|\^/| 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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y2[1]) < min_size) then # if number 1 > min_size := omniabs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (omniabs(array_y1[1]) < min_size) then # if number 1 > min_size := omniabs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y2[1]) < min_size then min_size := omniabs(array_y2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if omniabs(array_y1[1]) < min_size then min_size := omniabs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > value3 := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; value3 := omniabs(array_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr <> 0.0) 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_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[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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 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_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[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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc, 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_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[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float) 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[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_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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 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_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 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_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 3; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 3 > display_pole(); > fi;# end if 3 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, 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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 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[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (omniabs(array_y1_higher[1, m]) < glob_small_float 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[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_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[1, 1] := glob_large_float; array_complex_pole[1, 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[1, 1] := glob_large_float; array_complex_pole[1, 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[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_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[2, 1] := glob_large_float; array_complex_pole[2, 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[2, 1] := glob_large_float; array_complex_pole[2, 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[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_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 order_d = 1 > array_tmp1[1] := array_y1_higher[2,1]; > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_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; > #emit pre sin 1 $eq_no = 2 > array_tmp4[1] := sin(array_x[1]); > array_tmp4_g[1] := cos(array_x[1]); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 order_d = 1 > array_tmp1[2] := array_y1_higher[2,2]; > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_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; > #emit pre sin ID_LINEAR iii = 2 $eq_no = 2 > array_tmp4[2] := array_tmp4_g[1] * array_x[2] / 1; > array_tmp4_g[2] := -array_tmp4[1] * array_x[2] / 1; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 order_d = 1 > array_tmp1[3] := array_y1_higher[2,3]; > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_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; > #emit pre sin ID_LINEAR iii = 3 $eq_no = 2 > array_tmp4[3] := array_tmp4_g[2] * array_x[2] / 2; > array_tmp4_g[3] := -array_tmp4[2] * array_x[2] / 2; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 order_d = 1 > array_tmp1[4] := array_y1_higher[2,4]; > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_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; > #emit pre sin ID_LINEAR iii = 4 $eq_no = 2 > array_tmp4[4] := array_tmp4_g[3] * array_x[2] / 3; > array_tmp4_g[4] := -array_tmp4[3] * array_x[2] / 3; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 order_d = 1 > array_tmp1[5] := array_y1_higher[2,5]; > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_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; > #emit pre sin ID_LINEAR iii = 5 $eq_no = 2 > array_tmp4[5] := array_tmp4_g[4] * array_x[2] / 4; > array_tmp4_g[5] := -array_tmp4[4] * array_x[2] / 4; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y1_higher[2,kkk]; > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp2[kkk] * expt(glob_h , (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_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; > #emit sin LINEAR $eq_no = 2 > array_tmp4[kkk] := array_tmp4_g[kkk - 1] * array_x[2] / (kkk - 1); > array_tmp4_g[kkk] := -array_tmp4[kkk - 1] * array_x[2] / (kkk - 1); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp4[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; > 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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_y1_higher[2, 1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[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_tmp4[1] := sin(array_x[1]); array_tmp4_g[1] := cos(array_x[1]); if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[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_tmp1[2] := array_y1_higher[2, 2]; array_tmp2[2] := array_tmp1[2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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_tmp4[2] := array_tmp4_g[1]*array_x[2]; array_tmp4_g[2] := -array_tmp4[1]*array_x[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[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_tmp1[3] := array_y1_higher[2, 3]; array_tmp2[3] := array_tmp1[3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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_tmp4[3] := 1/2*array_tmp4_g[2]*array_x[2]; array_tmp4_g[3] := -1/2*array_tmp4[2]*array_x[2]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[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_tmp1[4] := array_y1_higher[2, 4]; array_tmp2[4] := array_tmp1[4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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_tmp4[4] := 1/3*array_tmp4_g[3]*array_x[2]; array_tmp4_g[4] := -1/3*array_tmp4[3]*array_x[2]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[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_tmp1[5] := array_y1_higher[2, 5]; array_tmp2[5] := array_tmp1[5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[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; array_tmp4[5] := 1/4*array_tmp4_g[4]*array_x[2]; array_tmp4_g[5] := -1/4*array_tmp4[4]*array_x[2]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[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; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y1_higher[2, kkk]; array_tmp2[kkk] := array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*expt(glob_h, order_d)/ factorial_3(kkk - 1, kkk + order_d - 1); array_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; array_tmp4[kkk] := array_tmp4_g[kkk - 1]*array_x[2]/(kkk - 1); array_tmp4_g[kkk] := -array_tmp4[kkk - 1]*array_x[2]/(kkk - 1); order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp4[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; 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(2.0 - cos(x)); > end; exact_soln_y1 := proc(x) return 2.0 - cos(x) end proc > exact_soln_y2 := proc(x) > return(2.0 - cos(x)); > end; exact_soln_y2 := proc(x) return 2.0 - cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, 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, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4_g, > array_tmp4, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_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/mtest5postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = sin ( x ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"#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(2.0 - cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(2.0 - cos(x));"); > omniout_str(ALWAYS,"end;"); > 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_y2_init:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4_g:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_m1:= Array(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_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[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_g[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_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_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 <= max_terms) do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := 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_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4_g[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_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_h := 0.00001 ; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > #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_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := false; > array_y2_set_initial[1,3] := false; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 3 > glob_h := glob_display_interval; > fi;# end if 3; > 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_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 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_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_log10normmin := -glob_large_float ; > 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) > ; > 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) > ; > 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_y2 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > 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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = sin ( x ) ;"); > 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,"2012-12-15T00:14:26-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest5") > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;") > ; > 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,"mtest5 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest5 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 ( y1 , x , 1 ) = sin ( x ) ;") > ; > 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_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_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/mtest5postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = sin ( x ) ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "#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(2.0 - cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(2.0 - cos(x));"); omniout_str(ALWAYS, "end;"); 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_y2_init := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4_g := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_m1 := Array(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_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[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_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_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 <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := 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_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4_g[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_h := 0.00001; glob_max_iter := 20; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_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_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := false; array_y2_set_initial[1, 3] := false; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; 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_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 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_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_log10normmin := -glob_large_float; 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); 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); 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_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; 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; 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 ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = sin ( x ) ;"); 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, "2012-12-15T00:14:26-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest5"); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = diff ( y1, x , 1) ;"); 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, "mtest5 diffeq.mxt"); logitem_str(html_log_file, "mtest5 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 ( y1 , x , 1 ) = sin ( x ) ;") ; 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/mtest5postode.ode################# diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_h := 0.00001 ; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(2.0 - cos(x)); end; exact_soln_y2 := proc(x) return(2.0 - cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 memory used=3.8MB, alloc=3.1MB, time=0.41 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 4.9 estimated_steps = 4900 step_error = 2.0408163265306122448979591836735e-14 est_needed_step_err = 2.0408163265306122448979591836735e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 1.0840891168028036962949267592986e-99 max_value3 = 1.0840891168028036962949267592986e-99 value3 = 1.0840891168028036962949267592986e-99 best_h = 0.001 START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.0049958347219742339044380121961 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.0049958347219742339044380121961 y1[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 x[1] = 0.1 y2[1] (analytic) = 1.0049958347219742339044380121961 y2[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.0049958347219742339044380121961 y1[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 1.005096165624023340621597000171 y2[1] (numeric) = 1.0050959168785386879913953446422 absolute error = 2.487454846526302016555288e-07 relative error = 2.4748426385468722246457892790858e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 1.005096165624023340621597000171 y1[1] (numeric) = 1.0050961656240233406699643058562 absolute error = 4.83673056852e-20 relative error = 4.8122067658243135951359049184283e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.90 NO POLE NO POLE x[1] = 0.102 y2[1] (analytic) = 1.0051974914298239146653143235401 y2[1] (numeric) = 1.0051969939639926090970839890418 absolute error = 4.974658313055682303344983e-07 relative error = 4.9489362592614262175472539598470e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 1.0051974914298239146653143235401 y1[1] (numeric) = 1.0051974914298239147620440482383 absolute error = 9.67297246982e-20 relative error = 9.6229572320767191925391374928029e-18 % Correct digits = 19 h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.4MB, time=1.40 NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 1.0052998120380501586788328071734 y2[1] (numeric) = 1.00529906587725892019067301343 absolute error = 7.461607912384881597937434e-07 relative error = 7.4222712697597351170754364123005e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 1.0052998120380501586788328071734 y1[1] (numeric) = 1.0052998120380501588239200158499 absolute error = 1.450872086765e-19 relative error = 1.4432232746802554115959902071276e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 1.0054031273463814729626255055154 y2[1] (numeric) = 1.0054021325162657165118438128773 absolute error = 9.948301157564507816926381e-07 relative error = 9.8948380873069626185062653545595e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 1.0054031273463814729626255055154 y1[1] (numeric) = 1.0054031273463814731560652147781 absolute error = 1.934397092627e-19 relative error = 1.9240014676824866665069432933987e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=1.90 NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 1.0055074372515025577949868753959 y2[1] (numeric) = 1.0055061937779463676426863638163 absolute error = 1.2434735561901523005115796e-06 relative error = 0.00012366627138921185968692360093448 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0055074372515025577949868753959 y1[1] (numeric) = 1.0055074372515025580367740535003 absolute error = 2.417871781044e-19 relative error = 2.4046284407931532749010893617440e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=2.41 NO POLE NO POLE x[1] = 0.106 y2[1] (analytic) = 1.0056127416491035167473238881278 y2[1] (numeric) = 1.0056112495582396205743210530664 absolute error = 1.4920908638961730028350614e-06 relative error = 0.00014837628861476977800318379483821 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0056127416491035167473238881278 y1[1] (numeric) = 1.0056127416491035170374534549817 absolute error = 2.901295668539e-19 relative error = 2.8851023345042024765847792310386e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.107 y2[1] (analytic) = 1.0057190404338799609940437656082 y2[1] (numeric) = 1.0057172997520897037681430149424 absolute error = 1.7406817902572259007506658e-06 relative error = 0.00017307833701808744513849995139014 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0057190404338799609940437656082 y1[1] (numeric) = 1.0057190404338799613325105927772 absolute error = 3.384668271690e-19 relative error = 3.3654212912483104042901073827821e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=2.92 NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 1.0058263334995331146169340305467 y2[1] (numeric) = 1.005824344253446432211584915212 absolute error = 1.9892460866824053491153347e-06 relative error = 0.00019777232116813818925278903740075 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0058263334995331146169340305467 y1[1] (numeric) = 1.005826333499533115003732941259 absolute error = 3.867989107123e-19 relative error = 3.8455834554114857509889324706029e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=3.43 NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 1.0059346207387699209039295664461 y2[1] (numeric) = 1.0059323829552653134682931261482 absolute error = 2.2377835046074356364402979e-06 relative error = 0.00022245814573555304907841866258608 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0059346207387699209039295664461 y1[1] (numeric) = 1.005934620738769921339055335598 absolute error = 4.351257691519e-19 relative error = 4.3255869733595474165389586317185e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.11 y2[1] (analytic) = 1.0060439020433031496421603885802 y2[1] (numeric) = 1.0060414157495076547226112425088 absolute error = 2.4862937954949195491460714e-06 relative error = 0.00024713571549364671766050163935921 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0060439020433031496421603885802 y1[1] (numeric) = 1.006043902043303150125607742741 absolute error = 4.834473541608e-19 relative error = 4.8054299934516274677430909566628e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=3.94 NO POLE NO POLE x[1] = 0.111 y2[1] (analytic) = 1.006154177303851505405172832928 y2[1] (numeric) = 1.0061514425271406708182638939685 absolute error = 2.7347767108345869089389595e-06 relative error = 0.00027180493531944096090606219549875 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.006154177303851505405172832928 y1[1] (numeric) = 1.0061541773038515059369364503455 absolute error = 5.317636174175e-19 relative error = 5.2851106660655558436180354567542e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=4.45 NO POLE NO POLE x[1] = 0.112 y2[1] (analytic) = 1.0062654464101397368342158758533 y2[1] (numeric) = 1.0062624631781375932911328153294 absolute error = 2.9832320021435430830605239e-06 relative error = 0.00029646571019468548853106019605915 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0062654464101397368342158758533 y1[1] (numeric) = 1.006265446410139737414290386459 absolute error = 5.800745106057e-19 relative error = 5.7646271436142480245422983030641e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.113 y2[1] (analytic) = 1.0063777092508987469134833032516 y2[1] (numeric) = 1.0063744775914777803960161417421 absolute error = 3.2316594209665174671615095e-06 relative error = 0.00032111794520687625509828646820487 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0063777092508987469134833032516 y1[1] (numeric) = 1.006377709250898747541863288666 absolute error = 6.283799854144e-19 relative error = 6.2439775805660197202163014286936e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=4.96 NO POLE NO POLE x[1] = 0.114 y2[1] (analytic) = 1.0064909657138657042392014539315 y2[1] (numeric) = 1.0064874856551468281272609021877 absolute error = 3.4800587188761119405517438e-06 relative error = 0.00034576154555027116894397091799198 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0064909657138657042392014539315 y1[1] (numeric) = 1.0064909657138657049158814474699 absolute error = 6.766799935384e-19 relative error = 6.7231601334688250843944272665536e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=5.47 NO POLE NO POLE x[1] = 0.115 y2[1] (analytic) = 1.0066052156857841552824512681535 y2[1] (numeric) = 1.0066014872561366822331576905975 absolute error = 3.7284296474730492935775560e-06 relative error = 0.0003703964165269031868965693026335 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0066052156857841552824512681535 y1[1] (numeric) = 1.006605215685784156007425754831 absolute error = 7.249744866775e-19 relative error = 7.2021729609615264110954250682799e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=5.97 NO POLE NO POLE x[1] = 0.116 y2[1] (analytic) = 1.006720459052404137645612378511 y2[1] (numeric) = 1.0067164822804457512239855002248 absolute error = 3.9767719583864216268782862e-06 relative error = 0.00039502246354759077279760714077843 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.006720459052404137645612378511 y1[1] (numeric) = 1.0067204590524041384188757950483 absolute error = 7.732634165373e-19 relative error = 7.6810142238010115510705293688028e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.117 y2[1] (analytic) = 1.006836695698482294312315986721 y2[1] (numeric) = 1.0068324706130790203735937132336 absolute error = 4.2250854032739387222734874e-06 relative error = 0.00041963959213294569794165509893348 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.006836695698482294312315986721 y1[1] (numeric) = 1.0068366956984822951338627215497 absolute error = 8.215467348287e-19 relative error = 8.1596820848763428675952957453976e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=6.46 NO POLE NO POLE x[1] = 0.118 y2[1] (analytic) = 1.00695392550778198889079227638 y2[1] (numeric) = 1.0069494521380481667144072439316 absolute error = 4.4733697338221763850324484e-06 relative error = 0.00044424770791437816166048127403506 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.00695392550778198889079227638 y1[1] (numeric) = 1.0069539255077819897606166696485 absolute error = 8.698243932685e-19 relative error = 8.6381747092337819386911163163761e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=6.96 NO POLE NO POLE x[1] = 0.119 y2[1] (analytic) = 1.0070721483630734218504971183478 y2[1] (numeric) = 1.0070674267383716750257398406521 absolute error = 4.7216247017468247572776957e-06 relative error = 0.00046884671663509921038516667384399 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0070721483630734218504971183478 y1[1] (numeric) = 1.007072148363073422768593461927 absolute error = 9.180963435792e-19 relative error = 9.1164902640938141450305670993177e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.12 y2[1] (analytic) = 1.0071913641461337477519018321424 y2[1] (numeric) = 1.007186394296074954815299557981 absolute error = 4.9698500587929366022741614e-06 relative error = 0.00049343652415112043362947370369853 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0071913641461337477519018321424 y1[1] (numeric) = 1.007191364146133748718264369631 absolute error = 9.663625374886e-19 relative error = 9.5946269188661363562533573747258e-17 % Correct digits = 18 h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.5MB, time=7.46 NO POLE NO POLE x[1] = 0.121 y2[1] (analytic) = 1.0073115727377471934693287735644 y2[1] (numeric) = 1.0073063546921904582937694178332 absolute error = 5.2180455567351755593557312e-06 relative error = 0.00051801703643225091544801688435515 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0073115727377471934693287735644 y1[1] (numeric) = 1.0073115727377471944839517002951 absolute error = 1.0146229267307e-18 relative error = 1.0072582845177500130002470317079e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=7.97 NO POLE NO POLE x[1] = 0.122 y2[1] (analytic) = 1.007432774017705177406714525728 y2[1] (numeric) = 1.0074273078067577993423452848074 absolute error = 5.4662109473780643692409206e-06 relative error = 0.00054258815956309142003379453065003 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.007432774017705177406714525728 y1[1] (numeric) = 1.007432774017705178469591988773 absolute error = 1.0628774630450e-18 relative error = 1.0550356216883613190328908353595e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.123 y2[1] (analytic) = 1.0075549678648064297061814777427 y2[1] (numeric) = 1.007549253518823873473111988292 absolute error = 5.7143459825562330694894507e-06 relative error = 0.0005671497997440257902313912453586 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0075549678648064297061814777427 y1[1] (numeric) = 1.0075549678648064308173075759196 absolute error = 1.1111260981769e-18 relative error = 1.1027945210091909631631075294724e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.5MB, time=8.47 NO POLE NO POLE x[1] = 0.124 y2[1] (analytic) = 1.007678154156857113449297582485 y2[1] (numeric) = 1.007672191706442978782137730955 absolute error = 5.9624504141346671598515300e-06 relative error = 0.00059170186329220953785464929288523 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.007678154156857113449297582485 y1[1] (numeric) = 1.007678154156857114608666366363 absolute error = 1.1593687838780e-18 relative error = 1.1505348003183270680482602094481e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=8.96 NO POLE NO POLE x[1] = 0.125 y2[1] (analytic) = 1.0078023327706709468509030922118 y2[1] (numeric) = 1.0077961222466769378951658305345 absolute error = 6.2105239940089557372616773e-06 relative error = 0.00061624425664255560481082363148166 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0078023327706709468509030922118 y1[1] (numeric) = 1.0078023327706709480585085641172 absolute error = 1.2076054719054e-18 relative error = 1.1982562776823766070710820311518e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.126 y2[1] (analytic) = 1.0079275035820693264453820781963 y2[1] (numeric) = 1.0079210450155952209057818492475 absolute error = 6.4585664741055396002289488e-06 relative error = 0.00064077688634871727414717432705123 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0079275035820693264453820781963 y1[1] (numeric) = 1.0079275035820693277012181922189 absolute error = 1.2558361140226e-18 relative error = 1.2459587713992219707818996616763e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=9.46 NO POLE NO POLE x[1] = 0.127 y2[1] (analytic) = 1.0080536664658814512652555481279 y2[1] (numeric) = 1.0080469598882750693059331726606 absolute error = 6.7065776063819593223754673e-06 relative error = 0.0006652996590840682102506051255071 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0080536664658814512652555481279 y1[1] (numeric) = 1.0080536664658814525693162101268 absolute error = 1.3040606619989e-18 relative error = 1.2936420999992833129922877011455e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=9.96 NO POLE NO POLE x[1] = 0.128 y2[1] (analytic) = 1.0081808212959444480119719826911 y2[1] (numeric) = 1.0081738667388016209086771075129 absolute error = 6.9545571428271032948751782e-06 relative error = 0.00068981248164267960754631975608026 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0081808212959444480119719826911 y1[1] (numeric) = 1.0081808212959444493642510503008 absolute error = 1.3522790676097e-18 relative error = 1.3413060822476684585473909402488e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.129 y2[1] (analytic) = 1.0083089679451034972187701205446 y2[1] (numeric) = 1.0083017654402680357630325757541 absolute error = 7.2025048354614557375447905e-06 relative error = 0.00071431526094029442715753260075991 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0083089679451034972187701205446 y1[1] (numeric) = 1.0083089679451034986192614031812 absolute error = 1.4004912826366e-18 relative error = 1.3889505371461186161198882003857e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=10.45 NO POLE NO POLE x[1] = 0.13 y2[1] (analytic) = 1.0084381062852119604054878288482 y2[1] (numeric) = 1.0084306558647756230608094899558 absolute error = 7.4504204363373446783388924e-06 relative error = 0.00073880790401529870110502985548359 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0084381062852119604054878288482 y1[1] (numeric) = 1.0084381062852119618541850877156 absolute error = 1.4486972588674e-18 relative error = 1.4365752839348491924192235518974e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=10.95 NO POLE NO POLE x[1] = 0.131 y2[1] (analytic) = 1.0085682361871315082251899045384 y2[1] (numeric) = 1.0085605378834339690352889032778 absolute error = 7.6983036975391899010012606e-06 relative error = 0.00076329031802968988374282424796756 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0085682361871315082251899045384 y1[1] (numeric) = 1.0085682361871315097220868526346 absolute error = 1.4968969480962e-18 relative error = 1.4841801420944840578262892420310e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.132 y2[1] (analytic) = 1.008699357520732249602486659737 y2[1] (numeric) = 1.0086914113663610658516260353194 absolute error = 7.9461543711837508606244176e-06 relative error = 0.0007877624102700422302442744879136 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.008699357520732249602486659737 y1[1] (numeric) = 1.0086993575207322511475769618601 absolute error = 1.5450903021231e-18 relative error = 1.5317649313475874471457328895013e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=11.45 NO POLE NO POLE x[1] = 0.133 y2[1] (analytic) = 1.0088314701548928618634141529829 y2[1] (numeric) = 1.0088232761826834414888472834641 absolute error = 8.1939722094203745668695188e-06 relative error = 0.0008122240881484691820718415163214 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0088314701548928618634141529829 y1[1] (numeric) = 1.008831470154892863456691425738 absolute error = 1.5932772727551e-18 relative error = 1.5793294716613798123378675326255e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.5MB, time=11.95 NO POLE NO POLE x[1] = 0.134 y2[1] (analytic) = 1.0089645739575007218567459364203 y2[1] (numeric) = 1.0089561322005362906133113377309 absolute error = 8.4417569644312434345986894e-06 relative error = 0.00083667525920358273948312202309177 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0089645739575007218567459364203 y1[1] (numeric) = 1.0089645739575007234982037482252 absolute error = 1.6414578118049e-18 relative error = 1.6268735832483658171712822631178e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.135 y2[1] (analytic) = 1.0090986687954520380666051976395 y2[1] (numeric) = 1.0090899792870636064435035256819 absolute error = 8.6895083884316231016719576e-06 relative error = 0.00086111583110144980124592627122883 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0090986687954520380666051976395 y1[1] (numeric) = 1.0090986687954520397562370687317 absolute error = 1.6896318710922e-18 relative error = 1.6743970865694348780525365324007e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=12.46 NO POLE NO POLE x[1] = 0.136 y2[1] (analytic) = 1.009233754534651983716245183572 y2[1] (numeric) = 1.0092248173084183136060315226038 absolute error = 8.9372262336701102136609682e-06 relative error = 0.00088554571163654545185594710906099 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.009233754534651983716245183572 y1[1] (numeric) = 1.0092337545346519854540445860148 absolute error = 1.7377994024428e-18 relative error = 1.7218998023347749176858209999829e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=12.96 NO POLE NO POLE x[1] = 0.137 y2[1] (analytic) = 1.0093698310400148308628648026684 y2[1] (numeric) = 1.0093606461297624019826895709775 absolute error = 9.1849102524288801752316909e-06 relative error = 0.0009099648087327031766719911522922 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0093698310400148308628648026684 y1[1] (numeric) = 1.0093698310400148326488251603576 absolute error = 1.7859603576892e-18 relative error = 1.7693815515062669794463110118429e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=13.46 NO POLE NO POLE x[1] = 0.138 y2[1] (analytic) = 1.0095068981754640854833253105562 y2[1] (numeric) = 1.0094974656152670615484573621834 absolute error = 9.4325601970239348679483728e-06 relative error = 0.00093437303044406198550580549367898 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0095068981754640854833253105562 y1[1] (numeric) = 1.0095068981754640873174399992266 absolute error = 1.8341146886704e-18 relative error = 1.8168421552990809308495612322067e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.139 y2[1] (analytic) = 1.0096449558039326235506329934705 y2[1] (numeric) = 1.0096352756281128182002987424545 absolute error = 9.6801758198053503342510160e-06 relative error = 0.00095877028495601042532622583856347 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0096449558039326235506329934705 y1[1] (numeric) = 1.0096449558039326254328953407028 absolute error = 1.8822623472323e-18 relative error = 1.8642814351838595922820219543277e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=13.97 NO POLE NO POLE x[1] = 0.14 y2[1] (analytic) = 1.0097840037873628281010517729886 y2[1] (numeric) = 1.0097740760304896705766244142903 absolute error = 9.9277568731575244273586983e-06 relative error = 0.00098315648058612746286068834444101 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 1.0097840037873628281010517729886 y1[1] (numeric) = 1.0097840037873628300314550582156 absolute error = 1.9304032852270e-18 relative error = 1.9116992128878071573709625453143e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=14.47 NO POLE NO POLE x[1] = 0.141 y2[1] (analytic) = 1.0099240419867067272917086649643 y2[1] (numeric) = 1.0099138666835972278672818138794 absolute error = 1.01753031094994244268510849e-05 relative error = 0.0010075315257851202180010790911536 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0099240419867067272917086649643 y1[1] (numeric) = 1.009924041986706729270246119478 absolute error = 1.9785374545137e-18 relative error = 1.9590953103973563867515560337493e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.142 y2[1] (analytic) = 1.0100650702619261334485540350706 y2[1] (numeric) = 1.0100546474476448486139343545536 absolute error = 1.04228142812848346196805170e-05 relative error = 0.0010318953291377585290454362217912 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0100650702619261334485540350706 y1[1] (numeric) = 1.0100650702619261354752188420288 absolute error = 2.0266648069582e-18 relative error = 2.0064695499594428989578491232858e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=14.97 NO POLE NO POLE x[1] = 0.143 y2[1] (analytic) = 1.0102070884719927831045376030009 y2[1] (numeric) = 1.0101964181818517805006912359043 absolute error = 1.06702901410026038463670966e-05 relative error = 0.0010562477993638063309321617700527 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0102070884719927831045376030009 y1[1] (numeric) = 1.0102070884719927851793228974339 absolute error = 2.0747852944330e-18 relative error = 2.0538217540833676612349685675523e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=15.48 NO POLE NO POLE x[1] = 0.144 y2[1] (analytic) = 1.0103500964748884780278601571639 y2[1] (numeric) = 1.0103391787444473011348480279447 absolute error = 1.09177304411768930121292192e-05 relative error = 0.0010805888453189498277491360150093 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0103500964748884780278601571639 y1[1] (numeric) = 1.0103500964748884801507590259818 absolute error = 2.1228988688179e-18 relative error = 2.1011517455431480905737774107984e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.145 y2[1] (analytic) = 1.010494094127605227240159951634 y2[1] (numeric) = 1.0104829289926708598175972495877 absolute error = 1.11651349343674225627020463e-05 relative error = 0.0011049183759957224409264503560354 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.010494094127605227240159951634 y1[1] (numeric) = 1.0104940941276052294111654336331 absolute error = 2.1710054819991e-18 relative error = 2.1484593473783780044156659137295e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=15.96 NO POLE NO POLE x[1] = 0.146 y2[1] (analytic) = 1.0106390812861453900244917671803 y2[1] (numeric) = 1.010627668782772220304567170741 absolute error = 1.14125033731697199245964393e-05 relative error = 0.0011292363005244265146483759496291 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0106390812861453900244917671803 y1[1] (numeric) = 1.0106390812861453922435968530504 absolute error = 2.2191050858701e-18 relative error = 2.1957443828968631257214266691320e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=16.46 NO POLE NO POLE x[1] = 0.147 y2[1] (analytic) = 1.0107850578055218199229556284092 y2[1] (numeric) = 1.0107733979700116045560460774931 absolute error = 1.16598355102153669095509161e-05 relative error = 0.0011535425281740517601476592847752 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0107850578055218199229556284092 y1[1] (numeric) = 1.0107850578055218221901532607404 absolute error = 2.2671976323312e-18 relative error = 2.2430066756758644686911304060840e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.148 y2[1] (analytic) = 1.0109320235397580097238311794022 y2[1] (numeric) = 1.0109201164086598374767482501771 absolute error = 1.19071310981722470829292251e-05 relative error = 0.0011778369683531904206732734173096 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0109320235397580097238311794022 y1[1] (numeric) = 1.0109320235397580120391142526922 absolute error = 2.3152830732900e-18 relative error = 2.2902460495643250095256831291931e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=16.96 NO POLE NO POLE x[1] = 0.149 y2[1] (analytic) = 1.0110799783418882374380727307282 y2[1] (numeric) = 1.0110678239519984926449769145591 absolute error = 1.21543898897447930958161691e-05 relative error = 0.0012021195306109491390513483103674 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0110799783418882374380727307282 y1[1] (numeric) = 1.0110799783418882398014340913892 absolute error = 2.3633613606610e-18 relative error = 2.3374623286841994257829779943102e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=17.46 NO POLE NO POLE x[1] = 0.15 y2[1] (analytic) = 1.0112289220639577132650190013457 y2[1] (numeric) = 1.0112165204523200390310384369996 absolute error = 1.24016116376742339805643461e-05 relative error = 0.0012263901246378575098881473688269 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0112289220639577132650190013457 y1[1] (numeric) = 1.0112289220639577156764514477116 absolute error = 2.4114324463659e-18 relative error = 2.3846553374324700116642796635051e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.151 y2[1] (analytic) = 1.0113788545570227275471705896988 y2[1] (numeric) = 1.0113662057609279887047610451868 absolute error = 1.26487960947388424095445120e-05 relative error = 0.001250648660266773298593642956255 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0113788545570227275471705896988 y1[1] (numeric) = 1.0113788545570227300066668720325 absolute error = 2.4594962823337e-18 relative error = 2.4318249004829581507305826754132e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=17.95 NO POLE NO POLE x[1] = 0.152 y2[1] (analytic) = 1.0115297756711507997138872192414 y2[1] (numeric) = 1.0115168797281370455319703669347 absolute error = 1.28959430137541819168523067e-05 relative error = 0.0012748950474737843095344634010764 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0115297756711507997138872192414 y1[1] (numeric) = 1.0115297756711508022214400397419 absolute error = 2.5075528205005e-18 relative error = 2.4789708427878326531668700763756e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=18.46 NO POLE NO POLE x[1] = 0.153 y2[1] (analytic) = 1.0116816852554208282138558147042 y2[1] (numeric) = 1.0116685422032732548597730905833 absolute error = 1.31430521475733540827241209e-05 relative error = 0.0012991291963791068857557302469522 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0116816852554208282138558147042 y1[1] (numeric) = 1.0116816852554208307694578275139 absolute error = 2.5556020128097e-18 relative error = 2.5260929895795071514578098122214e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.154 y2[1] (analytic) = 1.0118345831579232414361794766499 y2[1] (numeric) = 1.0118211930346741541904990617293 absolute error = 1.33901232490872456804149206e-05 relative error = 0.0013233510172479810228425701496693 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0118345831579232414361794766499 y1[1] (numeric) = 1.0118345831579232440398232878621 absolute error = 2.6036438112122e-18 relative error = 2.5731911663725307856684579723309e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=18.96 NO POLE NO POLE x[1] = 0.155 y2[1] (analytic) = 1.0119884692257601496199364332395 y2[1] (numeric) = 1.0119748320696889248441511423583 absolute error = 1.36371560712247757852908812e-05 relative error = 0.0013475604204915620796238624049056 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0119884692257601496199364332395 y1[1] (numeric) = 1.0119884692257601522716146009058 absolute error = 2.6516781676663e-18 relative error = 2.6202651989651756957298981116481e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.5MB, time=19.47 NO POLE NO POLE x[1] = 0.156 y2[1] (analytic) = 1.0121433433050454977520570596639 y2[1] (numeric) = 1.0121294591546785446092111699407 absolute error = 1.38841503669531428458897232e-05 relative error = 0.0013717573166678090685530639750861 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0121433433050454977520570596639 y1[1] (numeric) = 1.0121433433050455004517620938013 absolute error = 2.6997050341374e-18 relative error = 2.6673149134408204022223756791694e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.157 y2[1] (analytic) = 1.0122992052409052194533660673757 y2[1] (numeric) = 1.0122850741350159413816493656984 absolute error = 1.41311058892780717167016773e-05 relative error = 0.0013959416164823695087337304911831 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0122992052409052194533660673757 y1[1] (numeric) = 1.0122992052409052222010904299744 absolute error = 2.7477243625987e-18 relative error = 2.7143401361703146786772501791887e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.5MB, time=19.97 NO POLE NO POLE x[1] = 0.158 y2[1] (analytic) = 1.0124560548774773918526359770927 y2[1] (numeric) = 1.0124416768550861477919835530458 absolute error = 1.43780223912440606524240469e-05 relative error = 0.0014201132307894608246906172414841 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0124560548774773918526359770927 y1[1] (numeric) = 1.0124560548774773946483720821238 absolute error = 2.7957361050311e-18 relative error = 2.7613406938135469630723750404200e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=20.47 NO POLE NO POLE x[1] = 0.159 y2[1] (analytic) = 1.0126138920579123914484970015328 y2[1] (numeric) = 1.0125992671582864568202335591583 absolute error = 1.46248996259346282634423745e-05 relative error = 0.0014442720705927482741209903499192 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0126138920579123914484970015328 y1[1] (numeric) = 1.0126138920579123942922372149555 absolute error = 2.8437402134227e-18 relative error = 2.8083164133206101428445914766488e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=20.97 NO POLE NO POLE x[1] = 0.16 y2[1] (analytic) = 1.0127727166243730509590474759817 y2[1] (numeric) = 1.0127578448870265783986151847275 absolute error = 1.48717373464725604322912542e-05 relative error = 0.0014684180470462193879949973968718 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0127727166243730509590474759817 y1[1] (numeric) = 1.012772716624373053850784115751 absolute error = 2.8917366397693e-18 relative error = 2.8552671219339484613199650750846e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.161 y2[1] (analytic) = 1.0129325284180348171590079870976 y2[1] (numeric) = 1.0129174098827287970018171392216 absolute error = 1.51185353060201571908478760e-05 relative error = 0.0014925510714550549065086319914492 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0129325284180348171590079870976 y1[1] (numeric) = 1.0129325284180348200987333231723 absolute error = 2.9397253360747e-18 relative error = 2.9021926471902997544685282996129e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=21.47 NO POLE NO POLE x[1] = 0.162 y2[1] (analytic) = 1.0130933272790859097042613628125 y2[1] (numeric) = 1.0130779619858281302247033513874 absolute error = 1.53652932577794795580114251e-05 relative error = 0.0015166710552764961945279691876678 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0130933272790859097042613628125 y1[1] (numeric) = 1.0130933272790859126919676171625 absolute error = 2.9877062543500e-18 relative error = 2.9490928169216435361903438987142e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=21.98 NO POLE NO POLE x[1] = 0.163 y2[1] (analytic) = 1.0132551130467274809436196988004 y2[1] (numeric) = 1.0132395010357724883472820773051 absolute error = 1.56120109549925963376214953e-05 relative error = 0.0015407779101207091202989408547194 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0132551130467274809436196988004 y1[1] (numeric) = 1.0132551130467274839792990454148 absolute error = 3.0356793466144e-18 relative error = 2.9959674592576232947564062093475e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.164 y2[1] (analytic) = 1.0134178855591737767176586097624 y2[1] (numeric) = 1.0134020268710228348867822410396 absolute error = 1.58586881509418308763687228e-05 relative error = 0.0015648715477516443813329556954333 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0134178855591737767176586097624 y1[1] (numeric) = 1.0134178855591737798013031746572 absolute error = 3.0836445648948e-18 relative error = 3.0428164026267770676701105971594e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=22.47 NO POLE NO POLE x[1] = 0.165 y2[1] (analytic) = 1.0135816446536522981444579067051 y2[1] (numeric) = 1.0135655393290533481366764558256 absolute error = 1.61053245989500077814508795e-05 relative error = 0.0015889518800878942615151372665614 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0135816446536522981444579067051 y1[1] (numeric) = 1.013581644653652301276059767931 absolute error = 3.1316018612259e-18 relative error = 3.0896394757582548093508869821806e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=22.97 NO POLE NO POLE x[1] = 0.166 y2[1] (analytic) = 1.0137463901664039643920869144861 y2[1] (numeric) = 1.0137300382463515836924891867771 absolute error = 1.63519200523806995977277090e-05 relative error = 0.0016130188192035458036188498620377 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0137463901664039643920869144861 y1[1] (numeric) = 1.0137463901664039675716381021367 absolute error = 3.1795511876506e-18 relative error = 3.1364365076838246803101704773874e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.167 y2[1] (analytic) = 1.0139121219326832764376716571557 y2[1] (numeric) = 1.0138955234584186379642275293262 absolute error = 1.65984742646384734441278295e-05 relative error = 0.0016370722773290303815474972779544 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0139121219326832764376716571557 y1[1] (numeric) = 1.013912121932683279665164153375 absolute error = 3.2274924962193e-18 relative error = 3.1832073277387870974906539769479e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.5MB, time=23.48 NO POLE NO POLE x[1] = 0.168 y2[1] (analytic) = 1.014078839786758481812880152039 y2[1] (numeric) = 1.0140619947997693126752710909746 absolute error = 1.68449869891691376090610644e-05 relative error = 0.0016611121668519696567623053716469 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.014078839786758481812880152039 y1[1] (numeric) = 1.0140788397867584850883058910299 absolute error = 3.2754257389909e-18 relative error = 3.2299517655645588839622713621658e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=23.97 NO POLE NO POLE x[1] = 0.169 y2[1] (analytic) = 1.0142465435619117403356610670895 y2[1] (numeric) = 1.0142294521039322803475564774812 absolute error = 1.70914579794599881045896083e-05 relative error = 0.0016851384003180179034929296109545 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0142465435619117403356610670895 y1[1] (numeric) = 1.0142465435619117436590119351217 absolute error = 3.3233508680322e-18 relative error = 3.2766696511096719151843546305470e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.17 y2[1] (analytic) = 1.0144152330904392908280700097875 y2[1] (numeric) = 1.0143978952034502507728908983155 absolute error = 1.73378869890400551791114720e-05 relative error = 0.001709150890431700687466253576818 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0144152330904392908280700097875 y1[1] (numeric) = 1.0144152330904392941993378452054 absolute error = 3.3712678354179e-18 relative error = 3.3233608146313567875601322501998e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=24.47 NO POLE NO POLE x[1] = 0.171 y2[1] (analytic) = 1.0145849082036516188200167297711 y2[1] (numeric) = 1.0145673239298801384702284200764 absolute error = 1.75842737714803497883096947e-05 relative error = 0.001733149550057249883027657762527 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0145849082036516188200167297711 y1[1] (numeric) = 1.0145849082036516222391933230022 absolute error = 3.4191765932311e-18 relative error = 3.3700250866976122373288486174595e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=24.97 NO POLE NO POLE x[1] = 0.172 y2[1] (analytic) = 1.0147555687318736252387655314679 y2[1] (numeric) = 1.014737738113793231128741410615 absolute error = 1.78306180803941100241208529e-05 relative error = 0.001757134292219435013668331000429 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0147555687318736252387655314679 y1[1] (numeric) = 1.014755568731873628705842625031 absolute error = 3.4670770935631e-18 relative error = 3.4166622981885771506386195238858e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.173 y2[1] (analytic) = 1.0149272145044447960840202072392 y2[1] (numeric) = 1.0149091375847753590365187308034 absolute error = 1.80769196694370475014764358e-05 relative error = 0.0017811050301043909011118618398188 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0149272145044447960840202072392 y1[1] (numeric) = 1.0149272145044447995989894957526 absolute error = 3.5149692885134e-18 relative error = 3.4632722802980927071501197823198e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=25.46 NO POLE NO POLE x[1] = 0.174 y2[1] (analytic) = 1.0150998453497193730884238159675 y2[1] (numeric) = 1.0150815221714270654947212452652 absolute error = 1.83231782923075937025707023e-05 relative error = 0.0018050616770604416082533769533933 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0150998453497193730884238159675 y1[1] (numeric) = 1.0150998453497193766512769461573 absolute error = 3.5628531301898e-18 relative error = 3.5098548645353558862412599841521e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=25.97 NO POLE NO POLE x[1] = 0.175 y2[1] (analytic) = 1.0152734610950665253633026466005 y2[1] (numeric) = 1.0152548917013637782170242379274 absolute error = 1.85693937027471462784086731e-05 relative error = 0.0018290041465989206613848791491938 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0152734610950665253633026466005 y1[1] (numeric) = 1.0152734610950665289740312173089 absolute error = 3.6107285707084e-18 relative error = 3.5564098827264671992460207871527e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.176 y2[1] (analytic) = 1.0154480615668705220294827209227 y2[1] (numeric) = 1.0154292460012159817141753329644 absolute error = 1.88155656545403153073879583e-05 relative error = 0.0018529323523949875372811724804934 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0154480615668705220294827209227 y1[1] (numeric) = 1.0154480615668705256880782831166 absolute error = 3.6585955621939e-18 relative error = 3.6029371670162666520607629083433e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=26.47 NO POLE NO POLE x[1] = 0.177 y2[1] (analytic) = 1.0156236465905309058330062047525 y2[1] (numeric) = 1.0156045848966293906634955365913 absolute error = 1.90616939015151695106681612e-05 relative error = 0.0018768462082884404008618369369573 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0156236465905309058330062047525 y1[1] (numeric) = 1.0156236465905309095394602615317 absolute error = 3.7064540567792e-18 relative error = 3.6494365498694729370504428219258e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=26.97 NO POLE NO POLE x[1] = 0.178 y2[1] (analytic) = 1.0158002159904626677455741118622 y2[1] (numeric) = 1.0157809082122651242631500302194 absolute error = 1.93077781975434824240816428e-05 relative error = 0.0019007456282845250792861234051399 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0158002159904626677455741118622 y1[1] (numeric) = 1.015800215990462671499878118468 absolute error = 3.7543040066058e-18 relative error = 3.6959078640726033290008730721171e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.179 y2[1] (analytic) = 1.0159777695900964225495407001936 y2[1] (numeric) = 1.0159582157717998815710143607184 absolute error = 1.95538182965409785263394752e-05 relative error = 0.0019246305265547402584793727894602 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0159777695900964225495407001936 y1[1] (numeric) = 1.0159777695900964263516860640173 absolute error = 3.8021453638237e-18 relative error = 3.7423509427353937473477759723381e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=27.48 NO POLE NO POLE x[1] = 0.18 y2[1] (analytic) = 1.0161563072118785854072839753885 y2[1] (numeric) = 1.0161365073979261178279606889327 absolute error = 1.97998139524675793232864558e-05 relative error = 0.0019485008174376388882316135323134 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0161563072118785854072839753885 y1[1] (numeric) = 1.0161563072118785892572620559802 absolute error = 3.8499780805917e-18 relative error = 3.7887656192926052469450751301325e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=27.98 NO POLE NO POLE x[1] = 0.181 y2[1] (analytic) = 1.0163358286772715494147757322793 y2[1] (numeric) = 1.0163157829123522217653877731812 absolute error = 2.00457649193276493879590981e-05 relative error = 0.0019723564154396257821513514172918 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0163358286772715494147757322793 y1[1] (numeric) = 1.0163358286772715533125778413564 absolute error = 3.8978021090771e-18 relative error = 3.8351517275052325000509353419224e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=217.4MB, alloc=4.5MB, time=28.48 x[1] = 0.182 y2[1] (analytic) = 1.016516333806753864139173580784 y2[1] (numeric) = 1.0164960421358026938968173802246 absolute error = 2.02916709511702423562005594e-05 relative error = 0.0019961972352357513989002266536282 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.016516333806753864139173580784 y1[1] (numeric) = 1.0165163338067538680847909822397 absolute error = 3.9456174014557e-18 relative error = 3.8815091014620003490924327811112e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.183 y2[1] (analytic) = 1.0166978224198204151402564186277 y2[1] (numeric) = 1.0166772848880183257933788321192 absolute error = 2.05375318020893468775865085e-05 relative error = 0.0020200231916705017912771677269504 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0166978224198204151402564186277 y1[1] (numeric) = 1.0166978224198204191336803285401 absolute error = 3.9934239099124e-18 relative error = 3.9278375755814431147821424702048e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.5MB, time=28.98 NO POLE NO POLE x[1] = 0.184 y2[1] (analytic) = 1.0168802943349826044755238294719 y2[1] (numeric) = 1.0168595109877563803430024134876 absolute error = 2.07833472262241325214159843e-05 relative error = 0.0020438341997585847098639121499786 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0168802943349826044755238294719 y1[1] (numeric) = 1.0168802943349826085167454161124 absolute error = 4.0412215866405e-18 relative error = 3.9741369846126974335407210128112e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.6MB, time=29.49 NO POLE NO POLE x[1] = 0.185 y2[1] (analytic) = 1.0170637493697685321887789013652 y2[1] (numeric) = 1.017042720252790772993141380027 absolute error = 2.10291169777591956375213382e-05 relative error = 0.0020676301746857118480872821235034 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0170637493697685321887789013652 y1[1] (numeric) = 1.0170637493697685362777892852076 absolute error = 4.0890103838424e-18 relative error = 4.0204071636376649034420052084208e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.186 y2[1] (analytic) = 1.0172481873407231787820129769491 y2[1] (numeric) = 1.01722691249991225397684132555 absolute error = 2.12748408109248051716513991e-05 relative error = 0.002091411031809377215697391307179 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0172481873407231787820129769491 y1[1] (numeric) = 1.0172481873407231829188032306785 absolute error = 4.1367902537294e-18 relative error = 4.0666479480722817785129772963042e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.6MB, time=29.99 NO POLE NO POLE x[1] = 0.187 y2[1] (analytic) = 1.0174336080634085886704098635492 y2[1] (numeric) = 1.0174120875449285915219746815015 absolute error = 2.15205184799971484351820477e-05 relative error = 0.002115176686659631627805009344644 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0174336080634085886704098635492 y1[1] (numeric) = 1.0174336080634085928549710120707 absolute error = 4.1845611485215e-18 relative error = 4.1128591736677813815617321775032e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.6MB, time=30.49 NO POLE NO POLE x[1] = 0.188 y2[1] (analytic) = 1.0176200113524040546202860481617 y2[1] (numeric) = 1.0175982452026647560434571397346 absolute error = 2.17661497392985768289084271e-05 relative error = 0.0021389270549398532967656146768125 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0176200113524040546202860481617 y1[1] (numeric) = 1.0176200113524040588526090686097 absolute error = 4.2323230204480e-18 relative error = 4.1590406765127353635208875328300e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.189 y2[1] (analytic) = 1.0178073970213063031697824794125 y2[1] (numeric) = 1.0177853852869631053182618063426 absolute error = 2.20117343431978515206730699e-05 relative error = 0.0021626620525275145143422176607654 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0178073970213063031697824794125 y1[1] (numeric) = 1.0178073970213063074498583011593 absolute error = 4.2800758217468e-18 relative error = 4.2051922930338095176148428908066e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.6MB, time=30.99 NO POLE NO POLE x[1] = 0.19 y2[1] (analytic) = 1.0179957648827296810321224958101 y2[1] (numeric) = 1.0179735076106835706430459115496 absolute error = 2.22572720461103890765842605e-05 relative error = 0.0021863815954749444117238245131896 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0179957648827296810321224958101 y1[1] (numeric) = 1.0179957648827296853599420004753 absolute error = 4.3278195046652e-18 relative error = 4.2513138599979862709885854757964e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.6MB, time=31.49 NO POLE NO POLE x[1] = 0.191 y2[1] (analytic) = 1.0181851147483063424812494970519 y2[1] (numeric) = 1.0181626119857038439742039180484 absolute error = 2.25027626024985070455790035e-05 relative error = 0.0022100856000100877851214330491286 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0181851147483063424812494970519 y1[1] (numeric) = 1.0181851147483063468568035185115 absolute error = 4.3755540214596e-18 relative error = 4.2974052145136983624840197490505e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.192 y2[1] (analytic) = 1.0183754464286864377196569727608 y2[1] (numeric) = 1.0183526982229195660501598877471 absolute error = 2.27482057668716694970850137e-05 relative error = 0.0022337739825372599748086936392533 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0183754464286864377196569727608 y1[1] (numeric) = 1.0183754464286864421429362971562 absolute error = 4.4232793243954e-18 relative error = 4.3434661940321516254670190896853e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.6MB, time=32.01 NO POLE NO POLE x[1] = 0.193 y2[1] (analytic) = 1.0185667597335383022282225208382 y2[1] (numeric) = 1.0185437661322445154957109846493 absolute error = 2.29936012937867325115361889e-05 relative error = 0.002257446659637897785619826266259 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0185667597335383022282225208382 y1[1] (numeric) = 1.0185667597335383066992178865856 absolute error = 4.4709953657474e-18 relative error = 4.3894966363491311321460127117617e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.6MB, time=32.50 NO POLE NO POLE x[1] = 0.194 y2[1] (analytic) = 1.0187590544715486470978565056148 y2[1] (numeric) = 1.0187358155226107989082330095389 absolute error = 2.32389489378481896234960759e-05 relative error = 0.0022811035480713064370630494125854 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0187590544715486470978565056148 y1[1] (numeric) = 1.0187590544715486516165586034142 absolute error = 4.5187020977994e-18 relative error = 4.4354963796060139682344786737381e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.195 y2[1] (analytic) = 1.0189523304504227503427750241667 y2[1] (numeric) = 1.0189288462019690419255578802802 absolute error = 2.34842484537084172171438865e-05 relative error = 0.0023047445647754025313536402979537 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0189523304504227503427750241667 y1[1] (numeric) = 1.0189523304504227549091744970114 absolute error = 4.5663994728447e-18 relative error = 4.4814652622916580317285164102868e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.6MB, time=33.00 NO POLE NO POLE x[1] = 0.196 y2[1] (analytic) = 1.0191465874768846491952058675394 y2[1] (numeric) = 1.0191228579772885812753319898723 absolute error = 2.37294995960679198738776671e-05 relative error = 0.0023283696268674530278168011863641 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0191465874768846491952058675394 y1[1] (numeric) = 1.0191465874768846538092933107255 absolute error = 4.6140874431861e-18 relative error = 4.5274031232437919647437379615056e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.6MB, time=33.50 NO POLE NO POLE x[1] = 0.197 y2[1] (analytic) = 1.019341825356677333381335182191 y2[1] (numeric) = 1.0193178506545576578056633929145 absolute error = 2.39747021196755756717892765e-05 relative error = 0.0023519786516448102122567456432652 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.019341825356677333381335182191 y1[1] (numeric) = 1.0193418253566773380431011433264 absolute error = 4.6617659611354e-18 relative error = 4.5733098016499068457441038487099e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.198 y2[1] (analytic) = 1.0195380438945629393783015557216 y2[1] (numeric) = 1.0195138240387836104968647898521 absolute error = 2.42198557793288814367658695e-05 relative error = 0.0023755715565856426500348327268811 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0195380438945629393783015557216 y1[1] (numeric) = 1.0195380438945629440877365347359 absolute error = 4.7094349790143e-18 relative error = 4.6191851370495138711252819424346e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.6MB, time=34.01 NO POLE NO POLE x[1] = 0.199 y2[1] (analytic) = 1.0197352428943229456520432699139 y2[1] (numeric) = 1.0197107779339930714540982972759 absolute error = 2.44649603298741979449726380e-05 relative error = 0.002399148259349662111746160205213 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0197352428943229456520432699139 y1[1] (numeric) = 1.0197352428943229504091377190676 absolute error = 4.7570944491537e-18 relative error = 4.6650289693348242156686829236581e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.6MB, time=34.51 NO POLE NO POLE x[1] = 0.2 y2[1] (analytic) = 1.0199334221587583688758034832518 y2[1] (numeric) = 1.0199087121432321618807270116466 absolute error = 2.47100155262069950764716052e-05 relative error = 0.0024227086777788464605307701075615 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0199334221587583688758034832518 y1[1] (numeric) = 1.0199334221587583736805478071459 absolute error = 4.8047443238941e-18 relative error = 4.7108411387525004007355888001232e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.201 y2[1] (analytic) = 1.020132581489689961129097124429 y2[1] (numeric) = 1.0201076264685666890321773931092 absolute error = 2.49550211232720969197313198e-05 relative error = 0.0024462527298981584902025151786662 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.020132581489689961129097124429 y1[1] (numeric) = 1.0201325814896899659814816800147 absolute error = 4.8523845555857e-18 relative error = 4.7566214859051053183265605072761e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.6MB, time=35.00 NO POLE NO POLE x[1] = 0.202 y2[1] (analytic) = 1.0203327206879584080769422978976 y2[1] (numeric) = 1.0203075207110823441501155155508 absolute error = 2.51999768760639268267823468e-05 relative error = 0.0024697803339162607035256744357818 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0203327206879584080769422978976 y1[1] (numeric) = 1.0203327206879584129769573944857 absolute error = 4.9000150965881e-18 relative error = 4.8023698517521512804096771715860e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=35.51 NO POLE NO POLE x[1] = 0.203 y2[1] (analytic) = 1.0205338395534245281291580222406 y2[1] (numeric) = 1.0205083946708849013767392487427 absolute error = 2.54448825396267524187734979e-05 relative error = 0.0024932914082262260201165820925216 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0205338395534245281291580222406 y1[1] (numeric) = 1.0205338395534245330767939215116 absolute error = 4.9476358992710e-18 relative error = 4.8480860776121214439886604420036e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=274.6MB, alloc=4.6MB, time=36.01 x[1] = 0.204 y2[1] (analytic) = 1.020735937884969472579529142089 y2[1] (numeric) = 1.0207102481471004176489874582911 absolute error = 2.56897378690549305416837979e-05 relative error = 0.002516785871406244403594839853052 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.020735937884969472579529142089 y1[1] (numeric) = 1.0207359378849694775747760581024 absolute error = 4.9952469160134e-18 relative error = 4.8937700051630130267524506243702e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.205 y2[1] (analytic) = 1.0209390154804949267246382744327 y2[1] (numeric) = 1.0209130809378754335724663292034 absolute error = 2.59345426194931521719452293e-05 relative error = 0.0025402636422203253977561088112659 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0209390154804949267246382744327 y1[1] (numeric) = 1.0209390154804949317674863736371 absolute error = 5.0428480992044e-18 relative error = 4.9394214764444407481221822483032e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.6MB, time=36.52 NO POLE NO POLE x[1] = 0.206 y2[1] (analytic) = 1.0211430721369233119621636705127 y2[1] (numeric) = 1.021116892840377175274891939161 absolute error = 2.61792965461366872717313517e-05 relative error = 0.0025637246396189965616860177579863 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0211430721369233119621636705127 y1[1] (numeric) = 1.0211430721369233170526030717555 absolute error = 5.0904394012428e-18 relative error = 4.9850403338585562741036903044187e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.6MB, time=37.02 NO POLE NO POLE x[1] = 0.207 y2[1] (analytic) = 1.0213481076501979888684408950116 y2[1] (numeric) = 1.0213216836507937572388472280725 absolute error = 2.64239994042316295936669391e-05 relative error = 0.002587168782739997793882370258375 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0213481076501979888684408950116 y1[1] (numeric) = 1.021348107650197994006461669549 absolute error = 5.1380207745374e-18 relative error = 5.0306264201716455708435084262467e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.208 y2[1] (analytic) = 1.0215541218152834612550852449989 y2[1] (numeric) = 1.0215274531643343861136505311679 absolute error = 2.66686509490751414347138310e-05 relative error = 0.0026105959909089715356005770863812 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0215541218152834612550852449989 y1[1] (numeric) = 1.0215541218152834664406774165056 absolute error = 5.1855921715067e-18 relative error = 5.0761795785151306176129698739295e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.6MB, time=37.53 NO POLE NO POLE x[1] = 0.209 y2[1] (analytic) = 1.0217611144261655812044708520248 y2[1] (numeric) = 1.0217342011752295655061318637809 absolute error = 2.69132509360156983389882439e-05 relative error = 0.0026340061836401488437850749666075 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0217611144261655812044708520248 y1[1] (numeric) = 1.021761114426165586437624396604 absolute error = 5.2331535445792e-18 relative error = 5.1216996523871507316784553025777e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.6MB, time=38.03 NO POLE NO POLE x[1] = 0.21 y2[1] (analytic) = 1.0219690852758517550838614319006 y2[1] (numeric) = 1.0219419274767313017501121670618 absolute error = 2.71577991204533337492648388e-05 relative error = 0.0026573992806370313240974094264817 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0219690852758517550838614319006 y1[1] (numeric) = 1.0219690852758517603645662780945 absolute error = 5.2807048461939e-18 relative error = 5.1671864856543312551246525645520e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.211 y2[1] (analytic) = 1.0221780341563711505379866680538 y2[1] (numeric) = 1.0221506318611133106543797451574 absolute error = 2.74022952578398836069228964e-05 relative error = 0.0026807752017930689146996520893397 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0221780341563711505379866680538 y1[1] (numeric) = 1.0221780341563711558662326968529 absolute error = 5.3282460287991e-18 relative error = 5.2126399225518805249246049871162e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.6MB, time=38.55 NO POLE NO POLE x[1] = 0.212 y2[1] (analytic) = 1.022387960858774904459857235895 y2[1] (numeric) = 1.0223603141196712252289571458999 absolute error = 2.76467391036792309000899951e-05 relative error = 0.0027041338671923335115998813438518 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.022387960858774904459857235895 y1[1] (numeric) = 1.0223879608587749098356342807488 absolute error = 5.3757770448538e-18 relative error = 5.2580598076862233305349646800067e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.6MB, time=39.07 NO POLE NO POLE x[1] = 0.213 y2[1] (analytic) = 1.0225988651731363319396104974034 y2[1] (numeric) = 1.0225709740427228043894507587541 absolute error = 2.78911304135275501597386493e-05 relative error = 0.0027274751971101884265145754650358 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0225988651731363319396104974034 y1[1] (numeric) = 1.0225988651731363373629083442305 absolute error = 5.4232978468271e-18 relative error = 5.3034459860356688498162312543940e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.214 y2[1] (analytic) = 1.0228107468885511361911779170994 y2[1] (numeric) = 1.0227826114196081426392744256915 absolute error = 2.81354689429935519034914079e-05 relative error = 0.0027507991120139536683509374915599 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0228107468885511361911779170994 y1[1] (numeric) = 1.0228107468885511416619863042975 absolute error = 5.4708083871981e-18 relative error = 5.3487983029515601028452110133594e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.6MB, time=39.57 NO POLE NO POLE x[1] = 0.215 y2[1] (analytic) = 1.0230236057931376194565642727558 y2[1] (numeric) = 1.022995226038689880729537382785 absolute error = 2.83797544477387270268899708e-05 relative error = 0.0027741055325635670395603873451908 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0230236057931376194565642727558 y1[1] (numeric) = 1.0230236057931376249748728912119 absolute error = 5.5183086184561e-18 relative error = 5.3941166041597087073133979304512e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.6MB, time=40.07 NO POLE NO POLE x[1] = 0.216 y2[1] (analytic) = 1.0232374416740368948875277565849 y2[1] (numeric) = 1.0232088176873534172963858726537 absolute error = 2.86239866834775911418839312e-05 relative error = 0.0027973943796122410387627089261608 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0232374416740368948875277565849 y1[1] (numeric) = 1.023237441674036900453326249686 absolute error = 5.5657984931011e-18 relative error = 5.4394007357621144924640912279224e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.217 y2[1] (analytic) = 1.0234522543174130994044490852411 y2[1] (numeric) = 1.0234233861520071214755867904337 absolute error = 2.88681654059779288622948074e-05 relative error = 0.0028206655742071155611886220054315 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0234522543174130994044490852411 y1[1] (numeric) = 1.0234522543174131050177270488842 absolute error = 5.6132779636431e-18 relative error = 5.4846505442375038939562249491229e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.6MB, time=40.57 NO POLE NO POLE x[1] = 0.218 y2[1] (analytic) = 1.023668043508453607532176759785 y2[1] (numeric) = 1.0236389312180825464941407487092 absolute error = 2.91122903710610380360110758e-05 relative error = 0.0028439190375899063886368517527217 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.023668043508453607532176759785 y1[1] (numeric) = 1.0236680435084536131929237423876 absolute error = 5.6607469826026e-18 relative error = 5.5298658764430333456775276721205e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.6MB, time=41.07 NO POLE NO POLE x[1] = 0.219 y2[1] (analytic) = 1.0238848090313692462126346397834 y2[1] (numeric) = 1.0238554526700346442387109698088 absolute error = 2.93563613346019739236699746e-05 relative error = 0.0028671546911975494607900868772448 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0238848090313692462126346397834 y1[1] (numeric) = 1.0238848090313692519208401422942 absolute error = 5.7082055025108e-18 relative error = 5.5750465796156909201659312681854e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.22 y2[1] (analytic) = 1.0241025506693945105939770189553 y2[1] (numeric) = 1.0240729502913419808006534370552 absolute error = 2.96003780525297933235819001e-05 relative error = 0.0028903724566628409198825416085022 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0241025506693945105939770189553 y1[1] (numeric) = 1.0241025506693945163496304948643 absolute error = 5.7556534759090e-18 relative error = 5.6201925013729083977962387339646e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.6MB, time=41.58 NO POLE NO POLE x[1] = 0.221 y2[1] (analytic) = 1.0243212682047877807960754132258 y2[1] (numeric) = 1.0242914238645069529974327599573 absolute error = 2.98443402808277986426532685e-05 relative error = 0.0029135722558150729208601599966855 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0243212682047877807960754132258 y1[1] (numeric) = 1.0243212682047877865991662685751 absolute error = 5.8030908553493e-18 relative error = 5.6653034897144350524264611823284e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.6MB, time=42.08 NO POLE NO POLE x[1] = 0.222 y2[1] (analytic) = 1.0245409614188315396521202957203 y2[1] (numeric) = 1.0245108731710560058702072319458 absolute error = 3.00882477755337819130637745e-05 relative error = 0.0029367540106806651993228166434636 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0245409614188315396521202957203 y1[1] (numeric) = 1.0245409614188315455026378891146 absolute error = 5.8505175933943e-18 relative error = 5.7103793930232263371872566371674e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.223 y2[1] (analytic) = 1.024761630091832591426120037115 y2[1] (numeric) = 1.0247312979915398511573655830859 absolute error = 3.03321002927402687544540291e-05 relative error = 0.0029599176434837923896861670867306 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.024761630091832591426120037115 y1[1] (numeric) = 1.0247616300918325973240536797322 absolute error = 5.8979336426172e-18 relative error = 5.7554200600667150868423890062203e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.6MB, time=42.58 NO POLE NO POLE x[1] = 0.224 y2[1] (analytic) = 1.0249832740031222815060783338625 y2[1] (numeric) = 1.0249526981055336867437969542485 absolute error = 3.05758975885947622813796140e-05 relative error = 0.0029830630766470070861490773111209 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0249832740031222815060783338625 y1[1] (numeric) = 1.0249832740031222874514172894646 absolute error = 5.9453389556021e-18 relative error = 5.8004253399982695124774643603679e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.6MB, time=43.08 NO POLE NO POLE x[1] = 0.225 y2[1] (analytic) = 1.0252058929310567170726304311345 y2[1] (numeric) = 1.0251750732916374170856746434883 absolute error = 3.08196394192999869557876462e-05 relative error = 0.0030061902327918586392008075567884 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0252058929310567170726304311345 y1[1] (numeric) = 1.0252058929310567230653639160782 absolute error = 5.9927334849437e-18 relative error = 5.8453950823580573458382045117070e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=331.8MB, alloc=4.6MB, time=43.56 x[1] = 0.226 y2[1] (analytic) = 1.0254294866530169887429174718627 y2[1] (numeric) = 1.0253984233274758746105331998629 absolute error = 3.10633255411141323842719998e-05 relative error = 0.0030292990347395076805503329650103 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0254294866530169887429174718627 y1[1] (numeric) = 1.02542948665301699478303465511 absolute error = 6.0401171832473e-18 relative error = 5.8903291370741946893880734578914e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.227 y2[1] (analytic) = 1.0256540549454093931894773280223 y2[1] (numeric) = 1.0256227479896990420924174646351 absolute error = 3.13069557103510970598633872e-05 relative error = 0.0030523894055113363695083457054657 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0256540549454093931894773280223 y1[1] (numeric) = 1.0256540549454093992769673311516 absolute error = 6.0874900031293e-18 relative error = 5.9352273544643741137830565320757e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.6MB, time=44.06 NO POLE NO POLE x[1] = 0.228 y2[1] (analytic) = 1.0258795975836656567339292952864 y2[1] (numeric) = 1.0258480470539822760018811847272 absolute error = 3.15505296833807320481105592e-05 relative error = 0.0030754612683295543540005927541991 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0258795975836656567339292952864 y1[1] (numeric) = 1.0258795975836656628687811925033 absolute error = 6.1348518972169e-18 relative error = 5.9800895852367040348742682803984e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.6MB, time=44.54 NO POLE NO POLE x[1] = 0.229 y2[1] (analytic) = 1.0261061143422431599152290573844 y2[1] (numeric) = 1.0260743202950265308306118484476 absolute error = 3.17940472166290846172089368e-05 relative error = 0.0030985145466178004395392525106303 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0261061143422431599152290573844 y1[1] (numeric) = 1.0261061143422431660974318755325 absolute error = 6.1822028181481e-18 relative error = 6.0249156804908325683029746494696e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.23 y2[1] (analytic) = 1.0263336049946251630322693519284 y2[1] (numeric) = 1.0263015674865585843904574188835 absolute error = 3.20375080665786418119330449e-05 relative error = 0.0031215491640017399596270354427929 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0263336049946251630322693519284 y1[1] (numeric) = 1.0263336049946251692618120705006 absolute error = 6.2295427185722e-18 relative error = 6.0697054917195502698755849174400e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.6MB, time=45.03 NO POLE NO POLE x[1] = 0.231 y2[1] (analytic) = 1.0265620693133210326606007951267 y2[1] (numeric) = 1.0265297884013312640866296659515 absolute error = 3.22809119897685739711291752e-05 relative error = 0.0031445650443096578412166012233835 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0265620693133210326606007951267 y1[1] (numeric) = 1.0265620693133210389374723462759 absolute error = 6.2768715511492e-18 relative error = 6.1144588708093123908684523728069e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.6MB, time=45.52 NO POLE NO POLE x[1] = 0.232 y2[1] (analytic) = 1.0267915070698664691430463486806 y2[1] (numeric) = 1.0267589828111236741648578239225 absolute error = 3.25242587427949781885247581e-05 relative error = 0.0031675621115730473589957096919946 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0267915070698664691430463486806 y1[1] (numeric) = 1.0267915070698664754672356172308 absolute error = 6.3241892685502e-18 relative error = 6.1591756700417275102202689194223e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.233 y2[1] (analytic) = 1.0270219180348237350539819382704 y2[1] (numeric) = 1.0269891504867414239322653272846 absolute error = 3.27675480823111217166109858e-05 relative error = 0.0031905402900271945724162596347153 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0270219180348237350539819382704 y1[1] (numeric) = 1.027021918034823741425477761728 absolute error = 6.3714958234576e-18 relative error = 6.2038557420948425867228324324672e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.6MB, time=46.02 NO POLE NO POLE x[1] = 0.234 y2[1] (analytic) = 1.027253301977781884637054759369 y2[1] (numeric) = 1.0272202911980168569517414040882 absolute error = 3.30107797650276853133552808e-05 relative error = 0.0032134995041117584395330086295008 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.027253301977781884637054759369 y1[1] (numeric) = 1.0272533019777818910558459279337 absolute error = 6.4187911685647e-18 relative error = 6.2484989400438353327338683890067e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.6MB, time=46.50 NO POLE NO POLE x[1] = 0.235 y2[1] (analytic) = 1.0274856586673569942161098326828 y2[1] (numeric) = 1.027452404713809281209578332419 absolute error = 3.32539535477130065315002638e-05 relative error = 0.0032364396784713466018653036607589 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0274856586673569942161098326828 y1[1] (numeric) = 1.027485658667357000682185089259 absolute error = 6.4660752565762e-18 relative error = 6.2931051173625746945373840437436e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.236 y2[1] (analytic) = 1.0277189878711923935790943983139 y2[1] (numeric) = 1.0276854908020052002561441923825 absolute error = 3.34970691871933229502059314e-05 relative error = 0.00325936073795608683464257761755 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0277189878711923935790943983139 y1[1] (numeric) = 1.0277189878711924000924424385221 absolute error = 6.5133480402082e-18 relative error = 6.3376741279246858039891339137334e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.6MB, time=46.99 NO POLE NO POLE x[1] = 0.237 y2[1] (analytic) = 1.0279532893559588983347087647578 y2[1] (numeric) = 1.0279195492295185453193599729446 absolute error = 3.37401264403530153487918132e-05 relative error = 0.0032822626076221941569416746372656 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0279532893559588983347087647578 y1[1] (numeric) = 1.0279532893559589048953182369455 absolute error = 6.5606094721877e-18 relative error = 6.3822058260041201592285711498021e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.6MB, time=47.49 NO POLE NO POLE x[1] = 0.238 y2[1] (analytic) = 1.0281885628873550432415712561047 y2[1] (numeric) = 1.0281545797622909083907489201728 absolute error = 3.39831250641348508223359319e-05 relative error = 0.0033051452127325335963712496662113 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0281885628873550432415712561047 y1[1] (numeric) = 1.0281885628873550498494307613581 absolute error = 6.6078595052534e-18 relative error = 6.4267000662769824556637884243703e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.239 y2[1] (analytic) = 1.0284248082301073165096639283 y2[1] (numeric) = 1.0283905821652917762838250408457 absolute error = 3.42260648155402258388874543e-05 relative error = 0.0033280084787571786031055390208048 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0284248082301073165096639283 y1[1] (numeric) = 1.0284248082301073231647620204551 absolute error = 6.6550980921551e-18 relative error = 6.4711567038219866592035774401001e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.6MB, time=47.99 NO POLE NO POLE x[1] = 0.24 y2[1] (analytic) = 1.0286620251479703950738247530366 y2[1] (numeric) = 1.028627556202518765664586703064 absolute error = 3.44689454516294092380499726e-05 relative error = 0.0033508523313739651082167098609431 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0286620251479703950738247530366 y1[1] (numeric) = 1.0286620251479704017761499386911 absolute error = 6.7023251856545e-18 relative error = 6.5155755941222654789889399675776e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.6MB, time=48.49 NO POLE NO POLE x[1] = 0.241 y2[1] (analytic) = 1.0289002134037273808390509958078 y2[1] (numeric) = 1.0288655016369978590538803033873 absolute error = 3.47117667295217851706924205e-05 relative error = 0.0033736766964690412214017628888036 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0289002134037273808390509958078 y1[1] (numeric) = 1.0289002134037273875885917343321 absolute error = 6.7495407385243e-18 relative error = 6.5599565930655181099314186780786e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.242 y2[1] (analytic) = 1.0291393727591900378973775428355 y2[1] (numeric) = 1.0291044182307836418013979981536 absolute error = 3.49545284063960959795446819e-05 relative error = 0.0033964815001374125633465748097616 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0291393727591900378973775428355 y1[1] (numeric) = 1.0291393727591900446941222463844 absolute error = 6.7967447035489e-18 relative error = 6.6042995569457054734825130624137e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.6MB, time=48.98 NO POLE NO POLE x[1] = 0.243 y2[1] (analytic) = 1.0293795029751990307160929600163 y2[1] (numeric) = 1.0293443057449595400310725250032 absolute error = 3.51972302394906850204350131e-05 relative error = 0.0034192666686834832281161202868573 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0293795029751990307160929600163 y1[1] (numeric) = 1.0293795029751990375600299935408 absolute error = 6.8439370335245e-18 relative error = 6.6486043424641532152970258106991e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.6MB, time=49.47 NO POLE NO POLE x[1] = 0.244 y2[1] (analytic) = 1.0296206038116241632970550956892 y2[1] (numeric) = 1.0295851639396380595576311692323 absolute error = 3.54398719861037394239264569e-05 relative error = 0.0034420321286215923711061988672548 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0296206038116241632970550956892 y1[1] (numeric) = 1.0296206038116241701881727769479 absolute error = 6.8911176812587e-18 relative error = 6.6928708067301605185850649924486e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.245 y2[1] (analytic) = 1.0298626750273646193068670679285 y2[1] (numeric) = 1.0298269925739610257740699584416 absolute error = 3.56824534035935327971094869e-05 relative error = 0.0034647778066765464182381045458032 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0298626750273646193068670679285 y1[1] (numeric) = 1.0298626750273646262451536674994 absolute error = 6.9382865995709e-18 relative error = 6.7370988072623778271277933637098e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.6MB, time=49.95 NO POLE NO POLE x[1] = 0.246 y2[1] (analytic) = 1.0301057163803492031776735062069 y2[1] (numeric) = 1.0300697914060998245098081980267 absolute error = 3.59249742493786678653081802e-05 relative error = 0.0034875036297841468922236071639222 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0301057163803492031776735062069 y1[1] (numeric) = 1.0301057163803492101631172474991 absolute error = 6.9854437412922e-18 relative error = 6.7812882019896901881234324412615e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.6MB, time=50.44 NO POLE NO POLE x[1] = 0.247 y2[1] (analytic) = 1.0303497276275365821783359466519 y2[1] (numeric) = 1.0303135601932556438592824893747 absolute error = 3.61674342809383190534572772e-05 relative error = 0.003510209525091713851873358951518 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0303497276275365821783359466519 y1[1] (numeric) = 1.0303497276275365892109250059172 absolute error = 7.0325890592653e-18 relative error = 6.8254388492520922778612117369992e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=389.1MB, alloc=4.6MB, time=50.93 x[1] = 0.248 y2[1] (analytic) = 1.0305947085249155294557453097401 y2[1] (numeric) = 1.0305582986916597169807384021941 absolute error = 3.64098332558124750069075460e-05 relative error = 0.0035328954199586049405673891856154 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0305947085249155294557453097401 y1[1] (numeric) = 1.0305947085249155365354678160852 absolute error = 7.0797225063451e-18 relative error = 6.8695506078022343246715499072357e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.249 y2[1] (analytic) = 1.0308406588275051680460284191387 y2[1] (numeric) = 1.0308040066565735658649770022059 absolute error = 3.66521709316021810514169328e-05 relative error = 0.0035555612419567300401516990575235 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0308406588275051680460284191387 y1[1] (numeric) = 1.0308406588275051751728724545367 absolute error = 7.1268440353980e-18 relative error = 6.9136233368056976259367308055659e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.6MB, time=51.43 NO POLE NO POLE x[1] = 0.25 y2[1] (analytic) = 1.0310875782893552158554045505058 y2[1] (numeric) = 1.0310506838422892460738124654701 absolute error = 3.68944470659697815920850357e-05 relative error = 0.0035782069188710615266701094168535 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0310875782893552158554045505058 y1[1] (numeric) = 1.0310875782893552230293581498084 absolute error = 7.1739535993026e-18 relative error = 6.9576568958426203511644038180466e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.6MB, time=51.93 NO POLE NO POLE x[1] = 0.251 y2[1] (analytic) = 1.0313354666635462316104470294153 y2[1] (numeric) = 1.0312983300021295924479960409103 absolute error = 3.71366614166391624509885050e-05 relative error = 0.0036008323787001401244854411049856 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0313354666635462316104470294153 y1[1] (numeric) = 1.0313354666635462388314981803645 absolute error = 7.2210511509492e-18 relative error = 7.0016511449081503493502713035720e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.252 y2[1] (analytic) = 1.0315843237021898617775039281638 y2[1] (numeric) = 1.0315469448884484657843606531324 absolute error = 3.73788137413959931432750314e-05 relative error = 0.0036234375496565763554888127772462 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0315843237021898617775039281638 y1[1] (numeric) = 1.0315843237021898690456405714042 absolute error = 7.2681366432404e-18 relative error = 7.0456059444139564883182156200058e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.6MB, time=52.42 NO POLE NO POLE x[1] = 0.253 y2[1] (analytic) = 1.0318341491564290884510309420608 y2[1] (numeric) = 1.0317965282526310004819394684143 absolute error = 3.76209037980879690914736465e-05 relative error = 0.0036460223601675475802403189845826 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0318341491564290884510309420608 y1[1] (numeric) = 1.0318341491564290957662409711514 absolute error = 7.3152100290906e-18 relative error = 7.0895211551886645962708269736503e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.6MB, time=52.93 NO POLE NO POLE x[1] = 0.254 y2[1] (analytic) = 1.0320849427764384782105885568886 y2[1] (numeric) = 1.0320470798450938531568107777681 absolute error = 3.78629313446250537777791205e-05 relative error = 0.0036685867388752906280285945454724 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0320849427764384782105885568886 y1[1] (numeric) = 1.032084942776438485572859818315 absolute error = 7.3622712614264e-18 relative error = 7.1333966384791576288172557333442e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.255 y2[1] (analytic) = 1.0323367043114244319462546505563 y2[1] (numeric) = 1.0322985994152854522254205822501 absolute error = 3.81048961389797208340683062e-05 relative error = 0.0036911306146375900129807739249816 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0323367043114244319462546505563 y1[1] (numeric) = 1.0323367043114244393555749437431 absolute error = 7.4093202931868e-18 relative error = 7.1772322559516730325844487865970e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.6MB, time=53.43 NO POLE NO POLE x[1] = 0.256 y2[1] (analytic) = 1.0325894335096254356522027035565 y2[1] (numeric) = 1.0325510867116862484561332972184 absolute error = 3.83467979391871960694063381e-05 relative error = 0.0037136539165282617334981091268239 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0325894335096254356522027035565 y1[1] (numeric) = 1.0325894335096254431085597808791 absolute error = 7.4563570773226e-18 relative error = 7.2210278696921165627030563284795e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.6MB, time=53.95 NO POLE NO POLE x[1] = 0.257 y2[1] (analytic) = 1.032843130118312312188194824666 y2[1] (numeric) = 1.0328045414818089664887600240063 absolute error = 3.85886365033456994348006597e-05 relative error = 0.0037361565738376326524360108847754 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.032843130118312312188194824666 y1[1] (numeric) = 1.0328431301183123196915763914629 absolute error = 7.5033815667969e-18 relative error = 7.2647833422074334611076482992214e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.258 y2[1] (analytic) = 1.0330977938837884740087378304194 y2[1] (numeric) = 1.0330589634721988573218128695059 absolute error = 3.88304115896166869249609135e-05 relative error = 0.0037586385160730154555905185269948 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0330977938837884740087378304194 y1[1] (numeric) = 1.0330977938837884815591315450048 absolute error = 7.5503937145854e-18 relative error = 7.3084985364267768125957898423520e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.6MB, time=54.45 NO POLE NO POLE x[1] = 0.259 y2[1] (analytic) = 1.0333534245513901768596496492213 y2[1] (numeric) = 1.0333143524284339517672328264276 absolute error = 3.90721229562250924168227937e-05 relative error = 0.0037810996729591791861961780369323 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0333534245513901768596496492213 y1[1] (numeric) = 1.0333534245513901844570431228972 absolute error = 7.5973934736759e-18 relative error = 7.3521733157018927680568043206394e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.6MB, time=54.96 NO POLE NO POLE x[1] = 0.26 y2[1] (analytic) = 1.0336100218654867744417823535499 y2[1] (numeric) = 1.0335707080951253148723377595288 absolute error = 3.93137703614595694445940211e-05 relative error = 0.0038035399744388153532830081837768 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0336100218654867744417823535499 y1[1] (numeric) = 1.0336100218654867820861631506185 absolute error = 7.6443807970686e-18 relative error = 7.3958075438082719444891854208751e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.261 y2[1] (analytic) = 1.0338675855694809740416471565521 y2[1] (numeric) = 1.0338280302159173013087360758858 absolute error = 3.95553535636727329110806663e-05 relative error = 0.0038259593506729996118826560632366 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0338675855694809740416471565521 y1[1] (numeric) = 1.0338675855694809817330027943283 absolute error = 7.6913556377762e-18 relative error = 7.4394010849460984153579099157882e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.6MB, time=55.46 NO POLE NO POLE x[1] = 0.262 y2[1] (analytic) = 1.0341261154058090931286857424248 y2[1] (numeric) = 1.0340863185334878117279506903155 absolute error = 3.97968723212814007350521093e-05 relative error = 0.0038483577320416490132159785306829 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0341261154058090931286857424248 y1[1] (numeric) = 1.0341261154058091008670036912488 absolute error = 7.7383179488240e-18 relative error = 7.4829538037411900220505873257500e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.6MB, time=55.97 NO POLE NO POLE x[1] = 0.263 y2[1] (analytic) = 1.0343856111159413169189313333344 y2[1] (numeric) = 1.034345572789548550083496930345 absolute error = 4.00383263927668354344029894e-05 relative error = 0.0038707350491439748231361293615681 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0343856111159413169189313333344 y1[1] (numeric) = 1.0343856111159413247041990165839 absolute error = 7.7852676832495e-18 relative error = 7.5264655652454466235034025606692e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.264 y2[1] (analytic) = 1.0346460724403819569048019292326 y2[1] (numeric) = 1.0346057927248452819191570586721 absolute error = 4.02797155366749856448705605e-05 relative error = 0.0038930912327989309072427764885426 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0346460724403819569048019292326 y1[1] (numeric) = 1.0346460724403819647370067233356 absolute error = 7.8322047941030e-18 relative error = 7.5699362349382569029975711117256e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.6MB, time=56.47 NO POLE NO POLE x[1] = 0.265 y2[1] (analytic) = 1.0349074991186697103507671907983 y2[1] (numeric) = 1.0348669780791580936231931248646 absolute error = 4.05210395116167275740659337e-05 relative error = 0.0039154262140456576812243141281277 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0349074991186697103507671907983 y1[1] (numeric) = 1.0349074991186697182298964252458 absolute error = 7.8791292344475e-18 relative error = 7.6133656787272193687244398030589e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.6MB, time=56.97 NO POLE NO POLE x[1] = 0.266 y2[1] (analytic) = 1.0351698908893779207546294698607 y2[1] (numeric) = 1.0351291285913016526482388921059 absolute error = 4.07622980762681063905777548e-05 relative error = 0.0039377399241439216251258642124883 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0351698908893779207546294698607 y1[1] (numeric) = 1.0351698908893779286806704272191 absolute error = 7.9260409573584e-18 relative error = 7.6567537629486617492115560989847e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.267 y2[1] (analytic) = 1.0354332474901148392741585260421 y2[1] (numeric) = 1.0353922439991254686966106191176 absolute error = 4.10034909893705775479069245e-05 relative error = 0.0039600322945745503603814737365339 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0354332474901148392741585260421 y1[1] (numeric) = 1.0354332474901148472470984419663 absolute error = 7.9729399159242e-18 relative error = 7.7001003543691180629276129381290e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.6MB, time=57.47 NO POLE NO POLE x[1] = 0.268 y2[1] (analytic) = 1.0356975686575238871188185030108 y2[1] (numeric) = 1.0356563240395141558707755119699 absolute error = 4.12446180097312480429910409e-05 relative error = 0.0039823032570398632885892049859498 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0356975686575238871188185030108 y1[1] (numeric) = 1.0356975686575238951386445662566 absolute error = 8.0198260632458e-18 relative error = 7.7434053201854443616257745563918e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.6MB, time=57.97 NO POLE NO POLE x[1] = 0.269 y2[1] (analytic) = 1.0359628541272839189063247726353 y2[1] (numeric) = 1.0359213684483876957887156953328 absolute error = 4.14856788962231176090773025e-05 relative error = 0.0040045527434640977911477756866381 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0359628541272839189063247726353 y1[1] (numeric) = 1.0359628541272839269730241250723 absolute error = 8.0666993524370e-18 relative error = 7.7866685280260853006687983751577e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.27 y2[1] (analytic) = 1.0362291036341094869837672905078 y2[1] (numeric) = 1.0361873769607017016639245878267 absolute error = 4.17266734077853198427026811e-05 relative error = 0.0040267806859938309890130323983545 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0362291036341094869837672905078 y1[1] (numeric) = 1.0362291036341094950973270271325 absolute error = 8.1135597366247e-18 relative error = 7.8298898459520419073232128732926e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.6MB, time=58.47 NO POLE NO POLE x[1] = 0.271 y2[1] (analytic) = 1.0364963169117511067130361417346 y2[1] (numeric) = 1.0364543493104476833497716014973 absolute error = 4.19676013034233632645402373e-05 relative error = 0.004048987016998397061971825018996 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0364963169117511067130361417346 y1[1] (numeric) = 1.036496316911751114873443310683 absolute error = 8.1604071689484e-18 relative error = 7.8730691424571551454857601187483e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.6MB, time=58.97 NO POLE NO POLE x[1] = 0.272 y2[1] (analytic) = 1.0367644936929955227202839915894 y2[1] (numeric) = 1.0367222852306533133479701210729 absolute error = 4.22084623422093723138705165e-05 relative error = 0.0040711716690703001269697880930132 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0367644936929955227202839915894 y1[1] (numeric) = 1.03676449369299553092752559415 absolute error = 8.2072416025606e-18 relative error = 7.9162062864692497590642738803804e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.6MB, time=59.48 NO POLE NO POLE x[1] = 0.273 y2[1] (analytic) = 1.0370336337096659761091591915901 y2[1] (numeric) = 1.0369911844533826937808827545577 absolute error = 4.24492562832823282764370324e-05 relative error = 0.0040933345750256226751681200354102 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0370336337096659761091591915901 y1[1] (numeric) = 1.0370336337096659843632221822172 absolute error = 8.2540629906271e-18 relative error = 7.9593011473511725362896493911713e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.274 y2[1] (analytic) = 1.0373037366926224726375423277883 y2[1] (numeric) = 1.0372610467097366243273968828785 absolute error = 4.26899828858483101454449098e-05 relative error = 0.004115475667904429567542677756158 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0373037366926224726375423277883 y1[1] (numeric) = 1.0373037366926224809384136141146 absolute error = 8.3008712863263e-18 relative error = 8.0023535949008575306816809956050e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.6MB, time=59.98 NO POLE NO POLE x[1] = 0.275 y2[1] (analytic) = 1.0375748023717620518575180345561 y2[1] (numeric) = 1.0375318717298528711221025727313 absolute error = 4.29306419091807354154618248e-05 relative error = 0.0041375948809711675889765662554492 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0375748023717620518575180345561 y1[1] (numeric) = 1.0375748023717620602051844774061 absolute error = 8.3476664428500e-18 relative error = 8.0453634993528294623533182633784e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.6MB, time=60.48 NO POLE NO POLE x[1] = 0.276 y2[1] (analytic) = 1.0378468304760190572183129339225 y2[1] (numeric) = 1.0378036592429064366175039534727 absolute error = 4.31712331126206008089804498e-05 relative error = 0.004159692147715060560934894940233 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0378468304760190572183129339225 y1[1] (numeric) = 1.0378468304760190656127613473255 absolute error = 8.3944484134030e-18 relative error = 8.0883307313785411193858725124318e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.277 y2[1] (analytic) = 1.0381198207333654071319295975428 y2[1] (numeric) = 1.0380764089771098304089941958664 absolute error = 4.34117562555767229354016764e-05 relative error = 0.0041817674018505000129474883299189 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0381198207333654071319295975428 y1[1] (numeric) = 1.0381198207333654155731467487462 absolute error = 8.4412171512034e-18 relative error = 8.1312551620873771079355622905113e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.6MB, time=60.98 NO POLE NO POLE x[1] = 0.278 y2[1] (analytic) = 1.0383937728708108670012054656899 y2[1] (numeric) = 1.0383501206597133410223232677335 absolute error = 4.36522110975259788821979564e-05 relative error = 0.0042038205773174314132620732776619 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0383937728708108670012054656899 y1[1] (numeric) = 1.0383937728708108754891780751723 absolute error = 8.4879726094824e-18 relative error = 8.1741366630271670827037396241867e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.6MB, time=61.48 NO POLE NO POLE x[1] = 0.279 y2[1] (analytic) = 1.0386686866144033222100246952314 y2[1] (numeric) = 1.0386247940170053086632866790607 absolute error = 4.38925973980135467380161707e-05 relative error = 0.0042258516082817359591668123021074 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0386686866144033222100246952314 y1[1] (numeric) = 1.038668686614403330744739436716 absolute error = 8.5347147414846e-18 relative error = 8.2169751061851721177649518657992e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.28 y2[1] (analytic) = 1.0389445616892290520754099464035 y2[1] (numeric) = 1.0389004287743123989293624669003 absolute error = 4.41329149166531460474795032e-05 relative error = 0.0042478604291356079276170070457823 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0389445616892290520754099464035 y1[1] (numeric) = 1.0389445616892290606568534468713 absolute error = 8.5814435004678e-18 relative error = 8.2597703639885808128963164830972e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.6MB, time=61.98 NO POLE NO POLE x[1] = 0.281 y2[1] (analytic) = 1.0392213978194130047612201563121 y2[1] (numeric) = 1.0391770246559998774830227084486 absolute error = 4.43731634131272781974478635e-05 relative error = 0.0042698469744979275869363518627186 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0392213978194130047612201563121 y1[1] (numeric) = 1.0392213978194130133893789960154 absolute error = 8.6281588397033e-18 relative error = 8.3025223093054782891801192882212e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.6MB, time=62.49 NO POLE NO POLE x[1] = 0.282 y2[1] (analytic) = 1.0394991947281190731531793854871 y2[1] (numeric) = 1.0394545813854718856864448890133 absolute error = 4.46133426471874667344964738e-05 relative error = 0.0042918111792146296704982701095002 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0394991947281190731531793854871 y1[1] (numeric) = 1.0394991947281190818280400979629 absolute error = 8.6748607124758e-18 relative error = 8.3452308154454213779876469785000e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.283 y2[1] (analytic) = 1.0397779521375503716949608624835 y2[1] (numeric) = 1.0397330986851717171973474901821 absolute error = 4.48534523786544976133723014e-05 relative error = 0.004313752978359067413427608393535 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0397779521375503716949608624835 y1[1] (numeric) = 1.0397779521375503804165099345669 absolute error = 8.7215490720834e-18 relative error = 8.3878957561601015954237056384795e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.6MB, time=62.99 NO POLE NO POLE x[1] = 0.284 y2[1] (analytic) = 1.0400576697689495141850493904688 y2[1] (numeric) = 1.0400125762765820955256732023791 absolute error = 4.50934923674186593761880897e-05 relative error = 0.0043356723072323721534972924657847 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0400576697689495141850493904688 y1[1] (numeric) = 1.0400576697689495229532732623064 absolute error = 8.7682238718376e-18 relative error = 8.4305170056439995772784876554804e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.6MB, time=63.50 NO POLE NO POLE x[1] = 0.285 y2[1] (analytic) = 1.040338347342598892534104318956 y2[1] (numeric) = 1.0402930138802254525508422051503 absolute error = 4.53334623734399832621138057e-05 relative error = 0.0043575691013638084975284561078079 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.040338347342598892534104318956 y1[1] (numeric) = 1.0403383473425989013489893840199 absolute error = 8.8148850650639e-18 relative error = 8.4730944385356077132287255391897e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.286 y2[1] (analytic) = 1.0406199845778209564825443233454 y2[1] (numeric) = 1.0405744112156642079992969979463 absolute error = 4.55733621567484832473253991e-05 relative error = 0.0043794432965111250547360376889441 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0406199845778209564825443233454 y1[1] (numeric) = 1.0406199845778209653440769284462 absolute error = 8.8615326051008e-18 relative error = 8.5156279299171057669077293327371e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.6MB, time=64.00 NO POLE NO POLE x[1] = 0.287 y2[1] (analytic) = 1.0409025811929784942780742747098 y2[1] (numeric) = 1.0408567680015010498820593038828 absolute error = 4.58131914774443960149708270e-05 relative error = 0.0044012948286609007385948898627225 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0409025811929784942780742747098 y1[1] (numeric) = 1.0409025811929785031862407200108 absolute error = 8.9081664453010e-18 relative error = 8.5581173553161430761367624458006e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.6MB, time=64.50 NO POLE NO POLE x[1] = 0.288 y2[1] (analytic) = 1.0411861369054749143128735223236 y2[1] (numeric) = 1.0411400839553792158920186089432 absolute error = 4.60529500956984208549133804e-05 relative error = 0.0044231236340288866389340648750667 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0411861369054749143128735223236 y1[1] (numeric) = 1.0411861369054749232676600613541 absolute error = 8.9547865390305e-18 relative error = 8.6005625907055934186376328086465e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.289 y2[1] (analytic) = 1.0414706514317545277201639517677 y2[1] (numeric) = 1.04142435879398277576067093936 absolute error = 4.62926377717519594930124077e-05 relative error = 0.0044449296490603434660991114966524 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0414706514317545277201639517677 y1[1] (numeric) = 1.0414706514317545367215567914371 absolute error = 9.0013928396694e-18 relative error = 8.6429635125049350723910341036624e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.6MB, time=65.01 NO POLE NO POLE x[1] = 0.29 y2[1] (analytic) = 1.0417561244873028319298752220681 y2[1] (numeric) = 1.0417095922330369145740255204585 absolute error = 4.65322542659173558497016096e-05 relative error = 0.0044667128104303745691539486813206 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0417561244873028319298752220681 y1[1] (numeric) = 1.0417561244873028409778605226794 absolute error = 9.0479853006113e-18 relative error = 8.6853199975802772136734315972494e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.6MB, time=65.52 NO POLE NO POLE x[1] = 0.291 y2[1] (analytic) = 1.0420425557866467951831236262249 y2[1] (numeric) = 1.0419957839873082170473960010805 absolute error = 4.67717993385781357276251444e-05 relative error = 0.0044884730550442545302251572332204 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0420425557866467951831236262249 y1[1] (numeric) = 1.0420425557866468042776875014885 absolute error = 9.0945638752636e-18 relative error = 8.7276319232452424345003918134240e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.292 y2[1] (analytic) = 1.0423299450433551420052200606774 y2[1] (numeric) = 1.0422829337706049527587919688204 absolute error = 4.70112727501892464280918570e-05 relative error = 0.0045102103200377533372223513037087 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0423299450433551420052200606774 y1[1] (numeric) = 1.0423299450433551511463485777253 absolute error = 9.1411285170479e-18 relative error = 8.7698991672619362156307402243813e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.6MB, time=66.02 NO POLE NO POLE x[1] = 0.293 y2[1] (analytic) = 1.0426182919700386396369216307212 y2[1] (numeric) = 1.0425710412957773623406255227053 absolute error = 4.72506742612772962961080159e-05 relative error = 0.0045319245427774561372986501620864 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0426182919700386396369216307212 y1[1] (numeric) = 1.0426182919700386488246008101208 absolute error = 9.1876791793996e-18 relative error = 8.8121216078411399586837461320638e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.6MB, time=66.52 NO POLE NO POLE x[1] = 0.294 y2[1] (analytic) = 1.0429075962783503854236404606493 y2[1] (numeric) = 1.0428601062747179446294467116371 absolute error = 4.74900036324407941937490122e-05 relative error = 0.0045536156608610785735451626064783 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0429075962783503854236404606493 y1[1] (numeric) = 1.0429075962783503946578562764172 absolute error = 9.2342158157679e-18 relative error = 8.8542991236428796960050164162785e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=511.1MB, alloc=4.6MB, time=67.02 x[1] = 0.295 y2[1] (analytic) = 1.043197857678986095162322319432 y2[1] (numeric) = 1.0431501284183617447734206888849 absolute error = 4.77292606243503889016305471e-05 relative error = 0.0045752836121177777075428170634166 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.043197857678986095162322319432 y1[1] (numeric) = 1.0431978576789861044430606990482 absolute error = 9.2807383796162e-18 relative error = 8.8964315937773697432570435271558e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.296 y2[1] (analytic) = 1.0434890758816843924057067150814 y2[1] (numeric) = 1.0434411074366866432972584751743 absolute error = 4.79684449977491084482399071e-05 relative error = 0.0045969283346084585305238147302685 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0434890758816843924057067150814 y1[1] (numeric) = 1.0434890758816844017329535395035 absolute error = 9.3272468244221e-18 relative error = 8.9385188978055638930205130562036e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.6MB, time=67.53 NO POLE NO POLE x[1] = 0.297 y2[1] (analytic) = 1.0437812505952270987236791534653 y2[1] (numeric) = 1.0437330430387136461243122654673 absolute error = 4.82075565134525993668879980e-05 relative error = 0.0046185497666260760660234461068776 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0437812505952270987236791534653 y1[1] (numeric) = 1.0437812505952271080974202571422 absolute error = 9.3737411036769e-18 relative error = 8.9805609157392190952014872580163e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.6MB, time=68.04 NO POLE NO POLE x[1] = 0.298 y2[1] (analytic) = 1.0440743815274395249214253002402 y2[1] (numeric) = 1.0440259349325071755555452573616 absolute error = 4.84465949323493658800428786e-05 relative error = 0.004640147846695933067030988022671 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0440743815274395249214253002402 y1[1] (numeric) = 1.0440743815274395343416464711268 absolute error = 9.4202211708866e-18 relative error = 9.0225575280423881445981896628675e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.299 y2[1] (analytic) = 1.0443684683851907632140958277764 y2[1] (numeric) = 1.044319782825175362205085022163 absolute error = 4.86855600154010090108056134e-05 relative error = 0.0046617225135759733107758850696617 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0443684683851907632140958277764 y1[1] (numeric) = 1.0443684683851907726807828073473 absolute error = 9.4666869795709e-18 relative error = 9.0645086156309872505499206809331e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.6MB, time=68.54 NO POLE NO POLE x[1] = 0.3 y2[1] (analytic) = 1.044663510874393980357689772432 y2[1] (numeric) = 1.0446145864228703378920684831031 absolute error = 4.89244515236424656212893289e-05 relative error = 0.0046832737062570704944124094188207 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.044663510874393980357689772432 y1[1] (numeric) = 1.044663510874393989870828255696 absolute error = 9.5131384832640e-18 relative error = 9.1064140598740798014486730668192e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.6MB, time=69.05 NO POLE NO POLE x[1] = 0.301 y2[1] (analytic) = 1.0449595087000067117358632713184 y2[1] (numeric) = 1.044910345430788529488485608881 absolute error = 4.91632692181822473776624374e-05 relative error = 0.0047048013639633127349924842687054 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0449595087000067117358632713184 y1[1] (numeric) = 1.0449595087000067212954389068331 absolute error = 9.5595756355147e-18 relative error = 9.1482737425944804929100644732950e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.302 y2[1] (analytic) = 1.0452564615660311564023695917739 y2[1] (numeric) = 1.0452070595531709537227279747094 absolute error = 4.94020128602026796416170645e-05 relative error = 0.0047263054261522826772423420296295 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0452564615660311564023695917739 y1[1] (numeric) = 1.0452564615660311660083679816594 absolute error = 9.6059983898855e-18 relative error = 9.1900875460683941362978973613728e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.6MB, time=69.55 NO POLE NO POLE x[1] = 0.303 y2[1] (analytic) = 1.0455543691755144730788354111266 y2[1] (numeric) = 1.045504728493303512938547387342 absolute error = 4.96406822109601402880237846e-05 relative error = 0.0047477858325153332127841644920633 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0455543691755144730788354111266 y1[1] (numeric) = 1.0455543691755144827312421110804 absolute error = 9.6524066999538e-18 relative error = 9.2318553530270559963328221718186e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.6MB, time=70.06 NO POLE NO POLE x[1] = 0.304 y2[1] (analytic) = 1.0458532312305490771075773489994 y2[1] (numeric) = 1.0458033519535172918091288151479 absolute error = 4.98792770317852984485338515e-05 relative error = 0.0047692425229778588145688159579895 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0458532312305490771075773489994 y1[1] (numeric) = 1.0458532312305490868063778683107 absolute error = 9.6988005193113e-18 relative error = 9.2735770466566406490427515139756e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.305 y2[1] (analytic) = 1.0461530474322729383591617993617 y2[1] (numeric) = 1.0461029296351888550059809091843 absolute error = 5.01177970840833531808901774e-05 relative error = 0.0047906754376995624904102241654071 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0461530474322729383591617993617 y1[1] (numeric) = 1.0461530474322729481043416009258 absolute error = 9.7451798015641e-18 relative error = 9.3152525105988325106755471487195e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.6MB, time=70.56 NO POLE NO POLE x[1] = 0.306 y2[1] (analytic) = 1.0464538174808698800944101547946 y2[1] (numeric) = 1.0464034612387405458223464464025 absolute error = 5.03562421293342720637083921e-05 relative error = 0.0048120845170747183596358861551425 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0464538174808698800944101547946 y1[1] (numeric) = 1.0464538174808698898859546551276 absolute error = 9.7915445003330e-18 relative error = 9.3568816289515789047272069755270e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.6MB, time=71.07 NO POLE NO POLE x[1] = 0.307 y2[1] (analytic) = 1.0467555410755698787805505609892 y2[1] (numeric) = 1.0467049464636407857508340716011 absolute error = 5.05946119290930297164893881e-05 relative error = 0.0048334697017324298569913710252354 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0467555410755698787805505609892 y1[1] (numeric) = 1.0467555410755698886184451302426 absolute error = 9.8378945692534e-18 relative error = 9.3984642862694520889699153352035e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.308 y2[1] (analytic) = 1.0470582179146493648612163853508 y2[1] (numeric) = 1.0470073850084043750149717605203 absolute error = 5.08329062449898462446248305e-05 relative error = 0.0048548309325368835680595548401332 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0470582179146493648612163853508 y1[1] (numeric) = 1.0470582179146493747454463473258 absolute error = 9.8842299619750e-18 relative error = 9.4400003675638120315884117660562e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.6MB, time=71.58 NO POLE NO POLE x[1] = 0.309 y2[1] (analytic) = 1.0473618476954315244799906297348 y2[1] (numeric) = 1.0473107765705927940543814725478 absolute error = 5.10711248387304256091571870e-05 relative error = 0.0048761681505875987005776509050778 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0473618476954315244799906297348 y1[1] (numeric) = 1.0473618476954315344105412618975 absolute error = 9.9305506321627e-18 relative error = 9.4814897583041070265768015465396e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.6MB, time=72.08 NO POLE NO POLE x[1] = 0.31 y2[1] (analytic) = 1.0476664301142866021571945637978 y2[1] (numeric) = 1.0476151208468145059632735078878 absolute error = 5.13092674720961939210559100e-05 relative error = 0.0048974812972196721961568866732926 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0476664301142866021571945637978 y1[1] (numeric) = 1.0476664301142866121340510972933 absolute error = 9.9768565334955e-18 relative error = 9.5229323444172554233542684111222e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.311 y2[1] (analytic) = 1.0479719648666322044196179021966 y2[1] (numeric) = 1.0479204175327252598819581307235 absolute error = 5.15473339069445376597714731e-05 relative error = 0.004918770314004019487030921904077 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0479719648666322044196179021966 y1[1] (numeric) = 1.0479719648666322144427655218643 absolute error = 1.00231476196677e-17 relative error = 9.5643280122892155261106725625522e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.6MB, time=72.58 NO POLE NO POLE x[1] = 0.312 y2[1] (analytic) = 1.0482784516469336043828868959338 y2[1] (numeric) = 1.0482266663230283953410710668868 absolute error = 5.17853239052090418158290470e-05 relative error = 0.0049400351427476109025797989954044 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0482784516469336043828868959338 y1[1] (numeric) = 1.048278451646933614452310740322 absolute error = 1.00694238443882e-17 relative error = 9.6056766487647326283521034214739e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.6MB, time=73.08 NO POLE NO POLE x[1] = 0.313 y2[1] (analytic) = 1.0485858901487040472861657555049 y2[1] (numeric) = 1.0485338669114751475582085318349 absolute error = 5.20232372288997279572236700e-05 relative error = 0.0049612757254937037304963592119308 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0485858901487040472861657555049 y1[1] (numeric) = 1.0485858901487040574018509168857 absolute error = 1.01156851613808e-17 relative error = 9.6469781411480325243839734954240e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.314 y2[1] (analytic) = 1.0488942800645050569788858711721 y2[1] (numeric) = 1.0488420189908649536866664923248 absolute error = 5.22610736401032922193788473e-05 relative error = 0.0049824920045220699375816458156162 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0488942800645050569788858711721 y1[1] (numeric) = 1.0488942800645050671408173955563 absolute error = 1.01619315243842e-17 relative error = 9.6882323772032201553085210549772e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.6MB, time=73.58 NO POLE NO POLE x[1] = 0.315 y2[1] (analytic) = 1.0492036210859467433591963436608 y2[1] (numeric) = 1.049151122253045760015977913071 absolute error = 5.24988329009833432184305898e-05 relative error = 0.0050036839223492195552748418134653 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0492036210859467433591963436608 y1[1] (numeric) = 1.0492036210859467535673592308128 absolute error = 1.02081628871520e-17 relative error = 9.7294392451546699171826424593026e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.6MB, time=74.09 NO POLE NO POLE x[1] = 0.316 y2[1] (analytic) = 1.0495139129036881107638283868539 y2[1] (numeric) = 1.0494611763889143301239407878759 absolute error = 5.27365147737806398875989780e-05 relative error = 0.005024851421728619735141752311523 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0495139129036881107638283868539 y1[1] (numeric) = 1.0495139129036881210182075903067 absolute error = 1.02543792034528e-17 relative error = 9.7705986336875029243931523593460e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=568.3MB, alloc=4.6MB, time=74.59 x[1] = 0.317 y2[1] (analytic) = 1.0498251552074373673090652126448 y2[1] (numeric) = 1.0497721810884165539798288032292 absolute error = 5.29741190208133292364094156e-05 relative error = 0.005045994445650909479663735958045 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0498251552074373673090652126448 y1[1] (numeric) = 1.0498251552074373776096456397152 absolute error = 1.03005804270704e-17 relative error = 9.8117104319481510415872865004417e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.318 y2[1] (analytic) = 1.0501373476859522351825080570062 y2[1] (numeric) = 1.050084136040547757998475531193 absolute error = 5.32116454044771840325258132e-05 relative error = 0.0050671129373441100537863121324583 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0501373476859522351825080570062 y1[1] (numeric) = 1.0501373476859522455292745688096 absolute error = 1.03467665118034e-17 relative error = 9.8527745295443409163028034668620e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.6MB, time=75.10 NO POLE NO POLE x[1] = 0.319 y2[1] (analytic) = 1.0504504900270402618853280555329 y2[1] (numeric) = 1.0503970409333530160449220975128 absolute error = 5.34490936872458404059580201e-05 relative error = 0.0050882068402738310828034170729953 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0504504900270402618853280555329 y1[1] (numeric) = 1.0504504900270402722782654669988 absolute error = 1.03929374114659e-17 relative error = 9.8937908165461175664565964236966e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.6MB, time=75.61 NO POLE NO POLE x[1] = 0.32 y2[1] (analytic) = 1.0507645819175591324246927262339 y2[1] (numeric) = 1.0507108954539274613893173203332 absolute error = 5.36864636316710353754059007e-05 relative error = 0.0051092760981434723422694492030646 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0507645819175591324246927262339 y1[1] (numeric) = 1.0507645819175591428637858061209 absolute error = 1.04390930798870e-17 relative error = 9.9347591834857164668292119585503e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.321 y2[1] (analytic) = 1.0510796230434169824560548671731 y2[1] (numeric) = 1.0510256992884165996117583646447 absolute error = 5.39237550003828442965025284e-05 relative error = 0.005130320654894421245746827532256 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0510796230434169824560548671731 y1[1] (numeric) = 1.051079623043416992941288338084 absolute error = 1.04852334709109e-17 relative error = 9.9756795213579990573501717864591e-16 % Correct digits = 17 h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.6MB, time=76.11 NO POLE NO POLE x[1] = 0.322 y2[1] (analytic) = 1.0513956130895727123749907266948 y2[1] (numeric) = 1.051341452122016622456759007646 absolute error = 5.41609675560899182317190488e-05 relative error = 0.0051513404547062460363117839627372 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0513956130895727123749907266948 y1[1] (numeric) = 1.0513956130895727229063492650921 absolute error = 1.05313585383973e-17 relative error = 1.0016551721621165156649754055282e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.6MB, time=76.60 NO POLE NO POLE x[1] = 0.323 y2[1] (analytic) = 1.051712551740036302358273354424 y2[1] (numeric) = 1.0516581536389747226370316605805 absolute error = 5.43981010615797212416938435e-05 relative error = 0.0051723354419968846878555168455612 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.051712551740036302358273354424 y1[1] (numeric) = 1.0517125517400363129357415906451 absolute error = 1.05774682362211e-17 relative error = 1.0057375676196790859786257079329e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.324 y2[1] (analytic) = 1.0520304386778691283538660919921 y2[1] (numeric) = 1.0519758035225894095862683432908 absolute error = 5.46351552797187675977487013e-05 relative error = 0.0051933055614228295223316452169636 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0520304386778691283538660919921 y1[1] (numeric) = 1.0520304386778691389774286102647 absolute error = 1.06235625182726e-17 relative error = 1.0098151277470333986245087450570e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.6MB, time=77.11 NO POLE NO POLE x[1] = 0.325 y2[1] (analytic) = 1.0523492735851842790195202135225 y2[1] (numeric) = 1.0522944014552108261606048587367 absolute error = 5.48721299734528589153547858e-05 relative error = 0.0052142507578793075492141183192894 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0523492735851842790195202135225 y1[1] (numeric) = 1.0523492735851842896891615519801 absolute error = 1.06696413384576e-17 relative error = 1.0138878418291535934500991536070e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.6MB, time=77.62 NO POLE NO POLE x[1] = 0.326 y2[1] (analytic) = 1.0526690561431468736096597773046 y2[1] (numeric) = 1.0526139471182410662884514660389 absolute error = 5.51090249058073212083112657e-05 relative error = 0.005235170976500456533542348719393 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0526690561431468736096597773046 y1[1] (numeric) = 1.0526690561431468843253644280017 absolute error = 1.07157046506971e-17 relative error = 1.0179556991974435165564045098445e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.327 y2[1] (analytic) = 1.0529897860319743808102358017967 y2[1] (numeric) = 1.0529344401921344935683724022439 absolute error = 5.53458398398872418633995528e-05 relative error = 0.0052560661626594967990423467765144 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0529897860319743808102358017967 y1[1] (numeric) = 1.0529897860319743915719882107247 absolute error = 1.07617524089280e-17 relative error = 1.0220186892298322685110901005369e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.6MB, time=78.12 NO POLE NO POLE x[1] = 0.328 y2[1] (analytic) = 1.0533114629309369385212309311322 y2[1] (numeric) = 1.0532558803563980608146956549579 absolute error = 5.55825745388777065352761743e-05 relative error = 0.0052769362619688987729240361705575 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0533114629309369385212309311322 y1[1] (numeric) = 1.0533114629309369493290154982346 absolute error = 1.08077845671024e-17 relative error = 1.0260768013507358983461709373915e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.6MB, time=78.62 NO POLE NO POLE x[1] = 0.329 y2[1] (analytic) = 1.0536340865183576745864948076487 y2[1] (numeric) = 1.0535782672895916305505334402655 absolute error = 5.58192287660440359613673832e-05 relative error = 0.0052977812202805462790657206828261 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0536340865183576745864948076487 y1[1] (numeric) = 1.053634086518357685440295886837 absolute error = 1.08538010791883e-17 relative error = 1.0301300250311512755132380335682e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.33 y2[1] (analytic) = 1.0539576564716130284705894216338 y2[1] (numeric) = 1.0539016006693282964478928929406 absolute error = 5.60558022847320226965286932e-05 relative error = 0.0053186009836858955864068491009558 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0539576564716130284705894216338 y1[1] (numeric) = 1.0539576564716130393703913208029 absolute error = 1.08998018991691e-17 relative error = 1.0341783497886351674051174758197e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.6MB, time=79.12 NO POLE NO POLE x[1] = 0.331 y2[1] (analytic) = 1.0542821724671330738823227614669 y2[1] (numeric) = 1.0542258801722747057145555288642 absolute error = 5.62922948583681677672326027e-05 relative error = 0.0053393954985161302194797838615937 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0542821724671330738823227614669 y1[1] (numeric) = 1.0542821724671330848281097425109 absolute error = 1.09457869810440e-17 relative error = 1.0382217651873679558497681692060e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.6MB, time=79.63 NO POLE NO POLE x[1] = 0.332 y2[1] (analytic) = 1.0546076341804018423446481406519 y2[1] (numeric) = 1.0545511054741513824274030927981 absolute error = 5.65287062504599172450478538e-05 relative error = 0.0053601647113423115381202174046023 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0546076341804018423446481406519 y1[1] (numeric) = 1.0546076341804018533364044194798 absolute error = 1.09917562788279e-17 relative error = 1.0422602608381690595103171581856e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.333 y2[1] (analytic) = 1.0549340412859576477106056318672 y2[1] (numeric) = 1.0548772762497330518118664582142 absolute error = 5.67650362245958987391736530e-05 relative error = 0.0053809085689755250935041947423475 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0549340412859576477106056318672 y1[1] (numeric) = 1.0549340412859576587483153784186 absolute error = 1.10377097465514e-17 relative error = 1.0462938263985210413633340637503e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.6MB, time=80.16 NO POLE NO POLE x[1] = 0.334 y2[1] (analytic) = 1.0552613934573934116249810921192 y2[1] (numeric) = 1.0552043921728489654671732997583 absolute error = 5.70012845444461578077923609e-05 relative error = 0.0054016270184670227677673884180601 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0552613934573934116249810921192 y1[1] (numeric) = 1.0552613934573934227086284303804 absolute error = 1.10836473382612e-17 relative error = 1.0503224515726308112637267742166e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.6MB, time=80.67 NO POLE NO POLE x[1] = 0.335 y2[1] (analytic) = 1.0555896903673569899313573173679 y2[1] (numeric) = 1.0555324529163832275370693131278 absolute error = 5.72374509737623942880042401e-05 relative error = 0.0054223200071083607045693299724373 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0555896903673569899313573173679 y1[1] (numeric) = 1.0555896903673570010609263253877 absolute error = 1.11295690080198e-17 relative error = 1.0543461261114236354145521781274e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.336 y2[1] (analytic) = 1.0559189316875515000242309195995 y2[1] (numeric) = 1.0558614581522751218256868116686 absolute error = 5.74735352763781985441079309e-05 relative error = 0.0054429874824315330380717270332814 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0559189316875515000242309195995 y1[1] (numeric) = 1.0559189316875515111997056295048 absolute error = 1.11754747099053e-17 relative error = 1.0583648398125458618318674888293e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.6MB, time=81.18 NO POLE NO POLE x[1] = 0.337 y2[1] (analytic) = 1.056249117088735649145867574257 y2[1] (numeric) = 1.056191407551519439858233583851 absolute error = 5.77095372162092876339904060e-05 relative error = 0.0054636293922091014279057845356828 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.056249117088735649145867574257 y1[1] (numeric) = 1.0562491170887356603672319722691 absolute error = 1.12213643980121e-17 relative error = 1.0623785825204520827461018761631e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.6MB, time=81.69 NO POLE NO POLE x[1] = 0.338 y2[1] (analytic) = 1.0565802462407240636275673412012 y2[1] (numeric) = 1.056522300784166809886173950962 absolute error = 5.79454565572537413933902392e-05 relative error = 0.0054842456844543204078085996043138 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0565802462407240636275673412012 y1[1] (numeric) = 1.0565802462407240748948053676517 absolute error = 1.12672380264505e-17 relative error = 1.0663873441263872589199315801683e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=625.6MB, alloc=4.6MB, time=82.21 x[1] = 0.339 y2[1] (analytic) = 1.0569123188123876190750108179637 y2[1] (numeric) = 1.0568541375193240268365730198609 absolute error = 5.81812930635922384377981028e-05 relative error = 0.0055048363074212585557132088773374 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0569123188123876190750108179637 y1[1] (numeric) = 1.0569123188123876303881063673106 absolute error = 1.13130955493469e-17 relative error = 1.0703911145684248813501955845449e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.34 y2[1] (analytic) = 1.0572453344716537714973559399734 y2[1] (numeric) = 1.0571869174251543832052741814813 absolute error = 5.84170464993882920817584921e-05 relative error = 0.0055254012096049154931807325291745 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0572453344716537714973559399734 y1[1] (numeric) = 1.0572453344716537828562928608172 absolute error = 1.13589369208438e-17 relative error = 1.0743898838314853789955565809047e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.6MB, time=82.72 NO POLE NO POLE x[1] = 0.341 y2[1] (analytic) = 1.0575792928855068893797542986879 y2[1] (numeric) = 1.0575206401688780008935789619298 absolute error = 5.86527166288884861753367581e-05 relative error = 0.0055459403397413347221662777708619 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0575792928855068893797542986879 y1[1] (numeric) = 1.0575792928855069007845163937877 absolute error = 1.14047620950998e-17 relative error = 1.0783836419473537267985652615594e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.6MB, time=83.23 NO POLE NO POLE x[1] = 0.342 y2[1] (analytic) = 1.0579141937199885866989549051396 y2[1] (numeric) = 1.0578553054167721639880973895288 absolute error = 5.88883032164227108575156108e-05 relative error = 0.0055664536468077123072128334716146 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0579141937199885866989549051396 y1[1] (numeric) = 1.0579141937199885981495259314294 absolute error = 1.14505710262898e-17 relative error = 1.0823723789947151607650370623604e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.343 y2[1] (analytic) = 1.0582500366401980568816623833228 y2[1] (numeric) = 1.0581909128341716524834360979812 absolute error = 5.91238060264043982262853416e-05 relative error = 0.0055869410800225014112693047261578 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0582500366401980568816623833228 y1[1] (numeric) = 1.0582500366401980683780260519275 absolute error = 1.14963636686047e-17 relative error = 1.0863560850991428128219396619414e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.6MB, time=83.74 NO POLE NO POLE x[1] = 0.344 y2[1] (analytic) = 1.0585868213102924077053156350886 y2[1] (numeric) = 1.0585274620854690769473904429961 absolute error = 5.93592248233307579251920925e-05 relative error = 0.0056074025888455126934300980184388 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0585868213102924077053156350886 y1[1] (numeric) = 1.0585868213102924192474556113407 absolute error = 1.15421399762521e-17 relative error = 1.0903347504331790704234682953939e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.6MB, time=84.25 NO POLE NO POLE x[1] = 0.345 y2[1] (analytic) = 1.0589245473934869971409520758003 y2[1] (numeric) = 1.0588649528341152141283059672122 absolute error = 5.95945593717830126461085881e-05 relative error = 0.0056278381229780105769942731012378 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0589245473934869971409520758003 y1[1] (numeric) = 1.0589245473934870087288519792557 absolute error = 1.15878999034554e-17 relative error = 1.0943083652162649199828471116145e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.346 y2[1] (analytic) = 1.0592632145520557701378215979091 y2[1] (numeric) = 1.0592033847426193435042736060845 absolute error = 5.98298094364266335479918246e-05 relative error = 0.0056482476323628053963422225417559 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0592632145520557701378215979091 y1[1] (numeric) = 1.059263214552055781771465002364 absolute error = 1.16336434044549e-17 relative error = 1.0982769197148574719240839207269e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.6MB, time=84.76 NO POLE NO POLE x[1] = 0.347 y2[1] (analytic) = 1.0596028224473315963494134778678 y2[1] (numeric) = 1.0595427574725495847738220855675 absolute error = 6.00649747820115755913923003e-05 relative error = 0.0056686310671843414312271237565899 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0596028224473315963494134778678 y1[1] (numeric) = 1.0596028224473316080287839113749 absolute error = 1.16793704335071e-17 relative error = 1.1022404042423766217653909210331e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.6MB, time=85.27 NO POLE NO POLE x[1] = 0.348 y2[1] (analytic) = 1.0599433707397066088005585003816 y2[1] (numeric) = 1.0598830706845332362877700209308 absolute error = 6.03000551733725127884794508e-05 relative error = 0.0056889883778687808371770266682846 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0599433707397066088005585003816 y1[1] (numeric) = 1.0599433707397066205256394452664 absolute error = 1.17250809448848e-17 relative error = 1.1061988091592265256752465511480e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.349 y2[1] (analytic) = 1.0602848590886325434952676329222 y2[1] (numeric) = 1.060224324038257114421899284883 absolute error = 6.05350503754290733683480392e-05 relative error = 0.0057093195150840834808013924307487 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0602848590886325434952676329222 y1[1] (numeric) = 1.0602848590886325552660425257999 absolute error = 1.17707748928777e-17 relative error = 1.1101521248728634287758344265355e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.6MB, time=85.78 NO POLE NO POLE x[1] = 0.35 y2[1] (analytic) = 1.0606272871526210799649676426963 y2[1] (numeric) = 1.0605665171924678938901102723587 absolute error = 6.07699601531860748573703376e-05 relative error = 0.0057296244297400826888931818241732 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0606272871526210799649676426963 y1[1] (numeric) = 1.0606272871526210917814198744881 absolute error = 1.18164522317918e-17 relative error = 1.1141003418377494587685287924152e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.6MB, time=86.29 NO POLE NO POLE x[1] = 0.351 y2[1] (analytic) = 1.0609706545892441827567931078597 y2[1] (numeric) = 1.060909649804972448997718748842 absolute error = 6.10047842717337590743590177e-05 relative error = 0.0057499030729885569203142033706334 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0609706545892441827567931078597 y1[1] (numeric) = 1.0609706545892441946189060238094 absolute error = 1.18621129159497e-17 relative error = 1.1180434505553905741589944652429e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.352 y2[1] (analytic) = 1.0613149610551344438615933347137 y2[1] (numeric) = 1.0612537215326381958345530289579 absolute error = 6.12395224962480270403057558e-05 relative error = 0.0057701553962232973697473697878526 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0613149610551344438615933347137 y1[1] (numeric) = 1.0613149610551344557693502344044 absolute error = 1.19077568996907e-17 relative error = 1.1219814415743548320673952805200e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.6MB, time=86.80 NO POLE NO POLE x[1] = 0.353 y2[1] (analytic) = 1.0616602062059854260813117529063 y2[1] (numeric) = 1.0615987320313934354075092922629 absolute error = 6.14741745919906738024606434e-05 relative error = 0.0057903813510801715124947742396529 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0616602062059854260813117529063 y1[1] (numeric) = 1.0616602062059854380346958902772 absolute error = 1.19533841373709e-17 relative error = 1.1259143054902898583848196330111e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.6MB, time=87.31 NO POLE NO POLE x[1] = 0.354 y2[1] (analytic) = 1.0620063896965520073353944212866 y2[1] (numeric) = 1.0619446809562276977122219037083 absolute error = 6.17087403243096231725175783e-05 relative error = 0.0058105808894371825995950828268273 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0620063896965520073353944212866 y1[1] (numeric) = 1.0620063896965520193343890046497 absolute error = 1.19989945833631e-17 relative error = 1.1298420329459206897291237541898e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.355 y2[1] (analytic) = 1.062353511180650725905883338033 y2[1] (numeric) = 1.062291567961192086743504667134 absolute error = 6.19432194586391623786708990e-05 relative error = 0.0058307539634145251126276454686147 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.062353511180650725905883338033 y1[1] (numeric) = 1.0623535111806507379504715300897 absolute error = 1.20445881920567e-17 relative error = 1.1337646146310468581493654082917e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.6MB, time=87.82 NO POLE NO POLE x[1] = 0.356 y2[1] (analytic) = 1.0627015703111601266208493099901 y2[1] (numeric) = 1.0626393926993996264442180013814 absolute error = 6.21776117605001766313086087e-05 relative error = 0.0058509005253746361876639509647499 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0627015703111601266208493099901 y1[1] (numeric) = 1.0627015703111601387110142278483 absolute error = 1.20901649178582e-17 relative error = 1.1376820412825951804891389891459e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=671.3MB, alloc=4.6MB, time=88.34 NO POLE NO POLE x[1] = 0.357 y2[1] (analytic) = 1.0630505667400211079758181978111 y2[1] (numeric) = 1.0629881548230256075922160901856 absolute error = 6.24119169955003836021076255e-05 relative error = 0.0058710205279222430179195927271507 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0630505667400211079758181978111 y1[1] (numeric) = 1.063050566740021120111542913002 absolute error = 1.21357247151909e-17 relative error = 1.1415943036845964282459563417120e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.358 y2[1] (analytic) = 1.0634005001182372701928434155077 y2[1] (numeric) = 1.06333785398330793562502711893 absolute error = 6.26461349293345678162965777e-05 relative error = 0.00589111392390440624475176615435 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0634005001182372701928434155077 y1[1] (numeric) = 1.0634005001182372823741109540026 absolute error = 1.21812675384949e-17 relative error = 1.1455013926681894942957172366581e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.6MB, time=88.85 NO POLE NO POLE x[1] = 0.359 y2[1] (analytic) = 1.0637513700958752642168766253644 y2[1] (numeric) = 1.063688489830547479401918773611 absolute error = 6.28802653277848149578517534e-05 relative error = 0.0059111806664105593467384865651392 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0637513700958752642168766253644 y1[1] (numeric) = 1.0637513700958752764436699675919 absolute error = 1.22267933422275e-17 relative error = 1.1494032991116623943863119948464e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.6MB, time=89.36 NO POLE NO POLE x[1] = 0.36 y2[1] (analytic) = 1.0641031763220651416490876318753 y2[1] (numeric) = 1.0640400620141084209030002399772 absolute error = 6.31143079567207460873918981e-05 relative error = 0.0059312207087725440366661949272441 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0641031763220651416490876318753 y1[1] (numeric) = 1.0641031763220651539213897127382 absolute error = 1.22723020808629e-17 relative error = 1.1533000139404266449124682925632e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.361 y2[1] (analytic) = 1.064455918445000705616783541413 y2[1] (numeric) = 1.0643925701824186058650110037695 absolute error = 6.33482625820997517725376435e-05 relative error = 0.0059512340045646416763422065927605 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.064455918445000705616783541413 y1[1] (numeric) = 1.0644559184450007179345772503054 absolute error = 1.23177937088924e-17 relative error = 1.1571915281270379046825911996510e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.6MB, time=89.87 NO POLE NO POLE x[1] = 0.362 y2[1] (analytic) = 1.0648095961119398625795763177395 y2[1] (numeric) = 1.0647460139829698953534458163033 absolute error = 6.35821289699672261305014362e-05 relative error = 0.0059712205076036007192375533499399 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0648095961119398625795763177395 y1[1] (numeric) = 1.0648095961119398749428444985637 absolute error = 1.23632681808242e-17 relative error = 1.1610778326911782517072256014928e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.6MB, time=90.38 NO POLE NO POLE x[1] = 0.363 y2[1] (analytic) = 1.0651642089692049750714469272204 y2[1] (numeric) = 1.0651003930623185182706642532962 absolute error = 6.38159068864568007826739242e-05 relative error = 0.0059911801719486601910541704049976 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0651642089692049750714469272204 y1[1] (numeric) = 1.0651642089692049874801723784043 absolute error = 1.24087254511839e-17 relative error = 1.1649589186997034547769879116388e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.6MB, time=90.89 NO POLE NO POLE x[1] = 0.364 y2[1] (analytic) = 1.0655197566621832153783533317088 y2[1] (numeric) = 1.065455707066085424799632358862 absolute error = 6.40495960977905787209728468e-05 relative error = 0.006011112951901569218398085336661 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0655197566621832153783533317088 y1[1] (numeric) = 1.0655197566621832278325188062231 absolute error = 1.24541654745143e-17 relative error = 1.1688347772666236973493954397388e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.365 y2[1] (analytic) = 1.0658762388353269201510286515192 y2[1] (numeric) = 1.0658119556389566407829429309581 absolute error = 6.42831963702793680857205611e-05 relative error = 0.006031018802006602615827274207705 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0658762388353269201510286515192 y1[1] (numeric) = 1.0658762388353269326506168568945 absolute error = 1.24995882053753e-17 relative error = 1.1727053995530929645762807241632e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.6MB, time=91.40 NO POLE NO POLE x[1] = 0.366 y2[1] (analytic) = 1.0662336551321539459526148857234 y2[1] (numeric) = 1.066169138424683623036760069296 absolute error = 6.45167074703229158548164274e-05 relative error = 0.0060508976770505725416291595250457 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0662336551321539459526148857234 y1[1] (numeric) = 1.0662336551321539584976084840676 absolute error = 1.25449935983442e-17 relative error = 1.1765707767674352102097642503913e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.6MB, time=91.91 NO POLE NO POLE x[1] = 0.367 y2[1] (analytic) = 1.0665920051952480257407766421643 y2[1] (numeric) = 1.0665272550660836155993326717993 absolute error = 6.47501291644101414439703650e-05 relative error = 0.0060707495320628362327683340321603 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0665920051952480257407766421643 y1[1] (numeric) = 1.06659200519524803833115825018 absolute error = 1.25903816080157e-17 relative error = 1.1804309001651415877801824443727e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.368 y2[1] (analytic) = 1.0669512886662591262839383951033 y2[1] (numeric) = 1.0668863052050400069137206311264 absolute error = 6.49834612191193702177639769e-05 relative error = 0.0060905743223152998295300017771887 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0669512886662591262839383951033 y1[1] (numeric) = 1.066951288666259138919690584105 absolute error = 1.26357521890017e-17 relative error = 1.1842857610488481865660256511879e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.6MB, time=92.42 NO POLE NO POLE x[1] = 0.369 y2[1] (analytic) = 1.0673115051859038065112878542941 y2[1] (numeric) = 1.0672462884825026879443765485605 absolute error = 6.52167034011185669113057336e-05 relative error = 0.0061103720033224183004688328196194 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0673115051859038065112878542941 y1[1] (numeric) = 1.0673115051859038191923931502257 absolute error = 1.26811052959316e-17 relative error = 1.1881353507683599041139706400355e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.6MB, time=92.93 NO POLE NO POLE x[1] = 0.37 y2[1] (analytic) = 1.0676726543939655767961870955091 y2[1] (numeric) = 1.0676072045384884112272248487155 absolute error = 6.54498554771655689622467936e-05 relative error = 0.0061301425308411914783564281660583 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0676726543939655767961870955091 y1[1] (numeric) = 1.0676726543939655895226279789615 absolute error = 1.27264408834524e-17 relative error = 1.1919796607206547836101680647735e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.371 y2[1] (analytic) = 1.0680347359292952591726321691378 y2[1] (numeric) = 1.0679690530120811508528792450088 absolute error = 6.56829172141083197529241290e-05 relative error = 0.0061498858608711562179033865230441 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0680347359292952591726321691378 y1[1] (numeric) = 1.0680347359292952719443910753662 absolute error = 1.27717589062284e-17 relative error = 1.1958186823498501363461933809703e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.6MB, time=93.44 NO POLE NO POLE x[1] = 0.372 y2[1] (analytic) = 1.0683977494298113484844009704265 y2[1] (numeric) = 1.068331833541432463382638572713 absolute error = 6.59158883788851017623977135e-05 relative error = 0.0061696019496543746861140525114551 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0683977494298113484844009704265 y1[1] (numeric) = 1.0683977494298113613014602893682 absolute error = 1.28170593189417e-17 relative error = 1.1996524071472428581197674560727e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.6MB, time=93.96 NO POLE NO POLE x[1] = 0.373 y2[1] (analytic) = 1.0687616945325003744665282222431 y2[1] (numeric) = 1.0686955457637618496969000736212 absolute error = 6.61487687385247696281486219e-05 relative error = 0.0061892907536754187962134063855697 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0687616945325003744665282222431 y1[1] (numeric) = 1.0687616945325003873288702985349 absolute error = 1.28623420762918e-17 relative error = 1.2034808266512647010577781884391e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.374 y2[1] (analytic) = 1.0691265708734172647587454889206 y2[1] (numeric) = 1.0690601893153571177756282839423 absolute error = 6.63815580601469831172049783e-05 relative error = 0.0062089522296613507961662263018019 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0691265708734172647587454889206 y1[1] (numeric) = 1.0691265708734172776663526219165 absolute error = 1.29076071329959e-17 relative error = 1.2073039324475023584805541348783e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.6MB, time=94.47 NO POLE NO POLE x[1] = 0.375 y2[1] (analytic) = 1.0694923780876857088505232077704 y2[1] (numeric) = 1.0694257638315747464105167449884 absolute error = 6.66142561109624400064627820e-05 relative error = 0.006228586334581700022888615406744 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0694923780876857088505232077704 y1[1] (numeric) = 1.0694923780876857218033776515596 absolute error = 1.29528544437892e-17 relative error = 1.2111217161687167571506375865556e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.6MB, time=94.99 NO POLE NO POLE x[1] = 0.376 y2[1] (analytic) = 1.0698591158094985229573507932542 y2[1] (numeric) = 1.069792268946840249848478824522 absolute error = 6.68468626582731088719687322e-05 relative error = 0.0062481930256484358333312361149502 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0698591158094985229573507932542 y1[1] (numeric) = 1.0698591158094985359554347566783 absolute error = 1.29980839634241e-17 relative error = 1.2149341694947587414849263784643e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.377 y2[1] (analytic) = 1.070226783672118015827889937563 y2[1] (numeric) = 1.0701597042946485433661030053033 absolute error = 6.70793774694724617869322597e-05 relative error = 0.0062677722603159367236921314472041 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.070226783672118015827889937563 y1[1] (numeric) = 1.0702267836721180288711855842341 absolute error = 1.30432956466711e-17 relative error = 1.2187412841526430256490702746266e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.6MB, time=95.50 NO POLE NO POLE x[1] = 0.378 y2[1] (analytic) = 1.0705953813078763554816353004824 y2[1] (numeric) = 1.0705280695075643097747070664121 absolute error = 6.73118003120457069282340703e-05 relative error = 0.0062873239962809556480948386110858 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0705953813078763554816353004824 y1[1] (numeric) = 1.0705953813078763685701247488011 absolute error = 1.30884894483187e-17 relative error = 1.2225430519165278378466530623536e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.6MB, time=96.01 NO POLE NO POLE x[1] = 0.379 y2[1] (analytic) = 1.070964908348175936876715850913 y2[1] (numeric) = 1.0708973642172223668556246523215 absolute error = 6.75441309535700210911985915e-05 relative error = 0.0063068481914825815481446104609467 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.070964908348175936876715850913 y1[1] (numeric) = 1.070964908348175950010381174086 absolute error = 1.31336653231730e-17 relative error = 1.2263394646076658451831699273161e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.38 y2[1] (analytic) = 1.0713353644234897505074691922754 y2[1] (numeric) = 1.0712675880543280357253567944668 absolute error = 6.77763691617147821123978086e-05 relative error = 0.0063263448041021971048519568386264 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0713353644234897505074691922754 y1[1] (numeric) = 1.0713353644234897636862924183336 absolute error = 1.31788232260582e-17 relative error = 1.2301305140944384390680129277128e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.6MB, time=96.52 NO POLE NO POLE x[1] = 0.381 y2[1] (analytic) = 1.0717067491633617519314202742562 y2[1] (numeric) = 1.0716387406486575101302200201887 absolute error = 6.80085147042418012002540675e-05 relative error = 0.0063458137925634327244883982516645 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0717067491633617519314202742562 y1[1] (numeric) = 1.0717067491633617651553833860725 absolute error = 1.32239631118163e-17 relative error = 1.2339161922923145546884861805319e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.6MB, time=97.03 NO POLE NO POLE x[1] = 0.382 y2[1] (analytic) = 1.0720790621964072322252949639468 y2[1] (numeric) = 1.0720108216290582266701217544341 absolute error = 6.82405673490055551732095127e-05 relative error = 0.0063652551155321167700142884483782 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0720790621964072322252949639468 y1[1] (numeric) = 1.0720790621964072454943798992542 absolute error = 1.32690849353074e-17 relative error = 1.2376964911638647951092492008920e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.383 y2[1] (analytic) = 1.072452303150313189369698020393 y2[1] (numeric) = 1.0723838306234492359510927904694 absolute error = 6.84725268639534186052299236e-05 relative error = 0.0063846687319162220497928098083529 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.072452303150313189369698020393 y1[1] (numeric) = 1.0724523031503132026838866718028 absolute error = 1.33141886514098e-17 relative error = 1.2414714027187561309624703895872e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.6MB, time=97.54 NO POLE NO POLE x[1] = 0.384 y2[1] (analytic) = 1.0728264716518387005620840879077 y2[1] (numeric) = 1.0727577672588215746662056771049 absolute error = 6.87043930171258958784108028e-05 relative error = 0.006404054600865808575377774729179 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0728264716518387005620840879077 y1[1] (numeric) = 1.0728264716518387139213583029275 absolute error = 1.33592742150198e-17 relative error = 1.2452409190137179020663470694332e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.6MB, time=98.05 NO POLE NO POLE x[1] = 0.385 y2[1] (analytic) = 1.0732015673268152954576493952072 y2[1] (numeric) = 1.0731326311612386386045069415431 absolute error = 6.89361655766568531424536641e-05 relative error = 0.0064234126817729626002356774287121 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0732015673268152954576493952072 y1[1] (numeric) = 1.073201567326815308861990976259 absolute error = 1.34043415810518e-17 relative error = 1.2490050321525350991115151428126e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.6MB, time=98.56 NO POLE NO POLE x[1] = 0.386 y2[1] (analytic) = 1.0735775898001473303377709195101 y2[1] (numeric) = 1.0735084219558365565875901389494 absolute error = 6.91678443107737501807805607e-05 relative error = 0.0064427429342717319513345327941526 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0735775898001473303377709195101 y1[1] (numeric) = 1.0735775898001473437871616239484 absolute error = 1.34493907044383e-17 relative error = 1.2527637342860316008953640702249e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.387 y2[1] (analytic) = 1.0739545386958123632056188471909 y2[1] (numeric) = 1.0738851392668245653334357922039 absolute error = 6.93994289877978721830549870e-05 relative error = 0.0064620453182380576656034116877439 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0739545386958123632056188471909 y1[1] (numeric) = 1.0739545386958123767000403873212 absolute error = 1.34944215401303e-17 relative error = 1.2565170176120899491624993668657e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.6MB, time=99.08 NO POLE NO POLE x[1] = 0.388 y2[1] (analytic) = 1.0743324136368615298085672354074 y2[1] (numeric) = 1.0742627827174853852471433580247 absolute error = 6.96309193761445614238773827e-05 relative error = 0.0064813197937897019433372351937558 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0743324136368615298085672354074 y1[1] (numeric) = 1.0743324136368615433480012785045 absolute error = 1.35394340430971e-17 relative error = 1.2602648743756144906903635884152e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.6MB, time=99.58 NO POLE NO POLE x[1] = 0.389 y2[1] (analytic) = 1.0747112142454199205870268523226 y2[1] (numeric) = 1.0746413519301755971381794287629 absolute error = 6.98623152443234488474235597e-05 relative error = 0.0065005663212861724306913226728968 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0747112142454199205870268523226 y1[1] (numeric) = 1.0747112142454199341714550206486 absolute error = 1.35844281683260e-17 relative error = 1.2640072968684845504748906865949e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.39 y2[1] (analytic) = 1.0750909401426869585493232471189 y2[1] (numeric) = 1.0750208465263260198637654526524 absolute error = 7.00936163609386855577944665e-05 relative error = 0.0065197848613286428434794003322675 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0750909401426869585493232471189 y1[1] (numeric) = 1.0750909401426869721787271179418 absolute error = 1.36294038708229e-17 relative error = 1.2677442774295906770782220935733e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.6MB, time=100.08 NO POLE NO POLE x[1] = 0.391 y2[1] (analytic) = 1.0754715909489367780722421749589 y2[1] (numeric) = 1.0754012661264420888980273291574 absolute error = 7.03248224946891742148458015e-05 relative error = 0.006538975374759869944557267977704 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0754715909489367780722421749589 y1[1] (numeric) = 1.075471590948936791746603280571 absolute error = 1.36743611056121e-17 relative error = 1.2714758084447956853398574793367e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.6MB, time=100.59 NO POLE NO POLE x[1] = 0.392 y2[1] (analytic) = 1.0758531662835186046268635763786 y2[1] (numeric) = 1.0757826103501042358265283103007 absolute error = 7.05559334143688003352660779e-05 relative error = 0.0065581378226641068871420906471095 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0758531662835186046268635763786 y1[1] (numeric) = 1.0758531662835186183461634041151 absolute error = 1.37192998277365e-17 relative error = 1.2752018823469322222540616849300e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.393 y2[1] (analytic) = 1.0762356657648571354293043853106 y2[1] (numeric) = 1.0761648788159682687658057134707 absolute error = 7.07869488888666634986718399e-05 relative error = 0.0065772721663670129364843296960336 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0762356657648571354293043853106 y1[1] (numeric) = 1.076235665764857149193524377568 absolute error = 1.37642199922574e-17 relative error = 1.2789224916157624330602901832712e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.6MB, time=101.13 NO POLE NO POLE x[1] = 0.394 y2[1] (analytic) = 1.0766190890104529210159895150267 y2[1] (numeric) = 1.0765480711417657537075310262026 absolute error = 7.10178686871673084584888241e-05 relative error = 0.0065963783674355595823756536069246 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0766190890104529210159895150267 y1[1] (numeric) = 1.076619089010452934825111069281 absolute error = 1.38091215542543e-17 relative error = 1.2826376287779369757898172884894e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.6MB, time=101.65 NO POLE NO POLE x[1] = 0.395 y2[1] (analytic) = 1.0770034356368827477430694467592 y2[1] (numeric) = 1.076932186944304396786912058805 absolute error = 7.12486925783509561573879542e-05 relative error = 0.0066154563876779330550417724030485 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0770034356368827477430694467592 y1[1] (numeric) = 1.0770034356368827615970739155851 absolute error = 1.38540044688259e-17 relative error = 1.2863472864070648072549809823937e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.396 y2[1] (analytic) = 1.0773887052598000212096019216175 y2[1] (numeric) = 1.0773172258394684274749548764622 absolute error = 7.14794203315937346470451553e-05 relative error = 0.006634506189143433257034021302073 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0773887052598000212096019216175 y1[1] (numeric) = 1.0773887052598000351084706127069 absolute error = 1.38988686910894e-17 relative error = 1.2900514571236242949825657808143e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.6MB, time=102.18 NO POLE NO POLE x[1] = 0.397 y2[1] (analytic) = 1.0777748974939351506041143126486 y2[1] (numeric) = 1.0777031874422189826942023185815 absolute error = 7.17100517161679099119940671e-05 relative error = 0.0066535277341223691237976781942936 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0777748974939351506041143126486 y1[1] (numeric) = 1.077774897493935164547828488829 absolute error = 1.39437141761804e-17 relative error = 1.2937501335949294548457974594908e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.6MB, time=102.69 NO POLE NO POLE x[1] = 0.398 y2[1] (analytic) = 1.0781620119530959339741623305114 y2[1] (numeric) = 1.0780900713665944918575649896794 absolute error = 7.19405865014421165973408320e-05 relative error = 0.0066725209851459504256584364523759 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0781620119530959339741623305114 y1[1] (numeric) = 1.0781620119530959479627032097648 absolute error = 1.39885408792534e-17 relative error = 1.2974433085351511778253174120837e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.399 y2[1] (analytic) = 1.0785500482501679444184997932385 y2[1] (numeric) = 1.0784778772257110628298596830082 absolute error = 7.21710244568815886401102303e-05 relative error = 0.0066914859049861760240311690737146 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0785500482501679444184997932385 y1[1] (numeric) = 1.0785500482501679584518485487204 absolute error = 1.40333487554819e-17 relative error = 1.3011309747053005913349473990041e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.6MB, time=103.20 NO POLE NO POLE x[1] = 0.4 y2[1] (analytic) = 1.0789390059971149172014732679482 y2[1] (numeric) = 1.0788666046317628688116692754157 absolute error = 7.24013653520483898039925325e-05 relative error = 0.0067104224566557185947171124508543 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0789390059971149172014732679482 y1[1] (numeric) = 1.078939005997114931279611028006 absolute error = 1.40781377600578e-17 relative error = 1.3048131249131468455798685177044e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.6MB, time=103.71 NO POLE NO POLE x[1] = 0.401 y2[1] (analytic) = 1.0793288848049791377892544701431 y2[1] (numeric) = 1.079256253196022536145137209611 absolute error = 7.26316089566016441172605321e-05 relative error = 0.0067293306034078058312168676782239 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0793288848049791377892544701431 y1[1] (numeric) = 1.0793288848049791519121623183353 absolute error = 1.41229078481922e-17 relative error = 1.3084897520132640567953959259510e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.402 y2[1] (analytic) = 1.0797196842838818308075223843972 y2[1] (numeric) = 1.0796468225288415330413087580748 absolute error = 7.28617550402977662136263224e-05 relative error = 0.0067482103087360981410471653805059 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0797196842838818308075223843972 y1[1] (numeric) = 1.0797196842838818449751813595121 absolute error = 1.41676589751149e-17 relative error = 1.3121608489069570170940222340468e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.6MB, time=104.23 NO POLE NO POLE x[1] = 0.403 y2[1] (analytic) = 1.0801114040430235499202061487794 y2[1] (numeric) = 1.0800383122396505592286303413038 absolute error = 7.30918033729906915758074756e-05 relative error = 0.0067670615363745628481091656338167 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0801114040430235499202061487794 y1[1] (numeric) = 1.0801114040430235641325972448544 absolute error = 1.42123910960750e-17 relative error = 1.3158264085422881775496514377642e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.6MB, time=104.75 NO POLE NO POLE x[1] = 0.404 y2[1] (analytic) = 1.0805040436906845686288988243055 y2[1] (numeric) = 1.0804307219369599365222172519238 absolute error = 7.33217537246321066815723817e-05 relative error = 0.0067858842502973449142151687436982 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0805040436906845686288988243055 y1[1] (numeric) = 1.0805040436906845828860029906458 absolute error = 1.42571041663403e-17 relative error = 1.3194864239139927850203107138550e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.405 y2[1] (analytic) = 1.0808976028342252719925512500355 y2[1] (numeric) = 1.0808240512283600003134992154358 absolute error = 7.35516058652716790520345997e-05 relative error = 0.006804678414718634192938994886425 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0808976028342252719925512500355 y1[1] (numeric) = 1.0808976028342252862943493912331 absolute error = 1.43017981411976e-17 relative error = 1.3231408880634767406679659822148e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.6MB, time=105.25 NO POLE NO POLE x[1] = 0.406 y2[1] (analytic) = 1.0812920810800865492670542641556 y2[1] (numeric) = 1.0812182997205214919798522979818 absolute error = 7.37813595650572872019661738e-05 relative error = 0.0068234439940925292290129520633356 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0812920810800865492670542641556 y1[1] (numeric) = 1.0812920810800865636135272401087 absolute error = 1.43464729759531e-17 relative error = 1.3267897940788229852850291622359e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=801.1MB, alloc=4.6MB, time=105.77 NO POLE NO POLE x[1] = 0.407 y2[1] (analytic) = 1.0816874780337901874643166514964 y2[1] (numeric) = 1.0816134670191959522138247515317 absolute error = 7.40110145942352504918999647e-05 relative error = 0.0068421809531128976165512520413434 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0816874780337901874643166514964 y1[1] (numeric) = 1.0816874780337902018554452774283 absolute error = 1.43911286259319e-17 relative error = 1.3304331350947139419103186612504e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=804.9MB, alloc=4.6MB, time=106.28 x[1] = 0.408 y2[1] (analytic) = 1.0820837932999392658304452584406 y2[1] (numeric) = 1.0820095527292161152715634672977 absolute error = 7.42405707231505588817911429e-05 relative error = 0.0068608892567132329294359535218061 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0820837932999392658304452584406 y1[1] (numeric) = 1.0820837932999392802662103049189 absolute error = 1.44357650464783e-17 relative error = 1.3340709042924273355240716954568e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.409 y2[1] (analytic) = 1.0824810264822185512426327970737 y2[1] (numeric) = 1.0824065564544963041400467889834 absolute error = 7.44700277222471025860080903e-05 relative error = 0.0068795688700665082372570113913433 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0824810264822185512426327970737 y1[1] (numeric) = 1.0824810264822185657230149900296 absolute error = 1.44803821929559e-17 relative error = 1.3377030948998128227557737597424e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.6MB, time=106.79 NO POLE NO POLE x[1] = 0.41 y2[1] (analytic) = 1.082879177183394894524357941723 y2[1] (numeric) = 1.0828044777980328266227285186664 absolute error = 7.46993853620679016294230566e-05 relative error = 0.0068982197585850262202527908357637 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.082879177183394894524357941723 y1[1] (numeric) = 1.0828791771833949090493379624707 absolute error = 1.45249800207477e-17 relative error = 1.3413297001912679507651422441930e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.6MB, time=107.29 NO POLE NO POLE x[1] = 0.411 y2[1] (analytic) = 1.0832782450053176276785014027179 y2[1] (numeric) = 1.0832033163619043723431970297048 absolute error = 7.49286434132553353043730131e-05 relative error = 0.0069168418879202658967514653697199 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0832782450053176276785014027179 y1[1] (numeric) = 1.0832782450053176422480598879736 absolute error = 1.45695584852557e-17 relative error = 1.3449507134876672916658986081226e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.412 y2[1] (analytic) = 1.0836782295489189620379807442877 y2[1] (numeric) = 1.0836030717472724106664524830407 absolute error = 7.51578016465513715282612470e-05 relative error = 0.0069354352239627259766670597554583 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0836782295489189620379807442877 y1[1] (numeric) = 1.0836782295489189766520982861892 absolute error = 1.46141175419015e-17 relative error = 1.3485661281563832917905925417716e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.6MB, time=107.79 NO POLE NO POLE x[1] = 0.413 y2[1] (analytic) = 1.084079130414214387333505795996 y2[1] (numeric) = 1.0840037435543815895374042256569 absolute error = 7.53868598327977961015703391e-05 relative error = 0.0069539997328417648546565224408231 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.084079130414214387333505795996 y1[1] (numeric) = 1.0840791304142144019921629421221 absolute error = 1.46586571461261e-17 relative error = 1.3521759376112325605191334586715e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.6MB, time=108.28 NO POLE NO POLE x[1] = 0.414 y2[1] (analytic) = 1.0844809472003030716780555899898 y2[1] (numeric) = 1.0844053313825601352361895327226 absolute error = 7.56158177429364418660572672e-05 relative error = 0.006972535380925437256596118164949 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0844809472003030716780555899898 y1[1] (numeric) = 1.0844809472003030863812328433796 absolute error = 1.47031772533898e-17 relative error = 1.3557801353124307811161852256329e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.415 y2[1] (analytic) = 1.0848836795053682624676768396186 y2[1] (numeric) = 1.084807834830220253049913938143 absolute error = 7.58446751480094177629014756e-05 relative error = 0.006991042134820327553086620313119 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0848836795053682624676768396186 y1[1] (numeric) = 1.0848836795053682772153546587912 absolute error = 1.47476778191726e-17 relative error = 1.3593787147665930928645329651337e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.6MB, time=108.80 NO POLE NO POLE x[1] = 0.416 y2[1] (analytic) = 1.0852873269266776881982030586595 y2[1] (numeric) = 1.085211253494858528860412481805 absolute error = 7.60734318191593377905768545e-05 relative error = 0.0070095199613713797537472557330397 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0852873269266776881982030586595 y1[1] (numeric) = 1.0852873269266777029903618576334 absolute error = 1.47921587989739e-17 relative error = 1.3629716695266692575412798327607e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.6MB, time=109.31 NO POLE NO POLE x[1] = 0.417 y2[1] (analytic) = 1.0856918890605839611974925044623 y2[1] (numeric) = 1.0856155869730563316476302857924 absolute error = 7.63020875276295498622186699e-05 relative error = 0.0070279688276617241961081116679986 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0856918890605839611974925044623 y1[1] (numeric) = 1.085691889060583976034112652775 absolute error = 1.48366201483127e-17 relative error = 1.3665589931919243093676423643848e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.418 y2[1] (analytic) = 1.0860973655025249812727822128099 y2[1] (numeric) = 1.0860208348604802169082199562224 absolute error = 7.65306420447643645622565875e-05 relative error = 0.0070463887010125009429597571399096 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0860973655025249812727822128099 y1[1] (numeric) = 1.0860973655025249961538440355376 absolute error = 1.48810618227277e-17 relative error = 1.3701406794079093274841554077120e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.6MB, time=109.82 NO POLE NO POLE x[1] = 0.419 y2[1] (analytic) = 1.0865037558470243402727544771743 y2[1] (numeric) = 1.0864269967518823309889523921405 absolute error = 7.67590951420092838020850338e-05 relative error = 0.0070647795489826799020671594570659 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0865037558470243402727544771743 y1[1] (numeric) = 1.0865037558470243551982382549514 absolute error = 1.49254837777771e-17 relative error = 1.3737167218664039499241843300245e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.6MB, time=110.32 NO POLE NO POLE x[1] = 0.42 y2[1] (analytic) = 1.0869110596876917275639112103343 y2[1] (numeric) = 1.0868340722411008163345366680964 absolute error = 7.69874465909112293745422379e-05 relative error = 0.007083141339368877682202591703524 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0869110596876917275639112103343 y1[1] (numeric) = 1.0869110596876917425337971793734 absolute error = 1.49698859690391e-17 relative error = 1.3772871143054227080155137227783e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.421 y2[1] (analytic) = 1.087319276617223336420850712016 y2[1] (numeric) = 1.0872420609210602176494437426143 absolute error = 7.72156961631187714069694017e-05 relative error = 0.0071014740402051711994991302551051 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.087319276617223336420850712016 y1[1] (numeric) = 1.0873192766172233514351190641274 absolute error = 1.50142683521114e-17 relative error = 1.3808518505091286671219188623585e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.6MB, time=110.82 NO POLE NO POLE x[1] = 0.422 y2[1] (analytic) = 1.0877284062274022713300404523114 y2[1] (numeric) = 1.0876509623837718889733278307688 absolute error = 7.74438436303823567126215426e-05 relative error = 0.0071197776197629080481725323833257 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0877284062274022713300404523114 y1[1] (numeric) = 1.0877284062274022863886713349231 absolute error = 1.50586308826117e-17 relative error = 1.3844109243078384875408658006387e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.6MB, time=111.32 NO POLE NO POLE x[1] = 0.423 y2[1] (analytic) = 1.0881384481090989562066785671374 y2[1] (numeric) = 1.0880607762203344016696383654776 absolute error = 7.76718887645545370402016598e-05 relative error = 0.0071380520465505136497047654825815 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0881384481090989562066785671374 y1[1] (numeric) = 1.088138448109098971309652083315 absolute error = 1.51029735161776e-17 relative error = 1.3879643295779716262639962301029e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.424 y2[1] (analytic) = 1.088549401852271543524235848908 y2[1] (numeric) = 1.0884715020209339533270145589345 absolute error = 7.78998313375901972212899735e-05 relative error = 0.0071562972893132951946272305739475 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.088549401852271543524235848908 y1[1] (numeric) = 1.0885494018522715586715320573741 absolute error = 1.51472962084661e-17 relative error = 1.3915120602419622006525668151422e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.6MB, time=111.82 NO POLE NO POLE x[1] = 0.425 y2[1] (analytic) = 1.0889612670459663243562691029099 y2[1] (numeric) = 1.088883139374844777573053662821 absolute error = 7.81276711215467832154400889e-05 relative error = 0.0071745133170332423910857857244671 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0889612670459663243562691029099 y1[1] (numeric) = 1.0889612670459663395478680180647 absolute error = 1.51915989151548e-17 relative error = 1.3950541102683264585505773573969e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.6MB, time=112.31 NO POLE NO POLE x[1] = 0.426 y2[1] (analytic) = 1.0893740432783181393300958276049 y2[1] (numeric) = 1.0892956878704295548000431135629 absolute error = 7.83554078885845300527140420e-05 relative error = 0.0071927000989288250344130307418164 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0893740432783181393300958276049 y1[1] (numeric) = 1.0893740432783181545659774195459 absolute error = 1.52358815919410e-17 relative error = 1.3985904736715366199366479221150e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.427 y2[1] (analytic) = 1.089787730136550790491919265217 y2[1] (numeric) = 1.0897091470951398238022458369342 absolute error = 7.85830414109666896734282828e-05 relative error = 0.0072108576044547874119759632137213 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.089787730136550790491919265217 y1[1] (numeric) = 1.0897877301365508057720634597589 absolute error = 1.52801441945419e-17 relative error = 1.4021211445119952390649989080680e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.6MB, time=112.81 NO POLE NO POLE x[1] = 0.428 y2[1] (analytic) = 1.0902023272069774540829919575135 y2[1] (numeric) = 1.0901235166355163943243270747568 absolute error = 7.88105714610597586648827567e-05 relative error = 0.0072289858033019395576090599781401 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0902023272069774540829919575135 y1[1] (numeric) = 1.0902023272069774694073786362085 absolute error = 1.53243866786950e-17 relative error = 1.4056461168960272686917651115958e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.6MB, time=113.31 NO POLE NO POLE x[1] = 0.429 y2[1] (analytic) = 1.0906178340750010942264050306518 y2[1] (numeric) = 1.0905387960771897605205101853038 absolute error = 7.90379978113337058948453480e-05 relative error = 0.0072470846653969453699840777839211 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0906178340750010942264050306518 y1[1] (numeric) = 1.0906178340750011095950140308096 absolute error = 1.53686090001578e-17 relative error = 1.4091653849758072580544663640021e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=862.1MB, alloc=4.6MB, time=113.81 x[1] = 0.43 y2[1] (analytic) = 1.0910342503251148775240895223366 y2[1] (numeric) = 1.0909549850048805153240479582853 absolute error = 7.92653202343622000415640513e-05 relative error = 0.0072651541609021076093084035003209 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0910342503251148775240895223366 y1[1] (numeric) = 1.0910342503251148929369006370444 absolute error = 1.54128111147078e-17 relative error = 1.4126789429493135146602168419750e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.431 y2[1] (analytic) = 1.09145157554090258856361515432 y2[1] (numeric) = 1.0913720830023997657265950749794 absolute error = 7.94925385028228370200793406e-05 relative error = 0.0072831942602151497867836192793138 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.09145157554090258856361515432 y1[1] (numeric) = 1.0914515755409026040206081324632 absolute error = 1.54569929781432e-17 relative error = 1.4161867850603458078946607254904e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.6MB, time=114.32 NO POLE NO POLE x[1] = 0.432 y2[1] (analytic) = 1.0918698093050390463343710434825 y2[1] (numeric) = 1.091790089652649548967066434171 absolute error = 7.97196523894973673046093115e-05 relative error = 0.0073012049339689949612950827738996 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0918698093050390463343710434825 y1[1] (numeric) = 1.0918698093050390618355255897644 absolute error = 1.55011545462819e-17 relative error = 1.4196889055983866389191288828277e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.6MB, time=114.83 NO POLE NO POLE x[1] = 0.433 y2[1] (analytic) = 1.0922889511992905215527119353457 y2[1] (numeric) = 1.0922090045376232496295651550745 absolute error = 7.99466616672719231467802712e-05 relative error = 0.0073191861530315414578417574322201 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0922889511992905215527119353457 y1[1] (numeric) = 1.0922889511992905370980077103082 absolute error = 1.55452957749625e-17 relative error = 1.4231852988986452354184225048794e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.434 y2[1] (analytic) = 1.0927090008045151548956526349088 y2[1] (numeric) = 1.0926288272384060176499631593471 absolute error = 8.01735661091372456894755617e-05 relative error = 0.0073371378885054355222532659641755 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0927090008045151548956526349088 y1[1] (numeric) = 1.0927090008045151704850692549525 absolute error = 1.55894166200437e-17 relative error = 1.4266759593419543259770934389942e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.6MB, time=115.31 NO POLE NO POLE x[1] = 0.435 y2[1] (analytic) = 1.0931299577006633761426924011461 y2[1] (numeric) = 1.0930495573351751872307163256473 absolute error = 8.04003654881889119760754988e-05 relative error = 0.0073550601117278409267781803871434 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0931299577006633761426924011461 y1[1] (numeric) = 1.0931299577006633917762094385507 absolute error = 1.56335170374046e-17 relative error = 1.4301608813547487917237393648459e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.6MB, time=115.82 NO POLE NO POLE x[1] = 0.436 y2[1] (analytic) = 1.0935518214667783242253501633781 y2[1] (numeric) = 1.093471194407200696663495301958 absolute error = 8.06270595776275618548614201e-05 relative error = 0.0073729527942702055411639084523935 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0935518214667783242253501633781 y1[1] (numeric) = 1.093551821466778339902947146323 absolute error = 1.56775969829449e-17 relative error = 1.4336400594090345312741419772374e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.437 y2[1] (analytic) = 1.0939745916809962681839905100158 y2[1] (numeric) = 1.0938937380328455090592121530787 absolute error = 8.08536481507591247783569371e-05 relative error = 0.0073908159079380248838841881296028 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0939745916809962681839905100158 y1[1] (numeric) = 1.0939745916809962839056469226003 absolute error = 1.57216564125845e-17 relative error = 1.4371134880223018613966459921258e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.6MB, time=116.32 NO POLE NO POLE x[1] = 0.438 y2[1] (analytic) = 1.0943982679205470290315194928856 y2[1] (numeric) = 1.0943171877895660339850221132946 absolute error = 8.10801309809950464973795910e-05 relative error = 0.0074086494247706026682051616721066 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0943982679205470290315194928856 y1[1] (numeric) = 1.0943982679205470447972147751498 absolute error = 1.57656952822642e-17 relative error = 1.4405811617575389412283514897244e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.6MB, time=116.83 NO POLE NO POLE x[1] = 0.439 y2[1] (analytic) = 1.0948228497617544025235283834771 y2[1] (numeric) = 1.0947415432539125500078788072568 absolute error = 8.13065078418525156495762203e-05 relative error = 0.0074264533170408083578152702125029 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0948228497617544025235283834771 y1[1] (numeric) = 1.094822849761754418333241931422 absolute error = 1.58097135479449e-17 relative error = 1.4440430752231074691565769618022e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.44 y2[1] (analytic) = 1.0952483367800365828344626110016 y2[1] (numeric) = 1.0951668040015296281442203955532 absolute error = 8.15327785069546902422154484e-05 relative error = 0.0074442275572548317467777892309361 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0952483367800365828344626110016 y1[1] (numeric) = 1.0952483367800365986881737766102 absolute error = 1.58537111656086e-17 relative error = 1.4474992230727823286816364119973e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.6MB, time=117.35 NO POLE NO POLE x[1] = 0.441 y2[1] (analytic) = 1.0956747285499065871393922061318 y2[1] (numeric) = 1.0955929696071565562153631953189 absolute error = 8.17589427500309240290108129e-05 relative error = 0.0074619721181519345785977181384737 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0956747285499065871393922061318 y1[1] (numeric) = 1.0956747285499066030370802973892 absolute error = 1.58976880912574e-17 relative error = 1.4509496000056079210304190766689e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.6MB, time=117.85 NO POLE NO POLE x[1] = 0.442 y2[1] (analytic) = 1.0961020246449726811009591686834 y2[1] (numeric) = 1.0960200396446277641081784205284 absolute error = 8.19850003449169927807481550e-05 relative error = 0.0074796869727041992192269424464094 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0961020246449726811009591686834 y1[1] (numeric) = 1.0961020246449726970426034495979 absolute error = 1.59416442809145e-17 relative error = 1.4543942007659366140850289854863e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.443 y2[1] (analytic) = 1.0965302246379388052610762723304 y2[1] (numeric) = 1.0964480136868732499406267813281 absolute error = 8.22109510655553204494910023e-05 relative error = 0.0074973720941162743988631093586084 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0965302246379388052610762723304 y1[1] (numeric) = 1.0965302246379388212466559629542 absolute error = 1.59855796906238e-17 relative error = 1.4578330201433387438115996175984e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.6MB, time=118.35 NO POLE NO POLE x[1] = 0.444 y2[1] (analytic) = 1.0969593281006050023369509146883 y2[1] (numeric) = 1.0968768913059190071317247769101 absolute error = 8.24367946859952052261377782e-05 relative error = 0.0075150274558251180374284957382178 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0969593281006050023369509146883 y1[1] (numeric) = 1.0969593281006050183664451911381 absolute error = 1.60294942764498e-17 relative error = 1.4612660529725394935752719403939e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.6MB, time=118.84 NO POLE NO POLE x[1] = 0.445 y2[1] (analytic) = 1.0973893346038678454210067167782 y2[1] (numeric) = 1.0973066720728874523755156119961 absolute error = 8.26625309803930454911047821e-05 relative error = 0.0075326530314997371686453053192175 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0973893346038678454210067167782 y1[1] (numeric) = 1.0973893346038678614943947112561 absolute error = 1.60733879944779e-17 relative error = 1.4646932941333916922041743677432e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.446 y2[1] (analytic) = 1.0978202437177208670842746719854 y2[1] (numeric) = 1.097737355557997854518616762997 absolute error = 8.28881597230125656579089884e-05 relative error = 0.0075502487950409249776533097904868 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0978202437177208670842746719854 y1[1] (numeric) = 1.0978202437177208832015354727998 absolute error = 1.61172608008144e-17 relative error = 1.4681147385508206709831108264891e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=904.0MB, alloc=4.6MB, time=119.34 NO POLE NO POLE x[1] = 0.447 y2[1] (analytic) = 1.0982520550112549893828247411573 y2[1] (numeric) = 1.0981689413305667643409153163355 absolute error = 8.31136806882250419094248218e-05 relative error = 0.0075678147205809949671445488863692 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0982520550112549893828247411573 y1[1] (numeric) = 1.0982520550112550055439373927439 absolute error = 1.61611126515866e-17 relative error = 1.4715303811947776789574491013175e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.6MB, time=119.82 NO POLE NO POLE x[1] = 0.448 y2[1] (analytic) = 1.0986847680526589547668078874449 y2[1] (numeric) = 1.0986014289590084452389812982728 absolute error = 8.33390936505095278265891721e-05 relative error = 0.0075853507824835122670179287702002 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0986847680526589547668078874449 y1[1] (numeric) = 1.0986847680526589709717513903875 absolute error = 1.62049435029426e-17 relative error = 1.4749402170801654272365681531757e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.449 y2[1] (analytic) = 1.0991183824092197578916776418816 y2[1] (numeric) = 1.0990348180108353048117683128618 absolute error = 8.35643983844530799093290198e-05 relative error = 0.0076028569553430221025840081546662 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0991183824092197578916776418816 y1[1] (numeric) = 1.0991183824092197741404309529331 absolute error = 1.62487533110515e-17 relative error = 1.4783442412667995279768184407015e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.6MB, time=120.32 NO POLE NO POLE x[1] = 0.45 y2[1] (analytic) = 1.0995528976473230783311593885136 y2[1] (numeric) = 1.099469108052658327348169902362 absolute error = 8.37895946647509829894861516e-05 relative error = 0.0076203332139847754363770393412665 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0995528976473230783311593885136 y1[1] (numeric) = 1.099552897647323094623701420617 absolute error = 1.62925420321034e-17 relative error = 1.4817424488593511629030925038323e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.6MB, time=120.81 NO POLE NO POLE x[1] = 0.451 y2[1] (analytic) = 1.0999883133324537141915346561489 y2[1] (numeric) = 1.0999042986501875072159991425959 absolute error = 8.40146822662069755355135530e-05 relative error = 0.0076377795334644517986574385866945 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.0999883133324537141915346561489 y1[1] (numeric) = 1.0999883133324537305278442784588 absolute error = 1.63363096223099e-17 relative error = 1.4851348350073346715880785737327e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.452 y2[1] (analytic) = 1.1004246290291960166268068024775 y2[1] (numeric) = 1.1003403893682322831519580843031 absolute error = 8.42396609637334748487181744e-05 relative error = 0.007655195889067879321713298869351 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1004246290291960166268068024775 y1[1] (numeric) = 1.1004246290291960330068628403806 absolute error = 1.63800560379031e-17 relative error = 1.4885213949049581882858759482525e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.6MB, time=121.31 NO POLE NO POLE x[1] = 0.453 y2[1] (analytic) = 1.100861844301234325254313575431 y2[1] (numeric) = 1.1007773797707019734521627505595 absolute error = 8.44645305323518021508248715e-05 relative error = 0.0076725822563107519930943296066559 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.100861844301234325254313575431 y1[1] (numeric) = 1.1008618443012343416780948105677 absolute error = 1.64237812351367e-17 relative error = 1.4919021237911647252934411720041e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.6MB, time=121.80 NO POLE NO POLE x[1] = 0.454 y2[1] (analytic) = 1.101299958711353404470351136208 y2[1] (numeric) = 1.1012152694206062120627884997725 absolute error = 8.46892907471924075626364355e-05 relative error = 0.007689938610938344142935715472691 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.101299958711353404470351136208 y1[1] (numeric) = 1.1012999587113534209378363064936 absolute error = 1.64674851702856e-17 relative error = 1.4952770169495362891557255653864e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.6MB, time=122.30 NO POLE NO POLE x[1] = 0.455 y2[1] (analytic) = 1.1017389718214388806653732283767 y2[1] (numeric) = 1.1016540578800553855703996636428 absolute error = 8.49139413834950949735647339e-05 relative error = 0.0077072649289252221805528303587094 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1017389718214388806653732283767 y1[1] (numeric) = 1.1017389718214388971765410280224 absolute error = 1.65111677996457e-17 relative error = 1.4986460697082157130895593818887e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.456 y2[1] (analytic) = 1.1021788831924776803383282778904 y2[1] (numeric) = 1.1020937447102610710915264698002 absolute error = 8.51384822166092468018080902e-05 relative error = 0.0077245611864749535955105257538756 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1021788831924776803383282778904 y1[1] (numeric) = 1.1021788831924776968931573574248 absolute error = 1.65548290795344e-17 relative error = 1.5020092774398915229731552822672e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.6MB, time=122.79 NO POLE NO POLE x[1] = 0.457 y2[1] (analytic) = 1.1026196923845584691096963097179 y2[1] (numeric) = 1.1025343294715364750610513595728 absolute error = 8.53629130219940486449501451e-05 relative error = 0.0077418273600198132383928378357952 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1026196923845584691096963097179 y1[1] (numeric) = 1.1026196923845584857081652760085 absolute error = 1.65984689662906e-17 relative error = 1.5053666355617368306347682794120e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.6MB, time=123.28 NO POLE NO POLE x[1] = 0.458 y2[1] (analytic) = 1.1030613989568720916327866680871 y2[1] (numeric) = 1.1029758117232968729189659125394 absolute error = 8.55872335752187138207555477e-05 relative error = 0.0077590634262204868965204250156652 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1030613989568720916327866680871 y1[1] (numeric) = 1.1030613989568721082748740843613 absolute error = 1.66420874162742e-17 relative error = 1.5087181395353023840822763655689e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.459 y2[1] (analytic) = 1.1035040024677120124028566290802 y2[1] (numeric) = 1.1034181910240600496950586911457 absolute error = 8.58114436519627077979379345e-05 relative error = 0.0077762693619657721798838607262538 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1035040024677120124028566290802 y1[1] (numeric) = 1.103504002467712029088541014947 absolute error = 1.66856843858668e-17 relative error = 1.5120637848665179596680799480453e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.6MB, time=123.78 NO POLE NO POLE x[1] = 0.46 y2[1] (analytic) = 1.1039475024744747574636100964996 y2[1] (numeric) = 1.1038614669314467414910934207324 absolute error = 8.60355430280159725166757672e-05 relative error = 0.0077934451443722767325810670155627 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1039475024744747574636100964996 y1[1] (numeric) = 1.1039475024744747741928699279712 absolute error = 1.67292598314716e-17 relative error = 1.5154035671056206258239905562523e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.6MB, time=124.28 NO POLE NO POLE x[1] = 0.461 y2[1] (analytic) = 1.104391898533660357010634674543 y2[1] (numeric) = 1.1043056390021810778600360228337 absolute error = 8.62595314792791505986517093e-05 relative error = 0.0078105907507841137850666844052758 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.104391898533660357010634674543 y1[1] (numeric) = 1.104391898533660373783448384056 absolute error = 1.67728137095130e-17 relative error = 1.5187374818470553586332703602262e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.462 y2[1] (analytic) = 1.1048371902008727888913345138855 y2[1] (numeric) = 1.1047507067920910250818881225571 absolute error = 8.64834087817638094463913284e-05 relative error = 0.0078277061587725950625400348334803 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1048371902008727888913345138855 y1[1] (numeric) = 1.1048371902008728057076804903227 absolute error = 1.68163459764372e-17 relative error = 1.5220655247294657533860167521879e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.6MB, time=124.78 NO POLE NO POLE x[1] = 0.463 y2[1] (analytic) = 1.1052833770308204230009154312754 y2[1] (numeric) = 1.1051966698561088303356837542467 absolute error = 8.67071747115926652316770287e-05 relative error = 0.0078447913461359210648165506608723 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1052833770308204230009154312754 y1[1] (numeric) = 1.1052833770308204398607720199873 absolute error = 1.68598565887119e-17 relative error = 1.5253876914356026781261950170453e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.6MB, time=125.28 NO POLE NO POLE x[1] = 0.464 y2[1] (analytic) = 1.1057304585773164665739779066934 y2[1] (numeric) = 1.1056435277482714667672050934711 absolute error = 8.69308290449998067728132223e-05 relative error = 0.0078618462908988687330451136879555 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1057304585773164665739779066934 y1[1] (numeric) = 1.1057304585773164834773234095199 absolute error = 1.69033455028265e-17 relative error = 1.5287039776922777152631433481450e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.465 y2[1] (analytic) = 1.1061784343932794103712726665209 y2[1] (numeric) = 1.1060912800217210794519721476567 absolute error = 8.71543715583309193005188642e-05 relative error = 0.0078788709713124765186506784622533 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1061784343932794103712726665209 y1[1] (numeric) = 1.106178434393279427318085341813 absolute error = 1.69468126752921e-17 relative error = 1.5320143792702979854335741949788e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.6MB, time=125.78 NO POLE NO POLE x[1] = 0.466 y2[1] (analytic) = 1.1066273040307334757611726659979 y2[1] (numeric) = 1.1065399262287054322530604424146 absolute error = 8.73778020280435081122235833e-05 relative error = 0.0078958653658537268698978441893747 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1066273040307334757611726659979 y1[1] (numeric) = 1.1066273040307334927514307286393 absolute error = 1.69902580626414e-17 relative error = 1.5353188919843914442648951945512e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.6MB, time=126.28 NO POLE NO POLE x[1] = 0.467 y2[1] (analytic) = 1.1070770670408090626954143895363 y2[1] (numeric) = 1.1069894659205783555732998457797 absolute error = 8.76011202307071221145437566e-05 relative error = 0.0079128294532252261514866930599155 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1070770670408090626954143895363 y1[1] (numeric) = 1.1070770670408090797290960109655 absolute error = 1.70336816214292e-17 relative error = 1.5386175116931859103364935781689e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.468 y2[1] (analytic) = 1.107527722973743198578660493185 y2[1] (numeric) = 1.1074398986478001950014067782016 absolute error = 8.78243259430035772537149834e-05 relative error = 0.0079297632123548820126072309067038 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.107527722973743198578660493185 y1[1] (numeric) = 1.1075277229737432156557438014169 absolute error = 1.70770833082319e-17 relative error = 1.5419102342990972071870407414816e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.6MB, time=126.78 NO POLE NO POLE x[1] = 0.469 y2[1] (analytic) = 1.1079792713788799880314349197206 y2[1] (numeric) = 1.1078912239599382608516011621913 absolute error = 8.80474189417271798337575293e-05 relative error = 0.0079466666223955782188931519241855 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1079792713788799880314349197206 y1[1] (numeric) = 1.1079792713788800051518979993684 absolute error = 1.71204630796478e-17 relative error = 1.5451970557482891374525360909766e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.6MB, time=127.26 NO POLE NO POLE x[1] = 0.47 y2[1] (analytic) = 1.1084317118046710635459807234666 y2[1] (numeric) = 1.1083434414056672785962585720452 absolute error = 8.82703990037849497221514214e-05 relative error = 0.0079635396627248469637294046261494 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1084317118046710635459807234666 y1[1] (numeric) = 1.1084317118046710807098016157637 absolute error = 1.71638208922971e-17 relative error = 1.5484779720306058470106409659644e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.471 y2[1] (analytic) = 1.1088850437986760370345899490213 y2[1] (numeric) = 1.1087965505327698401911471510311 absolute error = 8.84932659061968434427979902e-05 relative error = 0.0079803823129445386743811640115853 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1088850437986760370345899490213 y1[1] (numeric) = 1.1088850437986760542417466518433 absolute error = 1.72071567028220e-17 relative error = 1.5517529791795127316297368468225e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.6MB, time=127.74 NO POLE NO POLE x[1] = 0.472 y2[1] (analytic) = 1.109339266907562952269954015601 y2[1] (numeric) = 1.1092505508881368562927979708375 absolute error = 8.87160194260959771560447635e-05 relative error = 0.0079971945528804893284243168300492 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.109339266907562952269954015601 y1[1] (numeric) = 1.1093392669075629695204244834878 absolute error = 1.72504704678868e-17 relative error = 1.5550220732720368489474215413633e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.6MB, time=128.24 NO POLE NO POLE x[1] = 0.473 y2[1] (analytic) = 1.1097943806771087382170821666872 y2[1] (numeric) = 1.1097054420177680093675566159528 absolute error = 8.89386593407288495255507344e-05 relative error = 0.0080139763625821852959694463224752 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1097943806771087382170821666872 y1[1] (numeric) = 1.1097943806771087555108443108647 absolute error = 1.72937621441775e-17 relative error = 1.5582852504286617853479839400650e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.474 y2[1] (analytic) = 1.1102503846521996632563346530956 y2[1] (numeric) = 1.1101612234667722076918628839614 absolute error = 8.91611854274555644717691342e-05 relative error = 0.0080307277223224257231825609359042 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1102503846521996632563346530956 y1[1] (numeric) = 1.1102503846521996805933663414982 absolute error = 1.73370316884026e-17 relative error = 1.5615425068133302288467331564196e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.6MB, time=128.74 NO POLE NO POLE x[1] = 0.475 y2[1] (analytic) = 1.1107072783768317902971164264731 y2[1] (numeric) = 1.110617894779368040243304601514 absolute error = 8.93835974637500538118249591e-05 relative error = 0.0080474486125969824726164523090886 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1107072783768317902971164264731 y1[1] (numeric) = 1.1107072783768318076773954837657 absolute error = 1.73802790572926e-17 relative error = 1.5647938386333288583546182355579e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.6MB, time=129.25 NO POLE NO POLE x[1] = 0.476 y2[1] (analytic) = 1.1111650613941114327817762295659 y2[1] (numeric) = 1.1110754554988842324819906649568 absolute error = 8.96058952272002997855646091e-05 relative error = 0.0080641390141242576358765921582828 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1111650613941114327817762295659 y1[1] (numeric) = 1.111165061394111450205280437166 absolute error = 1.74235042076001e-17 relative error = 1.5680392421392268809129328302913e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=984.2MB, alloc=4.6MB, time=129.75 x[1] = 0.477 y2[1] (analytic) = 1.1116237332462556115792550793985 y2[1] (numeric) = 1.1115339051677601030217875242844 absolute error = 8.98280784955085574675551141e-05 relative error = 0.0080807989078449386341548894768169 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1116237332462556115792550793985 y1[1] (numeric) = 1.1116237332462556290459621754983 absolute error = 1.74667070960998e-17 relative error = 1.5712787136248050934828848431311e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.478 y2[1] (analytic) = 1.1120832934745925127680272497516 y2[1] (numeric) = 1.111993243327546021190962439218 absolute error = 9.00501470464915770648105336e-05 relative error = 0.008097428274921650922173430113395 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1120832934745925127680272497516 y1[1] (numeric) = 1.1120832934745925302779149293406 absolute error = 1.75098876795890e-17 relative error = 1.5745122494270294510758262236463e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.6MB, time=130.26 NO POLE NO POLE x[1] = 0.479 y2[1] (analytic) = 1.1125437416195619463078759700387 y2[1] (numeric) = 1.1124534695189038654817759468031 absolute error = 9.02721006580808261000232356e-05 relative error = 0.0081140270967386083110885140273523 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1125437416195619463078759700387 y1[1] (numeric) = 1.1125437416195619638609218849258 absolute error = 1.75530459148871e-17 relative error = 1.5777398459259341878681602840129e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.6MB, time=130.77 NO POLE NO POLE x[1] = 0.48 y2[1] (analytic) = 1.1130050772207158056000451688413 y2[1] (numeric) = 1.1129145832816074828885650909739 absolute error = 9.04939391083227114800778674e-05 relative error = 0.0081305953549012609259128921086764 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1130050772207158056000451688413 y1[1] (numeric) = 1.1130050772207158231962269276771 absolute error = 1.75961817588358e-17 relative error = 1.5809614995445674943721441283030e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.481 y2[1] (analytic) = 1.1134672998167185279353077019906 y2[1] (numeric) = 1.1133765841545431491338580760378 absolute error = 9.07156621753788014496259528e-05 relative error = 0.0081471330312359408130210893930108 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1134672998167185279353077019906 y1[1] (numeric) = 1.11346729981671854557460287029 absolute error = 1.76392951682994e-17 relative error = 1.5841772067489456856652001937331e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.6MB, time=131.28 NO POLE NO POLE x[1] = 0.482 y2[1] (analytic) = 1.1139304089453475558294896171662 y2[1] (numeric) = 1.113839471675710029782060118005 absolute error = 9.09372696375260474294991612e-05 relative error = 0.0081636401077895052133090851078064 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1139304089453475558294896171662 y1[1] (numeric) = 1.1139304089453475735118757173304 absolute error = 1.76823861001642e-17 relative error = 1.5873869640479260652176210152646e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.6MB, time=131.79 NO POLE NO POLE x[1] = 0.483 y2[1] (analytic) = 1.1143944041434937992459891195241 y2[1] (numeric) = 1.1143032453822206422402493801148 absolute error = 9.11587612731570057397394093e-05 relative error = 0.0081801165668289775165854062301813 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1143944041434937992459891195241 y1[1] (numeric) = 1.1143944041434938169714436308636 absolute error = 1.77254545113395e-17 relative error = 1.5905907679932230597014526953486e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.484 y2[1] (analytic) = 1.1148592849471620987048280158762 y2[1] (numeric) = 1.114767904810301318645620991802 absolute error = 9.13801368607800592070240742e-05 relative error = 0.008196562390841185912775882645926 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1148592849471620987048280158762 y1[1] (numeric) = 1.1148592849471621164733283746331 absolute error = 1.77685003587569e-17 relative error = 1.5937886151792712077867398100789e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.6MB, time=132.31 NO POLE NO POLE x[1] = 0.485 y2[1] (analytic) = 1.1153250508914716892777725284065 y2[1] (numeric) = 1.1152334494952926696391162636975 absolute error = 9.16013961790196386562647090e-05 relative error = 0.0082129775625323997555289104547817 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1153250508914716892777725284065 y1[1] (numeric) = 1.1153250508914717070892961277769 absolute error = 1.78115235993704e-17 relative error = 1.5969805022431596008012416739436e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.6MB, time=132.81 NO POLE NO POLE x[1] = 0.486 y2[1] (analytic) = 1.115791701510656665469059482842 y2[1] (numeric) = 1.1156998789716500490247733250722 absolute error = 9.18225390066164442861577698e-05 relative error = 0.0082293620648279636538120791665176 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.115791701510656665469059482842 y1[1] (numeric) = 1.1157917015106566833235836729989 absolute error = 1.78545241901569e-17 relative error = 1.6001664258646017199337813572501e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.487 y2[1] (analytic) = 1.1162592363380664469812629903921 y2[1] (numeric) = 1.1161671927729440193143345244133 absolute error = 9.20435651224276669284659788e-05 relative error = 0.0082457158808719293070944405021696 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1162592363380664469812629903921 y1[1] (numeric) = 1.1162592363380664648787650785079 absolute error = 1.78975020881158e-17 relative error = 1.6033463827658241074549977811287e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.6MB, time=133.32 NO POLE NO POLE x[1] = 0.488 y2[1] (analytic) = 1.1167276549061662453658358576272 y2[1] (numeric) = 1.1166353904318608181566450485633 absolute error = 9.22644743054272091908090639e-05 relative error = 0.008262038994026685099711534144804 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1167276549061662453658358576272 y1[1] (numeric) = 1.1167276549061662633062931078964 absolute error = 1.79404572502692e-17 relative error = 1.6065203697115084323637497324035e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.6MB, time=133.81 NO POLE NO POLE x[1] = 0.489 y2[1] (analytic) = 1.117196956746537531557859073795 y2[1] (numeric) = 1.1171044714802028256513763310625 absolute error = 9.24852663347059064827427325e-05 relative error = 0.0082783313878725834700125419631906 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.117196956746537531557859073795 y1[1] (numeric) = 1.1171969567465375495412487074569 absolute error = 1.79833896336619e-17 relative error = 1.6096883835087151880836698017132e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.49 y2[1] (analytic) = 1.1176671413898785042945318408633 y2[1] (numeric) = 1.1175744354488890325466069360107 absolute error = 9.27059409894717479249048526e-05 relative error = 0.0082945930462075660698906194005022 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1176671413898785042945318408633 y1[1] (numeric) = 1.1176671413898785223208310362248 absolute error = 1.80262991953615e-17 relative error = 1.6128504210068159194518689281073e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.6MB, time=134.31 NO POLE NO POLE x[1] = 0.491 y2[1] (analytic) = 1.1181382083660045594169337278386 y2[1] (numeric) = 1.1180452818679555093197927199057 absolute error = 9.29264980490500971410079329e-05 relative error = 0.0083108239530467867302985541070571 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1181382083660045594169337278386 y1[1] (numeric) = 1.1181382083660045774861196202971 absolute error = 1.80691858924585e-17 relative error = 1.6160064790974250122423476247198e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.6MB, time=134.81 NO POLE NO POLE x[1] = 0.492 y2[1] (analytic) = 1.1186101572038487600545896476376 y2[1] (numeric) = 1.1185170102665558761416571905281 absolute error = 9.31469372928839129324571095e-05 relative error = 0.0083270240926222322483524297613322 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1186101572038487600545896476376 y1[1] (numeric) = 1.1186101572038487781666393297038 absolute error = 1.81120496820662e-17 relative error = 1.6191565547143131688792862628015e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.493 y2[1] (analytic) = 1.1190829874314623076923674719854 y2[1] (numeric) = 1.1189896201729617737225320990207 absolute error = 9.33672585005339698353729647e-05 relative error = 0.0083431934493823410116259305935004 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1190829874314623076923674719854 y1[1] (numeric) = 1.1190829874314623258472579933062 absolute error = 1.81548905213208e-17 relative error = 1.6223006448333383697570160631970e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.6MB, time=135.31 NO POLE NO POLE x[1] = 0.494 y2[1] (analytic) = 1.1195566985760150141192372174827 y2[1] (numeric) = 1.1194631111145633350406774188615 absolute error = 9.35874614516790785597986212e-05 relative error = 0.008359332007991619475237312034233 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1195566985760150141192372174827 y1[1] (numeric) = 1.1195566985760150323169455848641 absolute error = 1.81977083673814e-17 relative error = 1.6254387464723674740595978333368e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.6MB, time=135.81 NO POLE NO POLE x[1] = 0.495 y2[1] (analytic) = 1.1200312901637957742584198541208 y2[1] (numeric) = 1.1199374826178696579521089834493 absolute error = 9.38075459261163063108706715e-05 relative error = 0.0083754397533302565073298878895698 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1200312901637957742584198541208 y1[1] (numeric) = 1.1200312901637957924989230315511 absolute error = 1.82405031774303e-17 relative error = 1.6285708566912242028466569085545e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.496 y2[1] (analytic) = 1.1205067617202130398784529061372 y2[1] (numeric) = 1.1204127342085092786814611725142 absolute error = 9.40275117037611969917336230e-05 relative error = 0.0083915166704937356185451478356685 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1205067617202130398784529061372 y1[1] (numeric) = 1.1205067617202130581617278148099 absolute error = 1.82832749086727e-17 relative error = 1.6316969725915831071092905945432e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1033.7MB, alloc=4.6MB, time=136.29 NO POLE NO POLE x[1] = 0.497 y2[1] (analytic) = 1.1209831127697952941846991341835 y2[1] (numeric) = 1.1208888654112306461934111565292 absolute error = 9.42473585646479912879776543e-05 relative error = 0.0084075627447924450910853228202536 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1209831127697952941846991341835 y1[1] (numeric) = 1.1209831127697953125107226525202 absolute error = 1.83260235183367e-17 relative error = 1.6348170913168899695712280609216e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.6MB, time=136.78 NO POLE NO POLE x[1] = 0.498 y2[1] (analytic) = 1.1214603428361915272908237073372 y2[1] (numeric) = 1.1213658757499025974441903277382 absolute error = 9.44670862889298466333795990e-05 relative error = 0.0084235779617512860229593640631542 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1214603428361915272908237073372 y1[1] (numeric) = 1.121460342836191545659572671011 absolute error = 1.83687489636738e-17 relative error = 1.6379312100523263977078185549673e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1041.4MB, alloc=4.6MB, time=137.27 x[1] = 0.499 y2[1] (analytic) = 1.1219384514421717125697643935207 y2[1] (numeric) = 1.1218437647475148335127076663293 absolute error = 9.46866946568790570567271914e-05 relative error = 0.0084395623071092783030028959067974 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1219384514421717125697643935207 y1[1] (numeric) = 1.1219384514421717309812155954793 absolute error = 1.84114512019586e-17 relative error = 1.6410393260247026071640763451856e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1223225319261783966108089106687 absolute error = 9.49061834488872729095067275e-05 relative error = 0.0084555157668191645322587470155435 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1224174381096272838837184173962 y1[1] (numeric) = 1.1224174381096273023378486078849 absolute error = 1.84541301904887e-17 relative error = 1.6441414365023677046574630438253e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.6MB, time=137.77 NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228021768071261479721945213767 absolute error = 9.51255524454657204742344119e-05 relative error = 0.0084714383270470119073001610488564 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1228973023595716136926687557886 y1[1] (numeric) = 1.1228973023595716321894546423739 absolute error = 1.84967858865853e-17 relative error = 1.6472375387951819480284728423307e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.6MB, time=138.27 NO POLE NO POLE x[1] = 0.502 y2[1] (analytic) = 1.1233780437121404920409717621522 y2[1] (numeric) = 1.1232826989107132466195185503667 absolute error = 9.53448014272454214532117855e-05 relative error = 0.0084873299741718120810737406739964 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1233780437121404920409717621522 y1[1] (numeric) = 1.1233780437121405105803900097448 absolute error = 1.85394182475926e-17 relative error = 1.6503276302543816670999628246212e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.503 y2[1] (analytic) = 1.1238596616865926064215271335312 y2[1] (numeric) = 1.1237640977564176290091896477893 absolute error = 9.55639301749774123374857419e-05 relative error = 0.0085031906947850790168335889568639 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1238596616865926064215271335312 y1[1] (numeric) = 1.1238596616865926250035543644096 absolute error = 1.85820272308784e-17 relative error = 1.6534117082725507181712786345915e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.6MB, time=138.78 NO POLE NO POLE x[1] = 0.504 y2[1] (analytic) = 1.1243421558013100225170503558855 y2[1] (numeric) = 1.1242463728628404895533945621197 absolute error = 9.57829384695329636557937658e-05 relative error = 0.0085190204756904448507319848580422 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1243421558013100225170503558855 y1[1] (numeric) = 1.124342155801310041141663149719 absolute error = 1.86246127938335e-17 relative error = 1.6564897702834846967690874368662e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.6MB, time=139.29 NO POLE NO POLE x[1] = 0.505 y2[1] (analytic) = 1.1248255255737986658179668865485 y2[1] (numeric) = 1.1247295237477067620188636114049 absolute error = 9.60018260919037991032751436e-05 relative error = 0.0085348193039032537786252658868146 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1248255255737986658179668865485 y1[1] (numeric) = 1.1248255255737986844851417804209 absolute error = 1.86671748938724e-17 relative error = 1.6595618137621704889927896471550e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.506 y2[1] (analytic) = 1.1253097705206888041164464559634 y2[1] (numeric) = 1.1252135499278656018018967269461 absolute error = 9.62205928232023145497290173e-05 relative error = 0.0085505871666501539826463950405385 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1253097705206888041164464559634 y1[1] (numeric) = 1.1253097705206888228261599443965 absolute error = 1.87097134884331e-17 relative error = 1.6626278362246853151070159187244e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.6MB, time=139.79 NO POLE NO POLE x[1] = 0.507 y2[1] (analytic) = 1.1257948901577355308760949947039 y2[1] (numeric) = 1.1256984509192908690791677944297 absolute error = 9.64392384446617969272002742e-05 relative error = 0.0085663240513686876130879636782944 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1257948901577355308760949947039 y1[1] (numeric) = 1.1257948901577355496283235296809 absolute error = 1.87522285349770e-17 relative error = 1.6656878352281043352723350135281e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.6MB, time=140.30 NO POLE NO POLE x[1] = 0.508 y2[1] (analytic) = 1.1262808839998192494768208161278 y2[1] (numeric) = 1.1261842262370816128338241417431 absolute error = 9.66577627376366429966743847e-05 relative error = 0.008582029945706878841131129782464 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1262808839998192494768208161278 y1[1] (numeric) = 1.1262808839998192682715408071166 absolute error = 1.87947199909888e-17 relative error = 1.6687418083704079150072069665237e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.509 y2[1] (analytic) = 1.126767751560946158334390809836 y2[1] (numeric) = 1.1266708753954625557563971474161 absolute error = 9.68761654836025779936624199e-05 relative error = 0.0085977048375228199979472152921741 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.126767751560946158334390809836 y1[1] (numeric) = 1.1267677515609461771715786238134 absolute error = 1.88371878139774e-17 relative error = 1.6717897532904773029388092324378e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.6MB, time=140.80 NO POLE NO POLE x[1] = 0.51 y2[1] (analytic) = 1.1272554923542487368941915264245 y2[1] (numeric) = 1.1271583979077845800200390688177 absolute error = 9.70944464641568741524576068e-05 relative error = 0.0086133487148842558156893905254999 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1272554923542487368941915264245 y1[1] (numeric) = 1.1272554923542487557738234878993 absolute error = 1.88796319614748e-17 relative error = 1.6748316676679123220614565936706e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.6MB, time=141.30 NO POLE NO POLE x[1] = 0.511 y2[1] (analytic) = 1.1277441058919862324987091598053 y2[1] (numeric) = 1.1276467932865252139296003149122 absolute error = 9.73126054610185691088448931e-05 relative error = 0.0086289615660681657858820595501084 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1277441058919862324987091598053 y1[1] (numeric) = 1.1277441058919862514207615508422 absolute error = 1.89220523910369e-17 relative error = 1.6778675492230174381064206334074e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.512 y2[1] (analytic) = 1.1282335916855451481282415596589 y2[1] (numeric) = 1.1281360610432891194440605145373 absolute error = 9.75306422560286841810451216e-05 relative error = 0.0086445433795603446507052330672607 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1282335916855451481282415596589 y1[1] (numeric) = 1.1282335916855451670926906199022 absolute error = 1.89644490602433e-17 relative error = 1.6808973957166986582524295260091e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1075.7MB, alloc=4.6MB, time=141.79 NO POLE NO POLE x[1] = 0.513 y2[1] (analytic) = 1.1287239492454397310143545333464 y2[1] (numeric) = 1.1286262006888085805718258578145 absolute error = 9.77485566311504425286755319e-05 relative error = 0.0086600941440549810426603358829817 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1287239492454397310143545333464 y1[1] (numeric) = 1.1287239492454397500211764600437 absolute error = 1.90068219266973e-17 relative error = 1.6839212049503778469110975599727e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.6MB, time=142.29 NO POLE NO POLE x[1] = 0.514 y2[1] (analytic) = 1.1292151780813124621255938238659 y2[1] (numeric) = 1.1291172117329439926384043154347 absolute error = 9.79663483684694871895084312e-05 relative error = 0.008675613848454234288092548927906 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1292151780813124621255938238659 y1[1] (numeric) = 1.1292151780813124811747647718919 absolute error = 1.90491709480260e-17 relative error = 1.6869389747659155521076058511009e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.515 y2[1] (analytic) = 1.1297072777019345465249632781811 y2[1] (numeric) = 1.1296090936846843524259694681841 absolute error = 9.81840172501940989938099970e-05 relative error = 0.0086911024818678093900329333134883 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1297072777019345465249632781811 y1[1] (numeric) = 1.1297072777019345656164593600615 absolute error = 1.90914960818804e-17 relative error = 1.6899507030455334666381816957458e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.6MB, time=142.78 NO POLE NO POLE x[1] = 0.516 y2[1] (analytic) = 1.1302002476152064045986788484863 y2[1] (numeric) = 1.1301018460521477491843228071889 absolute error = 9.84015630586554143560412974e-05 relative error = 0.0087065600336125302058112296338416 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1302002476152064045986788484863 y1[1] (numeric) = 1.1302002476152064237324761344216 absolute error = 1.91337972859353e-17 relative error = 1.6929563877117188309847418469004e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.6MB, time=143.28 NO POLE NO POLE x[1] = 0.517 y2[1] (analytic) = 1.1306940873281581641557071976931 y2[1] (numeric) = 1.1305954683425818565127634939555 absolute error = 9.86189855763076429437037376e-05 relative error = 0.0087219864932119108348773725941664 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1306940873281581641557071976931 y1[1] (numeric) = 1.1306940873281581833317817155828 absolute error = 1.91760745178897e-17 relative error = 1.6959560267271727439222059919654e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.518 y2[1] (analytic) = 1.1311887963469501533975968096429 y2[1] (numeric) = 1.1310899600623644251123736983792 absolute error = 9.88362845857282852231112637e-05 relative error = 0.0087373818503957252322564121663857 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1311887963469501533975968096429 y1[1] (numeric) = 1.1311887963469501726159245451092 absolute error = 1.92183277354663e-17 relative error = 1.6989496180946784849407779877494e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.6MB, time=143.77 NO POLE NO POLE x[1] = 0.519 y2[1] (analytic) = 1.1316843741768733947581086342535 y2[1] (numeric) = 1.1315853207170037764082267624758 absolute error = 9.90534598696183498818717777e-05 relative error = 0.0087527460950995750630476910450982 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1316843741768733947581086342535 y1[1] (numeric) = 1.1316843741768734140186655306653 absolute error = 1.92605568964118e-17 relative error = 1.7019371598570403136723980860422e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1094.8MB, alloc=4.6MB, time=144.27 NO POLE NO POLE x[1] = 0.52 y2[1] (analytic) = 1.1321808203223500996121524280115 y2[1] (numeric) = 1.1320815498111392970410245676697 absolute error = 9.92705112108025711278603418e-05 relative error = 0.0087680792174644558133647974513582 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1321808203223500996121524280115 y1[1] (numeric) = 1.1321808203223501189149143865086 absolute error = 1.93027619584971e-17 relative error = 1.7049186500970130401172238509525e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.521 memory used=1098.6MB, alloc=4.6MB, time=144.76 y2[1] (analytic) = 1.1326781342869341638535340809147 y2[1] (numeric) = 1.1325786468485419342276696140423 absolute error = 9.94874383922296258644668724e-05 relative error = 0.0087833812078363211730979951773695 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1326781342869341638535340809147 y1[1] (numeric) = 1.1326781342869341831984769604319 absolute error = 1.93449428795172e-17 relative error = 1.7078940869372047383535684242734e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.522 y2[1] (analytic) = 1.1331763155733116643410183521593 y2[1] (numeric) = 1.13307661133211469199027645101 absolute error = 9.97042411969723507419011493e-05 relative error = 0.0087986520567656457058655327672592 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1331763155733116643410183521593 y1[1] (numeric) = 1.1331763155733116837281179694503 absolute error = 1.93870996172910e-17 relative error = 1.7108634685399703376178508588212e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1102.4MB, alloc=4.6MB, time=145.25 NO POLE NO POLE x[1] = 0.523 y2[1] (analytic) = 1.133675363683301356212210568549 y2[1] (numeric) = 1.133575442763893128253126230461 absolute error = 9.99209194082279590843380880e-05 relative error = 0.008813891755006985821504453579833 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.133675363683301356212210568549 y1[1] (numeric) = 1.133675363683301375641442698211 absolute error = 1.94292321296620e-17 relative error = 1.7138267931073843297033003227933e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1106.2MB, alloc=4.6MB, time=145.76 NO POLE NO POLE x[1] = 0.524 y2[1] (analytic) = 1.134175278117855171064759971788 y2[1] (numeric) = 1.1340751406450458528070672854391 absolute error = 0.0001001374728093182576926863489 relative error = 0.0088291002935185390664352719128246 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.134175278117855171064759971788 y1[1] (numeric) = 1.1341752781178551905361003462855 absolute error = 1.94713403744975e-17 relative error = 1.7167840588810807433763489888953e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.525 y2[1] (analytic) = 1.1346760583770587160043865334936 y2[1] (numeric) = 1.134575704475875026140863770014 absolute error = 0.0001003539011836898635227634796 relative error = 0.0088442776634617017472181499610186 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1346760583770587160043865334936 y1[1] (numeric) = 1.1346760583770587355178108431829 absolute error = 1.95134243096893e-17 relative error = 1.7197352641422251895572014019762e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1110.0MB, alloc=4.6MB, time=146.26 NO POLE NO POLE x[1] = 0.526 y2[1] (analytic) = 1.135177703960131773559232189945 y2[1] (numeric) = 1.1350771337558168591389935290319 absolute error = 0.0001005702043149144202386609131 relative error = 0.008859423856200624902601010014556 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.135177703960131773559232189945 y1[1] (numeric) = 1.1351777039601317931147160830985 absolute error = 1.95554838931535e-17 relative error = 1.7226804072114071512452630769738e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1113.9MB, alloc=4.6MB, time=146.75 NO POLE NO POLE x[1] = 0.527 y2[1] (analytic) = 1.1356802143654288024600365822581 y2[1] (numeric) = 1.1355794279834421136453954999901 absolute error = 0.000100786381986688814641082268 relative error = 0.0088745388633017686393423485265139 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1356802143654288024600365822581 y1[1] (numeric) = 1.1356802143654288220575556650886 absolute error = 1.95975190828305e-17 relative error = 1.7256194864485496245208012272811e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.528 y2[1] (analytic) = 1.1361835890904394392856365218521 y2[1] (numeric) = 1.1360825866564566038926660833294 absolute error = 0.0001010024339828353929704385227 relative error = 0.0088896226765334548470733872279124 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1361835890904394392856365218521 y1[1] (numeric) = 1.1361835890904394589251663585372 absolute error = 1.96395298366851e-17 relative error = 1.7285525002528272577446541701763e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1117.7MB, alloc=4.6MB, time=147.23 NO POLE NO POLE x[1] = 0.529 y2[1] (analytic) = 1.1366878276317890009732875357502 y2[1] (numeric) = 1.1365866092717016987962030519904 absolute error = 0.0001012183600873021770844837598 relative error = 0.0089046752878654183074456041881893 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1366878276317890009732875357502 y1[1] (numeric) = 1.1366878276317890206548036484569 absolute error = 1.96815161127067e-17 relative error = 1.7314794470625929646157318171445e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1121.5MB, alloc=4.6MB, time=147.71 NO POLE NO POLE x[1] = 0.53 y2[1] (analytic) = 1.1371929294852389881933049814358 y2[1] (numeric) = 1.1370914953251548251127947061314 absolute error = 0.0001014341600841630805102753044 relative error = 0.0089196966894683562127906382807902 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1371929294852389881933049814358 y1[1] (numeric) = 1.1371929294852390079167828503446 absolute error = 1.97234778689088e-17 relative error = 1.7344003253552426379908339186937e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.531 y2[1] (analytic) = 1.1376988941456875895875213566629 y2[1] (numeric) = 1.1375972443119299714631511144599 absolute error = 0.000101649833757618124370242203 relative error = 0.0089346868737134761095000564669578 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1376988941456875895875213566629 y1[1] (numeric) = 1.1376988941456876093529364199927 absolute error = 1.97654150633298e-17 relative error = 1.7373151336471939523789479856795e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1125.3MB, alloc=4.6MB, time=148.21 NO POLE NO POLE x[1] = 0.532 y2[1] (analytic) = 1.138205721107170186871055565808 y2[1] (numeric) = 1.1381038557262781932178734196901 absolute error = 0.0001018653808919936531821461179 relative error = 0.0089496458331720422813125187531165 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.138205721107170186871055565808 y1[1] (numeric) = 1.1382057211071702066783832198404 absolute error = 1.98073276540324e-17 relative error = 1.7402238704937416867910068284090e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1129.1MB, alloc=4.6MB, time=148.71 NO POLE NO POLE x[1] = 0.533 y2[1] (analytic) = 1.1387134098628598607968890410339 y2[1] (numeric) = 1.1386113290615881182463563221976 absolute error = 0.0001020808012717425505327188363 relative error = 0.0089645735606149205876754730564615 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1387134098628598607968890410339 y1[1] (numeric) = 1.138713409862859880646104640138 absolute error = 1.98492155991041e-17 relative error = 1.7431265344890095002819534362560e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.534 y2[1] (analytic) = 1.1392219599050678979827427537335 y2[1] (numeric) = 1.1391196638103864535281179930118 absolute error = 0.0001022960946814444546247607217 relative error = 0.0089794700490121217723276654878611 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1392219599050678979827427537335 y1[1] (numeric) = 1.1392219599050679178738216103904 absolute error = 1.98910788566569e-17 relative error = 1.7460231242658310812032574427884e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1132.9MB, alloc=4.6MB, time=149.21 NO POLE NO POLE x[1] = 0.535 y2[1] (analytic) = 1.1397313707252442985997482894172 y2[1] (numeric) = 1.1396288594643384926260508048581 absolute error = 0.0001025112609058059736974845591 relative error = 0.0089943352915323432572274632351093 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1397313707252442985997482894172 y1[1] (numeric) = 1.1397313707252443185326656742448 absolute error = 1.99329173848276e-17 relative error = 1.7489136384956837284716170577005e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1136.7MB, alloc=4.6MB, time=149.70 NO POLE NO POLE x[1] = 0.536 y2[1] (analytic) = 1.1402416418139782849224052974161 y2[1] (numeric) = 1.1401389155142486240210854080412 absolute error = 0.0001027262997296609013198893749 relative error = 0.0090091692815425094369302614469774 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1402416418139782849224052974161 y1[1] (numeric) = 1.1402416418139783048971364391938 absolute error = 1.99747311417777e-17 relative error = 1.7517980758885865023919423395225e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.537 y2[1] (analytic) = 1.1407527726609988107393167654858 y2[1] (numeric) = 1.1406498314500608403077598165484 absolute error = 0.0001029412109379704315569489374 relative error = 0.0090239720126073104884960846797823 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1407527726609988107393167654858 y1[1] (numeric) = 1.1407527726609988307558368511792 absolute error = 2.00165200856934e-17 relative error = 1.7546764351930068885294969240006e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1140.6MB, alloc=4.6MB, time=150.19 NO POLE NO POLE x[1] = 0.538 y2[1] (analytic) = 1.1412647627551750716241927086173 y2[1] (numeric) = 1.1411616067608592482501843088458 absolute error = 0.0001031559943158233740083997715 relative error = 0.0090387434784887397119859014721473 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1412647627551750716241927086173 y1[1] (numeric) = 1.1412647627551750916824768834031 absolute error = 2.00582841747858e-17 relative error = 1.7575487151957847123286676995479e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1144.4MB, alloc=4.6MB, time=150.68 NO POLE NO POLE x[1] = 0.539 y2[1] (analytic) = 1.1417776115845170160666120010952 y2[1] (numeric) = 1.1416742409348685796978920874449 absolute error = 0.0001033706496484363687199136503 relative error = 0.0090534836731456294165821506248003 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1417776115845170160666120010952 y1[1] (numeric) = 1.1417776115845170361666353683859 absolute error = 2.01000233672907e-17 relative error = 1.7604149147220207026878942970858e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.54 y2[1] (analytic) = 1.1422913186361758574620312210822 y2[1] (numeric) = 1.1421877334594547033610647814317 absolute error = 0.0001035851767211541009664396505 relative error = 0.0090681925907331853673455325122974 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1422913186361758574620312210822 y1[1] (numeric) = 1.1422913186361758776037688425511 absolute error = 2.01417376214689e-17 relative error = 1.7632750326350086065978769130968e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1148.2MB, alloc=4.6MB, time=151.18 NO POLE NO POLE x[1] = 0.541 y2[1] (analytic) = 1.1428058833964445869605285177651 y2[1] (numeric) = 1.1427020838211251374446210167756 absolute error = 0.0001037995753194495159075009895 relative error = 0.0090828702256025198075962525557544 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1428058833964445869605285177651 y1[1] (numeric) = 1.1428058833964446071439554133714 absolute error = 2.01834268956063e-17 relative error = 1.7661290678361494671993340385451e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.6MB, time=151.68 NO POLE NO POLE x[1] = 0.542 y2[1] (analytic) = 1.1433213053507584871737696523608 y2[1] (numeric) = 1.1432172915055295631406554203724 absolute error = 0.0001040138452289240331142319884 relative error = 0.0090975165723001830718836191229445 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1433213053507584871737696523608 y1[1] (numeric) = 1.1433213053507585073988608003745 absolute error = 2.02250911480137e-17 relative error = 1.7689770192648393767817530228129e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.543 y2[1] (analytic) = 1.1438375839836956467396825060591 y2[1] (numeric) = 1.143733355997460338978714565424 absolute error = 0.0001042279862353077609679406351 relative error = 0.0091121316255676938044831986255241 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1438375839836956467396825060591 y1[1] (numeric) = 1.1438375839836956670064128430856 absolute error = 2.02667303370265e-17 relative error = 1.7718188858983482754916967691584e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1155.8MB, alloc=4.6MB, time=152.17 NO POLE NO POLE x[1] = 0.544 y2[1] (analytic) = 1.1443547187789774757443254902696 y2[1] (numeric) = 1.1442502767808530160333955079234 absolute error = 0.0001044419981244597109299823462 relative error = 0.0091267153803410677983356189454057 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1443547187789774757443254902696 y1[1] (numeric) = 1.1443547187789774960526699112755 absolute error = 2.03083444210059e-17 relative error = 1.7746546667518296432415919728731e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1159.6MB, alloc=4.6MB, time=152.67 NO POLE NO POLE x[1] = 0.545 y2[1] (analytic) = 1.1448727092194692220004344373497 y2[1] (numeric) = 1.1447680533387868539887517066884 absolute error = 0.0001046558806823680116827306613 relative error = 0.009141267831750345469315593235482 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1448727092194692220004344373497 y1[1] (numeric) = 1.1448727092194692423503677956873 absolute error = 2.03499333583376e-17 relative error = 1.7774843608781112889643886803373e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1163.5MB, alloc=4.6MB, time=153.16 NO POLE NO POLE x[1] = 0.546 y2[1] (analytic) = 1.1453915547871804881821316933069 y2[1] (numeric) = 1.1452866851534853380589902625812 absolute error = 0.0001048696336951501231414307257 relative error = 0.0091557889751191179806938109046234 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1453915547871804881821316933069 y1[1] (numeric) = 1.1453915547871805085736288007396 absolute error = 2.03914971074327e-17 relative error = 1.7803079673676782718208977101088e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.547 y2[1] (analytic) = 1.1459112549632657498152802778119 y2[1] (numeric) = 1.1458061717063166967649435562596 absolute error = 0.0001050832569490530503367215523 relative error = 0.0091702788059640520326280166973355 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1459112549632657498152802778119 y1[1] (numeric) = 1.1459112549632657702483159045394 absolute error = 2.04330356267275e-17 relative error = 1.7831254853485593678801451001017e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1167.3MB, alloc=4.6MB, time=153.65 NO POLE NO POLE x[1] = 0.548 y2[1] (analytic) = 1.1464318092280248741229651212096 y2[1] (numeric) = 1.146326512477794420565797508032 absolute error = 0.0001052967502304535571676131776 relative error = 0.0091847373199944133314928735037837 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1464318092280248741229651212096 y1[1] (numeric) = 1.146431809228024894597513995893 absolute error = 2.04745488746834e-17 relative error = 1.7859369139862220623335259597628e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1171.1MB, alloc=4.6MB, time=154.15 NO POLE NO POLE x[1] = 0.549 y2[1] (analytic) = 1.1469532170609036397255825330915 y2[1] (numeric) = 1.1468477069475777813455578281305 absolute error = 0.000105510113325858380024704961 relative error = 0.0091991645131115887538310850232972 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1469532170609036397255825330915 y1[1] (numeric) = 1.1469532170609036602416193428787 absolute error = 2.05160368097872e-17 relative error = 1.7887422524835021987586593900511e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.55 y2[1] (analytic) = 1.1474754779404942571950182023822 y2[1] (numeric) = 1.1473697545944723527537347709791 absolute error = 0.0001057233460219044412834314031 relative error = 0.0092135603814086072196807423941134 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1474754779404942571950182023822 y1[1] (numeric) = 1.1474754779404942777525175929333 absolute error = 2.05574993905511e-17 relative error = 1.7915415000805071737909870491842e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1174.9MB, alloc=4.6MB, time=154.65 NO POLE NO POLE x[1] = 0.551 y2[1] (analytic) = 1.1479985913445358904623931748063 y2[1] (numeric) = 1.1478926548964305313997260528161 absolute error = 0.0001059364481053590626671219902 relative error = 0.0092279249211696592900059588264314 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1479985913445358904623931748063 y1[1] (numeric) = 1.1479985913445359110613297503186 absolute error = 2.05989365755123e-17 relative error = 1.7943346560544840524884723923908e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1178.7MB, alloc=4.6MB, time=155.15 NO POLE NO POLE x[1] = 0.552 y2[1] (analytic) = 1.1485225567499151790788564000321 y2[1] (numeric) = 1.148416407330552058900376738331 absolute error = 0.0001061494193631201784796617011 relative error = 0.0092422581288696155029295707869836 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1485225567499151790788564000321 y1[1] (numeric) = 1.1485225567499151997192047232658 absolute error = 2.06403483232337e-17 relative error = 1.7971217197197833211120986566592e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.553 y2[1] (analytic) = 1.1490473736326667613289015877443 y2[1] (numeric) = 1.1489410113730845447801940487992 absolute error = 0.0001063622595822165487075389451 relative error = 0.0092565600011735434634380172649832 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1490473736326667613289015877443 y1[1] (numeric) = 1.1490473736326667820106361800479 absolute error = 2.06817345923036e-17 relative error = 1.7999026904277352141336893381866e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1182.5MB, alloc=4.6MB, time=155.65 NO POLE NO POLE x[1] = 0.554 y2[1] (analytic) = 1.1495730414679737981956852593716 y2[1] (numeric) = 1.1494664664994239902236941915438 absolute error = 0.0001065749685498079719910678278 relative error = 0.009270830534936223701199462635061 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1495730414679737981956852593716 y1[1] (numeric) = 1.1495730414679738189187806007073 absolute error = 2.07230953413357e-17 relative error = 1.8026775675665519819577272288053e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1186.3MB, alloc=4.6MB, time=156.14 NO POLE NO POLE x[1] = 0.555 y2[1] (analytic) = 1.150099559730168498177822030195 y2[1] (numeric) = 1.1499927721841153126793574584209 absolute error = 0.0001067875460531854984645717741 relative error = 0.0092850697272016643111068078302479 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.150099559730168498177822030195 y1[1] (numeric) = 1.1500995597301685189422525591643 absolute error = 2.07644305289693e-17 relative error = 1.8054463505612473238676065339315e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.556 y2[1] (analytic) = 1.1506269278927326429571323050854 y2[1] (numeric) = 1.1505199279008528713146669894172 absolute error = 0.0001069999918797716424653156682 relative error = 0.0092992775752026143911274416126357 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1506269278927326429571323050854 y1[1] (numeric) = 1.1506269278927326637628724189545 absolute error = 2.08057401138691e-17 relative error = 1.8082090388735207877743902284280e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1190.2MB, alloc=4.6MB, time=156.64 NO POLE NO POLE x[1] = 0.557 y2[1] (analytic) = 1.1511551454282981139168167201663 y2[1] (numeric) = 1.151047933122480993321705746365 absolute error = 0.0001072123058171205951109738013 relative error = 0.0093134540763600762920114222535031 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1511551454282981139168167201663 y1[1] (numeric) = 1.151155145428298134763840774892 absolute error = 2.08470240547257e-17 relative error = 1.8109656320017028073531258931724e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1194.0MB, alloc=4.6MB, time=157.14 NO POLE NO POLE x[1] = 0.558 y2[1] (analytic) = 1.1516842118086474195095308122717 y2[1] (numeric) = 1.1515767873209945010727853912213 absolute error = 0.0001074244876529184367454210504 relative error = 0.0093275992282828166933792533407553 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1516842118086474195095308122717 y1[1] (numeric) = 1.1516842118086474403978131225267 absolute error = 2.08882823102550e-17 relative error = 1.8137161294806038911413847629649e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.559 y2[1] (analytic) = 1.1522141265047142234748325481675 y2[1] (numeric) = 1.1521064899675392401255799133259 absolute error = 0.0001076365371749833492526348416 relative error = 0.0093417130287668765206795286478109 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1522141265047142234748325481675 y1[1] (numeric) = 1.1522141265047142444043473873663 absolute error = 2.09295148391988e-17 relative error = 1.8164605308814678893144188432047e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1197.8MB, alloc=4.6MB, time=157.65 NO POLE NO POLE x[1] = 0.56 y2[1] (analytic) = 1.1527448889865838739054744961337 y2[1] (numeric) = 1.1526370405324126080772360005497 absolute error = 0.000107848454171265828238495584 relative error = 0.0093557954757950797174754738132604 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1527448889865838739054744961337 y1[1] (numeric) = 1.1527448889865838948761960964583 absolute error = 2.09707216003246e-17 relative error = 1.8191988358118555067150385364753e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1201.6MB, alloc=4.6MB, time=158.15 NO POLE NO POLE x[1] = 0.561 y2[1] (analytic) = 1.153276498723493933162011573659 y2[1] (numeric) = 1.1531684384850640842669313002658 absolute error = 0.0001080602384298488950802733932 relative error = 0.0093698465675365408874878100956031 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.153276498723493933162011573659 y1[1] (numeric) = 1.1532764987234939541739141260846 absolute error = 2.10119025524256e-17 relative error = 1.8219310439155449980283676204898e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.562 y2[1] (analytic) = 1.1538089551838347086351944566842 y2[1] (numeric) = 1.1537006832940957603263508676298 absolute error = 0.0001082718897389483088435890544 relative error = 0.0093838663023461718207894108179212 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1538089551838347086351944566842 y1[1] (numeric) = 1.1538089551838347296882521110052 absolute error = 2.10530576543210e-17 relative error = 1.8246571548724586589596183841925e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1205.4MB, alloc=4.6MB, time=158.64 NO POLE NO POLE x[1] = 0.563 y2[1] (analytic) = 1.1543422578351497843556178880455 y2[1] (numeric) = 1.1542337744272628715775512507373 absolute error = 0.0001084834078869127780666373082 relative error = 0.0093978546787641869185149179677358 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1543422578351497843556178880455 y1[1] (numeric) = 1.154342257835149805449804752901 absolute error = 2.10941868648555e-17 relative error = 1.8273771683985197397790459680931e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1209.2MB, alloc=4.6MB, time=159.14 NO POLE NO POLE x[1] = 0.564 y2[1] (analytic) = 1.1548764061441365534500922755128 y2[1] (numeric) = 1.1547677113514743292776808148386 absolute error = 0.0001086947926622241724114606742 relative error = 0.0094118116955156075304158378053594 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1548764061441365534500922755128 y1[1] (numeric) = 1.1548764061441365745853824184127 absolute error = 2.11352901428999e-17 relative error = 1.8300910842456045280200278829025e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.565 y2[1] (analytic) = 1.1554113995766467514442061230971 y2[1] (numeric) = 1.1553024935327932537100240609341 absolute error = 0.000108906043853497734182062163 relative error = 0.0094257373515097652195586439727717 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1554113995766467514442061230971 y1[1] (numeric) = 1.1554113995766467726205735704482 absolute error = 2.11763674473511e-17 relative error = 1.8327989022014421609449874707469e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1213.0MB, alloc=4.6MB, time=159.64 NO POLE NO POLE x[1] = 0.566 y2[1] (analytic) = 1.1559472375976869904105459931083 y2[1] (numeric) = 1.1558381204364375081208368477516 absolute error = 0.0001091171612494822897091453567 relative error = 0.0094396316458398039684300869740313 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1559472375976869904105459931083 y1[1] (numeric) = 1.15594723759768701162796473024 absolute error = 2.12174187371317e-17 relative error = 1.8355006220894796405717382905201e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1216.9MB, alloc=4.6MB, time=160.14 NO POLE NO POLE x[1] = 0.567 y2[1] (analytic) = 1.1564839196714192939620398507875 y2[1] (numeric) = 1.1563745915267802335014385803137 absolute error = 0.0001093281446390604606012704738 relative error = 0.0094534945777821813406802443944858 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1564839196714192939620398507875 y1[1] (numeric) = 1.1564839196714193152204838219779 absolute error = 2.12584439711904e-17 relative error = 1.8381962437688159292468881387571e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1220.7MB, alloc=4.6MB, time=160.63 x[1] = 0.568 y2[1] (analytic) = 1.157021445261161633089888798216 y2[1] (numeric) = 1.1569119062673503842150265830484 absolute error = 0.0001095389938112488748622151676 relative error = 0.0094673261467961686126998493768709 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.157021445261161633089888798216 y1[1] (numeric) = 1.1570214452611616543893319067179 absolute error = 2.12994431085019e-17 relative error = 1.8408857671340925463342018274913e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.569 y2[1] (analytic) = 1.1575598138293884628455513596132 y2[1] (numeric) = 1.1574500641208332644676770306726 absolute error = 0.0001097497085551983778743289406 relative error = 0.0094811263525233498891941092276609 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1575598138293884628455513596132 y1[1] (numeric) = 1.1575598138293884841859674676803 absolute error = 2.13404161080671e-17 relative error = 1.8435691921154099201627909337955e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1224.5MB, alloc=4.6MB, time=161.12 NO POLE NO POLE x[1] = 0.57 y2[1] (analytic) = 1.158099024837731259866243636084 y2[1] (numeric) = 1.157989064549071065622995965893 absolute error = 0.000109960288660194243247670191 relative error = 0.0094948951947871202168805748911152 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.158099024837731259866243636084 y1[1] (numeric) = 1.1580990248377312812476065649972 absolute error = 2.13813629289132e-17 relative error = 1.8462465186782348742261058890847e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1228.3MB, alloc=4.6MB, time=161.60 NO POLE NO POLE x[1] = 0.571 y2[1] (analytic) = 1.158639077746979060743417804361 y2[1] (numeric) = 1.1585289070130634043598830893173 absolute error = 0.0001101707339156563835347150437 relative error = 0.009508632673592182710403648919013 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.158639077746979060743417804361 y1[1] (numeric) = 1.1586390777469790821657013344541 absolute error = 2.14222835300931e-17 relative error = 1.8489177468232474935644987134526e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.572 y2[1] (analytic) = 1.1591799720170790012336805911064 y2[1] (numeric) = 1.1590695909729678616728701638576 absolute error = 0.0001103810441111395608104272488 relative error = 0.0095223387891240447045230270545163 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1591799720170790012336805911064 y1[1] (numeric) = 1.1591799720170790226968584617928 absolute error = 2.14631778706864e-17 relative error = 1.8515828765863259874943045347837e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1232.1MB, alloc=4.6MB, time=162.09 NO POLE NO POLE x[1] = 0.573 y2[1] (analytic) = 1.1597217071071368563116125119018 y2[1] (numeric) = 1.1596111158881005227144950333318 absolute error = 0.00011059121903633359711747857 relative error = 0.0095360135417485129465977611876781 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1597217071071368563116125119018 y1[1] (numeric) = 1.1597217071071368778156584217005 absolute error = 2.15040459097987e-17 relative error = 1.8542419080383845493818297335904e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1235.9MB, alloc=4.6MB, time=162.57 NO POLE NO POLE x[1] = 0.574 y2[1] (analytic) = 1.1602642824754175810639478221502 y2[1] (numeric) = 1.1601534812169365174791714129342 absolute error = 0.000110801258481063584776409216 relative error = 0.0095496569320111878433517110091418 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1602642824754175810639478221502 y1[1] (numeric) = 1.1602642824754176026088354287121 absolute error = 2.15448876065619e-17 relative error = 1.8568948412852974011191879451756e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.575 y2[1] (analytic) = 1.1608076975793458524245742857562 y2[1] (numeric) = 1.1606966864171105623280137677511 absolute error = 0.0001110111622352900965605180051 relative error = 0.0095632689606369567758699227814817 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1608076975793458524245742857562 y1[1] (numeric) = 1.1608076975793458740102772058906 absolute error = 2.15857029201344e-17 relative error = 1.8595416764678139813607148913235e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1239.7MB, alloc=4.6MB, time=163.06 NO POLE NO POLE x[1] = 0.576 y2[1] (analytic) = 1.1613519518755066117498110266296 y2[1] (numeric) = 1.1612407309454175023540757545404 absolute error = 0.0001112209300891093957352720892 relative error = 0.0095768496285294864967389389022732 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1613519518755066117498110266296 y1[1] (numeric) = 1.1613519518755066333763028363305 absolute error = 2.16264918097009e-17 relative error = 1.8621824137614394763845688447247e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.6MB, time=163.54 NO POLE NO POLE x[1] = 0.577 y2[1] (analytic) = 1.1618970448196456082334218877795 y2[1] (numeric) = 1.1617856142578128545874598615838 absolute error = 0.0001114305618327536459620261957 relative error = 0.0095903989367707146232072044084547 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1618970448196456082334218877795 y1[1] (numeric) = 1.1618970448196456299006761222519 absolute error = 2.16672542344724e-17 relative error = 1.8648170533763324489887405377339e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.578 y2[1] (analytic) = 1.162442975866669943160820883031 y2[1] (numeric) = 1.1623313358094133520397550415451 absolute error = 0.0001116400572565911210658414859 relative error = 0.0096039168866203402402046005371736 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.162442975866669943160820883031 y1[1] (numeric) = 1.1624429758666699648688110367176 absolute error = 2.17079901536866e-17 relative error = 1.8674455955572367167881799550071e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1247.4MB, alloc=4.6MB, time=164.03 NO POLE NO POLE x[1] = 0.579 y2[1] (analytic) = 1.1629897444706486150019254872046 y2[1] (numeric) = 1.1628778950544974885872582929441 absolute error = 0.0001118494161511264146671942605 relative error = 0.0096174034795153136270227028182717 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1629897444706486150019254872046 y1[1] (numeric) = 1.1629897444706486367506250138121 absolute error = 2.17486995266075e-17 relative error = 1.8700680405833441870318716019746e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1251.2MB, alloc=4.6MB, time=164.52 NO POLE NO POLE x[1] = 0.58 y2[1] (analytic) = 1.16353735008481306534211267195 y2[1] (numeric) = 1.1634252914465060646924353070688 absolute error = 0.0001120586383070006496773648812 relative error = 0.0096308587170693251214196364475119 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.16353735008481306534211267195 y1[1] (numeric) = 1.1635373500848130871314949844758 absolute error = 2.17893823125258e-17 relative error = 1.8726843887682263887534388865088e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.581 y2[1] (analytic) = 1.1640857921615577256507317563242 y2[1] (numeric) = 1.1639735244380427339630744589114 absolute error = 0.0001122677235149916876572974128 relative error = 0.0096442826010722931348753873332334 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1640857921615577256507317563242 y1[1] (numeric) = 1.1640857921615577474807702270829 absolute error = 2.18300384707587e-17 relative error = 1.8752946404597142123372998290945e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1255.0MB, alloc=4.6MB, time=165.00 NO POLE NO POLE x[1] = 0.582 y2[1] (analytic) = 1.1646350701524405648866273036464 y2[1] (numeric) = 1.1645225934808745505485875830191 absolute error = 0.0001124766715660143380397206273 relative error = 0.0096576751334898513326851268882624 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1646350701524405648866273036464 y1[1] (numeric) = 1.1646350701524405867572952642964 absolute error = 2.18706679606500e-17 relative error = 1.8778987960398033065686190193843e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1258.8MB, alloc=4.6MB, time=165.48 NO POLE NO POLE x[1] = 0.583 y2[1] (analytic) = 1.165185183508183637940124459152 y2[1] (numeric) = 1.1650724980259325173729101380051 absolute error = 0.0001126854822511205672143211469 relative error = 0.0096710363164628349925395253174159 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.165185183508183637940124459152 y1[1] (numeric) = 1.1651851835081836598513952007223 absolute error = 2.19112707415703e-17 relative error = 1.8804968559245678861514384742644e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.584 y2[1] (analytic) = 1.1657361316786736349109282865074 y2[1] (numeric) = 1.1656232375233121352034525268648 absolute error = 0.0001128941553614997074757596426 relative error = 0.0096843661523067665552021656041132 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1657361316786736349109282865074 y1[1] (numeric) = 1.1657361316786736568627750594241 absolute error = 2.19518467729167e-17 relative error = 1.8830888205640314542911563668162e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1262.6MB, alloc=4.6MB, time=165.96 NO POLE NO POLE x[1] = 0.585 y2[1] (analytic) = 1.1662879141129624312213878253303 y2[1] (numeric) = 1.166174811422273952555553504192 absolute error = 0.0001131026906884786658343211383 relative error = 0.0096976646435113403808550309287528 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1662879141129624312213878253303 y1[1] (numeric) = 1.1662879141129624532137838394435 absolute error = 2.19923960141132e-17 relative error = 1.8856746904420974754909642195197e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1266.5MB, alloc=4.6MB, time=166.45 NO POLE NO POLE x[1] = 0.586 y2[1] (analytic) = 1.1668405302592676385645747564984 y2[1] (numeric) = 1.1667272191712441164318857658875 absolute error = 0.0001133110880235221326889906109 relative error = 0.0097109317927399067246436262999046 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1668405302592676385645747564984 y1[1] (numeric) = 1.1668405302592676605974931811091 absolute error = 2.20329184246107e-17 relative error = 1.8882544660764455307113372505364e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.587 y2[1] (analytic) = 1.1673939795649731566866257272142 y2[1] (numeric) = 1.1672804602178149238962629820001 absolute error = 0.0001135193471582327903627452141 relative error = 0.0097241676028289549449136130543167 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1673939795649731566866257272142 y1[1] (numeric) = 1.1673939795649731787600396911007 absolute error = 2.20734139638865e-17 relative error = 1.8908281480183845050156172751767e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1270.3MB, alloc=4.6MB, time=166.93 NO POLE NO POLE x[1] = 0.588 y2[1] (analytic) = 1.1679482614766297260027965535271 y2[1] (numeric) = 1.1678345340087453744812966989392 absolute error = 0.0001137274678843515214998545879 relative error = 0.0097373720767875959575908858571508 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1679482614766297260027965535271 y1[1] (numeric) = 1.1679482614766297481166791449725 absolute error = 2.21138825914454e-17 relative error = 1.8933957368528427551029732410279e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1274.1MB, alloc=4.6MB, time=167.41 NO POLE NO POLE x[1] = 0.589 y2[1] (analytic) = 1.1685033754399554810466756843086 y2[1] (numeric) = 1.1683894399899617234293507034482 absolute error = 0.0001139354499937576173249808604 relative error = 0.0097505452177970439501168102643483 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1685033754399554810466756843086 y1[1] (numeric) = 1.1685033754399555032009999511272 absolute error = 2.21543242668186e-17 relative error = 1.8959572331981696017132813358620e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1277.9MB, alloc=4.6MB, time=167.90 x[1] = 0.59 y2[1] (analytic) = 1.1690593208998365047520034775093 y2[1] (numeric) = 1.1689451776065580357662396074299 absolute error = 0.0001141432932784689857638700794 relative error = 0.0097636870292100973683098659555804 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1690593208998365047520034775093 y1[1] (numeric) = 1.1690593208998365269467424270738 absolute error = 2.21947389495645e-17 relative error = 1.8985126377060994850620897100715e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.591 y2[1] (analytic) = 1.1696160973003273835665430069271 y2[1] (numeric) = 1.1695017463027967412071175799726 absolute error = 0.0001143509975306423594254269545 relative error = 0.0097767975145506191894842118488574 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1696160973003273835665430069271 y1[1] (numeric) = 1.1696160973003274058016696061954 absolute error = 2.22351265992683e-17 relative error = 1.9010619510616132006259129670551e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1281.7MB, alloc=4.6MB, time=168.38 NO POLE NO POLE x[1] = 0.592 y2[1] (analytic) = 1.1701737040846517633974472856612 y2[1] (numeric) = 1.170059145522109189894002320733 absolute error = 0.0001145585625425735034449649282 relative error = 0.0097898766775130164951147061546044 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1701737040846517633974472856612 y1[1] (numeric) = 1.1701737040846517856729344612037 absolute error = 2.22754871755425e-17 relative error = 1.9036051739828760202680516769703e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1285.5MB, alloc=4.6MB, time=168.87 NO POLE NO POLE x[1] = 0.593 y2[1] (analytic) = 1.1707321406952029063875669609314 y2[1] (numeric) = 1.1706173747070962089643785371992 absolute error = 0.0001147659881066974231884237322 relative error = 0.0098029245219617193562966806715749 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1707321406952029063875669609314 y1[1] (numeric) = 1.1707321406952029287033875989578 absolute error = 2.23158206380264e-17 relative error = 1.9061423072210901530657521369391e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.594 y2[1] (analytic) = 1.1712914065735442485221417040005 y2[1] (numeric) = 1.1711764332995286599503243572767 absolute error = 0.0001149732740155885718173467238 relative error = 0.0098159410519306590452072875556885 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1712914065735442485221417040005 y1[1] (numeric) = 1.1712914065735442708782686503871 absolute error = 2.23561269463866e-17 relative error = 1.9086733515604325853860436418979e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1289.3MB, alloc=4.6MB, time=169.35 NO POLE NO POLE x[1] = 0.595 y2[1] (analytic) = 1.1718515011604099580653176885558 y2[1] (numeric) = 1.1717363207403479970076032781168 absolute error = 0.000115180420061961057714410439 relative error = 0.0098289262716227455857335117614873 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1718515011604099580653176885558 y1[1] (numeric) = 1.1718515011604099804617237488727 absolute error = 2.23964060603169e-17 relative error = 1.9111983078179414812973114752193e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1293.2MB, alloc=4.6MB, time=169.84 NO POLE NO POLE x[1] = 0.596 y2[1] (analytic) = 1.172412423895705494825932721079 y2[1] (numeric) = 1.1722970364696668259741634221424 absolute error = 0.0001153874260386688517692989366 relative error = 0.0098418801854093446563899759447221 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.172412423895705494825932721079 y1[1] (numeric) = 1.172412423895705517262590660617 absolute error = 2.24366579395380e-17 relative error = 1.9137171768433854348186213762318e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.597 y2[1] (analytic) = 1.1729741742185081702520097574644 y2[1] (numeric) = 1.1728585799267694642574850418188 absolute error = 0.0001155942917387059945247156456 relative error = 0.0098548027978297538586074603632873 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1729741742185081702520097574644 y1[1] (numeric) = 1.1729741742185081927288923012625 absolute error = 2.24768825437981e-17 relative error = 1.9162299595192094125026957533703e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1297.0MB, alloc=4.6MB, time=170.32 NO POLE NO POLE x[1] = 0.598 y2[1] (analytic) = 1.1735367515670677083533987114403 y2[1] (numeric) = 1.173420950550112501550216385868 absolute error = 0.0001158010169552068031823255723 relative error = 0.0098676941135906783634306218805876 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1735367515670677083533987114403 y1[1] (numeric) = 1.173536751567067730870478544313 absolute error = 2.25170798328727e-17 relative error = 1.9187366567604122703075118664513e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1300.8MB, alloc=4.6MB, time=170.81 NO POLE NO POLE x[1] = 0.599 y2[1] (analytic) = 1.1741001553788068074520056321979 y2[1] (numeric) = 1.1739841477773253613735372113378 absolute error = 0.0001160076014814460784684208601 relative error = 0.009880554137565705949620725556507 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1741001553788068074520056321979 y1[1] (numeric) = 1.1741001553788068300092553987623 absolute error = 2.25572497665644e-17 relative error = 1.9212372695144242133052375388753e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6 y2[1] (analytic) = 1.1746643850903217027590475010446 y2[1] (numeric) = 1.174548171045210863447688398209 absolute error = 0.0001162140451108393113591028356 relative error = 0.0098933828747947814461163036377223 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1746643850903217027590475010446 y1[1] (numeric) = 1.1746643850903217253564398057478 absolute error = 2.25973923047032e-17 relative error = 1.9237317987610267661977159175383e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1304.6MB, alloc=4.6MB, time=171.28 NO POLE NO POLE x[1] = 0.601 y2[1] (analytic) = 1.1752294401373827297787700698751 y2[1] (numeric) = 1.1751130197897457868891052960577 absolute error = 0.0001164203476369428896647738174 relative error = 0.0099061803304836805917615330179044 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1752294401373827297787700698751 y1[1] (numeric) = 1.1752294401373827524162774770217 absolute error = 2.26375074071466e-17 relative error = 1.9262202455122555511512659640700e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1308.4MB, alloc=4.6MB, time=171.77 NO POLE NO POLE x[1] = 0.602 y2[1] (analytic) = 1.1757953199549348885380653377883 y2[1] (numeric) = 1.1756786934460814342335916056863 absolute error = 0.000116626508853454304473732102 relative error = 0.0099189465100034833251687759669172 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1757953199549348885380653377883 y1[1] (numeric) = 1.175795319954934911215660371568 absolute error = 2.26775950337797e-17 relative error = 1.9287026108123029424314946425358e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.603 y2[1] (analytic) = 1.1763620239770984086414244362806 y2[1] (numeric) = 1.1762451914485441962849697725968 absolute error = 0.0001168325285542123564546636838 relative error = 0.0099316814188900465175381640531228 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1763620239770984086414244362806 y1[1] (numeric) = 1.1763620239770984313590795807953 absolute error = 2.27176551445147e-17 relative error = 1.9311788957373695955952437674715e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1312.2MB, alloc=4.6MB, time=172.25 NO POLE NO POLE x[1] = 0.604 y2[1] (analytic) = 1.1769295516371693151506608681084 y2[1] (numeric) = 1.1768125132306361177886430437023 absolute error = 0.0001170384065331973620178244061 relative error = 0.0099443850628434761612133241998685 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1769295516371693151506608681084 y1[1] (numeric) = 1.1769295516371693379083485673999 absolute error = 2.27576876992915e-17 relative error = 1.9336491013956094695102686890316e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1316.0MB, alloc=4.6MB, time=172.73 NO POLE NO POLE x[1] = 0.605 y2[1] (analytic) = 1.177497902367619995288838220145 y2[1] (numeric) = 1.1773806582250354639295035137625 absolute error = 0.0001172441425845313593347063825 relative error = 0.0099570574477275990267083522866067 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.177497902367619995288838220145 y1[1] (numeric) = 1.1774979023676200180865308782227 absolute error = 2.27976926580777e-17 relative error = 1.9361132289270236541815852932555e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.606 y2[1] (analytic) = 1.1780670756000997659678356463513 y2[1] (numeric) = 1.1779496258635972876536196636819 absolute error = 0.0001174497365024783142159826694 relative error = 0.009969698579569433800896936404248 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1780670756000997659678356463513 y1[1] (numeric) = 1.1780670756000997888055056272194 absolute error = 2.28376699808681e-17 relative error = 1.9385712795033116674261480097469e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1319.9MB, alloc=4.6MB, time=173.21 NO POLE NO POLE x[1] = 0.607 y2[1] (analytic) = 1.1786370707654354421389835933405 y2[1] (numeric) = 1.1785194155773539978131360690308 absolute error = 0.0001176551880814443258475243097 relative error = 0.0099823084645586617190101218366934 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1786370707654354421389835933405 y1[1] (numeric) = 1.178637070765435465016603221026 absolute error = 2.28776196276855e-17 relative error = 1.9410232543278330853122804654344e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1323.7MB, alloc=4.6MB, time=173.69 NO POLE NO POLE x[1] = 0.608 y2[1] (analytic) = 1.1792078872936319059662014179512 y2[1] (numeric) = 1.179090026796515928133817133936 absolute error = 0.0001178604971159778323842840152 relative error = 0.0099948871090470967030445969899982 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 1.1792078872936319059662014179512 y1[1] (numeric) = 1.1792078872936319288837429765315 absolute error = 2.29175415585803e-17 relative error = 1.9434691546354671285690489564375e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.609 y2[1] (analytic) = 1.1797795246138726768210677237362 y2[1] (numeric) = 1.1796614589504719070046658828463 absolute error = 0.0001180656634007698164018408899 relative error = 0.010007434519548155019138565144426 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1797795246138726768210677237362 y1[1] (numeric) = 1.1797795246138726997785034573666 absolute error = 2.29574357336304e-17 relative error = 1.9459089816924976946440616245760e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1327.5MB, alloc=4.6MB, time=174.18 NO POLE NO POLE x[1] = 0.61 y2[1] (analytic) = 1.1803519821545204820992534213452 y2[1] (numeric) = 1.1802337114677898280890480205996 absolute error = 0.0001182706867306540102054007456 relative error = 0.010019950702736324466427256438141 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1803519821545204820992534213452 y1[1] (numeric) = 1.1803519821545205050965555342871 absolute error = 2.29973021129419e-17 relative error = 1.9483427367965661119342414810796e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1331.3MB, alloc=4.6MB, time=174.67 NO POLE NO POLE x[1] = 0.611 y2[1] (analytic) = 1.1809252593431178288577466964165 y2[1] (numeric) = 1.1808067837762172217567506497169 absolute error = 0.0001184755669006071009960466996 relative error = 0.010032435665446633109844928813051 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1809252593431178288577466964165 y1[1] (numeric) = 1.1809252593431178518948873530648 absolute error = 2.30371406566483e-17 relative error = 1.9507704212764966258137227344923e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.612 y2[1] (analytic) = 1.1814993556063875762722982477992 y2[1] (numeric) = 1.1813806753026818273364042129108 absolute error = 0.0001186803037057489358940348884 relative error = 0.010044889414674117569294810211948 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1814993556063875762722982477992 y1[1] (numeric) = 1.1814993556063875993492495727102 absolute error = 2.30769513249110e-17 relative error = 1.9531920364922320376528018525291e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1335.1MB, alloc=4.6MB, time=175.15 NO POLE NO POLE x[1] = 0.613 y2[1] (analytic) = 1.1820742703702335089145143387088 y2[1] (numeric) = 1.1819553854732921661876954084352 absolute error = 0.0001188848969413427268189302736 relative error = 0.010057311957573290877562849513024 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1820742703702335089145143387088 y1[1] (numeric) = 1.1820742703702335320312484166282 absolute error = 2.31167340779194e-17 relative error = 1.9556075838347353099708622180174e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1338.9MB, alloc=4.6MB, time=175.64 NO POLE NO POLE x[1] = 0.614 y2[1] (analytic) = 1.1826500030597409108480243837716 y2[1] (numeric) = 1.18253091371333811559279800611 absolute error = 0.0001190893464027952552263776616 relative error = 0.010069703301457609919305373967022 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1826500030597409108480243837716 y1[1] (numeric) = 1.1826500030597409340045132596622 absolute error = 2.31564888758906e-17 relative error = 1.9580170647258572552485776912588e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1342.7MB, alloc=4.6MB, time=176.13 NO POLE NO POLE x[1] = 0.615 y2[1] (analytic) = 1.1832265530991771405431489758368 y2[1] (numeric) = 1.1831072594472914834664476726389 absolute error = 0.0001192936518856570767013031979 relative error = 0.010082063453798942463394798495706 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1832265530991771405431489758368 y1[1] (numeric) = 1.1832265530991771637393646549069 absolute error = 2.31962156790701e-17 relative error = 1.9604204806182887466607185869625e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.616 y2[1] (analytic) = 1.1838039199119922066094934379379 y2[1] (numeric) = 1.1836844220988065838840860961925 absolute error = 0.0001194978131856227254073417454 relative error = 0.010094392422227033800861401447851 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1838039199119922066094934379379 y1[1] (numeric) = 1.1838039199119922298454078856687 absolute error = 2.32359144477308e-17 relative error = 1.9628178329953690863850647296643e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1346.6MB, alloc=4.6MB, time=176.61 NO POLE NO POLE x[1] = 0.617 y2[1] (analytic) = 1.1843821029208193443458911678558 y2[1] (numeric) = 1.1842624010907208134274988821612 absolute error = 0.0001197018300985309183922856946 relative error = 0.010106690214528973000622873640075 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1843821029208193443458911678558 y1[1] (numeric) = 1.18438210292081936762147631003 absolute error = 2.32755851421742e-17 relative error = 1.9652091233710803099546317541808e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1350.4MB, alloc=4.6MB, time=177.09 NO POLE NO POLE x[1] = 0.618 y2[1] (analytic) = 1.1849611015474755931071202253905 y2[1] (numeric) = 1.1848411958450552283473708744875 absolute error = 0.000119905702420364759749350903 relative error = 0.010118956838648658795146867500589 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1849611015474755931071202253905 y1[1] (numeric) = 1.1849611015474756164223479481199 absolute error = 2.33152277227294e-17 relative error = 1.9675943532898554738620198157556e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.619 y2[1] (analytic) = 1.1855409152129623744868157956707 y2[1] (numeric) = 1.1854208057830151225421817400708 absolute error = 0.0001201094299472519446340555999 relative error = 0.010131192302686265108145122054645 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1855409152129623744868157956707 y1[1] (numeric) = 1.1855409152129623978416579454246 absolute error = 2.33548421497539e-17 relative error = 1.9699735243265389626668930971579e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1354.2MB, alloc=4.6MB, time=177.57 NO POLE NO POLE x[1] = 0.62 y2[1] (analytic) = 1.1861215433374660713160003456393 y2[1] (numeric) = 1.1860012303249906063528638373972 absolute error = 0.0001203130124754649631365082421 relative error = 0.01014339661489770623635092207683 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1861215433374660713160003456393 y1[1] (numeric) = 1.1861215433374660947104287292725 absolute error = 2.33944283836332e-17 relative error = 1.9723466380862453728923744836766e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1358.0MB, alloc=4.6MB, time=178.05 NO POLE NO POLE x[1] = 0.621 y2[1] (analytic) = 1.1867029853403586074766524752305 y2[1] (numeric) = 1.1865824688905571861726435747845 absolute error = 0.000120516449801421304008900446 relative error = 0.010155569783694101697384667282511 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1867029853403586074766524752305 y1[1] (numeric) = 1.1867029853403586309106388600117 absolute error = 2.34339863847812e-17 relative error = 1.9747136962042858569154403088850e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.622 y2[1] (analytic) = 1.1872852406401980285297346497202 y2[1] (numeric) = 1.1871645208984763448714866484498 absolute error = 0.0001207197417216836582480012704 relative error = 0.010167711817641240755665184415647 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1872852406401980285297346497202 y1[1] (numeric) = 1.1872852406401980520032507633601 absolute error = 2.34735161136399e-17 relative error = 1.9770747003460353592725976038554e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1361.8MB, alloc=4.6MB, time=178.53 NO POLE NO POLE x[1] = 0.623 y2[1] (analytic) = 1.1878683086547290831570991852689 y2[1] (numeric) = 1.1877473857666961230345667360021 absolute error = 0.0001209228880329601225324492668 relative error = 0.010179822725459046638277113176518 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1878683086547290831570991852689 y1[1] (numeric) = 1.1878683086547291066701167159484 absolute error = 2.35130175306795e-17 relative error = 1.9794296522068335529973951926105e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1365.6MB, alloc=4.6MB, time=179.02 NO POLE NO POLE x[1] = 0.624 y2[1] (analytic) = 1.1884521888008838054166910457999 y2[1] (numeric) = 1.1883310629123517010141764069405 absolute error = 0.0001211258885321044025146388594 relative error = 0.010191902516021040452657239825053 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1884521888008838054166910457999 y1[1] (numeric) = 1.1884521888008838289691816421985 absolute error = 2.35524905963986e-17 relative error = 1.9817785535118941196902476876576e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.625 y2[1] (analytic) = 1.1890368804947820978104651960589 y2[1] (numeric) = 1.1889155517517659817944981982947 absolute error = 0.0001213287430161160159669977642 relative error = 0.010203951198353804817915042816598 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1890368804947820978104651960589 y1[1] (numeric) = 1.1890368804947821214024004673831 absolute error = 2.35919352713242e-17 relative error = 1.9841214060161971161236447355505e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1369.4MB, alloc=4.6MB, time=179.51 NO POLE NO POLE x[1] = 0.626 y2[1] (analytic) = 1.189622383151732315164435442986 y2[1] (numeric) = 1.1895008517004501746686529906863 absolute error = 0.0001215314512821404957824522997 relative error = 0.010215968781636447221554955386678 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.189622383151732315164435442986 y1[1] (numeric) = 1.1896223831517323387957869589975 absolute error = 2.36313515160115e-17 relative error = 1.9864582115043644875594434807444e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop memory used=1373.3MB, alloc=4.6MB, time=180.03 NO POLE NO POLE x[1] = 0.627 y2[1] (analytic) = 1.1902086961862318493202708853993 y2[1] (numeric) = 1.1900869621731043797274420078101 absolute error = 0.0001217340131274695928288775892 relative error = 0.010227955275200063113319944210588 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1902086961862318493202708853993 y1[1] (numeric) = 1.1902086961862318729910101764437 absolute error = 2.36707392910444e-17 relative error = 1.9887889717905944050300213554098e-15 % Correct digits = 16 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.628 y2[1] (analytic) = 1.1907958190119677146378552804441 y2[1] (numeric) = 1.1906738825836181731591979506428 absolute error = 0.0001219364283495414786573298013 relative error = 0.010239910688527198747827953559696 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 1.1907958190119677146378552804441 y1[1] (numeric) = 1.1907958190119677383479538374791 absolute error = 2.37100985570350e-17 relative error = 1.9911136887185114642747074072286e-15 % Correct digits = 16 h = 0.001 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 1 ) = diff ( y1, x , 1) ; diff ( y1 , x , 1 ) = sin ( x ) ; Iterations = 528 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 24 Minutes 50 Seconds Optimized Time Remaining = 24 Minutes 47 Seconds Expected Total Time = 27 Minutes 47 Seconds Time to Timeout Unknown Percent Done = 10.8 % > quit memory used=1376.7MB, alloc=4.6MB, time=180.47