (numeric) = 0.97412040241633434326607070471359 absolute error = 1e-32 relative error = 1.0265671445947241766491921447821e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.6MB, time=36.28 x[1] = 0.229 y2[1] (analytic) = 0.22700374331370847642362515111377 y2[1] (numeric) = 0.22700374331370847642362515111383 absolute error = 6e-32 relative error = 2.6431282200083734879599974447961e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97389388565775684008477094261565 y1[1] (numeric) = 0.97389388565775684008477094261566 absolute error = 1e-32 relative error = 1.0268059125605983115642842761920e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.6MB, time=36.51 x[1] = 0.23 y2[1] (analytic) = 0.22797752353518839540461721236007 y2[1] (numeric) = 0.22797752353518839540461721236013 absolute error = 6e-32 relative error = 2.6318383965925914177221340142687e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9736663950053748369677306480716 y1[1] (numeric) = 0.97366639500537483696773064807161 absolute error = 1e-32 relative error = 1.0270458189064641551739991395066e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.6MB, time=36.75 x[1] = 0.231 y2[1] (analytic) = 0.22895107577916377732354186380137 y2[1] (numeric) = 0.22895107577916377732354186380143 absolute error = 6e-32 relative error = 2.6206472188789094521869972439790e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97343793068667896733939920487326 y1[1] (numeric) = 0.97343793068667896733939920487328 absolute error = 2e-32 relative error = 2.0545737298208293906155630166519e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=602.7MB, alloc=4.6MB, time=36.99 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.6MB, time=37.23 x[1] = 0.232 y2[1] (analytic) = 0.22992439907208245933436814681645 y2[1] (numeric) = 0.2299243990720824593343681468165 absolute error = 5e-32 relative error = 2.1746278429687119762432133130018e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97320849293013353085695365131938 y1[1] (numeric) = 0.9732084929301335308569536513194 absolute error = 2e-32 relative error = 2.0550581037146576294729761161035e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.6MB, time=37.46 x[1] = 0.233 y2[1] (analytic) = 0.23089749244062122962868575679341 y2[1] (numeric) = 0.23089749244062122962868575679347 absolute error = 6e-32 relative error = 2.5985557212333046166284255435585e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97297808196517626494601806172955 y1[1] (numeric) = 0.97297808196517626494601806172957 absolute error = 2e-32 relative error = 2.0555447620777769444000659864397e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.6MB, time=37.70 x[1] = 0.234 y2[1] (analytic) = 0.2318703549116868007588357412751 y2[1] (numeric) = 0.23187035491168680075883574127515 absolute error = 5e-32 relative error = 2.1563774299238753035420026805565e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97274669802221811536294524063099 y1[1] (numeric) = 0.97274669802221811536294524063101 absolute error = 2e-32 relative error = 2.0560337075071919759901371534995e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.6MB, time=37.93 x[1] = 0.235 y2[1] (analytic) = 0.2328429855124167827311168565134 y2[1] (numeric) = 0.23284298551241678273111685651346 absolute error = 6e-32 relative error = 2.5768437845768984550100598248086e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97251434133264300578389016731721 y1[1] (numeric) = 0.97251434133264300578389016731723 absolute error = 2e-32 relative error = 2.0565249426135828691285854870897e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.6MB, time=38.16 x[1] = 0.236 y2[1] (analytic) = 0.23381538327018065586809448930743 y2[1] (numeric) = 0.23381538327018065586809448930749 absolute error = 6e-32 relative error = 2.5661271367533678789263393621021e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97228101212880760642090560168606 y1[1] (numeric) = 0.97228101212880760642090560168608 absolute error = 2e-32 relative error = 2.0570184700213402650641888651241e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.6MB, time=38.40 memory used=629.4MB, alloc=4.6MB, time=38.64 x[1] = 0.237 y2[1] (analytic) = 0.23478754721258074343903928189747 y2[1] (numeric) = 0.23478754721258074343903928189753 absolute error = 6e-32 relative error = 2.5555018020472334806623901118904e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97204671064404110166529123524216 y1[1] (numeric) = 0.97204671064404110166529123524218 absolute error = 2e-32 relative error = 2.0575142923686005052687688307275e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.6MB, time=38.88 x[1] = 0.238 y2[1] (analytic) = 0.23575947636745318405752282955735 y2[1] (numeric) = 0.23575947636745318405752282955741 absolute error = 6e-32 relative error = 2.5449666297393870547206316952574e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97181143711264495675842874389526 y1[1] (numeric) = 0.97181143711264495675842874389528 absolute error = 2e-32 relative error = 2.0580124123072810479872307770368e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.6MB, time=39.11 x[1] = 0.239 y2[1] (analytic) = 0.23673116976286890384519805337042 y2[1] (numeric) = 0.23673116976286890384519805337047 absolute error = 5e-32 relative error = 2.1121004069757467286422912608354e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97157519176989268349033607170002 y1[1] (numeric) = 0.97157519176989268349033607170003 absolute error = 1e-32 relative error = 1.0292564162515580491931700864721e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.6MB, time=39.34 x[1] = 0.24 y2[1] (analytic) = 0.23770262642713458836079208448982 y2[1] (numeric) = 0.23770262642713458836079208448987 absolute error = 5e-32 relative error = 2.1034685544514591305546015880043e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97133797485202960492617524696338 y1[1] (numeric) = 0.97133797485202960492617524696339 absolute error = 1e-32 relative error = 1.0295077778178462266084903163054e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.6MB, time=39.57 x[1] = 0.241 y2[1] (analytic) = 0.23867384538879365429333973097121 y2[1] (numeric) = 0.23867384538879365429333973097126 absolute error = 5e-32 relative error = 2.0949090554330016886684616093755e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97109978659627261916094900419216 y1[1] (numeric) = 0.97109978659627261916094900419217 absolute error = 1e-32 relative error = 1.0297602921992427804555332729677e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.6MB, time=39.81 x[1] = 0.242 y2[1] (analytic) = 0.23964482567662722091868583402537 y2[1] (numeric) = 0.23964482567662722091868583402543 absolute error = 6e-32 relative error = 2.5037052158581972208006143503979e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9708606272408099621026224571645 y1[1] (numeric) = 0.9708606272408099621026224571645 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=652.3MB, alloc=4.6MB, time=40.05 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.6MB, time=40.29 x[1] = 0.243 y2[1] (analytic) = 0.24061556631965508131828505726935 y2[1] (numeric) = 0.2406155663196550813182850572694 absolute error = 5e-32 relative error = 2.0780035458543675747488316740560e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97062049702480096928390703998371 y1[1] (numeric) = 0.97062049702480096928390703998371 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.6MB, time=40.52 x[1] = 0.244 y2[1] (analytic) = 0.2415860663471366733593278902572 y2[1] (numeric) = 0.24158606634713667335932789025725 absolute error = 5e-32 relative error = 2.0696557858661706735003998204806e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97037939618837583670294490431084 y1[1] (numeric) = 0.97037939618837583670294490431084 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.6MB, time=40.75 x[1] = 0.245 y2[1] (analytic) = 0.2425563247885720504352218862454 y2[1] (numeric) = 0.24255632478857205043522188624545 absolute error = 5e-32 relative error = 2.0613768799301881202392041660041e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.97013732497263538069313293207151 y1[1] (numeric) = 0.97013732497263538069313293207151 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.6MB, time=40.99 x[1] = 0.246 y2[1] (analytic) = 0.24352634067370285196545739379243 y2[1] (numeric) = 0.24352634067370285196545739379248 absolute error = 5e-32 relative error = 2.0531659886022030221462616106336e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96989428361965079682232649379306 y1[1] (numeric) = 0.96989428361965079682232649379306 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=671.3MB, alloc=4.6MB, time=41.22 x[1] = 0.247 y2[1] (analytic) = 0.24449611303251327365388728240771 y2[1] (numeric) = 0.24449611303251327365388728240776 absolute error = 5e-32 relative error = 2.0450222860332737919064669017560e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96965027237246341782166405334813 y1[1] (numeric) = 0.96965027237246341782166405334813 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.6MB, time=41.45 memory used=679.0MB, alloc=4.6MB, time=41.69 x[1] = 0.248 y2[1] (analytic) = 0.24546564089523103750445040405111 y2[1] (numeric) = 0.24546564089523103750445040405116 absolute error = 5e-32 relative error = 2.0369449596956366291926410072072e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96940529147508447054425469025992 y1[1] (numeric) = 0.96940529147508447054425469025992 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.6MB, time=41.93 x[1] = 0.249 y2[1] (analytic) = 0.24643492329232836159336877484025 y2[1] (numeric) = 0.2464349232923283615933687748403 absolute error = 5e-32 relative error = 2.0289332101152127651349383548332e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96915934117249483195397158086133 y1[1] (numeric) = 0.96915934117249483195397158086133 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.6MB, time=42.16 x[1] = 0.25 y2[1] (analytic) = 0.24740395925452292959684870484939 y2[1] (numeric) = 0.24740395925452292959684870484943 absolute error = 4e-32 relative error = 1.6167890004884284291332797332231e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96891242171064478414459544949419 y1[1] (numeric) = 0.96891242171064478414459544949419 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.6MB, time=42.39 x[1] = 0.251 y2[1] (analytic) = 0.24837274781277886007331634837941 y2[1] (numeric) = 0.24837274781277886007331634837945 absolute error = 4e-32 relative error = 1.6104826456303345999419089073192e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9686645333364537683895529705847 y1[1] (numeric) = 0.9686645333364537683895529705847 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.6MB, time=42.62 x[1] = 0.252 y2[1] (analytic) = 0.24934128799830767549921839254425 y2[1] (numeric) = 0.2493412879983076754992183925443 absolute error = 5e-32 relative error = 2.0052836175426894826860101397800e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96841567629781013822249607183617 y1[1] (numeric) = 0.96841567629781013822249607183617 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.6MB, time=42.86 x[1] = 0.253 y2[1] (analytic) = 0.25030957884256927105741884845382 y2[1] (numeric) = 0.25030957884256927105741884845386 absolute error = 4e-32 relative error = 1.5980211458530623546664444646677e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96816585084357091154896905793918 y1[1] (numeric) = 0.96816585084357091154896905793918 absolute error = 0 memory used=701.9MB, alloc=4.6MB, time=43.10 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.6MB, time=43.34 x[1] = 0.254 y2[1] (analytic) = 0.2512776193772728831772231566772 y2[1] (numeric) = 0.25127761937727288317722315667724 absolute error = 4e-32 relative error = 1.5918648106874674470851884246648e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96791505722356152178941144311144 y1[1] (numeric) = 0.96791505722356152178941144311144 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.6MB, time=43.57 x[1] = 0.255 y2[1] (analytic) = 0.25224540863437805782506106704299 y2[1] (numeric) = 0.25224540863437805782506106704303 absolute error = 4e-32 relative error = 1.5857573073997460407677699657068e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96766329568857556805374534944369 y1[1] (numeric) = 0.96766329568857556805374534944369 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.6MB, time=43.80 x[1] = 0.256 y2[1] (analytic) = 0.2532129456460956185448600021744 y2[1] (numeric) = 0.25321294564609561854486000217444 absolute error = 4e-32 relative error = 1.5796980639333585503255329464385e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96741056649037456434779729644346 y1[1] (numeric) = 0.96741056649037456434779729644346 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.6MB, time=44.04 x[1] = 0.257 y2[1] (analytic) = 0.25418022944488863424714086446645 y2[1] (numeric) = 0.25418022944488863424714086446649 absolute error = 4e-32 relative error = 1.5736865171361725174075139042305e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96715686988168768781180517533403 y1[1] (numeric) = 0.96715686988168768781180517533403 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.6MB, time=44.27 x[1] = 0.258 y2[1] (analytic) = 0.25514725906347338674586849749019 y2[1] (numeric) = 0.25514725906347338674586849749023 absolute error = 4e-32 relative error = 1.5677221125878972034642096832328e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9669022061162115259912621695806 y1[1] (numeric) = 0.9669022061162115259912621695806 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.6MB, time=44.51 memory used=728.6MB, alloc=4.6MB, time=44.75 x[1] = 0.259 y2[1] (analytic) = 0.25611403353482033804208926505403 y2[1] (numeric) = 0.25611403353482033804208926505407 absolute error = 4e-32 relative error = 1.5618043044315158394633792110645e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96664657544860982314035035077869 y1[1] (numeric) = 0.96664657544860982314035035077869 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.6MB, time=44.98 x[1] = 0.26 y2[1] (analytic) = 0.25708055189215509735338846436522 y2[1] (numeric) = 0.25708055189215509735338846436526 absolute error = 4e-32 relative error = 1.5559325552086079033359390319003e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96638997813451322555821764645006 y1[1] (numeric) = 0.96638997813451322555821764645006 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.6MB, time=45.21 x[1] = 0.261 y2[1] (analytic) = 0.25804681316895938788820054391467 y2[1] (numeric) = 0.2580468131689593878882005439147 absolute error = 3e-32 relative error = 1.1625797517738428211825091845988e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96613241443051902595835284344793 y1[1] (numeric) = 0.96613241443051902595835284344792 absolute error = 1e-32 relative error = 1.0350548072537696810652669310784e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.6MB, time=45.45 x[1] = 0.262 y2[1] (analytic) = 0.25901281639897201336400535185544 y2[1] (numeric) = 0.25901281639897201336400535185548 absolute error = 4e-32 relative error = 1.5443251247608438637474501249553e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96587388459419090687131425757517 y1[1] (numeric) = 0.96587388459419090687131425757516 absolute error = 1e-32 relative error = 1.0353318543446767699893385540080e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.6MB, time=45.68 x[1] = 0.263 y2[1] (analytic) = 0.25997856061618982426844389675928 y2[1] (numeric) = 0.25997856061618982426844389675931 absolute error = 3e-32 relative error = 1.1539413068868183164539142482061e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96561438888405868308106866666555 y1[1] (numeric) = 0.96561438888405868308106866666553 absolute error = 2e-32 relative error = 2.0712201713474466403121065860619e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.6MB, time=45.92 memory used=751.5MB, alloc=4.6MB, time=46.16 x[1] = 0.264 y2[1] (analytic) = 0.26094404485486868386238735971576 y2[1] (numeric) = 0.26094404485486868386238735971579 absolute error = 3e-32 relative error = 1.1496717626449508592499619053429e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9653539275596180430951980707674 y1[1] (numeric) = 0.96535392755961804309519807076738 absolute error = 2e-32 relative error = 2.0717790055051954921124663410533e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.6MB, time=46.39 x[1] = 0.265 y2[1] (analytic) = 0.26190926814952443392399335478576 y2[1] (numeric) = 0.2619092681495244339239933547858 absolute error = 4e-32 relative error = 1.5272464499867921401822881534778e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96509250088133028964923280920166 y1[1] (numeric) = 0.96509250088133028964923280920164 absolute error = 2e-32 relative error = 2.0723402142007981605562755841944e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.6MB, time=46.63 x[1] = 0.266 y2[1] (analytic) = 0.26287422953493386023278369383338 y2[1] (numeric) = 0.26287422953493386023278369383341 absolute error = 3e-32 relative error = 1.1412301636822578873920661190637e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96483010911062207924537053013933 y1[1] (numeric) = 0.96483010911062207924537053013932 absolute error = 1e-32 relative error = 1.0364519002436578559938278306555e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.6MB, time=46.86 x[1] = 0.267 y2[1] (analytic) = 0.26383892804613565779277817173887 y2[1] (numeric) = 0.2638389280461356577927781717389 absolute error = 3e-32 relative error = 1.1370573789912499563828822710051e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96456675250988516072584147395786 y1[1] (numeric) = 0.96456675250988516072584147395784 absolute error = 2e-32 relative error = 2.0734697674327142206663965213688e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.6MB, time=47.09 x[1] = 0.268 y2[1] (analytic) = 0.26480336271843139579371914893952 y2[1] (numeric) = 0.26480336271843139579371914893955 absolute error = 3e-32 relative error = 1.1329161265938817115695975932213e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96430243134247611288118149698917 y1[1] (numeric) = 0.96430243134247611288118149698916 absolute error = 1e-32 relative error = 1.0370190590599535092009394098472e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.6MB, time=47.33 x[1] = 0.269 y2[1] (analytic) = 0.26576753258738648230942197015403 y2[1] (numeric) = 0.26576753258738648230942197015406 absolute error = 3e-32 relative error = 1.1288060549734667444613188196938e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96403714587271608109367522736473 y1[1] (numeric) = 0.96403714587271608109367522736471 absolute error = 2e-32 relative error = 2.0746088556467971881910141351187e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=774.3MB, alloc=4.6MB, time=47.56 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.6MB, time=47.80 x[1] = 0.27 y2[1] (analytic) = 0.26673143668883112873228652102054 y2[1] (numeric) = 0.26673143668883112873228652102057 absolute error = 3e-32 relative error = 1.1247268178215527492773931171829e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9637708963658905130162327094922 y1[1] (numeric) = 0.96377089636589051301623270949219 absolute error = 1e-32 relative error = 1.0375909915631601514930305045560e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.6MB, time=48.03 x[1] = 0.271 y2[1] (analytic) = 0.26769507405886131394300548821702 y2[1] (numeric) = 0.26769507405886131394300548821705 absolute error = 3e-32 relative error = 1.1206780739418291128534822368237e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9635036830882488932869638582654 y1[1] (numeric) = 0.96350368308824889328696385826539 absolute error = 1e-32 relative error = 1.0378787518432437053629595128718e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.6MB, time=48.27 x[1] = 0.272 y2[1] (analytic) = 0.26865844373383974821450515343617 y2[1] (numeric) = 0.2686584437338397482145051534362 absolute error = 3e-32 relative error = 1.1166594871561541920496775767763e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96323550630700447727971600841062 y1[1] (numeric) = 0.96323550630700447727971600841061 absolute error = 1e-32 relative error = 1.0381677102352141333861486725854e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.6MB, time=48.50 x[1] = 0.273 y2[1] (analytic) = 0.26962154475039683684915481735437 y2[1] (numeric) = 0.2696215447503968368491548173544 absolute error = 3e-32 relative error = 1.1126707262126479277018643012367e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96296636629033402389084080840986 y1[1] (numeric) = 0.96296636629033402389084080840985 absolute error = 1e-32 relative error = 1.0384578683182174074499991923853e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.6MB, time=48.74 x[1] = 0.274 y2[1] (analytic) = 0.27058437614543164354828121646544 y2[1] (numeric) = 0.27058437614543164354828121646547 absolute error = 3e-32 relative error = 1.1087114646957970310468630753748e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96269626330737752736245767221169 y1[1] (numeric) = 0.96269626330737752736245767221168 absolute error = 1e-32 relative error = 1.0387492276790024589992260593720e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.6MB, time=48.97 memory used=801.1MB, alloc=4.6MB, time=49.21 x[1] = 0.275 y2[1] (analytic) = 0.27154693695611285351302456334528 y2[1] (numeric) = 0.27154693695611285351302456334531 absolute error = 3e-32 relative error = 1.1047813809385215135066388396712e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96242519762823794814248196544391 y1[1] (numeric) = 0.9624251976282379481424819654439 absolute error = 1e-32 relative error = 1.0390417899119431698247910750529e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.6MB, time=49.45 x[1] = 0.276 y2[1] (analytic) = 0.27250922621987973627557310957138 y2[1] (numeric) = 0.27250922621987973627557310957141 absolute error = 3e-32 relative error = 1.1008801579361528156187543010312e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96215316952398094278168706607751 y1[1] (numeric) = 0.9621531695239809427816870660775 absolute error = 1e-32 relative error = 1.0393355566190604888775408564490e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.6MB, time=49.68 x[1] = 0.277 y2[1] (analytic) = 0.27347124297444310825981340014308 y2[1] (numeric) = 0.27347124297444310825981340014311 absolute error = 3e-32 relative error = 1.0970074832622752275562243722136e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96188017926663459286807040245721 y1[1] (numeric) = 0.9618801792666345928680704024572 absolute error = 1e-32 relative error = 1.0396305294100446756971132525249e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.6MB, time=49.92 x[1] = 0.278 y2[1] (analytic) = 0.27443298625778629507043365883237 y2[1] (numeric) = 0.2744329862577862950704336588324 absolute error = 3e-32 relative error = 1.0931630489863836838254610233251e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96160622712918913299879453431011 y1[1] (numeric) = 0.9616062271291891329987945343101 absolute error = 1e-32 relative error = 1.0399267099022776710507260774222e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.6MB, time=50.15 x[1] = 0.279 y2[1] (analytic) = 0.27539445510816609350951801544215 y2[1] (numeric) = 0.27539445510816609350951801544218 absolute error = 3e-32 relative error = 1.0893465515933123600331269705123e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96133131338559667778997530476856 y1[1] (numeric) = 0.96133131338559667778997530476855 absolute error = 1e-32 relative error = 1.0402240997208555953805388055843e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.6MB, time=50.38 x[1] = 0.28 y2[1] (analytic) = 0.27635564856411373331966955845785 y2[1] (numeric) = 0.27635564856411373331966955845788 absolute error = 3e-32 relative error = 1.0855576919043898016729914701780e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96105543831077094792459005359648 y1[1] (numeric) = 0.96105543831077094792459005359646 absolute error = 2e-32 relative error = 2.0810454009972227513247622478529e-30 % Correct digits = 31 h = 0.001 memory used=823.9MB, alloc=4.6MB, time=50.62 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.6MB, time=50.86 x[1] = 0.281 y2[1] (analytic) = 0.27731656566443583865270047004946 y2[1] (numeric) = 0.27731656566443583865270047004949 absolute error = 3e-32 relative error = 1.0817961750002775752411582306367e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96077860218058699523877984368792 y1[1] (numeric) = 0.9607786021805869952387798436879 absolute error = 2e-32 relative error = 2.0816450277522750025655444172066e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.6MB, time=51.09 x[1] = 0.282 y2[1] (analytic) = 0.27827720544821538926292777481407 y2[1] (numeric) = 0.2782772054482153892629277748141 absolute error = 3e-32 relative error = 1.0780617101454506521211438170741e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96050080527188092684682061451294 y1[1] (numeric) = 0.96050080527188092684682061451292 absolute error = 2e-32 relative error = 2.0822470830036178190906230126467e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.6MB, time=51.33 x[1] = 0.283 y2[1] (analytic) = 0.27923756695481268142411350904312 y2[1] (numeric) = 0.27923756695481268142411350904315 absolute error = 3e-32 relative error = 1.0743540107142789170105736161186e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.96022204786244962830503913751647 y1[1] (numeric) = 0.96022204786244962830503913751645 absolute error = 2e-32 relative error = 2.0828515700636120028434117440175e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.6MB, time=51.56 x[1] = 0.284 y2[1] (analytic) = 0.28019764922386628856908839365443 y2[1] (numeric) = 0.28019764922386628856908839365446 absolute error = 3e-32 relative error = 1.0706727941186703365550279107632e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95994233023105048581495060953123 y1[1] (numeric) = 0.95994233023105048581495060953122 absolute error = 1e-32 relative error = 1.0417292461301377881669093671772e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.6MB, time=51.80 x[1] = 0.285 y2[1] (analytic) = 0.28115745129529402165109837124522 y2[1] (numeric) = 0.28115745129529402165109837124525 absolute error = 3e-32 relative error = 1.0670177817372374316253751126974e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95966165265740110746589568104396 y1[1] (numeric) = 0.95966165265740110746589568104395 absolute error = 1e-32 relative error = 1.0420339264686651694220910798325e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.6MB, time=52.03 memory used=850.6MB, alloc=4.6MB, time=52.27 x[1] = 0.286 y2[1] (analytic) = 0.28211697220929388922591364599979 y2[1] (numeric) = 0.28211697220929388922591364599982 absolute error = 3e-32 relative error = 1.0633886988459497695858133014184e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95938001542217904351745567665462 y1[1] (numeric) = 0.95938001542217904351745567665462 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.6MB, time=52.50 x[1] = 0.287 y2[1] (analytic) = 0.28307621100634505725374014442268 y2[1] (numeric) = 0.28307621100634505725374014442271 absolute error = 3e-32 relative error = 1.0597852745502362321654363005517e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95909741880702150572192572529021 y1[1] (numeric) = 0.95909741880702150572192572529021 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.6MB, time=52.73 x[1] = 0.288 y2[1] (analytic) = 0.28403516672720880861997359506588 y2[1] (numeric) = 0.28403516672720880861997359506591 absolute error = 3e-32 relative error = 1.0562072417185018213346857838671e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95881386309452508568712647767644 y1[1] (numeric) = 0.95881386309452508568712647767644 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.6MB, time=52.96 x[1] = 0.289 y2[1] (analytic) = 0.28499383841292950237383670657605 y2[1] (numeric) = 0.28499383841292950237383670657608 absolute error = 3e-32 relative error = 1.0526543369170247410233196967982e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95852934856824547227983604823229 y1[1] (numeric) = 0.95852934856824547227983604823229 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.6MB, time=53.20 x[1] = 0.29 y2[1] (analytic) = 0.28595222510483553268394020550437 y2[1] (numeric) = 0.2859522251048355326839402055044 absolute error = 3e-32 relative error = 1.0491263003462004376796670684356e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95824387551269716807012477793186 y1[1] (numeric) = 0.95824387551269716807012477793186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.6MB, time=53.43 memory used=873.5MB, alloc=4.6MB, time=53.67 x[1] = 0.291 y2[1] (analytic) = 0.28691032584454028750980877839799 y2[1] (numeric) = 0.28691032584454028750980877839802 absolute error = 3e-32 relative error = 1.0456228757781001986022294213089e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9579574442133532048168763737751 y1[1] (numeric) = 0.9579574442133532048168763737751 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.6MB, time=53.90 x[1] = 0.292 y2[1] (analytic) = 0.28786813967394310698841324672701 y2[1] (numeric) = 0.28786813967394310698841324672704 absolute error = 3e-32 relative error = 1.0421438104953127946752202036048e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95767005495664485799477993932263 y1[1] (numeric) = 0.95767005495664485799477993932263 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.6MB, time=54.14 x[1] = 0.293 y2[1] (analytic) = 0.28882566563523024153475058819466 y2[1] (numeric) = 0.28882566563523024153475058819469 absolute error = 3e-32 relative error = 1.0386888552310385145729131011315e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95738170802996136036307836927879 y1[1] (numeric) = 0.95738170802996136036307836927879 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.6MB, time=54.37 x[1] = 0.294 y2[1] (analytic) = 0.28978290277087580965551370393053 y2[1] (numeric) = 0.28978290277087580965551370393055 absolute error = 2e-32 relative error = 6.9017184274027051439410351875890e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95709240372164961457635953935068 y1[1] (numeric) = 0.95709240372164961457635953935068 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.6MB, time=54.61 x[1] = 0.295 y2[1] (analytic) = 0.29073985012364275547489311797684 y2[1] (numeric) = 0.29073985012364275547489311797686 absolute error = 2e-32 relative error = 6.8790019639532084860731128548838e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95680214232101390483767768056805 y1[1] (numeric) = 0.95680214232101390483767768056805 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.6MB, time=54.84 x[1] = 0.296 y2[1] (analytic) = 0.29169650673658380597155308334595 y2[1] (numeric) = 0.29169650673658380597155308334597 absolute error = 2e-32 relative error = 6.8564413827763035010565815181202e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9565109241183156075942932849186 y1[1] (numeric) = 0.9565109241183156075942932849186 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=896.4MB, alloc=4.6MB, time=55.08 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.6MB, time=55.32 x[1] = 0.297 y2[1] (analytic) = 0.29265287165304242792582485775268 y2[1] (numeric) = 0.2926528716530424279258248577527 absolute error = 2e-32 relative error = 6.8340351102760414028366108135360e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95621874940477290127632084653473 y1[1] (numeric) = 0.95621874940477290127632084653473 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=904.0MB, alloc=4.6MB, time=55.55 x[1] = 0.298 y2[1] (analytic) = 0.29360894391665378457616020190792 y2[1] (numeric) = 0.29360894391665378457616020190794 absolute error = 2e-32 relative error = 6.8117815939821513616839384463513e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95592561847256047507857469975975 y1[1] (numeric) = 0.95592561847256047507857469975976 absolute error = 1e-32 relative error = 1.0461064968609842370189411286174e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.6MB, time=55.79 x[1] = 0.299 y2[1] (analytic) = 0.29456472257134569198388844399979 y2[1] (numeric) = 0.29456472257134569198388844399982 absolute error = 3e-32 relative error = 1.0184518953295157222209899134082e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95563153161480923678590417222355 y1[1] (numeric) = 0.95563153161480923678590417222356 absolute error = 1e-32 relative error = 1.0464284265612476297779303508159e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.6MB, time=56.02 x[1] = 0.3 y2[1] (analytic) = 0.29552020666133957510532074568503 y2[1] (numeric) = 0.29552020666133957510532074568505 absolute error = 2e-32 relative error = 6.7677267236482451699209531029548e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95533648912560601964231022756805 y1[1] (numeric) = 0.95533648912560601964231022756806 absolute error = 1e-32 relative error = 1.0467516015380856009327908455870e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.6MB, time=56.25 x[1] = 0.301 y2[1] (analytic) = 0.29647539523115142357024549756582 y2[1] (numeric) = 0.29647539523115142357024549756584 absolute error = 2e-32 relative error = 6.7459223671518185903369715352226e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95504049129999328826413672868155 y1[1] (numeric) = 0.95504049129999328826413672868156 absolute error = 1e-32 relative error = 1.0470760235922648651553556551589e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.6MB, time=56.49 memory used=923.1MB, alloc=4.6MB, time=56.73 x[1] = 0.302 y2[1] (analytic) = 0.29743028732559274716585906573658 y2[1] (numeric) = 0.29743028732559274716585906573661 absolute error = 3e-32 relative error = 1.0086397141915618854100841480485e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.95474353843396884359763040822611 y1[1] (numeric) = 0.95474353843396884359763040822612 absolute error = 1e-32 relative error = 1.0474016945328204963890453285006e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.6MB, time=56.97 x[1] = 0.303 y2[1] (analytic) = 0.2983848819897715310251764055494 y2[1] (numeric) = 0.29838488198977153102517640554942 absolute error = 2e-32 relative error = 6.7027524540219798921377207460720e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95444563082448552692116458887338 y1[1] (numeric) = 0.95444563082448552692116458887339 absolute error = 1e-32 relative error = 1.0477286161770816843918665103297e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.6MB, time=57.20 x[1] = 0.304 y2[1] (analytic) = 0.29933917826909319051896635426711 y2[1] (numeric) = 0.29933917826909319051896635426713 absolute error = 2e-32 relative error = 6.6813840124932963469144207042997e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95414676876945092289242265100057 y1[1] (numeric) = 0.95414676876945092289242265100059 absolute error = 2e-32 relative error = 2.0961135807013952709233206390883e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.6MB, time=57.44 x[1] = 0.305 y2[1] (analytic) = 0.30029317520926152585025671074844 y2[1] (numeric) = 0.30029317520926152585025671074846 absolute error = 2e-32 relative error = 6.6601580225933711939616431032954e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95384695256772706164083820063833 y1[1] (numeric) = 0.95384695256772706164083820063835 absolute error = 2e-32 relative error = 2.0967724377753272361165087769283e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.6MB, time=57.67 x[1] = 0.306 y2[1] (analytic) = 0.30124687185627967635045450773953 y2[1] (numeric) = 0.30124687185627967635045450773955 absolute error = 2e-32 relative error = 6.6390730887129999246691597217107e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95354618251913011990558984520543 y1[1] (numeric) = 0.95354618251913011990558984520545 absolute error = 2e-32 relative error = 2.0974338072606943080840922951499e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.6MB, time=57.91 x[1] = 0.307 y2[1] (analytic) = 0.30220026725645107447612718073115 y2[1] (numeric) = 0.30220026725645107447612718073117 absolute error = 2e-32 relative error = 6.6181278334303192594347740093345e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95324445892443012121944943901075 y1[1] (numeric) = 0.95324445892443012121944943901077 absolute error = 2e-32 relative error = 2.0980976928590287125069033337796e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=946.0MB, alloc=4.6MB, time=58.14 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.6MB, time=58.38 x[1] = 0.308 y2[1] (analytic) = 0.30315336045638039950549063667997 y2[1] (numeric) = 0.30315336045638039950549063667998 absolute error = 1e-32 relative error = 3.2986604486077806514544984803300e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95294178208535063513878361464923 y1[1] (numeric) = 0.95294178208535063513878361464925 absolute error = 2e-32 relative error = 2.0987640982887128263251887501811e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.6MB, time=58.61 x[1] = 0.309 y2[1] (analytic) = 0.3041061505029745309336505261852 y2[1] (numeric) = 0.30410615050297453093365052618522 absolute error = 2e-32 relative error = 6.5766509381415406405753580251451e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95263815230456847552000937026516 y1[1] (numeric) = 0.95263815230456847552000937026519 absolute error = 3e-32 relative error = 3.1491495409275486639707446319845e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.6MB, time=58.85 x[1] = 0.31 y2[1] (analytic) = 0.30505863644344350156564332395896 y2[1] (numeric) = 0.30505863644344350156564332395898 absolute error = 2e-32 relative error = 6.5561166315997449231716170028411e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95233356988571339784280543620221 y1[1] (numeric) = 0.95233356988571339784280543620223 absolute error = 2e-32 relative error = 2.1001044836002303327454476474836e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.6MB, time=59.08 x[1] = 0.311 y2[1] (analytic) = 0.30601081732530145030632412462842 y2[1] (numeric) = 0.30601081732530145030632412462844 absolute error = 2e-32 relative error = 6.5357166700219028154506570746843e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95202803513336779558038209780341 y1[1] (numeric) = 0.95202803513336779558038209780344 absolute error = 3e-32 relative error = 3.1511677065053401599452838624770e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.6MB, time=59.32 x[1] = 0.312 y2[1] (analytic) = 0.30696269219636757464614836406167 y2[1] (numeric) = 0.30696269219636757464614836406169 absolute error = 2e-32 relative error = 6.5154497626069064197158482877813e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95172154835306639561711310406623 y1[1] (numeric) = 0.95172154835306639561711310406626 absolute error = 3e-32 relative error = 3.1521824899220105605467060196234e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.6MB, time=59.55 memory used=972.7MB, alloc=4.6MB, time=59.79 x[1] = 0.313 y2[1] (analytic) = 0.30791426010476708284189498051468 y2[1] (numeric) = 0.3079142601047670828418949805147 absolute error = 2e-32 relative error = 6.4953146350529684255131048315405e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95141410985129595271383424449514 y1[1] (numeric) = 0.95141410985129595271383424449517 absolute error = 3e-32 relative error = 3.1532010813555138074467692292650e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.6MB, time=60.03 x[1] = 0.314 y2[1] (analytic) = 0.30886552009893214579137883495571 y2[1] (numeric) = 0.30886552009893214579137883495573 absolute error = 2e-32 relative error = 6.4753100292948972877821378922601e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95110571993549494302111412882791 y1[1] (numeric) = 0.95110571993549494302111412882794 absolute error = 3e-32 relative error = 3.1542234865367683476061886094128e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.6MB, time=60.27 x[1] = 0.315 y2[1] (analytic) = 0.30981647122760284860120051593398 y2[1] (numeric) = 0.309816471227602848601200515934 absolute error = 2e-32 relative error = 6.4554347032463766995205337011874e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95079637891405325664080365633916 y1[1] (numeric) = 0.95079637891405325664080365633919 absolute error = 3e-32 relative error = 3.1552497112225365733798421694330e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.6MB, time=60.50 x[1] = 0.316 y2[1] (analytic) = 0.31076711253982814184658196132219 y2[1] (numeric) = 0.31076711253982814184658196132221 absolute error = 2e-32 relative error = 6.4356874305471385043547810197994e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95048608709631188923617161314611 y1[1] (numeric) = 0.95048608709631188923617161314613 absolute error = 2e-32 relative error = 2.1041865074636719244906864546751e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.6MB, time=60.74 x[1] = 0.317 y2[1] (analytic) = 0.3117174430849667925223366371764 y2[1] (numeric) = 0.31171744308496679252233663717642 absolute error = 2e-32 relative error = 6.4160670003149209920050297369240e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.95017484479256263269093478735519 y1[1] (numeric) = 0.95017484479256263269093478735522 absolute error = 3e-32 relative error = 3.1573136422643822250633452402979e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.6MB, time=60.97 memory used=995.6MB, alloc=4.6MB, time=61.21 x[1] = 0.318 y2[1] (analytic) = 0.31266746191268833468402332282246 y2[1] (numeric) = 0.31266746191268833468402332282248 absolute error = 2e-32 relative error = 6.3965722169021072380458691905243e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94986265231404776481749194299381 y1[1] (numeric) = 0.94986265231404776481749194299384 absolute error = 3e-32 relative error = 3.1583513602639540509071620918458e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.6MB, time=61.45 x[1] = 0.319 y2[1] (analytic) = 0.3136171680729740197783328610944 y2[1] (numeric) = 0.31361716807297401977833286109442 absolute error = 2e-32 relative error = 6.3772018996569407910858136085611e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94954950997295973811467194446714 y1[1] (numeric) = 0.94954950997295973811467194446716 absolute error = 2e-32 relative error = 2.1062619473701312053291348712343e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.6MB, time=61.68 x[1] = 0.32 y2[1] (analytic) = 0.31456656061611776666175754341715 y2[1] (numeric) = 0.31456656061611776666175754341717 absolute error = 2e-32 relative error = 6.3579548826892185779101948190767e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94923541808244086757530727376609 y1[1] (numeric) = 0.94923541808244086757530727376611 absolute error = 2e-32 relative error = 2.1069588870168985639438319667824e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.6MB, time=61.92 x[1] = 0.321 y2[1] (analytic) = 0.31551563859272711130659311114346 y2[1] (numeric) = 0.31551563859272711130659311114349 absolute error = 3e-32 relative error = 9.5082450219605450888555708630207e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94892037695658301754394513282693 y1[1] (numeric) = 0.94892037695658301754394513282694 absolute error = 1e-32 relative error = 1.0538291981959979386234151972264e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.6MB, time=62.15 x[1] = 0.322 y2[1] (analytic) = 0.31646440105372415619332366722217 y2[1] (numeric) = 0.3164644010537241561933236672222 absolute error = 3e-32 relative error = 9.4797392376866711416382730730160e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94860438691042728762500927330517 y1[1] (numeric) = 0.94860438691042728762500927330518 absolute error = 1e-32 relative error = 1.0541802397277188466181210406187e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.6MB, time=62.38 x[1] = 0.323 y2[1] (analytic) = 0.31741284705034651938844010589189 y2[1] (numeric) = 0.31741284705034651938844010589192 absolute error = 3e-32 relative error = 9.4514132867601109973660632749748e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94828744825996369764172664557596 y1[1] (numeric) = 0.94828744825996369764172664557598 absolute error = 2e-32 relative error = 2.1090651401849195704953185746421e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1018.5MB, alloc=4.6MB, time=62.62 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.6MB, time=62.86 x[1] = 0.324 y2[1] (analytic) = 0.31836097563414828330674298266094 y2[1] (numeric) = 0.31836097563414828330674298266097 absolute error = 3e-32 relative error = 9.4232655055295403481057765164132e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9479695613221308716461339080079 y1[1] (numeric) = 0.94796956132213087164613390800792 absolute error = 2e-32 relative error = 2.1097723825758759604580725337327e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.6MB, time=63.09 x[1] = 0.325 y2[1] (analytic) = 0.31930878585700094315718106234965 y2[1] (numeric) = 0.31930878585700094315718106234968 absolute error = 3e-32 relative error = 9.3952942508243986015112285108750e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94765072641481572098047978647747 y1[1] (numeric) = 0.94765072641481572098047978647749 absolute error = 2e-32 relative error = 2.1104822106415384101929695933287e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.6MB, time=63.33 x[1] = 0.326 y2[1] (analytic) = 0.32025627677109435507127709943546 y2[1] (numeric) = 0.32025627677109435507127709943549 absolute error = 3e-32 relative error = 9.3674978996407715939498291574676e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94733094385685312639034022269541 y1[1] (numeric) = 0.94733094385685312639034022269543 absolute error = 2e-32 relative error = 2.1111946284129940873533077614501e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1033.8MB, alloc=4.6MB, time=63.56 x[1] = 0.327 y2[1] (analytic) = 0.32120344742893768391319272235417 y2[1] (numeric) = 0.3212034474289376839131927223542 absolute error = 3e-32 relative error = 9.3398748488330379415339079840394e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94701021396802561918976419820327 y1[1] (numeric) = 0.94701021396802561918976419820329 absolute error = 2e-32 relative error = 2.1119096399392446289541554882507e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.6MB, time=63.80 x[1] = 0.328 y2[1] (analytic) = 0.32215029688336035077048461177134 y2[1] (numeric) = 0.32215029688336035077048461177137 absolute error = 3e-32 relative error = 9.3124235148111560246187326605114e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94668853706906306147876906886782 y1[1] (numeric) = 0.94668853706906306147876906886784 absolute error = 2e-32 relative error = 2.1126272492872653156470519384521e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.6MB, time=64.03 memory used=1045.2MB, alloc=4.6MB, time=64.27 x[1] = 0.329 y2[1] (analytic) = 0.32309682418751298012460448214665 y2[1] (numeric) = 0.32309682418751298012460448214668 absolute error = 3e-32 relative error = 9.2851423332434715923186952282986e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9463659134816423254135051923513 y1[1] (numeric) = 0.94636591348164232541350519235132 absolute error = 2e-32 relative error = 2.1133474605420645731750844564699e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.6MB, time=64.51 x[1] = 0.33 y2[1] (analytic) = 0.32404302839486834670019569617022 y2[1] (numeric) = 0.32404302839486834670019569617025 absolute error = 3e-32 relative error = 9.2580297587649288830101937482670e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94604234352838697152941057836621 y1[1] (numeric) = 0.94604234352838697152941057836622 absolute error = 1e-32 relative error = 1.0570351389033719013512246936692e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.6MB, time=64.74 x[1] = 0.331 y2[1] (analytic) = 0.32498890855922232199223966285307 y2[1] (numeric) = 0.3249889085592223219922396628531 absolute error = 3e-32 relative error = 9.2310842646905709870987738671208e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94571782753286692611767723853306 y1[1] (numeric) = 0.94571782753286692611767723853307 absolute error = 1e-32 relative error = 1.0573978526012787708620869831364e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.6MB, time=64.98 x[1] = 0.332 y2[1] (analytic) = 0.32593446373469482047010549220433 y2[1] (numeric) = 0.32593446373469482047010549220436 absolute error = 3e-32 relative error = 9.2043043427342179319118869158482e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94539236581959815765535185934806 y1[1] (numeric) = 0.94539236581959815765535185934807 absolute error = 1e-32 relative error = 1.0577618734344869786366647900379e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.6MB, time=65.21 x[1] = 0.333 y2[1] (analytic) = 0.32687969297573074545755670252426 y2[1] (numeric) = 0.32687969297573074545755670252429 absolute error = 3e-32 relative error = 9.1776885027322136477412299871028e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94506595871404235228939436813284 y1[1] (numeric) = 0.94506595871404235228939436813285 absolute error = 1e-32 relative error = 1.0581272034818678365774005026232e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.6MB, time=65.45 x[1] = 0.334 y2[1] (analytic) = 0.32782459533710093468776910038533 y2[1] (numeric) = 0.32782459533710093468776910038536 absolute error = 3e-32 relative error = 9.1512352723721355810282381325503e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94473860654260658837501890788084 y1[1] (numeric) = 0.94473860654260658837501890788085 absolute error = 1e-32 relative error = 1.0584938448314604664732464585477e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1068.1MB, alloc=4.6MB, time=65.69 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.6MB, time=65.92 x[1] = 0.335 y2[1] (analytic) = 0.32876916987390310553241427836219 y2[1] (numeric) = 0.32876916987390310553241427836222 absolute error = 3e-32 relative error = 9.1249431969263632576179144265266e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9444103096326430100686426826321 y1[1] (numeric) = 0.94441030963264301006864268263211 absolute error = 1e-32 relative error = 1.0588617995805025502603773619235e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1075.7MB, alloc=4.6MB, time=66.15 x[1] = 0.336 y2[1] (analytic) = 0.32971341564156279990386350150578 y2[1] (numeric) = 0.32971341564156279990386350150581 absolute error = 3e-32 relative error = 9.0988108389904045679842741210667e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94408106831244849997576908040049 y1[1] (numeric) = 0.9440810683124484999757690804005 absolute error = 1e-32 relative error = 1.0592310698354612499253941490363e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.6MB, time=66.39 x[1] = 0.337 y2[1] (analytic) = 0.33065733169583432882956708043654 y2[1] (numeric) = 0.33065733169583432882956708043657 absolute error = 3e-32 relative error = 9.0728367782258809493716695487264e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94375088291126435085413242574299 y1[1] (numeric) = 0.94375088291126435085413242574299 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.6MB, time=66.62 x[1] = 0.338 y2[1] (analytic) = 0.33160091709280171669766465675598 y2[1] (numeric) = 0.33160091709280171669766465675601 absolute error = 3e-32 relative error = 9.0470196111080749788509545914725e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9434197537592759363724326587988 y1[1] (numeric) = 0.9434197537592759363724326587988 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.6MB, time=66.86 x[1] = 0.339 y2[1] (analytic) = 0.33254417088887964517288215524501 y2[1] (numeric) = 0.33254417088887964517288215524504 absolute error = 3e-32 relative error = 9.0213579506779461682453428514205e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94308768118761238092498918203633 y1[1] (numeric) = 0.94308768118761238092498918203634 absolute error = 1e-32 relative error = 1.0603467948396049648049221839635e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.6MB, time=67.09 memory used=1094.8MB, alloc=4.6MB, time=67.32 x[1] = 0.34 y2[1] (analytic) = 0.33348709214081439678177148703079 y2[1] (numeric) = 0.33348709214081439678177148703082 absolute error = 3e-32 relative error = 8.9958504262985229685643473349653e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94275466552834622850264406002658 y1[1] (numeric) = 0.94275466552834622850264406002659 absolute error = 1e-32 relative error = 1.0607213483685831202937827622284e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1098.6MB, alloc=4.6MB, time=67.56 x[1] = 0.341 y2[1] (analytic) = 0.33442967990568479816634941856096 y2[1] (numeric) = 0.33442967990568479816634941856099 absolute error = 3e-32 relative error = 8.9704956834155811497628794338693e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9424207071144931106202457013121 y1[1] (numeric) = 0.94242070711449311062024570131211 absolute error = 1e-32 relative error = 1.0610972280753500863888943177504e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1102.4MB, alloc=4.6MB, time=67.80 x[1] = 0.342 y2[1] (analytic) = 0.33537193324090316300519235282508 y2[1] (numeric) = 0.33537193324090316300519235282511 absolute error = 3e-32 relative error = 8.9452923833225208230270992009987e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94208580628001141330104509486035 y1[1] (numeric) = 0.94208580628001141330104509486036 absolute error = 1e-32 relative error = 1.0614744361224088360359336403627e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1106.2MB, alloc=4.6MB, time=68.03 x[1] = 0.343 y2[1] (analytic) = 0.33631385120421623460104410180696 y2[1] (numeric) = 0.33631385120421623460104410180698 absolute error = 2e-32 relative error = 5.9468261352862376126898361662246e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94174996335980194311833761667723 y1[1] (numeric) = 0.94174996335980194311833761667724 absolute error = 1e-32 relative error = 1.0618529746817130869412443762045e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1110.0MB, alloc=4.6MB, time=68.27 x[1] = 0.344 y2[1] (analytic) = 0.33725543285370612813399406263873 y2[1] (numeric) = 0.33725543285370612813399406263875 absolute error = 2e-32 relative error = 5.9302232230238239522322537416644e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94141317868970759229468436491135 y1[1] (numeric) = 0.94141317868970759229468436491137 absolute error = 2e-32 relative error = 2.1244656918693992222276878524492e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1113.9MB, alloc=4.6MB, time=68.51 memory used=1117.7MB, alloc=4.6MB, time=68.75 x[1] = 0.345 y2[1] (analytic) = 0.33819667724779127257928354435702 y2[1] (numeric) = 0.33819667724779127257928354435705 absolute error = 3e-32 relative error = 8.8705779856079076508266194878811e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9410754526065130028590479241997 y1[1] (numeric) = 0.94107545260651300285904792419971 absolute error = 1e-32 relative error = 1.0626140520723207222680759522906e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1121.5MB, alloc=4.6MB, time=68.99 x[1] = 0.346 y2[1] (analytic) = 0.33913758344522735228879832753336 y2[1] (numeric) = 0.33913758344522735228879832753338 absolute error = 2e-32 relative error = 5.8973115857063697274562997455123e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94073678544794422986217840209091 y1[1] (numeric) = 0.94073678544794422986217840209092 absolute error = 1e-32 relative error = 1.0629965952950769420315896605940e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1125.3MB, alloc=4.6MB, time=69.22 x[1] = 0.347 y2[1] (analytic) = 0.34007815050510824823530587536464 y2[1] (numeric) = 0.34007815050510824823530587536466 absolute error = 2e-32 relative error = 5.8810011670242789860347597758740e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94039717755266840365058652213218 y1[1] (numeric) = 0.94039717755266840365058652213219 absolute error = 1e-32 relative error = 1.0633804778130498459098030686006e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1129.1MB, alloc=4.6MB, time=69.46 x[1] = 0.348 y2[1] (analytic) = 0.34101837748686697891849595206509 y2[1] (numeric) = 0.34101837748686697891849595206511 absolute error = 2e-32 relative error = 5.8647865688030914569893312878755e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.94005662926029339119944149961845 y1[1] (numeric) = 0.94005662926029339119944149961847 absolute error = 2e-32 relative error = 2.1275314036918701799290595057299e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1132.9MB, alloc=4.6MB, time=69.69 x[1] = 0.349 y2[1] (analytic) = 0.34195826345027664093188374259728 y2[1] (numeric) = 0.3419582634502766409318837425973 absolute error = 2e-32 relative error = 5.8486669683618140368106221416793e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93971514091136745650473236707785 y1[1] (numeric) = 0.93971514091136745650473236707786 absolute error = 1e-32 relative error = 1.0641522696230756191710175065205e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1136.7MB, alloc=4.6MB, time=69.93 x[1] = 0.35 y2[1] (analytic) = 0.34289780745545134918963490691763 y2[1] (numeric) = 0.34289780745545134918963490691765 absolute error = 2e-32 relative error = 5.8326415524247302509246725756321e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93937271284737892003503235730367 y1[1] (numeric) = 0.93937271284737892003503235730368 absolute error = 1e-32 relative error = 1.0645401833834950584242632965675e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1140.6MB, alloc=4.6MB, time=70.17 TOP MAIN SOLVE Loop memory used=1144.4MB, alloc=4.6MB, time=70.40 x[1] = 0.351 y2[1] (analytic) = 0.34383700856284717681237234198958 y2[1] (numeric) = 0.3438370085628471768123723419896 absolute error = 2e-32 relative error = 5.8167095169874252454697073797481e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93902934541075581724320689214026 y1[1] (numeric) = 0.93902934541075581724320689214027 absolute error = 1e-32 relative error = 1.0649294453759312871721322950171e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1148.2MB, alloc=4.6MB, time=70.64 x[1] = 0.352 y2[1] (analytic) = 0.34477586583326309467102476583608 y2[1] (numeric) = 0.3447758658332630946710247658361 absolute error = 2e-32 relative error = 5.8008700671850944555902509149653e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93868503894486555613840666528628 y1[1] (numeric) = 0.93868503894486555613840666528629 absolute error = 1e-32 relative error = 1.0653200578588701986595199608805e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.6MB, time=70.87 x[1] = 0.353 y2[1] (analytic) = 0.34571437832784191058777757986105 y2[1] (numeric) = 0.34571437832784191058777757986107 absolute error = 2e-32 relative error = 5.7851224171630906648987283987257e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93833979379401457391868824709369 y1[1] (numeric) = 0.93833979379401457391868824709371 absolute error = 2e-32 relative error = 2.1314240462011592895491111435640e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1155.8MB, alloc=4.6MB, time=71.10 x[1] = 0.354 y2[1] (analytic) = 0.34665254510807120819318680856723 y2[1] (numeric) = 0.34665254510807120819318680856725 absolute error = 2e-32 relative error = 5.7694657899496651941524927796915e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93799361030344799266460557871336 y1[1] (numeric) = 0.93799361030344799266460557871338 absolute error = 2e-32 relative error = 2.1322106867582871349893072961513e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1159.6MB, alloc=4.6MB, time=71.34 x[1] = 0.355 y2[1] (analytic) = 0.34759036523578428543851725963473 y2[1] (numeric) = 0.34759036523578428543851725963475 absolute error = 2e-32 relative error = 5.7538994173308599546467358853767e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93764648881934927409411666196697 y1[1] (numeric) = 0.93764648881934927409411666196699 absolute error = 2e-32 relative error = 2.1330000419649926358741535716774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1163.5MB, alloc=4.6MB, time=71.57 memory used=1167.3MB, alloc=4.6MB, time=71.81 x[1] = 0.356 y2[1] (analytic) = 0.34852783777316109276236639210034 y2[1] (numeric) = 0.34852783777316109276236639210036 absolute error = 2e-32 relative error = 5.7384225397275080740597658116525e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93729842968883987337915069000988 y1[1] (numeric) = 0.9372984296888398733791506900099 absolute error = 2e-32 relative error = 2.1337921164169143280511598573652e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1171.1MB, alloc=4.6MB, time=72.05 x[1] = 0.357 y2[1] (analytic) = 0.34946496178272917091063572609188 y2[1] (numeric) = 0.3494649617827291709106357260919 absolute error = 2e-32 relative error = 5.7230344060743017502130041612439e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9369494332599788920241818021889 y1[1] (numeric) = 0.93694943325997889202418180218892 absolute error = 2e-32 relative error = 2.1345869147295299755833249527566e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1174.9MB, alloc=4.6MB, time=72.29 x[1] = 0.358 y2[1] (analytic) = 0.35040173632736458840891197422432 y2[1] (numeric) = 0.35040173632736458840891197422434 absolute error = 2e-32 relative error = 5.7077342737008869121084178377934e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93659949988176272980715658449232 y1[1] (numeric) = 0.93659949988176272980715658449234 absolute error = 2e-32 relative error = 2.1353844415382263466719225378625e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1178.7MB, alloc=4.6MB, time=72.52 x[1] = 0.359 y2[1] (analytic) = 0.35133816047029287868632042235473 y2[1] (numeric) = 0.35133816047029287868632042235475 absolute error = 2e-32 relative error = 5.6925214082149451683446139099083e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93624862990412473578312337463565 y1[1] (numeric) = 0.93624862990412473578312337463567 absolute error = 2e-32 relative error = 2.1361847014983693729647496396533e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1182.5MB, alloc=4.6MB, time=72.76 x[1] = 0.36 y2[1] (analytic) = 0.35227423327508997684991343592073 y2[1] (numeric) = 0.35227423327508997684991343592075 absolute error = 2e-32 relative error = 5.6773950833872244012328772236860e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93589682367793485835091236812474 y1[1] (numeric) = 0.93589682367793485835091236812476 absolute error = 2e-32 relative error = 2.1369876992853746943292352547215e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1186.3MB, alloc=4.6MB, time=72.99 x[1] = 0.361 y2[1] (analytic) = 0.35320995380568315610865731755197 y2[1] (numeric) = 0.35320995380568315610865731755199 absolute error = 2e-32 relative error = 5.6623545810384802212597990920377e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93554408155499929438321645858698 y1[1] (numeric) = 0.93554408155499929438321645858699 absolute error = 1e-32 relative error = 1.0688967197973892955920633977559e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1190.2MB, alloc=4.6MB, time=73.23 TOP MAIN SOLVE Loop memory used=1194.0MB, alloc=4.6MB, time=73.47 x[1] = 0.362 y2[1] (analytic) = 0.35414532112635196384608109204584 y2[1] (numeric) = 0.35414532112635196384608109204587 absolute error = 3e-32 relative error = 8.4710987863924369973679855140868e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93519040388806013742042368226048 y1[1] (numeric) = 0.9351904038880601374204236822605 absolute error = 2e-32 relative error = 2.1386019271423093064978960029775e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1197.8MB, alloc=4.6MB, time=73.70 x[1] = 0.363 y2[1] (analytic) = 0.35508033430172915734065114613672 y2[1] (numeric) = 0.35508033430172915734065114613675 absolute error = 3e-32 relative error = 8.4487923159685689998157860561307e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93483579103079502492855307277957 y1[1] (numeric) = 0.93483579103079502492855307277959 absolute error = 2e-32 relative error = 2.1394131666639587595765347843993e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1201.6MB, alloc=4.6MB, time=73.94 x[1] = 0.364 y2[1] (analytic) = 0.35601499239680163913293600276189 y2[1] (numeric) = 0.35601499239680163913293600276192 absolute error = 3e-32 relative error = 8.4266114182525964437504788459696e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93448024333781678462164666829116 y1[1] (numeric) = 0.93448024333781678462164666829119 absolute error = 3e-32 relative error = 3.2103407443740819806670689607284e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1205.4MB, alloc=4.6MB, time=74.18 x[1] = 0.365 y2[1] (analytic) = 0.35694929447691139203862586273754 y2[1] (numeric) = 0.35694929447691139203862586273757 absolute error = 3e-32 relative error = 8.4045550626352322904814345700421e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93412376116467307984897134848078 y1[1] (numeric) = 0.93412376116467307984897134848081 absolute error = 3e-32 relative error = 3.2115658810129994704585127467235e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1209.2MB, alloc=4.6MB, time=74.42 x[1] = 0.366 y2[1] (analytic) = 0.35788323960775641380647190090305 y2[1] (numeric) = 0.35788323960775641380647190090308 absolute error = 3e-32 relative error = 8.3826222297753585921281912340699e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93376634486784605404738511427659 y1[1] (numeric) = 0.93376634486784605404738511427661 absolute error = 2e-32 relative error = 2.1418634447390109202467784263031e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1213.0MB, alloc=4.6MB, time=74.65 memory used=1216.9MB, alloc=4.6MB, time=74.89 x[1] = 0.367 y2[1] (analytic) = 0.35881682685539165142021065887221 y2[1] (numeric) = 0.35881682685539165142021065887224 absolute error = 3e-32 relative error = 8.3608119114465141939971291741662e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.93340799480475197425922335783568 y1[1] (numeric) = 0.93340799480475197425922335783571 absolute error = 3e-32 relative error = 3.2140286098872902205587667048194e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1220.7MB, alloc=4.6MB, time=75.13 x[1] = 0.368 y2[1] (analytic) = 0.35975005528622993504353923254485 y2[1] (numeric) = 0.35975005528622993504353923254489 absolute error = 4e-32 relative error = 1.1118830813847847162642485895703e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93304871133374087371606160489668 y1[1] (numeric) = 0.9330487113337408737160616048967 absolute error = 2e-32 relative error = 2.1435108110712805315619229001641e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1224.5MB, alloc=4.6MB, time=75.36 x[1] = 0.369 y2[1] (analytic) = 0.36068292396704291160720730948157 y2[1] (numeric) = 0.36068292396704291160720730948161 absolute error = 4e-32 relative error = 1.1090073120194335898487888947677e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9326884948140961934887121457059 y1[1] (numeric) = 0.93268849481409619348871214570592 absolute error = 2e-32 relative error = 2.1443386630373742520625535405678e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1228.3MB, alloc=4.6MB, time=75.60 x[1] = 0.37 y2[1] (analytic) = 0.36161543196496197803729246912715 y2[1] (numeric) = 0.36161543196496197803729246912719 absolute error = 4e-32 relative error = 1.1061474833263123013366890623216e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93232734560603442320381290449088 y1[1] (numeric) = 0.9323273456060344232038129044909 absolute error = 2e-32 relative error = 2.1451693007030203111482463335611e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1232.1MB, alloc=4.6MB, time=75.84 x[1] = 0.371 y2[1] (analytic) = 0.36254757834747921412372551768536 y2[1] (numeric) = 0.3625475783474792141237255176854 absolute error = 4e-32 relative error = 1.1033034666049402720989445229844e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93196526407070474082736783086223 y1[1] (numeric) = 0.93196526407070474082736783086225 absolute error = 2e-32 relative error = 2.1460027289689494620836279766311e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1235.9MB, alloc=4.6MB, time=76.07 memory used=1239.7MB, alloc=4.6MB, time=76.30 x[1] = 0.372 y2[1] (analytic) = 0.36347936218244831502813298919735 y2[1] (numeric) = 0.36347936218244831502813298919739 absolute error = 4e-32 relative error = 1.1004751345393309179764135211502e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93160225057018865151559902957351 y1[1] (numeric) = 0.93160225057018865151559902957354 absolute error = 3e-32 relative error = 3.2202584291352293199803267718887e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.6MB, time=76.54 x[1] = 0.373 y2[1] (analytic) = 0.36441078253808552343006430505902 y2[1] (numeric) = 0.36441078253808552343006430505906 absolute error = 4e-32 relative error = 1.0976623611794334170806292783522e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93123830546749962553347177775691 y1[1] (numeric) = 0.93123830546749962553347177775694 absolute error = 3e-32 relative error = 3.2215169655139368702971343067719e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1247.4MB, alloc=4.6MB, time=76.77 x[1] = 0.374 y2[1] (analytic) = 0.3653418384829705613106714458277 y2[1] (numeric) = 0.36534183848297056131067144582774 absolute error = 4e-32 relative error = 1.0948650219228722055164396825076e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93087342912658273524125451107944 y1[1] (numeric) = 0.93087342912658273524125451107947 absolute error = 3e-32 relative error = 3.2227797100351563791641245956237e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1251.2MB, alloc=4.6MB, time=77.01 x[1] = 0.375 y2[1] (analytic) = 0.36627252908604756137290935171626 y2[1] (numeric) = 0.3662725290860475613729093517163 absolute error = 4e-32 relative error = 1.0920829934969786434427304968245e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93050762191231429114947679222956 y1[1] (numeric) = 0.93050762191231429114947679222958 absolute error = 2e-32 relative error = 2.1493644467841538487627575793853e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1255.0MB, alloc=4.6MB, time=77.24 x[1] = 0.376 y2[1] (analytic) = 0.36720285341662599809732563165185 y2[1] (numeric) = 0.36720285341662599809732563165189 absolute error = 4e-32 relative error = 1.0893161539411094121339663861261e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.93014088419050147704264920674576 y1[1] (numeric) = 0.93014088419050147704264920674578 absolute error = 2e-32 relative error = 2.1502119022975679205362494158054e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1258.8MB, alloc=4.6MB, time=77.48 x[1] = 0.377 y2[1] (analytic) = 0.36813281054438161843250852518704 y2[1] (numeric) = 0.36813281054438161843250852518708 absolute error = 4e-32 relative error = 1.0865643825892463181289021788142e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92977321632788198417211006243701 y1[1] (numeric) = 0.92977321632788198417211006243703 absolute error = 2e-32 relative error = 2.1510621782577843852572932650619e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1262.6MB, alloc=4.6MB, time=77.72 memory used=1266.5MB, alloc=4.6MB, time=77.95 x[1] = 0.378 y2[1] (analytic) = 0.3690623995393573721192624268931 y2[1] (numeric) = 0.36906239953935737211926242689314 absolute error = 4e-32 relative error = 1.0838275600528722932282535607949e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92940461869212364451836469951764 y1[1] (numeric) = 0.92940461869212364451836469951766 absolute error = 2e-32 relative error = 2.1519152797136290470958762441867e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1270.3MB, alloc=4.6MB, time=78.19 x[1] = 0.379 y2[1] (analytic) = 0.36999161947196434164758064913733 y2[1] (numeric) = 0.36999161947196434164758064913737 absolute error = 4e-32 relative error = 1.0811055682041184891028832146629e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92903509165182406312328414908702 y1[1] (numeric) = 0.92903509165182406312328414908704 absolute error = 2e-32 relative error = 2.1527712117353938806083264650535e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1274.1MB, alloc=4.6MB, time=78.43 x[1] = 0.38 y2[1] (analytic) = 0.3709204694129826718454854663492 y2[1] (numeric) = 0.37092046941298267184548546634924 absolute error = 4e-32 relative error = 1.0783982901591774726685676408678e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92866463557651024949253080772456 y1[1] (numeric) = 0.92866463557651024949253080772458 absolute error = 2e-32 relative error = 2.1536299794149157443180906061186e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1277.9MB, alloc=4.6MB, time=78.66 x[1] = 0.381 y2[1] (analytic) = 0.37184894843356249909880585201274 y2[1] (numeric) = 0.37184894843356249909880585201277 absolute error = 3e-32 relative error = 8.0677920769648322493078074402625e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92829325083663824806857972574377 y1[1] (numeric) = 0.92829325083663824806857972574379 absolute error = 2e-32 relative error = 2.1544915878656555269033631973377e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1281.7MB, alloc=4.6MB, time=78.90 x[1] = 0.382 y2[1] (analytic) = 0.3727770556052248802009636886848 y2[1] (numeric) = 0.37277705560522488020096368868484 absolute error = 4e-32 relative error = 1.0730274140681140148721756394895e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9279209378035927677747050360532 y1[1] (numeric) = 0.92792093780359276777470503605322 absolute error = 2e-32 relative error = 2.1553560422227777284114282620204e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1285.5MB, alloc=4.6MB, time=79.13 memory used=1289.3MB, alloc=4.6MB, time=79.37 x[1] = 0.383 y2[1] (analytic) = 0.37370478999986272083183960133056 y2[1] (numeric) = 0.3737047899998627208318396013306 absolute error = 4e-32 relative error = 1.0703635883290308872493579457888e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92754769684968681063030197960704 y1[1] (numeric) = 0.92754769684968681063030197960706 absolute error = 2e-32 relative error = 2.1562233476432304789363959907495e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1293.2MB, alloc=4.6MB, time=79.61 x[1] = 0.384 y2[1] (analytic) = 0.37463215068974170366478993518755 y2[1] (numeric) = 0.37463215068974170366478993518759 absolute error = 4e-32 relative error = 1.0677140209764514661780071678786e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92717352834816129943791591209232 y1[1] (numeric) = 0.92717352834816129943791591209234 absolute error = 2e-32 relative error = 2.1570935093058259972139643108382e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1297.0MB, alloc=4.6MB, time=79.84 x[1] = 0.385 y2[1] (analytic) = 0.3755591367475012161008867712188 y2[1] (numeric) = 0.37555913674750121610088677121884 absolute error = 4e-32 relative error = 1.0650786011070502900226307392373e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92679843267318470454235060479278 y1[1] (numeric) = 0.9267984326731847045423506047928 absolute error = 2e-32 relative error = 2.1579665324113214916039086279442e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1300.8MB, alloc=4.6MB, time=80.08 x[1] = 0.386 y2[1] (analytic) = 0.37648574724615527762945324499228 y2[1] (numeric) = 0.37648574724615527762945324499232 absolute error = 4e-32 relative error = 1.0624572189673638516139410531302e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92642241019985266966222908048989 y1[1] (numeric) = 0.92642241019985266966222908048991 absolute error = 2e-32 relative error = 2.1588424221825005059482037320620e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1304.6MB, alloc=4.6MB, time=80.31 x[1] = 0.387 y2[1] (analytic) = 0.37741198125909346681396680852865 y2[1] (numeric) = 0.37741198125909346681396680852868 absolute error = 3e-32 relative error = 7.9488732445420138207187043972286e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92604546130418763679438115280913 y1[1] (numeric) = 0.92604546130418763679438115280915 absolute error = 2e-32 relative error = 2.1597211838642547128100109657835e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1308.4MB, alloc=4.6MB, time=80.55 x[1] = 0.388 y2[1] (analytic) = 0.37833783786008184790240344929121 y2[1] (numeric) = 0.37833783786008184790240344929125 absolute error = 4e-32 relative error = 1.0572561345236881240422016538709e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92566758636313847019143276459259 y1[1] (numeric) = 0.92566758636313847019143276459261 absolute error = 2e-32 relative error = 2.1606028227236661566162223461015e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1312.2MB, alloc=4.6MB, time=80.79 TOP MAIN SOLVE Loop memory used=1316.0MB, alloc=4.6MB, time=81.03 x[1] = 0.389 y2[1] (analytic) = 0.37926331612326389706109625605126 y2[1] (numeric) = 0.37926331612326389706109625605129 absolute error = 3e-32 relative error = 7.9100716374714546448062525300382e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92528878575458007941297314767738 y1[1] (numeric) = 0.9252887857545800794129731476774 absolute error = 2e-32 relative error = 2.1614873440500899492438425199386e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1319.9MB, alloc=4.6MB, time=81.26 x[1] = 0.39 y2[1] (analytic) = 0.38018841512316142823118209784716 y2[1] (numeric) = 0.38018841512316142823118209784719 absolute error = 3e-32 relative error = 7.8908243404211956440396798999009e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9249090598573130414506767528811 y1[1] (numeric) = 0.92490905985731304145067675288112 absolute error = 2e-32 relative error = 2.1623747531552374206082103360578e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1323.7MB, alloc=4.6MB, time=81.50 x[1] = 0.391 y2[1] (analytic) = 0.38111313393467551860671055966795 y2[1] (numeric) = 0.38111313393467551860671055966798 absolute error = 3e-32 relative error = 7.8716783361084934559119100366176e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92452840905106322192775782504114 y1[1] (numeric) = 0.92452840905106322192775782504115 absolute error = 1e-32 relative error = 1.0816325276866298634144577802357e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1327.5MB, alloc=4.6MB, time=81.74 x[1] = 0.392 y2[1] (analytic) = 0.38203747163308743373348965682936 y2[1] (numeric) = 0.3820374716330874337334896568294 absolute error = 4e-32 relative error = 1.0470177134460882312795693133407e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92414683371648139537313642362145 y1[1] (numeric) = 0.92414683371648139537313642362146 absolute error = 1e-32 relative error = 1.0820791280304159592836269938865e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1331.3MB, alloc=4.6MB, time=81.97 x[1] = 0.393 y2[1] (analytic) = 0.3829614272940595522277432292739 y2[1] (numeric) = 0.38296142729405955222774322927394 absolute error = 4e-32 relative error = 1.0444916158432250231287895580197e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92376433423514286457069561468935 y1[1] (numeric) = 0.92376433423514286457069561468937 absolute error = 2e-32 relative error = 2.1650543605972374721471870564276e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1335.1MB, alloc=4.6MB, time=82.21 memory used=1338.9MB, alloc=4.6MB, time=82.45 x[1] = 0.394 y2[1] (analytic) = 0.38388499999363629011365529721442 y2[1] (numeric) = 0.38388499999363629011365529721445 absolute error = 3e-32 relative error = 7.8148403820147475858635608660367e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92338091098954707898401048497331 y1[1] (numeric) = 0.92338091098954707898401048497332 absolute error = 1e-32 relative error = 1.0829766871922266430450156110356e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1342.7MB, alloc=4.6MB, time=82.68 x[1] = 0.395 y2[1] (analytic) = 0.38480818880824502477887704065397 y2[1] (numeric) = 0.38480818880824502477887704065401 absolute error = 4e-32 relative error = 1.0394789186758321671100504698038e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92299656436311725225693055324085 y1[1] (numeric) = 0.92299656436311725225693055324087 absolute error = 2e-32 relative error = 2.1668553028472351457114989502150e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1346.6MB, alloc=4.6MB, time=82.92 x[1] = 0.396 y2[1] (analytic) = 0.38573099281469701854707244735207 y2[1] (numeric) = 0.3857309928146970185470724473521 absolute error = 3e-32 relative error = 7.7774409002213181943742619975788e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92261129474019997879039807838253 y1[1] (numeric) = 0.92261129474019997879039807838255 absolute error = 2e-32 relative error = 2.1677601514332036584482484402148e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1350.4MB, alloc=4.6MB, time=83.15 x[1] = 0.397 y2[1] (analytic) = 0.38665341109018834186657905676835 y2[1] (numeric) = 0.38665341109018834186657905676838 absolute error = 3e-32 relative error = 7.7588866771958695480201344845105e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92222510250606484939588568735141 y1[1] (numeric) = 0.92222510250606484939588568735143 absolute error = 2e-32 relative error = 2.1686679256129306625997742787701e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1354.2MB, alloc=4.6MB, time=83.39 x[1] = 0.398 y2[1] (analytic) = 0.38757544271230079611426061140022 y2[1] (numeric) = 0.38757544271230079611426061140025 absolute error = 3e-32 relative error = 7.7404284931099597948527116185963e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92183798804690406602583766948861 y1[1] (numeric) = 0.92183798804690406602583766948863 absolute error = 2e-32 relative error = 2.1695786308800261121902873474963e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1358.0MB, alloc=4.6MB, time=83.62 x[1] = 0.399 y2[1] (analytic) = 0.3884970867590028360136288117384 y2[1] (numeric) = 0.38849708675900283601362881173843 absolute error = 3e-32 relative error = 7.7220656273826730554503806882742e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.92144995174983205558150020676146 y1[1] (numeric) = 0.92144995174983205558150020676148 absolute error = 2e-32 relative error = 2.1704922727512254406741906904415e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1361.8MB, alloc=4.6MB, time=83.87 TOP MAIN SOLVE Loop memory used=1365.6MB, alloc=4.6MB, time=84.10 x[1] = 0.4 y2[1] (analytic) = 0.38941834230865049166631175679571 y2[1] (numeric) = 0.38941834230865049166631175679574 absolute error = 3e-32 relative error = 7.7037973666433492110340618900883e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9210609940028850827985267320518 y1[1] (numeric) = 0.92106099400288508279852673205182 absolute error = 2e-32 relative error = 2.1714088567664774062278599103175e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1369.5MB, alloc=4.6MB, time=84.33 x[1] = 0.401 y2[1] (analytic) = 0.39033920843998829019594703881735 y2[1] (numeric) = 0.39033920843998829019594703881739 absolute error = 4e-32 relative error = 1.0247497339522247446882379722206e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92067111519502086221074552985688 y1[1] (numeric) = 0.9206711151950208622107455298569 absolute error = 2e-32 relative error = 2.1723283884890324213896832446833e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1373.3MB, alloc=4.6MB, time=84.56 x[1] = 0.402 y2[1] (analytic) = 0.39125968423215017700357784835651 y2[1] (numeric) = 0.39125968423215017700357784835655 absolute error = 4e-32 relative error = 1.0223389122878907210759821616286e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.92028031571611816919247761560285 y1[1] (numeric) = 0.92028031571611816919247761560287 absolute error = 2e-32 relative error = 2.1732508735055313698297090249359e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1377.1MB, alloc=4.6MB, time=84.80 x[1] = 0.403 y2[1] (analytic) = 0.39217976876466043663363083439577 y2[1] (numeric) = 0.39217976876466043663363083439581 absolute error = 4e-32 relative error = 1.0199404249229193009725824470568e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.91988859595697645007979385122064 y1[1] (numeric) = 0.91988859595697645007979385122065 absolute error = 1e-32 relative error = 1.0870881587130474565248940015103e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1380.9MB, alloc=4.6MB, time=85.03 x[1] = 0.404 y2[1] (analytic) = 0.39309946111743461324955485361347 y2[1] (numeric) = 0.39309946111743461324955485361351 absolute error = 4e-32 relative error = 1.0175541804686013506291784439434e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.91949595630931543137110117569449 y1[1] (numeric) = 0.9194959563093154313711011756945 absolute error = 1e-32 relative error = 1.0875523629422066449173931581915e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1384.7MB, alloc=4.6MB, time=85.26 memory used=1388.5MB, alloc=4.6MB, time=85.50 x[1] = 0.405 y2[1] (analytic) = 0.39401876037078043071820013323271 y2[1] (numeric) = 0.39401876037078043071820013323275 absolute error = 4e-32 relative error = 1.0151800884394212335267764694996e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.91910239716577472800744874996453 y1[1] (numeric) = 0.91910239716577472800744874996454 absolute error = 1e-32 relative error = 1.0880180522689183056476414679602e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1392.3MB, alloc=4.6MB, time=85.74 x[1] = 0.406 y2[1] (analytic) = 0.39493766560539871230201776315066 y2[1] (numeric) = 0.3949376656053987123020177631507 absolute error = 4e-32 relative error = 1.0128180592419344230910570637555e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.9187079189199134507329457358444 y1[1] (numeric) = 0.91870791891991345073294573584441 absolute error = 1e-32 relative error = 1.0884852295337328271810773008416e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1396.2MB, alloc=4.6MB, time=85.97 x[1] = 0.407 y2[1] (analytic) = 0.39585617590238429995815982522535 y2[1] (numeric) = 0.39585617590238429995815982522538 absolute error = 3e-32 relative error = 7.5785100312285681301900029526487e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91831252196620981253568334850355 y1[1] (numeric) = 0.91831252196620981253568334850356 absolute error = 1e-32 relative error = 1.0889538975891215783067964030870e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1400.0MB, alloc=4.6MB, time=86.21 x[1] = 0.408 y2[1] (analytic) = 0.39677429034322697324356086069621 y2[1] (numeric) = 0.39677429034322697324356086069625 absolute error = 4e-32 relative error = 1.0081298353630288090788803260249e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.91791620670006073416955474155938 y1[1] (numeric) = 0.91791620670006073416955474155939 absolute error = 1e-32 relative error = 1.0894240592995228076676963284722e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1403.8MB, alloc=4.6MB, time=86.44 x[1] = 0.409 y2[1] (analytic) = 0.39769200800981236782508177073383 y2[1] (numeric) = 0.39769200800981236782508177073387 absolute error = 4e-32 relative error = 1.0058034658572537530934404694972e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.91751897351778144875736720292634 y1[1] (numeric) = 0.91751897351778144875736720292635 absolute error = 1e-32 relative error = 1.0898957175413877968679018864632e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1407.6MB, alloc=4.6MB, time=86.68 memory used=1411.4MB, alloc=4.6MB, time=86.91 x[1] = 0.41 y2[1] (analytic) = 0.39860932798442289359379764005114 y2[1] (numeric) = 0.39860932798442289359379764005118 absolute error = 4e-32 relative error = 1.0034888095133374599884491128482e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.91712082281660510547564205827702 y1[1] (numeric) = 0.91712082281660510547564205827703 absolute error = 1e-32 relative error = 1.0903688752032272686284200446165e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1415.2MB, alloc=4.6MB, time=87.15 x[1] = 0.411 y2[1] (analytic) = 0.3995262493497386523825113693651 y2[1] (numeric) = 0.39952624934973865238251136936513 absolute error = 3e-32 relative error = 7.5088933577774754823854262655155e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91672175499468237232149859728209 y1[1] (numeric) = 0.91672175499468237232149859728211 absolute error = 2e-32 relative error = 2.1816870703713161029447099224486e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1419.0MB, alloc=4.6MB, time=87.38 x[1] = 0.412 y2[1] (analytic) = 0.40044277118883835528557539927145 y2[1] (numeric) = 0.40044277118883835528557539927148 absolute error = 3e-32 relative error = 7.4917072197197395039179107831999e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91632177045108103796201925571231 y1[1] (numeric) = 0.91632177045108103796201925571232 absolute error = 1e-32 relative error = 1.0913197004014500024314756274700e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1422.9MB, alloc=4.6MB, time=87.61 x[1] = 0.413 y2[1] (analytic) = 0.40135889258520023958010420578745 y2[1] (numeric) = 0.40135889258520023958010420578749 absolute error = 4e-32 relative error = 9.9661427064329520336276200726753e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91592086958578561266649420400396 y1[1] (numeric) = 0.91592086958578561266649420400397 absolute error = 1e-32 relative error = 1.0917973737755731892764706588433e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1426.7MB, alloc=4.6MB, time=87.85 x[1] = 0.414 y2[1] (analytic) = 0.40227461262270298524766064642639 y2[1] (numeric) = 0.40227461262270298524766064642643 absolute error = 4e-32 relative error = 9.9434562224080403230295990120675e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91551905279969692832194441001016 y1[1] (numeric) = 0.91551905279969692832194441001017 absolute error = 1e-32 relative error = 1.0922765582452453337838477924483e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1430.5MB, alloc=4.6MB, time=88.08 x[1] = 0.415 y2[1] (analytic) = 0.4031899303856266310954996351939 y2[1] (numeric) = 0.40318993038562663109549963519394 absolute error = 4e-32 relative error = 9.9208826871599780080242332572797e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91511632049463173753232316038139 y1[1] (numeric) = 0.9151163204946317375323231603814 absolute error = 1e-32 relative error = 1.0927572567599795175631403259152e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1434.3MB, alloc=4.6MB, time=88.32 TOP MAIN SOLVE Loop memory used=1438.1MB, alloc=4.6MB, time=88.56 x[1] = 0.416 y2[1] (analytic) = 0.40410484495865349047645302533885 y2[1] (numeric) = 0.40410484495865349047645302533889 absolute error = 4e-32 relative error = 9.8984212881913483864819381196430e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9147126730733223118017969413405 y1[1] (numeric) = 0.91471267307332231180179694134051 absolute error = 1e-32 relative error = 1.0932394722816321519788697873839e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1441.9MB, alloc=4.6MB, time=88.79 x[1] = 0.417 y2[1] (analytic) = 0.40501935542686906660653998005014 y2[1] (numeric) = 0.40501935542686906660653998005018 absolute error = 4e-32 relative error = 9.8760712208042766159547279682507e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91430811093941603880250749553771 y1[1] (numeric) = 0.91430811093941603880250749553772 absolute error = 1e-32 relative error = 1.0937232077844512137125842737185e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1445.7MB, alloc=4.6MB, time=89.03 x[1] = 0.418 y2[1] (analytic) = 0.40593346087576296747938751356535 y2[1] (numeric) = 0.40593346087576296747938751356539 absolute error = 4e-32 relative error = 9.8538316880071406773623546361553e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91390263449747501872721778719006 y1[1] (numeric) = 0.91390263449747501872721778719007 absolute error = 1e-32 relative error = 1.0942084662551247475212458618211e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1449.6MB, alloc=4.6MB, time=89.26 x[1] = 0.419 y2[1] (analytic) = 0.40684716039122982037654628834693 y2[1] (numeric) = 0.40684716039122982037654628834697 absolute error = 4e-32 relative error = 9.8317019004226182419508846578534e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91349624415297565972724552282569 y1[1] (numeric) = 0.9134962441529756597272455228257 absolute error = 1e-32 relative error = 1.0946952506928296377592790186274e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1453.4MB, alloc=4.6MB, time=89.50 x[1] = 0.42 y2[1] (analytic) = 0.40776045305957018597278715808634 y2[1] (numeric) = 0.40776045305957018597278715808638 absolute error = 4e-32 relative error = 9.8096810761970471765127527641685e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91308894031230827243608878966567 y1[1] (numeric) = 0.91308894031230827243608878966567 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1457.2MB, alloc=4.6MB, time=89.73 memory used=1461.0MB, alloc=4.6MB, time=89.97 x[1] = 0.421 y2[1] (analytic) = 0.40867333796749147203546435131582 y2[1] (numeric) = 0.40867333796749147203546435131586 absolute error = 4e-32 relative error = 9.7877684409110778449455816005453e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91268072338277666357914928798398 y1[1] (numeric) = 0.91268072338277666357914928798398 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1464.8MB, alloc=4.6MB, time=90.21 x[1] = 0.422 y2[1] (analytic) = 0.40958581420210884671703159634065 y2[1] (numeric) = 0.40958581420210884671703159634069 absolute error = 4e-32 relative error = 9.7659632274915957782921014440664e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91227159377259772866995954768862 y1[1] (numeric) = 0.91227159377259772866995954768862 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1468.6MB, alloc=4.6MB, time=90.44 x[1] = 0.423 y2[1] (analytic) = 0.41049788085094615143979789505198 y2[1] (numeric) = 0.41049788085094615143979789505202 absolute error = 4e-32 relative error = 9.7442646761248936906586534022070e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91186155189090104379332143286255 y1[1] (numeric) = 0.91186155189090104379332143286254 absolute error = 1e-32 relative error = 1.0966577085373638073046360026921e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1472.4MB, alloc=4.6MB, time=90.67 x[1] = 0.424 y2[1] (analytic) = 0.41140953700193681337201006094047 y2[1] (numeric) = 0.41140953700193681337201006094051 absolute error = 4e-32 relative error = 9.7226720341710722150627957056176e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.911450598147728456475764151092 y1[1] (numeric) = 0.91145059814772845647576415109199 absolute error = 1e-32 relative error = 1.0971521682384363345023532372612e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1476.3MB, alloc=4.6MB, time=90.91 x[1] = 0.425 y2[1] (analytic) = 0.41232078174342475749434954530431 y2[1] (numeric) = 0.41232078174342475749434954530435 absolute error = 4e-32 relative error = 9.7011845560796491215138579323319e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91103873295403367564373089709014 y1[1] (numeric) = 0.91103873295403367564373089709013 absolute error = 1e-32 relative error = 1.0976481721666326253890210251424e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1480.1MB, alloc=4.6MB, time=91.14 x[1] = 0.426 y2[1] (analytic) = 0.41323161416416531825593148523067 y2[1] (numeric) = 0.41323161416416531825593148523071 absolute error = 4e-32 relative error = 9.6798015033063571596810786359151e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91062595672168186066990417239512 y1[1] (numeric) = 0.91062595672168186066990417239511 absolute error = 1e-32 relative error = 1.0981457234099399545808867643122e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1483.9MB, alloc=4.6MB, time=91.38 TOP MAIN SOLVE Loop memory used=1487.7MB, alloc=4.6MB, time=91.62 x[1] = 0.427 y2[1] (analytic) = 0.41414203335332615081889431742766 y2[1] (numeric) = 0.4141420333533261508188943174277 absolute error = 4e-32 relative error = 9.6585221442311110405443147258658e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.91021226986344920950808073478303 y1[1] (numeric) = 0.91021226986344920950808073478302 absolute error = 1e-32 relative error = 1.0986448250692344757482343403711e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1491.5MB, alloc=4.6MB, time=91.85 x[1] = 0.428 y2[1] (analytic) = 0.41505203840048814189066871339302 y2[1] (numeric) = 0.41505203840048814189066871339306 absolute error = 4e-32 relative error = 9.6373457540771244356393858276575e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90979767279302254591700804248653 y1[1] (numeric) = 0.90979767279302254591700804248652 absolute error = 1e-32 relative error = 1.0991454802583324844035923962031e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1495.3MB, alloc=4.6MB, time=92.09 x[1] = 0.429 y2[1] (analytic) = 0.41596162839564632014301500372652 y2[1] (numeric) = 0.41596162839564632014301500372656 absolute error = 4e-32 relative error = 9.6162716148311582290862745264907e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90938216592499890577359496934819 y1[1] (numeric) = 0.90938216592499890577359496934817 absolute error = 2e-32 relative error = 2.1992953842080839315059628708188e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1499.2MB, alloc=4.6MB, time=92.32 x[1] = 0.43 y2[1] (analytic) = 0.41687080242921076621691867262457 y2[1] (numeric) = 0.4168708024292107662169186726246 absolute error = 3e-32 relative error = 7.1964742613736612050260047179132e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90896574967488512247591047766345 y1[1] (numeric) = 0.90896574967488512247591047766343 absolute error = 2e-32 relative error = 2.2003029274924288586094653589129e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1503.0MB, alloc=4.6MB, time=92.56 x[1] = 0.431 y2[1] (analytic) = 0.41777955959200752231243391773727 y2[1] (numeric) = 0.41777955959200752231243391773731 absolute error = 4e-32 relative error = 9.5744272503573279083175749020690e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90854842445909741143638484567998 y1[1] (numeric) = 0.90854842445909741143638484567997 absolute error = 1e-32 relative error = 1.1006567983377970319425245429763e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1506.8MB, alloc=4.6MB, time=92.80 memory used=1510.6MB, alloc=4.6MB, time=93.04 x[1] = 0.432 y2[1] (analytic) = 0.41868789897527950136256568562034 y2[1] (numeric) = 0.41868789897527950136256568562037 absolute error = 3e-32 relative error = 7.1652417166638206281038838563030e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90813019069496095366562895651753 y1[1] (numeric) = 0.90813019069496095366562895651752 absolute error = 1e-32 relative error = 1.1011636990448849911814902803781e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1514.4MB, alloc=4.6MB, time=93.27 x[1] = 0.433 y2[1] (analytic) = 0.41959581967068739579028100897533 y2[1] (numeric) = 0.41959581967068739579028100897536 absolute error = 3e-32 relative error = 7.1497375792602002127720640230471e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90771104880070947844728806465426 y1[1] (numeric) = 0.90771104880070947844728806465425 absolute error = 1e-32 relative error = 1.1016721690467742903385536275006e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1518.2MB, alloc=4.6MB, time=93.51 x[1] = 0.434 y2[1] (analytic) = 0.42050332077031058584774088874292 y2[1] (numeric) = 0.42050332077031058584774088874294 absolute error = 2e-32 relative error = 4.7562050076946953334654772190974e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90729099919548484510434736509116 y1[1] (numeric) = 0.90729099919548484510434736509115 absolute error = 1e-32 relative error = 1.1021822115360146773605489601626e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1522.0MB, alloc=4.6MB, time=93.74 x[1] = 0.435 y2[1] (analytic) = 0.42141040136664804753684438189271 y2[1] (numeric) = 0.42141040136664804753684438189273 absolute error = 2e-32 relative error = 4.7459673361500641806108164098112e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90687004229933662385730759885391 y1[1] (numeric) = 0.9068700422993366238573075988539 absolute error = 1e-32 relative error = 1.1026938297184629590661794710113e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1525.9MB, alloc=4.6MB, time=93.97 x[1] = 0.436 y2[1] (analytic) = 0.4223170605526192601101769744414 y2[1] (numeric) = 0.42231706055261926011017697444143 absolute error = 3e-32 relative error = 7.1036675527016987970064851551608e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90644817853322167577464983662187 y1[1] (numeric) = 0.90644817853322167577464983662186 absolute error = 1e-32 relative error = 1.1032070268133365925704619891571e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1529.7MB, alloc=4.6MB, time=94.21 x[1] = 0.437 y2[1] (analytic) = 0.42322329742156511315145573882644 y2[1] (numeric) = 0.42322329742156511315145573882647 absolute error = 3e-32 relative error = 7.0884566569872782011051919607947e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90602540831900373181600948998423 y1[1] (numeric) = 0.90602540831900373181600948998422 absolute error = 1e-32 relative error = 1.1037218060532675756730012041528e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1533.5MB, alloc=4.6MB, time=94.45 TOP MAIN SOLVE Loop memory used=1537.3MB, alloc=4.6MB, time=94.68 x[1] = 0.438 y2[1] (analytic) = 0.42412911106724881323456419526555 y2[1] (numeric) = 0.42412911106724881323456419526557 absolute error = 2e-32 relative error = 4.7155452144450541631758957129002e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90560173207945297096848050711436 y1[1] (numeric) = 0.90560173207945297096848050711436 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1541.1MB, alloc=4.6MB, time=94.92 x[1] = 0.439 y2[1] (analytic) = 0.42503450058385679016027021814296 y2[1] (numeric) = 0.42503450058385679016027021814299 absolute error = 3e-32 relative error = 7.0582505558466253593918757866471e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90517715023824559747647161652294 y1[1] (numeric) = 0.90517715023824559747647161652294 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1544.9MB, alloc=4.6MB, time=95.15 x[1] = 0.44 y2[1] (analytic) = 0.42593946506599960276972075077992 y2[1] (numeric) = 0.42593946506599960276972075077994 absolute error = 2e-32 relative error = 4.6955029153969066303347553414383e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90475166321996341716553738899837 y1[1] (numeric) = 0.90475166321996341716553738899837 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1548.7MB, alloc=4.6MB, time=95.38 x[1] = 0.441 y2[1] (analytic) = 0.42684400360871284433380751517007 y2[1] (numeric) = 0.4268440036087128443338075151701 absolute error = 3e-32 relative error = 7.0283287914010261741292161093605e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90432527145009341286060779386822 y1[1] (numeric) = 0.90432527145009341286060779386822 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1552.6MB, alloc=4.6MB, time=95.62 x[1] = 0.442 y2[1] (analytic) = 0.42774811530745804751749832738978 y2[1] (numeric) = 0.42774811530745804751749832738981 absolute error = 3e-32 relative error = 7.0134733331172042282027198338809e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90389797535502731889904083131662 y1[1] (numeric) = 0.90389797535502731889904083131662 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1556.4MB, alloc=4.6MB, time=95.85 memory used=1560.2MB, alloc=4.6MB, time=96.09 x[1] = 0.443 y2[1] (analytic) = 0.42865179925812358891822905442715 y2[1] (numeric) = 0.42865179925812358891822905442718 absolute error = 3e-32 relative error = 6.9986875249145371214266665345893e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90346977536206119473892372766962 y1[1] (numeric) = 0.90346977536206119473892372766962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1564.0MB, alloc=4.6MB, time=96.32 x[1] = 0.444 y2[1] (analytic) = 0.42955505455702559317745167411342 y2[1] (numeric) = 0.42955505455702559317745167411345 absolute error = 3e-32 relative error = 6.9839708977321204279363593187274e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9030406718993949976630490853117 y1[1] (numeric) = 0.9030406718993949976630490853117 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1567.8MB, alloc=4.6MB, time=96.56 x[1] = 0.445 y2[1] (analytic) = 0.43045788030090883666443432668387 y2[1] (numeric) = 0.4304578803009088366644343266839 absolute error = 3e-32 relative error = 6.9693229867295474477654143642488e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9026106653961321545789932832218 y1[1] (numeric) = 0.9026106653961321545789932832218 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1571.6MB, alloc=4.6MB, time=96.79 x[1] = 0.446 y2[1] (analytic) = 0.43136027558694765073140967424357 y2[1] (numeric) = 0.4313602755869476507314096742436 absolute error = 3e-32 relative error = 6.9547433312395995210476414867604e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90217975628227913291572532801462 y1[1] (numeric) = 0.90217975628227913291572532801461 absolute error = 1e-32 relative error = 1.1084265558349707781717733888835e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1575.4MB, alloc=4.6MB, time=97.03 x[1] = 0.447 y2[1] (analytic) = 0.43226223951274682453916831306481 y2[1] (numeric) = 0.43226223951274682453916831306484 absolute error = 3e-32 relative error = 6.9402314747215713879872932643911e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.9017479449887450106171752588427 y1[1] (numeric) = 0.90174794498874501061717525884269 absolute error = 1e-32 relative error = 1.1089573373105733033385910269229e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1579.3MB, alloc=4.6MB, time=97.26 x[1] = 0.448 y2[1] (analytic) = 0.43316377117634250745219441319813 y2[1] (numeric) = 0.43316377117634250745219441319816 absolute error = 3e-32 relative error = 6.9257869647152216720414392570399e-30 % Correct digits = 31 h = 0.001 memory used=1583.1MB, alloc=4.6MB, time=97.50 y1[1] (analytic) = 0.90131523194734104523319211255506 y1[1] (numeric) = 0.90131523194734104523319211255505 absolute error = 1e-32 relative error = 1.1094897373912622059132403946480e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1586.9MB, alloc=4.6MB, time=97.74 x[1] = 0.449 y2[1] (analytic) = 0.43406486967620311100244119033643 y2[1] (numeric) = 0.43406486967620311100244119033646 absolute error = 3e-32 relative error = 6.9114093527953387405522176262936e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90088161759078024210832235811838 y1[1] (numeric) = 0.90088161759078024210832235811837 absolute error = 1e-32 relative error = 1.1100237594749587332642771591024e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1590.7MB, alloc=4.6MB, time=97.97 x[1] = 0.45 y2[1] (analytic) = 0.4349655341112302104208442462319 y2[1] (numeric) = 0.43496553411123021042084424623192 absolute error = 2e-32 relative error = 4.5980654630179415802165551129761e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90044710235267692166884061148645 y1[1] (numeric) = 0.90044710235267692166884061148644 absolute error = 1e-32 relative error = 1.1105594069737272884444606710116e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1594.5MB, alloc=4.6MB, time=98.20 x[1] = 0.451 y2[1] (analytic) = 0.43586576358075944573567124622747 y2[1] (numeric) = 0.43586576358075944573567124622749 absolute error = 2e-32 relative error = 4.5885686996139345436318695362377e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.90001168666754628580846534385106 y1[1] (numeric) = 0.90001168666754628580846534385105 absolute error = 1e-32 relative error = 1.1110966833138337004656911332807e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1598.3MB, alloc=4.6MB, time=98.44 x[1] = 0.452 y2[1] (analytic) = 0.43676555718456142243680683562839 y2[1] (numeric) = 0.43676555718456142243680683562841 absolute error = 2e-32 relative error = 4.5791156539270606940477515154839e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89957537097080398337319319752249 y1[1] (numeric) = 0.89957537097080398337319319752248 absolute error = 1e-32 relative error = 1.1116355919358038218513076101737e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1602.2MB, alloc=4.6MB, time=98.67 x[1] = 0.453 y2[1] (analytic) = 0.43766491402284261170507213070383 y2[1] (numeric) = 0.43766491402284261170507213070385 absolute error = 2e-32 relative error = 4.5697060374723480333168661495391e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89913815569876567474568642456905 y1[1] (numeric) = 0.89913815569876567474568642456903 absolute error = 2e-32 relative error = 2.2243522725889649109288115083088e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1606.0MB, alloc=4.6MB, time=98.90 memory used=1609.8MB, alloc=4.6MB, time=99.14 x[1] = 0.454 y2[1] (analytic) = 0.43856383319624625020567855507421 y2[1] (numeric) = 0.43856383319624625020567855507423 absolute error = 2e-32 relative error = 4.5603395643093315924199699858656e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89870004128864659552964886379195 y1[1] (numeric) = 0.89870004128864659552964886379193 absolute error = 2e-32 relative error = 2.2254366397181852252507064117118e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1613.6MB, alloc=4.6MB, time=99.38 x[1] = 0.455 y2[1] (analytic) = 0.43946231380585323944491622810532 y2[1] (numeric) = 0.43946231380585323944491622810533 absolute error = 1e-32 relative error = 2.2755079755070476920620552155018e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89826102817856111933462677162328 y1[1] (numeric) = 0.89826102817856111933462677162326 absolute error = 2e-32 relative error = 2.2265242922265902090926318300223e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1617.4MB, alloc=4.6MB, time=99.61 x[1] = 0.456 y2[1] (analytic) = 0.44036035495318304468917754869582 y2[1] (numeric) = 0.44036035495318304468917754869583 absolute error = 1e-32 relative error = 2.2708674583258411178118926462703e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89782111680752231966167172210963 y1[1] (numeric) = 0.89782111680752231966167172210961 absolute error = 2e-32 relative error = 2.2276152371104969382507223666644e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1621.2MB, alloc=4.6MB, time=99.85 x[1] = 0.457 y2[1] (analytic) = 0.44125795574019459344541705550947 y2[1] (numeric) = 0.44125795574019459344541705550948 absolute error = 1e-32 relative error = 2.2662480913744329331323879533012e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89738030761544153089030369028207 y1[1] (numeric) = 0.89738030761544153089030369028205 absolute error = 2e-32 relative error = 2.2287094813953384703151482029441e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1625.0MB, alloc=4.6MB, time=100.08 x[1] = 0.458 y2[1] (analytic) = 0.44215511526928717350214908326701 y2[1] (numeric) = 0.44215511526928717350214908326703 absolute error = 2e-32 relative error = 4.5232994732672796738766541225653e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89693860104312790836721333191287 y1[1] (numeric) = 0.89693860104312790836721333191285 absolute error = 2e-32 relative error = 2.2298070321357850520712286179923e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1628.9MB, alloc=4.6MB, time=100.32 memory used=1632.7MB, alloc=4.6MB, time=100.56 x[1] = 0.459 y2[1] (analytic) = 0.44305183264330133053008517417501 y2[1] (numeric) = 0.44305183264330133053008517417503 absolute error = 2e-32 relative error = 4.5141445145768967897363232810856e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89649599753228798759714337091984 y1[1] (numeric) = 0.89649599753228798759714337091983 absolute error = 1e-32 relative error = 1.1154539482079330050272507269036e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1636.5MB, alloc=4.6MB, time=100.80 x[1] = 0.46 y2[1] (analytic) = 0.4439481069655197652415136439289 y2[1] (numeric) = 0.44394810696551976524151364392892 absolute error = 2e-32 relative error = 4.5050310354298560567933411674058e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89605249752552524253638990350041 y1[1] (numeric) = 0.89605249752552524253638990350039 absolute error = 2e-32 relative error = 2.2320120813490923284652883710187e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1640.3MB, alloc=4.6MB, time=101.03 x[1] = 0.461 y2[1] (analytic) = 0.44484393733966823010752414298558 y2[1] (numeric) = 0.44484393733966823010752414298561 absolute error = 3e-32 relative error = 6.7439381504019430178237138850905e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89560810146633964298936532545704 y1[1] (numeric) = 0.89560810146633964298936532545703 absolute error = 1e-32 relative error = 1.1165597970392899593395027960309e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1644.1MB, alloc=4.6MB, time=101.27 x[1] = 0.462 y2[1] (analytic) = 0.44573932286991642563218049595565 y2[1] (numeric) = 0.44573932286991642563218049595567 absolute error = 2e-32 relative error = 4.4869274425305203769366094750099e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89516280979912721110866548611451 y1[1] (numeric) = 0.8951628097991272111086654861145 absolute error = 1e-32 relative error = 1.1171152208885867923097136025077e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1647.9MB, alloc=4.6MB, time=101.50 x[1] = 0.463 y2[1] (analytic) = 0.44663426266087889618274554501705 y2[1] (numeric) = 0.44663426266087889618274554501707 absolute error = 2e-32 relative error = 4.4779367979625039867327561071813e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8947166229691795769990845687246 y1[1] (numeric) = 0.89471662296917957699908456872459 absolute error = 1e-32 relative error = 1.1176723158237858441466576232054e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1651.7MB, alloc=4.6MB, time=101.74 x[1] = 0.464 y2[1] (analytic) = 0.44752875581761592537506216720012 y2[1] (numeric) = 0.44752875581761592537506216720015 absolute error = 3e-32 relative error = 6.7034798568845662522405651063585e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89426954142268353342602209330656 y1[1] (numeric) = 0.89426954142268353342602209330655 absolute error = 1e-32 relative error = 1.1182310854612257599081449800410e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1655.6MB, alloc=4.6MB, time=101.98 TOP MAIN SOLVE Loop memory used=1659.4MB, alloc=4.6MB, time=102.21 x[1] = 0.465 y2[1] (analytic) = 0.44842280144563443101319508023752 y2[1] (numeric) = 0.44842280144563443101319508023755 absolute error = 3e-32 relative error = 6.6901147540413640076473167541059e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89382156560672058962872733347906 y1[1] (numeric) = 0.89382156560672058962872733347905 absolute error = 1e-32 relative error = 1.1187915334322976881457635646674e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1663.2MB, alloc=4.6MB, time=102.45 x[1] = 0.466 y2[1] (analytic) = 0.44931639865088885958243849741175 y2[1] (numeric) = 0.44931639865088885958243849741179 absolute error = 4e-32 relative error = 8.9024126695805986808530238806749e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89337269596926652423882733400213 y1[1] (numeric) = 0.89337269596926652423882733400212 absolute error = 1e-32 relative error = 1.1193536633835086769674197558954e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1667.0MB, alloc=4.6MB, time=102.69 x[1] = 0.467 y2[1] (analytic) = 0.45020954653978208029479513846738 y2[1] (numeric) = 0.45020954653978208029479513846742 absolute error = 4e-32 relative error = 8.8847516245339015650426257227857e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89292293295919093730458561046372 y1[1] (numeric) = 0.89292293295919093730458561046372 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1670.8MB, alloc=4.6MB, time=102.92 x[1] = 0.468 y2[1] (analytic) = 0.45110224421916627868603255118318 y2[1] (numeric) = 0.45110224421916627868603255118321 absolute error = 3e-32 relative error = 6.6503770230468230967162567400517e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.892472277026256801421339506815 y1[1] (numeric) = 0.892472277026256801421339506815 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1674.6MB, alloc=4.6MB, time=103.16 x[1] = 0.469 y2[1] (analytic) = 0.45199449079634384976342314662252 y2[1] (numeric) = 0.45199449079634384976342314662255 absolute error = 3e-32 relative error = 6.6372490397271602754827602645252e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89202072862112001196856508027942 y1[1] (numeric) = 0.89202072862112001196856508027942 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1678.4MB, alloc=4.6MB, time=103.39 memory used=1682.3MB, alloc=4.6MB, time=103.63 x[1] = 0.47 y2[1] (analytic) = 0.45288628537906829070327480039641 y2[1] (numeric) = 0.45288628537906829070327480039644 absolute error = 3e-32 relative error = 6.6241793952514672404578861362144e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89156828819532893645401927653339 y1[1] (numeric) = 0.89156828819532893645401927653339 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1686.1MB, alloc=4.6MB, time=103.87 x[1] = 0.471 y2[1] (analytic) = 0.45377762707554509309735932248279 y2[1] (numeric) = 0.45377762707554509309735932248283 absolute error = 4e-32 relative error = 8.8148902928043173274099934196001e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89111495620132396296541005097869 y1[1] (numeric) = 0.89111495620132396296541005097869 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1689.9MB, alloc=4.6MB, time=104.11 x[1] = 0.472 y2[1] (analytic) = 0.45466851499443263474734654924825 y2[1] (numeric) = 0.45466851499443263474734654924829 absolute error = 4e-32 relative error = 8.7976181945410923249048812269718e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89066073309243704773004598439895 y1[1] (numeric) = 0.89066073309243704773004598439894 absolute error = 1e-32 relative error = 1.1227619707988352486577934387919e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1693.7MB, alloc=4.6MB, time=104.34 x[1] = 0.473 y2[1] (analytic) = 0.45555894824484307100635226331207 y2[1] (numeric) = 0.45555894824484307100635226331211 absolute error = 4e-32 relative error = 8.7804224138522999913929785756948e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.89020561932289126178291783331278 y1[1] (numeric) = 0.89020561932289126178291783331277 absolute error = 1e-32 relative error = 1.1233359779964325620130509045629e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1697.5MB, alloc=4.6MB, time=104.58 x[1] = 0.474 y2[1] (analytic) = 0.45644892593634322566670859977923 y2[1] (numeric) = 0.45644892593634322566670859977927 absolute error = 4e-32 relative error = 8.7633024698098283349560546802955e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.88974961534780033674366534690441 y1[1] (numeric) = 0.8897496153478003367436653469044 absolute error = 1e-32 relative error = 1.1239116968981246857282291654267e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1701.3MB, alloc=4.6MB, time=104.81 x[1] = 0.475 y2[1] (analytic) = 0.45733844717895548139306605114609 y2[1] (numeric) = 0.45733844717895548139306605114613 absolute error = 4e-32 relative error = 8.7462578855409661407826410222987e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.88929272162316820970288357352693 y1[1] (numeric) = 0.88929272162316820970288357352692 absolute error = 1e-32 relative error = 1.1244891312893745379301824617937e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1705.1MB, alloc=4.6MB, time=105.05 TOP MAIN SOLVE Loop memory used=1709.0MB, alloc=4.6MB, time=105.29 x[1] = 0.476 y2[1] (analytic) = 0.45822751108315866969993663785086 y2[1] (numeric) = 0.45822751108315866969993663785091 absolute error = 5e-32 relative error = 1.0911610235232264368679234991757e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88883493860588856721822377043406 y1[1] (numeric) = 0.88883493860588856721822377043405 absolute error = 1e-32 relative error = 1.1250682849714150061864524533318e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1712.8MB, alloc=4.6MB, time=105.52 x[1] = 0.477 y2[1] (analytic) = 0.45911611675988896047278826700008 y2[1] (numeric) = 0.45911611675988896047278826700013 absolute error = 5e-32 relative error = 1.0890491136069020089842364419873e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88837626675374438842074492060154 y1[1] (numeric) = 0.88837626675374438842074492060153 absolute error = 1e-32 relative error = 1.1256491617613164161140392157565e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1716.6MB, alloc=4.6MB, time=105.76 x[1] = 0.478 y2[1] (analytic) = 0.46000426332054075103180075825063 y2[1] (numeric) = 0.46000426332054075103180075825068 absolute error = 5e-32 relative error = 1.0869464478236571674625043523921e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88791670652540748723197275024844 y1[1] (numeric) = 0.88791670652540748723197275024843 absolute error = 1e-32 relative error = 1.1262317654920543842678767071606e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1720.4MB, alloc=4.6MB, time=106.00 x[1] = 0.479 y2[1] (analytic) = 0.46089194987696755473739447316549 y2[1] (numeric) = 0.46089194987696755473739447316554 absolute error = 5e-32 relative error = 1.0848529685395288710723081657152e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88745625838043805369212402996133 y1[1] (numeric) = 0.88745625838043805369212402996132 absolute error = 1e-32 relative error = 1.1268161000125780577258209249590e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1724.2MB, alloc=4.6MB, time=106.23 x[1] = 0.48 y2[1] (analytic) = 0.46177917554148288913664294258864 y2[1] (numeric) = 0.46177917554148288913664294258869 absolute error = 5e-32 relative error = 1.0827686186015194819756811270705e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88699492277928419439995483115874 y1[1] (numeric) = 0.88699492277928419439995483115873 absolute error = 1e-32 relative error = 1.1274021691878787428048684309357e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1728.0MB, alloc=4.6MB, time=106.47 memory used=1731.9MB, alloc=4.6MB, time=106.71 x[1] = 0.481 y2[1] (analytic) = 0.46266593942686116364968134570045 y2[1] (numeric) = 0.4626659394268611636496813457005 absolute error = 5e-32 relative error = 1.0806933413325980384527613285318e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88653270018328147206469229800935 y1[1] (numeric) = 0.88653270018328147206469229800934 absolute error = 1e-32 relative error = 1.1279899768990589253613794742235e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1735.7MB, alloc=4.6MB, time=106.94 x[1] = 0.482 y2[1] (analytic) = 0.4635522406463385667952231544191 y2[1] (numeric) = 0.46355224064633856679522315441915 absolute error = 5e-32 relative error = 1.0786270805267637551828371284237e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88606959105465244417051038283381 y1[1] (numeric) = 0.88606959105465244417051038283379 absolute error = 2e-32 relative error = 2.2571590540868033702925698905256e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1739.5MB, alloc=4.6MB, time=107.18 x[1] = 0.483 y2[1] (analytic) = 0.46443807831361395295429771770524 y2[1] (numeric) = 0.4644380783136139529542977177053 absolute error = 6e-32 relative error = 1.2918837365330050190856999804713e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88560559585650620075401088047591 y1[1] (numeric) = 0.8856055958565062007540108804759 absolute error = 1e-32 relative error = 1.1291708235344405067046112164811e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1743.3MB, alloc=4.6MB, time=107.42 x[1] = 0.484 y2[1] (analytic) = 0.46532345154284972867132202210636 y2[1] (numeric) = 0.46532345154284972867132202210642 absolute error = 6e-32 relative error = 1.2894256629675765658245570455974e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88514071505283790129517198412375 y1[1] (numeric) = 0.88514071505283790129517198412374 absolute error = 1e-32 relative error = 1.1297638703020294893271629500802e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1747.1MB, alloc=4.6MB, time=107.65 x[1] = 0.485 y2[1] (analytic) = 0.46620835944867273849162032754275 y2[1] (numeric) = 0.46620835944867273849162032754281 absolute error = 6e-32 relative error = 1.2869782101495266456026110018749e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88467494910852831072222747159347 y1[1] (numeric) = 0.88467494910852831072222747159346 absolute error = 1e-32 relative error = 1.1303586712924139585808625763331e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1750.9MB, alloc=4.6MB, time=107.88 x[1] = 0.486 y2[1] (analytic) = 0.46709280114617515033450584088946 y2[1] (numeric) = 0.46709280114617515033450584088952 absolute error = 6e-32 relative error = 1.2845413128348171233867659410990e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88420829848934333453094051715798 y1[1] (numeric) = 0.88420829848934333453094051715796 absolute error = 2e-32 relative error = 2.2619104609366029639261155555265e-30 % Correct digits = 31 h = 0.001 memory used=1754.7MB, alloc=4.6MB, time=108.12 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1758.6MB, alloc=4.6MB, time=108.36 x[1] = 0.487 y2[1] (analytic) = 0.46797677575091534040103905434617 y2[1] (numeric) = 0.46797677575091534040103905434623 absolute error = 6e-32 relative error = 1.2821149063161099152631923366510e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88374076366193355301873700960789 y1[1] (numeric) = 0.88374076366193355301873700960788 absolute error = 1e-32 relative error = 1.1315535518089332912440763803658e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1762.4MB, alloc=4.6MB, time=108.59 x[1] = 0.488 y2[1] (analytic) = 0.46886028237891877761557784091055 y2[1] (numeric) = 0.46886028237891877761557784091061 absolute error = 6e-32 relative error = 1.2796989264172691153353038613703e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88327234509383375463416414237277 y1[1] (numeric) = 0.88327234509383375463416414237276 absolute error = 1e-32 relative error = 1.1321536393101561140814329919753e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1766.2MB, alloc=4.6MB, time=108.83 x[1] = 0.489 y2[1] (analytic) = 0.46974332014667890760023486547853 y2[1] (numeric) = 0.46974332014667890760023486547859 absolute error = 6e-32 relative error = 1.2772933094879305844715825535970e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88280304325346246844214092620495 y1[1] (numeric) = 0.88280304325346246844214092620494 absolute error = 1e-32 relative error = 1.1327554969844944175083749939063e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1770.0MB, alloc=4.6MB, time=109.07 x[1] = 0.49 y2[1] (analytic) = 0.47062588817115803618135833718796 y2[1] (numeric) = 0.47062588817115803618135833718801 absolute error = 5e-32 relative error = 1.0624149936651150309747700341755e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88233285861012149570546815913666 y1[1] (numeric) = 0.88233285861012149570546815913665 absolute error = 1e-32 relative error = 1.1333591288612230659188985538320e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1773.8MB, alloc=4.6MB, time=109.31 x[1] = 0.491 y2[1] (analytic) = 0.47150798556978821242715259659826 y2[1] (numeric) = 0.47150798556978821242715259659831 absolute error = 5e-32 relative error = 1.0604274271108705654216490220639e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88186179163399544058306627216136 y1[1] (numeric) = 0.88186179163399544058306627216136 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1777.6MB, alloc=4.6MB, time=109.54 memory used=1781.4MB, alloc=4.6MB, time=109.78 x[1] = 0.492 y2[1] (analytic) = 0.47238961146047211121555550015936 y2[1] (numeric) = 0.47238961146047211121555550015941 absolute error = 5e-32 relative error = 1.0584483398230662154614424236148e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88138984279615123994541035236238 y1[1] (numeric) = 0.88138984279615123994541035236238 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1785.3MB, alloc=4.6MB, time=110.02 x[1] = 0.493 y2[1] (analytic) = 0.47327076496158391533149003416583 y2[1] (numeric) = 0.47327076496158391533149003416588 absolute error = 5e-32 relative error = 1.0564776804681475223242563326647e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88091701256853769230763252801455 y1[1] (numeric) = 0.88091701256853769230763252801455 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1789.1MB, alloc=4.6MB, time=110.25 x[1] = 0.494 y2[1] (analytic) = 0.47415144519197019709260806101824 y2[1] (numeric) = 0.47415144519197019709260806101829 absolute error = 5e-32 relative error = 1.0545153981288920698828757795271e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.88044330142398498588076278251734 y1[1] (numeric) = 0.88044330142398498588076278251734 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1792.9MB, alloc=4.6MB, time=110.48 x[1] = 0.495 y2[1] (analytic) = 0.47503165127095079950264457212144 y2[1] (numeric) = 0.47503165127095079950264457212149 absolute error = 5e-32 relative error = 1.0525614423002050355653096301856e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87996870983620422574158014587922 y1[1] (numeric) = 0.87996870983620422574158014587922 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1796.7MB, alloc=4.6MB, time=110.72 x[1] = 0.496 y2[1] (analytic) = 0.47591138231831971693150129413895 y2[1] (numeric) = 0.475911382318319716931501294139 absolute error = 5e-32 relative error = 1.0506157628849656042785807241024e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87949323827978696012154709386275 y1[1] (numeric) = 0.87949323827978696012154709386276 absolute error = 1e-32 relative error = 1.1370184061402380862236670991261e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1800.5MB, alloc=4.6MB, time=110.95 memory used=1804.3MB, alloc=4.6MB, time=111.19 x[1] = 0.497 y2[1] (analytic) = 0.47679063745434597532117896859318 y2[1] (numeric) = 0.47679063745434597532117896859324 absolute error = 6e-32 relative error = 1.2584139722279082347632426540342e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.8790168872302047058153008658165 y1[1] (numeric) = 0.87901688723020470581530086581651 absolute error = 1e-32 relative error = 1.1376345716758808617769342573840e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1808.1MB, alloc=4.6MB, time=111.42 x[1] = 0.498 y2[1] (analytic) = 0.47766941579977451191667809895267 y2[1] (numeric) = 0.47766941579977451191667809895273 absolute error = 6e-32 relative error = 1.2560988419059741595461893034857e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87853965716380847270917629266282 y1[1] (numeric) = 0.87853965716380847270917629266284 absolute error = 2e-32 relative error = 2.2765050885199701102791259835467e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1812.0MB, alloc=4.6MB, time=111.66 x[1] = 0.499 y2[1] (analytic) = 0.47854771647582705452098843437875 y2[1] (numeric) = 0.47854771647582705452098843437881 absolute error = 6e-32 relative error = 1.2537934658190096725520241235896e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87806154855782828743023560647926 y1[1] (numeric) = 0.87806154855782828743023560647928 absolute error = 2e-32 relative error = 2.2777446561518368633259521541912e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1815.8MB, alloc=4.6MB, time=111.89 x[1] = 0.5 y2[1] (analytic) = 0.47942553860420300027328793521557 y2[1] (numeric) = 0.47942553860420300027328793521563 absolute error = 6e-32 relative error = 1.2514977857600929114635010052756e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87758256189037271611628158260383 y1[1] (numeric) = 0.87758256189037271611628158260385 absolute error = 2e-32 relative error = 2.2789878546490982446266555364099e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1819.6MB, alloc=4.6MB, time=112.13 x[1] = 0.501 y2[1] (analytic) = 0.4803028813070802939494724420977 y2[1] (numeric) = 0.48030288130708029394947244209776 absolute error = 6e-32 relative error = 1.2492117439878352311009403325577e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87710269764042838630733124421144 y1[1] (numeric) = 0.87710269764042838630733124421146 absolute error = 2e-32 relative error = 2.2802346924486460398070351204458e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1823.4MB, alloc=4.6MB, time=112.37 x[1] = 0.502 y2[1] (analytic) = 0.48117974370711630578413774821874 y2[1] (numeric) = 0.4811797437071163057841377482188 absolute error = 6e-32 relative error = 1.2469352832217455359012105707935e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87662195628785950795902823784783 y1[1] (numeric) = 0.87662195628785950795902823784785 absolute error = 2e-32 relative error = 2.2814851780226832457280758047914e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1827.2MB, alloc=4.6MB, time=112.60 memory used=1831.0MB, alloc=4.6MB, time=112.84 x[1] = 0.503 y2[1] (analytic) = 0.48205612492744870881313625285219 y2[1] (numeric) = 0.48205612492744870881313625285225 absolute error = 6e-32 relative error = 1.2446683466376499119225596428735e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87614033831340739357847286646878 y1[1] (numeric) = 0.8761403383134073935784728664688 absolute error = 2e-32 relative error = 2.2827393198788806588855679181949e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1834.9MB, alloc=4.6MB, time=113.08 x[1] = 0.504 y2[1] (analytic) = 0.48293202409169635573583085364091 y2[1] (numeric) = 0.48293202409169635573583085364097 absolute error = 6e-32 relative error = 1.2424108778631657903336583275225e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87565784419868997748294964411447 y1[1] (numeric) = 0.87565784419868997748294964411449 absolute error = 2e-32 relative error = 2.2839971265605343704915932179880e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1838.7MB, alloc=4.6MB, time=113.31 x[1] = 0.505 y2[1] (analytic) = 0.48380744032396015529616921547434 y2[1] (numeric) = 0.4838074403239601552961692154744 absolute error = 6e-32 relative error = 1.2401628209732298865122395500300e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87517447442620133418203311345153 y1[1] (numeric) = 0.87517447442620133418203311345154 absolute error = 1e-32 relative error = 1.1426293033233620870529366873743e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1842.5MB, alloc=4.6MB, time=113.54 x[1] = 0.506 y2[1] (analytic) = 0.48468237274882394818170203495237 y2[1] (numeric) = 0.48468237274882394818170203495243 absolute error = 6e-32 relative error = 1.2379241204856791708293296749595e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87469022947931119588355354403665 y1[1] (numeric) = 0.87469022947931119588355354403667 absolute error = 2e-32 relative error = 2.2865237687524728917294014720894e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1846.3MB, alloc=4.6MB, time=113.78 x[1] = 0.507 y2[1] (analytic) = 0.48555682049135538243966940149045 y2[1] (numeric) = 0.48555682049135538243966940149051 absolute error = 6e-32 relative error = 1.2356947213568841389335391829543e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87420510984226446912390500529606 y1[1] (numeric) = 0.87420510984226446912390500529608 absolute error = 2e-32 relative error = 2.2877926215289066243175759534846e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1850.1MB, alloc=4.6MB, time=114.02 memory used=1853.9MB, alloc=4.6MB, time=114.25 x[1] = 0.508 y2[1] (analytic) = 0.48643078267710678840927983905261 y2[1] (numeric) = 0.48643078267710678840927983905267 absolute error = 6e-32 relative error = 1.2334745689774336608803864232663e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87371911600018075052317918387225 y1[1] (numeric) = 0.87371911600018075052317918387227 absolute error = 2e-32 relative error = 2.2890651736634159327152332651751e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1857.7MB, alloc=4.6MB, time=114.49 x[1] = 0.509 y2[1] (analytic) = 0.48730425843211605316930709630622 y2[1] (numeric) = 0.48730425843211605316930709630627 absolute error = 5e-32 relative error = 1.0260530076398922498152126967148e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87323224843905384166560919016402 y1[1] (numeric) = 0.87323224843905384166560919016404 absolute error = 2e-32 relative error = 2.2903414338798179550615337415318e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1861.6MB, alloc=4.6MB, time=114.72 x[1] = 0.51 y2[1] (analytic) = 0.48817724688290749450013023767457 y2[1] (numeric) = 0.48817724688290749450013023767463 absolute error = 6e-32 relative error = 1.2290617881744782017493327657050e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87274450764575126310580847357551 y1[1] (numeric) = 0.87274450764575126310580847357552 absolute error = 1e-32 relative error = 1.1458107054692597333792993299734e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1865.4MB, alloc=4.6MB, time=114.96 x[1] = 0.511 y2[1] (analytic) = 0.48904974715649273435934307332011 y2[1] (numeric) = 0.48904974715649273435934307332016 absolute error = 5e-32 relative error = 1.0223908772209287249455410961681e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87225589410801376750129084019472 y1[1] (numeric) = 0.87225589410801376750129084019473 absolute error = 1e-32 relative error = 1.1464525568183404445720642484331e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1869.2MB, alloc=4.6MB, time=115.19 x[1] = 0.512 y2[1] (analytic) = 0.48992175838037157187005945252148 y2[1] (numeric) = 0.48992175838037157187005945252153 absolute error = 5e-32 relative error = 1.0205711247709144550091459697206e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87176640831445485187175844034113 y1[1] (numeric) = 0.87176640831445485187175844034114 absolute error = 1e-32 relative error = 1.1470962754041906265274784616296e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1873.0MB, alloc=4.6MB, time=115.43 x[1] = 0.513 y2[1] (analytic) = 0.49079327968253285582104143221207 y2[1] (numeric) = 0.49079327968253285582104143221213 absolute error = 6e-32 relative error = 1.2225106268531365332375653422479e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87127605075456026898564546665356 y1[1] (numeric) = 0.87127605075456026898564546665358 absolute error = 2e-32 relative error = 2.2954837313247841235156157031524e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1876.8MB, alloc=4.6MB, time=115.67 TOP MAIN SOLVE Loop memory used=1880.6MB, alloc=4.6MB, time=115.91 x[1] = 0.514 y2[1] (analytic) = 0.49166431019145535667777782062445 y2[1] (numeric) = 0.4916643101914553566777778206245 absolute error = 5e-32 relative error = 1.0169540266310945045135398115910e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87078482191868753787440617613407 y1[1] (numeric) = 0.87078482191868753787440617613409 absolute error = 2e-32 relative error = 2.2967786640943044918335061579724e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1884.4MB, alloc=4.6MB, time=116.14 x[1] = 0.515 y2[1] (analytic) = 0.4925348490361086381036410850348 y2[1] (numeric) = 0.49253484903610863810364108503486 absolute error = 6e-32 relative error = 1.2181879133511076563327099106899e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.87029272229806545347503672181887 y1[1] (numeric) = 0.87029272229806545347503672181889 absolute error = 2e-32 relative error = 2.2980773580627766414301970265977e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1888.3MB, alloc=4.6MB, time=116.38 x[1] = 0.516 y2[1] (analytic) = 0.49340489534595392799025110252325 y2[1] (numeric) = 0.4934048953459539279902511025233 absolute error = 5e-32 relative error = 1.0133665164578917952113038787809e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86979975238479359540132115151374 y1[1] (numeric) = 0.86979975238479359540132115151376 absolute error = 2e-32 relative error = 2.2993798222136229937867002199696e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1892.1MB, alloc=4.6MB, time=116.61 x[1] = 0.517 y2[1] (analytic) = 0.49427444825094498899617472345866 y2[1] (numeric) = 0.49427444825094498899617472345871 absolute error = 5e-32 relative error = 1.0115837502207844799052531210517e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86930591267184183584429280230693 y1[1] (numeric) = 0.86930591267184183584429280230695 absolute error = 2e-32 relative error = 2.3006860655680239409293190136215e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1895.9MB, alloc=4.6MB, time=116.84 x[1] = 0.518 y2[1] (analytic) = 0.49514350688152898859309060908113 y2[1] (numeric) = 0.49514350688152898859309060908119 absolute error = 6e-32 relative error = 1.2117699044038148038709388666307e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86881120365304984660240319035711 y1[1] (numeric) = 0.86881120365304984660240319035714 absolute error = 3e-32 relative error = 3.4529941457776330063977323335995e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1899.7MB, alloc=4.6MB, time=117.08 memory used=1903.5MB, alloc=4.6MB, time=117.31 x[1] = 0.519 y2[1] (analytic) = 0.49601207036864736861854929708972 y2[1] (numeric) = 0.49601207036864736861854929708978 absolute error = 6e-32 relative error = 1.2096479820623446813662790751742e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.8683156258231266052418913657465 y1[1] (numeric) = 0.86831562582312660524189136574652 absolute error = 2e-32 relative error = 2.3033099261620269929592701474078e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1907.3MB, alloc=4.6MB, time=117.55 x[1] = 0.52 y2[1] (analytic) = 0.49688013784373671433445894254775 y2[1] (numeric) = 0.49688013784373671433445894254781 absolute error = 6e-32 relative error = 1.2075346835229975266236197928669e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86781917967764990038784757198851 y1[1] (numeric) = 0.86781917967764990038784757198854 absolute error = 3e-32 relative error = 3.4569413424514832526432563583826e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1911.1MB, alloc=4.6MB, time=117.78 x[1] = 0.521 y2[1] (analytic) = 0.49774770843872962299042767569256 y2[1] (numeric) = 0.49774770843872962299042767569262 absolute error = 6e-32 relative error = 1.2054299594507468196092774921751e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86732186571306583614646591908526 y1[1] (numeric) = 0.86732186571306583614646591908529 absolute error = 3e-32 relative error = 3.4589235191638571323700547785014e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1915.0MB, alloc=4.6MB, time=118.02 x[1] = 0.522 y2[1] (analytic) = 0.49861478128605557189109401337953 y2[1] (numeric) = 0.49861478128605557189109401337958 absolute error = 5e-32 relative error = 1.0027781340745085681233190377070e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.8668236844266883356589816478407 y1[1] (numeric) = 0.86682368442668833565898164784073 absolute error = 3e-32 relative error = 3.4609114331989912041964714015839e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1918.8MB, alloc=4.6MB, time=118.26 x[1] = 0.523 y2[1] (analytic) = 0.49948135551864178596657725690241 y2[1] (numeric) = 0.49948135551864178596657725690246 absolute error = 5e-32 relative error = 1.0010383660483576489288883961085e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86632463631669864378778943145095 y1[1] (numeric) = 0.86632463631669864378778943145097 absolute error = 2e-32 relative error = 2.3086033989559410780819264207953e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1922.6MB, alloc=4.6MB, time=118.49 x[1] = 0.524 y2[1] (analytic) = 0.50034743026991410484518030581186 y2[1] (numeric) = 0.50034743026991410484518030581192 absolute error = 6e-32 relative error = 1.1991667463472890849055906541211e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 0.86582472188214482893524002821195 y1[1] (numeric) = 0.86582472188214482893524002821197 absolute error = 2e-32 relative error = 2.3099363525360713181124047205097e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1926.4MB, alloc=4.6MB, time=118.73 TOP MAIN SOLVE Loop memory used=1930.2MB, alloc=4.6MB, time=118.97 x[1] = 0.525 y2[1] (analytic) = 0.5012130046737978494274778151016 y2[1] (numeric) = 0.50121300467379784942747781510165 absolute error = 5e-32 relative error = 9.9757986192998463064501037467325e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86532394162294128399561346650638 y1[1] (numeric) = 0.8653239416229412839956134665064 absolute error = 2e-32 relative error = 2.3112731588691968604037791170458e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1934.0MB, alloc=4.6MB, time=119.20 x[1] = 0.526 y2[1] (analytic) = 0.50207807786471868796092312174618 y2[1] (numeric) = 0.50207807786471868796092312174623 absolute error = 5e-32 relative error = 9.9586104640625514218616456205807e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86482229603986822644076781005499 y1[1] (numeric) = 0.864822296039868226440767810055 absolute error = 1e-32 relative error = 1.1563069136620641590525037439531e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1937.9MB, alloc=4.6MB, time=119.44 x[1] = 0.527 y2[1] (analytic) = 0.50294264897760350161410786605581 y2[1] (numeric) = 0.50294264897760350161410786605586 absolute error = 5e-32 relative error = 9.9414913612201032392958319900360e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86431978563457119753996341774188 y1[1] (numeric) = 0.8643197856345711975399634177419 absolute error = 2e-32 relative error = 2.3139583673091883090458120626103e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1941.7MB, alloc=4.6MB, time=119.67 x[1] = 0.528 y2[1] (analytic) = 0.50380671714788124954980873366049 y2[1] (numeric) = 0.50380671714788124954980873366054 absolute error = 5e-32 relative error = 9.9244409211248393806166819572952e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86381641090956056071436347814793 y1[1] (numeric) = 0.86381641090956056071436347814795 absolute error = 2e-32 relative error = 2.3153067882723925786883240193812e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1945.5MB, alloc=4.6MB, time=119.91 x[1] = 0.529 y2[1] (analytic) = 0.50467028151148383349595624514904 y2[1] (numeric) = 0.50467028151148383349595624514909 absolute error = 5e-32 relative error = 9.9074587570820224595801099150725e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86331217236821099902671246424977 y1[1] (numeric) = 0.86331217236821099902671246424979 absolute error = 2e-32 relative error = 2.3166590997016321906956012844838e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1949.3MB, alloc=4.6MB, time=120.14 memory used=1953.1MB, alloc=4.6MB, time=120.38 x[1] = 0.53 y2[1] (analytic) = 0.50553334120484696181366102246608 y2[1] (numeric) = 0.50553334120484696181366102246613 absolute error = 5e-32 relative error = 9.8905444853219918713510338381691e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8628070705147610118066950185642 y1[1] (numeric) = 0.86280707051476101180669501856422 absolute error = 2e-32 relative error = 2.3180153111248567922165470502791e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1956.9MB, alloc=4.6MB, time=120.62 x[1] = 0.531 y2[1] (analytic) = 0.50639589536491101306143346411287 y2[1] (numeric) = 0.50639589536491101306143346411292 absolute error = 5e-32 relative error = 9.8736977249726302787621661760390e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86230110585431241041247864333708 y1[1] (numeric) = 0.86230110585431241041247864333709 absolute error = 1e-32 relative error = 1.1596877160551294805208445428365e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1960.7MB, alloc=4.6MB, time=120.85 x[1] = 0.532 y2[1] (analytic) = 0.50725794312912189905473326500416 y2[1] (numeric) = 0.50725794312912189905473326500421 absolute error = 5e-32 relative error = 9.8569180980321406546316427523245e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86179427889282981312894443419202 y1[1] (numeric) = 0.86179427889282981312894443419203 absolute error = 1e-32 relative error = 1.1603697361332298209198435369779e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1964.6MB, alloc=4.6MB, time=121.09 x[1] = 0.533 y2[1] (analytic) = 0.50811948363543192741998572150358 y2[1] (numeric) = 0.50811948363543192741998572150363 absolute error = 5e-32 relative error = 9.8402052293421298016059498842182e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86128659013714013920311095896611 y1[1] (numeric) = 0.86128659013714013920311095896612 absolute error = 1e-32 relative error = 1.1610537206213473393701607787774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1968.4MB, alloc=4.6MB, time=121.33 x[1] = 0.534 y2[1] (analytic) = 0.508980516022300663642202267693 y2[1] (numeric) = 0.50898051602230066364220226769305 absolute error = 5e-32 relative error = 9.8235587465609943320964552454462e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86077804009493210201725724626652 y1[1] (numeric) = 0.86077804009493210201725724626653 absolute error = 1e-32 relative error = 1.1617396743645012257930441125052e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1972.2MB, alloc=4.6MB, time=121.56 memory used=1976.0MB, alloc=4.6MB, time=121.80 x[1] = 0.535 y2[1] (analytic) = 0.50984103942869579260534319532731 y2[1] (numeric) = 0.50984103942869579260534319532736 absolute error = 5e-32 relative error = 9.8069782801376051509518124966504e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.86026862927475570140025171058284 y1[1] (numeric) = 0.86026862927475570140025171058285 absolute error = 1e-32 relative error = 1.1624276022282063116156899598612e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1979.8MB, alloc=4.6MB, time=122.04 x[1] = 0.536 y2[1] (analytic) = 0.51070105299409397962456101718358 y2[1] (numeric) = 0.51070105299409397962456101718362 absolute error = 4e-32 relative error = 7.8323707706282292340590162236980e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85975835818602171507759470258392 y1[1] (numeric) = 0.85975835818602171507759470258393 absolute error = 1e-32 relative error = 1.1631175090985680026627953047615e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1983.6MB, alloc=4.6MB, time=122.27 x[1] = 0.537 y2[1] (analytic) = 0.51156055585848173096946344163303 y2[1] (numeric) = 0.51156055585848173096946344163307 absolute error = 4e-32 relative error = 7.8192111455648688178074055026212e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85924722733900118926068323451424 y1[1] (numeric) = 0.85924722733900118926068323451425 absolute error = 1e-32 relative error = 1.1638093998823777750371627040419e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1987.4MB, alloc=4.6MB, time=122.51 x[1] = 0.538 y2[1] (analytic) = 0.51241954716235625387753543524462 y2[1] (numeric) = 0.51241954716235625387753543524465 absolute error = 3e-32 relative error = 5.8545775948891987011932596138791e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85873523724482492837580729138267 y1[1] (numeric) = 0.85873523724482492837580729138267 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1991.3MB, alloc=4.6MB, time=122.74 x[1] = 0.539 y2[1] (analytic) = 0.51327802604672631605686036006966 y2[1] (numeric) = 0.5132780260467263160568603600697 absolute error = 4e-32 relative error = 7.7930474265731757682917824914102e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85822238841548298393338799890475 y1[1] (numeric) = 0.85822238841548298393338799890475 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1995.1MB, alloc=4.6MB, time=122.97 x[1] = 0.54 y2[1] (analytic) = 0.51413599165311310467728068295824 y2[1] (numeric) = 0.51413599165311310467728068295828 absolute error = 4e-32 relative error = 7.7800427609409513559610975078009e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8577086813638241425379687789178 y1[1] (numeric) = 0.8577086813638241425379687789178 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1998.9MB, alloc=4.6MB, time=123.21 memory used=2002.7MB, alloc=4.6MB, time=123.45 x[1] = 0.541 y2[1] (analytic) = 0.514993443123551084849139265818 y2[1] (numeric) = 0.51499344312355108484913926581803 absolute error = 3e-32 relative error = 5.8253168852098875737381175155704e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85719411660355541303947148223492 y1[1] (numeric) = 0.85719411660355541303947148223493 absolute error = 1e-32 relative error = 1.1665969010173351744704636303864e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2006.5MB, alloc=4.6MB, time=123.68 x[1] = 0.542 y2[1] (analytic) = 0.51585037960058885758874275814576 y2[1] (numeric) = 0.51585037960058885758874275814579 absolute error = 3e-32 relative error = 5.8156398030041798894677144667936e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85667869464924151282623034763916 y1[1] (numeric) = 0.85667869464924151282623034763917 absolute error = 1e-32 relative error = 1.1672987857010263995794483466827e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2010.3MB, alloc=4.6MB, time=123.92 x[1] = 0.543 y2[1] (analytic) = 0.51670680022729001726968912644003 y2[1] (numeric) = 0.51670680022729001726968912644007 absolute error = 4e-32 relative error = 7.7413341536060141390367898964552e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85616241601630435326031749394093 y1[1] (numeric) = 0.85616241601630435326031749394093 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2014.1MB, alloc=4.6MB, time=124.15 x[1] = 0.544 y2[1] (analytic) = 0.51756270414723400855920186923829 y2[1] (numeric) = 0.51756270414723400855920186923832 absolute error = 3e-32 relative error = 5.7963991144666655176298499935634e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85564528122102252425567450973039 y1[1] (numeric) = 0.85564528122102252425567450973039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2018.0MB, alloc=4.6MB, time=124.39 x[1] = 0.545 y2[1] (analytic) = 0.5184180905045169828386139815162 y2[1] (numeric) = 0.51841809050451698283861398151624 absolute error = 4e-32 relative error = 7.7157801266295662835892017081006e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85512729078053077799956556265031 y1[1] (numeric) = 0.85512729078053077799956556265031 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2021.8MB, alloc=4.6MB, time=124.62 memory used=2025.6MB, alloc=4.6MB, time=124.86 x[1] = 0.546 y2[1] (analytic) = 0.51927295844375265410714524803636 y2[1] (numeric) = 0.51927295844375265410714524803639 absolute error = 3e-32 relative error = 5.7773083524143463773839641211561e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85460844521281951181786830669308 y1[1] (numeric) = 0.85460844521281951181786830669308 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2029.4MB, alloc=4.6MB, time=125.09 x[1] = 0.547 y2[1] (analytic) = 0.52012730711007315436811696194029 y2[1] (numeric) = 0.52012730711007315436811696194033 absolute error = 4e-32 relative error = 7.6904249119792717814511771399165e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8540887450367342501847197221881 y1[1] (numeric) = 0.8540887450367342501847197221881 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2033.2MB, alloc=4.6MB, time=125.33 x[1] = 0.548 y2[1] (analytic) = 0.52098113564912988849674868244063 y2[1] (numeric) = 0.52098113564912988849674868244066 absolute error = 3e-32 relative error = 5.7583658883580738349895190725948e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8535681907719751258770348787904 y1[1] (numeric) = 0.8535681907719751258770348787904 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2037.0MB, alloc=4.6MB, time=125.57 x[1] = 0.549 y2[1] (analytic) = 0.52183444320709438858868216388758 y2[1] (numeric) = 0.52183444320709438858868216388762 absolute error = 4e-32 relative error = 7.6652663542420988700411171335493e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85304678293909636027441746690851 y1[1] (numeric) = 0.85304678293909636027441746690851 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2040.8MB, alloc=4.6MB, time=125.80 x[1] = 0.55 y2[1] (analytic) = 0.52268722893065916778837810775729 y2[1] (numeric) = 0.52268722893065916778837810775733 absolute error = 4e-32 relative error = 7.6527601567449981793694067295567e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85252452205950574280498179761777 y1[1] (numeric) = 0.85252452205950574280498179761777 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2044.7MB, alloc=4.6MB, time=126.03 x[1] = 0.551 y2[1] (analytic) = 0.52353949196703857359653190923621 y2[1] (numeric) = 0.52353949196703857359653190923625 absolute error = 4e-32 relative error = 7.6403023293834637080830167026486e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8520014086554641095376068251937 y1[1] (numeric) = 0.8520014086554641095376068251937 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2048.5MB, alloc=4.6MB, time=126.27 TOP MAIN SOLVE Loop memory used=2052.3MB, alloc=4.6MB, time=126.51 x[1] = 0.552 y2[1] (analytic) = 0.52439123146396964065565509105708 y2[1] (numeric) = 0.52439123146396964065565509105712 absolute error = 4e-32 relative error = 7.6278926114630040525974842467482e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85147744325008482092114359996793 y1[1] (numeric) = 0.85147744325008482092114359996793 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2056.1MB, alloc=4.6MB, time=126.74 x[1] = 0.553 y2[1] (analytic) = 0.52524244656971294301296963907598 y2[1] (numeric) = 0.52524244656971294301296963907601 absolute error = 3e-32 relative error = 5.7116480581350429842175618003783e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85095262636733323867109841225574 y1[1] (numeric) = 0.85095262636733323867109841225573 absolute error = 1e-32 relative error = 1.1751535502850978221647035755014e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2059.9MB, alloc=4.6MB, time=126.98 x[1] = 0.554 y2[1] (analytic) = 0.52609313643305344585976297676717 y2[1] (numeric) = 0.52609313643305344585976297676721 absolute error = 4e-32 relative error = 7.6032164706049327885297264098144e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.85042695853202620180431474062843 y1[1] (numeric) = 0.85042695853202620180431474062842 absolute error = 1e-32 relative error = 1.1758799388558435871604104083937e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2063.7MB, alloc=4.6MB, time=127.22 x[1] = 0.555 y2[1] (analytic) = 0.52694330020330135674635183935189 y2[1] (numeric) = 0.52694330020330135674635183935192 absolute error = 3e-32 relative error = 5.6932121517487028401436579231192e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84990044026983150182217796980501 y1[1] (numeric) = 0.84990044026983150182217796980501 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2067.6MB, alloc=4.6MB, time=127.45 x[1] = 0.556 y2[1] (analytic) = 0.52779293703029297627180383266784 y2[1] (numeric) = 0.52779293703029297627180383266787 absolute error = 3e-32 relative error = 5.6840472645957619002502663340334e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84937307210726735704286769491463 y1[1] (numeric) = 0.84937307210726735704286769491463 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2071.4MB, alloc=4.6MB, time=127.69 memory used=2075.2MB, alloc=4.6MB, time=127.93 x[1] = 0.557 y2[1] (analytic) = 0.52864204606439154824756598712908 y2[1] (numeric) = 0.52864204606439154824756598712911 absolute error = 3e-32 relative error = 5.6749175029384311890480677232296e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8488448545717018860831832798337 y1[1] (numeric) = 0.8488448545717018860831832798337 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2079.0MB, alloc=4.6MB, time=128.16 x[1] = 0.558 y2[1] (analytic) = 0.52949062645648810933415014321829 y2[1] (numeric) = 0.52949062645648810933415014321832 absolute error = 3e-32 relative error = 5.6658226795758596058277856398849e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84831578819135258049046918772829 y1[1] (numeric) = 0.84831578819135258049046918772829 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2082.8MB, alloc=4.6MB, time=128.40 x[1] = 0.559 y2[1] (analytic) = 0.53033867735800233815002553189701 y2[1] (numeric) = 0.53033867735800233815002553189705 absolute error = 4e-32 relative error = 7.5423501448675617015034887192760e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8477858734952857765251674518325 y1[1] (numeric) = 0.8477858734952857765251674518325 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2086.6MB, alloc=4.6MB, time=128.63 x[1] = 0.56 y2[1] (analytic) = 0.53118619792088340385186944111203 y2[1] (numeric) = 0.53118619792088340385186944111207 absolute error = 4e-32 relative error = 7.5303161408493015494038179548360e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84725511101341612609452550386632 y1[1] (numeric) = 0.84725511101341612609452550386632 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2090.4MB, alloc=4.6MB, time=128.87 x[1] = 0.561 y2[1] (analytic) = 0.53203318729761081418532738821783 y2[1] (numeric) = 0.53203318729761081418532738821787 absolute error = 4e-32 relative error = 7.5183279831046785576477323742143e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84672350127650606683798842634102 y1[1] (numeric) = 0.84672350127650606683798842634102 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2094.3MB, alloc=4.6MB, time=129.11 x[1] = 0.562 y2[1] (analytic) = 0.53287964464119526300543474762577 y2[1] (numeric) = 0.53287964464119526300543474762581 absolute error = 4e-32 relative error = 7.5063854291025258614803510225564e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84619104481616529136480554331576 y1[1] (numeric) = 0.84619104481616529136480554331576 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2098.1MB, alloc=4.6MB, time=129.34 TOP MAIN SOLVE Loop memory used=2101.9MB, alloc=4.6MB, time=129.58 x[1] = 0.563 y2[1] (analytic) = 0.53372556910517947726585231332886 y2[1] (numeric) = 0.5337255691051794772658523133289 absolute error = 4e-32 relative error = 7.4944882380400509624972996176848e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8456577421648502156443821119545 y1[1] (numeric) = 0.8456577421648502156443821119545 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2105.7MB, alloc=4.6MB, time=129.82 x[1] = 0.564 y2[1] (analytic) = 0.53457095984363906347606880713726 y2[1] (numeric) = 0.5345709598436390634760688071373 absolute error = 4e-32 relative error = 7.4826361708275211944517779328377e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84512359385586344654990772448725 y1[1] (numeric) = 0.84512359385586344654990772448725 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2109.5MB, alloc=4.6MB, time=130.05 x[1] = 0.565 y2[1] (analytic) = 0.53541581601118335362572387549242 y2[1] (numeric) = 0.53541581601118335362572387549246 absolute error = 4e-32 relative error = 7.4708289900731118438359744412784e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84458860042335324855579387690292 y1[1] (numeric) = 0.84458860042335324855579387690292 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2113.3MB, alloc=4.6MB, time=130.28 x[1] = 0.566 y2[1] (analytic) = 0.53626013676295625057520565060748 y2[1] (numeric) = 0.53626013676295625057520565060752 absolute error = 4e-32 relative error = 7.4590664600679149136592016156646e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84405276240231300958945400689171 y1[1] (numeric) = 0.8440527624023130095894540068917 absolute error = 1e-32 relative error = 1.1847600583094302051465310145105e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2117.1MB, alloc=4.6MB, time=130.51 x[1] = 0.567 y2[1] (analytic) = 0.5371039212546370729116774854067 y2[1] (numeric) = 0.53710392125463707291167748540674 absolute error = 4e-32 relative error = 7.4473483467711065472273566978521e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84351608032858070603796014921248 y1[1] (numeric) = 0.84351608032858070603796014921247 absolute error = 1e-32 relative error = 1.1855138548283075060794702669386e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2121.0MB, alloc=4.6MB, time=130.75 memory used=2124.8MB, alloc=4.6MB, time=130.99 x[1] = 0.568 y2[1] (analytic) = 0.53794716864244139926968900630767 y2[1] (numeric) = 0.53794716864244139926968900630771 absolute error = 4e-32 relative error = 7.4356744177952711566608263240600e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84297855473883836691011120178398 y1[1] (numeric) = 0.84297855473883836691011120178397 absolute error = 1e-32 relative error = 1.1862697981798696620198927304605e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2128.6MB, alloc=4.6MB, time=131.22 x[1] = 0.569 y2[1] (analytic) = 0.53878987808312191211552716330558 y2[1] (numeric) = 0.53878987808312191211552716330562 absolute error = 4e-32 relative error = 7.4240444423918803283786527614498e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84244018617061153715444864038683 y1[1] (numeric) = 0.84244018617061153715444864038683 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2132.4MB, alloc=4.6MB, time=131.46 x[1] = 0.57 y2[1] (analytic) = 0.53963204873396924099446349307883 y2[1] (numeric) = 0.53963204873396924099446349307887 absolute error = 4e-32 relative error = 7.4124581914369246048334158139102e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84190097516226874013375636391601 y1[1] (numeric) = 0.84190097516226874013375636391601 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2136.2MB, alloc=4.6MB, time=131.69 x[1] = 0.571 y2[1] (analytic) = 0.54047367975281280524005434793895 y2[1] (numeric) = 0.54047367975281280524005434793899 absolute error = 4e-32 relative error = 7.4009154374166962684114594947070e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84136092225302093925658219563904 y1[1] (numeric) = 0.84136092225302093925658219563904 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2140.0MB, alloc=4.6MB, time=131.93 x[1] = 0.572 y2[1] (analytic) = 0.54131477029802165614465138139488 y2[1] (numeric) = 0.54131477029802165614465138139492 absolute error = 4e-32 relative error = 7.3894159544137212796242619605902e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84082002798292099876631940889362 y1[1] (numeric) = 0.84082002798292099876631940889362 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2143.8MB, alloc=4.6MB, time=132.16 x[1] = 0.573 y2[1] (analytic) = 0.54215531952850531859028011989125 y2[1] (numeric) = 0.54215531952850531859028011989128 absolute error = 3e-32 relative error = 5.5334696385696289106371675858671e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.84027829289286314368838748809822 y1[1] (numeric) = 0.84027829289286314368838748809822 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2147.7MB, alloc=4.6MB, time=132.40 TOP MAIN SOLVE Loop memory used=2151.5MB, alloc=4.6MB, time=132.64 x[1] = 0.574 y2[1] (analytic) = 0.54299532660371463213904498991224 y2[1] (numeric) = 0.54299532660371463213904498991227 absolute error = 3e-32 relative error = 5.5249094292655685517068268018154e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83973571752458241893605217784984 y1[1] (numeric) = 0.83973571752458241893605217784984 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2155.3MB, alloc=4.6MB, time=132.88 x[1] = 0.575 y2[1] (analytic) = 0.54383479068364259158221971011618 y2[1] (numeric) = 0.54383479068364259158221971011621 absolute error = 3e-32 relative error = 5.5163811719893221237755998510549e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83919230242065414757542571424383 y1[1] (numeric) = 0.83919230242065414757542571424383 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2159.1MB, alloc=4.6MB, time=133.11 x[1] = 0.576 y2[1] (analytic) = 0.54467371092882518694718249948034 y2[1] (numeric) = 0.54467371092882518694718249948037 absolute error = 3e-32 relative error = 5.5078847019881645508323074605453e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83864804812449338825018897337042 y1[1] (numeric) = 0.83864804812449338825018897337042 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2162.9MB, alloc=4.6MB, time=133.35 x[1] = 0.577 y2[1] (analytic) = 0.54551208650034224296135609459091 y2[1] (numeric) = 0.54551208650034224296135609459094 absolute error = 3e-32 relative error = 5.4994198556554216003843940170005e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83810295518035439176657811222054 y1[1] (numeric) = 0.83810295518035439176657811222053 absolute error = 1e-32 relative error = 1.1931708316012397312128987897276e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2166.7MB, alloc=4.6MB, time=133.59 x[1] = 0.578 y2[1] (analytic) = 0.54634991655981825797231311220796 y2[1] (numeric) = 0.54634991655981825797231311220799 absolute error = 3e-32 relative error = 5.4909864705205619900262581166744e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83755702413333005683917911696904 y1[1] (numeric) = 0.83755702413333005683917911696903 absolute error = 1e-32 relative error = 1.1939485565591898983237556230465e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2170.6MB, alloc=4.6MB, time=133.82 memory used=2174.4MB, alloc=4.6MB, time=134.06 x[1] = 0.579 y2[1] (analytic) = 0.54718720026942324232320783707006 y2[1] (numeric) = 0.54718720026942324232320783707009 absolute error = 3e-32 relative error = 5.4825843852393921835492712020519e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83701025552935138499807451279544 y1[1] (numeric) = 0.83701025552935138499807451279543 absolute error = 1e-32 relative error = 1.1947284915494480032405807715253e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2178.2MB, alloc=4.6MB, time=134.29 x[1] = 0.58 y2[1] (analytic) = 0.54802393679187355618269605957646 y2[1] (numeric) = 0.54802393679187355618269605957649 absolute error = 3e-32 relative error = 5.4742134395843526372782926957189e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83646264991518693465788732805002 y1[1] (numeric) = 0.83646264991518693465788732805001 absolute error = 1e-32 relative error = 1.1955106424672935751964175215789e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2182.0MB, alloc=4.6MB, time=134.53 x[1] = 0.581 y2[1] (analytic) = 0.54886012529043274682850513349703 y2[1] (numeric) = 0.54886012529043274682850513349706 absolute error = 3e-32 relative error = 5.4658734744349142743842118543434e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83591420783844227434926824367577 y1[1] (numeric) = 0.83591420783844227434926824367576 absolute error = 1e-32 relative error = 1.1962950152335138941297119390945e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2185.8MB, alloc=4.6MB, time=134.76 x[1] = 0.582 y2[1] (analytic) = 0.54969576492891238538381697020945 y2[1] (numeric) = 0.54969576492891238538381697020948 absolute error = 3e-32 relative error = 5.4575643317680739817228813941505e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83536492984755943511337269635362 y1[1] (numeric) = 0.8353649298475594351133726963536 absolute error = 2e-32 relative error = 2.3941632315890584435406322071426e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2189.6MB, alloc=4.6MB, time=135.00 x[1] = 0.583 y2[1] (analytic) = 0.55053085487167290300562723315059 y2[1] (numeric) = 0.55053085487167290300562723315062 absolute error = 3e-32 relative error = 5.4492858546489479402922821487880e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83481481649181636205987554084799 y1[1] (numeric) = 0.83481481649181636205987554084798 absolute error = 1e-32 relative error = 1.1978704501225188042203089102396e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2193.4MB, alloc=4.6MB, time=135.23 x[1] = 0.584 y2[1] (analytic) = 0.55136539428362442652424454419241 y2[1] (numeric) = 0.55136539428362442652424454419244 absolute error = 3e-32 relative error = 5.4410378872214616166863127194491e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8342638683213263650890717134926 y1[1] (numeric) = 0.83426386832132636508907171349259 absolute error = 1e-32 relative error = 1.1986615242155476514676190684673e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2197.3MB, alloc=4.6MB, time=135.47 TOP MAIN SOLVE Loop memory used=2201.1MB, alloc=4.6MB, time=135.71 x[1] = 0.585 y2[1] (analytic) = 0.5521993823302276135330940625129 y2[1] (numeric) = 0.55219938233022761353309406251293 absolute error = 3e-32 relative error = 5.4328202746991352589595908659091e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83371208588703756877861217466974 y1[1] (numeric) = 0.83371208588703756877861217466973 absolute error = 1e-32 relative error = 1.1994548440976940993146958247041e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2204.9MB, alloc=4.6MB, time=135.94 x[1] = 0.586 y2[1] (analytic) = 0.55303281817749448692799034622804 y2[1] (numeric) = 0.55303281817749448692799034622807 absolute error = 3e-32 relative error = 5.4246328633559637561073600681857e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83315946974073236143542524350155 y1[1] (numeric) = 0.83315946974073236143542524350154 absolute error = 1e-32 relative error = 1.2002504158191781592491377943504e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2208.7MB, alloc=4.6MB, time=136.18 x[1] = 0.587 y2[1] (analytic) = 0.55386570099198926889504495758147 y2[1] (numeric) = 0.55386570099198926889504495758149 absolute error = 2e-32 relative error = 3.6109836670115931572748072923335e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83260602043502684331337427278583 y1[1] (numeric) = 0.83260602043502684331337427278583 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2212.5MB, alloc=4.6MB, time=136.42 x[1] = 0.588 y2[1] (analytic) = 0.55469802994082921434637482385373 y2[1] (numeric) = 0.55469802994082921434637482385375 absolute error = 2e-32 relative error = 3.6055653563675791941459801121521e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83205173852337027399720344647288 y1[1] (numeric) = 0.83205173852337027399720344647288 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2216.3MB, alloc=4.6MB, time=136.65 x[1] = 0.589 y2[1] (analytic) = 0.55552980419168544380277791835226 y2[1] (numeric) = 0.55552980419168544380277791835228 absolute error = 2e-32 relative error = 3.6001668765730171598498798328587e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83149662456004451895332431569136 y1[1] (numeric) = 0.83149662456004451895332431569136 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2220.1MB, alloc=4.6MB, time=136.89 memory used=2224.0MB, alloc=4.6MB, time=137.13 x[1] = 0.59 y2[1] (analytic) = 0.55636102291278377572254337887577 y2[1] (numeric) = 0.55636102291278377572254337887579 absolute error = 2e-32 relative error = 3.5947881279122672250783008540811e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83094067910016349524799652249068 y1[1] (numeric) = 0.83094067910016349524799652249068 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2227.8MB, alloc=4.6MB, time=137.36 x[1] = 0.591 y2[1] (analytic) = 0.55719168527290555827556373491228 y2[1] (numeric) = 0.55719168527290555827556373491229 absolute error = 1e-32 relative error = 1.7947145056735949602045751440722e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.83038390269967261643345699307291 y1[1] (numeric) = 0.83038390269967261643345699307291 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2231.6MB, alloc=4.6MB, time=137.60 x[1] = 0.592 y2[1] (analytic) = 0.55802179044138850056191746952789 y2[1] (numeric) = 0.55802179044138850056191746952791 absolute error = 2e-32 relative error = 3.5840894285114280954324759573787e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82982629591534823660255271433876 y1[1] (numeric) = 0.82982629591534823660255271433876 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2235.4MB, alloc=4.6MB, time=137.84 x[1] = 0.593 y2[1] (analytic) = 0.55885133758812750327409069743309 y2[1] (numeric) = 0.55885133758812750327409069743311 absolute error = 2e-32 relative error = 3.5787692817047467447625992623881e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82926785930479709361243303906856 y1[1] (numeric) = 0.82926785930479709361243303906857 absolute error = 1e-32 relative error = 1.2058829831392878950376086568880e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2239.2MB, alloc=4.6MB, time=138.07 x[1] = 0.594 y2[1] (analytic) = 0.55968032588357548880200729707396 y2[1] (numeric) = 0.55968032588357548880200729707398 absolute error = 2e-32 relative error = 3.5734684738874300190315801648858e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82870859342645575147785829599953 y1[1] (numeric) = 0.82870859342645575147785829599954 absolute error = 1e-32 relative error = 1.2066967905633834948956206931193e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2243.0MB, alloc=4.6MB, time=138.31 x[1] = 0.595 y2[1] (analytic) = 0.56050875449874423078003739178746 y2[1] (numeric) = 0.56050875449874423078003739178748 memory used=2246.8MB, alloc=4.6MB, time=138.55 absolute error = 2e-32 relative error = 3.5681869086747347481278051331522e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82814849883959004193468231144419 y1[1] (numeric) = 0.8281484988395900419346823114442 absolute error = 1e-32 relative error = 1.2075129054767472258992223861655e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2250.7MB, alloc=4.6MB, time=138.79 x[1] = 0.596 y2[1] (analytic) = 0.56133662260520518307515463308144 y2[1] (numeric) = 0.56133662260520518307515463308146 absolute error = 2e-32 relative error = 3.5629244903313998129736013603178e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.827587576104294505174067278921 y1[1] (numeric) = 0.82758757610429450517406727892101 absolute error = 1e-32 relative error = 1.2083313341982524897322440439095e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2254.5MB, alloc=4.6MB, time=139.03 x[1] = 0.597 y2[1] (analytic) = 0.56216392937509030821541329795109 y2[1] (numeric) = 0.56216392937509030821541329795111 absolute error = 2e-32 relative error = 3.5576811237662107110297610014002e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82702582578149182974799024253562 y1[1] (numeric) = 0.82702582578149182974799024253562 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2258.3MB, alloc=4.6MB, time=139.26 x[1] = 0.598 y2[1] (analytic) = 0.56299067398109290525791677182386 y2[1] (numeric) = 0.56299067398109290525791677182388 absolute error = 2e-32 relative error = 3.5524567145266186694749840409574e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82646324843293229164660128855966 y1[1] (numeric) = 0.82646324843293229164660128855966 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2262.1MB, alloc=4.6MB, time=139.50 x[1] = 0.599 y2[1] (analytic) = 0.56381685559646843709544954923328 y2[1] (numeric) = 0.5638168555964684370954495492333 absolute error = 2e-32 relative error = 3.5472511687934136686367523512493e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82589984462119319254799436780206 y1[1] (numeric) = 0.82589984462119319254799436780206 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2265.9MB, alloc=4.6MB, time=139.73 x[1] = 0.6 y2[1] (analytic) = 0.56464247339503535720094544565866 y2[1] (numeric) = 0.56464247339503535720094544565868 absolute error = 2e-32 relative error = 3.5420643933754507467492242142109e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82533561490967829724095249895538 y1[1] (numeric) = 0.82533561490967829724095249895538 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2269.7MB, alloc=4.6MB, time=139.97 memory used=2273.6MB, alloc=4.6MB, time=140.21 x[1] = 0.601 y2[1] (analytic) = 0.56546752655117593580896527613138 y2[1] (numeric) = 0.5654675265511759358089652761314 absolute error = 2e-32 relative error = 3.5368962957044289654855415920115e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82477055986261727022122993012494 y1[1] (numeric) = 0.82477055986261727022122993012494 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2277.4MB, alloc=4.6MB, time=140.44 x[1] = 0.602 y2[1] (analytic) = 0.56629201423983708553335781919889 y2[1] (numeric) = 0.5662920142398370855333578191989 absolute error = 1e-32 relative error = 1.7658733919148612119792929614689e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82420468004506511146193466221171 y1[1] (numeric) = 0.82420468004506511146193466221171 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2281.2MB, alloc=4.6MB, time=140.68 x[1] = 0.603 y2[1] (analytic) = 0.56711593563653118642027844865423 y2[1] (numeric) = 0.56711593563653118642027844865425 absolute error = 2e-32 relative error = 3.5266157664132627170077778070294e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82363797602290159135857556371942 y1[1] (numeric) = 0.82363797602290159135857556371942 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2285.0MB, alloc=4.6MB, time=140.91 x[1] = 0.604 y2[1] (analytic) = 0.56793928991733691043574038008136 y2[1] (numeric) = 0.56793928991733691043574038008138 absolute error = 2e-32 relative error = 3.5215031527244722415920294436459e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82307044836283068484933913189164 y1[1] (numeric) = 0.82307044836283068484933913189164 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2288.8MB, alloc=4.6MB, time=141.15 x[1] = 0.605 y2[1] (analytic) = 0.5687620762589000453868740447335 y2[1] (numeric) = 0.56876207625890004538687404473351 absolute error = 1e-32 relative error = 1.7582044263176238814962134270530e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82250209763238000471116177985496 y1[1] (numeric) = 0.82250209763238000471116177985495 absolute error = 1e-32 relative error = 1.2158023704481216553642113912672e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2292.6MB, alloc=4.6MB, time=141.39 memory used=2296.4MB, alloc=4.6MB, time=141.62 x[1] = 0.606 y2[1] (analytic) = 0.56958429383843431827607066955397 y2[1] (numeric) = 0.56958429383843431827607066955398 absolute error = 1e-32 relative error = 1.7556663883074968301473031061881e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8219329243999002340321643536487 y1[1] (numeric) = 0.82193292439990023403216435364869 absolute error = 1e-32 relative error = 1.2166442909317788361553515139966e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2300.3MB, alloc=4.6MB, time=141.86 x[1] = 0.607 y2[1] (analytic) = 0.57040594183372221808718670926455 y2[1] (numeric) = 0.57040594183372221808718670926456 absolute error = 1e-32 relative error = 1.7531374178628521391360119308460e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82136292923456455786101640665948 y1[1] (numeric) = 0.82136292923456455786101640665947 absolute error = 1e-32 relative error = 1.2174885965841055454323041561505e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2304.1MB, alloc=4.6MB, time=142.09 x[1] = 0.608 y2[1] (analytic) = 0.57122701942311581800298634438536 y2[1] (numeric) = 0.57122701942311581800298634438537 absolute error = 1e-32 relative error = 1.7506174708085474101646483821199e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82079211270636809403379858204876 y1[1] (numeric) = 0.82079211270636809403379858204875 absolute error = 1e-32 relative error = 1.2183352940645789496055681503129e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2307.9MB, alloc=4.6MB, time=142.33 x[1] = 0.609 y2[1] (analytic) = 0.57204752578553759705299982781237 y2[1] (numeric) = 0.57204752578553759705299982781238 absolute error = 1e-32 relative error = 1.7481065032608901122956844773267e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.82022047538612732317893227626382 y1[1] (numeric) = 0.82022047538612732317893227626382 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2311.7MB, alloc=4.6MB, time=142.57 x[1] = 0.61 y2[1] (analytic) = 0.57286746010048126119097603216272 y2[1] (numeric) = 0.57286746010048126119097603216273 absolute error = 1e-32 relative error = 1.7456044716252507362706331249149e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81964801784547951790074657865482 y1[1] (numeric) = 0.81964801784547951790074657865482 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2315.5MB, alloc=4.6MB, time=142.80 x[1] = 0.611 y2[1] (analytic) = 0.57368682154801256380110812050361 y2[1] (numeric) = 0.57368682154801256380110812050362 absolute error = 1e-32 relative error = 1.7431113325936993934092146667660e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81907474065688217114225330358349 y1[1] (numeric) = 0.81907474065688217114225330358349 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2319.3MB, alloc=4.6MB, time=143.04 memory used=2323.1MB, alloc=4.6MB, time=143.28 x[1] = 0.612 y2[1] (analytic) = 0.57450560930877012563221183430752 y2[1] (numeric) = 0.57450560930877012563221183430753 absolute error = 1e-32 relative error = 1.7406270431426655909464127387828e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81850064439361242372770175220081 y1[1] (numeric) = 0.81850064439361242372770175220081 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2327.0MB, alloc=4.6MB, time=143.51 x[1] = 0.613 y2[1] (analytic) = 0.57532382256396625415903646452381 y2[1] (numeric) = 0.57532382256396625415903646452382 absolute error = 1e-32 relative error = 1.7381515605306209191644805365481e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81792572962976649108548566129119 y1[1] (numeric) = 0.81792572962976649108548566129119 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2330.8MB, alloc=4.6MB, time=143.75 x[1] = 0.614 y2[1] (analytic) = 0.57614146049538776236988914452402 y2[1] (numeric) = 0.57614146049538776236988914452402 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.81734999694025908915197561622843 y1[1] (numeric) = 0.81734999694025908915197561622844 absolute error = 1e-32 relative error = 1.2234660839829806450085651131168e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2334.6MB, alloc=4.6MB, time=143.98 x[1] = 0.615 y2[1] (analytic) = 0.5769585222853967869797536773647 y2[1] (numeric) = 0.5769585222853967869797536773647 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.8167734469008228594568510241632 y1[1] (numeric) = 0.81677344690082285945685102416321 absolute error = 1e-32 relative error = 1.2243297132080072627997464947452e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2338.4MB, alloc=4.6MB, time=144.22 x[1] = 0.616 y2[1] (analytic) = 0.57777500711693160606808568431733 y2[1] (numeric) = 0.57777500711693160606808568431733 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.81619608008800779339050656206213 y1[1] (numeric) = 0.81619608008800779339050656206214 absolute error = 1e-32 relative error = 1.2251957886053229049734029448165e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2342.2MB, alloc=4.6MB, time=144.46 memory used=2346.0MB, alloc=4.6MB, time=144.70 x[1] = 0.617 y2[1] (analytic) = 0.57859091417350745614046643693812 y2[1] (numeric) = 0.57859091417350745614046643693812 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.8156178970791806556541088321442 y1[1] (numeric) = 0.8156178970791806556541088321442 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2349.8MB, alloc=4.6MB, time=144.93 x[1] = 0.618 y2[1] (analytic) = 0.57940624263921734861329831109204 y2[1] (numeric) = 0.57940624263921734861329831109204 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.81503889845252440689287977460952 y1[1] (numeric) = 0.81503889845252440689287977460953 absolute error = 1e-32 relative error = 1.2269353056628983473485246712077e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2353.7MB, alloc=4.6MB, time=145.17 x[1] = 0.619 y2[1] (analytic) = 0.58022099169873288572072537830366 y2[1] (numeric) = 0.58022099169873288572072537830366 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 0.81445908478703762551318420432926 y1[1] (numeric) = 0.81445908478703762551318420432927 absolute error = 1e-32 relative error = 1.2278087612731056578691568555630e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2357.5MB, alloc=4.6MB, time=145.40 x[1] = 0.62 y2[1] (analytic) = 0.58103516053730507584296322758221 y2[1] (numeric) = 0.58103516053730507584296322758222 absolute error = 1e-32 relative error = 1.7210662416285829802640352190038e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8138784566625339286839996543607 y1[1] (numeric) = 0.8138784566625339286839996543607 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2361.3MB, alloc=4.6MB, time=145.63 x[1] = 0.621 y2[1] (analytic) = 0.58184874834076514825522268945897 y2[1] (numeric) = 0.58184874834076514825522268945898 absolute error = 1e-32 relative error = 1.7186597081314690218398514150300e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81329701465964139252334752476951 y1[1] (numeric) = 0.81329701465964139252334752476951 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2365.1MB, alloc=4.6MB, time=145.87 x[1] = 0.622 y2[1] (analytic) = 0.58266175429552536729641271338109 y2[1] (numeric) = 0.5826617542955253672964127133811 absolute error = 1e-32 relative error = 1.7162616091201365476753762341968e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81271475935980197147026535027979 y1[1] (numeric) = 0.81271475935980197147026535027979 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2368.9MB, alloc=4.6MB, time=146.10 TOP MAIN SOLVE Loop memory used=2372.7MB, alloc=4.6MB, time=146.34 x[1] = 0.623 y2[1] (analytic) = 0.58347417758857984595680822982696 y2[1] (numeric) = 0.58347417758857984595680822982697 absolute error = 1e-32 relative error = 1.7138719045508839004365041781868e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81213169134527091684290081473111 y1[1] (numeric) = 0.8121316913452709168429008147311 absolute error = 1e-32 relative error = 1.2313273951217579826626046849425e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2376.5MB, alloc=4.6MB, time=146.58 x[1] = 0.624 y2[1] (analytic) = 0.58428601740750535888386940954296 y2[1] (numeric) = 0.58428601740750535888386940954297 absolute error = 1e-32 relative error = 1.7114905546380009078770898151837e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81154781119911619458330895420011 y1[1] (numeric) = 0.81154781119911619458330895420011 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2380.4MB, alloc=4.6MB, time=146.82 x[1] = 0.625 y2[1] (analytic) = 0.58509727294046215480539931415008 y2[1] (numeric) = 0.58509727294046215480539931415009 absolute error = 1e-32 relative error = 1.7091175198517070755793982318091e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81096311950521790218953480394108 y1[1] (numeric) = 0.81096311950521790218953480394108 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2384.2MB, alloc=4.6MB, time=147.05 x[1] = 0.626 y2[1] (analytic) = 0.58590794337619476836922751503053 y2[1] (numeric) = 0.58590794337619476836922751503054 absolute error = 1e-32 relative error = 1.7067527609161095473382661082851e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.81037761684826768483556455701403 y1[1] (numeric) = 0.81037761684826768483556455701403 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2388.0MB, alloc=4.6MB, time=147.29 x[1] = 0.627 y2[1] (analytic) = 0.5867180279040328313986078408783 y2[1] (numeric) = 0.58671802790403283139860784087831 absolute error = 1e-32 relative error = 1.7043962388071806125125361845920e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80979130381376815067972911460066 y1[1] (numeric) = 0.80979130381376815067972911460067 absolute error = 1e-32 relative error = 1.2348860691519294412650345483321e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2391.8MB, alloc=4.6MB, time=147.53 memory used=2395.6MB, alloc=4.6MB, time=147.77 x[1] = 0.628 y2[1] (analytic) = 0.58752752571389188356251899858354 y2[1] (numeric) = 0.58752752571389188356251899858355 absolute error = 1e-32 relative error = 1.7020479147507545424785435804942e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80920418098803228536214471955587 y1[1] (numeric) = 0.80920418098803228536214471955588 absolute error = 1e-32 relative error = 1.2357820479610071205311551907818e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2399.4MB, alloc=4.6MB, time=148.00 x[1] = 0.629 y2[1] (analytic) = 0.5883364359962741824600573972178 y2[1] (numeric) = 0.58833643599627418246005739721781 absolute error = 1e-32 relative error = 1.6997077502205435410914242297545e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80861624895818286569177617570531 y1[1] (numeric) = 0.80861624895818286569177617570532 absolute error = 1e-32 relative error = 1.2366805654578361525135769551621e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2403.3MB, alloc=4.6MB, time=148.24 x[1] = 0.63 y2[1] (analytic) = 0.58914475794226951311811209079462 y2[1] (numeric) = 0.58914475794226951311811209079463 absolute error = 1e-32 relative error = 1.6973757069361725967914220639108e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80802750831215187252370896577706 y1[1] (numeric) = 0.80802750831215187252370896577706 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2407.1MB, alloc=4.6MB, time=148.47 x[1] = 0.631 y2[1] (analytic) = 0.58995249074355599690151234219815 y2[1] (numeric) = 0.58995249074355599690151234219816 absolute error = 1e-32 relative error = 1.6950517468612330266848198786233e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.8074379596386799028272173906462 y1[1] (numeric) = 0.80743795963867990282721739064621 absolute error = 1e-32 relative error = 1.2384852459097781449353441408811e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2410.9MB, alloc=4.6MB, time=148.71 x[1] = 0.632 y2[1] (analytic) = 0.59075963359240089983483889819962 y2[1] (numeric) = 0.59075963359240089983483889819963 absolute error = 1e-32 relative error = 1.6927358322013545055832254618128e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80684760352731558094521666177536 y1[1] (numeric) = 0.80684760352731558094521666177537 absolute error = 1e-32 relative error = 1.2393914236446577030015644544833e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2414.7MB, alloc=4.6MB, time=148.95 x[1] = 0.633 y2[1] (analytic) = 0.59156618568166144033509065381761 y2[1] (numeric) = 0.59156618568166144033509065381762 absolute error = 1e-32 relative error = 1.6904279254022953756013152716085e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80625644056841496904568768734982 y1[1] (numeric) = 0.80625644056841496904568768734983 absolute error = 1e-32 relative error = 1.2403001696271657904202456594462e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2418.5MB, alloc=4.6MB, time=149.18 TOP MAIN SOLVE Loop memory used=2422.3MB, alloc=4.6MB, time=149.42 x[1] = 0.634 y2[1] (analytic) = 0.59237214620478559635439897342298 y2[1] (numeric) = 0.59237214620478559635439897342299 absolute error = 1e-32 relative error = 1.6881279891480510344923679282894e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80566447135314097676566410063355 y1[1] (numeric) = 0.80566447135314097676566410063355 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2426.1MB, alloc=4.6MB, time=149.66 x[1] = 0.635 y2[1] (analytic) = 0.59317751435581291193198252594122 y2[1] (numeric) = 0.59317751435581291193198252594123 absolute error = 1e-32 relative error = 1.6858359863589802034435939220918e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80507169647346277004837188650966 y1[1] (numeric) = 0.80507169647346277004837188650966 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2430.0MB, alloc=4.6MB, time=149.90 x[1] = 0.636 y2[1] (analytic) = 0.59398228932937530315453608226469 y2[1] (numeric) = 0.59398228932937530315453608226471 absolute error = 2e-32 relative error = 3.3671037603798977551199220320364e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80447811652215517917411276901668 y1[1] (numeric) = 0.80447811652215517917411276901668 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2433.8MB, alloc=4.6MB, time=150.13 x[1] = 0.637 y2[1] (analytic) = 0.59478647032069786352424731455312 y2[1] (numeric) = 0.59478647032069786352424731455314 absolute error = 2e-32 relative error = 3.3625512680569835294729833843493e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80388373209279810598548332894764 y1[1] (numeric) = 0.80388373209279810598548332894765 absolute error = 1e-32 relative error = 1.2439609859956250197880253239322e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2437.6MB, alloc=4.6MB, time=150.37 x[1] = 0.638 y2[1] (analytic) = 0.59559005652559966873363622947259 y2[1] (numeric) = 0.5955900565255996687336362294726 absolute error = 1e-32 relative error = 1.6790072114929910210554247653679e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80328854377977593030752262624373 y1[1] (numeric) = 0.80328854377977593030752262624374 absolute error = 1e-32 relative error = 1.2448826859830745095213196848991e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2441.4MB, alloc=4.6MB, time=150.60 memory used=2445.2MB, alloc=4.6MB, time=150.84 x[1] = 0.639 y2[1] (analytic) = 0.59639304714049458084641246060074 y2[1] (numeric) = 0.59639304714049458084641246060076 absolute error = 2e-32 relative error = 3.3534931528617441864934670529949e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80269255217827691556338190698517 y1[1] (numeric) = 0.80269255217827691556338190698518 absolute error = 1e-32 relative error = 1.2458069995620208155747425630590e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2449.0MB, alloc=4.6MB, time=151.08 x[1] = 0.64 y2[1] (analytic) = 0.59719544136239205188354623920793 y2[1] (numeric) = 0.59719544136239205188354623920794 absolute error = 1e-32 relative error = 1.6744936929168164811188136616446e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80209575788429261358611077926032 y1[1] (numeric) = 0.80209575788429261358611077926033 absolute error = 1e-32 relative error = 1.2467339344091835043765333244264e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2452.8MB, alloc=4.6MB, time=151.31 x[1] = 0.641 y2[1] (analytic) = 0.59799723838889792681374945741014 y2[1] (numeric) = 0.59799723838889792681374945741016 absolute error = 2e-32 relative error = 3.3444970505019824704024454009541e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80149816149461726862715504607705 y1[1] (numeric) = 0.80149816149461726862715504607706 absolute error = 1e-32 relative error = 1.2476634982358794062620039495917e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2456.7MB, alloc=4.6MB, time=151.55 x[1] = 0.642 y2[1] (analytic) = 0.59879843741821524594756383327983 y2[1] (numeric) = 0.59879843741821524594756383327985 absolute error = 2e-32 relative error = 3.3400220759145900142873736602745e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80089976360684722056216218676894 y1[1] (numeric) = 0.80089976360684722056216218676895 absolute error = 1e-32 relative error = 1.2485956987882054980512047377118e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2460.5MB, alloc=4.6MB, time=151.78 x[1] = 0.643 y2[1] (analytic) = 0.59959903764914504673425378389305 y2[1] (numeric) = 0.59959903764914504673425378389307 absolute error = 2e-32 relative error = 3.3355623915632409453713993159584e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.80030056481938030729469128104118 y1[1] (numeric) = 0.80030056481938030729469128104119 absolute error = 1e-32 relative error = 1.2495305438472229778515559294847e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2464.3MB, alloc=4.6MB, time=152.02 x[1] = 0.644 y2[1] (analytic) = 0.6003990382810871649607022094871 y2[1] (numeric) = 0.60039903828108716496070220948712 absolute error = 2e-32 relative error = 3.3311179273802658984988426249423e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79970056573141526635842497189628 y1[1] (numeric) = 0.79970056573141526635842497189629 absolute error = 1e-32 relative error = 1.2504680412291425410605890579101e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2468.1MB, alloc=4.6MB, time=152.25 TOP MAIN SOLVE Loop memory used=2471.9MB, alloc=4.6MB, time=152.49 x[1] = 0.645 y2[1] (analytic) = 0.60119843851404103535150798989947 y2[1] (numeric) = 0.60119843851404103535150798989949 absolute error = 2e-32 relative error = 3.3266886137351300648314739932490e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79909976694295113571848186517791 y1[1] (numeric) = 0.79909976694295113571848186517792 absolute error = 1e-32 relative error = 1.2514081987855108666216063064170e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2475.7MB, alloc=4.6MB, time=152.73 x[1] = 0.646 y2[1] (analytic) = 0.6019972375486064915694845932574 y2[1] (numeric) = 0.60199723754860649156948459325743 absolute error = 3e-32 relative error = 4.9834115721465812331592057121551e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79849816905478665377242856437044 y1[1] (numeric) = 0.79849816905478665377242856437045 absolute error = 1e-32 relative error = 1.2523510244033983226634860075774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2479.5MB, alloc=4.6MB, time=152.96 x[1] = 0.647 y2[1] (analytic) = 0.60279543458598456561575979648616 y2[1] (numeric) = 0.60279543458598456561575979648619 absolute error = 3e-32 relative error = 4.9768127425525000690439786175868e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79789577266851965855159133959223 y1[1] (numeric) = 0.79789577266851965855159133959224 absolute error = 1e-32 relative error = 1.2532965260055879007350458310562e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2483.4MB, alloc=4.6MB, time=153.19 x[1] = 0.648 y2[1] (analytic) = 0.60359302882797828662867711760275 y2[1] (numeric) = 0.60359302882797828662867711760278 absolute error = 3e-32 relative error = 4.9702363293115311463091204428679e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79729257838654648612326822942085 y1[1] (numeric) = 0.79729257838654648612326822942085 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2487.2MB, alloc=4.6MB, time=153.43 x[1] = 0.649 y2[1] (analytic) = 0.60439001947699347908070016096041 y2[1] (numeric) = 0.60439001947699347908070016096044 absolute error = 3e-32 relative error = 4.9636822305504617272620533144429e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79668858681206136819444317328799 y1[1] (numeric) = 0.79668858681206136819444317328799 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2491.0MB, alloc=4.6MB, time=153.67 memory used=2494.8MB, alloc=4.6MB, time=153.91 x[1] = 0.65 y2[1] (analytic) = 0.60518640573603956037252167860594 y2[1] (numeric) = 0.60518640573603956037252167860597 absolute error = 3e-32 relative error = 4.9571503450269033048518397165628e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79608379854905582891760457067991 y1[1] (numeric) = 0.79608379854905582891760457067991 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2498.6MB, alloc=4.6MB, time=154.14 x[1] = 0.651 y2[1] (analytic) = 0.60598218680873033782357975370724 y2[1] (numeric) = 0.60598218680873033782357975370727 absolute error = 3e-32 relative error = 4.9506405721244531397209601525967e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79547821420231808089927146127429 y1[1] (numeric) = 0.7954782142023180808992714612743 absolute error = 1e-32 relative error = 1.2571054519736537215445087119633e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2502.4MB, alloc=4.6MB, time=154.38 x[1] = 0.652 y2[1] (analytic) = 0.60677736189928480505818411560141 y2[1] (numeric) = 0.60677736189928480505818411560144 absolute error = 3e-32 relative error = 4.9441528118479003411920111061232e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7948718343774324204118313174373 y1[1] (numeric) = 0.79487183437743242041183131743731 absolute error = 1e-32 relative error = 1.2580644536024227627151643637900e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2506.3MB, alloc=4.6MB, time=154.61 x[1] = 0.653 y2[1] (analytic) = 0.60757193021252793778645620040338 y2[1] (numeric) = 0.60757193021252793778645620040341 absolute error = 3e-32 relative error = 4.9376869648184760147363344846620e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7942646596807786218092942371924 y1[1] (numeric) = 0.79426465968077862180929423719241 absolute error = 1e-32 relative error = 1.2590261795128944452876514505279e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2510.1MB, alloc=4.6MB, time=154.84 x[1] = 0.654 y2[1] (analytic) = 0.60836589095389148897928717630129 y2[1] (numeric) = 0.60836589095389148897928717630132 absolute error = 3e-32 relative error = 4.9312429322691470043121536297316e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79365669071953133114756912185648 y1[1] (numeric) = 0.79365669071953133114756912185649 absolute error = 1e-32 relative error = 1.2599906378832354567444027432598e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2513.9MB, alloc=4.6MB, time=155.08 x[1] = 0.655 y2[1] (analytic) = 0.60915924332941478343651875864697 y2[1] (numeric) = 0.609159243329414783436518758647 absolute error = 3e-32 relative error = 4.9248206160399527637201034133141e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7930479281016594590098682180164 y1[1] (numeric) = 0.79304792810165945900986821801641 memory used=2517.7MB, alloc=4.6MB, time=155.32 absolute error = 1e-32 relative error = 1.2609578369288819432657999874737e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2521.5MB, alloc=4.6MB, time=155.55 x[1] = 0.656 y2[1] (analytic) = 0.60995198654574551174755224672681 y2[1] (numeric) = 0.60995198654574551174755224672684 absolute error = 3e-32 relative error = 4.9184199185733848968053262605786e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79243837243592557253784719839097 y1[1] (numeric) = 0.79243837243592557253784719839098 absolute error = 1e-32 relative error = 1.2619277849027399292381260511423e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2525.3MB, alloc=4.6MB, time=155.78 x[1] = 0.657 y2[1] (analytic) = 0.61074411981014052364359182167023 y2[1] (numeric) = 0.61074411981014052364359182167026 absolute error = 3e-32 relative error = 4.9120407429098089119387650074190e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79182802433188528666908875038748 y1[1] (numeric) = 0.79182802433188528666908875038749 absolute error = 1e-32 relative error = 1.2629004900953870619893086618886e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2529.1MB, alloc=4.6MB, time=156.01 x[1] = 0.658 y2[1] (analytic) = 0.61153564233046662074072875331851 y2[1] (numeric) = 0.61153564233046662074072875331854 absolute error = 3e-32 relative error = 4.9056829926829277417371000759070e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79121688439988665458153843481859 y1[1] (numeric) = 0.7912168843998866545815384348186 absolute error = 1e-32 relative error = 1.2638759608352756918867192807970e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2533.0MB, alloc=4.6MB, time=156.25 x[1] = 0.659 y2[1] (analytic) = 0.61232655331520134867307377303585 y2[1] (numeric) = 0.61232655331520134867307377303588 absolute error = 3e-32 relative error = 4.8993465721152865844321155455050e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.79060495325106955734550237029284 y1[1] (numeric) = 0.79060495325106955734550237029285 absolute error = 1e-32 relative error = 1.2648542054889372980203115652805e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2536.8MB, alloc=4.6MB, time=156.49 x[1] = 0.66 y2[1] (analytic) = 0.6131168519734337886151454793963 y2[1] (numeric) = 0.61311685197343378861514547939633 absolute error = 3e-32 relative error = 4.8930313860138186286772799436418e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78999223149736509278381709123024 y1[1] (numeric) = 0.78999223149736509278381709123025 absolute error = 1e-32 relative error = 1.2658352324611882697842840177057e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2540.6MB, alloc=4.6MB, time=156.72 memory used=2544.4MB, alloc=4.6MB, time=156.96 x[1] = 0.661 y2[1] (analytic) = 0.61390653751486534819272325442414 y2[1] (numeric) = 0.61390653751486534819272325442417 absolute error = 3e-32 relative error = 4.8867373397654312288831175751684e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7893787197514949635408027192822 y1[1] (numeric) = 0.78937871975149496354080271928221 absolute error = 1e-32 relative error = 1.2668190501953370547612404662198e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2548.2MB, alloc=4.6MB, time=157.19 x[1] = 0.662 y2[1] (analytic) = 0.61469560914981055178137377960066 y2[1] (numeric) = 0.61469560914981055178137377960069 absolute error = 3e-32 relative error = 4.8804643393326321034046308687363e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78876441862697086436061137915158 y1[1] (numeric) = 0.78876441862697086436061137915159 absolute error = 1e-32 relative error = 1.2678056671733926834045097624308e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2552.0MB, alloc=4.6MB, time=157.43 x[1] = 0.663 y2[1] (analytic) = 0.61548406608919783019186085317667 y2[1] (numeric) = 0.61548406608919783019186085317671 absolute error = 4e-32 relative error = 6.4989497216655935107529348043719e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78814932873809386857558358041344 y1[1] (numeric) = 0.78814932873809386857558358041345 absolute error = 1e-32 relative error = 1.2687950919162746811068824087803e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2555.8MB, alloc=4.6MB, time=157.66 x[1] = 0.664 y2[1] (analytic) = 0.61627190754457030974164882344686 y2[1] (numeric) = 0.61627190754457030974164882344689 absolute error = 3e-32 relative error = 4.8679811026158653425881135366565e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78753345069995381380522607692892 y1[1] (numeric) = 0.78753345069995381380522607692893 absolute error = 1e-32 relative error = 1.2697873329840243783375367682794e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2559.7MB, alloc=4.6MB, time=157.90 x[1] = 0.665 y2[1] (analytic) = 0.61705913272808660071171056654808 y2[1] (numeric) = 0.61705913272808660071171056654812 absolute error = 4e-32 relative error = 6.4823609081281368700569003287235e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78691678512842868686642550482327 y1[1] (numeric) = 0.78691678512842868686642550482327 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2563.5MB, alloc=4.6MB, time=158.13 memory used=2567.3MB, alloc=4.6MB, time=158.37 x[1] = 0.666 y2[1] (analytic) = 0.61784574085252158518785155203961 y2[1] (numeric) = 0.61784574085252158518785155203965 absolute error = 4e-32 relative error = 6.4741079132158186591171391909045e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78629933264018400789551288876302 y1[1] (numeric) = 0.78629933264018400789551288876302 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2571.1MB, alloc=4.6MB, time=158.60 x[1] = 0.667 y2[1] (analytic) = 0.61863173113126720428576215500663 y2[1] (numeric) = 0.61863173113126720428576215500667 absolute error = 4e-32 relative error = 6.4658823637858978476246473956213e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78568109385267221368279489441666 y1[1] (numeric) = 0.78568109385267221368279489441666 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2574.9MB, alloc=4.6MB, time=158.84 x[1] = 0.668 y2[1] (analytic) = 0.61941710277833324475901098970051 y2[1] (numeric) = 0.61941710277833324475901098970055 absolute error = 4e-32 relative error = 6.4576841389403060920164771420494e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78506206938413204022016849251592 y1[1] (numeric) = 0.78506206938413204022016849251592 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2578.7MB, alloc=4.6MB, time=159.07 x[1] = 0.669 y2[1] (analytic) = 0.62020185500834812498919265678791 y2[1] (numeric) = 0.62020185500834812498919265678795 absolute error = 4e-32 relative error = 6.4495131185090677588625538544030e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78444225985358790446243648685181 y1[1] (numeric) = 0.78444225985358790446243648685181 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2582.5MB, alloc=4.6MB, time=159.30 x[1] = 0.67 y2[1] (analytic) = 0.62098598703655968035744391412659 y2[1] (numeric) = 0.62098598703655968035744391412663 absolute error = 4e-32 relative error = 6.4413691830448753775237599965938e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78382166588084928530294214483812 y1[1] (numeric) = 0.78382166588084928530294214483812 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2586.4MB, alloc=4.6MB, time=159.54 x[1] = 0.671 y2[1] (analytic) = 0.62176949807883594799654289961709 y2[1] (numeric) = 0.62176949807883594799654289961713 absolute error = 4e-32 relative error = 6.4332522138177136232289449586541e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78320028808651010376414195495638 y1[1] (numeric) = 0.78320028808651010376414195495638 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2590.2MB, alloc=4.6MB, time=159.78 memory used=2594.0MB, alloc=4.6MB, time=160.02 x[1] = 0.672 y2[1] (analytic) = 0.62255238735166595092280665409653 y2[1] (numeric) = 0.62255238735166595092280665409657 absolute error = 4e-32 relative error = 6.4251620928095313251107423102801e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78257812709194810240373632045772 y1[1] (numeric) = 0.78257812709194810240373632045772 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2597.8MB, alloc=4.6MB, time=160.25 x[1] = 0.673 y2[1] (analytic) = 0.62333465407216048154700281244236 y2[1] (numeric) = 0.62333465407216048154700281244239 absolute error = 3e-32 relative error = 4.8128240270317207498115542760429e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78195518351932422393697878313928 y1[1] (numeric) = 0.78195518351932422393697878313928 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2601.6MB, alloc=4.6MB, time=160.48 x[1] = 0.674 y2[1] (analytic) = 0.62411629745805288456349195203955 y2[1] (numeric) = 0.62411629745805288456349195203958 absolute error = 3e-32 relative error = 4.8067964451795640625227283102779e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78133145799158198907578515483418 y1[1] (numeric) = 0.78133145799158198907578515483418 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2605.4MB, alloc=4.6MB, time=160.72 x[1] = 0.675 y2[1] (analytic) = 0.6248973167276998392168177095343 y2[1] (numeric) = 0.62489731672769983921681770953433 absolute error = 3e-32 relative error = 4.8007887371154380312415782600538e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78070695113244687358526471745402 y1[1] (numeric) = 0.78070695113244687358526471745401 absolute error = 1e-32 relative error = 1.2808903501492586015379228845732e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2609.3MB, alloc=4.6MB, time=160.95 x[1] = 0.676 y2[1] (analytic) = 0.62567771110008214094496239934914 y2[1] (numeric) = 0.62567771110008214094496239934917 absolute error = 3e-32 relative error = 4.7948008164224441565376270226373e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.78008166356642568455829643500084 y1[1] (numeric) = 0.78008166356642568455829643500084 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2613.1MB, alloc=4.6MB, time=161.18 memory used=2616.9MB, alloc=4.6MB, time=161.42 x[1] = 0.677 y2[1] (analytic) = 0.62645747979480548239848649076909 y2[1] (numeric) = 0.62645747979480548239848649076911 absolute error = 2e-32 relative error = 3.1925550647988029394072508668424e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77945559591880593590877390292041 y1[1] (numeric) = 0.7794555959188059359087739029204 absolute error = 1e-32 relative error = 1.2829467197823128569746433614469e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2620.7MB, alloc=4.6MB, time=161.65 x[1] = 0.678 y2[1] (analytic) = 0.62723662203210123383477092452439 y2[1] (numeric) = 0.62723662203210123383477092452441 absolute error = 2e-32 relative error = 3.1885893293673824235583652700314e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77882874881565522308414354149961 y1[1] (numeric) = 0.77882874881565522308414354149961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2624.5MB, alloc=4.6MB, time=161.89 x[1] = 0.679 y2[1] (analytic) = 0.6280151370328272228865818746926 y2[1] (numeric) = 0.62801513703282722288658187469263 absolute error = 3e-32 relative error = 4.7769549220963854507430250033235e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77820112288382059699786132071801 y1[1] (numeric) = 0.77820112288382059699786132071801 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2628.3MB, alloc=4.6MB, time=162.13 x[1] = 0.68 y2[1] (analytic) = 0.62879302401846851370417818742025 y2[1] (numeric) = 0.62879302401846851370417818742027 absolute error = 2e-32 relative error = 3.1806968646351541844819338546206e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77757271875092793718239408404432 y1[1] (numeric) = 0.77757271875092793718239408404432 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2632.1MB, alloc=4.6MB, time=162.36 x[1] = 0.681 y2[1] (analytic) = 0.62957028221113818547018235442143 y2[1] (numeric) = 0.62957028221113818547018235442145 absolute error = 2e-32 relative error = 3.1767700231588481199215366273036e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77694353704538132416339231812446 y1[1] (numeric) = 0.77694353704538132416339231812446 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2636.0MB, alloc=4.6MB, time=162.60 x[1] = 0.682 y2[1] (analytic) = 0.63034691083357811028643650644746 y2[1] (numeric) = 0.63034691083357811028643650644749 absolute error = 3e-32 relative error = 4.7592840520670831773595059183183e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77631357839636241105566199413604 y1[1] (numeric) = 0.77631357839636241105566199413604 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2639.8MB, alloc=4.6MB, time=162.83 TOP MAIN SOLVE Loop memory used=2643.6MB, alloc=4.6MB, time=163.07 x[1] = 0.683 y2[1] (analytic) = 0.63112290910915973043206553993625 y2[1] (numeric) = 0.63112290910915973043206553993627 absolute error = 2e-32 relative error = 3.1689548440303531169619741314575e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77568284343382979438156388478507 y1[1] (numeric) = 0.77568284343382979438156388478507 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2647.4MB, alloc=4.6MB, time=163.30 x[1] = 0.684 y2[1] (analytic) = 0.63189827626188483499197011884303 y2[1] (numeric) = 0.63189827626188483499197011884305 absolute error = 2e-32 relative error = 3.1650663961791171417881861476900e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77505133278851838411246953849312 y1[1] (numeric) = 0.77505133278851838411246953849313 absolute error = 1e-32 relative error = 1.2902371206848326666390019169482e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2651.2MB, alloc=4.6MB, time=163.54 x[1] = 0.685 y2[1] (analytic) = 0.63267301151638633585497292322433 y2[1] (numeric) = 0.63267301151638633585497292322436 absolute error = 3e-32 relative error = 4.7417859548167236825337217708106e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77441904709193877293390386926657 y1[1] (numeric) = 0.77441904709193877293390386926658 absolute error = 1e-32 relative error = 1.2912905535512743283615987235738e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2655.0MB, alloc=4.6MB, time=163.77 x[1] = 0.686 y2[1] (analytic) = 0.63344711409792904308084214649343 y2[1] (numeric) = 0.63344711409792904308084214649346 absolute error = 3e-32 relative error = 4.7359912662514852143706603987940e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77378598697637660473500509705261 y1[1] (numeric) = 0.77378598697637660473500509705262 absolute error = 1e-32 relative error = 1.2923470014074183848379492153398e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2658.8MB, alloc=4.6MB, time=164.01 x[1] = 0.687 y2[1] (analytic) = 0.63422058323241043963541687438845 y2[1] (numeric) = 0.63422058323241043963541687438848 absolute error = 3e-32 relative error = 4.7302154476128828954295380686367e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77315215307489194232293354906961 y1[1] (numeric) = 0.77315215307489194232293354906962 absolute error = 1e-32 relative error = 1.2934064737748124423394677949525e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2662.7MB, alloc=4.6MB, time=164.24 memory used=2666.5MB, alloc=4.6MB, time=164.48 x[1] = 0.688 y2[1] (analytic) = 0.63499341814636145549305961059239 y2[1] (numeric) = 0.63499341814636145549305961059241 absolute error = 2e-32 relative error = 3.1496389456103216799687326898757e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77251754602131863436286160765029 y1[1] (numeric) = 0.7725175460213186343628616076503 absolute error = 1e-32 relative error = 1.2944689802196462850523152078977e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2670.3MB, alloc=4.6MB, time=164.72 x[1] = 0.689 y2[1] (analytic) = 0.63576561806694724110566184661687 y2[1] (numeric) = 0.63576561806694724110566184661689 absolute error = 2e-32 relative error = 3.1458133990967037036237642879066e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77188216645026368154417786455494 y1[1] (numeric) = 0.77188216645026368154417786455494 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2674.1MB, alloc=4.6MB, time=164.95 x[1] = 0.69 y2[1] (analytic) = 0.63653718222196794023742920700872 y2[1] (numeric) = 0.63653718222196794023742920700874 absolute error = 2e-32 relative error = 3.1420002725034476796470444715189e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77124601499710660197353931549777 y1[1] (numeric) = 0.77124601499710660197353931549777 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2677.9MB, alloc=4.6MB, time=165.18 x[1] = 0.691 y2[1] (analytic) = 0.63730810983985946216467333515846 y2[1] (numeric) = 0.63730810983985946216467333515848 absolute error = 2e-32 relative error = 3.1381995131092133094993404240904e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.77060909229799879579540620178138 y1[1] (numeric) = 0.77060909229799879579540620178138 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2681.7MB, alloc=4.6MB, time=165.41 x[1] = 0.692 y2[1] (analytic) = 0.63807840014969425323983831998321 y2[1] (numeric) = 0.63807840014969425323983831998323 absolute error = 2e-32 relative error = 3.1344110685000411795074126006437e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76997139898986290904069487845139 y1[1] (numeric) = 0.76997139898986290904069487845139 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2685.5MB, alloc=4.6MB, time=165.65 x[1] = 0.693 y2[1] (analytic) = 0.63884805238118206781899009952198 y2[1] (numeric) = 0.638848052381182067818990099522 absolute error = 2e-32 relative error = 3.1306348865671396308054613962184e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7693329357103921967041848602655 y1[1] (numeric) = 0.7693329357103921967041848602655 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2689.4MB, alloc=4.6MB, time=165.88 TOP MAIN SOLVE Loop memory used=2693.2MB, alloc=4.6MB, time=166.11 x[1] = 0.694 y2[1] (analytic) = 0.63961706576467073855199791401804 y2[1] (numeric) = 0.63961706576467073855199791401806 absolute error = 2e-32 relative error = 3.1268709155046907756975906190421e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76869370309804988505131696801677 y1[1] (numeric) = 0.76869370309804988505131696801677 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2697.0MB, alloc=4.6MB, time=166.35 x[1] = 0.695 y2[1] (analytic) = 0.64038543953114694603463751837122 y2[1] (numeric) = 0.64038543953114694603463751837125 absolute error = 3e-32 relative error = 4.6846786557115132014505074700963e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76805370179206853315502026835991 y1[1] (numeric) = 0.76805370179206853315502026835991 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2700.8MB, alloc=4.6MB, time=166.58 x[1] = 0.696 y2[1] (analytic) = 0.64115317291223698782184650192101 y2[1] (numeric) = 0.64115317291223698782184650192104 absolute error = 3e-32 relative error = 4.6790691004045755513109322114436e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76741293243244939366320627026033 y1[1] (numeric) = 0.76741293243244939366320627026033 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2704.6MB, alloc=4.6MB, time=166.81 x[1] = 0.697 y2[1] (analytic) = 0.64192026514020754680136270236923 y2[1] (numeric) = 0.64192026514020754680136270236925 absolute error = 2e-32 relative error = 3.1156517539809435847721197273669e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76677139565996177279756961051859 y1[1] (numeric) = 0.76677139565996177279756961051859 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2708.4MB, alloc=4.6MB, time=167.05 x[1] = 0.698 y2[1] (analytic) = 0.64268671544796645892697734026787 y2[1] (numeric) = 0.64268671544796645892697734026789 absolute error = 2e-32 relative error = 3.1119361143258687064325941068582e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76612909211614238958433522951618 y1[1] (numeric) = 0.76612909211614238958433522951618 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2712.2MB, alloc=4.6MB, time=167.28 memory used=2716.1MB, alloc=4.6MB, time=167.52 x[1] = 0.699 y2[1] (analytic) = 0.64345252306906348031063514088304 y2[1] (numeric) = 0.64345252306906348031063514088307 absolute error = 3e-32 relative error = 4.6623486464719355464444562915859e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76548602244329473431759280638201 y1[1] (numeric) = 0.76548602244329473431759280638202 absolute error = 1e-32 relative error = 1.3063595816004301595871539146873e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2719.9MB, alloc=4.6MB, time=167.76 x[1] = 0.7 y2[1] (analytic) = 0.64421768723769105367261435139872 y2[1] (numeric) = 0.64421768723769105367261435139875 absolute error = 3e-32 relative error = 4.6568109808713117359699209228648e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76484218728448842625585999019186 y1[1] (numeric) = 0.76484218728448842625585999019187 absolute error = 1e-32 relative error = 1.3074592597335938698746728353053e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2723.7MB, alloc=4.6MB, time=168.00 x[1] = 0.701 y2[1] (analytic) = 0.64498220718868507414902020334415 y2[1] (numeric) = 0.64498220718868507414902020334418 absolute error = 3e-32 relative error = 4.6512911000696346246566817930041e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76419758728355857055251673058384 y1[1] (numeric) = 0.76419758728355857055251673058384 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2727.5MB, alloc=4.6MB, time=168.24 x[1] = 0.702 y2[1] (analytic) = 0.64574608215752565445582601281535 y2[1] (numeric) = 0.64574608215752565445582601281538 absolute error = 3e-32 relative error = 4.6457889298787399508483892036349e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76355222308510511442075377730208 y1[1] (numeric) = 0.76355222308510511442075377730208 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2731.3MB, alloc=4.6MB, time=168.47 x[1] = 0.703 y2[1] (analytic) = 0.64650931138033788940869675451334 y2[1] (numeric) = 0.64650931138033788940869675451337 absolute error = 3e-32 relative error = 4.6403043965365510715860237738692e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7629060953344922025336791836665 y1[1] (numeric) = 0.7629060953344922025336791836665 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2735.1MB, alloc=4.6MB, time=168.70 x[1] = 0.704 y2[1] (analytic) = 0.64727189409389261979783058983915 y2[1] (numeric) = 0.64727189409389261979783058983918 absolute error = 3e-32 relative error = 4.6348374267040598114858362881597e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7622592046778475316602274138083 y1[1] (numeric) = 0.7622592046778475316602274138083 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2739.0MB, alloc=4.6MB, time=168.94 TOP MAIN SOLVE Loop memory used=2742.8MB, alloc=4.6MB, time=169.18 x[1] = 0.705 y2[1] (analytic) = 0.64803382953560719561705447426787 y2[1] (numeric) = 0.6480338295356071956170544742679 absolute error = 3e-32 relative error = 4.6293879474623330258832951971515e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76161155176206170453751641770848 y1[1] (numeric) = 0.76161155176206170453751641770848 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2746.6MB, alloc=4.6MB, time=169.41 x[1] = 0.706 y2[1] (analytic) = 0.64879511694354623864641061496962 y2[1] (numeric) = 0.64879511694354623864641061496966 absolute error = 4e-32 relative error = 6.1652745150793928311172208826032e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76096313723478758298029880162827 y1[1] (numeric) = 0.76096313723478758298029880162828 absolute error = 1e-32 relative error = 1.3141241028229465708823773382326e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2750.4MB, alloc=4.6MB, time=169.65 x[1] = 0.707 y2[1] (analytic) = 0.64955575555642240438747119615466 y2[1] (numeric) = 0.64955575555642240438747119615469 absolute error = 3e-32 relative error = 4.6185411711580327954783808449991e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.76031396174443964022815398442661 y1[1] (numeric) = 0.76031396174443964022815398442662 absolute error = 1e-32 relative error = 1.3152461355643562094593720346897e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2754.2MB, alloc=4.6MB, time=169.88 x[1] = 0.708 y2[1] (analytic) = 0.6503157446135971433506194368912 y2[1] (numeric) = 0.65031574461359714335061943689123 absolute error = 3e-32 relative error = 4.6131437303313822050152357663582e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7596640259401933125310689925183 y1[1] (numeric) = 0.75966402594019331253106899251831 absolute error = 1e-32 relative error = 1.3163714034797901738747780195774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2758.0MB, alloc=4.6MB, time=170.12 x[1] = 0.709 y2[1] (analytic) = 0.65107508335508146169353569417858 y2[1] (numeric) = 0.65107508335508146169353569417861 absolute error = 3e-32 relative error = 4.6077634925615308855601536333626e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75901333047198434997405630783822 y1[1] (numeric) = 0.75901333047198434997405630783823 absolute error = 1e-32 relative error = 1.3174999171334193274588603440274e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2761.8MB, alloc=4.6MB, time=170.35 memory used=2765.7MB, alloc=4.6MB, time=170.59 x[1] = 0.71 y2[1] (analytic) = 0.65183377102153668121012797285284 y2[1] (numeric) = 0.65183377102153668121012797285286 absolute error = 2e-32 relative error = 3.0682669246572677397779021813019e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75836187599050816654145794413955 y1[1] (numeric) = 0.75836187599050816654145794413957 absolute error = 2e-32 relative error = 2.6372633742799492530594693858876e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2769.5MB, alloc=4.6MB, time=170.82 x[1] = 0.711 y2[1] (analytic) = 0.6525918068542751986691468534576 y2[1] (numeric) = 0.65259180685427519866914685345762 absolute error = 2e-32 relative error = 3.0647028954297049894997902804717e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7577096631472191894215856872678 y1[1] (numeric) = 0.75770966314721918942158568726782 absolute error = 2e-32 relative error = 2.6395334483300762990080584996728e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2773.3MB, alloc=4.6MB, time=171.06 x[1] = 0.712 y2[1] (analytic) = 0.65334919009526124450172549952873 y2[1] (numeric) = 0.65334919009526124450172549952875 absolute error = 2e-32 relative error = 3.0611501939849210234947991530388e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7570566925943302075523481947161 y1[1] (numeric) = 0.75705669259433020755234819471612 absolute error = 2e-32 relative error = 2.6418100778506723352722503489935e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2777.1MB, alloc=4.6MB, time=171.29 x[1] = 0.713 y2[1] (analytic) = 0.65410591998711164083708605681577 y2[1] (numeric) = 0.65410591998711164083708605681579 absolute error = 2e-32 relative error = 3.0576087738808533640200861711349e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75640296498481171940851640878051 y1[1] (numeric) = 0.75640296498481171940851640878053 absolute error = 2e-32 relative error = 2.6440932843780685480432926678575e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2780.9MB, alloc=4.6MB, time=171.53 x[1] = 0.714 y2[1] (analytic) = 0.65486199577309655888565440879708 y2[1] (numeric) = 0.6548619957730965588856544087971 absolute error = 2e-32 relative error = 3.0540785889382729445544723434355e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75574848097239128003127949599547 y1[1] (numeric) = 0.75574848097239128003127949599549 absolute error = 2e-32 relative error = 2.6463830895520691753125739647100e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2784.7MB, alloc=4.6MB, time=171.76 x[1] = 0.715 y2[1] (analytic) = 0.655617416697140275668825905437 y2[1] (numeric) = 0.65561741669714027566882590543702 absolute error = 2e-32 relative error = 3.0505595932389508765356171733896e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75509324121155284730074428323906 y1[1] (numeric) = 0.75509324121155284730074428323908 absolute error = 2e-32 relative error = 2.6486795151165500989962365024474e-30 % Correct digits = 31 h = 0.001 memory used=2788.5MB, alloc=4.6MB, time=172.00 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2792.4MB, alloc=4.6MB, time=172.24 x[1] = 0.716 y2[1] (analytic) = 0.65637218200382193009462533548235 y2[1] (numeric) = 0.65637218200382193009462533548237 absolute error = 2e-32 relative error = 3.0470517411238405914812493785611e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75443724635753612745203191795418 y1[1] (numeric) = 0.75443724635753612745203191795419 absolute error = 1e-32 relative error = 1.3254912914600308276402197034088e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2796.2MB, alloc=4.6MB, time=172.47 x[1] = 0.717 y2[1] (analytic) = 0.65712629093837627837850506670131 y2[1] (numeric) = 0.65712629093837627837850506670133 absolute error = 2e-32 relative error = 3.0435549871912752084216757062203e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75378049706633591983562623633442 y1[1] (numeric) = 0.75378049706633591983562623633444 absolute error = 2e-32 relative error = 2.6532923149164356977217203840425e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2800.0MB, alloc=4.6MB, time=172.71 x[1] = 0.718 y2[1] (analytic) = 0.6578797427466944488085259333295 y2[1] (numeric) = 0.65787974274669444880852593332952 absolute error = 2e-32 relative error = 3.0400692862951799782430323929886e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75312299399470146092262907907173 y1[1] (numeric) = 0.75312299399470146092262907907175 absolute error = 2e-32 relative error = 2.6556087331653969479610449159774e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2803.8MB, alloc=4.6MB, time=172.94 x[1] = 0.719 y2[1] (analytic) = 0.65863253667532469585416610560527 y2[1] (numeric) = 0.65863253667532469585416610560529 absolute error = 2e-32 relative error = 3.0365945935432996581920544702167e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75246473780013576755557854935575 y1[1] (numeric) = 0.75246473780013576755557854935577 absolute error = 2e-32 relative error = 2.6579318598331786692376963393421e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2807.6MB, alloc=4.6MB, time=173.18 x[1] = 0.72 y2[1] (analytic) = 0.65938467197147315361800383264817 y2[1] (numeric) = 0.65938467197147315361800383264818 absolute error = 1e-32 relative error = 1.5165654321477203357119039156049e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75180572914089497944548696225195 y1[1] (numeric) = 0.75180572914089497944548696225197 absolute error = 2e-32 relative error = 2.6602617171931426982201891539493e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2811.4MB, alloc=4.6MB, time=173.41 memory used=2815.2MB, alloc=4.6MB, time=173.65 x[1] = 0.721 y2[1] (analytic) = 0.6601361478830045886295206070606 y2[1] (numeric) = 0.66013614788300458862952060706061 absolute error = 1e-32 relative error = 1.5148390270808639540420720176833e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75114596867598770091575598836582 y1[1] (numeric) = 0.75114596867598770091575598836584 absolute error = 2e-32 relative error = 2.6625983276264038710059220138567e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2819.1MB, alloc=4.6MB, time=173.89 x[1] = 0.722 y2[1] (analytic) = 0.66088696365844315198027195751232 y2[1] (numeric) = 0.66088696365844315198027195751233 absolute error = 1e-32 relative error = 1.5131180595004380130044400750321e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.75048545706517434189362724782304 y1[1] (numeric) = 0.75048545706517434189362724782307 absolute error = 3e-32 relative error = 3.9974125704336883192190511506016e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2822.9MB, alloc=4.6MB, time=174.12 x[1] = 0.723 y2[1] (analytic) = 0.66163711854697313079967373419959 y2[1] (numeric) = 0.6616371185469731307996737341996 absolute error = 1e-32 relative error = 1.5114025074592375553460765783703e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74982419496896645814982736306022 y1[1] (numeric) = 0.74982419496896645814982736306025 absolute error = 3e-32 relative error = 4.0009378466697293918403961876370e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2826.7MB, alloc=4.6MB, time=174.36 x[1] = 0.724 y2[1] (analytic) = 0.66238661179843969907065241145532 y2[1] (numeric) = 0.66238661179843969907065241145534 absolute error = 2e-32 relative error = 3.0193846982652905557273239879750e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74916218304862609078706723072606 y1[1] (numeric) = 0.74916218304862609078706723072608 absolute error = 2e-32 relative error = 2.6696489028066508932185774413614e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2830.5MB, alloc=4.6MB, time=174.59 x[1] = 0.725 y2[1] (analytic) = 0.66313544266334966778440859192254 y2[1] (numeric) = 0.66313544266334966778440859192256 absolute error = 2e-32 relative error = 3.0159751256355770264554793839155e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7484994219661651049780560241387 y1[1] (numeric) = 0.74849942196616510497805602413872 absolute error = 2e-32 relative error = 2.6720127515214130264819665863725e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2834.3MB, alloc=4.6MB, time=174.83 memory used=2838.1MB, alloc=4.6MB, time=175.07 x[1] = 0.726 y2[1] (analytic) = 0.66388361039287223443354355759009 y2[1] (numeric) = 0.66388361039287223443354355759011 absolute error = 2e-32 relative error = 3.0125762538654063710692656459284e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74783591238434452795369118823017 y1[1] (numeric) = 0.74783591238434452795369118823019 absolute error = 2e-32 relative error = 2.6743834668535085660141875155337e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2842.0MB, alloc=4.6MB, time=175.30 x[1] = 0.727 y2[1] (analytic) = 0.66463111423883973184279937462657 y2[1] (numeric) = 0.66463111423883973184279937462659 absolute error = 2e-32 relative error = 3.0091880400310093449137481970644e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.7471716549666738862420864387327 y1[1] (numeric) = 0.74717165496667388624208643873272 absolute error = 2e-32 relative error = 2.6767610718439339671993118882144e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2845.8MB, alloc=4.6MB, time=175.54 x[1] = 0.728 y2[1] (analytic) = 0.66537795345374837633666372133474 y2[1] (numeric) = 0.66537795345374837633666372133476 absolute error = 2e-32 relative error = 3.0058104414471310152014818608646e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74650665037741054215910052652369 y1[1] (numeric) = 0.74650665037741054215910052652371 absolute error = 2e-32 relative error = 2.6791455896459357870268996432580e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2849.6MB, alloc=4.6MB, time=175.77 x[1] = 0.729 y2[1] (analytic) = 0.66612412729075901524309127168396 y2[1] (numeric) = 0.66612412729075901524309127168398 absolute error = 2e-32 relative error = 3.0024434156653997148162522887653e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74584089928155902955103027654531 y1[1] (numeric) = 0.74584089928155902955103027654533 absolute error = 2e-32 relative error = 2.6815370435256715954373709805841e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2853.4MB, alloc=4.6MB, time=176.01 x[1] = 0.73 y2[1] (analytic) = 0.66686963500369787373259413076153 y2[1] (numeric) = 0.66686963500369787373259413076155 absolute error = 2e-32 relative error = 2.9990869204727094153192585309935e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74517440234487038879013215855033 y1[1] (numeric) = 0.74517440234487038879013215855035 absolute error = 2e-32 relative error = 2.6839354568628756191548285450706e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2857.2MB, alloc=4.6MB, time=176.24 x[1] = 0.731 y2[1] (analytic) = 0.66761447584705730099195448311474 y2[1] (numeric) = 0.66761447584705730099195448311476 absolute error = 2e-32 relative error = 2.9957409138896153906930961305745e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74450716023384150102363739409716 y1[1] (numeric) = 0.74450716023384150102363739409717 absolute error = 1e-32 relative error = 1.3431704265757645787032644145165e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2861.0MB, alloc=4.6MB, time=176.48 TOP MAIN SOLVE Loop memory used=2864.8MB, alloc=4.6MB, time=176.71 x[1] = 0.732 y2[1] (analytic) = 0.66835864907599651573181328033319 y2[1] (numeric) = 0.66835864907599651573181328033322 absolute error = 3e-32 relative error = 4.4886080312531145671445171086879e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74383917361571442167692635072351 y1[1] (numeric) = 0.74383917361571442167692635072352 absolute error = 1e-32 relative error = 1.3443766280002679046520701249114e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2868.7MB, alloc=4.6MB, time=176.95 x[1] = 0.733 y2[1] (analytic) = 0.66910215394634235102738946034485 y2[1] (numeric) = 0.66910215394634235102738946034487 absolute error = 2e-32 relative error = 2.9890801997932097766217692211727e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74317044315847571321152872006884 y1[1] (numeric) = 0.74317044315847571321152872006885 absolute error = 1e-32 relative error = 1.3455863445672007765209508248948e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2872.5MB, alloc=4.6MB, time=177.19 x[1] = 0.734 y2[1] (analytic) = 0.66984498971458999849158485776852 y2[1] (numeric) = 0.66984498971458999849158485776854 absolute error = 2e-32 relative error = 2.9857654094750597597543434053820e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74250096953085577713861672188964 y1[1] (numeric) = 0.74250096953085577713861672188965 absolute error = 1e-32 relative error = 1.3467995881969598587254286818316e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2876.3MB, alloc=4.6MB, time=177.42 x[1] = 0.735 y2[1] (analytic) = 0.67058715563790375177973063228011 y2[1] (numeric) = 0.67058715563790375177973063228014 absolute error = 3e-32 relative error = 4.4736914132305672678675986236346e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74183075340232818528865932041883 y1[1] (numeric) = 0.74183075340232818528865932041884 absolute error = 1e-32 relative error = 1.3480163708684304434182711974633e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2880.1MB, alloc=4.6MB, time=177.66 x[1] = 0.736 y2[1] (analytic) = 0.67132865097411774942523171030799 y2[1] (numeric) = 0.67132865097411774942523171030802 absolute error = 3e-32 relative error = 4.4687501354916272011796261628125e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74115979544310901033790618335927 y1[1] (numeric) = 0.74115979544310901033790618335928 absolute error = 1e-32 relative error = 1.3492367046193338902099365869454e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2883.9MB, alloc=4.6MB, time=177.89 memory used=2887.7MB, alloc=4.6MB, time=178.13 x[1] = 0.737 y2[1] (analytic) = 0.67206947498173671700536640447498 y2[1] (numeric) = 0.67206947498173671700536640447501 absolute error = 3e-32 relative error = 4.4638242200801101477933105770503e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.74048809632415615559237085697158 y1[1] (numeric) = 0.7404880963241561555923708569716 absolute error = 2e-32 relative error = 2.7009212030931551480976160252618e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2891.5MB, alloc=4.6MB, time=178.36 x[1] = 0.738 y2[1] (analytic) = 0.67280962691993670863649904504927 y2[1] (numeric) = 0.67280962691993670863649904504929 absolute error = 2e-32 relative error = 2.9726090709430304661153395306775e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73981565671716868402998337321739 y1[1] (numeric) = 0.73981565671716868402998337321741 absolute error = 2e-32 relative error = 2.7033761476132147246397077043472e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2895.4MB, alloc=4.6MB, time=178.60 x[1] = 0.739 y2[1] (analytic) = 0.67354910604856584779796412825327 y2[1] (numeric) = 0.67354910604856584779796412825329 absolute error = 2e-32 relative error = 2.9693454894969324165319591238240e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73914247729458614660158324674932 y1[1] (numeric) = 0.73914247729458614660158324674933 absolute error = 1e-32 relative error = 1.3529191336157626424229708466991e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2899.2MB, alloc=4.6MB, time=178.83 x[1] = 0.74 y2[1] (analytic) = 0.67428791162814506748388115760817 y2[1] (numeric) = 0.6742879116281450674838811576082 absolute error = 3e-32 relative error = 4.4491380436528334605194900702897e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73846855872958790979142456069883 y1[1] (numeric) = 0.73846855872958790979142456069885 absolute error = 2e-32 relative error = 2.7083075865012678425941625899104e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2903.0MB, alloc=4.6MB, time=179.07 x[1] = 0.741 y2[1] (analytic) = 0.67502604291986884968216002656091 y2[1] (numeric) = 0.67502604291986884968216002656094 absolute error = 3e-32 relative error = 4.4442729750444972177418708385651e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73779390169609248243786558070087 y1[1] (numeric) = 0.73779390169609248243786558070089 absolute error = 2e-32 relative error = 2.7107841300968460371261817659908e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2906.8MB, alloc=4.6MB, time=179.30 x[1] = 0.742 y2[1] (analytic) = 0.67576349918560596417995746344981 y2[1] (numeric) = 0.67576349918560596417995746344983 absolute error = 2e-32 relative error = 2.9596153127688800283540701399498e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73711850686875684181491607640942 y1[1] (numeric) = 0.73711850686875684181491607640944 absolute error = 2e-32 relative error = 2.7132679228146117503361941332522e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2910.6MB, alloc=4.6MB, time=179.54 TOP MAIN SOLVE Loop memory used=2914.4MB, alloc=4.6MB, time=179.78 x[1] = 0.743 y2[1] (analytic) = 0.67650027968790020669484573341403 y2[1] (numeric) = 0.67650027968790020669484573341406 absolute error = 3e-32 relative error = 4.4345879670353336555976767611827e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73644237492297575897531626890064 y1[1] (numeric) = 0.73644237492297575897531626890066 absolute error = 2e-32 relative error = 2.7157589895735959992495926244224e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2918.2MB, alloc=4.6MB, time=180.01 x[1] = 0.744 y2[1] (analytic) = 0.67723638368997113633095546613973 y2[1] (numeric) = 0.67723638368997113633095546613976 absolute error = 3e-32 relative error = 4.4297679100675074059160819995172e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73576550653488112335582206082836 y1[1] (numeric) = 0.73576550653488112335582206082838 absolute error = 2e-32 relative error = 2.7182573554162451483077989369126e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2922.1MB, alloc=4.6MB, time=180.25 x[1] = 0.745 y2[1] (analytic) = 0.67797181045571481235935515336133 y2[1] (numeric) = 0.67797181045571481235935515336136 absolute error = 3e-32 relative error = 4.4249627399456017725405899014717e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 0.73508790238134126664537194399042 y1[1] (numeric) = 0.73508790238134126664537194399044 absolute error = 2e-32 relative error = 2.7207630455091624865071119439783e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 3 ) = m1 * cos(x) ; diff ( y1 , x , 1 ) = m1 * y2; Iterations = 646 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 19 Minutes 45 Seconds Optimized Time Remaining = 19 Minutes 43 Seconds Expected Total Time = 22 Minutes 44 Seconds Time to Timeout Unknown Percent Done = 13.2 % > quit memory used=2924.3MB, alloc=4.6MB, time=180.38