|\^/| 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > 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 (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 (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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y1[1]) < min_size then min_size := omniabs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if omniabs(array_y2[1]) < min_size then min_size := omniabs(array_y2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_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; > 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; > 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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_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_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; 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; 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_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 <> 0.0) 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_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 <> 0.0) 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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_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_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 relerr <> 0. 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_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 relerr <> 0. 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_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 (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 (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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, 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 - 1 - 1; > while ((m >= 10) and ((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 ))) 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-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > 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_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 ))) 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-1)*rm0-convfloat(m-2)*rm1; > if (omniabs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > 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 - 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 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 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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))) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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_y2_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 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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))) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 := false; > #TOP WHICH RADII EQ = 1 > if ( not found 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 := true; > 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"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found 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] > 0.0) 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 := true; > 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"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found 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 := true; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4; > fi;# end if 3; > if ( not found 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] > 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 := true; > 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"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found 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 := true; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found ) 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"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if ( not found 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 := true; > 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"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found 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] > 0.0) 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 := true; > 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"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found 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 := true; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4; > fi;# end if 3; > if ( not found 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] > 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 := true; > 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"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found 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 := true; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if ( not found ) 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"); > 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_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 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, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found, 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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (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) 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 - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; 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_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) 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 - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; 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 - 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 array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := 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]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := 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 array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := 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_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 array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := 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]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := 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 array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := 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 := false; if not found 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 := true; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found 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 0. < 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 := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found 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 := true; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < 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 := true; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found 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 := true; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found 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") end if end if; found := false; if not found 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 := true; array_type_pole[2] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found 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 0. < 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 := true; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found 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 := true; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < 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 := true; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used") end if end if end if; if not found 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 := true; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if end if; if not found 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") 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_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_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 > ; > 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 > #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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_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_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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 mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_y2[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h; > array_y1_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp5[1] := array_y1[1] - array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h; > array_y2_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h; > array_y1_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp5[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h; > array_y2_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp5[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (3.0); > array_y1_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp5[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_y2,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (4.0); > array_y1_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp5[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_y2,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 2; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 1) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary / glob_h; > 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; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp5[kkk] := array_y1[kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp5[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 2; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 1) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary / glob_h; > 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; > 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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_m1[1]*array_y2[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_y1[1] - array_const_1D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y2, 1); array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := array_y1[2]; if not array_y2_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y2, 1); array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := array_y1[3]; if not array_y2_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y2, 1); array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*3.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := array_y1[4]; if not array_y2_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y2, 1); array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*4.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := array_y1[5]; if not array_y2_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_y2, 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 2; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 1 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary/glob_h end if; array_y1_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; array_tmp5[kkk] := array_y1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp5[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 2; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 1 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary/glob_h end if; array_y2_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 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 := 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 15 > # Begin Function number 16 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 16 > # Begin Function number 17 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error <> 0.0) 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 rel_error <> 0. then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 20 > # Begin Function number 21 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 21 > # Begin Function number 22 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > 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 22 > # Begin Function number 23 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 24 > # Begin Function number 25 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 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 25 > # Begin Function number 26 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 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 26 > # Begin Function number 27 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 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 27 > # Begin Function number 28 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 28 > # Begin Function number 29 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 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 29 > # Begin Function number 30 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 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 30 > # Begin Function number 31 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 31 > # Begin Function number 32 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 33 > # Begin Function number 34 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 34 > # Begin Function number 35 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 35 > # Begin Function number 36 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 36 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(1.0 + cos(x)); > end; exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > return(1.0 + sin(x)); > end; exact_soln_y2 := proc(x) return 1.0 + sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h; > 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_log10normmin, > 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_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > 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_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #END CONST > array_y1_init, > array_y2_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y1, > array_x, > array_y2, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_poles, > array_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_log10normmin := 0.1; > 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_hmax := 1.0; > glob_hmin := 0.00000000001; > glob_hmin_init := 0.001; > 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_log10_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > 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-50; > 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_log10abserr := 0.0; > glob_log10relerr := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest2postode.ode#################"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 - 1.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=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 := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.01 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"glob_display_interval := 0.1;"); > omniout_str(ALWAYS,"glob_max_minutes := 10;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y1_init:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(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_y1:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(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_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > 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_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_y1[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_y2[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[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 <=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 <= 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 <=2) 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 <=2) 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 <= 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_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_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_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_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 := 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_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_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_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1D0[1] := 1.0; > 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 := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_h := 0.01 ; > glob_look_poles := true; > glob_max_iter := 1000000; > glob_display_interval := 0.1; > glob_max_minutes := 10; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=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); > glob_abserr := expt(10.0 , (glob_log10_abserr)); > glob_relerr := expt(10.0 , (glob_log10_relerr)); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := false; > array_y2_set_initial[2,3] := false; > array_y2_set_initial[2,4] := false; > array_y2_set_initial[2,5] := false; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 3 > glob_h := glob_display_interval; > 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 := 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 > ; > order_diff := 1; > #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 > ; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 2) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 2 + 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 := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_log10normmin := -glob_large_float ; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 5 > tmp := omniabs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 6 > glob_log10normmin := log10norm; > fi;# end if 6 > fi;# end if 5; > display_alot(current_iter) > ; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 5 > tmp := omniabs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 6 > glob_log10normmin := log10norm; > fi;# end if 6 > fi;# end if 5; > display_alot(current_iter) > ; > 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 <= 2) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 2 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 6; > 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_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =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_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 > #Jump Series array_y2 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 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 =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_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 > display_alot(current_iter) > ; > 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 ( y1 , x , 1 ) = m1 * y2 + 1.0;"); > omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 - 1.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2012-12-14T23:44:43-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest2") > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 + 1.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_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," 151 ") > ; > logitem_str(html_log_file,"mtest2 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest2 maple results") > ; > logitem_str(html_log_file,"Languages compared") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 - 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > 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, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h; 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_log10normmin, 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_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, 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_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, array_y1_init, array_y2_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y1, array_x, array_y2, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_poles, array_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_log10normmin := 0.1; 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_hmax := 1.0; glob_hmin := 0.1*10^(-10); glob_hmin_init := 0.001; 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_log10_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); 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^(-50); 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_log10abserr := 0.; glob_log10relerr := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest2postode.ode#################"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 - 1.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=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 := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_h := 0.01 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "glob_display_interval := 0.1;"); omniout_str(ALWAYS, "glob_max_minutes := 10;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y1_init := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. 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_y1 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 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_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= 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_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 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); glob_abserr := expt(10.0, glob_log10_abserr); glob_relerr := expt(10.0, glob_log10_relerr); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := false; array_y2_set_initial[2, 3] := false; array_y2_set_initial[2, 4] := false; array_y2_set_initial[2, 5] := false; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval 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 := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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 := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_log10normmin := -glob_large_float; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and glob_check_sign*array_x[1] < glob_check_sign*x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do if reached_interval() then omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop") end if; glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; 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 := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 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 := 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; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 - 1.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-12-14T23:44:43-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest2"); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 + 1.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_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, " 151 "); logitem_str(html_log_file, "mtest2 diffeq.mxt"); logitem_str(html_log_file, "mtest2 maple results"); logitem_str(html_log_file, "Languages compared"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = y1 - 1.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); 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/mtest2postode.ode################# diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_h := 0.01 ; glob_look_poles := true; glob_max_iter := 1000000; glob_display_interval := 0.1; glob_max_minutes := 10; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(1.0 + cos(x)); end; exact_soln_y2 := proc(x) return(1.0 + sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 memory used=3.8MB, alloc=3.1MB, time=0.49 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 9.9 estimated_steps = 9900 step_error = 1.0101010101010101010101010101010e-14 est_needed_step_err = 1.0101010101010101010101010101010e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.7823424015867847624175005921290e-56 max_value3 = 2.7823424015867847624175005921290e-56 value3 = 2.7823424015867847624175005921290e-56 best_h = 0.001 START of Soultion x[1] = 0.1 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 x[1] = 0.1 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.101 y1[1] (analytic) = 1.994903834375976659378402999829 y1[1] (numeric) = 1.994903834375976659330072446903 absolute error = 4.83305529260e-20 relative error = 2.4227008887933798081809577766315e-18 % Correct digits = 19 h = 0.001 y2[1] (analytic) = 1.1008283707295679951297521195232 y2[1] (numeric) = 1.1008283707295679951245513567548 absolute error = 5.2007627684e-21 relative error = 4.7244083698108387754059116643976e-19 % Correct digits = 20 h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=1.13 NO POLE NO POLE x[1] = 0.102 y1[1] (analytic) = 1.9948025085701760853346856764599 y1[1] (numeric) = 1.9948025085701760852380350204623 absolute error = 9.66506559976e-20 relative error = 4.8451240452307603269412816161354e-18 % Correct digits = 19 h = 0.001 y2[1] (analytic) = 1.1018232239839455107486422960806 y2[1] (numeric) = 1.101823223983945510738144114655 absolute error = 1.04981814256e-20 relative error = 9.5280088466831656795935497512387e-19 % Correct digits = 20 h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.4MB, time=1.78 NO POLE NO POLE x[1] = 0.103 y1[1] (analytic) = 1.9947001879619498413211671928266 y1[1] (numeric) = 1.9947001879619498411762070285878 absolute error = 1.449601642388e-19 relative error = 7.2672657832809712535180716324922e-18 % Correct digits = 19 h = 0.001 y2[1] (analytic) = 1.1028179754151075276904042105046 y2[1] (numeric) = 1.1028179754151075276745119702799 absolute error = 1.58922402247e-20 relative error = 1.4410574164533419203619092413278e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.104 y1[1] (analytic) = 1.9945968726536185270373744944846 y1[1] (numeric) = 1.9945968726536185268441155617897 absolute error = 1.932589326949e-19 relative error = 9.6891224158888634205388013077512e-18 % Correct digits = 19 h = 0.001 y2[1] (analytic) = 1.1038126240283026976889707546695 y2[1] (numeric) = 1.1038126240283026976675878314446 absolute error = 2.13829232249e-20 relative error = 1.9371877762064554536234939434273e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=2.42 NO POLE NO POLE x[1] = 0.105 y1[1] (analytic) = 1.9944925627484974422050131246041 y1[1] (numeric) = 1.9944925627484974419634663081717 absolute error = 2.415468164324e-19 relative error = 1.2110690254945748612340991454953e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1048071688288824904365536000268 y2[1] (numeric) = 1.1048071688288824904095833857344 absolute error = 2.69702142924e-20 relative error = 2.4411693780905641683081842988073e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=3.07 NO POLE NO POLE x[1] = 0.106 y1[1] (analytic) = 1.9943872583508964832526761118722 y1[1] (numeric) = 1.9943872583508964829628524413332 absolute error = 2.898236705390e-19 relative error = 1.4531965611264843115167125080392e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1058016088223021882320906180187 y2[1] (numeric) = 1.1058016088223021881994365209186 absolute error = 3.26540971001e-20 relative error = 2.9529797062673093216658040407707e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=3.70 NO POLE NO POLE x[1] = 0.107 y1[1] (analytic) = 1.9942809595661200390059562343918 y1[1] (numeric) = 1.994280959566120038667866884267 absolute error = 3.380893501248e-19 relative error = 1.6952944794616874357674530846156e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1067959430141218805258807024165 y2[1] (numeric) = 1.1067959430141218804874461472886 absolute error = 3.84345551279e-20 relative error = 3.4725963146586636970802274806927e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.108 y1[1] (analytic) = 1.9941736665004668853830659694533 y1[1] (numeric) = 1.9941736665004668849967222591317 absolute error = 3.863437103216e-19 relative error = 1.9373624113670420257795693283422e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1077901704100074583594114490316 y2[1] (numeric) = 1.1077901704100074583150998773695 absolute error = 4.43115716621e-20 relative error = 3.9999968266282516910837357922884e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=4.35 NO POLE NO POLE x[1] = 0.109 y1[1] (analytic) = 1.9940653792612300790960704335539 y1[1] (numeric) = 1.9940653792612300786614838272702 absolute error = 4.345866062837e-19 relative error = 2.1793999876007451453060318257181e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1087842900157316086993852530554 y2[1] (numeric) = 1.1087842900157316086491001232592 absolute error = 5.02851297962e-20 relative error = 4.5351589347903320800553168500177e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=5.00 NO POLE NO POLE x[1] = 0.11 y1[1] (analytic) = 1.9939560979566968503578396114198 y1[1] (numeric) = 1.993956097956696849875021718232 absolute error = 4.828178931878e-19 relative error = 2.4214068388093740982082108337834e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1097783008371748086649494900834 y2[1] (numeric) = 1.1097783008371748086085942776529 absolute error = 5.63552124305e-20 relative error = 5.0780604007113634819183322827101e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.111 y1[1] (analytic) = 1.993845822696148494594827167072 y1[1] (numeric) = 1.9938458226961484940637897408385 absolute error = 5.310374262335e-19 relative error = 2.6633825955279355675241193226084e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1107722018803263196471365536769 y2[1] (numeric) = 1.1107722018803263195846147514047 absolute error = 6.25218022722e-20 relative error = 5.6286790546578737104513747791630e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=5.64 NO POLE NO POLE x[1] = 0.112 y1[1] (analytic) = 1.9937345535898602631657841241467 y1[1] (numeric) = 1.9937345535898602625865390635034 absolute error = 5.792450606433e-19 relative error = 2.9053268881774067930080390019212e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1117659921512851813195196301052 y2[1] (numeric) = 1.1117659921512851812507347482699 absolute error = 6.87848818353e-20 relative error = 6.1869927953273818733037261582423e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=6.28 NO POLE NO POLE x[1] = 0.113 y1[1] (analytic) = 1.9936222907491012530865166967484 y1[1] (numeric) = 1.9936222907491012524590760450855 absolute error = 6.274406516629e-19 relative error = 3.1472393470637806027697108700383e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1127596706562612055390901996952 y2[1] (numeric) = 1.1127596706562612054639457662543 absolute error = 7.51444334409e-20 relative error = 6.7529795896164007036105741242238e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=6.92 NO POLE NO POLE x[1] = 0.114 y1[1] (analytic) = 1.9935090342861342957607985460685 y1[1] (numeric) = 1.9935090342861342950851744915067 absolute error = 6.756240545618e-19 relative error = 3.3891196023786148788148794727919e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1137532364015759701363633639937 y2[1] (numeric) = 1.1137532364015759700547629247767 absolute error = 8.16004392170e-20 relative error = 7.3266174723444812336556340826865e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.115 y1[1] (analytic) = 1.9933947843142158447175487318465 y1[1] (numeric) = 1.9933947843142158439937536072134 absolute error = 7.237951246331e-19 relative error = 3.6309672841955688330198347242800e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1147466883936638125937172087197 y2[1] (numeric) = 1.1147466883936638125055643276211 absolute error = 8.81528810986e-20 relative error = 7.9078845460063407876823468703747e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=7.57 NO POLE NO POLE x[1] = 0.116 y1[1] (analytic) = 1.993279540947595862354387621489 y1[1] (numeric) = 1.9932795409475958615824339042952 absolute error = 7.719537171938e-19 relative error = 3.8727820224694463977227677572002e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1157400256390728236109725242508 y2[1] (numeric) = 1.1157400256390728235161707834229 absolute error = 9.48017408279e-20 relative error = 8.4967589805339754184835880559269e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=8.21 NO POLE NO POLE x[1] = 0.117 y1[1] (analytic) = 1.993163304301517705687684013279 y1[1] (numeric) = 1.9931633043015177048675843256939 absolute error = 8.200996875851e-19 relative error = 4.1145634470352391504512297267748e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1167332471444658405572193181459 y2[1] (numeric) = 1.1167332471444658404556723181919 absolute error = 1.015469999540e-19 relative error = 9.0932190130149679979160720889905e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.118 y1[1] (analytic) = 1.99304607449221801110920772362 y1[1] (numeric) = 1.9930460744922180102409748324471 absolute error = 8.682328911729e-19 relative error = 4.3563111876081722591741322559435e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.117726351916621440807896667961 y2[1] (numeric) = 1.1177263519166214406995080281278 absolute error = 1.083886398332e-19 relative error = 9.6972429474656799941811462110628e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=8.84 NO POLE NO POLE x[1] = 0.119 y1[1] (analytic) = 1.9929278516369265781495028816522 y1[1] (numeric) = 1.9929278516369265772331496983044 absolute error = 9.163531833478e-19 relative error = 4.5980248737812414418891143286486e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1187193389624349349661325773612 y2[1] (numeric) = 1.1187193389624349348508059357321 absolute error = 1.153266416291e-19 relative error = 1.0308809154587476999281413529051e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=9.49 NO POLE NO POLE x[1] = 0.12 y1[1] (analytic) = 1.9928086358538662522480981678576 y1[1] (numeric) = 1.9928086358538662512836377483326 absolute error = 9.644604195250e-19 relative error = 4.8397041350222471151822012203744e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.119712207288919359967350614271 y2[1] (numeric) = 1.119712207288919359844989627959 absolute error = 1.223609863120e-19 relative error = 1.0927896071461440503205691531038e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=61.0MB, alloc=4.4MB, time=10.14 x[1] = 0.121 y1[1] (analytic) = 1.9926884272622528065306712264356 y1[1] (numeric) = 1.9926884272622528055181167712902 absolute error = 1.0125544551454e-18 relative error = 5.0813486006768493509757294659088e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1207049559032064720661502265403 y2[1] (numeric) = 1.1207049559032064719366585718805 absolute error = 1.294916546598e-19 relative error = 1.1554482201378253828048812550553e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.122 y1[1] (analytic) = 1.992567225982294822593285474272 y1[1] (numeric) = 1.992567225982294821532650328597 absolute error = 1.0606351456750e-18 relative error = 5.3229578999630920929075439569264e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1216975838125477397044677483272 y2[1] (numeric) = 1.1216975838125477395677491210697 absolute error = 1.367186272575e-19 relative error = 1.2188546113543889489825385209719e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=10.79 NO POLE NO POLE x[1] = 0.123 y1[1] (analytic) = 1.9924450321351935702938185222573 y1[1] (numeric) = 1.992445032135193569185116175652 absolute error = 1.1087023466053e-18 relative error = 5.5645316619709441989791125878824e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1226900900243153362600252291201 y2[1] (numeric) = 1.1226900900243153361159833446227 absolute error = 1.440418844974e-19 relative error = 1.2830066442848918903527208272762e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=11.44 NO POLE NO POLE x[1] = 0.124 y1[1] (analytic) = 1.992321845843142886550702417515 y1[1] (numeric) = 1.9923218458431428853939465040607 absolute error = 1.1567559134543e-18 relative error = 5.8060695156648517243198215245480e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1236824735460031326740743370329 y2[1] (numeric) = 1.1236824735460031325226129304539 absolute error = 1.514614065790e-19 relative error = 1.3479021889612059316056800864928e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.125 y1[1] (analytic) = 1.9921976672293290531490969077882 y1[1] (numeric) = 1.9921976672293290519443012060226 absolute error = 1.2047957017656e-18 relative error = 6.0475710898767538051266636756011e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1246747333852276899574427087121 y2[1] (numeric) = 1.1246747333852276897984655352027 absolute error = 1.589771735094e-19 relative error = 1.4135391219369250197174710113365e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=12.08 NO POLE NO POLE x[1] = 0.126 y1[1] (analytic) = 1.9920724964179306735546179218037 y1[1] (numeric) = 1.992072496417930672301796354694 absolute error = 1.2528215671097e-18 relative error = 6.2890360133101395637902749953587e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1256668685497292515738902398917 y2[1] (numeric) = 1.1256668685497292514073010747891 absolute error = 1.665891651026e-19 relative error = 1.4799153262565841595901340808809e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=12.73 NO POLE NO POLE x[1] = 0.127 y1[1] (analytic) = 1.9919463335341185487347444518721 y1[1] (numeric) = 1.9919463335341185474339110867888 absolute error = 1.3008333650833e-18 relative error = 6.5304639145340659593987397168872e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1266588780473727356997829333235 y2[1] (numeric) = 1.126658878047372735525485572343 absolute error = 1.742973609805e-19 relative error = 1.5470286914401015519095097612826e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.128 y1[1] (analytic) = 1.9918191787040555519880280173089 y1[1] (numeric) = 1.9918191787040555506391970659988 absolute error = 1.3488309513101e-18 relative error = 6.7718544219847040236435512405753e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1276507608861487273590920444897 y2[1] (numeric) = 1.1276507608861487271769903039178 absolute error = 1.821017405719e-19 relative error = 1.6148771134495388457640617817000e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=13.37 NO POLE NO POLE x[1] = 0.129 y1[1] (analytic) = 1.9916910320548965027812298794554 y1[1] (numeric) = 1.9916910320548965013844156980143 absolute error = 1.3968141814411e-18 relative error = 7.0132071639643750996304573244244e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.128642516074174470432726390184 y2[1] (numeric) = 1.1286425160741744702427241070704 absolute error = 1.900022831136e-19 relative error = 1.6834584946746152505050905542129e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=14.02 NO POLE NO POLE x[1] = 0.13 y1[1] (analytic) = 1.9915618937147880395945121711518 y1[1] (numeric) = 1.9915618937147880381497292599974 absolute error = 1.4447829111544e-18 relative error = 7.2545217686380759680459885615648e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1296341426196948595412058107083 y2[1] (numeric) = 1.1296341426196948593432068430589 absolute error = 1.979989676494e-19 relative error = 1.7527707438996802028768291735070e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=14.67 NO POLE NO POLE x[1] = 0.131 y1[1] (analytic) = 1.9914317638128684917748100954616 y1[1] (numeric) = 1.9914317638128684902820730993056 absolute error = 1.4927369961560e-18 relative error = 7.4957978640350239786815166052499e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1306256395310834317996839030976 y2[1] (numeric) = 1.1306256395310834315935921300667 absolute error = 2.060917730309e-19 relative error = 1.8228117762867527421468227273933e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.132 y1[1] (analytic) = 1.991300642479267750397513340263 y1[1] (numeric) = 1.9913006424792677488568370480836 absolute error = 1.5406762921794e-18 relative error = 7.7370350780441764169325861697022e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1316170058168433584443282704301 y2[1] (numeric) = 1.1316170058168433582300475925128 absolute error = 2.142806779173e-19 relative error = 1.8935795133497858233704999947121e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.5MB, time=15.31 NO POLE NO POLE x[1] = 0.133 y1[1] (analytic) = 1.9911685298451071381365858470171 y1[1] (numeric) = 1.9911685298451071365479851920305 absolute error = 1.5886006549866e-18 relative error = 7.9782330384167789895381769263193e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1326082404856084363290666609268 y2[1] (numeric) = 1.1326082404856084361065010001515 absolute error = 2.225656607753e-19 relative error = 1.9650718829299215725785166851166e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=15.95 NO POLE NO POLE x[1] = 0.134 y1[1] (analytic) = 1.9910354260424992781432540635797 y1[1] (numeric) = 1.9910354260424992765067441232122 absolute error = 1.6365099403675e-18 relative error = 8.2193913727608791426299677279037e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1335993425461440792917075001763 y2[1] (numeric) = 1.1335993425461440790607608002971 absolute error = 2.309466998792e-19 relative error = 2.0372868191726136921927055140190e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.135 y1[1] (analytic) = 1.9909013312045479619333948023605 y1[1] (numeric) = 1.9909013312045479602489907982195 absolute error = 1.6844040041410e-18 relative error = 8.4605097085443758650034012416460e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1345903110073483093884434504466 y2[1] (numeric) = 1.1345903110073483091490196771357 absolute error = 2.394237733109e-19 relative error = 2.1102222625039616030501601556162e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=16.61 NO POLE NO POLE x[1] = 0.136 y1[1] (analytic) = 1.990766245465348016283754816428 y1[1] (numeric) = 1.9907662454653480145514721142736 absolute error = 1.7322827021544e-18 relative error = 8.7015876730895311306670325250387e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1355811448782527479957467626642 y2[1] (numeric) = 1.135581144878252747747749903704 absolute error = 2.479968589602e-19 relative error = 2.1838761596097836946298479627842e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=17.26 NO POLE NO POLE x[1] = 0.137 y1[1] (analytic) = 1.9906301689599851691371351973316 y1[1] (numeric) = 1.9906301689599851673569893070473 absolute error = 1.7801458902843e-18 relative error = 8.9426248935750142459467811629611e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1365718431680236067786653192461 y2[1] (numeric) = 1.1365718431680236065219993847216 absolute error = 2.566659345245e-19 relative error = 2.2582464634094945498511451930536e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=17.92 NO POLE NO POLE x[1] = 0.138 y1[1] (analytic) = 1.9904931018245359145166746894438 y1[1] (numeric) = 1.9904931018245359126886812650074 absolute error = 1.8279934244364e-18 relative error = 9.1836209970324205924677240428908e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1375624048859626785245283995723 y2[1] (numeric) = 1.1375624048859626782590974220633 absolute error = 2.654309775090e-19 relative error = 2.3333311330344877497306007328348e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.139 y1[1] (analytic) = 1.9903550441960673764493670065295 y1[1] (numeric) = 1.9903550441960673745735418459833 absolute error = 1.8758251605462e-18 relative error = 9.4245756103473105705509047047901e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1385528290415083278410713344755 y2[1] (numeric) = 1.1385528290415083275667793692487 absolute error = 2.742919652268e-19 relative error = 2.4091281338057270942944040683375e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=18.56 NO POLE NO POLE x[1] = 0.14 y1[1] (analytic) = 1.9902159962126371718989482270114 y1[1] (numeric) = 1.9902159962126371699753072724328 absolute error = 1.9236409545786e-18 relative error = 9.6654883602547217644075419741395e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1395431146442364817179883517054 y2[1] (numeric) = 1.1395431146442364814347394769066 absolute error = 2.832488747988e-19 relative error = 2.4856354372096736403941677491031e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=19.22 NO POLE NO POLE x[1] = 0.141 y1[1] (analytic) = 1.9900759580132932727082913350357 y1[1] (numeric) = 1.9900759580132932707368506725068 absolute error = 1.9714406625289e-18 relative error = 9.9063588733417139598198527132018e-17 % Correct digits = 18 h = 0.001 y2[1] (analytic) = 1.1405332607038616199509230508977 y2[1] (numeric) = 1.1405332607038616196586213677442 absolute error = 2.923016831535e-19 relative error = 2.5628510208734355793842844418558e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.142 y1[1] (analytic) = 1.9899349297380738665514459649294 y1[1] (numeric) = 1.989934929738073864532221824507 absolute error = 2.0192241404224e-18 relative error = 1.0147186776042879652164912790633e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1415232662302377654269060841403 y2[1] (numeric) = 1.1415232662302377651254557171125 absolute error = 3.014503670278e-19 relative error = 2.6407728685487820409832344363236e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=19.87 NO POLE NO POLE x[1] = 0.143 y1[1] (analytic) = 1.9897929115280072168954623969991 y1[1] (numeric) = 1.9897929115280072148284711526842 absolute error = 2.0669912443149e-18 relative error = 1.0387971694640375556310389904528e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1425131302333594742702497567803 y2[1] (numeric) = 1.1425131302333594739595548538141 absolute error = 3.106949029662e-19 relative error = 2.7193989700822103339946357985823e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=20.52 NO POLE NO POLE x[1] = 0.144 y1[1] (analytic) = 1.9896499035251115219721398428361 y1[1] (numeric) = 1.989649903525111519857398012543 absolute error = 2.1147418302931e-18 relative error = 1.0628713255263451343943875826455e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.143502851723362825847909402661 y2[1] (numeric) = 1.1435028517233628255278741353396 absolute error = 3.200352673214e-19 relative error = 2.7987273213973864381875829596501e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.145 y1[1] (analytic) = 1.989505905872394772759840048366 y1[1] (numeric) = 1.9895059058723947705973642938916 absolute error = 2.1624757544744e-18 relative error = 1.0869411083884962174787257897387e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1444924297105264126333215285089 y2[1] (numeric) = 1.144492429710526412303850092255 memory used=125.8MB, alloc=4.5MB, time=21.17 absolute error = 3.294714362539e-19 relative error = 2.8787559244689139661754647149247e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.146 y1[1] (analytic) = 1.9893609187138546099755082328197 y1[1] (numeric) = 1.9893609187138546077653153598121 absolute error = 2.2101928730076e-18 relative error = 1.1110064806322403595585313578381e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1454818632052723299277288637166 y2[1] (numeric) = 1.145481863205272329588725477984 absolute error = 3.390033857326e-19 relative error = 2.9594827873049440616668278891743e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=21.83 NO POLE NO POLE x[1] = 0.147 y1[1] (analytic) = 1.9892149421944781800770443715908 y1[1] (numeric) = 1.9892149421944781778191513295179 absolute error = 2.2578930420729e-18 relative error = 1.1350674048235427727071354491635e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1464711512181671654380025942768 y2[1] (numeric) = 1.1464711512181671650893715027426 absolute error = 3.486310915342e-19 relative error = 3.0409059239193836236485271164514e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=22.47 NO POLE NO POLE x[1] = 0.148 y1[1] (analytic) = 1.9890679764602419902761688205978 y1[1] (numeric) = 1.9890679764602419879705927027155 absolute error = 2.3055761178823e-18 relative error = 1.1591238435125369165790780167764e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1474602927599229887099722031298 y2[1] (numeric) = 1.1474602927599229883516176738862 absolute error = 3.583545292436e-19 relative error = 3.1230233543129375310701122309899e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.149 y1[1] (analytic) = 1.9889200216581117625619272692718 y1[1] (numeric) = 1.9889200216581117602086853125923 absolute error = 2.3532419566795e-18 relative error = 1.1831757592332256560207231033339e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.148449286841398340416273483676 y2[1] (numeric) = 1.1484492868413983400480998094219 absolute error = 3.681736742541e-19 relative error = 3.2058331044524828467368048931008e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=23.12 NO POLE NO POLE x[1] = 0.15 y1[1] (analytic) = 1.9887710779360422867349809986543 y1[1] (numeric) = 1.9887710779360422843340905839138 absolute error = 2.4008904147405e-18 relative error = 1.2072231145035342422675357534337e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1494381324735992214977254386876 y2[1] (numeric) = 1.1494381324735992211196369369206 absolute error = 3.780885017670e-19 relative error = 3.2893332062453052099333053139046e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=23.78 NO POLE NO POLE x[1] = 0.151 y1[1] (analytic) = 1.9886211454429772724528294103012 y1[1] (numeric) = 1.9886211454429772700043080619274 absolute error = 2.4485213483738e-18 relative error = 1.2312658718251621539680624332369e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1504268286676800821572469233262 y2[1] (numeric) = 1.150426828667680081769147936534 absolute error = 3.880989867922e-19 relative error = 3.3735216975221363282038872200746e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.152 y1[1] (analytic) = 1.9884702243288492002861127807586 y1[1] (numeric) = 1.9884702243288491977899781668383 absolute error = 2.4961346139203e-18 relative error = 1.2553039936832839824114401688326e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1514153744349448107053240384303 y2[1] (numeric) = 1.1514153744349448103071189342829 absolute error = 3.982051041474e-19 relative error = 3.4583966220080958688821160832605e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=24.43 NO POLE NO POLE x[1] = 0.153 y1[1] (analytic) = 1.9883183147445791717861441852958 y1[1] (numeric) = 1.9883183147445791692424141175417 absolute error = 2.5437300677541e-18 relative error = 1.2793374425467028045457977939837e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1524037687868477222560394286898 y2[1] (numeric) = 1.1524037687868477218476326002308 absolute error = 4.084068284590e-19 relative error = 3.5439560293085107914737749898354e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.5MB, time=25.10 NO POLE NO POLE x[1] = 0.154 y1[1] (analytic) = 1.9881654168420767585638205233501 y1[1] (numeric) = 1.988165416842076755972512957068 absolute error = 2.5913075662821e-18 relative error = 1.3033661808674000348839553240284e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1533920107349945472726747897587 y2[1] (numeric) = 1.1533920107349945468539706555971 absolute error = 4.187041341616e-19 relative error = 3.6301979748826457389287350337818e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.5MB, time=25.77 NO POLE NO POLE x[1] = 0.155 y1[1] (analytic) = 1.9880115307742398503800635667605 y1[1] (numeric) = 1.9880115307742398477411966008156 absolute error = 2.6388669659449e-18 relative error = 1.3273901710807389696308661144234e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1543800992911434199618980387873 y2[1] (numeric) = 1.1543800992911434195328010432889 absolute error = 4.290969954984e-19 relative error = 3.7171205200253411674496246385125e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.156 y1[1] (analytic) = 1.9878566566949545022479429403361 y1[1] (numeric) = 1.9878566566949544995615348171197 absolute error = 2.6864081232164e-18 relative error = 1.3514093756050144342214652277108e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1553680334672058665155467542681 y2[1] (numeric) = 1.155368033467205866075961367747 absolute error = 4.395853865211e-19 relative error = 3.8047217318443946305922312891469e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=26.44 NO POLE NO POLE x[1] = 0.157 y1[1] (analytic) = 1.9877007947590947805466339326243 y1[1] (numeric) = 1.9877007947590947778127030380198 absolute error = 2.7339308946045e-18 relative error = 1.3754237568415556034344133572480e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1563558122752477931990196434946 y2[1] (numeric) = 1.1563558122752477927488503624049 absolute error = 4.501692810897e-19 relative error = 3.8929996832371699345637798124916e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=27.12 NO POLE NO POLE x[1] = 0.158 y1[1] (analytic) = 1.9875439451225226081473640229073 y1[1] (numeric) = 1.987543945122522605365928886256 absolute error = 2.7814351366513e-18 relative error = 1.3994332771745772820899101189866e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1573434347274904742852879493246 y2[1] (numeric) = 1.1573434347274904738244392964517 absolute error = 4.608486528729e-19 relative error = 3.9819524528724872184122388707744e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.159 y1[1] (analytic) = 1.9873861079420876085515029984672 y1[1] (numeric) = 1.9873861079420876057225822925343 absolute error = 2.8289207059329e-18 relative error = 1.4234378989708298256897269325264e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1583308998363115398335388623175 y2[1] (numeric) = 1.1583308998363115393619153869696 absolute error = 4.716234753479e-19 relative error = 4.0715781251674028153406759121433e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=27.79 NO POLE NO POLE x[1] = 0.16 y1[1] (analytic) = 1.9872272833756269490409525240183 y1[1] (numeric) = 1.9872272833756269461645650649581 absolute error = 2.8763874590602e-18 relative error = 1.4474375845797520867556960036101e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.159318206614245963311463159686 y2[1] (numeric) = 1.1593182066142459628289694378853 absolute error = 4.824937218007e-19 relative error = 4.1618747902683978123171942017372e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=28.43 NO POLE NO POLE x[1] = 0.161 y1[1] (analytic) = 1.9870674715819651828409920129024 y1[1] (numeric) = 1.9870674715819651799171567602234 absolute error = 2.9238352526790e-18 relative error = 1.4714322963332721350890991162043e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1603053540739870490601994488555 y2[1] (numeric) = 1.1603053540739870485667400835298 absolute error = 4.934593653257e-19 relative error = 4.2528405440266070495300826734804e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=171.6MB, alloc=4.5MB, time=29.07 x[1] = 0.162 y1[1] (analytic) = 1.9869066727209140902957386371875 y1[1] (numeric) = 1.9869066727209140873244746937177 absolute error = 2.9712639434698e-18 relative error = 1.4954219965454568727484723810267e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1612923412283874196009475507708 y2[1] (numeric) = 1.1612923412283874190964271719444 absolute error = 5.045203788264e-19 relative error = 4.3444734879826241018452736549483e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.163 y1[1] (analytic) = 1.9867448869532725190563803011996 y1[1] (numeric) = 1.9867448869532725160377069130508 absolute error = 3.0186733881488e-18 relative error = 1.5194066475127654601419703267946e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1622791670904600027822637164169 y2[1] (numeric) = 1.1622791670904600022665869814022 absolute error = 5.156767350147e-19 relative error = 4.4367717293393159623067531739427e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=29.74 NO POLE NO POLE x[1] = 0.164 y1[1] (analytic) = 1.9865821144408262232823413902376 y1[1] (numeric) = 1.9865821144408262202162779467703 absolute error = 3.0660634434673e-18 relative error = 1.5433862115134974407166458567322e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1632658306733790187670505293435 y2[1] (numeric) = 1.1632658306733790182401221229319 absolute error = 5.269284064116e-19 relative error = 4.5297333809467889043570522394615e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.5MB, time=30.40 NO POLE NO POLE x[1] = 0.165 y1[1] (analytic) = 1.9864183553463477018555420932949 y1[1] (numeric) = 1.9864183553463476987421081270823 absolute error = 3.1134339662126e-18 relative error = 1.5673606508079957006910781815180e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1642523309904809668582545072829 y2[1] (numeric) = 1.1642523309904809663199791419361 absolute error = 5.382753653468e-19 relative error = 4.6233565612779605285865744014813e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.166 y1[1] (analytic) = 1.9862536098335960356079130855139 y1[1] (numeric) = 1.9862536098335960324471282723057 absolute error = 3.1607848132082e-18 relative error = 1.5913299276384970842745598408669e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1652386670552656121622845772482 y2[1] (numeric) = 1.1652386670552656116125669932893 absolute error = 5.497175839589e-19 relative error = 4.7176393944093830615278199928041e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=31.06 NO POLE NO POLE x[1] = 0.167 y1[1] (analytic) = 1.9860878780673167235623283428443 y1[1] (numeric) = 1.986087878067316720354212501531 absolute error = 3.2081158413133e-18 relative error = 1.6152940042286304614590950410868e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1662248378813969720891647607741 y2[1] (numeric) = 1.1662248378813969715279097265787 absolute error = 5.612550341954e-19 relative error = 4.8125800100004271742746130732508e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=31.71 NO POLE NO POLE x[1] = 0.168 y1[1] (analytic) = 1.985921160213241518187119847961 y1[1] (numeric) = 1.9859211602132415149316929405369 absolute error = 3.2554269074241e-18 relative error = 1.6392528427838209020907083452833e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1672108424827043026884345692303 y2[1] (numeric) = 1.1672108424827043021155468814174 absolute error = 5.728876878129e-19 relative error = 4.9081765432742630951392975784414e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.169 y1[1] (analytic) = 1.9857534564380882596643389329105 y1[1] (numeric) = 1.9857534564380882563616210644373 absolute error = 3.3027178684732e-18 relative error = 1.6632064054907372148398175187619e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1681966798731830848198107733898 y2[1] (numeric) = 1.1681966798731830842351952570126 absolute error = 5.846155163772e-19 relative error = 5.0044271349980604391928989311666e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=32.36 NO POLE NO POLE x[1] = 0.17 y1[1] (analytic) = 1.9855847669095607091719299902125 y1[1] (numeric) = 1.9855847669095607058219414087824 absolute error = 3.3499885814301e-18 relative error = 1.6871546545172931770743290855110e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1691823490669960101576243766708 y2[1] (numeric) = 1.1691823490669960095611858854082 absolute error = 5.964384912626e-19 relative error = 5.1013299314564243802954915521185e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=33.01 NO POLE NO POLE x[1] = 0.171 y1[1] (analytic) = 1.9854150917963483811799832702289 y1[1] (numeric) = 1.985415091796348377782744366927 absolute error = 3.3972389033019e-18 relative error = 1.7110975520127494761817616959939e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1701678490784739670280467877005 y2[1] (numeric) = 1.1701678490784739664196902040473 absolute error = 6.083565836532e-19 relative error = 5.1988830844420363323867270748185e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=33.67 NO POLE NO POLE x[1] = 0.172 y1[1] (analytic) = 1.9852444312681263747612344685321 y1[1] (numeric) = 1.9852444312681263713167657773994 absolute error = 3.4444686911327e-18 relative error = 1.7350350601071608492777212168808e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1711531789221170260781193550527 y2[1] (numeric) = 1.1711531789221170254577495905109 absolute error = 6.203697645418e-19 relative error = 5.2970847512258280891723667453514e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.173 y1[1] (analytic) = 1.9850727854955552039159797927608 y1[1] (numeric) = 1.9850727854955552004243019907562 absolute error = 3.4916778020046e-18 relative error = 1.7589671409116289304243470161310e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1721383376125954257756005952159 y2[1] (numeric) = 1.1721383376125954251431225904853 absolute error = 6.324780047306e-19 relative error = 5.3959330945426419138545727613097e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=34.31 NO POLE NO POLE x[1] = 0.174 y1[1] (analytic) = 1.9849001546502806269115761840325 y1[1] (numeric) = 1.9849001546502806233727100909952 absolute error = 3.5388660930373e-18 relative error = 1.7828937565178498798659660504237e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1731233241647505577386456140236 y2[1] (numeric) = 1.1731233241647505570939643391926 absolute error = 6.446812748310e-19 relative error = 5.4954262825692701468572121164407e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=34.97 NO POLE NO POLE x[1] = 0.175 y1[1] (analytic) = 1.9847265389049334746366973533995 y1[1] (numeric) = 1.9847265389049334710506639320107 absolute error = 3.5860334213888e-18 relative error = 1.8068148689982159862530115786579e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1741081375935959518943323919514 y2[1] (numeric) = 1.1741081375935959512373528466876 absolute error = 6.569795452638e-19 relative error = 5.5955624889059914231849227755926e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.176 y1[1] (analytic) = 1.9845519384331294779705172790773 y1[1] (numeric) = 1.9845519384331294743373376348217 absolute error = 3.6331796442556e-18 relative error = 1.8307304404056653517739070493416e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1750927769143182614650497748359 y2[1] (numeric) = 1.1750927769143182607956769885768 absolute error = 6.693727862591e-19 relative error = 5.6963398925556261037932987093708e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=35.60 NO POLE NO POLE x[1] = 0.177 y1[1] (analytic) = 1.9843763534094690941669937952475 y1[1] (numeric) = 1.9843763534094690904866891763748 absolute error = 3.6803046188727e-18 relative error = 1.8546404327734306870097952556231e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1760772411422782477817621837097 y2[1] (numeric) = 1.1760772411422782470999012158533 absolute error = 6.818609678564e-19 relative error = 5.7977566779043769785889043394244e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=36.25 NO POLE NO POLE x[1] = 0.178 y1[1] (analytic) = 1.9841997840095373322544258881378 y1[1] (numeric) = 1.9841997840095373285270176856238 absolute error = 3.7274082025140e-18 relative error = 1.8785448081149895407962510993609e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1770615292930117649231662305697 y2[1] (numeric) = 1.1770615292930117642287221706651 absolute error = 6.944440599046e-19 relative error = 5.8998110347018961623108369191779e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.5MB, time=36.90 NO POLE NO POLE x[1] = 0.179 y1[1] (analytic) = 1.9840222304099035774504592998064 y1[1] (numeric) = 1.9840222304099035736759690473141 absolute error = 3.7744902524923e-18 relative error = 1.9024435284238128681661014219710e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1780456403822307441797546010046 y2[1] (numeric) = 1.1780456403822307434726325689425 absolute error = 7.071220320621e-19 relative error = 6.0025011580422805311869413891419e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.18 y1[1] (analytic) = 1.9838436927881214145927160246115 y1[1] (numeric) = 1.9838436927881214107711653984514 absolute error = 3.8215506261601e-18 relative error = 1.9263365556735166959720976615507e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1790295734258241783418027396992 y2[1] (numeric) = 1.1790295734258241776219078859022 absolute error = 7.198948537970e-19 relative error = 6.1058252483459903685761366341029e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.5MB, time=37.53 NO POLE NO POLE x[1] = 0.181 y1[1] (analytic) = 1.9836641713227284505852242677207 y1[1] (numeric) = 1.9836641713227284467166350868114 absolute error = 3.8685891809093e-18 relative error = 1.9502238518174593163071267401234e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1800133274398591058102940509108 y2[1] (numeric) = 1.180013327439859105077531556524 absolute error = 7.327624943868e-19 relative error = 6.2097815113376012380797003917894e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.5MB, time=38.19 NO POLE NO POLE x[1] = 0.182 y1[1] (analytic) = 1.983483666193246135860826419216 y1[1] (numeric) = 1.9834836661932461319452206450445 absolute error = 3.9156057741715e-18 relative error = 1.9741053787886407347742797755531e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1809969014405815945297995030755 y2[1] (numeric) = 1.1809969014405815937840745801567 absolute error = 7.457249229188e-19 relative error = 6.3143681580295743794565106216123e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.183 y1[1] (analytic) = 1.9833021775801795848597435813723 y1[1] (numeric) = 1.9833021775801795808971433179537 absolute error = 3.9626002634186e-18 relative error = 1.9979810984997533009387699979419e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1819802944444177257423277047451 y2[1] (numeric) = 1.1819802944444177249835455964553 absolute error = 7.587821082898e-19 relative error = 6.4195834047001661290555858011388e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.5MB, time=38.84 NO POLE NO POLE x[1] = 0.184 y1[1] (analytic) = 1.9831197056650173955244761705281 y1[1] (numeric) = 1.9831197056650173915149036643656 absolute error = 4.0095725061625e-18 relative error = 2.0218509728427785108924965447354e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1829635054679745775611616980887 y2[1] (numeric) = 1.1829635054679745767892276788821 absolute error = 7.719340192066e-19 relative error = 6.5254254728781905836756857093131e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=232.6MB, alloc=4.5MB, time=39.50 NO POLE NO POLE x[1] = 0.185 y1[1] (analytic) = 1.9829362506302314678112210986348 y1[1] (numeric) = 1.9829362506302314637546987386789 absolute error = 4.0565223599559e-18 relative error = 2.0457149636891382946430151247998e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1839465335280412083636988962014 y2[1] (numeric) = 1.1839465335280412075785182720159 absolute error = 7.851806241855e-19 relative error = 6.6318925893193923676936246764408e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.186 y1[1] (analytic) = 1.9827518126592768212179870230509 y1[1] (numeric) = 1.9827518126592768171145373406587 absolute error = 4.1034496823922e-18 relative error = 2.0695730328893924468637493993042e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1849293776415896400023107714653 y2[1] (numeric) = 1.1849293776415896392037888799123 absolute error = 7.985218915530e-19 relative error = 6.7389829859930448260251252745990e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.5MB, time=40.14 NO POLE NO POLE x[1] = 0.187 y1[1] (analytic) = 1.9825663919365914113295901364508 y1[1] (numeric) = 1.9825663919365914071792358053452 absolute error = 4.1503543311056e-18 relative error = 2.0934251422730367426498195346717e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.185912036825775840832239084182 y2[1] (numeric) = 1.1859120368257758400202812947368 absolute error = 8.119577894452e-19 relative error = 6.8466949000576335848766986329319e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.5MB, time=40.80 NO POLE NO POLE x[1] = 0.188 y1[1] (analytic) = 1.9823799886475959453797139518383 y1[1] (numeric) = 1.9823799886475959411824777880664 absolute error = 4.1972361637719e-18 relative error = 2.1172712536486540242798838041599e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1868945100979407085555456236643 y2[1] (numeric) = 1.1868945100979407077300573378562 absolute error = 8.254882858081e-19 relative error = 6.9550265738442245969568498431212e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.5MB, time=41.44 NO POLE NO POLE x[1] = 0.189 y1[1] (analytic) = 1.9821926029786936968302175205875 y1[1] (numeric) = 1.9821926029786936925861224824794 absolute error = 4.2440950381081e-18 relative error = 2.1411113288034599567576644495174e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.187876796475611052880132617919 y2[1] (numeric) = 1.1878767964756110520410192695212 absolute error = 8.391133483978e-19 relative error = 7.0639762548390538777017592154839e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.19 y1[1] (analytic) = 1.9820042351172703189678775041899 y1[1] (numeric) = 1.9820042351172703146769466923169 absolute error = 4.2909308118730e-18 relative error = 2.1649453295033530393345123830090e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1888588949765005779928511529813 y2[1] (numeric) = 1.1888588949765005771400182082007 absolute error = 8.528329447806e-19 relative error = 7.1735421956653435270314640948669e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.5MB, time=42.09 NO POLE NO POLE x[1] = 0.191 y1[1] (analytic) = 1.9818148852516936575187505029481 y1[1] (numeric) = 1.9818148852516936531810071600807 absolute error = 4.3377433428674e-18 relative error = 2.1887732174927627831446845534532e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.189840804618510864845715128875 y2[1] (numeric) = 1.1898408046185108639790680865424 absolute error = 8.666470423326e-19 relative error = 7.2837226540609868023490741717054e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.5MB, time=42.74 NO POLE NO POLE x[1] = 0.192 y1[1] (analytic) = 1.9816245535713135622803430272392 y1[1] (numeric) = 1.9816245535713135578958105383049 absolute error = 4.3845324889343e-18 relative error = 2.2125949544944977751616680735961e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1908225244197323532542384660668 y2[1] (numeric) = 1.1908225244197323523736828578264 absolute error = 8.805556082404e-19 relative error = 7.3945158928655622599826397489613e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.193 y1[1] (analytic) = 1.9814332402664616977717774791618 y1[1] (numeric) = 1.9814332402664616933404793712028 absolute error = 4.4312981079590e-18 relative error = 2.2364105022095431591056843381025e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1918040533984453238069134641578 y2[1] (numeric) = 1.1918040533984453229123548546574 absolute error = 8.945586095004e-19 relative error = 7.5059201799956466530096523984681e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.5MB, time=43.39 NO POLE NO POLE x[1] = 0.194 y1[1] (analytic) = 1.9812409455284513529021434943852 y1[1] (numeric) = 1.9812409455284513484241034365156 absolute error = 4.4780400578696e-18 relative error = 2.2602198223170598652453688983105e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1927853905731208795848484034179 y2[1] (numeric) = 1.1927853905731208786761923904985 absolute error = 9.086560129194e-19 relative error = 7.6179337884311301688187296066529e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.5MB, time=44.05 NO POLE NO POLE x[1] = 0.195 y1[1] (analytic) = 1.9810476695495772496572249758333 y1[1] (numeric) = 1.9810476695495772451324667791963 absolute error = 4.5247581966370e-18 relative error = 2.2840228764741314205060469720885e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1937665349624219276905826696054 y2[1] (numeric) = 1.1937665349624219267677348844907 absolute error = 9.228477851147e-19 relative error = 7.7305549961973924446114859710721e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.5MB, time=44.69 NO POLE NO POLE x[1] = 0.196 y1[1] (analytic) = 1.9808534125231153508047941324606 y1[1] (numeric) = 1.9808534125231153462333417501851 absolute error = 4.5714523822755e-18 relative error = 2.3078196263158134826110062128478e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1947474855852041605850978733388 y2[1] (numeric) = 1.1947474855852041596479639808252 absolute error = 9.371338925136e-19 relative error = 7.8437820863425262521891763887310e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.197 y1[1] (analytic) = 1.980658174643322666618664817809 y1[1] (numeric) = 1.9806581746433226620005423449666 absolute error = 4.6181224728424e-18 relative error = 2.3316100334546784930306212166935e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1957282414605170372320436270931 y2[1] (numeric) = 1.1957282414605170362805293257388 absolute error = 9.515143013543e-19 relative error = 7.9576133469263635783235670216979e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.5MB, time=45.34 NO POLE NO POLE x[1] = 0.198 y1[1] (analytic) = 1.9804619561054370606216984442784 y1[1] (numeric) = 1.9804619561054370559569301178394 absolute error = 4.6647683264390e-18 relative error = 2.3553940594810669383858168664117e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1967088016076047640481968356735 y2[1] (numeric) = 1.1967088016076047630822078579887 absolute error = 9.659889776848e-19 relative error = 8.0720470709928252161684119365036e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.5MB, time=45.98 NO POLE NO POLE x[1] = 0.199 y1[1] (analytic) = 1.9802647571056770543479567300861 y1[1] (numeric) = 1.9802647571056770496365669288759 absolute error = 4.7113898012102e-18 relative error = 2.3791716659626317565944280493370e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1976891650459072756591735497928 y2[1] (numeric) = 1.1976891650459072746786156624285 absolute error = 9.805578873643e-19 relative error = 8.1870815565632618795033640217641e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.2 y1[1] (analytic) = 1.9800665778412416311241965167482 y1[1] (numeric) = 1.9800665778412416263662097614032 absolute error = 4.7579867553450e-18 relative error = 2.4029428144443369730585975536981e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1986693307950612154594126271184 y2[1] (numeric) = 1.1986693307950612144641916310564 absolute error = 9.952209960620e-19 relative error = 8.3027151066081195518091063370504e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.5MB, time=46.61 NO POLE NO POLE x[1] = 0.201 y1[1] (analytic) = 1.979867418510310038870902875571 y1[1] (numeric) = 1.9798674185103100340663438284942 absolute error = 4.8045590470768e-18 relative error = 2.4267074664483552900553008525720e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.1996492978749009159754506408903 y2[1] (numeric) = 1.1996492978749009149654723716323 absolute error = 1.0099782692580e-18 relative error = 8.4189460290362312508805799857096e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.5MB, time=47.28 NO POLE NO POLE x[1] = 0.202 y1[1] (analytic) = 1.9796672793120415919230577021024 y1[1] (numeric) = 1.9796672793120415870719511674188 absolute error = 4.8511065346836e-18 relative error = 2.4504655834739150721600299296162e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2006290653054593790315076729148 y2[1] (numeric) = 1.2006290653054593780066780006717 absolute error = 1.0248296722431e-18 relative error = 8.5357726366749818694811665924484e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=282.2MB, alloc=4.5MB, time=47.94 x[1] = 0.203 y1[1] (analytic) = 1.9794661604465754718708419777594 y1[1] (numeric) = 1.9794661604465754669732129012711 absolute error = 4.8976290764883e-18 relative error = 2.4742171269971977288059864950144e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2016086321069692557164038254306 y2[1] (numeric) = 1.2016086321069692546766286553119 absolute error = 1.0397751701187e-18 relative error = 8.6531932472513848908263400491192e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.204 y1[1] (analytic) = 1.979264062115030527420470857911 y1[1] (numeric) = 1.9792640621150305224763443270525 absolute error = 4.9441265308585e-18 relative error = 2.4979620584709823862490551461080e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2025879972998638261508264850126 y2[1] (numeric) = 1.2025879972998638250960117572154 absolute error = 1.0548147277972e-18 relative error = 8.7712061833773920112514372880812e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.5MB, time=48.59 NO POLE NO POLE x[1] = 0.205 y1[1] (analytic) = 1.9790609845195050732753617255673 y1[1] (numeric) = 1.97906098451950506828476296936 absolute error = 4.9905987562073e-18 relative error = 2.5217003393247956023777423591898e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2035671599047779790539685713266 y2[1] (numeric) = 1.2035671599047779779840202613252 absolute error = 1.0699483100014e-18 relative error = 8.8898097725269486850786091554442e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.5MB, time=49.25 NO POLE NO POLE x[1] = 0.206 y1[1] (analytic) = 1.9788569278630766880378363294873 y1[1] (numeric) = 1.978856927863076683000790718494 absolute error = 5.0370456109933e-18 relative error = 2.5454319309646568700099203798314e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2045461189425491911085582041808 y2[1] (numeric) = 1.2045461189425491900233823229152 absolute error = 1.0851758812656e-18 relative error = 9.0090023470272577185910252264327e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.207 y1[1] (analytic) = 1.9786518923498020111315591049884 y1[1] (numeric) = 1.9786518923498020060480921512674 absolute error = 5.0834669537210e-18 relative error = 2.5691567947730260913808507434941e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2055248734342185061233004239223 y2[1] (numeric) = 1.2055248734342185050228030179878 absolute error = 1.1004974059345e-18 relative error = 9.1287822440318191686714317536390e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.5MB, time=49.90 NO POLE NO POLE x[1] = 0.208 y1[1] (analytic) = 1.9784458781847165387449147550011 y1[1] (numeric) = 1.9784458781847165336150521120605 absolute error = 5.1298626429406e-18 relative error = 2.5928748921084477219806632745494e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.206503422401031513991751802823 y2[1] (numeric) = 1.2065034224010315128758389546587 absolute error = 1.1159128481643e-18 relative error = 9.2491478055118191388122779984017e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.5MB, time=50.56 NO POLE NO POLE x[1] = 0.209 y1[1] (analytic) = 1.9782388855738344187955291479752 y1[1] (numeric) = 1.9782388855738344136192966107266 absolute error = 5.1762325372486e-18 relative error = 2.6165861843055990620165093207649e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2074817648644393294466489886571 y2[1] (numeric) = 1.2074817648644393283152268167354 absolute error = 1.1314221719217e-18 relative error = 9.3700973782301521412566223715153e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.21 y1[1] (analytic) = 1.9780309147241482449161385680994 y1[1] (numeric) = 1.9780309147241482396935620728111 absolute error = 5.2225764952883e-18 relative error = 2.6402906326752879921267343239923e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2084598998460995706087124262276 y2[1] (numeric) = 1.2084598998460995694616870852425 absolute error = 1.1470253409851e-18 relative error = 9.4916293137337580063736972606877e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.5MB, time=51.22 NO POLE NO POLE x[1] = 0.211 y1[1] (analytic) = 1.9778219658436288494620133319462 y1[1] (numeric) = 1.9778219658436288441931189561972 absolute error = 5.2688943757490e-18 relative error = 2.6639881985037933892679077396241e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2094378263678773373289467081163 y2[1] (numeric) = 1.2094378263678773361662243891725 absolute error = 1.1627223189438e-18 relative error = 9.6137419683294428422510885279170e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.5MB, time=51.89 NO POLE NO POLE x[1] = 0.212 y1[1] (analytic) = 1.977612039141225095540142764105 y1[1] (numeric) = 1.9776120391412250902249567267374 absolute error = 5.3151860373676e-18 relative error = 2.6876788430534186784491761367902e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2104155434518461893234592124401 y2[1] (numeric) = 1.210415543451846188144946143242 absolute error = 1.1785130691981e-18 relative error = 9.7364337030672362521608601907462e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.5MB, time=52.56 NO POLE NO POLE x[1] = 0.213 y1[1] (analytic) = 1.9774011348268636680603895025966 y1[1] (numeric) = 1.9774011348268636626989381636686 absolute error = 5.3614513389280e-18 relative error = 2.7113625275619331343109521231793e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2113930501202891240998188928769 y2[1] (numeric) = 1.2113930501202891229054213379169 absolute error = 1.1943975549600e-18 relative error = 9.8597028837287658008536604054854e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.214 y1[1] (analytic) = 1.9771892531114488638088220829006 y1[1] (numeric) = 1.9771892531114488584011319436393 absolute error = 5.4076901392613e-18 relative error = 2.7350392132424174102121512608641e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.212370345395699554673977294682 y2[1] (numeric) = 1.2123703453956995534636015554293 absolute error = 1.2103757392527e-18 relative error = 9.9835478808057735439733356856325e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.5MB, time=53.22 NO POLE NO POLE x[1] = 0.215 y1[1] (analytic) = 1.9769763942068623805434357272442 y1[1] (numeric) = 1.976976394206862375089533429998 absolute error = 5.4539022972462e-18 relative error = 2.7587088612832101007518071296869e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2133474283007822870767740798571 y2[1] (numeric) = 1.2133474283007822858503264949463 absolute error = 1.2264475849108e-18 relative error = 1.0107967069484489439362571001729e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.5MB, time=53.88 NO POLE NO POLE x[1] = 0.216 y1[1] (analytic) = 1.9767625583259631051124722434151 y1[1] (numeric) = 1.9767625583259630996123845716054 absolute error = 5.5000876718097e-18 relative error = 2.7823714328480060012208231099635e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2143242978584544976490495550473 y2[1] (numeric) = 1.214324297858454496406436500467 absolute error = 1.2426130545803e-18 relative error = 1.0232958829628417184217743651084e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.217 y1[1] (analytic) = 1.9765477456825869005955509147589 y1[1] (numeric) = 1.9765477456825868950493047928324 absolute error = 5.5462461219265e-18 relative error = 2.8060268890752966874566025152617e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2153009530918467101243869071349 y2[1] (numeric) = 1.2153009530918467088655147964161 absolute error = 1.2588721107188e-18 relative error = 1.0358521545762832849740310295720e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.5MB, time=54.50 NO POLE NO POLE x[1] = 0.218 y1[1] (analytic) = 1.976331956491546392467823240215 y1[1] (numeric) = 1.9763319564915463868754457335952 absolute error = 5.5923775066198e-18 relative error = 2.8296751910785190825349663776982e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2162773930243037724985070638692 y2[1] (numeric) = 1.2162773930243037712232823482735 absolute error = 1.2752247155957e-18 relative error = 1.0484653607059342394608150269739e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.5MB, time=55.14 NO POLE NO POLE x[1] = 0.219 y1[1] (analytic) = 1.9761151909686307537873653602166 y1[1] (numeric) = 1.9761151909686307481488836752551 absolute error = 5.6384816849615e-18 relative error = 2.8533162999459004622041421379456e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2172536166793858336843393102186 y2[1] (numeric) = 1.2172536166793858323926684789271 absolute error = 1.2916708312915e-18 relative error = 1.0611353407313104107347693599267e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=328.0MB, alloc=4.5MB, time=55.77 x[1] = 0.22 y1[1] (analytic) = 1.9758974493306054894060229810447 y1[1] (numeric) = 1.9758974493306054837214644649725 absolute error = 5.6845585160722e-18 relative error = 2.8769501767402021069272918370995e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.218229623080869319951791005457 y2[1] (numeric) = 1.2182296230808693186435805857582 absolute error = 1.3082104196988e-18 relative error = 1.0738619344934099633492520940961e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.221 y1[1] (analytic) = 1.9756787317952122192039245867742 y1[1] (numeric) = 1.9756787317952122134733167276527 absolute error = 5.7306078591215e-18 relative error = 2.9005767824986145988013358831282e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2192054112527479111512399612945 y2[1] (numeric) = 1.2192054112527479098263965187725 absolute error = 1.3248434425220e-18 relative error = 1.0866449822927768736440790859765e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.5MB, time=56.40 NO POLE NO POLE x[1] = 0.222 y1[1] (analytic) = 1.9754590385811684603478797042797 y1[1] (numeric) = 1.9754590385811684545712501309514 absolute error = 5.7766295733283e-18 relative error = 2.9241960782326530161432894555125e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.220180980219233516719773257642 y2[1] (numeric) = 1.2201809802192335153782033963649 absolute error = 1.3415698612771e-18 relative error = 1.0994843248876541124879801598585e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.5MB, time=57.03 NO POLE NO POLE x[1] = 0.223 y1[1] (analytic) = 1.975238369908167408573879962885 y1[1] (numeric) = 1.9752383699081674027512564449239 absolute error = 5.8226235179611e-18 relative error = 2.9478080249280520254149658256522e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.221156329004757251469196489853 y2[1] (numeric) = 1.2211563290047572501108068525608 absolute error = 1.3583896372922e-18 relative error = 1.1123798034927173763561026981227e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.224 y1[1] (analytic) = 1.9750167259968777184939216661375 y1[1] (numeric) = 1.9750167259968777126253321137993 absolute error = 5.8685895523382e-18 relative error = 2.9714125835446102376737693403695e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2221314566339704111548376595133 y2[1] (numeric) = 1.2221314566339704097795349278062 absolute error = 1.3753027317071e-18 relative error = 1.1253312597770769420026572855506e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.5MB, time=57.64 NO POLE NO POLE x[1] = 0.225 y1[1] (analytic) = 1.9747941070689432829273695688655 y1[1] (numeric) = 1.9747941070689432770128420330377 absolute error = 5.9145275358278e-18 relative error = 2.9950097150159837892646863802632e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2231063621317454478241701400572 y2[1] (numeric) = 1.2231063621317454464318610345834 absolute error = 1.3923091054738e-18 relative error = 1.1383385358630233989554015752871e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.5MB, time=58.28 NO POLE NO POLE x[1] = 0.226 y1[1] (analytic) = 1.9745705133469830112570825281373 y1[1] (numeric) = 1.9745705133469830052966452002889 absolute error = 5.9604373278484e-18 relative error = 3.0185993802496316814299655792683e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2240810445231769449442793686679 y2[1] (numeric) = 1.2240810445231769435348706493116 absolute error = 1.4094087193563e-18 relative error = 1.1514014743242060157731866438275e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.227 y1[1] (analytic) = 1.9743459450545906068105226719777 y1[1] (numeric) = 1.9743459450545906008042038841088 absolute error = 6.0063187878689e-18 relative error = 3.0421815401266091002591331490020e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2250555028335825923071981370765 y2[1] (numeric) = 1.2250555028335825908805966031457 absolute error = 1.4266015339308e-18 relative error = 1.1645199181841448256331281498875e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.5MB, time=58.89 NO POLE NO POLE x[1] = 0.228 y1[1] (analytic) = 1.9741204024163343432660707047136 y1[1] (numeric) = 1.9741204024163343372138989293046 absolute error = 6.0521717754090e-18 relative error = 3.0657561555015125285075515090914e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2260297360885041607121355760063 y2[1] (numeric) = 1.2260297360885041592682480664208 absolute error = 1.4438875095855e-18 relative error = 1.1776937109144220679322566233509e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.5MB, time=59.53 NO POLE NO POLE x[1] = 0.229 y1[1] (analytic) = 1.9738938856577568400847709426156 y1[1] (numeric) = 1.9738938856577568339867747925764 absolute error = 6.0979961500392e-18 relative error = 3.0893231872022221409259054900933e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2270037433137084764236251511138 y2[1] (numeric) = 1.2270037433137084749623585445927 absolute error = 1.4612666065211e-18 relative error = 1.1909226964334512672823578829776e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.5MB, time=60.16 NO POLE NO POLE x[1] = 0.23 y1[1] (analytic) = 1.9736663950053748369677306480716 y1[1] (numeric) = 1.9736663950053748308239388766902 absolute error = 6.1437917713814e-18 relative error = 3.1128825960299479910568436700938e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2279775235351883954046172123601 y2[1] (numeric) = 1.2279775235351883939258784276097 absolute error = 1.4787387847504e-18 relative error = 1.2042067191045177935777204930296e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.231 y1[1] (analytic) = 1.9734379306866789673393992048733 y1[1] (numeric) = 1.9734379306866789611498407057647 absolute error = 6.1895584991086e-18 relative error = 3.1364343427588201390182797057775e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2289510757791637773235418638014 y2[1] (numeric) = 1.2289510757791637758272378597027 absolute error = 1.4963040040987e-18 relative error = 1.2175456237344782441785130508757e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.5MB, time=60.77 NO POLE NO POLE x[1] = 0.232 y1[1] (analytic) = 1.9732084929301335308569536513194 y1[1] (numeric) = 1.9732084929301335246216574583737 absolute error = 6.2352961929457e-18 relative error = 3.1599783881360359280327705807626e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2299243990720824593343681468164 y2[1] (numeric) = 1.2299243990720824578204059226128 absolute error = 1.5139622242036e-18 relative error = 1.2309392555719767220970104428763e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.5MB, time=61.40 NO POLE NO POLE x[1] = 0.233 y1[1] (analytic) = 1.9729780819651762649460180617296 y1[1] (numeric) = 1.9729780819651762586650133490602 absolute error = 6.2810047126694e-18 relative error = 3.1835146928815511657596639321508e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2308974924406212296286857567934 y2[1] (numeric) = 1.2308974924406212280969723522779 absolute error = 1.5317134045155e-18 relative error = 1.2443874603062368308939153634896e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.234 y1[1] (analytic) = 1.972746698022218115362945240631 y1[1] (numeric) = 1.9727466980222181090362613225226 absolute error = 6.3266839181084e-18 relative error = 3.2070432176879231272779748520401e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2318703549116868007588357412751 y2[1] (numeric) = 1.231870354911686799209278236978 absolute error = 1.5495575042971e-18 relative error = 1.2578900840650461936130618900409e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.5MB, time=62.01 NO POLE NO POLE x[1] = 0.235 y1[1] (analytic) = 1.9725143413326430057838901673172 y1[1] (numeric) = 1.9725143413326429994115564981733 absolute error = 6.3723336691439e-18 relative error = 3.2305639232203055025611096463546e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2328429855124167827311168565134 y2[1] (numeric) = 1.2328429855124167811636223738897 absolute error = 1.5674944826237e-18 relative error = 1.2714469734133980025609593142285e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.5MB, time=62.63 NO POLE NO POLE x[1] = 0.236 y1[1] (analytic) = 1.9722810121288076064209056016861 y1[1] (numeric) = 1.9722810121288076000029517759763 absolute error = 6.4179538257098e-18 relative error = 3.2540767701162911972157895765561e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2338153832701806558680944893074 y2[1] (numeric) = 1.2338153832701806542825701909239 absolute error = 1.5855242983835e-18 relative error = 1.2850579753521375842586928298909e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=373.8MB, alloc=4.5MB, time=63.25 x[1] = 0.237 y1[1] (analytic) = 1.9720467106440411016652912352422 y1[1] (numeric) = 1.9720467106440410952017469874498 absolute error = 6.4635442477924e-18 relative error = 3.2775817189855014432728921806352e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2347875472125807434390392818975 y2[1] (numeric) = 1.2347875472125807418353923716201 absolute error = 1.6036469102774e-18 relative error = 1.2987229373162090307864009196304e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.238 y1[1] (analytic) = 1.9718114371126449567584287438953 y1[1] (numeric) = 1.9718114371126449502493239484639 absolute error = 6.5091047954314e-18 relative error = 3.3010787304098338735606062956116e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2357594763674531840575228295574 y2[1] (numeric) = 1.2357594763674531824356605527385 absolute error = 1.6218622768189e-18 relative error = 1.3124417071729896375153460350809e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.5MB, time=63.86 NO POLE NO POLE x[1] = 0.239 y1[1] (analytic) = 1.9715751917698926834903360717 y1[1] (numeric) = 1.9715751917698926769357007429804 absolute error = 6.5546353287196e-18 relative error = 3.3245677649430513664860400159532e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2367311697628689038451980533704 y2[1] (numeric) = 1.2367311697628689022050276970358 absolute error = 1.6401703563346e-18 relative error = 1.3262141332211159609947518082237e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.5MB, time=64.48 NO POLE NO POLE x[1] = 0.24 y1[1] (analytic) = 1.9713379748520296049261752469634 y1[1] (numeric) = 1.9713379748520295983260395391598 absolute error = 6.6001357078036e-18 relative error = 3.3480487831108778296442824806928e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2377026264271345883607920844898 y2[1] (numeric) = 1.2377026264271345867022209775257 absolute error = 1.6585711069641e-18 relative error = 1.3400400641888292630929063007805e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.241 y1[1] (analytic) = 1.9710997865962726191609490041922 y1[1] (numeric) = 1.9710997865962726125153432113088 absolute error = 6.6456057928834e-18 relative error = 3.3715217454105359525953321927945e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2386738453887936542933397309712 y2[1] (numeric) = 1.2386738453887936526162752443113 absolute error = 1.6770644866599e-18 relative error = 1.3539193492323273755679429939592e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.5MB, time=65.12 NO POLE NO POLE x[1] = 0.242 y1[1] (analytic) = 1.9708606272408099621026224571645 y1[1] (numeric) = 1.9708606272408099554115770129514 absolute error = 6.6910454442131e-18 relative error = 3.3949866123108427202602568223868e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2396448256766272209186858340254 y2[1] (numeric) = 1.2396448256766272192230353808378 absolute error = 1.6956504531876e-18 relative error = 1.3678518379343649599553275173993e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.5MB, time=65.77 NO POLE NO POLE x[1] = 0.243 y1[1] (analytic) = 1.9706204970248009692839070399837 y1[1] (numeric) = 1.9706204970248009625474525178825 absolute error = 6.7364545221012e-18 relative error = 3.4184433442521019772080586247246e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2406155663196550813182850572694 y2[1] (numeric) = 1.2406155663196550796039560931434 absolute error = 1.7143289641260e-18 relative error = 1.3818373803027783868952917688003e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.244 y1[1] (analytic) = 1.9703793961883758367029449043108 y1[1] (numeric) = 1.9703793961883758299211120174004 absolute error = 6.7818328869104e-18 relative error = 3.4418919016457431192030151489812e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2415860663471366733593278902572 y2[1] (numeric) = 1.2415860663471366716262279133903 absolute error = 1.7330999768669e-18 relative error = 1.3958758267687745692474500916722e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.5MB, time=66.40 NO POLE NO POLE x[1] = 0.245 y1[1] (analytic) = 1.9701373249726353806931329320715 y1[1] (numeric) = 1.9701373249726353738659525330131 absolute error = 6.8271803990584e-18 relative error = 3.4653322448744670616566288542110e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2425563247885720504352218862454 y2[1] (numeric) = 1.2425563247885720486832584376296 absolute error = 1.7519634486158e-18 relative error = 1.4099670281859507960118421883618e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.5MB, time=67.04 NO POLE NO POLE x[1] = 0.246 y1[1] (analytic) = 1.9698942836196507968223264937931 y1[1] (numeric) = 1.9698942836196507899498295747756 absolute error = 6.8724969190175e-18 relative error = 3.4887643342917831090181315874954e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2435263406737028519654573937924 y2[1] (numeric) = 1.2435263406737028501945380574013 absolute error = 1.7709193363911e-18 relative error = 1.4241108358281115849847538759971e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.5MB, time=67.68 NO POLE NO POLE x[1] = 0.247 y1[1] (analytic) = 1.9696502723724634178216640533481 y1[1] (numeric) = 1.9696502723724634109038817460329 absolute error = 6.9177823073152e-18 relative error = 3.5121881302220531488266229530077e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2444961130325132736538872824077 y2[1] (numeric) = 1.2444961130325132718639196853827 absolute error = 1.7899675970250e-18 relative error = 1.4383071013884604456086618445610e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.248 y1[1] (analytic) = 1.9694052914750844705442546902599 y1[1] (numeric) = 1.9694052914750844635812182657252 absolute error = 6.9630364245347e-18 relative error = 3.5356035929604850640080886144295e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2454656408952310375044504040511 y2[1] (numeric) = 1.2454656408952310356953422168882 absolute error = 1.8091081871629e-18 relative error = 1.4525556769775897424728417324523e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.5MB, time=68.31 NO POLE NO POLE x[1] = 0.249 y1[1] (analytic) = 1.9691593411724948319539715808613 y1[1] (numeric) = 1.9691593411724948249457124495469 absolute error = 7.0082591313144e-18 relative error = 3.5590106827726182725162958523162e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2464349232923283615933687748402 y2[1] (numeric) = 1.2464349232923283597650277115763 absolute error = 1.8283410632639e-18 relative error = 1.4668564151223611595441134425538e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.5MB, time=68.94 NO POLE NO POLE x[1] = 0.25 y1[1] (analytic) = 1.9689124217106447841445954494942 y1[1] (numeric) = 1.9689124217106447770911451611452 absolute error = 7.0534502883490e-18 relative error = 3.5824093598946214752535752159240e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2474039592545229295968487048494 y2[1] (numeric) = 1.2474039592545229277491825232486 absolute error = 1.8476661816008e-18 relative error = 1.4812091687643892615065642582886e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.251 y1[1] (analytic) = 1.9686645333364537683895529705847 y1[1] (numeric) = 1.9686645333364537612909432141959 absolute error = 7.0986097563888e-18 relative error = 3.6057995845326762646190754593926e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2483727478127788600733163483794 y2[1] (numeric) = 1.2483727478127788582062328501197 absolute error = 1.8670834982597e-18 relative error = 1.4956137912582104194487200126930e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.5MB, time=69.54 NO POLE NO POLE x[1] = 0.252 y1[1] (analytic) = 1.9684156762978101382224960718362 y1[1] (numeric) = 1.9684156762978101310787586755953 absolute error = 7.1437373962409e-18 relative error = 3.6291813168633254729223324508754e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2493412879983076754992183925442 y2[1] (numeric) = 1.2493412879983076736126254234033 absolute error = 1.8865929691409e-18 relative error = 1.5100701363704995305411521943635e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.5MB, time=70.16 NO POLE NO POLE x[1] = 0.253 y1[1] (analytic) = 1.9681658508435709115489690579392 y1[1] (numeric) = 1.9681658508435709043601359891706 absolute error = 7.1888330687686e-18 relative error = 3.6525545170329071894953598818371e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2503095788425692710574188484538 y2[1] (numeric) = 1.2503095788425692691512242984954 absolute error = 1.9061945499584e-18 relative error = 1.5245780582781693901143799646015e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.5MB, time=70.78 NO POLE NO POLE x[1] = 0.254 y1[1] (analytic) = 1.9679150572235615217894114431114 y1[1] (numeric) = 1.9679150572235615145555148082193 absolute error = 7.2338966348921e-18 relative error = 3.6759191451576489065573136617991e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2512776193772728831772231566772 y2[1] (numeric) = 1.2512776193772728812513349604373 absolute error = 1.9258881962399e-18 relative error = 1.5391374115668772232169493411614e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.255 y1[1] (analytic) = 1.9676632956885755680537453494437 y1[1] (numeric) = 1.9676632956885755607748173938549 absolute error = 7.2789279555888e-18 relative error = 3.6992751613235584111480416160473e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.252245408634378057825061067043 y2[1] (numeric) = 1.2522454086343780558793872037158 absolute error = 1.9456738633272e-18 relative error = 1.5537480512298563197536838261832e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.5MB, time=71.38 NO POLE NO POLE x[1] = 0.256 y1[1] (analytic) = 1.9674105664903745643477972964435 y1[1] (numeric) = 1.9674105664903745570238704045504 absolute error = 7.3239268918931e-18 relative error = 3.7226225255860604139829747818570e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2532129456460956185448600021744 y2[1] (numeric) = 1.2532129456460956165793084957982 absolute error = 1.9655515063762e-18 relative error = 1.5684098326664326620337781593302e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.5MB, time=71.99 NO POLE NO POLE x[1] = 0.257 y1[1] (analytic) = 1.967156869881687687811805175334 y1[1] (numeric) = 1.9671568698816876804429118704371 absolute error = 7.3688933048969e-18 relative error = 3.7459611979699887028832070626424e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2541802294448886342471408644664 y2[1] (numeric) = 1.2541802294448886322616197841096 absolute error = 1.9855210803568e-18 relative error = 1.5831226116804674517347299852143e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.258 y1[1] (analytic) = 1.9669022061162115259912621695806 y1[1] (numeric) = 1.9669022061162115185774351138304 absolute error = 7.4138270557502e-18 relative error = 3.7692911384696290919168873642229e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2551472590634733867458684974902 y2[1] (numeric) = 1.255147259063473384740285957437 absolute error = 2.0055825400532e-18 relative error = 1.5978862444791243004485365824360e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.5MB, time=72.62 NO POLE NO POLE x[1] = 0.259 y1[1] (analytic) = 1.9666465754486098231403503507787 y1[1] (numeric) = 1.9666465754486098156816223451182 absolute error = 7.4587280056605e-18 relative error = 3.7926123070481521895692988589464e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.256114033534820338042089265054 y2[1] (numeric) = 1.2561140335348203360163534249904 absolute error = 2.0257358400636e-18 relative error = 1.6127005876711632331083371188869e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.5MB, time=73.23 NO POLE NO POLE x[1] = 0.26 y1[1] (analytic) = 1.9663899781345132255582176464501 y1[1] (numeric) = 1.9663899781345132180546216305564 absolute error = 7.5035960158937e-18 relative error = 3.8159246636378085044364082196157e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2570805518921550973533884643652 y2[1] (numeric) = 1.2570805518921550953074075295644 absolute error = 2.0459809348008e-18 relative error = 1.6275654982659572977877681468547e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.261 y1[1] (analytic) = 1.9661324144305190259583528434479 y1[1] (numeric) = 1.9661324144305190184099218956739 absolute error = 7.5484309477740e-18 relative error = 3.8392281681396150506781999642700e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2580468131689593878882005439147 y2[1] (numeric) = 1.2580468131689593858218827654228 absolute error = 2.0663177784919e-18 relative error = 1.6424808336717971111975718117152e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.5MB, time=73.84 NO POLE NO POLE x[1] = 0.262 y1[1] (analytic) = 1.9658738845941909068713142575752 y1[1] (numeric) = 1.9658738845941908992780815948906 absolute error = 7.5932326626846e-18 relative error = 3.8625227804234486113601989522027e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2590128163989720133640053518554 y2[1] (numeric) = 1.2590128163989720112772590266773 absolute error = 2.0867463251781e-18 relative error = 1.6574464516942814441727699559806e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.5MB, time=74.46 NO POLE NO POLE x[1] = 0.263 y1[1] (analytic) = 1.9656143888840586830810686666656 y1[1] (numeric) = 1.9656143888840586754430676445985 absolute error = 7.6380010220671e-18 relative error = 3.8858084603274776648906046957916e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2599785606161898242684438967593 y2[1] (numeric) = 1.2599785606161898221611773680435 absolute error = 2.1072665287158e-18 relative error = 1.6724622105357457863365274923644e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.5MB, time=75.07 NO POLE NO POLE x[1] = 0.264 y1[1] (analytic) = 1.9653539275596180430951980707674 y1[1] (numeric) = 1.965353927559618035412462183345 absolute error = 7.6827358874224e-18 relative error = 3.9090851676583570426715136752864e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2609440448548686838623873597158 y2[1] (numeric) = 1.2609440448548686817345090169403 absolute error = 2.1278783427755e-18 relative error = 1.6875279687929476324462538706506e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.265 y1[1] (analytic) = 1.9650925008813302896492328092017 y1[1] (numeric) = 1.9650925008813302819217956888907 absolute error = 7.7274371203110e-18 relative error = 3.9323528621911173713003906220324e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2619092681495244339239933547858 y2[1] (numeric) = 1.2619092681495244317754116339434 absolute error = 2.1485817208424e-18 relative error = 1.7026435854561083877469049449960e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.5MB, time=75.68 NO POLE NO POLE x[1] = 0.266 y1[1] (analytic) = 1.9648301091106220792453705301393 y1[1] (numeric) = 1.9648301091106220714732659477868 absolute error = 7.7721045823525e-18 relative error = 3.9556115036686472269329763334560e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2628742295349338602327836938334 y2[1] (numeric) = 1.2628742295349338580634070776167 absolute error = 2.1693766162167e-18 relative error = 1.7178089199077209479832168495509e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.5MB, time=76.29 NO POLE NO POLE x[1] = 0.267 y1[1] (analytic) = 1.9645667525098851607258414739579 y1[1] (numeric) = 1.9645667525098851529091033387309 absolute error = 7.8167381352270e-18 relative error = 3.9788610518021419681931348208480e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2638389280461356577927781717389 y2[1] (numeric) = 1.2638389280461356556025151897257 absolute error = 2.1902629820132e-18 relative error = 1.7330238319208077166806279122383e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.268 y1[1] (analytic) = 1.9643024313424761128811814969892 y1[1] (numeric) = 1.9643024313424761050198438563153 absolute error = 7.8613376406739e-18 relative error = 4.0021014662702292641390591340761e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2648033627184313957937191489395 y2[1] (numeric) = 1.2648033627184313935824783777779 absolute error = 2.2112407711616e-18 relative error = 1.7482881816577388900093447324806e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.5MB, time=76.90 NO POLE NO POLE x[1] = 0.269 y1[1] (analytic) = 1.9640371458727160810936752273647 y1[1] (numeric) = 1.9640371458727160731877722668715 absolute error = 7.9059029604932e-18 relative error = 4.0253327067193667638570440145746e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.265767532587386482309421970154 y2[1] (numeric) = 1.2657675325873864800771120337473 absolute error = 2.2323099364067e-18 relative error = 1.7636018296689759973052301452911e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.6MB, time=77.52 NO POLE NO POLE x[1] = 0.27 y1[1] (analytic) = 1.9637708963658905130162327094922 y1[1] (numeric) = 1.9637708963658905050657987529466 absolute error = 7.9504339565456e-18 relative error = 4.0485547327636289767351857490409e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2667314366888311287322865210205 y2[1] (numeric) = 1.2667314366888311264788160907123 absolute error = 2.2534704303082e-18 relative error = 1.7789646368915042708351976784257e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=465.3MB, alloc=4.6MB, time=78.13 NO POLE NO POLE x[1] = 0.271 y1[1] (analytic) = 1.9635036830882488932869638582654 y1[1] (numeric) = 1.9635036830882488852920333675131 absolute error = 7.9949304907523e-18 relative error = 4.0717675039843411508648332345393e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.267695074058861313943005488217 y2[1] (numeric) = 1.2676950740588613116682832829759 absolute error = 2.2747222052411e-18 relative error = 1.7943764646477443388585959210221e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.272 y1[1] (analytic) = 1.9632355063070044772797160084106 y1[1] (numeric) = 1.9632355063070044692403235833151 absolute error = 8.0393924250955e-18 relative error = 4.0949709799300693652139778593101e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2686584437338397482145051534362 y2[1] (numeric) = 1.2686584437338397459184399400408 absolute error = 2.2960652133954e-18 relative error = 1.8098371746439159932742096581160e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.6MB, time=78.74 NO POLE NO POLE x[1] = 0.273 y1[1] (analytic) = 1.9629663662903340238908408084099 y1[1] (numeric) = 1.9629663662903340158070211867911 absolute error = 8.0838196216188e-18 relative error = 4.1181651201165596281182799794742e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2696215447503968368491548173544 y2[1] (numeric) = 1.2696215447503968345316554105781 absolute error = 2.3174994067763e-18 relative error = 1.8253466289688021105827604561963e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.6MB, time=79.35 NO POLE NO POLE x[1] = 0.274 y1[1] (analytic) = 1.9626962633073775273624576722117 y1[1] (numeric) = 1.9626962633073775192342457297848 absolute error = 8.1282119424269e-18 relative error = 4.1413498840263202318560632249207e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2705843761454316435482812164654 y2[1] (numeric) = 1.270584376145431641209256479261 absolute error = 2.3390247372044e-18 relative error = 1.8409046900925170870384651693101e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.275 y1[1] (analytic) = 1.9624251976282379481424819654439 y1[1] (numeric) = 1.9624251976282379399699127157575 absolute error = 8.1725692496864e-18 relative error = 4.1645252311087642510639015414287e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2715469369561128535130245633453 y2[1] (numeric) = 1.2715469369561128511523834070293 absolute error = 2.3606411563160e-18 relative error = 1.8565112208653584133519340100179e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.6MB, time=79.96 NO POLE NO POLE x[1] = 0.276 y1[1] (analytic) = 1.9621531695239809427816870660775 y1[1] (numeric) = 1.9621531695239809345647956604517 absolute error = 8.2168914056258e-18 relative error = 4.1876911207799444011983882855127e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2725092262198797362755731095714 y2[1] (numeric) = 1.272509226219879733893224494009 absolute error = 2.3823486155624e-18 relative error = 1.8721660845158765199181170836145e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.6MB, time=80.57 NO POLE NO POLE x[1] = 0.277 y1[1] (analytic) = 1.9618801792666345928680704024572 y1[1] (numeric) = 1.9618801792666345846068921299216 absolute error = 8.2611782725356e-18 relative error = 4.2108475124223386059785166519666e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2734712429744431082598134001431 y2[1] (numeric) = 1.2734712429744431058556663339323 absolute error = 2.4041470662108e-18 relative error = 1.8878691446502086952500301256549e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.278 y1[1] (analytic) = 1.9616062271291891329987945343101 y1[1] (numeric) = 1.9616062271291891246933648215413 absolute error = 8.3054297127688e-18 relative error = 4.2339943653848392574531480317961e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2744329862577862950704336588324 y2[1] (numeric) = 1.2744329862577862926443971994884 absolute error = 2.4260364593440e-18 relative error = 1.9036202652504733462698401065709e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.6MB, time=81.18 NO POLE NO POLE x[1] = 0.279 y1[1] (analytic) = 1.9613313133855966777899753047686 y1[1] (numeric) = 1.9613313133855966694403297160277 absolute error = 8.3496455887409e-18 relative error = 4.2571316389824874952647841077356e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2753944551081660935095180154422 y2[1] (numeric) = 1.2753944551081660910615012695819 absolute error = 2.4480167458603e-18 relative error = 1.9194193106733272659223959636543e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.6MB, time=81.78 NO POLE NO POLE x[1] = 0.28 y1[1] (analytic) = 1.9610554383107709479245900535965 y1[1] (numeric) = 1.9610554383107709395307642906663 absolute error = 8.3938257629302e-18 relative error = 4.2802592924963601984146819302869e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2763556485641137333196695584578 y2[1] (numeric) = 1.2763556485641137308495816819839 absolute error = 2.4700878764739e-18 relative error = 1.9352661456489200959847363036524e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.6MB, time=82.40 NO POLE NO POLE x[1] = 0.281 y1[1] (analytic) = 1.9607786021805869952387798436879 y1[1] (numeric) = 1.9607786021805869868008097458098 absolute error = 8.4379700978781e-18 relative error = 4.3033772851734568381890713943774e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2773165656644358386527004700495 y2[1] (numeric) = 1.2773165656644358361604506683343 absolute error = 2.4922498017152e-18 relative error = 1.9511606352797741622897902574677e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.282 y1[1] (analytic) = 1.9605008052718809268468206145129 y1[1] (numeric) = 1.9605008052718809183647421583235 absolute error = 8.4820784561894e-18 relative error = 4.3264855762265861918613774739034e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2782772054482153892629277748141 y2[1] (numeric) = 1.2782772054482153867484253028842 absolute error = 2.5145024719299e-18 relative error = 1.9671026450387295471124598476152e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.6MB, time=83.00 NO POLE NO POLE x[1] = 0.283 y1[1] (analytic) = 1.9602220478624496283050391375165 y1[1] (numeric) = 1.9602220478624496197788884369842 absolute error = 8.5261507005323e-18 relative error = 4.3495841248340998728983949709189e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2792375669548126814241135090431 y2[1] (numeric) = 1.279237566954812678887267671763 absolute error = 2.5368458372801e-18 relative error = 1.9830920407684608060071998490756e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.6MB, time=83.61 NO POLE NO POLE x[1] = 0.284 y1[1] (analytic) = 1.9599423302310504858149506095312 y1[1] (numeric) = 1.9599423302310504772447639158926 absolute error = 8.5701866936386e-18 relative error = 4.3726728901397276339367351565447e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2801976492238662885690883936544 y2[1] (numeric) = 1.2801976492238662860098085459103 absolute error = 2.5592798477441e-18 relative error = 1.9991286886799793522298715519281e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.285 y1[1] (analytic) = 1.959661652657401107465895681044 y1[1] (numeric) = 1.9596616526574010988517093827395 absolute error = 8.6141862983045e-18 relative error = 4.3957518312527186596134013461262e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2811574512952940216510983712452 y2[1] (numeric) = 1.2811574512952940190692939181291 absolute error = 2.5818044531161e-18 relative error = 2.0152124553510634888997729821925e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.6MB, time=84.23 NO POLE NO POLE x[1] = 0.286 y1[1] (analytic) = 1.9593800154221790435174556766546 y1[1] (numeric) = 1.9593800154221790348593062992647 absolute error = 8.6581493773899e-18 relative error = 4.4188209072472173887633706602973e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2821169722092938892259136459998 y2[1] (numeric) = 1.282116972209293886621494042993 absolute error = 2.6044196030068e-18 relative error = 2.0313432077253964310695582825032e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.6MB, time=84.85 NO POLE NO POLE x[1] = 0.287 y1[1] (analytic) = 1.9590974188070215057219257252902 y1[1] (numeric) = 1.9590974188070214970198499314707 absolute error = 8.7020757938195e-18 relative error = 4.4418800771625575445947778715077e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2830762110063450572537401444227 y2[1] (numeric) = 1.2830762110063450546266148975798 absolute error = 2.6271252468429e-18 relative error = 2.0475208131108498614448920551949e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.6MB, time=85.47 NO POLE NO POLE x[1] = 0.288 y1[1] (analytic) = 1.9588138630945250856871264776764 y1[1] (numeric) = 1.958813863094525076941161067094 absolute error = 8.7459654105824e-18 relative error = 4.4649293000027906047805393619786e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2840351667272088086199735950659 y2[1] (numeric) = 1.2840351667272088059700522611981 absolute error = 2.6499213338678e-18 relative error = 2.0637451391787087208502431614049e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.289 y1[1] (analytic) = 1.9585293485682454722798360482323 y1[1] (numeric) = 1.9585293485682454634900179574994 absolute error = 8.7898180907329e-18 relative error = 4.4879685347368265223470259878256e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.284993838412929502373836706576 y2[1] (numeric) = 1.2849938384129294997010288934347 absolute error = 2.6728078131413e-18 relative error = 2.0800160539621202494107448064730e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.6MB, time=86.09 NO POLE NO POLE x[1] = 0.29 y1[1] (analytic) = 1.9582438755126971680701247779319 y1[1] (numeric) = 1.9582438755126971592364910805417 absolute error = 8.8336336973902e-18 relative error = 4.5109977402980127964799464256858e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2859522251048355326839402055044 y2[1] (numeric) = 1.2859522251048355299881555719645 absolute error = 2.6957846335399e-18 relative error = 2.0963334258550155458670637443749e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.6MB, time=86.72 NO POLE NO POLE x[1] = 0.291 y1[1] (analytic) = 1.9579574442133532048168763737751 y1[1] (numeric) = 1.9579574442133531959394642800362 absolute error = 8.8774120937389e-18 relative error = 4.5340168755841217195016456116888e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.286910325844540287509808778398 y2[1] (numeric) = 1.2869103258445402847909570346417 absolute error = 2.7188517437563e-18 relative error = 2.1126971236104133081727474125397e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.292 y1[1] (analytic) = 1.9576700549566448579947799393226 y1[1] (numeric) = 1.9576700549566448490736267962934 absolute error = 8.9211531430292e-18 relative error = 4.5570258994571843236333468363620e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.287868139673943106988413246727 y2[1] (numeric) = 1.2878681396739431042464041544266 absolute error = 2.7420090923004e-18 relative error = 2.1291070163398948735830640178095e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.6MB, time=87.33 NO POLE NO POLE x[1] = 0.293 y1[1] (analytic) = 1.9573817080299613603630783692788 y1[1] (numeric) = 1.9573817080299613513982216607016 absolute error = 8.9648567085772e-18 relative error = 4.5800247707433752248858413988275e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2888256656352302415347505881947 y2[1] (numeric) = 1.2888256656352302387694939606959 absolute error = 2.7652566274988e-18 relative error = 2.1455629735119167681286106549682e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.6MB, time=87.95 NO POLE NO POLE x[1] = 0.294 y1[1] (analytic) = 1.9570924037216496145763595393507 y1[1] (numeric) = 1.9570924037216496055678368855858 absolute error = 9.0085226537649e-18 relative error = 4.6030134482327440311427342335438e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2897829027708758096555137039305 y2[1] (numeric) = 1.2897829027708758068669194064358 absolute error = 2.7885942974947e-18 relative error = 2.1620648649504399281481487089222e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.295 y1[1] (analytic) = 1.956802142321013904837677680568 y1[1] (numeric) = 1.9568021423210138957855268385274 absolute error = 9.0521508420406e-18 relative error = 4.6259918906791508813800421559701e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2907398501236427554748931179768 y2[1] (numeric) = 1.2907398501236427526628710677281 absolute error = 2.8120220502487e-18 relative error = 2.1786125608342613268399815185698e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.6MB, time=88.58 NO POLE NO POLE x[1] = 0.296 y1[1] (analytic) = 1.9565109241183156075942932849186 y1[1] (numeric) = 1.9565109241183155984985521479993 absolute error = 9.0957411369193e-18 relative error = 4.6489600568002018813149667305811e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.291696506736583805971553083346 y2[1] (numeric) = 1.2916965067365838031360132498077 absolute error = 2.8355398335383e-18 relative error = 2.1952059316953411809728286132159e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.6MB, time=89.20 NO POLE NO POLE x[1] = 0.297 y1[1] (analytic) = 1.9562187494047729012763208465347 y1[1] (numeric) = 1.9562187494047728921370274445522 absolute error = 9.1392934019825e-18 relative error = 4.6719179052768777214885423255516e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2926528716530424279258248577527 y2[1] (numeric) = 1.292652871653042425066677262795 absolute error = 2.8591475949577e-18 relative error = 2.2118448484173687105780570274486e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.6MB, time=89.82 NO POLE NO POLE x[1] = 0.298 y1[1] (analytic) = 1.9559256184725604750785746997598 y1[1] (numeric) = 1.955925618472560465895767198881 absolute error = 9.1828075008788e-18 relative error = 4.6948653947535709298252528817025e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2936089439166537845761602019079 y2[1] (numeric) = 1.293608943916653781693314919989 absolute error = 2.8828452819189e-18 relative error = 2.2285291822353382501821199846608e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.299 y1[1] (analytic) = 1.9556315316148092367859041722236 y1[1] (numeric) = 1.9556315316148092275596208748997 absolute error = 9.2262832973239e-18 relative error = 4.7178024838378163046733107485576e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2945647225713456919838884439998 y2[1] (numeric) = 1.2945647225713456890772556023488 absolute error = 2.9066328416510e-18 relative error = 2.2452588047337358653331860369075e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.6MB, time=90.44 NO POLE NO POLE x[1] = 0.3 y1[1] (analytic) = 1.955336489125606019642310227568 y1[1] (numeric) = 1.9553364891256060103725895724672 absolute error = 9.2697206551008e-18 relative error = 4.7407291311001233423206299146228e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.295520206661339575105320745685 y2[1] (numeric) = 1.2955202066613395721748105244847 absolute error = 2.9305102212003e-18 relative error = 2.2620335878453505711978000776019e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.6MB, time=91.05 NO POLE NO POLE x[1] = 0.301 y1[1] (analytic) = 1.9550404912999932882641367286816 y1[1] (numeric) = 1.9550404912999932789510172906209 absolute error = 9.3131194380607e-18 relative error = 4.7636452950741665144400924321486e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2964753952311514235702454975658 y2[1] (numeric) = 1.2964753952311514206157681301351 absolute error = 2.9544773674307e-18 relative error = 2.2788534038503212716906969652774e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.302 y1[1] (analytic) = 1.9547435384339688435976304082261 y1[1] (numeric) = 1.9547435384339688342411508981042 absolute error = 9.3564795101219e-18 relative error = 4.7865509342559525198644175439945e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2974302873255927471658590657366 y2[1] (numeric) = 1.2974302873255927441873248387129 absolute error = 2.9785342270237e-18 relative error = 2.2957181253748786803531257338398e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.6MB, time=91.66 NO POLE NO POLE x[1] = 0.303 y1[1] (analytic) = 1.9544456308244855269211645888734 y1[1] (numeric) = 1.9544456308244855175213638536019 absolute error = 9.3998007352715e-18 relative error = 4.8094460071044193614296764612602e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2983848819897715310251764055494 y2[1] (numeric) = 1.2983848819897715280224956590712 absolute error = 3.0026807464782e-18 relative error = 2.3126276253899378350252702195865e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.6MB, time=92.27 NO POLE NO POLE x[1] = 0.304 y1[1] (analytic) = 1.9541467687694509228924226510006 y1[1] (numeric) = 1.9541467687694509134493396734361 absolute error = 9.4430829775645e-18 relative error = 4.8323304720407054187892517721129e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.2993391782690931905189663542671 y2[1] (numeric) = 1.2993391782690931874920494821561 absolute error = 3.0269168721110e-18 relative error = 2.3295817772102346374378731300577e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.6MB, time=92.89 NO POLE NO POLE x[1] = 0.305 y1[1] (analytic) = 1.9538469525677270616408382006383 y1[1] (numeric) = 1.9538469525677270521545120995137 absolute error = 9.4863261011246e-18 relative error = 4.8552042874482878821825876318008e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3002931752092615258502567107484 y2[1] (numeric) = 1.3002931752092615227990141606917 absolute error = 3.0512425500567e-18 relative error = 2.3465804544930038516601497454042e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.306 y1[1] (analytic) = 1.9535461825191301199055898452054 y1[1] (numeric) = 1.953546182519130110376059875061 absolute error = 9.5295299701444e-18 relative error = 4.8780674116728141314402475173440e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3012468718562796763504545077395 y2[1] (numeric) = 1.3012468718562796732747967814719 absolute error = 3.0756577262676e-18 relative error = 2.3636235312366620151191530890154e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.6MB, time=93.49 NO POLE NO POLE x[1] = 0.307 y1[1] (analytic) = 1.9532444589244301212194494390108 y1[1] (numeric) = 1.9532444589244301116467549901253 absolute error = 9.5726944488855e-18 relative error = 4.9009198030218817149234075129861e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3022002672564510744761271807312 y2[1] (numeric) = 1.3022002672564510713759648342171 absolute error = 3.1001623465141e-18 relative error = 2.3807108817798792052855121906808e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.6MB, time=94.11 NO POLE NO POLE x[1] = 0.308 y1[1] (analytic) = 1.9529417820853506351387836146492 y1[1] (numeric) = 1.9529417820853506255229642129708 absolute error = 9.6158194016784e-18 relative error = 4.9237614197647156670598809277341e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.30315336045638039950549063668 y2[1] (numeric) = 1.3031533604563803963807342802955 absolute error = 3.1247563563845e-18 relative error = 2.3978423808001935676236992157252e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.309 y1[1] (analytic) = 1.9526381523045684755200093702652 y1[1] (numeric) = 1.9526381523045684658611046773416 absolute error = 9.6589046929236e-18 relative error = 4.9465922201324600301546899434276e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3041061505029745309336505261852 y2[1] (numeric) = 1.3041061505029745277842108248999 absolute error = 3.1494397012853e-18 relative error = 2.4150179033130144374250273908133e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=568.3MB, alloc=4.6MB, time=94.72 NO POLE NO POLE x[1] = 0.31 y1[1] (analytic) = 1.9523335698857133978428054362022 y1[1] (numeric) = 1.9523335698857133881408552491113 absolute error = 9.7019501870909e-18 relative error = 4.9694121623175476262234785730603e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.305058636443443501565643323959 y2[1] (numeric) = 1.3050586364434434983914309975177 absolute error = 3.1742123264413e-18 relative error = 2.4322373246704756981581874150286e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.6MB, time=95.34 NO POLE NO POLE x[1] = 0.311 y1[1] (analytic) = 1.9520280351333677955803820978034 y1[1] (numeric) = 1.9520280351333677858354263490831 absolute error = 9.7449557487203e-18 relative error = 4.9922212044738888511453563695854e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3060108173253014503063241246284 y2[1] (numeric) = 1.3060108173253014471072499477331 absolute error = 3.1990741768953e-18 relative error = 2.4495005205599870067046621651377e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.312 y1[1] (analytic) = 1.9517215483530663956171131040662 y1[1] (numeric) = 1.9517215483530663858291918616444 absolute error = 9.7879212424218e-18 relative error = 5.0150193047164969918821154399441e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3069626921963675746461483640617 y2[1] (numeric) = 1.3069626921963675714221231665528 absolute error = 3.2240251975089e-18 relative error = 2.4668073670036321283318204810136e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.6MB, time=95.95 NO POLE NO POLE x[1] = 0.313 y1[1] (analytic) = 1.9514141098512959527138342444951 y1[1] (numeric) = 1.9514141098512959428829877116192 absolute error = 9.8308465328759e-18 relative error = 5.0378064211214718562555627027876e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3079142601047670828418949805147 y2[1] (numeric) = 1.3079142601047670795928296475529 absolute error = 3.2490653329618e-18 relative error = 2.4841577403564221711473228197359e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.6MB, time=96.56 NO POLE NO POLE x[1] = 0.314 y1[1] (analytic) = 1.9511057199354949430211141288279 y1[1] (numeric) = 1.9511057199354949331473826439942 absolute error = 9.8737314848337e-18 relative error = 5.0605825117257783259767311369420e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3088655200989321457913788349557 y2[1] (numeric) = 1.3088655200989321425171843072033 absolute error = 3.2741945277524e-18 relative error = 2.5015515173055488088533973380176e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.6MB, time=97.18 NO POLE NO POLE x[1] = 0.315 y1[1] (analytic) = 1.9507963789140532566408036563392 y1[1] (numeric) = 1.9507963789140532467242276932221 absolute error = 9.9165759631171e-18 relative error = 5.0833475345270759116759679344687e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.309816471227602848601200515934 y2[1] (numeric) = 1.3098164712276028453017877897362 absolute error = 3.2994127261978e-18 relative error = 2.5189885748691818250664644133505e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.316 y1[1] (analytic) = 1.9504860870963118892361716131461 y1[1] (numeric) = 1.9504860870963118792767917805271 absolute error = 9.9593798326190e-18 relative error = 5.1061014474835480961630201931793e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3107671125398281418465819613222 y2[1] (numeric) = 1.3107671125398281385218620888886 absolute error = 3.3247198724336e-18 relative error = 2.5364687903951184625306313159100e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.6MB, time=97.78 NO POLE NO POLE x[1] = 0.317 y1[1] (analytic) = 1.9501748447925626326909347873552 y1[1] (numeric) = 1.9501748447925626226887918290514 absolute error = 1.00021429583038e-17 relative error = 5.1288442085138852972705976396348e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3117174430849667925223366371764 y2[1] (numeric) = 1.3117174430849667891722207267621 absolute error = 3.3501159104143e-18 relative error = 2.5539920415598952190659260852843e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.6MB, time=98.39 NO POLE NO POLE x[1] = 0.318 y1[1] (analytic) = 1.9498626523140477648174919429938 y1[1] (numeric) = 1.9498626523140477547726267377865 absolute error = 1.00448652052073e-17 relative error = 5.1515757754969600507109164410448e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3126674619126883346840233228225 y2[1] (numeric) = 1.312667461912688331308422538909 absolute error = 3.3756007839135e-18 relative error = 2.5715582063677503034313303474825e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.319 y1[1] (analytic) = 1.9495495099729597381146719444671 y1[1] (numeric) = 1.94954950997295972802712550603 absolute error = 1.00875464384371e-17 relative error = 5.1742961062717583006064932364269e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3136171680729740197783328610944 y2[1] (numeric) = 1.313617168072974016377158424571 absolute error = 3.4011744365234e-18 relative error = 2.5891671631490568827789183836691e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.6MB, time=99.00 NO POLE NO POLE x[1] = 0.32 y1[1] (analytic) = 1.9492354180824408675753072737661 y1[1] (numeric) = 1.9492354180824408574451207505934 absolute error = 1.01301865231727e-17 relative error = 5.1970051586371566668960482619357e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3145665606161177666617575434172 y2[1] (numeric) = 1.3145665606161177632349207317616 absolute error = 3.4268368116556e-18 relative error = 2.6068187905597512146272929635099e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.6MB, time=99.61 NO POLE NO POLE x[1] = 0.321 y1[1] (analytic) = 1.9489203769565830175439451328269 y1[1] (numeric) = 1.948920376956583007371159808161 absolute error = 1.01727853246659e-17 relative error = 5.2197028903518533783672504031383e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3155156385927271113065931111435 y2[1] (numeric) = 1.3155156385927271078540052586029 absolute error = 3.4525878525406e-18 relative error = 2.6245129675797742285293503774562e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.6MB, time=100.23 NO POLE NO POLE x[1] = 0.322 y1[1] (analytic) = 1.9486043869104272876250092733052 y1[1] (numeric) = 1.9486043869104272774096665650643 absolute error = 1.02153427082409e-17 relative error = 5.2423892591341451317722828821457e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3164644010537241561933236672222 y2[1] (numeric) = 1.3164644010537241527148961649938 absolute error = 3.4784275022284e-18 relative error = 2.6422495735123546050303561653274e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.323 y1[1] (analytic) = 1.948287448259963697641726645576 y1[1] (numeric) = 1.9482874482599636873838681062815 absolute error = 1.02578585392945e-17 relative error = 5.2650642226617550103703624459448e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3174128470503465193884401058919 y2[1] (numeric) = 1.3174128470503465158840844023038 absolute error = 3.5043557035881e-18 relative error = 2.6600284879825350785849625758587e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.6MB, time=100.83 NO POLE NO POLE x[1] = 0.324 y1[1] (analytic) = 1.9479695613221308716461339080079 y1[1] (numeric) = 1.9479695613221308613458012247114 absolute error = 1.03003326832965e-17 relative error = 5.2877277385717628544332462223165e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3183609756341482833067429826609 y2[1] (numeric) = 1.3183609756341482797763705833526 absolute error = 3.5303723993083e-18 relative error = 2.6778495909363111108124801525495e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.6MB, time=101.45 NO POLE NO POLE x[1] = 0.325 y1[1] (analytic) = 1.9476507264148157209804797864775 y1[1] (numeric) = 1.9476507264148157106377147806876 absolute error = 1.03427650057899e-17 relative error = 5.3103797644604328247123273625051e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3193087858570009431571810623496 y2[1] (numeric) = 1.3193087858570009396007035304524 absolute error = 3.5564775318972e-18 relative error = 2.6957127626395450856768604755882e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.326 y1[1] (analytic) = 1.9473309438568531263903402226954 y1[1] (numeric) = 1.9473309438568531160051848503047 absolute error = 1.03851553723907e-17 relative error = 5.3330202578828353362893561771211e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3202562767710943550712770994355 y2[1] (numeric) = 1.3202562767710943514886060557529 absolute error = 3.5826710436826e-18 relative error = 2.7136178836768086441395923334842e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.6MB, time=102.05 NO POLE NO POLE x[1] = 0.327 y1[1] (analytic) = 1.9470102139680256191897641982033 y1[1] (numeric) = 1.9470102139680256087622605494144 absolute error = 1.04275036487889e-17 relative error = 5.3556491763530848977101150714538e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3212034474289376839131927223542 y2[1] (numeric) = 1.3212034474289376803042398455425 absolute error = 3.6089528768117e-18 relative error = 2.7315648349500778332724037054464e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.6MB, time=102.67 NO POLE NO POLE x[1] = 0.328 y1[1] (analytic) = 1.9466885370690630614787690688678 y1[1] (numeric) = 1.9466885370690630510089593681199 absolute error = 1.04698097007479e-17 relative error = 5.3782664773437562249466337780087e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3221502968833603507704846117713 y2[1] (numeric) = 1.3221502968833603471351616385196 absolute error = 3.6353229732517e-18 relative error = 2.7495534976780381538627401024971e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.329 y1[1] (analytic) = 1.9463659134816423254135051923513 y1[1] (numeric) = 1.9463659134816423149014317982459 absolute error = 1.05120733941054e-17 relative error = 5.4008721182860703919899224915945e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3230968241875129801246044821466 y2[1] (numeric) = 1.3230968241875129764628232073568 absolute error = 3.6617812747898e-18 relative error = 2.7675837533949383304214451476586e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.6MB, time=103.27 NO POLE NO POLE x[1] = 0.33 y1[1] (analytic) = 1.9460423435283869715294105783662 y1[1] (numeric) = 1.946042343528386960975115983593 absolute error = 1.05542945947732e-17 relative error = 5.4234660565695158644226265737032e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3240430283948683467001956961702 y2[1] (numeric) = 1.3240430283948683430118679731373 absolute error = 3.6883277230329e-18 relative error = 2.7856554839492216446130762151712e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.6MB, time=103.89 NO POLE NO POLE x[1] = 0.331 y1[1] (analytic) = 1.9457178275328669261176772385331 y1[1] (numeric) = 1.9457178275328669155212040697954 absolute error = 1.05964731687377e-17 relative error = 5.4460482495418288675514555091784e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3249889085592223219922396628531 y2[1] (numeric) = 1.3249889085592223182772774034451 absolute error = 3.7149622594080e-18 relative error = 2.8037685715026906694040041609200e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.6MB, time=104.50 NO POLE NO POLE x[1] = 0.332 y1[1] (analytic) = 1.9453923658195981576553518593481 y1[1] (numeric) = 1.9453923658195981470167428772883 absolute error = 1.06386089820598e-17 relative error = 5.4686186545086652613880330551922e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3259344637346948204701054922043 y2[1] (numeric) = 1.3259344637346948167284206670421 absolute error = 3.7416848251622e-18 relative error = 2.8219228985293731389229925188319e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.333 y1[1] (analytic) = 1.9450659587140423522893943681328 y1[1] (numeric) = 1.9450659587140423416086924672573 absolute error = 1.06807019008755e-17 relative error = 5.4911772287336319186956228241478e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3268796929757307454575567025243 y2[1] (numeric) = 1.3268796929757307416890613411611 absolute error = 3.7684953613632e-18 relative error = 2.8401183478147687313455479411743e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.6MB, time=105.13 NO POLE NO POLE x[1] = 0.334 y1[1] (analytic) = 1.9447386065426065883750189078808 y1[1] (numeric) = 1.9447386065426065776522671164848 absolute error = 1.07227517913960e-17 relative error = 5.5137239294380609778494366194009e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3278245953371009346877691003853 y2[1] (numeric) = 1.327824595337100930892375291487 absolute error = 3.7953938088983e-18 relative error = 2.8583548024539686466822024532020e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.6MB, time=105.79 NO POLE NO POLE x[1] = 0.335 y1[1] (analytic) = 1.9444103096326430100686426826321 y1[1] (numeric) = 1.9444103096326429993038841627244 absolute error = 1.07647585199077e-17 relative error = 5.5362587138007323858425153378239e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3287691698739031055324142783622 y2[1] (numeric) = 1.3287691698739031017100341698862 absolute error = 3.8223801084760e-18 relative error = 2.8766321458517391550539447041468e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.336 y1[1] (analytic) = 1.9440810683124484999757690804005 y1[1] (numeric) = 1.9440810683124484891690471276279 absolute error = 1.08067219527726e-17 relative error = 5.5587815389578018597625876546840e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3297134156415627999038635015058 y2[1] (numeric) = 1.3297134156415627960544093008811 absolute error = 3.8494542006247e-18 relative error = 2.8949502617204231217808860763296e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.6MB, time=106.44 NO POLE NO POLE x[1] = 0.337 y1[1] (analytic) = 1.943750882911264350854132425743 y1[1] (numeric) = 1.9437508829112643400054904693143 absolute error = 1.08486419564287e-17 relative error = 5.5812923620027287214949060172014e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3306573316958343288295670804365 y2[1] (numeric) = 1.3306573316958343249529510547429 absolute error = 3.8766160256936e-18 relative error = 2.9133090340795030449489738920120e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.6MB, time=107.09 NO POLE NO POLE x[1] = 0.338 y1[1] (analytic) = 1.9434197537592759363724326587988 y1[1] (numeric) = 1.9434197537592759254819142614089 absolute error = 1.08905183973899e-17 relative error = 5.6037911399859463273406528671032e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.331600917092801716697664656756 y2[1] (numeric) = 1.3316009170928017127937991329032 absolute error = 3.9038655238528e-18 relative error = 2.9317083472545644338257114867339e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.6MB, time=107.74 NO POLE NO POLE x[1] = 0.339 y1[1] (analytic) = 1.9430876811876123809249891820363 y1[1] (numeric) = 1.9430876811876123699926380397899 absolute error = 1.09323511422464e-17 relative error = 5.6262778299147894297129276226886e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.332544170888879645172882155245 y2[1] (numeric) = 1.3325441708888796412416795201522 absolute error = 3.9312026350928e-18 relative error = 2.9501480858758125940540119041102e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.34 y1[1] (analytic) = 1.9427546655283462285026440600266 y1[1] (numeric) = 1.9427546655283462175285040023615 absolute error = 1.09741400576651e-17 relative error = 5.6487523887534214103440736512051e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3334870921408143967817714870308 y2[1] (numeric) = 1.3334870921408143928231441878055 absolute error = 3.9586272992253e-18 relative error = 2.9686281348775698684587039359062e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.6MB, time=108.35 NO POLE NO POLE x[1] = 0.341 y1[1] (analytic) = 1.9424207071144931106202457013121 y1[1] (numeric) = 1.9424207071144930996043606909229 absolute error = 1.10158850103892e-17 relative error = 5.6712147734223495279055338420104e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.334429679905684798166349418561 y2[1] (numeric) = 1.3344296799056847941802099626783 absolute error = 3.9861394558827e-18 relative error = 2.9871483794968000878992012247203e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.6MB, time=108.96 NO POLE NO POLE x[1] = 0.342 y1[1] (analytic) = 1.9420858062800114133010450948604 y1[1] (numeric) = 1.9420858062800114022434592276211 absolute error = 1.10575858672393e-17 relative error = 5.6936649407987119767170274085271e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3353719332409031630051923528251 y2[1] (numeric) = 1.3353719332409031589914533083065 absolute error = 4.0137390445186e-18 relative error = 3.0057087052723874089598979137245e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.343 y1[1] (analytic) = 1.9417499633598019431183376166772 y1[1] (numeric) = 1.9417499633598019320190951215644 absolute error = 1.10992424951128e-17 relative error = 5.7161028477156896890990860034829e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.336313851204216234601044101807 y2[1] (numeric) = 1.3363138512042162305596180973992 absolute error = 4.0414260044078e-18 relative error = 3.0243089980440433256793272739794e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.6MB, time=109.57 NO POLE NO POLE x[1] = 0.344 y1[1] (analytic) = 1.9414131786897075922946843649114 y1[1] (numeric) = 1.9414131786897075811538296039264 absolute error = 1.11408547609850e-17 relative error = 5.7385284509627931240775307340066e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3372554328537061281339940626387 y2[1] (numeric) = 1.3372554328537061240647937879926 absolute error = 4.0692002746461e-18 relative error = 3.0429491439510680321610254416961e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.6MB, time=110.18 NO POLE NO POLE x[1] = 0.345 y1[1] (analytic) = 1.9410754526065130028590479241997 y1[1] (numeric) = 1.9410754526065129916766253922915 absolute error = 1.11824225319082e-17 relative error = 5.7609417072851189433405766571245e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.338196677247791272579283544357 y2[1] (numeric) = 1.3381966772477912684822217502061 absolute error = 4.0970617941509e-18 relative error = 3.0616290294317141295901146547332e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.346 y1[1] (analytic) = 1.9407367854479442298621784020909 y1[1] (numeric) = 1.9407367854479442186382327270779 absolute error = 1.12239456750130e-17 relative error = 5.7833425733837394466331362157268e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3391375834452273522887983275334 y2[1] (numeric) = 1.3391375834452273481637878258724 absolute error = 4.1250105016610e-18 relative error = 3.0803485412219549175815243032104e-16 % Correct digits = 17 h = 0.001 memory used=667.5MB, alloc=4.6MB, time=110.79 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.347 y1[1] (analytic) = 1.9403971775526684036505865221322 y1[1] (numeric) = 1.9403971775526683923851624646243 absolute error = 1.12654240575079e-17 relative error = 5.8057310059152162500472054325779e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3400781505051082482353058753646 y2[1] (numeric) = 1.3400781505051082440822595396281 absolute error = 4.1530463357365e-18 relative error = 3.0991075663543318022653988481172e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=671.3MB, alloc=4.6MB, time=111.41 NO POLE NO POLE x[1] = 0.348 y1[1] (analytic) = 1.9400566292602933911994414996184 y1[1] (numeric) = 1.9400566292602933798925839529388 absolute error = 1.13068575466796e-17 relative error = 5.8281069614914742134160205315659e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3410183774868669789184959520651 y2[1] (numeric) = 1.3410183774868669747373267173056 absolute error = 4.1811692347595e-18 relative error = 3.1179059921574024254005057143966e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.6MB, time=112.02 NO POLE NO POLE x[1] = 0.349 y1[1] (analytic) = 1.9397151409113674565047323670778 y1[1] (numeric) = 1.9397151409113674451564863571841 absolute error = 1.13482460098937e-17 relative error = 5.8504703966798813949669041995787e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3419582634502766409318837425973 y2[1] (numeric) = 1.3419582634502766367225046056639 absolute error = 4.2093791369334e-18 relative error = 3.1367437062541471757260271507386e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.35 y1[1] (analytic) = 1.9393727128473789200350323573037 y1[1] (numeric) = 1.9393727128473789086454430427094 absolute error = 1.13895893145943e-17 relative error = 5.8728212680027618416655593020176e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3428978074554513491896349069176 y2[1] (numeric) = 1.342897807455451344951958926634 absolute error = 4.2376759802836e-18 relative error = 3.1556205965614242318630123089780e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.6MB, time=112.62 NO POLE NO POLE x[1] = 0.351 y1[1] (analytic) = 1.9390293454107558172432068921403 y1[1] (numeric) = 1.9390293454107558058123195638361 absolute error = 1.14308873283042e-17 relative error = 5.8951595319372172413822067818555e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3438370085628471768123723419896 y2[1] (numeric) = 1.343837008562847172546312639332 absolute error = 4.2660597026576e-18 relative error = 3.1745365512889797305085922338729e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.6MB, time=113.25 NO POLE NO POLE x[1] = 0.352 y1[1] (analytic) = 1.9386850389448655561384066652863 y1[1] (numeric) = 1.9386850389448655446662667466605 absolute error = 1.14721399186258e-17 relative error = 5.9174851449153093982916663055622e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3447758658332630946710247658361 y2[1] (numeric) = 1.3447758658332630903764945241115 absolute error = 4.2945302417246e-18 relative error = 3.1934914589380896006188820517727e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.353 y1[1] (analytic) = 1.9383397937940145739186882470937 y1[1] (numeric) = 1.9383397937940145624053412938529 absolute error = 1.15133469532408e-17 relative error = 5.9397980633236237603192224451496e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.345714378327841910587777579861 y2[1] (numeric) = 1.345714378327841906264690044885 absolute error = 4.3230875349760e-18 relative error = 3.2124852083008752036798602425868e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.6MB, time=113.85 NO POLE NO POLE x[1] = 0.354 y1[1] (analytic) = 1.9379936103034479926646055787134 y1[1] (numeric) = 1.9379936103034479811100972788029 absolute error = 1.15545082999105e-17 relative error = 5.9620982435031420232287560297430e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3466525451080712081931868085672 y2[1] (numeric) = 1.3466525451080712038414552888416 absolute error = 4.3517315197256e-18 relative error = 3.2315176884593983959764012975831e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.6MB, time=114.46 NO POLE NO POLE x[1] = 0.355 y1[1] (analytic) = 1.937646488819349274094116661967 y1[1] (numeric) = 1.937646488819349262498492835491 absolute error = 1.15956238264760e-17 relative error = 5.9843856417490629325433746485936e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3475903652357842854385172596347 y2[1] (numeric) = 1.3475903652357842810580551265256 absolute error = 4.3804621331091e-18 relative error = 3.2505887887842402651654849149599e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.6MB, time=115.06 NO POLE NO POLE x[1] = 0.356 y1[1] (analytic) = 1.9372984296888398733791506900099 y1[1] (numeric) = 1.9372984296888398617424572891513 absolute error = 1.16366934008586e-17 relative error = 6.0066602143107260727266182615659e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3485278377731610927623663921003 y2[1] (numeric) = 1.3485278377731610883530870800154 absolute error = 4.4092793120849e-18 relative error = 3.2696983989340491551727535807283e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.357 y1[1] (analytic) = 1.9369494332599788920241818021889 y1[1] (numeric) = 1.936949433259978880346464911129 absolute error = 1.16777168910599e-17 relative error = 6.0289219173913806348791156774485e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3494649617827291709106357260919 y2[1] (numeric) = 1.349464961782729166472452732658 absolute error = 4.4381829934339e-18 relative error = 3.2888464088543488882369090324888e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=698.0MB, alloc=4.6MB, time=115.67 NO POLE NO POLE x[1] = 0.358 y1[1] (analytic) = 1.9365994998817627298071565844923 y1[1] (numeric) = 1.9365994998817627180884624193303 absolute error = 1.17186941651620e-17 relative error = 6.0511707071480055147613526105924e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3504017363273645884089119742243 y2[1] (numeric) = 1.350401736327364583941738860465 absolute error = 4.4671731137593e-18 relative error = 3.3080327087763513019122863347400e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.6MB, time=116.28 NO POLE NO POLE x[1] = 0.359 y1[1] (analytic) = 1.9362486299041247357831233746356 y1[1] (numeric) = 1.9362486299041247240234982833079 absolute error = 1.17596250913277e-17 relative error = 6.0734065396911291587017899665824e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3513381604702928786863204223547 y2[1] (numeric) = 1.3513381604702928741900708128675 absolute error = 4.4962496094872e-18 relative error = 3.3272571892163650868511554052617e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.36 y1[1] (analytic) = 1.9358968236779348583509123681247 y1[1] (numeric) = 1.9358968236779348465504028303238 absolute error = 1.18005095378009e-17 relative error = 6.0956293710847524675926374471351e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3522742332750899768499134359207 y2[1] (numeric) = 1.3522742332750899723245010190542 absolute error = 4.5254124168665e-18 relative error = 3.3465197409746887944492058893643e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.6MB, time=116.88 NO POLE NO POLE x[1] = 0.361 y1[1] (analytic) = 1.935544081554999294383216458587 y1[1] (numeric) = 1.9355440815549992825418690856803 absolute error = 1.18413473729067e-17 relative error = 6.1178391573461165643805834546860e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.353209953805683156108657317552 y2[1] (numeric) = 1.353209953805683151553995845583 absolute error = 4.5546614719690e-18 relative error = 3.3658202551346556005922788763708e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.6MB, time=117.50 NO POLE NO POLE x[1] = 0.362 y1[1] (analytic) = 1.9351904038880601374204236822605 y1[1] (numeric) = 1.9351904038880601255382852172091 absolute error = 1.18821384650514e-17 relative error = 6.1400358544454185758665490019775e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3541453211263519638460810920458 y2[1] (numeric) = 1.3541453211263519592620843813566 absolute error = 4.5839967106892e-18 relative error = 3.3851586230614598564533892983435e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.363 y1[1] (analytic) = 1.9348357910307950249285530727796 y1[1] (numeric) = 1.9348357910307950130056703900565 absolute error = 1.19228826827231e-17 relative error = 6.1622194183058371486358647423107e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3550803343017291573406511461367 y2[1] (numeric) = 1.3550803343017291527272330773916 memory used=713.3MB, alloc=4.6MB, time=118.10 absolute error = 4.6134180687451e-18 relative error = 3.4045347364017258351330566873999e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.364 y1[1] (analytic) = 1.9344802433378167846216466682912 y1[1] (numeric) = 1.9344802433378167726580667737993 absolute error = 1.19635798944919e-17 relative error = 6.1843898048033511610769336974677e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3560149923968016391329360027619 y2[1] (numeric) = 1.3560149923968016344900105210843 absolute error = 4.6429254816776e-18 relative error = 3.4239484870820452020630079514740e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.6MB, time=118.72 NO POLE NO POLE x[1] = 0.365 y1[1] (analytic) = 1.9341237611646730798489713484808 y1[1] (numeric) = 1.9341237611646730678447413794711 absolute error = 1.20042299690097e-17 relative error = 6.2065469697663513660030333806713e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3569492944769113920386258627375 y2[1] (numeric) = 1.3569492944769113873661069778866 absolute error = 4.6725188848509e-18 relative error = 3.4433997673082568578480271806441e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.6MB, time=119.34 NO POLE NO POLE x[1] = 0.366 y1[1] (analytic) = 1.9337663448678460540473851142766 y1[1] (numeric) = 1.9337663448678460420025523392656 absolute error = 1.20448327750110e-17 relative error = 6.2286908689757686709839650144670e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.357883239607756413806471900903 y2[1] (numeric) = 1.3578832396077564091042736874504 absolute error = 4.7021982134526e-18 relative error = 3.4628884695645082060886183262578e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.367 y1[1] (analytic) = 1.9334079948047519742592233578357 y1[1] (numeric) = 1.9334079948047519621738351765231 absolute error = 1.20853881813126e-17 relative error = 6.2508214581646335588700859581197e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3588168268553916514202106588722 y2[1] (numeric) = 1.3588168268553916466882472563783 absolute error = 4.7319634024939e-18 relative error = 3.4824144866123932743874926332969e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.6MB, time=119.95 NO POLE NO POLE x[1] = 0.368 y1[1] (analytic) = 1.9330487113337408737160616048967 y1[1] (numeric) = 1.9330487113337408615901655480825 absolute error = 1.21258960568142e-17 relative error = 6.2729386930181005458505745699674e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3597500552862299350435392325448 y2[1] (numeric) = 1.3597500552862299302817248457355 absolute error = 4.7618143868093e-18 relative error = 3.5019777114897260637480713568777e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.6MB, time=120.57 NO POLE NO POLE x[1] = 0.369 y1[1] (analytic) = 1.9326884948140961934887121457059 y1[1] (numeric) = 1.9326884948140961813223558752075 absolute error = 1.21663562704984e-17 relative error = 6.2950425291731621594424277182478e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3606829239670429116072073094816 y2[1] (numeric) = 1.3606829239670429068154562084242 absolute error = 4.7917511010574e-18 relative error = 3.5215780375101267594538716065541e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.37 y1[1] (analytic) = 1.9323273456060344232038129044909 y1[1] (numeric) = 1.9323273456060344109970442130598 absolute error = 1.22067686914311e-17 relative error = 6.3171329222185695422022049368005e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3616154319649619780372924691272 y2[1] (numeric) = 1.3616154319649619732155189894071 absolute error = 4.8217734797201e-18 relative error = 3.5412153582614339681613136569587e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.6MB, time=121.18 NO POLE NO POLE x[1] = 0.371 y1[1] (analytic) = 1.9319652640707047408273678308622 y1[1] (numeric) = 1.9319652640707047285802346421008 absolute error = 1.22471331887614e-17 relative error = 6.3392098276944941035350611306116e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3625475783474792141237255176854 y2[1] (numeric) = 1.3625475783474792092718440605819 absolute error = 4.8518814571035e-18 relative error = 3.5608895676053705417596163213011e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.6MB, time=121.81 NO POLE NO POLE x[1] = 0.372 y1[1] (analytic) = 1.9316022505701886515155990295735 y1[1] (numeric) = 1.9316022505701886392281493978512 absolute error = 1.22874496317223e-17 relative error = 6.3612732010926028956254791790232e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3634793621824483150281329891974 y2[1] (numeric) = 1.3634793621824483101460580218599 absolute error = 4.8820749673375e-18 relative error = 3.5806005596762567361091285928271e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.6MB, time=122.44 NO POLE NO POLE x[1] = 0.373 y1[1] (analytic) = 1.9312383054674996255334717777569 y1[1] (numeric) = 1.9312383054674996132057538881264 absolute error = 1.23277178896305e-17 relative error = 6.3833229978556679926889067901078e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.364410782538085523430064305059 y2[1] (numeric) = 1.3644107825380855185177103606828 absolute error = 4.9123539443762e-18 relative error = 3.6003482288803143881432850396719e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.374 y1[1] (analytic) = 1.9308734291265827352412545110794 y1[1] (numeric) = 1.9308734291265827228733166791925 absolute error = 1.23679378318869e-17 relative error = 6.4053591733775378995239207206735e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3653418384829705613106714458277 y2[1] (numeric) = 1.3653418384829705563679531238297 absolute error = 4.9427183219980e-18 relative error = 3.6201324698947536309188698862741e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.6MB, time=123.05 NO POLE NO POLE x[1] = 0.375 y1[1] (analytic) = 1.9305076219123142911494767922296 y1[1] (numeric) = 1.9305076219123142787413674642529 absolute error = 1.24081093279767e-17 relative error = 6.4273816830029016683814876362290e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3662725290860475613729093517163 y2[1] (numeric) = 1.366272529086047556399741317911 absolute error = 4.9731680338053e-18 relative error = 3.6399531776665699947994924524684e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.6MB, time=123.69 NO POLE NO POLE x[1] = 0.376 y1[1] (analytic) = 1.9301408841905014770426492067458 y1[1] (numeric) = 1.9301408841905014645944169592765 absolute error = 1.24482322474693e-17 relative error = 6.4493904820269490686302994556794e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3672028534166259980973256316518 y2[1] (numeric) = 1.3672028534166259930936226184269 absolute error = 5.0037030132249e-18 relative error = 3.6598102474118578384982454881891e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.377 y1[1] (analytic) = 1.929773216327881984172110062437 y1[1] (numeric) = 1.9297732163278819716838036024178 absolute error = 1.24883064600192e-17 relative error = 6.4713855256955485040229048394313e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.368132810544381618432508525187 y2[1] (numeric) = 1.3681328105443816133981853316785 absolute error = 5.0343231935085e-18 relative error = 3.6797035746151990994931924925063e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.6MB, time=124.30 NO POLE NO POLE x[1] = 0.378 y1[1] (analytic) = 1.9294046186921236445183646995176 y1[1] (numeric) = 1.9294046186921236319900328641518 absolute error = 1.25283318353658e-17 relative error = 6.4933667692048549489392259224251e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3690623995393573721192624268931 y2[1] (numeric) = 1.3690623995393573670542339191611 absolute error = 5.0650285077320e-18 relative error = 3.6996330550281774539002904905272e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.6MB, time=124.94 NO POLE NO POLE x[1] = 0.379 y1[1] (analytic) = 1.929035091651824063123284149087 y1[1] (numeric) = 1.9290350916518240505549759057532 absolute error = 1.25683082433338e-17 relative error = 6.5153341677012284118179499191056e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3699916194719643416475806491373 y2[1] (numeric) = 1.3699916194719643365517617603412 absolute error = 5.0958188887961e-18 relative error = 3.7195985846688468703643178401141e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.38 y1[1] (analytic) = 1.9286646355765102494925308077246 y1[1] (numeric) = 1.9286646355765102368842952538916 absolute error = 1.26082355538330e-17 relative error = 6.5372876762808411482812745701371e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3709204694129826718454854663492 y2[1] (numeric) = 1.3709204694129826667187911969229 absolute error = 5.1266942694263e-18 relative error = 3.7396000598207640998186041091629e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.6MB, time=125.56 NO POLE NO POLE x[1] = 0.381 y1[1] (analytic) = 1.9282932508366382480685797257438 y1[1] (numeric) = 1.9282932508366382354204660888848 absolute error = 1.26481136368590e-17 relative error = 6.5592272499897510945935669382069e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3718489484335624990988058520127 y2[1] (numeric) = 1.3718489484335624939411512698397 absolute error = 5.1576545821730e-18 relative error = 3.7596373770320974311150504743893e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.6MB, time=126.20 NO POLE NO POLE x[1] = 0.382 y1[1] (analytic) = 1.9279209378035927677747050360532 y1[1] (numeric) = 1.92792093780359275508676267356 absolute error = 1.26879423624932e-17 relative error = 6.5811528438236122392831362926131e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3727770556052248802009636886848 y2[1] (numeric) = 1.3727770556052248750122639292731 absolute error = 5.1886997594117e-18 relative error = 3.7797104331148113529066493043295e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.6MB, time=126.83 NO POLE NO POLE x[1] = 0.383 y1[1] (analytic) = 1.927547696849686810630301979607 y1[1] (numeric) = 1.9275476968496867979025803787038 absolute error = 1.27277216009032e-17 relative error = 6.6030644127275921159686023588735e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3737047899998627208318396013306 y2[1] (numeric) = 1.3737047899998627156120098679877 absolute error = 5.2198297333429e-18 relative error = 3.7998191251436355812726398749070e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.384 y1[1] (analytic) = 1.9271735283481612994379159120923 y1[1] (numeric) = 1.9271735283481612866704646897495 absolute error = 1.27674512223428e-17 relative error = 6.6249619115960815813634447324295e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3746321506897417036647899351876 y2[1] (numeric) = 1.3746321506897416984137454991952 absolute error = 5.2510444359924e-18 relative error = 3.8199633504553287006417553731930e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.6MB, time=127.46 NO POLE NO POLE x[1] = 0.385 y1[1] (analytic) = 1.9267984326731847045423506047928 y1[1] (numeric) = 1.9267984326731846917352195076406 absolute error = 1.28071310971522e-17 relative error = 6.6468452952725079930744221933690e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3755591367475012161008867712188 y2[1] (numeric) = 1.3755591367475012108185429720077 absolute error = 5.2823437992111e-18 relative error = 3.8401430066475807496869532457467e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.6MB, time=128.09 NO POLE NO POLE x[1] = 0.386 y1[1] (analytic) = 1.9264224101998526696622290804899 y1[1] (numeric) = 1.9264224101998526568154679847315 absolute error = 1.28467610957584e-17 relative error = 6.6687145185492519266595664814941e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3764857472461552776294532449923 y2[1] (numeric) = 1.3764857472461552723157254903165 absolute error = 5.3137277546758e-18 relative error = 3.8603579915786461876338482826055e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.387 y1[1] (analytic) = 1.9260454613041876367943811528091 y1[1] (numeric) = 1.9260454613041876239080400641337 absolute error = 1.28863410886754e-17 relative error = 6.6905695361674598936087841042648e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3774119812590934668139668085286 y2[1] (numeric) = 1.3774119812590934614687705746403 absolute error = 5.3451962338883e-18 relative error = 3.8806082033657436055387776891496e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.6MB, time=128.70 NO POLE NO POLE x[1] = 0.388 y1[1] (analytic) = 1.9256675863631384701914327645926 y1[1] (numeric) = 1.9256675863631384572655618180882 absolute error = 1.29258709465044e-17 relative error = 6.7124103028168567777605385097690e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3783378378600818479024034492912 y2[1] (numeric) = 1.3783378378600818425256542811148 absolute error = 5.3767491681764e-18 relative error = 3.9008935403848398274183472801769e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.6MB, time=129.32 NO POLE NO POLE x[1] = 0.389 y1[1] (analytic) = 1.9252887857545800794129731476774 y1[1] (numeric) = 1.9252887857545800664476226077435 absolute error = 1.29653505399339e-17 relative error = 6.7342367731355060487414857146374e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3792633161232638970610962560513 y2[1] (numeric) = 1.3792633161232638916527097673577 absolute error = 5.4083864886936e-18 relative error = 3.9212139012694918171225962649093e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.6MB, time=129.94 NO POLE NO POLE x[1] = 0.39 y1[1] (analytic) = 1.9249090598573130414506767528811 y1[1] (numeric) = 1.9249090598573130284458970131412 absolute error = 1.30047797397399e-17 relative error = 6.7560489017096215805620664609697e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3801884151231614282311820978472 y2[1] (numeric) = 1.3801884151231614227910739714282 absolute error = 5.4401081264190e-18 relative error = 3.9415691849098376251147479120562e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.391 y1[1] (analytic) = 1.9245284090510632219277578250411 y1[1] (numeric) = 1.9245284090510632088835994082547 absolute error = 1.30441584167864e-17 relative error = 6.7778466430735350670900009039970e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.381113133934675518606710559668 y2[1] (numeric) = 1.3811131339346755131347965475101 absolute error = 5.4719140121579e-18 relative error = 3.9619592904520977033515838607562e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.6MB, time=130.56 NO POLE NO POLE x[1] = 0.392 y1[1] (analytic) = 1.9241468337164813953731364236214 y1[1] (numeric) = 1.924146833716481382289649981596 absolute error = 1.30834864420254e-17 relative error = 6.7996299517094034809443642689120e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3820374716330874337334896568294 y2[1] (numeric) = 1.3820374716330874282296855802878 absolute error = 5.5038040765416e-18 relative error = 3.9823841172974988454847169617966e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.6MB, time=131.19 NO POLE NO POLE x[1] = 0.393 y1[1] (analytic) = 1.9237643342351428645706956146894 y1[1] (numeric) = 1.9237643342351428514479319281921 absolute error = 1.31227636864973e-17 relative error = 6.8213987820471240475811758643024e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3829614272940595522277432292739 y2[1] (numeric) = 1.3829614272940595466919649792463 absolute error = 5.5357782500276e-18 relative error = 4.0028435651014911593832559983217e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.394 y1[1] (analytic) = 1.9233809109895470789840104849733 y1[1] (numeric) = 1.9233809109895470658220204636428 absolute error = 1.31619900213305e-17 relative error = 6.8431530884638331209548107853237e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3838849999936362901136552972144 y2[1] (numeric) = 1.3838849999936362845458188343148 absolute error = 5.5678364628996e-18 relative error = 4.0233375337728231412579598949027e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.6MB, time=131.79 NO POLE NO POLE x[1] = 0.395 y1[1] (analytic) = 1.9229965643631172522569305532408 y1[1] (numeric) = 1.9229965643631172390557652354982 absolute error = 1.32011653177426e-17 relative error = 6.8648928252842364310352825137472e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.384808188808245024778877040654 y2[1] (numeric) = 1.3848081888082450191788983953862 absolute error = 5.5999786452678e-18 relative error = 4.0438659234728365763246344372022e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=801.0MB, alloc=4.6MB, time=132.41 NO POLE NO POLE x[1] = 0.396 y1[1] (analytic) = 1.9226112947401999787903980783825 y1[1] (numeric) = 1.9226112947401999655501086313426 absolute error = 1.32402894470399e-17 relative error = 6.8866179467800554498645466676854e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3857309928146970185470724473521 y2[1] (numeric) = 1.3857309928146970129148677202833 absolute error = 5.6322047270688e-18 relative error = 4.0644286346144750937938455526904e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.397 y1[1] (analytic) = 1.9222251025060648493958856873514 y1[1] (numeric) = 1.9222251025060648361165234067335 absolute error = 1.32793622806179e-17 relative error = 6.9083284071699932597426867354246e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3866534110901883418665790567684 y2[1] (numeric) = 1.3866534110901883362020644187026 absolute error = 5.6645146380658e-18 relative error = 4.0850255678615125243808956845404e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.6MB, time=133.02 NO POLE NO POLE x[1] = 0.398 y1[1] (analytic) = 1.9218379880469040660258376694886 y1[1] (numeric) = 1.9218379880469040527074539795273 absolute error = 1.33183836899613e-17 relative error = 6.9300241606194401487757746958266e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3875754427123007961142606114002 y2[1] (numeric) = 1.3875754427123007904173523035515 absolute error = 5.6969083078487e-18 relative error = 4.1056566241277117659322506713806e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.6MB, time=133.65 NO POLE NO POLE x[1] = 0.399 y1[1] (analytic) = 1.9214499517498320555815002067615 y1[1] (numeric) = 1.9214499517498320422241466601169 absolute error = 1.33573535466446e-17 relative error = 6.9517051612404910509951233475646e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3884970867590028360136288117384 y2[1] (numeric) = 1.388497086759002830284243145904 absolute error = 5.7293856658344e-18 relative error = 4.1263217045761305428639018968574e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.6MB, time=134.27 NO POLE NO POLE x[1] = 0.4 y1[1] (analytic) = 1.9210609940028850827985267320518 y1[1] (numeric) = 1.92106099400288506940225500972 absolute error = 1.33962717223318e-17 relative error = 6.9733713630914944526912849384773e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3894183423086504916663117567957 y2[1] (numeric) = 1.3894183423086504859043651155293 absolute error = 5.7619466412664e-18 relative error = 4.1470207106179256259720513225975e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.401 y1[1] (analytic) = 1.9206711151950208622107455298569 y1[1] (numeric) = 1.9206711151950208487756074410796 absolute error = 1.34351380887773e-17 relative error = 6.9950227201772254683630637756879e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3903392084399882901959470388174 y2[1] (numeric) = 1.3903392084399882844013558756018 absolute error = 5.7945911632156e-18 relative error = 4.1677535439120244131502975657790e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.6MB, time=134.88 NO POLE NO POLE x[1] = 0.402 y1[1] (analytic) = 1.9202803157161181691924776156028 y1[1] (numeric) = 1.9202803157161181557185250977775 absolute error = 1.34739525178253e-17 relative error = 7.0166591864482779273572253266330e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3912596842321501770035778483565 y2[1] (numeric) = 1.3912596842321501711762586877768 absolute error = 5.8273191605797e-18 relative error = 4.1885201063637910432863525664640e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.6MB, time=135.49 NO POLE NO POLE x[1] = 0.403 y1[1] (analytic) = 1.9198885959569764500797938512206 y1[1] (numeric) = 1.9198885959569764365670789698098 absolute error = 1.35127148814108e-17 relative error = 7.0382807158012890356939757688973e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3921797687646604366336308343958 y2[1] (numeric) = 1.3921797687646604307735002723119 absolute error = 5.8601305620839e-18 relative error = 4.2093203001246311039451146453602e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.404 y1[1] (analytic) = 1.9194959563093154313711011756945 y1[1] (numeric) = 1.9194959563093154178196761241353 absolute error = 1.35514250515592e-17 relative error = 7.0598872620784348899659085778125e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3930994611174346132495548536135 y2[1] (numeric) = 1.3930994611174346073565295573328 absolute error = 5.8930252962807e-18 relative error = 4.2301540275909513813126152900835e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.6MB, time=136.11 NO POLE NO POLE x[1] = 0.405 y1[1] (analytic) = 1.9191023971657747280074487499645 y1[1] (numeric) = 1.9191023971657747144173658495777 absolute error = 1.35900829003868e-17 relative error = 7.0814787790673942769868691145507e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3940187603707804307182001332327 y2[1] (numeric) = 1.3940187603707804247921968416828 absolute error = 5.9260032915499e-18 relative error = 4.2510211914032667190643119296757e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.6MB, time=136.75 NO POLE NO POLE x[1] = 0.406 y1[1] (analytic) = 1.9187079189199134507329457358444 y1[1] (numeric) = 1.9187079189199134371042574357432 absolute error = 1.36286883001012e-17 relative error = 7.1030552205012602451573459985043e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3949376656053987123020177631507 y2[1] (numeric) = 1.3949376656053987063429532870514 absolute error = 5.9590644760993e-18 relative error = 4.2719216944458117468119636587303e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.6MB, time=137.38 NO POLE NO POLE x[1] = 0.407 y1[1] (analytic) = 1.9183125219662098125356833485036 y1[1] (numeric) = 1.9183125219662097988684422255025 absolute error = 1.36672411230011e-17 relative error = 7.1246165400581387272516253707390e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3958561759023842999581598252254 y2[1] (numeric) = 1.3958561759023842939659510472615 absolute error = 5.9922087779639e-18 relative error = 4.2928554398450790598779419706279e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.408 y1[1] (analytic) = 1.9179162067000607341695547415594 y1[1] (numeric) = 1.9179162067000607204638135000827 absolute error = 1.37057412414767e-17 relative error = 7.1461626913610594412958912659783e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3967742903432269732435608606962 y2[1] (numeric) = 1.3967742903432269672181247356894 absolute error = 6.0254361250068e-18 relative error = 4.3138223309695797867462385027803e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.6MB, time=138.01 NO POLE NO POLE x[1] = 0.409 y1[1] (analytic) = 1.9175189735177814487573672029263 y1[1] (numeric) = 1.9175189735177814350131786749162 absolute error = 1.37441885280101e-17 relative error = 7.1676936279778866151832649855905e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3976920080098123678250817707338 y2[1] (numeric) = 1.3976920080098123617663353258148 absolute error = 6.0587464449190e-18 relative error = 4.3348222714288176207532439375602e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.6MB, time=138.64 NO POLE NO POLE x[1] = 0.41 y1[1] (analytic) = 1.917120822816605105475642058277 y1[1] (numeric) = 1.9171208228166050916930592031016 absolute error = 1.37825828551754e-17 relative error = 7.1892093034210730503939868386694e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3986093279844228935937976400511 y2[1] (numeric) = 1.3986093279844228875016579748316 absolute error = 6.0921396652195e-18 relative error = 4.3558551650724809261363228808077e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.411 y1[1] (analytic) = 1.9167217549946823723214985972821 y1[1] (numeric) = 1.9167217549946823585005745016434 absolute error = 1.38209240956387e-17 relative error = 7.2107096711473616416113203440471e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.3995262493497386523825113693651 y2[1] (numeric) = 1.3995262493497386462568956561096 absolute error = 6.1256157132555e-18 relative error = 4.3769209159897090127796037577715e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.6MB, time=139.27 NO POLE NO POLE x[1] = 0.412 y1[1] (analytic) = 1.9163217704510810379620192557123 y1[1] (numeric) = 1.9163217704510810241028071335538 absolute error = 1.38592121221585e-17 relative error = 7.2321946845576951906914444850503e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4004427711888383552855753992714 y2[1] (numeric) = 1.4004427711888383491264008830692 absolute error = 6.1591745162022e-18 relative error = 4.3980194285080752111694315130332e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.6MB, time=139.90 NO POLE NO POLE x[1] = 0.413 y1[1] (analytic) = 1.915920869585785612666494204004 y1[1] (numeric) = 1.915920869585785598769047396418 absolute error = 1.38974468075860e-17 relative error = 7.2536642969970738471592346972308e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4013588925852002395801042057874 y2[1] (numeric) = 1.4013588925852002333872882047239 absolute error = 6.1928160010635e-18 relative error = 4.4191506071932157161707061052263e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.414 y1[1] (analytic) = 1.9155190527996969283219444100102 y1[1] (numeric) = 1.915519052799696914386316385145 absolute error = 1.39356280248652e-17 relative error = 7.2751184617543078934392195050466e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4022746126227029852476606464264 y2[1] (numeric) = 1.4022746126227029790211205517548 absolute error = 6.2265400946716e-18 relative error = 4.4403143568476749934576341508426e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.6MB, time=140.53 NO POLE NO POLE x[1] = 0.415 y1[1] (analytic) = 1.9151163204946317375323231603814 y1[1] (numeric) = 1.9151163204946317235585675133484 absolute error = 1.39737556470330e-17 relative error = 7.2965571320617701528251933467784e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4031899303856266310954996351939 y2[1] (numeric) = 1.4031899303856266248351529115067 absolute error = 6.2603467236872e-18 relative error = 4.4615105825101828549109371312430e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.6MB, time=141.15 NO POLE NO POLE x[1] = 0.416 y1[1] (analytic) = 1.9147126730733223118017969413405 y1[1] (numeric) = 1.9147126730733222977899673941207 absolute error = 1.40118295472198e-17 relative error = 7.3179802610954091541319040609870e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4041048449586534904764530253388 y2[1] (numeric) = 1.404104844958653484182217210739 absolute error = 6.2942358145998e-18 relative error = 4.4827391894550051343127290581461e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.6MB, time=141.78 NO POLE NO POLE x[1] = 0.417 y1[1] (analytic) = 1.9143081109394160388025074955377 y1[1] (numeric) = 1.9143081109394160247526578968884 absolute error = 1.40498495986493e-17 relative error = 7.3393878019743443409607762346180e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4050193554268690666065399800501 y2[1] (numeric) = 1.4050193554268690602783326863222 absolute error = 6.3282072937279e-18 relative error = 4.5040000831912252827950425234770e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.418 y1[1] (analytic) = 1.9139026344974750187272177871901 y1[1] (numeric) = 1.913902634497475004639402112551 absolute error = 1.40878156746391e-17 relative error = 7.3607797077608786952715653142794e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4059334608757629674793875135654 y2[1] (numeric) = 1.4059334608757629611171264263466 absolute error = 6.3622610872188e-18 relative error = 4.5252931694617438190837142458666e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.6MB, time=142.41 NO POLE NO POLE x[1] = 0.419 y1[1] (analytic) = 1.9134962441529756597272455228257 y1[1] (numeric) = 1.9134962441529756456015178742254 absolute error = 1.41257276486003e-17 relative error = 7.3821559314599887065027913091293e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4068471603912298203765462883469 y2[1] (numeric) = 1.4068471603912298139801491672984 absolute error = 6.3963971210485e-18 relative error = 4.5466183542423523234386427579700e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.6MB, time=143.04 NO POLE NO POLE x[1] = 0.42 y1[1] (analytic) = 1.9130889403123082724360887896657 y1[1] (numeric) = 1.9130889403123082582725033956272 absolute error = 1.41635853940385e-17 relative error = 7.4035164260195454242904302258009e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4077604530595701859727871580863 y2[1] (numeric) = 1.4077604530595701795421718370636 absolute error = 6.4306153210227e-18 relative error = 4.5679755437415919847125935891538e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.421 y1[1] (analytic) = 1.912680723382776663579149287984 y1[1] (numeric) = 1.9126807233827766493777605034306 absolute error = 1.42013887845534e-17 relative error = 7.4248611443298037691547191364042e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4086733379674914720354643513158 y2[1] (numeric) = 1.4086733379674914655705487385397 absolute error = 6.4649156127761e-18 relative error = 4.5893646443994054559737179290488e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.6MB, time=143.65 NO POLE NO POLE x[1] = 0.422 y1[1] (analytic) = 1.9122715937725977286699595476886 y1[1] (numeric) = 1.9122715937725977144308218538493 absolute error = 1.42391376938393e-17 relative error = 7.4461900392233617667148777772136e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4095858142021088467170315963406 y2[1] (numeric) = 1.4095858142021088402177336745678 absolute error = 6.4992979217728e-18 relative error = 4.6107855628865738907226652818113e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.6MB, time=144.27 NO POLE NO POLE x[1] = 0.423 y1[1] (analytic) = 1.9118615518909010437933214328626 y1[1] (numeric) = 1.9118615518909010295164894371771 absolute error = 1.42768319956855e-17 relative error = 7.4675030634750673566007798528541e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.410497880850946151439797895052 y2[1] (numeric) = 1.4104978808509461449060357217455 absolute error = 6.5337621733065e-18 relative error = 4.6322382061040139429088656391368e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.6MB, time=144.90 NO POLE NO POLE x[1] = 0.424 y1[1] (analytic) = 1.911450598147728456475764151092 y1[1] (numeric) = 1.9114505981477284421612925871163 absolute error = 1.43144715639757e-17 relative error = 7.4888001698014018513806227192783e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4114095370019368133720100609405 y2[1] (numeric) = 1.4114095370019368068037017684403 absolute error = 6.5683082925002e-18 relative error = 4.6537224811817228127946420416381e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.425 y1[1] (analytic) = 1.9110387329540336756437308970901 y1[1] (numeric) = 1.9110387329540336612916746244007 absolute error = 1.43520562726894e-17 relative error = 7.5100813108609090831425797151811e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4123207817434247574943495453043 y2[1] (numeric) = 1.4123207817434247508914133409973 absolute error = 6.6029362043070e-18 relative error = 4.6752382954785058168421835951389e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.6MB, time=145.51 NO POLE NO POLE x[1] = 0.426 y1[1] (analytic) = 1.9106259567216818606699041723951 y1[1] (numeric) = 1.9106259567216818462803181764938 absolute error = 1.43895859959013e-17 relative error = 7.5313464392535782594433780562858e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4132316141641653182559314852307 y2[1] (numeric) = 1.4132316141641653116182856517209 absolute error = 6.6376458335098e-18 relative error = 4.6967855565809262347311386629049e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.6MB, time=146.12 NO POLE NO POLE x[1] = 0.427 y1[1] (analytic) = 1.910212269863449209508080734783 y1[1] (numeric) = 1.9102122698634491950810201270014 absolute error = 1.44270606077816e-17 relative error = 7.5525955075206971038970812198943e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4141420333533261508188943174277 y2[1] (numeric) = 1.4141420333533261441464572127064 absolute error = 6.6724371047213e-18 relative error = 4.7183641723024709419966655487458e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.428 y1[1] (analytic) = 1.9097976727930225459170080424865 y1[1] (numeric) = 1.9097976727930225314525280598901 absolute error = 1.44644799825964e-17 relative error = 7.5738284681447570985693041935930e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.415052038400488141890668713393 y2[1] (numeric) = 1.4150520384004881351833587710088 absolute error = 6.7073099423842e-18 relative error = 4.7399740506828601873877057754906e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.6MB, time=146.75 NO POLE NO POLE x[1] = 0.429 y1[1] (analytic) = 1.9093821659249989057735949693482 y1[1] (numeric) = 1.9093821659249988912717509746402 absolute error = 1.45018439947080e-17 relative error = 7.5950452735493061613812536693633e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4159616283956463201430150037265 y2[1] (numeric) = 1.4159616283956463134007507329547 absolute error = 6.7422642707718e-18 relative error = 4.7616150999876421140929921801618e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.6MB, time=147.37 NO POLE NO POLE x[1] = 0.43 y1[1] (analytic) = 1.9089657496748851224759104776634 y1[1] (numeric) = 1.9089657496748851079367579590888 absolute error = 1.45391525185746e-17 relative error = 7.6162458760984867566121138763043e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4168708024292107662169186726246 y2[1] (numeric) = 1.4168708024292107594396186586372 absolute error = 6.7773000139874e-18 relative error = 4.7832872287069414982066178067831e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.431 y1[1] (analytic) = 1.90854842445909741143638484568 y1[1] (numeric) = 1.9085484244590973968599794169287 absolute error = 1.45764054287513e-17 relative error = 7.6374302280972544777593508948204e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4177795595920075223124339177373 y2[1] (numeric) = 1.4177795595920075155000168217726 absolute error = 6.8124170959647e-18 relative error = 4.8049903455549182246270960580087e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.6MB, time=147.99 NO POLE NO POLE x[1] = 0.432 y1[1] (analytic) = 1.9081301906949609536656289565175 y1[1] (numeric) = 1.908130190694960939052026356628 absolute error = 1.46136025998895e-17 relative error = 7.6585982817907583309840861859701e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4186878989752795013625656856203 y2[1] (numeric) = 1.4186878989752794945149502451523 absolute error = 6.8476154404680e-18 relative error = 4.8267243594690864653322362382440e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.6MB, time=148.60 NO POLE NO POLE x[1] = 0.433 y1[1] (analytic) = 1.9077110488007094784472880646543 y1[1] (numeric) = 1.9077110488007094637965441579165 absolute error = 1.46507439067378e-17 relative error = 7.6797499893645064173315937126549e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4195958196706873957902810089753 y2[1] (numeric) = 1.4195958196706873889073860378829 absolute error = 6.8828949710924e-18 relative error = 4.8484891796096360710754228740967e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=904.0MB, alloc=4.6MB, time=149.23 NO POLE NO POLE x[1] = 0.434 y1[1] (analytic) = 1.9072909991954848451043473650912 y1[1] (numeric) = 1.9072909991954848304165181409495 absolute error = 1.46878292241417e-17 relative error = 7.7008853029439025992004202115298e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4205033207703105858477408887429 y2[1] (numeric) = 1.4205033207703105789294852774792 absolute error = 6.9182556112637e-18 relative error = 4.8702847153585449752182636520426e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.435 y1[1] (analytic) = 1.9068700422993366238573075988539 y1[1] (numeric) = 1.9068700422993366091324491718097 absolute error = 1.47248584270442e-17 relative error = 7.7220041745942544630762627590532e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4214104013666480475368443818927 y2[1] (numeric) = 1.4214104013666480405831470976542 absolute error = 6.9536972842385e-18 relative error = 4.8921108763188353079062197220362e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.6MB, time=149.85 NO POLE NO POLE x[1] = 0.436 y1[1] (analytic) = 1.9064481785332216757746498366219 y1[1] (numeric) = 1.9064481785332216610128184461361 absolute error = 1.47618313904858e-17 relative error = 7.7431065563204665017320616550037e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4223170605526192601101769744414 y2[1] (numeric) = 1.422317060552619253120957061337 absolute error = 6.9892199131044e-18 relative error = 4.9139675723139022715388710583062e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.6MB, time=150.49 NO POLE NO POLE x[1] = 0.437 y1[1] (analytic) = 1.9060254083190037318160094899842 y1[1] (numeric) = 1.9060254083190037170172615003796 absolute error = 1.47987479896046e-17 relative error = 7.7641924000667852848691910850084e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4232232974215651131514557388264 y2[1] (numeric) = 1.4232232974215651061266323180461 absolute error = 7.0248234207803e-18 relative error = 4.9358547133869154541052308614035e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.438 y1[1] (analytic) = 1.9056017320794529709684805071144 y1[1] (numeric) = 1.9056017320794529561328724074774 absolute error = 1.48356080996370e-17 relative error = 7.7852616577168590816160099756932e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4241291110672488132345641952656 y2[1] (numeric) = 1.4241291110672488061740564652492 absolute error = 7.0605077300164e-18 relative error = 4.9577722098000113857679905387586e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.6MB, time=151.12 NO POLE NO POLE x[1] = 0.439 y1[1] (analytic) = 1.9051771502382455974764716165229 y1[1] (numeric) = 1.9051771502382455826040600206057 absolute error = 1.48724115959172e-17 relative error = 7.8063142810931676301134754218233e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.425034500583856790160270218143 y2[1] (numeric) = 1.425034500583856783063997454749 absolute error = 7.0962727633940e-18 relative error = 4.9797199720333484426037535225575e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.6MB, time=151.77 NO POLE NO POLE x[1] = 0.44 y1[1] (analytic) = 1.9047516632199634171655373889984 y1[1] (numeric) = 1.9047516632199634022563790351203 absolute error = 1.49091583538781e-17 relative error = 7.8273502219571860785018617956965e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4259394650659996027697207507799 y2[1] (numeric) = 1.4259394650659995956376023074539 absolute error = 7.1321184433260e-18 relative error = 5.0016979107846558722701952383791e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=923.1MB, alloc=4.6MB, time=152.41 x[1] = 0.441 y1[1] (analytic) = 1.9043252714500934128606077938682 y1[1] (numeric) = 1.9043252714500933979147595448173 absolute error = 1.49458482490509e-17 relative error = 7.8483694320088664185753271963314e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4268440036087128443338075151701 y2[1] (numeric) = 1.426844003608712837165762823113 absolute error = 7.1680446920571e-18 relative error = 5.0237059369685739009348619355504e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.442 y1[1] (analytic) = 1.9038979753550273188990408313166 y1[1] (numeric) = 1.9038979753550273039165596742507 absolute error = 1.49824811570659e-17 relative error = 7.8693718628867484383451625566462e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4277481153074580475174983273898 y2[1] (numeric) = 1.4277481153074580403134468957263 absolute error = 7.2040514316635e-18 relative error = 5.0457439617156457693923838391997e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.6MB, time=153.05 NO POLE NO POLE x[1] = 0.443 y1[1] (analytic) = 1.9034697753620611947389237276696 y1[1] (numeric) = 1.9034697753620611797198667740173 absolute error = 1.50190569536523e-17 relative error = 7.8903574661675453968698775676719e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4286517992581235889182290544272 y2[1] (numeric) = 1.4286517992581235816780904703738 absolute error = 7.2401385840534e-18 relative error = 5.0678118963718731896168604372398e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=930.7MB, alloc=4.6MB, time=153.69 NO POLE NO POLE x[1] = 0.444 y1[1] (analytic) = 1.9030406718993949976630490853117 y1[1] (numeric) = 1.9030406718993949826074735706732 absolute error = 1.50555755146385e-17 relative error = 7.9113261933659918069118212675375e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4295550545570255931774516741134 y2[1] (numeric) = 1.4295550545570255859011456031467 absolute error = 7.2763060709667e-18 relative error = 5.0899096524977134994605280993237e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.445 y1[1] (analytic) = 1.9026106653961321545789932832218 y1[1] (numeric) = 1.9026106653961321394869565672694 absolute error = 1.50920367159524e-17 relative error = 7.9322779959346909404351793403549e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4304578803009088366644343266839 y2[1] (numeric) = 1.4304578803009088293518805127081 absolute error = 7.3125538139758e-18 relative error = 5.1120371418678492306639365472525e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.6MB, time=154.33 NO POLE NO POLE x[1] = 0.446 y1[1] (analytic) = 1.9021797562822791329157253280146 y1[1] (numeric) = 1.902179756282279117787284894393 absolute error = 1.51284404336216e-17 relative error = 7.9532128252639094850036231467821e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4313602755869476507314096742436 y2[1] (numeric) = 1.4313602755869476433825279397586 absolute error = 7.3488817344850e-18 relative error = 5.1341942764699800901120408188677e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.6MB, time=154.97 NO POLE NO POLE x[1] = 0.447 y1[1] (analytic) = 1.9017479449887450106171752588427 y1[1] (numeric) = 1.9017479449887449954523887150691 absolute error = 1.51647865437736e-17 relative error = 7.9741306326813718500471871818365e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4322622395127468245391683130648 y2[1] (numeric) = 1.4322622395127468171538785593337 absolute error = 7.3852897537311e-18 relative error = 5.1563809685044569776478889817037e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.448 y1[1] (analytic) = 1.9013152319473410452331921125551 y1[1] (numeric) = 1.9013152319473410300321171899193 absolute error = 1.52010749226358e-17 relative error = 7.9950313694519489313401662678369e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4331637711763425074521944131981 y2[1] (numeric) = 1.4331637711763425000304166204149 absolute error = 7.4217777927832e-18 relative error = 5.1785971303833588163899099460798e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.6MB, time=155.61 NO POLE NO POLE x[1] = 0.449 y1[1] (analytic) = 1.9008816175907802421083223581184 y1[1] (numeric) = 1.9008816175907802268710169115823 absolute error = 1.52373054465361e-17 relative error = 8.0159149867776620217542790918312e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4340648696762031110024411903364 y2[1] (numeric) = 1.4340648696762031035440954177932 absolute error = 7.4583457725432e-18 relative error = 5.2008426747300606270644760295580e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.6MB, time=156.24 NO POLE NO POLE x[1] = 0.45 y1[1] (analytic) = 1.9004471023526769216688406114864 y1[1] (numeric) = 1.9004471023526769063953626195836 absolute error = 1.52734779919028e-17 relative error = 8.0367814357973183213061179876416e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4349655341112302104208442462319 y2[1] (numeric) = 1.4349655341112302029258506324864 absolute error = 7.4949936137455e-18 relative error = 5.2231175143782453661517077212060e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.6MB, time=156.88 NO POLE NO POLE x[1] = 0.451 y1[1] (analytic) = 1.9000116866675462858084653438511 y1[1] (numeric) = 1.900011686667546270498872908586 absolute error = 1.53095924352651e-17 relative error = 8.0576306675864616631817244792213e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4358657635807594457356712462275 y2[1] (numeric) = 1.4358657635807594382039500092702 absolute error = 7.5317212369573e-18 relative error = 5.2454215623713369930022376515553e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.452 y1[1] (analytic) = 1.8995753709708039833731931975225 y1[1] (numeric) = 1.8995753709708039680275445442698 absolute error = 1.53456486532527e-17 relative error = 8.0784626331568493100644043015386e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4367655571845614224368068356284 y2[1] (numeric) = 1.4367655571845614148682782730495 absolute error = 7.5685285625789e-18 relative error = 5.2677547319619353135849741791367e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.6MB, time=157.52 NO POLE NO POLE x[1] = 0.453 y1[1] (analytic) = 1.899138155698765674745686424569 y1[1] (numeric) = 1.8991381556987656593640399019721 absolute error = 1.53816465225969e-17 relative error = 8.0992772834567177889556731196730e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4376649140228426117050721307038 y2[1] (numeric) = 1.4376649140228426040996566198603 absolute error = 7.6054155108435e-18 relative error = 5.2901169366109048084779033725055e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.6MB, time=158.16 NO POLE NO POLE x[1] = 0.454 y1[1] (analytic) = 1.898700041288646595529648863792 y1[1] (numeric) = 1.8987000412886465801120629436617 absolute error = 1.54175859201303e-17 relative error = 8.1200745693703116742621800846963e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4385638331962462502056785550742 y2[1] (numeric) = 1.4385638331962462425632965532565 absolute error = 7.6423820018177e-18 relative error = 5.3125080899869531254597646432240e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.455 y1[1] (analytic) = 1.8982610281785611193346267716233 y1[1] (numeric) = 1.8982610281785611038811600488366 absolute error = 1.54534667227867e-17 relative error = 8.1408544417175170065950761547814e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4394623138058532394449162281053 y2[1] (numeric) = 1.4394623138058532317654882727041 absolute error = 7.6794279554012e-18 relative error = 5.3349281059656550408081754152107e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.6MB, time=158.82 NO POLE NO POLE x[1] = 0.456 y1[1] (analytic) = 1.8978211168075223196616717221096 y1[1] (numeric) = 1.8978211168075223041723829145076 absolute error = 1.54892888076020e-17 relative error = 8.1616168512540210497297279448541e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4403603549531830446891775486958 y2[1] (numeric) = 1.4403603549531830369726242573686 absolute error = 7.7165532913272e-18 relative error = 5.3573768986289657179896102249413e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.6MB, time=159.48 NO POLE NO POLE x[1] = 0.457 y1[1] (analytic) = 1.8973803076154415308903036902821 y1[1] (numeric) = 1.8973803076154415153652516385679 absolute error = 1.55250520517142e-17 relative error = 8.1823617486709978586805574720040e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4412579557401945934454170555095 y2[1] (numeric) = 1.4412579557401945856916591263469 absolute error = 7.7537579291626e-18 relative error = 5.3798543822645966750095832413386e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=968.9MB, alloc=4.6MB, time=160.13 x[1] = 0.458 y1[1] (analytic) = 1.8969386010431279083672133319129 y1[1] (numeric) = 1.8969386010431278928064569995499 absolute error = 1.55607563323630e-17 relative error = 8.2030890845945824714816465243828e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.442155115269287173502149083267 y2[1] (numeric) = 1.4421551152692871657111072949594 absolute error = 7.7910417883076e-18 relative error = 5.4023604713649776975803239767567e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.459 y1[1] (analytic) = 1.8964959975322879875971433709198 y1[1] (numeric) = 1.896495997532287972000741844029 absolute error = 1.55964015268908e-17 relative error = 8.2237988095860824963511066677347e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.443051832643301330530085174175 y2[1] (numeric) = 1.4430518326433013227016803861783 absolute error = 7.8284047879967e-18 relative error = 5.4248950806271924518414757868996e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.6MB, time=160.77 NO POLE NO POLE x[1] = 0.46 y1[1] (analytic) = 1.8960524975255252425363899035004 y1[1] (numeric) = 1.8960524975255252269044023907575 absolute error = 1.56319875127429e-17 relative error = 8.2444908741417679922907715614547e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4439481069655197652415136439289 y2[1] (numeric) = 1.4439481069655197573756667966309 absolute error = 7.8658468472980e-18 relative error = 5.4474581249517366727538220196077e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.6MB, time=161.42 NO POLE NO POLE x[1] = 0.461 y1[1] (analytic) = 1.895608101466339642989365325457 y1[1] (numeric) = 1.8956081014663396273218511579902 absolute error = 1.56675141674668e-17 relative error = 8.2651652286921862009934351258559e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4448439373396682301075241429856 y2[1] (numeric) = 1.4448439373396682222041562578719 absolute error = 7.9033678851137e-18 relative error = 5.4700495194421111801575737389178e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.462 y1[1] (analytic) = 1.8951628097991272111086654861145 y1[1] (numeric) = 1.8951628097991271954056841174009 absolute error = 1.57029813687136e-17 relative error = 8.2858218236025833252625583570999e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4457393228699164256321804959556 y2[1] (numeric) = 1.4457393228699164176912126757755 absolute error = 7.9409678201801e-18 relative error = 5.4926691794040702313226348476971e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.6MB, time=162.06 NO POLE NO POLE x[1] = 0.463 y1[1] (analytic) = 1.8947166229691795769990845687246 y1[1] (numeric) = 1.8947166229691795612606955744874 absolute error = 1.57383889942372e-17 relative error = 8.3064606091721657047050290330802e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.446634262660878896182745545017 y2[1] (numeric) = 1.4466342626608788882040989739489 absolute error = 7.9786465710681e-18 relative error = 5.5153170203452179646332358177131e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.6MB, time=162.69 NO POLE NO POLE x[1] = 0.464 y1[1] (analytic) = 1.8942695414226835334260220933066 y1[1] (numeric) = 1.8942695414226835176522851714114 absolute error = 1.57737369218952e-17 relative error = 8.3270815356342573178668483980587e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4475287558176159253750621672001 y2[1] (numeric) = 1.4475287558176159173586581110173 absolute error = 8.0164040561828e-18 relative error = 5.5379929579739842632318023208635e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.465 y1[1] (analytic) = 1.8938215656067205896287273334791 y1[1] (numeric) = 1.8938215656067205738197023038303 absolute error = 1.58090250296488e-17 relative error = 8.3476845531559294002836086912904e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4484228014456344310131950802375 y2[1] (numeric) = 1.4484228014456344229589548864737 absolute error = 8.0542401937638e-18 relative error = 5.5606969081990873721946238695621e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.6MB, time=163.31 NO POLE NO POLE x[1] = 0.466 y1[1] (analytic) = 1.8933726959692665242388273340021 y1[1] (numeric) = 1.8933726959692665083945741384391 absolute error = 1.58442531955630e-17 relative error = 8.3682696118377879107634361117049e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4493163986508888595824384974118 y2[1] (numeric) = 1.4493163986508888514902835955262 absolute error = 8.0921549018856e-18 relative error = 5.5834287871290671784600919869648e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.6MB, time=163.94 NO POLE NO POLE x[1] = 0.467 y1[1] (analytic) = 1.8929229329591909373045856104637 y1[1] (numeric) = 1.8929229329591909214251643126566 absolute error = 1.58794212978071e-17 relative error = 8.3888366617139191061136951617723e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4502095465397820802947951384674 y2[1] (numeric) = 1.4502095465397820721646470400102 absolute error = 8.1301480984572e-18 relative error = 5.6061885110712682503395758761597e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.6MB, time=164.56 NO POLE NO POLE x[1] = 0.468 y1[1] (analytic) = 1.892472277026256801421339506815 y1[1] (numeric) = 1.8924722770262567855068102921606 absolute error = 1.59145292146544e-17 relative error = 8.4093856527514122368516179129638e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4511022442191662786860325511832 y2[1] (numeric) = 1.4511022442191662705178128499604 absolute error = 8.1682197012228e-18 relative error = 5.6289759965315843574887139265403e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.469 y1[1] (analytic) = 1.8920207286211200119685650802794 y1[1] (numeric) = 1.8920207286211199960189882557966 absolute error = 1.59495768244828e-17 relative error = 8.4299165348503571684864445559234e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4519944907963438497634231466225 y2[1] (numeric) = 1.4519944907963438415570535188609 absolute error = 8.2063696277616e-18 relative error = 5.6517911602135837784182162015140e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.6MB, time=165.18 NO POLE NO POLE x[1] = 0.47 y1[1] (analytic) = 1.8915682881953289364540192765334 y1[1] (numeric) = 1.8915682881953289204694552707584 absolute error = 1.59845640057750e-17 relative error = 8.4504292578436304597666612128537e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4528862853790682907032748003964 y2[1] (numeric) = 1.4528862853790682824586770049085 absolute error = 8.2445977954879e-18 relative error = 5.6746339190178440014326932394232e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.6MB, time=165.81 NO POLE NO POLE x[1] = 0.471 y1[1] (analytic) = 1.8911149562013239629654100509787 y1[1] (numeric) = 1.8911149562013239469459194138603 absolute error = 1.60194906371184e-17 relative error = 8.4709237714965224231162087464763e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4537776270755450930973593224828 y2[1] (numeric) = 1.4537776270755450848144552008314 absolute error = 8.2829041216514e-18 relative error = 5.6975041900414261331459640361720e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.472 y1[1] (analytic) = 1.890660733092437047730045984399 y1[1] (numeric) = 1.8906607330924370316756893871932 absolute error = 1.60543565972058e-17 relative error = 8.4914000255067867062680015303766e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4546685149944326347473465492482 y2[1] (numeric) = 1.4546685149944326264260580259111 absolute error = 8.3212885233371e-18 relative error = 5.7204018905770759510229805996684e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.6MB, time=166.43 NO POLE NO POLE x[1] = 0.473 y1[1] (analytic) = 1.8902056193228912617829178333128 y1[1] (numeric) = 1.8902056193228912456937560684779 absolute error = 1.60891617648349e-17 relative error = 8.5118579695040550189528617263975e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4555589482448430710063522633121 y2[1] (numeric) = 1.4555589482448430626466013458462 absolute error = 8.3597509174659e-18 relative error = 5.7433269381129084953273396483999e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.6MB, time=167.07 NO POLE NO POLE x[1] = 0.474 y1[1] (analytic) = 1.8897496153478003367436653469044 y1[1] (numeric) = 1.889749615347800320619759327995 absolute error = 1.61239060189094e-17 relative error = 8.5322975530500976119272945088328e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4564489259363432256667085997792 y2[1] (numeric) = 1.4564489259363432172684173789854 absolute error = 8.3982912207938e-18 relative error = 5.7662792503311322686100628820774e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1014.7MB, alloc=4.6MB, time=167.70 x[1] = 0.475 y1[1] (analytic) = 1.8892927216231682097028835735269 y1[1] (numeric) = 1.8892927216231681935442943350884 absolute error = 1.61585892384385e-17 relative error = 8.5527187256382371801091017135757e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4573384471789554813930660511461 y2[1] (numeric) = 1.4573384471789554729561567012328 absolute error = 8.4369093499133e-18 relative error = 5.7892587451082874054993822284439e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.476 y1[1] (analytic) = 1.8888349386058885672182237704341 y1[1] (numeric) = 1.8888349386058885510250124678967 absolute error = 1.61932113025374e-17 relative error = 8.5731214366932912674310462437867e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4582275110831586696999366378509 y2[1] (numeric) = 1.4582275110831586612243314165985 absolute error = 8.4756052212524e-18 relative error = 5.8122653405138368332016883009768e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.6MB, time=168.33 NO POLE NO POLE x[1] = 0.477 y1[1] (analytic) = 1.8883762667537443884207449206015 y1[1] (numeric) = 1.8883762667537443721929728301743 absolute error = 1.62277720904272e-17 relative error = 8.5935056355711967788130225352022e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4591161167598889604727882670001 y2[1] (numeric) = 1.4591161167598889519584095159249 absolute error = 8.5143787510752e-18 relative error = 5.8352989548098588359239179914252e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.6MB, time=168.98 NO POLE NO POLE x[1] = 0.478 y1[1] (analytic) = 1.8879167065254074872319727502484 y1[1] (numeric) = 1.8879167065254074709697012688126 absolute error = 1.62622714814358e-17 relative error = 8.6138712715591635534107201742359e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4600042633205407510318007582506 y2[1] (numeric) = 1.4600042633205407424785709027684 absolute error = 8.5532298554822e-18 relative error = 5.8583595064505349625736372965201e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.479 y1[1] (analytic) = 1.8874562583804380536921240299613 y1[1] (numeric) = 1.8874562583804380373954146749639 absolute error = 1.62967093549974e-17 relative error = 8.6342182938750863476303302831711e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4608919498769675547373944731655 y2[1] (numeric) = 1.4608919498769675461452360227552 absolute error = 8.5921584504103e-18 relative error = 5.8814469140814341509114649020515e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.6MB, time=169.61 NO POLE NO POLE x[1] = 0.48 y1[1] (analytic) = 1.8869949227792841943999548311587 y1[1] (numeric) = 1.8869949227792841780688692405057 absolute error = 1.63310855906530e-17 relative error = 8.6545466516674858251995215532860e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4617791755414828891366429425886 y2[1] (numeric) = 1.4617791755414828805054784909561 absolute error = 8.6311644516325e-18 relative error = 5.9045610965385939352723763170355e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.6MB, time=170.25 NO POLE NO POLE x[1] = 0.481 y1[1] (analytic) = 1.8865327001832814720646922980094 y1[1] (numeric) = 1.8865327001832814556992922299586 absolute error = 1.63654000680508e-17 relative error = 8.6748562940153963768999058287286e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4626659394268611636496813457004 y2[1] (numeric) = 1.4626659394268611549794335709417 absolute error = 8.6702477747587e-18 relative error = 5.9277019728483567553024413581847e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.482 y1[1] (analytic) = 1.8860695910546524441705103828338 y1[1] (numeric) = 1.8860695910546524277708577158882 absolute error = 1.63996526669456e-17 relative error = 8.6951471699277234965722713541250e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4635522406463385667952231544191 y2[1] (numeric) = 1.4635522406463385580858148191836 absolute error = 8.7094083352355e-18 relative error = 5.9508694622265232982725977577273e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1033.7MB, alloc=4.6MB, time=170.88 NO POLE NO POLE x[1] = 0.483 y1[1] (analytic) = 1.8856055958565062007540108804759 y1[1] (numeric) = 1.8856055958565061843201676132757 absolute error = 1.64338432672002e-17 relative error = 8.7154192283436608007905904985109e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4644380783136139529542977177052 y2[1] (numeric) = 1.4644380783136139442056516693591 absolute error = 8.7486460483461e-18 relative error = 5.9740634840775769117624015249329e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.6MB, time=171.52 NO POLE NO POLE x[1] = 0.484 y1[1] (analytic) = 1.8851407150528379012951719841238 y1[1] (numeric) = 1.8851407150528378848272002353389 absolute error = 1.64679717487849e-17 relative error = 8.7356724181320997053653789184274e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4653234515428497286713220221064 y2[1] (numeric) = 1.4653234515428497198833611928952 absolute error = 8.7879608292112e-18 relative error = 5.9972839579945929839880539653932e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.6MB, time=172.15 NO POLE NO POLE x[1] = 0.485 y1[1] (analytic) = 1.8846749491085283107222274715935 y1[1] (numeric) = 1.8846749491085282942201894798161 absolute error = 1.65020379917774e-17 relative error = 8.7559066880912503911569756427065e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4662083594486727384916203275428 y2[1] (numeric) = 1.4662083594486727296642677347548 absolute error = 8.8273525927880e-18 relative error = 6.0205308037578525066264530150089e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.486 y1[1] (analytic) = 1.884208298489343334530940517158 y1[1] (numeric) = 1.8842082984893433179948986407941 absolute error = 1.65360418763639e-17 relative error = 8.7761219869488990025964329597957e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4670928011461751503345058408895 y2[1] (numeric) = 1.4670928011461751414676845870182 absolute error = 8.8668212538713e-18 relative error = 6.0438039413348917730004547103496e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.6MB, time=172.78 NO POLE NO POLE x[1] = 0.487 y1[1] (analytic) = 1.8837407636619335530187370096079 y1[1] (numeric) = 1.8837407636619335364487537267694 absolute error = 1.65699832828385e-17 relative error = 8.7963182633617626919980506877889e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4679767757509153404010390543462 y2[1] (numeric) = 1.4679767757509153314946723272529 absolute error = 8.9063667270933e-18 relative error = 6.0671032908796660404118664001224e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.6MB, time=173.41 NO POLE NO POLE x[1] = 0.488 y1[1] (analytic) = 1.8832723450938337546341641423728 y1[1] (numeric) = 1.883272345093833738030302050769 absolute error = 1.66038620916038e-17 relative error = 8.8164954659154808157702045491808e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4688602823789187776155778409106 y2[1] (numeric) = 1.468860282378918768669588913987 absolute error = 8.9459889269236e-18 relative error = 6.0904287727318520920301544801420e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.489 y1[1] (analytic) = 1.882803043253462468442140926205 y1[1] (numeric) = 1.8828030432534624518044627430339 absolute error = 1.66376781831711e-17 relative error = 8.8366535431243935907488867317364e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4697433201466789076002348654785 y2[1] (numeric) = 1.4697433201466788986145470978092 absolute error = 8.9856877676693e-18 relative error = 6.1137803074162210740310495838169e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.6MB, time=174.02 NO POLE NO POLE x[1] = 0.49 y1[1] (analytic) = 1.8823328586101214957054681591367 y1[1] (numeric) = 1.8823328586101214790340367209762 absolute error = 1.66714314381605e-17 relative error = 8.8567924434312672170656159553988e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.470625888171158036181358337188 y2[1] (numeric) = 1.4706258881711580271558951737122 absolute error = 9.0254631634758e-18 relative error = 6.1371578156424893021736040025318e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.6MB, time=174.65 NO POLE NO POLE x[1] = 0.491 y1[1] (analytic) = 1.8818617916339954405830662721614 y1[1] (numeric) = 1.8818617916339954238779445348603 absolute error = 1.67051217373011e-17 relative error = 8.8769121152070716507268380275902e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4715079855697882124271525965983 y2[1] (numeric) = 1.4715079855697882033618375682726 absolute error = 9.0653150283257e-18 relative error = 6.1605612183038781375519290046103e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1060.5MB, alloc=4.6MB, time=175.28 x[1] = 0.492 y1[1] (analytic) = 1.8813898427961512399454103523624 y1[1] (numeric) = 1.8813898427961512232066613909312 absolute error = 1.67387489614312e-17 relative error = 8.8970125067507579648878323502108e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4723896114604721112155555001594 y2[1] (numeric) = 1.4723896114604721021103122241193 absolute error = 9.1052432760401e-18 relative error = 6.1839904364773087684999219111267e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.493 y1[1] (analytic) = 1.8809170125685376923076325280146 y1[1] (numeric) = 1.8809170125685376755353195365159 absolute error = 1.67723129914987e-17 relative error = 8.9170935662891416294610739460869e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4732707649615839153314900341658 y2[1] (numeric) = 1.4732707649615839061862422138877 absolute error = 9.1452478202781e-18 relative error = 6.2074453914223742488584804811226e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.6MB, time=175.91 NO POLE NO POLE x[1] = 0.494 y1[1] (analytic) = 1.8804433014239849858807627825173 y1[1] (numeric) = 1.8804433014239849690749490739564 absolute error = 1.68058137085609e-17 relative error = 8.9371552419764664634876022658728e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4741514451919701970926080610182 y2[1] (numeric) = 1.4741514451919701879072794864809 absolute error = 9.1853285745373e-18 relative error = 6.2309260045809933095653749715484e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.6MB, time=176.54 NO POLE NO POLE x[1] = 0.495 y1[1] (analytic) = 1.8799687098362042257415801458792 y1[1] (numeric) = 1.8799687098362042089023291520939 absolute error = 1.68392509937853e-17 relative error = 8.9571974818944997742714974460782e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4750316512709507995026445721214 y2[1] (numeric) = 1.4750316512709507902771591199679 absolute error = 9.2254854521535e-18 relative error = 6.2544321975765227804129057927532e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.496 y1[1] (analytic) = 1.8794932382797869601215470938628 y1[1] (numeric) = 1.8794932382797869432489223654136 absolute error = 1.68726247284492e-17 relative error = 8.9772202340519890928029773839262e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.475911382318319716931501294139 y2[1] (numeric) = 1.4759113823183197076657829278377 absolute error = 9.2657183663013e-18 relative error = 6.2779638922134827136419617916246e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.6MB, time=177.18 NO POLE NO POLE x[1] = 0.497 y1[1] (analytic) = 1.8790168872302047058153008658165 y1[1] (numeric) = 1.8790168872302046889093660718765 absolute error = 1.69059347939400e-17 relative error = 8.9972234463844905420323297884307e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4767906374543459753211789685932 y2[1] (numeric) = 1.4767906374543459660151517385996 absolute error = 9.3060272299936e-18 relative error = 6.3015210104765373661345446335237e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1075.7MB, alloc=4.6MB, time=177.80 NO POLE NO POLE x[1] = 0.498 y1[1] (analytic) = 1.8785396571638084727091762926628 y1[1] (numeric) = 1.8785396571638084557699952209068 absolute error = 1.69391810717560e-17 relative error = 9.0172070667544630293064715078384e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4776694157997745119166780989527 y2[1] (numeric) = 1.4776694157997745025702661428702 absolute error = 9.3464119560825e-18 relative error = 6.3251034745304269939396038508309e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.499 y1[1] (analytic) = 1.8780615485578282874302356064793 y1[1] (numeric) = 1.8780615485578282704578721629733 absolute error = 1.69723634435060e-17 relative error = 9.0371710429507235477975302721019e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4785477164758270545209884343788 y2[1] (numeric) = 1.4785477164758270451341159771198 absolute error = 9.3868724572590e-18 relative error = 6.3487112067190880206279837299929e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.6MB, time=178.43 NO POLE NO POLE x[1] = 0.5 y1[1] (analytic) = 1.8775825618903727161162815826038 y1[1] (numeric) = 1.8775825618903726991107997916944 absolute error = 1.70054817909094e-17 relative error = 9.0571153226881678679799710020717e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4794255386042030002732879352156 y2[1] (numeric) = 1.4794255386042029908458792891625 absolute error = 9.4274086460531e-18 relative error = 6.3723441295650464553106325158691e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.6MB, time=179.06 NO POLE NO POLE x[1] = 0.501 y1[1] (analytic) = 1.8771026976404283863073312442114 y1[1] (numeric) = 1.8771026976404283692687952484143 absolute error = 1.70385359957971e-17 relative error = 9.0770398536079169109555371034283e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4803028813070802939494724420977 y2[1] (numeric) = 1.4803028813070802844814520072636 absolute error = 9.4680204348341e-18 relative error = 6.3960021657689483175667811081865e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.6MB, time=179.69 NO POLE NO POLE x[1] = 0.502 y1[1] (analytic) = 1.8766219562878595079590282378478 y1[1] (numeric) = 1.8766219562878594908875022977367 absolute error = 1.70715259401111e-17 relative error = 9.0969445832767705337064710630062e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4811797437071163057841377482187 y2[1] (numeric) = 1.481179743707116296275430012408 absolute error = 9.5087077358107e-18 relative error = 6.4196852382089564467266147134465e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.503 y1[1] (analytic) = 1.8761403383134073935784728664688 y1[1] (numeric) = 1.876140338313407376474021360564 absolute error = 1.71044515059048e-17 relative error = 9.1168294591870335029792176772996e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4820561249274487088131362528522 y2[1] (numeric) = 1.4820561249274486992636657918211 absolute error = 9.5494704610311e-18 relative error = 6.4433932699401491973584373721129e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.6MB, time=180.32 NO POLE NO POLE x[1] = 0.504 y1[1] (analytic) = 1.8756578441986899774829496441145 y1[1] (numeric) = 1.8756578441986899603456370687712 absolute error = 1.71373125753433e-17 relative error = 9.1366944287563411217135672433291e-16 % Correct digits = 17 h = 0.001 y2[1] (analytic) = 1.4829320240916963557358308536409 y2[1] (numeric) = 1.4829320240916963461455223312578 absolute error = 9.5903085223831e-18 relative error = 6.4671261841939210133516193114452e-16 % Correct digits = 17 h = 0.001 Finished! Maximum Time Reached before Solution Completed! diff ( y1 , x , 1 ) = m1 * y2 + 1.0; diff ( y2 , x , 1 ) = y1 - 1.0; Iterations = 404 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 1 Hours 10 Minutes 32 Seconds Optimized Time Remaining = 1 Hours 10 Minutes 21 Seconds Expected Total Time = 1 Hours 13 Minutes 21 Seconds Time to Timeout Unknown Percent Done = 4.091 % > quit memory used=1092.9MB, alloc=4.6MB, time=180.63