|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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_const_2D0, array_const_5, 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, 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, > array_const_2D0, > array_const_5, > #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, > 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 add CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre sub FULL - CONST $eq_no = 1 i = 1 > array_tmp2[1] := array_tmp1[1] - array_const_2D0[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 diff $eq_no = 2 i = 1 order_d = 5 > array_tmp4[1] := array_y2_higher[6,1]; > #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 add CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_y1[2]; > #emit pre sub FULL CONST $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 diff $eq_no = 2 i = 2 order_d = 5 > array_tmp4[2] := array_y2_higher[6,2]; > #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 add CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_y1[3]; > #emit pre sub FULL CONST $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 diff $eq_no = 2 i = 3 order_d = 5 > array_tmp4[3] := array_y2_higher[6,3]; > #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 add CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_y1[4]; > #emit pre sub FULL CONST $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 diff $eq_no = 2 i = 4 order_d = 5 > array_tmp4[4] := array_y2_higher[6,4]; > #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 add CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_y1[5]; > #emit pre sub FULL CONST $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 diff $eq_no = 2 i = 5 order_d = 5 > array_tmp4[5] := array_y2_higher[6,5]; > #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 NOT FULL - FULL add $eq_no = 1 > array_tmp1[kkk] := array_y1[kkk]; > #emit FULL - NOT FULL sub $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 diff $eq_no = 2 > array_tmp4[kkk] := array_y2_higher[6,kkk]; > #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_const_2D0, array_const_5, 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, 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_const_0D0[1] + array_y1[1]; array_tmp2[1] := array_tmp1[1] - array_const_2D0[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] := array_y2_higher[6, 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[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_y2_higher[6, 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[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] := array_y2_higher[6, 3]; 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[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] := array_y2_higher[6, 4]; 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[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] := array_y2_higher[6, 5]; 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[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_y2_higher[6, kkk]; 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 + sin(x)); > end; exact_soln_y1 := proc(x) return 2.0 + sin(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 > exact_soln_y2p := proc(x) > return(sin(x)); > end; exact_soln_y2p := proc(x) return sin(x) end proc > exact_soln_y2pp := proc(x) > return(cos(x)); > end; exact_soln_y2pp := proc(x) return cos(x) end proc > exact_soln_y2ppp := proc(x) > return(-sin(x)); > end; exact_soln_y2ppp := proc(x) return -sin(x) end proc > exact_soln_y2pppp := proc(x) > return(-cos(x)); > end; exact_soln_y2pppp := proc(x) return -cos(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_log10normmin, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_hmax, > glob_hmin, > glob_hmin_init, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_log10_abserr, > glob_log10_relerr, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_log10abserr, > glob_log10relerr, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_2D0, > array_const_5, > #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, > 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/mtest9_revpostode.ode#################"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.5;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"glob_subiter_method := 3;"); > 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 + sin(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,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return(sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return(cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"return(-sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"return(-cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > 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:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(6+ 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[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 <=6) 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 <=6) 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 <=6) 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 := 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_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_2D0[1] := 2.0; > array_const_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_5[1] := 5; > 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 := 0.5; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > glob_subiter_method := 3; > #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] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := true; > array_y2_set_initial[1,5] := true; > 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 := 5; > #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 := 5; > #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 := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,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 := 6; > 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 := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > 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 := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,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 := 5; > 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 := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 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 := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 5; > #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 := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 4; > #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 := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 6; > #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 := 6; > #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 := 5; > #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 := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 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) = y1 - 2.0;"); > omniout_str(INFO,"diff(y1,x,1) = diff(y2,x,5);"); > 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,"2012-12-15T01:27:39-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9_rev") > ; > logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 151 ") > ; > logitem_str(html_log_file,"mtest9_rev diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9_rev 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) = diff(y2,x,5);") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 7 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 7; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_log10normmin, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_hmax, glob_hmin, glob_hmin_init, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_log10_abserr, glob_log10_relerr, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_log10abserr, glob_log10relerr, glob_max_minutes, array_const_1, array_const_0D0, array_const_2D0, array_const_5, 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, 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/mtest9_revpostode.ode#################"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.5;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "glob_subiter_method := 3;"); 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 + sin(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, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return(cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "return(-sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "return(-cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; 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 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 7, 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[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 <= 6 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 <= 6 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 <= 6 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 := 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_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.5; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; 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] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := true; array_y2_set_initial[1, 5] := true; 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 := 5; 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 := 5; 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 := 5; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; 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 := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; 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 := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; 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 := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 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 := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 5; 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 := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 4; 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 := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 6; 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 := 6; 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 := 5; 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 := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 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) = y1 - 2.0;"); omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"); 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, "2012-12-15T01:27:39-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9_rev"); logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 151 "); logitem_str(html_log_file, "mtest9_rev diffeq.mxt"); logitem_str(html_log_file, "mtest9_rev 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) = diff(y2,x,5);"); 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/mtest9_revpostode.ode################# diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; #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 + sin(x)); end; exact_soln_y2 := proc(x) return(2.0 - cos(x)); end; exact_soln_y2p := proc(x) return(sin(x)); end; exact_soln_y2pp := proc(x) return(cos(x)); end; exact_soln_y2ppp := proc(x) return(-sin(x)); end; exact_soln_y2pppp := proc(x) return(-cos(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 9.5 estimated_steps = 9500 step_error = 1.0526315789473684210526315789474e-14 est_needed_step_err = 1.0526315789473684210526315789474e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_value3 = 0 value3 = 0 best_h = 0.001 START of Soultion x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.0MB, time=0.48 NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228973023595716096962371645635 absolute error = 3.9964315912251e-18 relative error = 3.5590357041799818917528935659069e-16 % Correct digits = 17 h = 0.001 y1[1] (analytic) = 2.4803028813070802939494724420977 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008773427028772936761845068821 relative error = 0.035372401874360924089566086208289 % Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.502 y2[1] (analytic) = 1.1233780437121404920409717621522 y2[1] (numeric) = 1.1233780437121403641161663103213 absolute error = 1.279248054518309e-16 relative error = 1.1387511636698049527321551304247e-14 % Correct digits = 15 h = 0.001 y1[1] (analytic) = 2.4811797437071163057841377482187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0017542051029133055108498130031 relative error = 0.070700444309300938093178385518425 % Correct digits = 3 h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=1.12 NO POLE NO POLE x[1] = 0.503 y2[1] (analytic) = 1.1238596616865926064215271335312 y2[1] (numeric) = 1.1238596616865916346964672953222 absolute error = 9.717250598382090e-16 relative error = 8.6463202921610960949418515093497e-14 % Correct digits = 15 h = 0.001 y1[1] (analytic) = 2.4820561249274487088131362528522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0026305863232457085398483176366 relative error = 0.10598415953719021627869493626097 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.504 y2[1] (analytic) = 1.1243421558013100225170503558855 y2[1] (numeric) = 1.1243421558013059264282111875027 absolute error = 4.0960888391683828e-15 relative error = 3.6430981601407017699748432374480e-13 % Correct digits = 14 h = 0.001 y1[1] (analytic) = 2.4829320240916963557358308536409 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035064854874933554625429184253 relative error = 0.14122357976256294749295818319025 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.505 y2[1] (analytic) = 1.1248255255737986658179668865485 y2[1] (numeric) = 1.124825525573786161740578682083 absolute error = 1.25040773882044655e-14 relative error = 1.1116459489862533014706793539627e-12 % Correct digits = 13 h = 0.001 y1[1] (analytic) = 2.4838074403239601552961692154743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0043819017197571550228812802587 relative error = 0.17641873716207358683165415092659 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=1.75 NO POLE NO POLE x[1] = 0.506 y2[1] (analytic) = 1.1253097705206888041164464559634 y2[1] (numeric) = 1.1253097705206576805008601015673 absolute error = 3.11236155863543961e-14 relative error = 2.7657820452365999314295612731972e-12 % Correct digits = 13 h = 0.001 y1[1] (analytic) = 2.4846823727488239481817020349524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0052568341446209479084140997368 relative error = 0.2115696638844533806737925932691 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.507 y2[1] (analytic) = 1.1257948901577355308760949947039 y2[1] (numeric) = 1.1257948901576682400144553957437 absolute error = 6.72908616395989602e-14 relative error = 5.9771866285670219323854670962975e-12 % Correct digits = 13 h = 0.001 y1[1] (analytic) = 2.4855568204913553824396694014904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0061312818871523821663814662748 relative error = 0.24667639205046716400687694163286 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=2.38 NO POLE NO POLE x[1] = 0.508 y2[1] (analytic) = 1.1262808839998192494768208161278 y2[1] (numeric) = 1.1262808839996880150248741416841 absolute error = 1.312344519466744437e-13 relative error = 1.1652018054378653982694624370328e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 2.4864307826771067884092798390526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.007005244072903788135991903837 relative error = 0.28173895375287042897210788637658 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.509 y2[1] (analytic) = 1.126767751560946158334390809836 y2[1] (numeric) = 1.1267677515607095977137355437444 absolute error = 2.365606206552660916e-13 relative error = 2.0994621147752175134343597888834e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 2.4873042584321160531693070963062 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0078787198279130528960191610906 relative error = 0.31675738105636666356223183993781 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=3.02 NO POLE NO POLE x[1] = 0.51 y2[1] (analytic) = 1.1272554923542487368941915264245 y2[1] (numeric) = 1.1272554923538479977007684335643 absolute error = 4.007391934230928602e-13 relative error = 3.5549988103065944200239348593181e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 2.4881772468829074945001302376746 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008751708278704494226842302459 relative error = 0.35173170599756495940790535457244 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.511 y2[1] (analytic) = 1.1277441058919862324987091598053 y2[1] (numeric) = 1.1277441058913406420438112700674 absolute error = 6.455904548978897379e-13 relative error = 5.7246183023697709038133538255325e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 2.4890497471564927343593430733201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0096242085522897340860551381045 relative error = 0.38666196058493788759169880261458 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.512 y2[1] (analytic) = 1.1282335916855451481282415596589 y2[1] (numeric) = 1.1282335916845473752388121394612 absolute error = 9.977728894294201977e-13 relative error = 8.8436729484253273713900937808655e-11 % Correct digits = 12 h = 0.001 y1[1] (analytic) = 2.4899217583803715718700594525215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0104962197761685715967715173059 relative error = 0.42154817679877964143210727811901 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=3.66 NO POLE NO POLE x[1] = 0.513 y2[1] (analytic) = 1.1287239492454397310143545333464 y2[1] (numeric) = 1.1287239492439504592198287552371 absolute error = 1.4892717945257781093e-12 relative error = 1.3194296050166803556963687023898e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4907932796825328558210414322121 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0113677410783298555477534969965 relative error = 0.45639038659116444518317374841848 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.514 y2[1] (analytic) = 1.1292151780813124621255938238659 y2[1] (numeric) = 1.1292151780791545733590284581703 absolute error = 2.1578887665653656956e-12 relative error = 1.9109633030543453821668290298872e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4916643101914553566777778206244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0122387715872523564044898854088 relative error = 0.4911886218859052275985589770279 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=4.29 NO POLE NO POLE x[1] = 0.515 y2[1] (analytic) = 1.1297072777019345465249632781811 y2[1] (numeric) = 1.12970727769888681446668821632 absolute error = 3.0477320582750618611e-12 relative error = 2.6978068730112092719404051664209e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4925348490361086381036410850348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0131093104319056378303531498192 relative error = 0.5259429145785125593121146588246 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.516 y2[1] (analytic) = 1.1302002476152064045986788484863 y2[1] (numeric) = 1.1302002476109966967911946250292 absolute error = 4.2097078074842234571e-12 relative error = 3.7247450762526124546953832005182e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4934048953459539279902511025232 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0139793567417509277169631673076 relative error = 0.5606532965361538529902305589296 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=4.3MB, time=4.93 x[1] = 0.517 y2[1] (analytic) = 1.1306940873281581641557071976931 y2[1] (numeric) = 1.1306940873224561520190439069248 absolute error = 5.7020121366632907683e-12 relative error = 5.0429308869361866809505202241791e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4942744482509449889961747234587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0148489096467419887228867882431 relative error = 0.59531979959761282521443323237872 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.518 y2[1] (analytic) = 1.1311887963469501533975968096429 y2[1] (numeric) = 1.1311887963393595292748419119177 absolute error = 7.5906241227548977252e-12 relative error = 6.7103070214874685469833382583942e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4951435068815289885930906090811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0157179682773259883198026738655 relative error = 0.62994245557324921905591312628167 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.519 y2[1] (analytic) = 1.1316843741768733947581086342535 y2[1] (numeric) = 1.1316843741669235951213041172024 absolute error = 9.9497996368045170511e-12 relative error = 8.7920270561670239858508448512629e-10 % Correct digits = 11 h = 0.001 y1[1] (analytic) = 2.4960120703686473686185492970897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0165865317644443683452613618741 relative error = 0.6645212962449587863068485349416 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=5.57 NO POLE NO POLE x[1] = 0.52 y2[1] (analytic) = 1.1321808203223500996121524280115 y2[1] (numeric) = 1.1321808203094875335592556272576 absolute error = 1.28625660528968007539e-11 relative error = 1.1360876126866926788887946083009e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.4968801378437367143344589425478 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0174545992395337140611710073322 relative error = 0.69905635336613352833657899470403 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.521 y2[1] (analytic) = 1.1326781342869341638535340809147 y2[1] (numeric) = 1.1326781342705129460276311738457 absolute error = 1.64212178259029070690e-11 relative error = 1.4497691205313780838993891625955e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.4977477084387296229904276756926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.018322169834526622717139740477 relative error = 0.73354765866162219454385727487693 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=6.21 NO POLE NO POLE x[1] = 0.522 y2[1] (analytic) = 1.1331763155733116643410183521593 y2[1] (numeric) = 1.133176315552583851403475116013 absolute error = 2.07278129375432361463e-11 relative error = 1.8291780945894853766377648320273e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.4986147812860555718910940133795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0191892426818525716178060781639 relative error = 0.76799524382769103737957814754559 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.523 y2[1] (analytic) = 1.133675363683301356212210568549 y2[1] (numeric) = 1.1336753636574066860019414400897 absolute error = 2.58946702102691284593e-11 relative error = 2.2841345097363297270984737912638e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.4994813555186417859665772569024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0200558169144387856932893216868 relative error = 0.80239914053198482291754360789496 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.524 y2[1] (analytic) = 1.134175278117855171064759971788 y2[1] (numeric) = 1.13417527808581030357629375969 absolute error = 3.20448674884662120980e-11 relative error = 2.8253893473717864488146139728092e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.5003474302699141048451803058119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0209218916657111045718923705963 relative error = 0.83675938041348809595397817241225 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=6.85 NO POLE NO POLE x[1] = 0.525 y2[1] (analytic) = 1.1346760583770587160043865334936 y2[1] (numeric) = 1.1346760583377459753179053157118 absolute error = 3.93127406864812177818e-11 relative error = 3.4646664478591995601679747345454e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.5012130046737978494274778151016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.021787466069594849154189879886 relative error = 0.87107599508248669861965431007077 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.526 y2[1] (analytic) = 1.135177703960131773559232189945 y2[1] (numeric) = 1.1351777039122873898562589763369 absolute error = 4.78443837029732136081e-11 relative error = 4.2147043177526627557257281746367e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.5020780778647186879609231217462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0226525392605156876876351865306 relative error = 0.90534901612052954149162696626603 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=7.50 NO POLE NO POLE x[1] = 0.527 y2[1] (analytic) = 1.1356802143654288024600365822581 y2[1] (numeric) = 1.1356802143076306532589472370312 absolute error = 5.77981492010893452269e-11 relative error = 5.0892978912540590312042186574573e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.5029426489776035016141078660558 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0235171103734005013408199308402 relative error = 0.9395784750803906261947075261474 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.528 y2[1] (analytic) = 1.1361835890904394392856365218521 y2[1] (numeric) = 1.1361835890210942890316722205442 absolute error = 6.93451502539643013079e-11 relative error = 6.1033402453451978712143861671488e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.5038067171478812495498087336605 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0243811785436782492765207984449 relative error = 0.97376440348603131848593143841097 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=8.15 NO POLE NO POLE x[1] = 0.529 y2[1] (analytic) = 1.1366878276317890009732875357502 y2[1] (numeric) = 1.1366878275491192381182456769095 absolute error = 8.26697628550418588407e-11 relative error = 7.2728642680443433955661990116202e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.504670281511483833495956245149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0252447429072808332226683099334 relative error = 1.0079068328325628708183900876048 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.53 y2[1] (analytic) = 1.1371929294852389881933049814358 y2[1] (numeric) = 1.1371929293872688589005889834444 absolute error = 9.79701292927159979914e-11 relative error = 8.6150842792403829836699138019396e-09 % Correct digits = 10 h = 0.001 y1[1] (analytic) = 2.5055333412048469618136610224661 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0261078026006439615403730872505 relative error = 1.042005794586209193383906368475 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.531 y2[1] (analytic) = 1.1376988941456875895875213566629 y2[1] (numeric) = 1.1376988940302289271987331447503 absolute error = 1.154586623887882119126e-10 relative error = 1.0148437603561843472019507283895e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5063958953649110130614334641129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0269703567607080127881455288973 relative error = 1.0760613201842698726371347848636 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=8.79 NO POLE NO POLE x[1] = 0.532 y2[1] (analytic) = 1.138205721107170186871055565808 y2[1] (numeric) = 1.1382057209718076362708187927123 absolute error = 1.353625506002367730957e-10 relative error = 1.1892626094741920866350061657138e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5072579431291218990547332650042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0278324045249188987814453297886 relative error = 1.1100734410350834363067607743614 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.533 y2[1] (analytic) = 1.1387134098628598607968890410339 y2[1] (numeric) = 1.1387134097049355968130961864994 absolute error = 1.579242639837928545345e-10 relative error = 1.3868657610944649443247738245995e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5081194836354319274199857215036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.028693945031228927146697786288 relative error = 1.1440421885179908639025603534242 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.3MB, time=9.44 NO POLE NO POLE x[1] = 0.534 y2[1] (analytic) = 1.1392219599050678979827427537335 y2[1] (numeric) = 1.1392219597216658369599252125646 absolute error = 1.834020610228175411689e-10 relative error = 1.6098887440521296957581391040888e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.508980516022300663642202267693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0295549774180976633689143324774 relative error = 1.1779675939832993417301600923899 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.535 y2[1] (analytic) = 1.1397313707252442985997482894172 y2[1] (numeric) = 1.1397313705131738022837753846447 absolute error = 2.120704963159729047725e-10 relative error = 1.8607059677670034240010904963685e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5098410394286957926053431953273 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0304155008244927923320552601117 relative error = 1.211849688752246261428408871237 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.536 memory used=61.0MB, alloc=4.3MB, time=10.09 y2[1] (analytic) = 1.1402416418139782849224052974161 y2[1] (numeric) = 1.1402416415697573557952258437604 absolute error = 2.442209291271794536557e-10 relative error = 2.1418348547475889585605201294029e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5107010529940939796245610171836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.031275514389890979351273081968 relative error = 1.2456885041169634610473368412739 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.537 y2[1] (analytic) = 1.1407527726609988107393167654858 y2[1] (numeric) = 1.1407527723808367779429653582163 absolute error = 2.801620327963514072695e-10 relative error = 2.4559399679811960821711452251050e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.511560555858481730969463441633 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0321350172542787306961755064174 relative error = 1.2794840713404417076877335311725 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.538 y2[1] (analytic) = 1.1412647627551750716241927086173 y2[1] (numeric) = 1.1412647624349547666137923236009 absolute error = 3.202203050104003850164e-10 relative error = 2.8058371331586820623881426203049e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5124195471623562538775354352446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.032994008558153253604247500029 relative error = 1.3132364216564954207264260941613 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.3MB, time=10.74 NO POLE NO POLE x[1] = 0.539 y2[1] (analytic) = 1.1417776115845170160666120010952 y2[1] (numeric) = 1.1417776112197764371326147627865 absolute error = 3.647405789339972383087e-10 relative error = 3.1944975556827013347411501295589e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5132780260467263160568603600697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0338524874425233157835724248541 relative error = 1.346945586269727634654380302806 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.54 y2[1] (analytic) = 1.1422913186361758574620312210822 y2[1] (numeric) = 1.1422913182220893222624503259293 absolute error = 4.140865351995808951529e-10 relative error = 3.6250519324087504183275863412490e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5141359916531131046772806829582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0347104530489101044039927477426 relative error = 1.3806115963554952005577810653469 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.3MB, time=11.39 NO POLE NO POLE x[1] = 0.541 y2[1] (analytic) = 1.1428058833964445869605285177651 y2[1] (numeric) = 1.1428058829278033722044262904695 absolute error = 4.686412147561022272956e-10 relative error = 4.1007945580686903658269625567168e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.514993443123551084849139265818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0355679045193480845758513306024 relative error = 1.414234483059874225275275969045 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.542 y2[1] (analytic) = 1.1433213053507584871737696523608 y2[1] (numeric) = 1.1433213048219509545977795611311 absolute error = 5.288075325759900912297e-10 relative error = 4.6251874263268252206176299731652e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5158503796005888575887427581458 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0364248409963858573154548229302 relative error = 1.4478142774996257472675846581109 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.543 y2[1] (analytic) = 1.1438375839836956467396825060591 y2[1] (numeric) = 1.1438375833886868545198566699219 absolute error = 5.950087922198258361372e-10 relative error = 5.2018643254190110568581165927099e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.51670680022729001726968912644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0372812616230870169964011912244 relative error = 1.4813510107621616482386887333922 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.3MB, time=12.03 NO POLE NO POLE x[1] = 0.544 y2[1] (analytic) = 1.1443547187789774757443254902696 y2[1] (numeric) = 1.1443547181112882744861137761337 absolute error = 6.676892012582117141359e-10 relative error = 5.8346349283256661969756470778293e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5175627041472340085592018692383 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0381371655430310082859139340227 relative error = 1.5148447139055107995508213241878 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.545 y2[1] (analytic) = 1.1448727092194692220004344373497 y2[1] (numeric) = 1.1448727084721548344501166663422 absolute error = 7.473143875503177710075e-10 relative error = 6.5274888774299491180630107260169e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5184180905045169828386139815162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0389925519003139825653260463006 relative error = 1.548295417958285442478472536587 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.3MB, time=12.67 NO POLE NO POLE x[1] = 0.546 y2[1] (analytic) = 1.1453915547871804881821316933069 y2[1] (numeric) = 1.1453915539528085718035407544069 absolute error = 8.343719163785909389000e-10 relative error = 7.2845998636127663572328145765780e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5192729584437526541071452480364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0398474198395496538338573128208 relative error = 1.5817031539196478013496166344112 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.547 y2[1] (analytic) = 1.1459112549632657498152802778119 y2[1] (numeric) = 1.1459112540338939413761710814713 absolute error = 9.293718084391091963406e-10 relative error = 8.1103296997366683894528023985370e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5201273071100731543681169619403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0407017685058701540948290267247 relative error = 1.6150679527592769286253490645899 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=80.1MB, alloc=4.3MB, time=13.32 x[1] = 0.548 y2[1] (analytic) = 1.1464318092280248741229651212096 y2[1] (numeric) = 1.1464318081951778154359023159626 absolute error = 1.0328470586870628052470e-09 relative error = 9.0092323884710869629615624089630e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5209811356491298884967486824406 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041555597044926888223460747225 relative error = 1.6483898454173357809720963064167 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.549 y2[1] (analytic) = 1.1469532170609036397255825330915 y2[1] (numeric) = 1.146953215915549483688738753592 absolute error = 1.1453541560368437794995e-09 relative error = 9.9860581844117627206174715170316e-08 % Correct digits = 9 h = 0.001 y1[1] (analytic) = 2.5218344432070943885886821638876 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.042408904602891388315394228672 relative error = 1.6816688628044385253835290098796 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.55 y2[1] (analytic) = 1.1474754779404942571950182023822 y2[1] (numeric) = 1.1474754766730206532787943173546 absolute error = 1.2674736039162238850276e-09 relative error = 1.1045757650447607093970242858435e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5226872289306591677883781077573 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0432616903264561675150901725417 relative error = 1.7149050358016180744122689999509 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.3MB, time=13.95 NO POLE NO POLE x[1] = 0.551 y2[1] (analytic) = 1.1479985913445358904623931748063 y2[1] (numeric) = 1.1479985899447254487882925575294 absolute error = 1.3998104416741006172769e-09 relative error = 1.2193485708328637414163453383014e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5235394919670385735965319092362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0441139533628355733232439740206 relative error = 1.7480983952602938495744334681979 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.552 y2[1] (analytic) = 1.1485225567499151790788564000321 y2[1] (numeric) = 1.1485225552069204122375666516792 absolute error = 1.5429947668412897483529e-09 relative error = 1.3434605683389018923731526529230e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5243912314639696406556550910571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0449656928597666403823671558415 relative error = 1.7812489720022397719930050577058 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.3MB, time=14.59 NO POLE NO POLE x[1] = 0.553 y2[1] (analytic) = 1.1490473736326667613289015877443 y2[1] (numeric) = 1.1490473719349845030850594046507 absolute error = 1.6976822582438421830936e-09 relative error = 1.4774693343379641879876018897131e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.525242446569712943012969639076 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0458169079655099427396817038604 relative error = 1.8143567968195524793489545796575 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.554 y2[1] (analytic) = 1.1495730414679737981956852593716 y2[1] (numeric) = 1.1495730396034190982273232485745 absolute error = 1.8645546999683620107971e-09 relative error = 1.6219540931365056196833440053716e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5260931364330534458597629767672 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0466675978288504455864750415516 relative error = 1.8474219004746197682119737872459 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.555 y2[1] (analytic) = 1.150099559730168498177822030195 y2[1] (numeric) = 1.1500995576858479919990202428652 absolute error = 2.0443205061788017873298e-09 relative error = 1.7775161192639980066629485464989e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5269433002033013567463518393519 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0475177615990983564730639041363 relative error = 1.8804443137000892608255989824759 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.3MB, time=15.23 NO POLE NO POLE x[1] = 0.556 y2[1] (analytic) = 1.1506269278927326429571323050854 y2[1] (numeric) = 1.150626925655017396172922074221 absolute error = 2.2377152467842102308644e-09 relative error = 1.9447791395620992708049404567576e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5277929370302929762718038326678 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0483673984260899759985158974522 relative error = 1.9134240671988372954244222515677 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.557 y2[1] (analytic) = 1.1511551454282981139168167201663 y2[1] (numeric) = 1.1511551429827959399599100566243 absolute error = 2.4455021739569066635420e-09 relative error = 2.1243897346669414807331658596099e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5286420460643915482475659871291 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0492165074601885479742780519135 relative error = 1.946361191643938039163995822631 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.3MB, time=15.86 NO POLE NO POLE x[1] = 0.558 y2[1] (analytic) = 1.1516842118086474195095308122717 y2[1] (numeric) = 1.1516842091401746700089751313412 absolute error = 2.6684727495005556809305e-09 relative error = 2.3170177398801773315433507323963e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5294906264564881093341501432183 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0500650878522851090608622080027 relative error = 1.9792557176786328227469364228357 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.559 y2[1] (analytic) = 1.1522141265047142234748325481675 y2[1] (numeric) = 1.1522141235972670504072178669217 absolute error = 2.9074471730676146812458e-09 relative error = 2.5233566454244640040112937125557e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.530338677358002338150025531897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0509131387537993378767375966814 relative error = 2.0121076759162996958316305894297 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.3MB, time=16.50 NO POLE NO POLE x[1] = 0.56 y2[1] (analytic) = 1.1527448889865838739054744961337 y2[1] (numeric) = 1.1527448858233089626798484591997 absolute error = 3.1632749112256260369340e-09 relative error = 2.7441239960791025901346767538929e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.531186197920883403851869441112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0517606593166804035785815058964 relative error = 2.0449170969404232023128286671607 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.561 y2[1] (analytic) = 1.153276498723493933162011573659 y2[1] (numeric) = 1.1532764952866587057901867312931 absolute error = 3.4368352273718248423659e-09 relative error = 2.9800617901915904790373703432270e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5320331872976108141853273882178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0526076486934078139120394530022 relative error = 2.0776840113045643745662947124054 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.562 y2[1] (analytic) = 1.1538089551838347086351944566842 y2[1] (numeric) = 1.1538089514547969961396621336035 absolute error = 3.7290377124955323230807e-09 relative error = 3.2319368780608832670873468208395e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5328796446411952630054347476258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0534541060369922627321468124102 relative error = 2.1104084495323309457525517291988 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.3MB, time=17.16 NO POLE NO POLE x[1] = 0.563 y2[1] (analytic) = 1.1543422578351497843556178880455 y2[1] (numeric) = 1.1543422537943269675678137438164 absolute error = 4.0408228167878041442291e-09 relative error = 3.5005413596882018870401421693270e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5337255691051794772658523133289 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0543000305009764769925643781133 relative error = 2.143090442117347779277626592704 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.564 y2[1] (analytic) = 1.1548764061441365534500922755128 y2[1] (numeric) = 1.1548764017709741713522902669013 absolute error = 4.3731623820978020086115e-09 relative error = 3.7866929818912597416316436021516e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5345709598436390634760688071373 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0551454212394360632027808719217 relative error = 2.1757300195232275145115566796189 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.3MB, time=17.81 NO POLE NO POLE x[1] = 0.565 y2[1] (analytic) = 1.1554113995766467514442061230971 y2[1] (numeric) = 1.1554113948495865762088500351116 absolute error = 4.7270601752353560879855e-09 relative error = 4.0912355347778236758271489018801e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5354158160111833536257238754924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0559902774069803533524359402768 relative error = 2.2083272121835414278682706306582 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.566 y2[1] (analytic) = 1.1559472375976869904105459931083 y2[1] (numeric) = 1.1559472324941345682913610079844 absolute error = 5.1035524221191849851239e-09 relative error = 4.4150392475745616274150225663225e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5362601367629562505752056506075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0568345981587532503019177153919 relative error = 2.2408820505017905083532988261491 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=110.6MB, alloc=4.3MB, time=18.45 x[1] = 0.567 y2[1] (analytic) = 1.1564839196714192939620398507875 y2[1] (numeric) = 1.1564839141677109511918007723409 absolute error = 5.5037083427702390784466e-09 relative error = 4.7590011838071687563606138794095e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5371039212546370729116774854067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0576783826504340726383895501911 relative error = 2.2733945648513767466886050699314 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.568 y2[1] (analytic) = 1.157021445261161633089888798216 y2[1] (numeric) = 1.157021439332530945940256542286 absolute error = 5.9286306871496322559300e-09 relative error = 5.1240456358278027678649408422451e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5379471686424413992696890063077 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0585216300382383989964010710921 relative error = 2.3058647855755746371266596580326 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.569 y2[1] (analytic) = 1.1575598138293884628455513596132 y2[1] (numeric) = 1.1575598074499321910049251592086 absolute error = 6.3794562718406262004046e-09 relative error = 5.5111245186858980109577058700382e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5387898780831219121155271633056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.05936433947891891184223922809 relative error = 2.3382927429875028910686954649239 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.3MB, time=19.10 NO POLE NO POLE x[1] = 0.57 y2[1] (analytic) = 1.158099024837731259866243636084 y2[1] (numeric) = 1.1580990179803747422921130917814 absolute error = 6.8573565175741305443026e-09 relative error = 5.9212177633384667522858433901231e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5396320487339692409944634930788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0602065101297662407211755578632 relative error = 2.3706784673700963616049029207394 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.571 y2[1] (analytic) = 1.158639077746979060743417804361 y2[1] (numeric) = 1.1586390703834410731462364359611 absolute error = 7.3635379875971813683999e-09 relative error = 6.3553337091960347921129750944765e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.540473679752812805240054347939 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0610481411486098049667664127234 relative error = 2.4030219889760781780971267856779 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.3MB, time=19.74 NO POLE NO POLE x[1] = 0.572 y2[1] (analytic) = 1.1591799720170790012336805911064 y2[1] (numeric) = 1.1591799641178360743498209149881 absolute error = 7.8992429268838596761183e-09 relative error = 6.8145094960003973050262303111130e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5413147702980216561446513813949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0618892316938186558713634461793 relative error = 2.4353233380279320899274274619847 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.573 y2[1] (analytic) = 1.1597217071071368563116125119018 y2[1] (numeric) = 1.1597216986413870541235018793869 absolute error = 8.4657498021881106325149e-09 relative error = 7.2998114550304194500650515907324e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5421553195285053185902801198912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0627297809243023183169921846756 relative error = 2.467582544717875018538662228083 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.574 y2[1] (analytic) = 1.1602642824754175810639478221502 y2[1] (numeric) = 1.1602642734110437381260243069658 absolute error = 9.0643738429379235151844e-09 relative error = 7.8123354996321449025604646161770e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5429953266037146321390449899122 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0635697879995116318657570546966 relative error = 2.4997996392078298168960272420956 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.3MB, time=20.36 NO POLE NO POLE x[1] = 0.575 y2[1] (analytic) = 1.1608076975793458524245742857562 y2[1] (numeric) = 1.1608076878828782694542428028169 absolute error = 9.6964675829703314829393e-09 relative error = 8.3532075150695140115374273326135e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5438347906836425915822197101162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0644092520794395913089317749006 relative error = 2.5319746516293982355012794525378 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.576 y2[1] (analytic) = 1.1613519518755066117498110266296 y2[1] (numeric) = 1.1613519415120852086431215993162 absolute error = 1.03634214031066894273134e-08 relative error = 8.9235837476920317807309290798064e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5446737109288251869471824994803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0652481723246221866738945642647 relative error = 2.5641076120838340940941286808358 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.3MB, time=21.00 NO POLE NO POLE x[1] = 0.577 y2[1] (analytic) = 1.1618970448196456082334218877795 y2[1] (numeric) = 1.1618970337529815336657345561237 absolute error = 1.10666640745676873316558e-08 relative error = 9.5246511934157643067532825274992e-07 % Correct digits = 8 h = 0.001 y1[1] (analytic) = 2.5455120865003422429613560945909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0660865478961392426880681593753 relative error = 2.5961985506420166581780541127425 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.578 y2[1] (analytic) = 1.162442975866669943160820883031 y2[1] (numeric) = 1.1624429640590066399332651601833 absolute error = 1.18076633032275557228477e-08 relative error = 1.0157627985514080683393048305269e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.546349916559818257972313112208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0669243779556152576990251769924 relative error = 2.628247497344424219510556262531 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.3MB, time=21.65 NO POLE NO POLE x[1] = 0.579 y2[1] (analytic) = 1.1629897444706486150019254872046 y2[1] (numeric) = 1.1629897318827223402950065257226 absolute error = 1.25879262747069189614820e-08 relative error = 1.0823763781714595695101866858895e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5471872002694232423232078370701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0677616616652202420499199018545 relative error = 2.6602544822011078797006051644972 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.58 y2[1] (analytic) = 1.16353735008481306534211267195 y2[1] (numeric) = 1.1635373366758128650383613942532 absolute error = 1.34090002003037512776968e-08 relative error = 1.1524340150598806874123405494702e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5480239367918735561826960595765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0685983981876705559094081243609 relative error = 2.6922195351916655360587881093964 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.581 y2[1] (analytic) = 1.1640857921615577256507317563242 y2[1] (numeric) = 1.1640857778890848618888421345706 absolute error = 1.42724728637618896217536e-08 relative error = 1.2260670957300957683143062698452e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.548860125290432746828505133497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0694345866862297465552171982814 relative error = 2.724142686265216068848395688654 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.3MB, time=22.29 NO POLE NO POLE x[1] = 0.582 y2[1] (analytic) = 1.1646350701524405648866273036464 y2[1] (numeric) = 1.1646350549724673960100707427541 absolute error = 1.51799731688765565608923e-08 relative error = 1.3034102748502696707493281464582e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5496957649289123853838169702094 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0702702263247093851105290349938 relative error = 2.7560239653403737290884132455654 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.583 y2[1] (analytic) = 1.165185183508183637940124459152 y2[1] (numeric) = 1.1651851673750119500037788421669 absolute error = 1.61331716879363456169851e-08 relative error = 1.3846015136720140796566093225912e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5505308548716729030056272331506 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.071105316267469902732339297935 relative error = 2.7878634023052227260621060694901 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.3MB, time=22.94 NO POLE NO POLE x[1] = 0.584 y2[1] (analytic) = 1.1657361316786736349109282865074 y2[1] (numeric) = 1.1657361145448924239098076834562 absolute error = 1.71337812110011206030512e-08 relative error = 1.4697821183879988081896832965331e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5513653942836244265242445441924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0719398556794214262509566089768 relative error = 2.8196610270172920136876008158076 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.585 y2[1] (analytic) = 1.1662879141129624312213878253303 y2[1] (numeric) = 1.166287895929405135206108144553 absolute error = 1.81835572960152796807773e-08 relative error = 1.5590967784181364718130688992125e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5521993823302276135330940625129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0727738437260246132598061272973 relative error = 2.8514168693035302749095727003818 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=141.1MB, alloc=4.3MB, time=23.58 x[1] = 0.586 y2[1] (analytic) = 1.1668405302592676385645747564984 y2[1] (numeric) = 1.1668405109749688188087407306722 absolute error = 1.92842988197558340258262e-08 relative error = 1.6526936046240127041533064151578e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.553032818177494486927990346228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0736072795732914866547024110124 relative error = 2.8831309589602811032738480119188 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.587 y2[1] (analytic) = 1.1673939795649731566866257272142 y2[1] (numeric) = 1.1673939591271246270718755743125 absolute error = 2.04378485296147501529017e-08 relative error = 1.7507241674512378617619025894479e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5538657009919892688950449575815 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0744401623877862686217570223659 relative error = 2.9148033257532583808494244187152 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.588 y2[1] (analytic) = 1.1679482614766297260027965535271 y2[1] (numeric) = 1.1679482398305361297877924352566 absolute error = 2.16460935962150041182705e-08 relative error = 1.8533435349993999353634309869858e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5546980299408292143463748238537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0752724913366262140730868886381 relative error = 2.9464339994175218516650974269552 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.3MB, time=24.21 NO POLE NO POLE x[1] = 0.589 y2[1] (analytic) = 1.1685033754399554810466756843086 y2[1] (numeric) = 1.168503352528989314186880700571 absolute error = 2.29109661668597949837376e-08 relative error = 1.9607103110193021481825722819279e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5555298041916854438027779183523 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0761042655874824435294899831367 relative error = 2.9780230096574528898305601861543 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.59 y2[1] (analytic) = 1.1690593208998365047520034775093 y2[1] (numeric) = 1.1690592966653925849376393846061 absolute error = 2.42344439198143640929032e-08 relative error = 2.0729866728371724774471100147809e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5563610229127837757225433788758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0769354843085807754492554436602 relative error = 3.0095703861467304615145156424937 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.3MB, time=24.85 NO POLE NO POLE x[1] = 0.591 y2[1] (analytic) = 1.1696160973003273835665430069271 y2[1] (numeric) = 1.1696160716817767641466771289963 absolute error = 2.56185506194198658779308e-08 relative error = 2.1903384092055360830341558906666e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5571916852729055582755637349123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0777661466687025580022757996967 relative error = 3.0410761585283072799550048232859 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.592 y2[1] (analytic) = 1.1701737040846517633974472856612 y2[1] (numeric) = 1.1701736770192950913587122026597 absolute error = 2.70653566720387350830015e-08 relative error = 2.3129349580804453673444019579756e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5580217904413885005619174695279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0785962518371855002886295343123 relative error = 3.0725403564143861526798128044012 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.593 y2[1] (analytic) = 1.1707321406952029063875669609314 y2[1] (numeric) = 1.1707321121182232235565725017985 absolute error = 2.85769796828309944591329e-08 relative error = 2.4409494443247661227388837431058e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5588513375881275032740906974331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0794257989839245030008027622175 relative error = 3.103963009386396520117464677924 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.3MB, time=25.49 NO POLE NO POLE x[1] = 0.594 y2[1] (analytic) = 1.1712914065735442485221417040005 y2[1] (numeric) = 1.1712913764179592351611955498985 absolute error = 3.01555850133609461541020e-08 relative error = 2.5745587173372219471393389530249e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.559680325883575488802007297074 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0802547872793724885287193618584 relative error = 3.1353441469949711847819676087763 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.595 y2[1] (analytic) = 1.1718515011604099580653176885558 y2[1] (numeric) = 1.1718514693570236180316284977296 absolute error = 3.18033863400336891908262e-08 relative error = 2.7139433886069028245623593994840e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5605087544987442307800373917875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0810832158945412305067494565719 relative error = 3.1666837987599232302170918568458 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.3MB, time=26.12 NO POLE NO POLE x[1] = 0.596 y2[1] (analytic) = 1.172412423895705494825932721079 y2[1] (numeric) = 1.1724123903730592814650281233456 absolute error = 3.35226462133609045977334e-08 relative error = 2.8592878691929474753169552436195e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5613366226052051830751546330814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0819110840010021828018666978658 relative error = 3.1979819941702231288886134550952 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.597 y2[1] (analytic) = 1.1729741742185081702520097574644 y2[1] (numeric) = 1.172974138902831552196660832084 absolute error = 3.53156766180553489253804e-08 relative error = 3.0107804071291127802321558807728e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5621639293750903082154132979511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0827383907708873079421253627355 relative error = 3.2292387626839760382155640842174 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=160.2MB, alloc=4.3MB, time=26.77 x[1] = 0.598 y2[1] (analytic) = 1.1735367515670677083533987114403 y2[1] (numeric) = 1.1735367143822281743999026565663 absolute error = 3.71848395339534960548740e-08 relative error = 3.1686131247529472744865442458321e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5629906739810929052579167718239 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0835651353768899049846288366083 relative error = 3.2604541337283992839341495806934 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.599 y2[1] (analytic) = 1.1741001553788068074520056321979 y2[1] (numeric) = 1.1741001162462593096862392566979 absolute error = 3.91325474977657663755000e-08 relative error = 3.3329820559592893892746650758697e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5638168555964684370954495492333 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0843913169922654368221616140177 relative error = 3.2916281366998000299906074678557 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6 y2[1] (analytic) = 1.1746643850903217027590475010446 y2[1] (numeric) = 1.1746643439290575371052659196681 absolute error = 4.11612641656537815813765e-08 relative error = 3.5040871833778147935580859879562e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5646424733950353572009454456587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0852169347908323569276575104431 relative error = 3.3227608009635531341618759185234 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.3MB, time=27.41 NO POLE NO POLE x[1] = 0.601 y2[1] (analytic) = 1.1752294401373827297787700698751 y2[1] (numeric) = 1.17522939686387785314468755995 absolute error = 4.32735048766340825099251e-08 relative error = 3.6821324754743608534047463712396e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5654675265511759358089652761314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0860419879469729355356773409158 relative error = 3.3538521558540791886055416535691 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.602 y2[1] (analytic) = 1.1757953199549348885380653377883 y2[1] (numeric) = 1.1757952744830976717303187193006 absolute error = 4.54718372168077466184877e-08 relative error = 3.8673259235757598828122066604227e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5662920142398370855333578191989 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0868664756356340852600698839833 relative error = 3.3849022306748227445431224633943 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.4MB, time=28.05 NO POLE NO POLE x[1] = 0.603 y2[1] (analytic) = 1.1763620239770984086414244362806 y2[1] (numeric) = 1.1763619762182168242260835667609 absolute error = 4.77588815844153408695197e-08 relative error = 4.0598795788179165073345514560156e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5671159356365311864202784486542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0876903970323281861469905134386 relative error = 3.4159110546982307202833213189365 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.604 y2[1] (analytic) = 1.1769295516371693151506608681084 y2[1] (numeric) = 1.1769295014998575594340158986556 absolute error = 5.01373117557166449694528e-08 relative error = 4.2600095890168681001843192620531e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5679392899173369104357403800814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0885137513131339101624524448658 relative error = 3.4468786571657309917944634260815 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.605 y2[1] (analytic) = 1.177497902367619995288838220145 y2[1] (numeric) = 1.1774978497577645435942591385934 absolute error = 5.26098554516945790815516e-08 relative error = 4.4679362354625708796579920535269e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5687620762589000453868740447335 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0893365376546970451135861095179 relative error = 3.4778050672877111650378950822063 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=28.69 NO POLE NO POLE x[1] = 0.606 y2[1] (analytic) = 1.1780670756000997659678356463513 y2[1] (numeric) = 1.1780670204208048603850663374669 absolute error = 5.51792949055827693088844e-08 relative error = 4.6838839696351578766343883715683e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.569584293838434318276070669554 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0901587552342313180027827343384 relative error = 3.5086903142434975292766838268634 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.607 y2[1] (analytic) = 1.1786370707654354421389835933405 y2[1] (numeric) = 1.1786370129169680109228001734525 absolute error = 5.78484674312161834198880e-08 relative error = 4.9080814498434185914191204450909e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5704059418337222180871867092646 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.090980403229519217813898774049 relative error = 3.5395344271813341905765131501844 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=29.33 NO POLE NO POLE x[1] = 0.608 y2[1] (analytic) = 1.1792078872936319059662014179512 y2[1] (numeric) = 1.1792078266733659137619329520105 absolute error = 6.06202659922042684659407e-08 relative error = 5.1407615777852537602567520239646e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5712270194231158180029863443854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0918014808189128177296984091698 relative error = 3.5703374352183623847182119436167 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.609 y2[1] (analytic) = 1.1797795246138726768210677237362 y2[1] (numeric) = 1.1797794611162329048950466058852 absolute error = 6.34976397719260211178510e-08 relative error = 5.3821615350298622433058361881207e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5720475257855375970529998278124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0926219871813345967797118925968 relative error = 3.6010993674405999687438989579265 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=29.99 NO POLE NO POLE x[1] = 0.61 y2[1] (analytic) = 1.1803519821545204820992534213452 y2[1] (numeric) = 1.1803519156709257377528326951047 absolute error = 6.64835947443464207262405e-08 relative error = 5.6325228194214206276751149326696e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5728674601004812611909760321627 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0934419214962782609176880969471 relative error = 3.6318202529029210903612557840579 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.611 y2[1] (analytic) = 1.1809252593431178288577466964165 y2[1] (numeric) = 1.1809251897619235832040924069809 absolute error = 6.95811942456536542894356e-08 relative error = 5.8920912814040197111547718488005e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5736868215480125638011081205036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.094261282943809563527820185288 relative error = 3.6625001206290360344329683037879 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.612 y2[1] (analytic) = 1.1814993556063875762722982477992 y2[1] (numeric) = 1.1814992828128280295557365561097 absolute error = 7.27935595467165616916895e-08 relative error = 6.1611171602676255944503664983205e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5745056093087701256322118343075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0950800707045671253589238990919 relative error = 3.6931389996114712457808961797835 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=30.63 NO POLE NO POLE x[1] = 0.613 y2[1] (analytic) = 1.1820742703702335089145143387088 y2[1] (numeric) = 1.1820741942463630825527855843708 absolute error = 7.61238704263617287543380e-08 relative error = 6.4398551203148366619455612644929e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5753238225639662541590364645238 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0958982839597632538857485293082 relative error = 3.7237369188115495275370427794905 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.614 y2[1] (analytic) = 1.1826500030597409108480243837716 y2[1] (numeric) = 1.1826499234843751653783695609279 absolute error = 7.95753657454696548228437e-08 relative error = 6.7285642869482112731898383570718e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.576141460495387762369889144524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0967159218911847620966012093084 relative error = 3.7542939071593704142759039646728 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=31.28 NO POLE NO POLE x[1] = 0.615 y2[1] (analytic) = 1.1832265530991771405431489758368 y2[1] (numeric) = 1.1832264699478331186537281822285 absolute error = 8.31513440218894207936083e-08 relative error = 7.0275082826779445193379935880058e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5769585222853967869797536773647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0975329836811937867064657421491 relative error = 3.7848099935537907191652734394429 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.616 y2[1] (analytic) = 1.1838039199119922066094934379379 y2[1] (numeric) = 1.1838038330568282004382107720039 absolute error = 8.68551640061712826659340e-08 relative error = 7.3369552630496759205690631628517e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5777750071169316060680856843173 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0983494685127286057947977491017 relative error = 3.8152852068624052543750748447606 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=190.7MB, alloc=4.4MB, time=31.92 x[1] = 0.617 y2[1] (analytic) = 1.1843821029208193443458911678558 y2[1] (numeric) = 1.1843820122305740862292762812695 absolute error = 9.06902452581166148865863e-08 relative error = 7.6571779524922134519936680194446e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5785909141735074561404664369381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0991653755693044558671785017225 relative error = 3.8457195759215277239862765276675 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.618 y2[1] (analytic) = 1.1849611015474755931071202253905 y2[1] (numeric) = 1.1849610068874068689624932883244 absolute error = 9.46600687241446269370661e-08 relative error = 7.9884536800849627866335654078763e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.579406242639217348613298311092 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0999807040350143483400103758764 relative error = 3.8761131295361717886444239095876 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.619 y2[1] (analytic) = 1.1855409152129623744868157956707 y2[1] (numeric) = 1.1855408164447850590115399987517 absolute error = 9.87681773154752757969190e-08 relative error = 8.3310644152448541346367116482967e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5802209916987328857207253783037 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1007954530945298854474374430881 relative error = 3.9064658964800323012047966410118 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=32.56 NO POLE NO POLE x[1] = 0.62 y2[1] (analytic) = 1.1861215433374660713160003456393 y2[1] (numeric) = 1.1861214403192895841882042454183 absolute error = 1.030181764871277961002210e-07 relative error = 8.6852968033325625378916531677419e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5810351605373050758429632275822 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1016096219331020755696752923666 relative error = 3.9367779054954667126186632703545 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.621 y2[1] (analytic) = 1.1867029853403586074766524752305 y2[1] (numeric) = 1.1867028779266237897423834884751 absolute error = 1.074137348177342689867554e-07 relative error = 9.0514422011778209485394112942781e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.581848748340765148255222689459 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1024232097365621479819347542434 relative error = 3.9670491852934766473125649841116 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=33.20 NO POLE NO POLE x[1] = 0.622 y2[1] (analytic) = 1.1872852406401980285297346497202 y2[1] (numeric) = 1.1872851286816134383620848153567 absolute error = 1.119585845901676498343635e-07 relative error = 9.4297967125236288784677806911502e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.5826617542955253672964127133811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1032362156913223670231247781655 relative error = 3.9972797645536896473150121040467 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.623 y2[1] (analytic) = 1.1878683086547290831570991852689 y2[1] (numeric) = 1.1878681919982067101734249407817 absolute error = 1.166565223729836742444872e-07 relative error = 9.8206612233891628546273644460728e-06 % Correct digits = 7 h = 0.001 y1[1] (analytic) = 2.583474177588579845956808229827 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1040486389843768456835202946114 relative error = 4.0274696719243410843874224667694 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.624 y2[1] (analytic) = 1.1884521888008838054166910457999 y2[1] (numeric) = 1.1884520672894742027406302067526 absolute error = 1.215114096026760608390473e-07 relative error = 1.0224341437351198351851022564245e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.584286017407505358883869409543 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1048604788033023586105814743274 relative error = 4.0576189360222562394185695718972 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.4MB, time=33.84 NO POLE NO POLE x[1] = 0.625 y2[1] (analytic) = 1.1890368804947820978104651960589 y2[1] (numeric) = 1.1890367539676089310660365825557 absolute error = 1.265271731667444286135032e-07 relative error = 1.0641147910743856300707027625499e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5850972729404621548053993141501 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1056717343362591545321113789345 relative error = 4.0877275854328325483442404789218 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.626 y2[1] (analytic) = 1.189622383151732315164435442986 y2[1] (numeric) = 1.1896222514439263275900896647613 absolute error = 1.317078059875743457782247e-07 relative error = 1.1071396087776490682692265673327e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5859079433761947683692275150305 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1064824047719917680959395798149 relative error = 4.1177956487100220138562288703778 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.4MB, time=34.49 NO POLE NO POLE x[1] = 0.627 y2[1] (analytic) = 1.1902086961862318493202708853993 y2[1] (numeric) = 1.1902085591288642421913446772234 absolute error = 1.370573676071289262081759e-07 relative error = 1.1515406335569537128697059401777e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5867180279040328313986078408783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1072924892998298311253199056627 relative error = 4.1478231543763137821672074915037 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.628 y2[1] (analytic) = 1.1907958190119677146378552804441 y2[1] (numeric) = 1.1907956764319829421864664710801 absolute error = 1.425799847724513888093640e-07 relative error = 1.1973503979108145829070305962466e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5875275257138918835625189985835 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1081019871096888832892310633679 relative error = 4.1778101309227168841004363351864 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=35.14 NO POLE NO POLE x[1] = 0.629 y2[1] (analytic) = 1.1913837510418171343082238242947 y2[1] (numeric) = 1.1913836027619651123302295247533 absolute error = 1.482798520219779942995414e-07 relative error = 1.2446019336113425444706383419491e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5883364359962741824600573972178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1089108973920711821867694620022 relative error = 4.2077566068087431397756684770144 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.63 y2[1] (analytic) = 1.1919724916878481274762910342229 y2[1] (numeric) = 1.1919723375266158548155179439487 absolute error = 1.541612322726607730902742e-07 relative error = 1.2933287751831128078289122808145e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5891447579422695131181120907946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.109719219338066512844824155579 relative error = 4.2376626104623902261650143896036 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.631 y2[1] (analytic) = 1.1925620403613200971727826093538 y2[1] (numeric) = 1.192561880132862689273325461656 absolute error = 1.602284574078994571476978e-07 relative error = 1.3435649633737608723088524720731e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5899524907435559969015123421982 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1105269521393529966282244069826 relative error = 4.2675281702801249067949178897863 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=35.78 NO POLE NO POLE x[1] = 0.632 y2[1] (analytic) = 1.1931523964726844190547833382246 y2[1] (numeric) = 1.1931522299867555527727554381488 absolute error = 1.664859288662820279000758e-07 relative error = 1.3953450486162895953440290782023e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5907596335924008998348388981996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.111334094988197899561550962984 relative error = 4.2973533146268664228727826073781 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.633 y2[1] (analytic) = 1.1937435594315850309543123126502 y2[1] (numeric) = 1.1937433864934667998210208609844 absolute error = 1.729381182311332914516658e-07 relative error = 1.4487040944830713956175093737015e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5915661856816614403350906538176 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.112140647077458440061802718602 relative error = 4.3271380718359700451191670220827 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.4MB, time=36.43 NO POLE NO POLE x[1] = 0.634 y2[1] (analytic) = 1.1943355286468590232343358993664 y2[1] (numeric) = 1.1943353490572912023634443450042 absolute error = 1.795895678208708915543622e-07 relative error = 1.5036776811315299325731934113203e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.592372146204785596354398973423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1129466076005825960811110382074 relative error = 4.3568824702092107855888387062452 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.635 y2[1] (analytic) = 1.1949283035265372299516281134903 y2[1] (numeric) = 1.1949281170816459497834581323333 absolute error = 1.864448912801681699811570e-07 relative error = 1.5603019087414859357420291652100e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5931775143558129119319825259412 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1137519757516099116586945907256 relative error = 4.3865865380167672687663444477524 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=221.2MB, alloc=4.4MB, time=37.07 x[1] = 0.636 y2[1] (analytic) = 1.1955218834778448208258872309833 y2[1] (numeric) = 1.1955216899690706489026040923809 absolute error = 1.935087741719232831386024e-07 relative error = 1.6186134009441521873217653417544e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5939822893293753031545360822647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1145567507251723028812481470491 relative error = 4.416250303497205761224112420087 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.637 y2[1] (analytic) = 1.1961162679072018940145166710524 y2[1] (numeric) = 1.1961160671212273239805337218398 absolute error = 2.007859745700339829492126e-07 relative error = 1.6786493082427629902538004724156e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5947864703206978635242473145531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1153609317164948632509593793375 relative error = 4.4458737948574643591334555272216 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.638 y2[1] (analytic) = 1.1967114562202240696924773737563 y2[1] (numeric) = 1.1967112479389004167150081446869 absolute error = 2.082813236529774692290694e-07 relative error = 1.7404473114248237816513296049036e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5955900565255996687336362294726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.116164517921396668460348294257 relative error = 4.4754570402728373329211914910751 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=37.71 NO POLE NO POLE x[1] = 0.639 y2[1] (analytic) = 1.1973074478217230844366180930148 y2[1] (numeric) = 1.197307231821996786241898112183 absolute error = 2.159997262981947199808318e-07 relative error = 1.8040456249659668778431120387181e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5963930471404945808464124606007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1169675085362915805731245253851 relative error = 4.505000067886959628366935179818 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.64 y2[1] (analytic) = 1.1979042421157073864138892207397 y2[1] (numeric) = 1.1979040181695457091351840028726 absolute error = 2.239461616772787052178671e-07 relative error = 1.8694830004253996625001118034397e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5971954413623920518835462392079 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1177699027581890516102583039923 relative error = 4.5345029058117915234384521083715 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.4MB, time=38.35 NO POLE NO POLE x[1] = 0.641 y2[1] (analytic) = 1.198501838505382731372844953923 y2[1] (numeric) = 1.1985016063796988794069558225843 absolute error = 2.321256838519658891313387e-07 relative error = 1.9367987298329318533018078634426e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5979972383888979268137494574101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1185716997846949265404615221945 relative error = 4.5639655821276034401647889889422 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.642 y2[1] (analytic) = 1.1991002363931527794378378132311 y2[1] (numeric) = 1.1990999958497304085074132044304 absolute error = 2.405434223709304246088007e-07 relative error = 2.0060326490675688053688646067930e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.5987984374182152459475638332798 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1193728988140122456742758980642 relative error = 4.5933881248829609108492176815203 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.643 y2[1] (analytic) = 1.1996994351806196927053087189588 y2[1] (numeric) = 1.1996991859760368253248654088071 absolute error = 2.492045828673804433101517e-07 relative error = 2.0772251412276581312328749101287e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.599599037649145046734253783893 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1201734990449420464609658486774 relative error = 4.6227705620947096979263429028712 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=232.6MB, alloc=4.4MB, time=38.98 NO POLE NO POLE x[1] = 0.644 y2[1] (analytic) = 1.2002994342685847336415750281037 y2[1] (numeric) = 1.2002991761541370761857313233947 absolute error = 2.581144476574558437047090e-07 relative error = 2.1504171399925772374261621818599e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6003990382810871649607022094871 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1209734996768841646874142742715 relative error = 4.6521129217479610667700316098188 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.645 y2[1] (analytic) = 1.2009002330570488642815181348221 y2[1] (numeric) = 1.2008999657786725248545394631571 absolute error = 2.672783763394269786716650e-07 relative error = 2.2256501329759496968490989178380e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6011984385140410353515079898995 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1217728999098380350782200546839 relative error = 4.681415231796077210761123089686 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=39.63 NO POLE NO POLE x[1] = 0.646 y2[1] (analytic) = 1.2015018309452133462275714356296 y2[1] (numeric) = 1.2015015542434069525339279703422 absolute error = 2.767018063936936434652874e-07 relative error = 2.3029661650703786939032991009736e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6019972375486064915694845932574 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1225716989444034912961966580418 relative error = 4.7106775201606568279261734796457 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.647 y2[1] (analytic) = 1.2021042273314803414484086604078 y2[1] (numeric) = 1.2021039409412265578646446144819 absolute error = 2.863902537835837640459259e-07 relative error = 2.3824078417836860959606594709984e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6027954345859845656157597964862 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1233698959817815653424718612706 relative error = 4.7398998147315208484607767087401 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=240.3MB, alloc=4.4MB, time=40.27 x[1] = 0.648 y2[1] (analytic) = 1.2027074216134535138767317705792 y2[1] (numeric) = 1.2027071252641399569255467923918 absolute error = 2.963493135569511849781874e-07 relative error = 2.4640183325666460200649078200981e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6035930288279782866286771176028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1241674902237752863553891823872 relative error = 4.769082143366698312453285723345 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.649 y2[1] (analytic) = 1.203311413187938631805556826712 y2[1] (numeric) = 1.2033111066032781832336015281715 absolute error = 3.065846604485719552985405e-07 relative error = 2.5478413741322020778285505351274e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6043900194769934790807001609604 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1249644808727904788074122257448 relative error = 4.7982245338924123971270333305875 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.65 y2[1] (analytic) = 1.2039162014509441710823954293201 y2[1] (numeric) = 1.2039158843488946877438854732044 absolute error = 3.171020494833385099561157e-07 relative error = 2.6339212737661577942885327543259e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6051864057360395603725216786059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1257608671318365600992337433903 relative error = 4.8273270141030665929214210861246 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.4MB, time=40.90 NO POLE NO POLE x[1] = 0.651 y2[1] (analytic) = 1.2045217857976819191007285387257 y2[1] (numeric) = 1.2045214578903653388495849061578 absolute error = 3.279073165802511436325679e-07 relative error = 2.7223029126293300080131071346011e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6059821868087303378235797537072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1265566482045273375502918184916 relative error = 4.8563896117612310277345073747963 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.652 y2[1] (analytic) = 1.2051281656225675795881686825627 y2[1] (numeric) = 1.205127826616188422381995732983 absolute error = 3.390063791572061729495797e-07 relative error = 2.8130317490511553700052695028470e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6067773618992848050581841156014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1273518232950818047848961803858 relative error = 4.8854123545976289386519821965807 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=41.54 NO POLE NO POLE x[1] = 0.653 y2[1] (analytic) = 1.2057353403192213781907057628076 y2[1] (numeric) = 1.205734989913984641610523486915 absolute error = 3.504052367365801822758926e-07 relative error = 2.9061538218147403679194124289458e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6075719302125279377864562004034 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1281463916083249375131682651878 relative error = 4.9143952703111232904896661877052 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.654 y2[1] (analytic) = 1.2063433092804686688524308781435 y2[1] (numeric) = 1.2063429471704971172426833284729 absolute error = 3.621099715516097475496706e-07 relative error = 3.0017157534333456097926464599817e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6083658909538914889792871763013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1289403523496884887059992410857 relative error = 4.9433383865687035404789150896414 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.655 y2[1] (analytic) = 1.2069520718983405409901317819836 y2[1] (numeric) = 1.2069516977715913874241000454595 absolute error = 3.741267491535660317365241e-07 relative error = 3.0997647534182954078855937091876e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.609159243329414783436518758647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1297337047252117831632308234314 relative error = 4.9722417310054725484265482387333 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.4MB, time=42.18 NO POLE NO POLE x[1] = 0.656 y2[1] (analytic) = 1.207561627564074427462152801609 y2[1] (numeric) = 1.2075612411022554077385080529615 absolute error = 3.864618190197236447486475e-07 relative error = 3.2003486215383040083245094922043e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6099519865457455117475522467268 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1305264479415425114742643115112 relative error = 5.0011053312246336316831506982117 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.657 y2[1] (analytic) = 1.2081719756681147133309112496125 y2[1] (numeric) = 1.2081715765465995512077513933496 absolute error = 3.991215151621231598562629e-07 relative error = 3.3035157510702101160326994012387e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6107441198101405236435918216702 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1313185812059375233703038864546 relative error = 5.029929214797477764255823404278 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=42.83 NO POLE NO POLE x[1] = 0.658 y2[1] (analytic) = 1.2087831156001133454184615651814 y2[1] (numeric) = 1.2087827034878566082917837362783 absolute error = 4.121122567371266778289031e-07 relative error = 3.4093151320411116669296422573621e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6115356423304666207407287533185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1321101037262636204674408181029 relative error = 5.0587134092633709194036741604268 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.659 y2[1] (analytic) = 1.2093950467489304426544976297072 y2[1] (numeric) = 1.209394621308381786888668378686 absolute error = 4.254405486557658292510212e-07 relative error = 3.5177963544618931005565640065103e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6123265533152013486730737730358 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1329010147109983483997858378202 relative error = 5.0874579421297415550565545014021 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=43.47 NO POLE NO POLE x[1] = 0.66 y2[1] (analytic) = 1.2100077685026349072161829087698 y2[1] (numeric) = 1.2100073293896527123345782447949 absolute error = 4.391129821948816046639749e-07 relative error = 3.6290096115521376861529407096256e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6131168519734337886151454793963 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1336913133692307883418575441807 relative error = 5.116162840872068241399753371776 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.661 y2[1] (analytic) = 1.2106212802485050364591972807178 y2[1] (numeric) = 1.2106208271122694274037958861113 absolute error = 4.531362356090554013946065e-07 relative error = 3.7430057029564177537552429766997e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6139065375148653481927232544241 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1344809989106623479194353192085 relative error = 5.1448281329338674299695582360836 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.662 y2[1] (analytic) = 1.2112355813730291356393886208484 y2[1] (numeric) = 1.2112351138559543923087134814251 absolute error = 4.675170747433306751394233e-07 relative error = 3.8598360379519559791129125099128e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6146956091498105517813737796007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1352700705456075515080858443851 relative error = 5.1734538457266813636067876698688 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=44.11 NO POLE NO POLE x[1] = 0.663 y2[1] (analytic) = 1.2118506712619061314244164195866 y2[1] (numeric) = 1.2118501889995524846998328368104 absolute error = 4.822623536467245835827762e-07 relative error = 3.9795526386476511671129215623734e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6154840660891978301918608531767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1360585274849948299185729179611 relative error = 5.2020400066300661266175866853581 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.664 y2[1] (analytic) = 1.2124665493000461861947739230711 y2[1] (numeric) = 1.2124660519210309996657653856249 absolute error = 4.973790151865290085374462e-07 relative error = 4.1022081431744622729693299679597e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6162719075445703097416488234469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1368463689403673094683608882313 relative error = 5.230586642991579834492957034435 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=44.75 NO POLE NO POLE x[1] = 0.665 y2[1] (analytic) = 1.2130832148715713131335744951767 y2[1] (numeric) = 1.2130827019974796497332321885103 absolute error = 5.128740916634003423066664e-07 relative error = 4.2278558088671446936639549868778e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6170591327280866007117105665481 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1376335941238836004384226313325 relative error = 5.2590937821267709625406695162698 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.666 y2[1] (analytic) = 1.213700667359815992104487111237 y2[1] (numeric) = 1.2137001386051105648670639333922 absolute error = 5.287547054272374231778448e-07 relative error = 4.3565495154373331540148534692407e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6178457408525215851878515520396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.138420202248318584914563616824 relative error = 5.2875614513191668127853739102098 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=270.8MB, alloc=4.4MB, time=45.38 x[1] = 0.667 y2[1] (analytic) = 1.2143189061473277863172051055833 y2[1] (numeric) = 1.2143183611192582924702009354801 absolute error = 5.450280694938470041701032e-07 relative error = 4.4883437681379658022969483412931e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6186317311312672042857621550066 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.139206192527064204012474219791 relative error = 5.3159896778202621184948845676121 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.668 y2[1] (analytic) = 1.2149379306158679597798315074841 y2[1] (numeric) = 1.2149373689143797973836931372674 absolute error = 5.617014881623961383702167e-07 relative error = 4.6232937009190444195401888496295e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6194171027783332447590109897005 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1399915641741302444857230544849 relative error = 5.3443784888495077856927759417571 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.669 y2[1] (analytic) = 1.2155577401464120955375635131482 y2[1] (numeric) = 1.2155571613640544618867001085312 absolute error = 5.787823576336508634046170e-07 relative error = 4.7614550795747259344814489409678e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6202018550083481249891926567879 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1407763164041451247159047215723 relative error = 5.3727279115942997710195724244993 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.4MB, time=46.01 NO POLE NO POLE x[1] = 0.67 y2[1] (analytic) = 1.2161783341191507146970578551619 y2[1] (numeric) = 1.2161777378409840856964910463327 absolute error = 5.962781666290005668088292e-07 relative error = 4.9028843048817407226435961896245e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6209859870365596803574439141266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.141560448432356680084155978911 relative error = 5.4010379732099680953069608041498 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.671 y2[1] (analytic) = 1.2167997119134898962358580450436 y2[1] (numeric) = 1.2167990977169928859684447750169 absolute error = 6.141964970102674132700267e-07 relative error = 5.0476384157291334531552415768829e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6217694980788359479965428996171 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1423439594746329477232549644015 relative error = 5.4293087008197659922315914731123 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=46.65 NO POLE NO POLE x[1] = 0.672 y2[1] (analytic) = 1.2174218729080518975962636795423 y2[1] (numeric) = 1.2174212403630274972960497462127 absolute error = 6.325450244003002139333296e-07 relative error = 5.1957750922393225307044403284929e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6225523873516659509228066540965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1431268487474629506495187188809 relative error = 5.4575401215148591914171662082766 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.673 y2[1] (analytic) = 1.2180448164806757760630212168607 y2[1] (numeric) = 1.2180441651491569717109040388328 absolute error = 6.513315188043521171780279e-07 relative error = 5.3473526588804744624357458576258e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6233346540721604815470028124424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1439091154679574812737148772268 relative error = 5.4857322623543153353556359339891 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.674 y2[1] (analytic) = 1.2186685420084180109242148451658 y2[1] (numeric) = 1.2186678714445727786827153590739 absolute error = 6.705638452322414994860919e-07 relative error = 5.5024300875701897606494750198234e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6241162974580528845634919520396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.144690758853849884290204016824 relative error = 5.5138851503650935295204513687649 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=47.28 NO POLE NO POLE x[1] = 0.675 y2[1] (analytic) = 1.219293048867553126414735282546 y2[1] (numeric) = 1.2192923586175888051193010404165 absolute error = 6.902499643212954342421295e-07 relative error = 5.6610670007704972718417086071690e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6248973167276998392168177095343 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1454717781234968389435297743187 relative error = 5.5419988125420340250469228649757 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.676 y2[1] (analytic) = 1.2199183364335743154417035649992 y2[1] (numeric) = 1.2199176260356413553665880436251 absolute error = 7.103979329600751155213741e-07 relative error = 5.8233236745741541009305612992942e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6256777111000821409449623993491 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1462521724958791406716744641335 relative error = 5.5700732758478480333568530873214 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.4MB, time=47.92 NO POLE NO POLE x[1] = 0.677 y2[1] (analytic) = 1.2205444040811940640912260970796 y2[1] (numeric) = 1.220543673065289151208612956748 absolute error = 7.310159049128826131403316e-07 relative error = 5.9892610417822485764456993289262e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6264574797948054823984864907691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1470319411906024821251985555535 relative error = 5.5981085672131076721067074535381 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.678 y2[1] (analytic) = 1.2211712511843447769158564585004 y2[1] (numeric) = 1.2211704990722133318675219951173 absolute error = 7.521121314450483344633831e-07 relative error = 6.1589406949731039780112086901207e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6272366220321012338347709245244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1478110834278982335614829893088 relative error = 5.6261047135362360418406824912812 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.4MB, time=48.54 NO POLE NO POLE x[1] = 0.679 y2[1] (analytic) = 1.221798877116179403002138679282 y2[1] (numeric) = 1.2217981034212174540035710013491 absolute error = 7.736949619489985676779329e-07 relative error = 6.3324248895624810216240491746603e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6280151370328272228865818746926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.148589598428624222613293939477 relative error = 5.6540617416834974327321214608247 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.68 y2[1] (analytic) = 1.2224272812490720628176059159557 y2[1] (numeric) = 1.2224264854762274917151254453434 absolute error = 7.957728445711024804706123e-07 relative error = 6.5097765468550773710188961725016e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6287930240184685137041781874202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1493674854142655134308902522046 relative error = 5.6819796784889876607988097660643 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.681 y2[1] (analytic) = 1.2230564629546186758366076818755 y2[1] (numeric) = 1.223055644600291836538660424284 absolute error = 8.183543268392979472575915e-07 relative error = 6.6910592570873227148126045029021e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6295702822111381854701823544214 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1501447436069351851968944192058 relative error = 5.7098585507546245329797598387687 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=49.15 NO POLE NO POLE x[1] = 0.682 y2[1] (analytic) = 1.223686421603637588944338005864 y2[1] (numeric) = 1.2236855801555812974487606626387 absolute error = 8.414480562914955773432253e-07 relative error = 6.8763372824614682191354896012975e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6303469108335781102864365064475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1509213722293751100131485712319 relative error = 5.7376983852501384404631663449404 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.683 y2[1] (analytic) = 1.2243171565661702056184361152149 y2[1] (numeric) = 1.224316291503389100858120512159 absolute error = 8.650627811047603156030559e-07 relative error = 7.0656755601709694340797119857213e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6311229091091597304320655399362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1516973705049567301587776047206 relative error = 5.7654992087130630796572777399649 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.4MB, time=49.77 NO POLE NO POLE x[1] = 0.684 y2[1] (analytic) = 1.2249486672114816158875304615069 y2[1] (numeric) = 1.2249477780041308906175439518804 absolute error = 8.892073507252699865096265e-07 relative error = 7.2591397054171619995250884408953e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.631898276261884834991970118843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1524727376576818347186821836274 relative error = 5.7932610478487263001979894029834 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.685 y2[1] (analytic) = 1.2255809529080612270660961307334 y2[1] (numeric) = 1.2255800390173447280159445881224 absolute error = 9.138907164990501515426110e-07 relative error = 7.4567960144172297617373750505178e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6326730115163863358549729232243 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1532474729121833355816849880087 relative error = 5.8209839293302410793890168227644 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=301.3MB, alloc=4.4MB, time=50.40 x[1] = 0.686 y2[1] (analytic) = 1.2262140130236233952649949029474 y2[1] (numeric) = 1.2262130739016910917803456544881 absolute error = 9.391219323034846492484593e-07 relative error = 7.6587114674034651765715646048145e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6334471140979290430808421464934 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1540215754937260428075542112778 relative error = 5.8486678797984966224725545998463 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.687 y2[1] (analytic) = 1.2268478469251080576770664509304 y2[1] (numeric) = 1.2268468820149528780758800118647 absolute error = 9.649101551796011864390657e-07 relative error = 7.8649537316138221381507794713414e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6342205832324104396354168743884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1547950446282074393621289391728 relative error = 5.8763129258621495881303683844685 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.688 y2[1] (analytic) = 1.2274824539786813656371383923497 y2[1] (numeric) = 1.2274814627140354005057901484233 absolute error = 9.912646459651313482439264e-07 relative error = 8.0755911642737616335283047497340e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6349934181463614554930596105924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1555678795421584552197716753768 relative error = 5.9039190940976154386173022996708 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.4MB, time=51.04 NO POLE NO POLE x[1] = 0.689 y2[1] (analytic) = 1.2281178335497363184558221354451 y2[1] (numeric) = 1.2281168153549663901114281796187 absolute error = 1.0181947699283443939558264e-06 relative error = 8.2906928155693908840740794603983e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6357656180669472411056618466169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1563400794627442408323739114013 relative error = 5.9314864110490599139312139156503 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.69 y2[1] (analytic) = 1.2287539850028933980264606845022 y2[1] (numeric) = 1.2287529392928959953722558481898 absolute error = 1.0457099974026542048363124e-06 relative error = 8.5103284316118968931560094880296e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6365371822219679402374292070087 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1571116436177649399641412717931 relative error = 5.9590149032283906294253724576355 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.4MB, time=51.66 NO POLE NO POLE x[1] = 0.691 y2[1] (analytic) = 1.2293909077020012042045937982186 y2[1] (numeric) = 1.2293898338820967822058445241592 absolute error = 1.0738199044219987492740594e-06 relative error = 8.7345684573932755771090580441939e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6373081098398594621646733351585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1578825712356564618913853999429 relative error = 5.9865045971152487962713736570507 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.692 y2[1] (analytic) = 1.2300286010101370909593051215486 y2[1] (numeric) = 1.2300274984759637339678752048335 absolute error = 1.1025341733569914299167151e-06 relative error = 8.9634840397333579124995437635384e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6380784001496942532398383199832 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1586528615454912529665503847676 relative error = 6.0139555191570010641826365071518 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.693 y2[1] (analytic) = 1.2306670642896078032958151397345 y2[1] (numeric) = 1.2306659324270142514521385148031 absolute error = 1.1318625935518436766249314e-06 relative error = 9.1971470302181347872971190846709e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.638848052381182067818990099522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1594225137769790675457021643064 relative error = 6.0413676957687314858105531718217 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.4MB, time=52.29 NO POLE NO POLE x[1] = 0.694 y2[1] (analytic) = 1.2313062969019501149486830319832 y2[1] (numeric) = 1.2313051350868881528905347059423 absolute error = 1.1618150619620581483260409e-06 relative error = 9.4356299881293824967608804824033e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.639617065764670738551997914018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1601915271604677382787099788024 relative error = 6.0687411533332336022273634317269 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.695 y2[1] (analytic) = 1.2319462982079314668449797316401 y2[1] (numeric) = 1.2319451058063476739530736574094 absolute error = 1.1924015837928919060742307e-06 relative error = 9.6790061833655910766278148157698e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.6403854395311469460346375183712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1609599009269439457613495831556 relative error = 6.0960759182010026489118193485249 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.4MB, time=52.91 NO POLE NO POLE x[1] = 0.696 y2[1] (analytic) = 1.2325870675675506063367937297397 y2[1] (numeric) = 1.2325858439352774677478748756464 absolute error = 1.2236322731385889188540933e-06 relative error = 9.9273495993541979165599436439779e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 2.641153172912236987821846501921 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1617276343080339875485585667054 relative error = 6.123372016690227881655694296687 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.697 y2[1] (analytic) = 1.2332286043400382272024303894814 y2[1] (numeric) = 1.2332273488226846048211674943794 absolute error = 1.2555173536223812628951020e-06 relative error = 0.00010180734935955129345759960273691 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6419202651402075468013627023692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1624947265360045465280747671536 relative error = 6.1506294750867850218111731668764 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=320.4MB, alloc=4.4MB, time=53.54 x[1] = 0.698 y2[1] (analytic) = 1.2338709078838576104156647704838 y2[1] (numeric) = 1.2338696198166985731572902746182 absolute error = 1.2880671590372583744958656e-06 relative error = 0.00010439237612355653130202751954653 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6426867154479664589269773402679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1632611768437634586536894050523 relative error = 6.1778483196442288203011373962789 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.699 y2[1] (analytic) = 1.234513977556705265682407193618 y2[1] (numeric) = 1.2345126562645712781786916046565 absolute error = 1.3212921339875037155889615e-06 relative error = 0.00010702933769956545067050908361265 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.643452523069063480310635140883 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1640269844648604800373472056674 relative error = 6.2050285765837857398163295425691 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7 y2[1] (analytic) = 1.2351578127155115737441400098081 y2[1] (numeric) = 1.235156457512677042745929500072 absolute error = 1.3552028345309982105097361e-06 relative error = 0.00010971900275249573106525254281057 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6442176872376910536726143513987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1647921486334880533993264161831 relative error = 6.2321702720943467546253474014694 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.4MB, time=54.16 NO POLE NO POLE x[1] = 0.701 y2[1] (analytic) = 1.2358024127164414294474832694162 y2[1] (numeric) = 1.2358010229065126071576716037262 absolute error = 1.3898099288222898116656900e-06 relative error = 0.00011246214722686302674785678974938 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6449822071886850741490202033442 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1655566685844820738757322681286 relative error = 6.2592734323324602674253771851652 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.702 y2[1] (analytic) = 1.2364477769148948855792462226979 y2[1] (numeric) = 1.2364463517906971291506951857645 absolute error = 1.4251241977564285510369334e-06 relative error = 0.00011525955437538227113242271602378 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6457460821575256544558260128154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1663205435533226541825380775998 relative error = 6.2863380834223251426635290430358 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.4MB, time=54.79 NO POLE NO POLE x[1] = 0.703 y2[1] (analytic) = 1.2370939046655077974663208163335 y2[1] (numeric) = 1.2370924435089721838998871436161 absolute error = 1.4611565356135664336727174e-06 relative error = 0.00011811201478748227390161393727528 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6465093113803378894086967545133 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1670837727761348891354088192977 relative error = 6.313364251455783855760586228899 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.704 y2[1] (analytic) = 1.2377407953221524683397725861917 y2[1] (numeric) = 1.2377392974042017640182440019943 absolute error = 1.4979179507043215285841974e-06 relative error = 0.00012102032641773365479454998075955 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6472718940938926197978305898392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1678463554896896195245426546236 relative error = 6.340351962492315757670921513011 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.705 y2[1] (analytic) = 1.2383884482379382954624835822915 y2[1] (numeric) = 1.238386912818372279556871912896 absolute error = 1.5354195660159056116693955e-06 relative error = 0.00012398529461419016039143906583506 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6480338295356071956170544742679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1686082909314041953437665390523 relative error = 6.3673012425590304542142710145098 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.4MB, time=55.41 NO POLE NO POLE x[1] = 0.706 y2[1] (analytic) = 1.2390368627652124170197011983717 y2[1] (numeric) = 1.2390352890925925580049866556023 absolute error = 1.5736726198590147145427694e-06 relative error = 0.00012700773214664341258166145770044 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6487951169435462386464106149696 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.169369578339343238373122679754 relative error = 6.3942121176506612996169865033523 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.707 y2[1] (analytic) = 1.2396860382555603597718460155734 y2[1] (numeric) = 1.2396844255670938442899136366779 absolute error = 1.6126884665154819323788955e-06 relative error = 0.00013008845923479113974959618130596 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6495557555564224043874711961547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1701302169522194041141832609391 relative error = 6.421084613729559003702312401921 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.4MB, time=56.05 NO POLE NO POLE x[1] = 0.708 y2[1] (analytic) = 1.2403359740598066874689310074817 y2[1] (numeric) = 1.2403343215812298007770878899715 absolute error = 1.6524785768866918431175102e-06 relative error = 0.00013322830357631894404583822034671 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6503157446135971433506194368912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1708902060093941430773315016756 relative error = 6.4479187567256853521711532183191 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.709 y2[1] (analytic) = 1.2409866695280156500259436921618 y2[1] (numeric) = 1.2409849764734765072700540766157 absolute error = 1.6930545391427558896155461e-06 relative error = 0.00013642810037489566043057903753938 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6510750833550814616935356941786 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.171649544750878461420247758963 relative error = 6.4747145725366070394167109778115 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.4MB, time=56.68 NO POLE NO POLE x[1] = 0.71 y2[1] (analytic) = 1.2416381240094918334585420558604 y2[1] (numeric) = 1.241636389581432461010466485027 absolute error = 1.7344280593724480755708334e-06 relative error = 0.00013968869236808236548081700774009 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6518337710215366812101279728528 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1724082324173336809368400376372 relative error = 6.5014720870274896133182803981574 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.711 y2[1] (analytic) = 1.2422903368527808105784143127322 y2[1] (numeric) = 1.2422885602418185766780890309057 absolute error = 1.7766109622339003252818265e-06 relative error = 0.00014301092985515509624372602029505 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6525918068542751986691468534576 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.173166268250072198395858918242 relative error = 6.5281913260310915314613920915587 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.712 y2[1] (analytic) = 1.2429433074056697924476518052839 y2[1] (numeric) = 1.2429414877904781863907952572361 absolute error = 1.8196151916060568565480478e-06 relative error = 0.0001463956707248413416949383174046 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6533491900952612445017254995287 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1739236514910582442284375643131 relative error = 6.5548723153477583282333909822048 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.4MB, time=57.30 NO POLE NO POLE x[1] = 0.713 y2[1] (analytic) = 1.2435970350151882805914835912195 y2[1] (numeric) = 1.2435951715623770397045683342863 absolute error = 1.8634528112408869152569332e-06 relative error = 0.00014984378048297037162269311245352 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6541059199871116408370860568158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1746803813829086405637981216002 relative error = 6.5815150807454168922454284169874 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.714 y2[1] (analytic) = 1.2442515190276087199687205040045 y2[1] (numeric) = 1.2442496108916033036135010596083 absolute error = 1.9081360054163552194443962e-06 relative error = 0.00015335613228003747000676477086673 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6548619957730965588856544087971 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1754364571688935586123664735815 relative error = 6.6081196479595698535337321295107 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.4MB, time=57.95 NO POLE NO POLE x[1] = 0.715 y2[1] (analytic) = 1.2449067587884471526992557167609 y2[1] (numeric) = 1.2449048051113675625497958580379 absolute error = 1.9536770795901494598587230e-06 relative error = 0.00015693360693868214219481665352921 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.655617416697140275668825905437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1761918780929372753955379702214 relative error = 6.6346860426932900799948983070395 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.716 y2[1] (analytic) = 1.2455627536424638725479680820458 y2[1] (numeric) = 1.245560753554002818383764781695 absolute error = 2.0000884610541642033003508e-06 relative error = 0.00016057709298108036739832974337244 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6563721820038219300946253354824 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1769466433996189298213374002668 relative error = 6.6612142906172152825118245181599 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=350.9MB, alloc=4.4MB, time=58.59 x[1] = 0.717 y2[1] (analytic) = 1.2462195029336640801643737636656 y2[1] (numeric) = 1.2462174555509644904238295099832 absolute error = 2.0473826995897405442536824e-06 relative error = 0.00016428748665625097023553307314644 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6571262909383762783785050667013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1777007523341732781052171314857 relative error = 6.687704417369542728228771198571 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.718 y2[1] (analytic) = 1.2468770060052985390773709209283 y2[1] (numeric) = 1.24687491043283041541652134959 absolute error = 2.0955724681236608495713383e-06 relative error = 0.00016806569196727618723981812929043 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6578797427466944488085259333295 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1784542041424914485352379981139 relative error = 6.7141564485560240614359027755712 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.719 y2[1] (analytic) = 1.2475352621998642324444214506442 y2[1] (numeric) = 1.2475331175293008475464812344869 absolute error = 2.1446705633848979402161573e-06 relative error = 0.00017191262069843650642895716222807 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6586325366753246958541661056053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1792069980711216955808781703897 relative error = 6.7405704097499602315255173507357 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.4MB, time=59.23 NO POLE NO POLE x[1] = 0.72 y2[1] (analytic) = 1.248194270859105020554513037748 y2[1] (numeric) = 1.2481920761691984584364597259291 absolute error = 2.1946899065621180533118189e-06 relative error = 0.00017582919244225986019306978899823 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6593846719714731536180038326482 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1799591333672701533447158974326 relative error = 6.7669463264921965274840261676881 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.721 y2[1] (analytic) = 1.2488540313240122990842440116342 y2[1] (numeric) = 1.2488517856804683371473170124559 absolute error = 2.2456435439619369269991783e-06 relative error = 0.00017981633462648525390769915143548 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6601361478830045886295206070606 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.180710609278801588356232671845 relative error = 6.7932842242911177183855908795733 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.4MB, time=59.87 NO POLE NO POLE x[1] = 0.722 y2[1] (analytic) = 1.249514542934825658106372752177 y2[1] (numeric) = 1.2495122453901779901780229098903 absolute error = 2.2975446476679283498422867e-06 relative error = 0.0001838749825409409148125750899999 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6608869636584431519802719575123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1814614250542401517069840222967 relative error = 6.819584128622643299355167911546 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.723 y2[1] (analytic) = 1.2501758050310335418501726369398 y2[1] (numeric) = 1.2501734546245173414656568613393 absolute error = 2.3504065162003845157756005e-06 relative error = 0.00018800607936433704781666288769272 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6616371185469731307996737341996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.182211579942770130526385798984 relative error = 6.8458460649302228424705449994247 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.724 y2[1] (analytic) = 1.2508378169513739092129327692739 y2[1] (numeric) = 1.2508354127087987323854079371937 absolute error = 2.4042425751768275248320802e-06 relative error = 0.00019221057619097328699593097620581 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6623866117984396990706524114553 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1829610731942366987973644762397 relative error = 6.8720700586248314520747852889943 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.4MB, time=60.51 NO POLE NO POLE x[1] = 0.725 y2[1] (analytic) = 1.2515005780338348950219439758613 y2[1] (numeric) = 1.2514981189674569217505748351282 absolute error = 2.4590663779732713691407331e-06 relative error = 0.00019648943205736093364192685932508 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6631354426633496677844085919225 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1837099040591466675111206567069 relative error = 6.898256135084965323972319213603 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.726 y2[1] (analytic) = 1.2521640876156554720463088117698 y2[1] (numeric) = 1.2521615727240490858125658801015 absolute error = 2.5148916063862337429316683e-06 relative error = 0.00020084361396876007379673653297922 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6638836103928722344335435575901 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1844580717886692341602556223745 relative error = 6.9244043196566374079837437428849 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.4MB, time=61.14 NO POLE NO POLE x[1] = 0.727 y2[1] (analytic) = 1.2528283450333261137579135612673 y2[1] (numeric) = 1.252825773301254818260899024356 absolute error = 2.5717320712954970145369113e-06 relative error = 0.00020527409692563167027322849605806 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6646311142388397318427993746266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.185205575634636731569511439411 relative error = 6.9505146376533731733362025251764 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.728 y2[1] (analytic) = 1.2534933496225894578408994734763 y2[1] (numeric) = 1.2534907200208761302232018474181 absolute error = 2.6296017133276176976260582e-06 relative error = 0.00020978186395000472620865820279824 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6653779534537483763366637213347 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1859524148495453760633757861191 relative error = 6.9765871143562064763680289425739 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.4MB, time=61.79 NO POLE NO POLE x[1] = 0.729 y2[1] (analytic) = 1.2541591007184409704489697234547 y2[1] (numeric) = 1.2541564122038374502652115560981 absolute error = 2.6885146035201837581673566e-06 relative error = 0.00021436790611175861923474475420748 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.666124127290759015243091271684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1866985886865560149698033364684 relative error = 7.0026217750136755300281371729956 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.73 y2[1] (analytic) = 1.2548255976551296112098678414497 y2[1] (numeric) = 1.2548228491701856243907749844901 absolute error = 2.7484849439868190928569596e-06 relative error = 0.00021903322255482070736823821277512 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6668696350036978737325941307615 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1874440963994948734593061955459 relative error = 7.028618644841818974652444020332 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.731 y2[1] (analytic) = 1.2554928397661584989763626059028 y2[1] (numeric) = 1.2554900302390899160418485939721 absolute error = 2.8095270685829345140119307e-06 relative error = 0.00022377882052327930973278657439534 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6676144758470573009919544831147 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1881889372428543007186665478991 relative error = 7.0545777490241720495013965443032 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.4MB, time=62.42 NO POLE NO POLE x[1] = 0.732 y2[1] (analytic) = 1.2561608263842855783230736492765 y2[1] (numeric) = 1.256157954728842006098498473206 absolute error = 2.8716554435722245751760705e-06 relative error = 0.00022860571538741216721559774917041 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6683586490759965157318132803332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1889331104717935154585253451176 relative error = 7.0804991127117628645444674077163 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.733 y2[1] (analytic) = 1.2568295568415242867884712799312 y2[1] (numeric) = 1.2568266219568559928789003381377 absolute error = 2.9348846682939095709417935e-06 relative error = 0.00023351493066963049014098713129893 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6691021539463423510273894603448 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1896766153421393507541015251292 relative error = 7.1063827610231087719792613735486 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.4MB, time=63.05 NO POLE NO POLE x[1] = 0.734 y2[1] (analytic) = 1.2574990304691442228613832781104 y2[1] (numeric) = 1.2574960312396683921393395319968 absolute error = 2.9992294758307220437461136e-06 relative error = 0.00023850749807033870200741978928485 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6698449897145899984915848577685 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1904194511103869982182969225529 relative error = 7.1322287190442128369746525391931 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.735 y2[1] (analytic) = 1.2581692465976718147113406795812 y2[1] (numeric) = 1.2581661818929381370742110252969 absolute error = 3.0647047336776371296542843e-06 relative error = 0.00024358445749370999028511093728274 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6705871556379037517797306322801 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1911616170337007515064426970645 relative error = 7.1580370118285604071291427029629 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=381.4MB, alloc=4.4MB, time=63.69 x[1] = 0.736 y2[1] (analytic) = 1.2588402045568909896620938166407 y2[1] (numeric) = 1.2588370732314465783160194158354 absolute error = 3.1313254444113460744008053e-06 relative error = 0.00024874685707337777720765564149643 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.671328650974117749425231710308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1919031123699147491519437750924 relative error = 7.1838076643971157801373967309282 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.737 y2[1] (analytic) = 1.2595119036758438444076291430284 y2[1] (numeric) = 1.2595087045690974839353789286936 absolute error = 3.1991067463604722502143348e-06 relative error = 0.00025399575319804322541353273899896 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.672069474981736717005366404475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1926439363775337167320784692594 relative error = 7.2095407017383189691596709422136 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.738 y2[1] (analytic) = 1.2601843432828313159700166267826 y2[1] (numeric) = 1.2601810752189170394410134162368 absolute error = 3.2680639142765290032105458e-06 relative error = 0.00025933221053699889520168540154239 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6728096269199367086364990450493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1933840883157337083632111098337 relative error = 7.2352361488080825653906053707657 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.4MB, time=64.33 NO POLE NO POLE x[1] = 0.739 y2[1] (analytic) = 1.2608575227054138533984167532507 y2[1] (numeric) = 1.260854184493053847779756358114 absolute error = 3.3382123600056186603951367e-06 relative error = 0.00026475730206556867205973830064351 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6735491060485658477979641282533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1941235674443628475246761930377 relative error = 7.2608940305297886973256003032031 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.74 y2[1] (analytic) = 1.2615314412704120902085754393012 y2[1] (numeric) = 1.2615280317027789293365508612583 absolute error = 3.4095676331608720245780429e-06 relative error = 0.00027027210909046408500378531098361 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6742879116281450674838811576082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1948623730239420672105932223926 relative error = 7.2865143717942860862247417481814 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.4MB, time=64.97 NO POLE NO POLE x[1] = 0.741 y2[1] (analytic) = 1.2622060983039075175621344192991 y2[1] (numeric) = 1.2622026161584857219344496598865 absolute error = 3.4821454217956276847594126e-06 relative error = 0.0002758777212750571381350910003841 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6750260429198688496821600265609 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1956005043156658494088720913453 relative error = 7.3120971974598871972759794748446 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.742 y2[1] (analytic) = 1.2628814931312431581850839235906 y2[1] (numeric) = 1.2628779371696900808346151154993 absolute error = 3.5559615530773504688080913e-06 relative error = 0.00028157523666456977967151075814896 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6757634991856059641799574634498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1963379605814029639066695282342 relative error = 7.3376425323523654859609949787623 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.743 y2[1] (analytic) = 1.2635576250770242410246837310994 y2[1] (numeric) = 1.2635539940450302787363192168814 absolute error = 3.6310319939622883645142180e-06 relative error = 0.00028736576171118013454996801569122 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.676500279687900206694845733414 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1970747410836972064215577981984 relative error = 7.3631504012649527391289252053945 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.4MB, time=65.60 NO POLE NO POLE x[1] = 0.744 y2[1] (analytic) = 1.2642344934651188766441779391716 y2[1] (numeric) = 1.2642307860922670057769435801012 absolute error = 3.7073728518708672343590704e-06 relative error = 0.00029325041129904562852095176284498 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6772363836899711363309554661397 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1978108450857681360576675309241 relative error = 7.3886208289583365102848310959776 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.745 y2[1] (analytic) = 1.2649120976186587333546280560096 y2[1] (numeric) = 1.2649083126182833695319794485112 absolute error = 3.7850003753638226486074984e-06 relative error = 0.00029923030876924313346673261437117 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6779718104557148123593551533613 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1985462718515118120860672181457 relative error = 7.4140538401606576486015180307971 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.4MB, time=66.24 NO POLE NO POLE x[1] = 0.746 y2[1] (analytic) = 1.2655904368600397140831882839174 y2[1] (numeric) = 1.2655865729290848950150276927477 absolute error = 3.8639309548190681605911697e-06 relative error = 0.00030530658594462626547186253061514 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6787065592497045303219305358001 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1992810206455015300486426005845 relative error = 7.4394494595675079211650280426061 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.747 y2[1] (analytic) = 1.266269510510922633977146125141 y2[1] (numeric) = 1.2662655663297995246777988107308 absolute error = 3.9441811231092993473144102e-06 relative error = 0.000311480383154599968957542149413 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6794406293371915574580277757215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2000150907329885571847398405059 relative error = 7.4648077118419277279658312704014 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=400.5MB, alloc=4.4MB, time=66.88 x[1] = 0.748 y2[1] (analytic) = 1.2669493178922338987430507063167 y2[1] (numeric) = 1.2669452921246776184101129276646 absolute error = 4.0257675562803329377786521e-06 relative error = 0.00031775284925981252196063166566687 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6801740199841058674531249885306 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.200748481379902867179837053315 relative error = 7.4901286216144039091494465333956 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.749 y2[1] (analytic) = 1.2676298583241661837202504824584 y2[1] (numeric) = 1.267625749617091953539899796037 absolute error = 4.1087070742301803506864214e-06 relative error = 0.00032412514167676509939346954722205 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6809067304570568745087973847929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2014811918528538742355094495773 relative error = 7.5154122134828676440419181386171 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.75 y2[1] (analytic) = 1.2683111311261791136881612469999 y2[1] (numeric) = 1.2683069381095377248331987956198 absolute error = 4.1930166413888549624513801e-06 relative error = 0.00033059842640233903286226860713322 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6816387600233341667332419527799 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2022132214191311664599540175643 relative error = 7.5406585120126924414672681059768 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.4MB, time=67.51 NO POLE NO POLE x[1] = 0.751 y2[1] (analytic) = 1.2689931356169999434065846406836 y2[1] (numeric) = 1.2689888569036325444941589334687 absolute error = 4.2787133673989124257072149e-06 relative error = 0.00033717387803824090734970617338674 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6823701079509082388516282910726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.202944569346705238578340355857 relative error = 7.5658675417366922208757299131905 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.752 y2[1] (analytic) = 1.2696758711146242388883966190315 y2[1] (numeric) = 1.2696715053001164421650388439233 absolute error = 4.3658145077967233577751082e-06 relative error = 0.00034385267981536563678143568895124 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6831007735084312242355428809353 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2036752349042282239622549457197 relative error = 7.5910393271551194838032516427375 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.4MB, time=68.16 NO POLE NO POLE x[1] = 0.753 y2[1] (analytic) = 1.270359336936316559403924605769 y2[1] (numeric) = 1.2703548825988518649262067886071 absolute error = 4.4543374646944777178171619e-06 relative error = 0.00035063602361807766219664674903364 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6838307559652376262507947690758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2044052173610346259775068338602 relative error = 7.6161738927356635751844330655286 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.754 y2[1] (analytic) = 1.2710435323986111402163313278786 y2[1] (numeric) = 1.2710389880988236772961406564274 absolute error = 4.5442997874629201906714512e-06 relative error = 0.00035752511000841041792951223005254 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6845600545913450489228513130465 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2051345159871420486495633778309 relative error = 7.6412712629134490340427327336982 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.755 y2[1] (analytic) = 1.2717284568173125760473225969591 y2[1] (numeric) = 1.2717238210981391612314279635755 absolute error = 4.6357191734148158946333836e-06 relative error = 0.00036452114825018421288141115646598 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6852886686574549269191733239135 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2058631300532519266458853886979 relative error = 7.666331462091034033083447590102 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.4MB, time=68.79 NO POLE NO POLE x[1] = 0.756 y2[1] (analytic) = 1.2724141095074965052724955712377 y2[1] (numeric) = 1.2724093808940280161267658535265 absolute error = 4.7286134684891457297177112e-06 relative error = 0.00037162535633304267562322831988102 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6860165974349532548477196239165 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2065910588307502545744316887009 relative error = 7.6913545146384089067166289464939 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.757 y2[1] (analytic) = 1.2731004897835102948456433029448 y2[1] (numeric) = 1.2730956667828423588149610970394 absolute error = 4.8230006679360306822059054e-06 relative error = 0.00037883896099640791371283324699261 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.686743840195911315870891720679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2073183015917083155976037854634 relative error = 7.7163404448929947670387549487574 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.4MB, time=69.43 NO POLE NO POLE x[1] = 0.758 y2[1] (analytic) = 1.2737875969589737259513306468032 y2[1] (numeric) = 1.273782678060056723566930092157 absolute error = 4.9188989170023844005546462e-06 relative error = 0.00038616319775335453924505769921488 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6874703962130864096341899840818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2080448576088834093609020488662 relative error = 7.7412892771596422073036308473205 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.759 y2[1] (analytic) = 1.274475430346779680385055877114 y2[1] (numeric) = 1.2744704140202680620916988642062 absolute error = 5.0163265116182933570129078e-06 relative error = 0.00039359931091440271427014954023763 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6881962647599225795088533972068 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2087707261557195792355654619912 relative error = 7.7662010357106300924146345369539 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.4MB, time=70.08 NO POLE NO POLE x[1] = 0.76 y2[1] (analytic) = 1.275163989259094827660311633333 y2[1] (numeric) = 1.2751588739571957435364030657975 absolute error = 5.1153018990841239085675355e-06 relative error = 0.00040114855361123037132180850430291 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6889214451105513391477556387697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2094959065063483388744677035541 relative error = 7.7910757447856644359720659339063 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.761 y2[1] (analytic) = 1.2758532730073603128418580871366 y2[1] (numeric) = 1.2758480571636815544862879768256 absolute error = 5.2158436787583555701103110e-06 relative error = 0.00040881218782030476588753416205051 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6896459365397923983538309412086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.210220397935589398080543005993 relative error = 7.81591342859187736341099483257 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.762 y2[1] (analytic) = 1.2765432809022924451045204977583 y2[1] (numeric) = 1.2765379629316896989647085044688 absolute error = 5.3179706027461398119932895e-06 relative error = 0.00041659148438643351923216592843771 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6903697383231543882603038560603 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2109441997189513879870159208447 relative error = 7.8407141113038261607666329400224 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.4MB, time=70.71 NO POLE NO POLE x[1] = 0.763 y2[1] (analytic) = 1.2772340122538833870168225968583 y2[1] (numeric) = 1.2772285905523067984331291831895 absolute error = 5.4217015765885836934136688e-06 relative error = 0.00042448772304623531155019830122448 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6910928497368355858219977464571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2116673111326325855487098112415 relative error = 7.8654778170634924086058818376643 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.764 y2[1] (analytic) = 1.277925466371401844548766519348 y2[1] (numeric) = 1.2779199393157418917911241747338 absolute error = 5.5270556599527576423446142e-06 relative error = 0.00043250219245153038697374032210883 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6918152700577246376169975154955 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2123897314535216373437095802799 relative error = 7.8902045699802812006653296762428 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.4MB, time=71.34 NO POLE NO POLE x[1] = 0.765 y2[1] (analytic) = 1.2786176425633937578030692724491 y2[1] (numeric) = 1.2786120085113264353763772681318 absolute error = 5.6340520673224266920043173e-06 relative error = 0.00044063619019265103350088620611513 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6925369985634012829579427688738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2131114599591982826846548336582 relative error = 7.9148943941310204467375854862449 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.766 y2[1] (analytic) = 1.2793105401376829924691650118068 y2[1] (numeric) = 1.2793047974275143029646818796975 absolute error = 5.7427101686895044831321093e-06 relative error = 0.00044889102282167220243380380240093 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6932580345321370763122283005656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.21383249592793407603894036535 relative error = 7.9395473135599602593494510919709 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=431.0MB, alloc=4.4MB, time=71.99 x[1] = 0.767 y2[1] (analytic) = 1.2800041584013720319992816707128 y2[1] (numeric) = 1.2799983053518817857699410530287 absolute error = 5.8530494902462293406176841e-06 relative error = 0.00045726800587556243342705957518713 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6939783772428961090303894813906 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.214552838638693108757101546175 relative error = 7.9641633522787724237770367666475 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.768 y2[1] (analytic) = 1.2806984966608426705058997664195 y2[1] (numeric) = 1.2806925315711275924441674590071 absolute error = 5.9650897150780617323074124e-06 relative error = 0.00046576846389925525274461369451981 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6946980259753357303819508221551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2152724873711327301086628869395 relative error = 7.9887425342665499509445279695173 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.769 y2[1] (analytic) = 1.2813935542217567063799004861449 y2[1] (numeric) = 1.2813874753710728490774833957984 absolute error = 6.0788506838573024170903465e-06 relative error = 0.00047439373046864121380856776910308 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6954169800098072678980166755753 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2159914414056042676247287403597 relative error = 8.0132848834698067127549067764678 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.4MB, time=72.62 NO POLE NO POLE x[1] = 0.77 y2[1] (analytic) = 1.2820893303890566366287094346757 y2[1] (numeric) = 1.282083136036661099198120788852 absolute error = 6.1943523955374305886458237e-06 relative error = 0.00048314514821348075059416197334976 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6961352386273567470198837344522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2167097000231537467465957992366 relative error = 8.0377904238024771594025229649946 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.771 y2[1] (analytic) = 1.2827858244669663519337417054856 y2[1] (numeric) = 1.2827795128519583037724211909013 absolute error = 6.3116150080481613205145843e-06 relative error = 0.00049202406884023801588373047734307 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.696852801109725610052955677546 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2174272625055226097796677423304 relative error = 8.0622591791459161182189961544647 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.4MB, time=73.27 NO POLE NO POLE x[1] = 0.772 y2[1] (analytic) = 1.2834830357589918324264532179796 y2[1] (numeric) = 1.2834766051001528412048357819635 absolute error = 6.4306588389912216174360161e-06 relative error = 0.00050103185315483587783736549453708 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6975696667393514344252410092942 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2181441281351484341519530740786 relative error = 8.0866911733488986736055119455824 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.773 y2[1] (analytic) = 1.2841809635679218441823025448716 y2[1] (numeric) = 1.2841744120635555073379253693398 absolute error = 6.5515043663368443771755318e-06 relative error = 0.00051016987108533224976994441050775 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6982858347993686502497158349369 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2188602961951656499764278997213 relative error = 8.1110864302276201276061516608929 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.774 y2[1] (analytic) = 1.2848796071958286364319267357915 y2[1] (numeric) = 1.2848729330235995154523603876153 absolute error = 6.6741722291209795663481762e-06 relative error = 0.00051943950170451792944297417775675 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6990013045736092571898340087447 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2195757659694062569165460735291 relative error = 8.1354449735656960406784670727505 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.4MB, time=73.89 NO POLE NO POLE x[1] = 0.775 y2[1] (analytic) = 1.2855789659440686394888339260045 y2[1] (numeric) = 1.2855721672608404962669208986588 absolute error = 6.7986832281432219130273457e-06 relative error = 0.00052884213325243612558543580187604 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.6997160753466035406274677899009 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2202905367424005403541798546853 relative error = 8.1597668271141623522190784288308 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.776 y2[1] (analytic) = 1.2862790391132831633929148026071 y2[1] (numeric) = 1.2862721140549564979384965916231 absolute error = 6.9250583266654544182109840e-06 relative error = 0.00053837916315882385075050314973439 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7004301464035807871325628381541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2210046077993777868592749029385 relative error = 8.1840520145914755804036361594389 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.4MB, time=74.54 NO POLE NO POLE x[1] = 0.777 y2[1] (analytic) = 1.2869798260033990972690742847478 y2[1] (numeric) = 1.2869727726847479860620867829449 absolute error = 7.0533186511112069875018029e-06 relative error = 0.00054805199806547536099469924986439 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7011435170304699992337920796493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2217179784262669989605041444337 relative error = 8.2083005596835131009020438881901 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.778 y2[1] (analytic) = 1.2876813259136296094002840592981 y2[1] (numeric) = 1.2876741424281378436708004163448 absolute error = 7.1834854917657294836429533e-06 relative error = 0.00055786205384852782423277329216351 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7018561865139006094894936723398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2224306479096976092162057371242 relative error = 8.23251248604357350403139277924 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.4MB, time=75.18 NO POLE NO POLE x[1] = 0.779 y2[1] (analytic) = 1.28838353814247484801435589898 y2[1] (numeric) = 1.2883762225621713712358560628272 absolute error = 7.3155803034767784998361528e-06 relative error = 0.00056781075564066940047536864034449 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7025681541412031938581790001042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2231426155370001935848910648886 relative error = 8.2566878172923770299106048529499 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.78 y2[1] (analytic) = 1.2890864619877226427837349762354 y2[1] (numeric) = 1.2890790123630162866665819206804 absolute error = 7.4496247063561171530555550e-06 relative error = 0.00057789953785326991849744099297984 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7032794192004101843678973251179 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2238538805962071840946093899023 relative error = 8.2808265770180660811823256988019 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.781 y2[1] (analytic) = 1.289790096746449207037611673102 y2[1] (numeric) = 1.2897825111059627253104158154767 absolute error = 7.5856404864817271958576253e-06 relative error = 0.00058812984419843433481341224587558 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7039899809802565810837444291757 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2245644423760535808104564939601 relative error = 8.3049287887762058128691450221179 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.4MB, time=75.82 NO POLE NO POLE x[1] = 0.782 y2[1] (analytic) = 1.2904944417150198406856496750424 y2[1] (numeric) = 1.2904867180654232399529052000721 absolute error = 7.7236495966007327444749703e-06 relative error = 0.00059850312771097916215024568882208 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7046998387701806633728032765141 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2252743001659776630995153412985 relative error = 8.3289944760897847989327566910316 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.783 y2[1] (analytic) = 1.2911994961890896338526274250576 y2[1] (numeric) = 1.2911916325149328008177071546066 absolute error = 7.8636741568330349202704510e-06 relative error = 0.0006090208507703320559120380608178 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.705408991860324700465805433254 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2259834532561217001925174980384 relative error = 8.3530236624492157751061984146479 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.4MB, time=76.46 NO POLE NO POLE x[1] = 0.784 y2[1] (analytic) = 1.2919052594636041712232893035015 y2[1] (numeric) = 1.2918972537271487955665883865041 absolute error = 8.0057364553756567009169974e-06 relative error = 0.00061968448512235474841938058572255 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.70611743954153566131480268186 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2266919009373326610415147466444 relative error = 8.3770163713123364575708348937478 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.785 y2[1] (analytic) = 1.2926117308328002370967021888034 y2[1] (numeric) = 1.2926035809738510292994252304724 absolute error = 8.1498589492077972769583310e-06 relative error = 0.00063049551190108952198368115497623 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7068251811053659237461389730047 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2273996425011629234728510377891 relative error = 8.4009726261044104370512672540994 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.786 memory used=461.5MB, alloc=4.4MB, time=77.10 y2[1] (analytic) = 1.293318909590206521149412344802 y2[1] (numeric) = 1.293310613525941724554203648503 absolute error = 8.2960642647965952086962990e-06 relative error = 0.00064145542165042941314090113506513 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.707532215844073982908013561925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2281066772398709826347256267094 relative error = 8.4248924502181281479028658109598 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.787 y2[1] (analytic) = 1.2940267950286443249066968715924 y2[1] (numeric) = 1.2940183506534455213070192298715 absolute error = 8.4443751988035996776417209e-06 relative error = 0.0006525657143457123416207797814342 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7082385430506251590119268817658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2288130044464221587386389465502 relative error = 8.4487758670136079117681327336798 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.788 y2[1] (analytic) = 1.2947353864402282689212032486917 y2[1] (numeric) = 1.2947267916255094769720771911373 absolute error = 8.5948147187919491260575544e-06 relative error = 0.00066382789941523935886663561594138 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7089441620186923043673014125252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2295186234144893040940134773096 relative error = 8.4726228998183970553796059933374 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=465.3MB, alloc=4.4MB, time=77.74 NO POLE NO POLE x[1] = 0.789 y2[1] (analytic) = 1.2954446831163670006582697919461 y2[1] (numeric) = 1.2954359357104030664016923761436 absolute error = 8.7474059639342565774158025e-06 relative error = 0.00067524349576171721214728557244465 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7096490720426565097085705110381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2302235334384535094352825758225 relative error = 8.4964335719274731020885160956598 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.79 y2[1] (analytic) = 1.296154684347763903087219138915 y2[1] (numeric) = 1.2961457821755181818862892560176 absolute error = 8.9021722457212009298828974e-06 relative error = 0.00068681403178362542151654700456761 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7103532724176078098140288749692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2309277338134048095407409397536 relative error = 8.5202079066032450366999025382318 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.4MB, time=78.38 NO POLE NO POLE x[1] = 0.791 y2[1] (analytic) = 1.2968653894244178039779161714986 y2[1] (numeric) = 1.2968563302873691331544019291704 absolute error = 9.0591370486708235142423282e-06 relative error = 0.00069854104539650806807722510445231 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.711056762439345888415739022023 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2316312238351428881424510868074 relative error = 8.5439459270755546431963876966559 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.792 y2[1] (analytic) = 1.2975767976356236859018810793109 y2[1] (numeric) = 1.2975675793115926473726741212969 absolute error = 9.2183240310385292069580140e-06 relative error = 0.00071042608405419049319547693450757 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7117595414043807823997888745235 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2323340028001777821265009393079 relative error = 8.5676476565416779149342919509374 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.793 y2[1] (analytic) = 1.2982889082699733969372475627432 y2[1] (numeric) = 1.2982795285129478691458591853759 absolute error = 9.3797570255277913883773673e-06 relative error = 0.00072247070476992110948802300190372 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7124616086099335852961962491652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2330360700057305850229083139496 relative error = 8.5913131181663265368972553225627 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.4MB, time=79.03 NO POLE NO POLE x[1] = 0.794 y2[1] (analytic) = 1.2990017206153563620768554708199 y2[1] (numeric) = 1.2989921771553163605168201016701 absolute error = 9.5434600400015600353691498e-06 relative error = 0.00073467647413743852556888824949912 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7131629633539371500577567620875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2337374247497341497844688268719 relative error = 8.6149423350816494395940077162244 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.795 y2[1] (analytic) = 1.2997152339589602953387664658126 y2[1] (numeric) = 1.2997055245017021009665294777261 absolute error = 9.7094572581943722369880865e-06 relative error = 0.00074704496835196418769423596115351 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.713863604935036791127132370486 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2344380663308337908538444352704 relative error = 8.6385353303872344241884020600185 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.4MB, time=79.67 NO POLE NO POLE x[1] = 0.796 y2[1] (analytic) = 1.3004294475872719125784906041565 y2[1] (numeric) = 1.3004195698142314874140695483744 absolute error = 9.8777730404251644210557821e-06 relative error = 0.00075957777323112074258345128711918 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7145635326525909857914784837286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.235137994048387985518190548513 relative error = 8.6620921271501098584512922253465 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.797 y2[1] (analytic) = 1.3011443607860776450022110215024 y2[1] (numeric) = 1.3011343123541533342166321757293 absolute error = 1.00484319243107855788457731e-05 relative error = 0.00077227648423577632682197624124704 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7152627458066720748239082894086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.235837207202469074550620354193 relative error = 8.6856127484047464431253005950171 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=480.6MB, alloc=4.4MB, time=80.32 x[1] = 0.798 y2[1] (analytic) = 1.3018599728404643533802932087375 y2[1] (numeric) = 1.301849751381838873169518849189 absolute error = 1.02214586254802107743595485e-05 relative error = 0.00078514270649081498936653587376071 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7159612436980669624110936529281 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2365357050938639621378057177125 relative error = 8.7090972171530590482949785464574 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.799 y2[1] (analytic) = 1.3025762830348200429603646655274 y2[1] (numeric) = 1.3025658861567817535061406854357 absolute error = 1.03968780382894542239800917e-05 relative error = 0.00079817805480583345477636778576658 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7166590256282778153663026630705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2372334870240748150930147278549 relative error = 8.7325455563644086193563169384766 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8 y2[1] (analytic) = 1.3032932906528345790792500183577 y2[1] (numeric) = 1.3032827159375980418980184284354 absolute error = 1.05747152365371812315899223e-05 relative error = 0.00081138415369576443588491455468198 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7173560908995227616271746105814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2379305522953197613538866753658 relative error = 8.7559577889756041521810129460799 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.4MB, time=80.96 NO POLE NO POLE x[1] = 0.801 y2[1] (analytic) = 1.3040109949775004034730459911998 y2[1] (numeric) = 1.3040002399820262224547824494379 absolute error = 1.07549954741810182635417619e-05 relative error = 0.00082476263740142670570520362735844 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.718052438814736588037533902042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2386269002105335877642459668264 relative error = 8.7793339378909047370723442904032 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.802 y2[1] (analytic) = 1.3047293952911132512846199187868 y2[1] (numeric) = 1.304718457546927196724172746977 absolute error = 1.09377441860545604471718098e-05 relative error = 0.00083831514991000213942886349233266 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7187480686775714374125451272789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2393225300733684371392571920633 relative error = 8.8026740259820216711109420713074 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.4MB, time=81.60 NO POLE NO POLE x[1] = 0.803 y2[1] (analytic) = 1.3054484908752728687678147950589 y2[1] (numeric) = 1.3054373678882842836920389468704 absolute error = 1.11229869885850757758481885e-05 relative error = 0.00085204334497543993843345029969125 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7194429797923975048865122152131 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2400174411881945046132242799975 relative error = 8.8259780760881206384901890403286 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.804 y2[1] (analytic) = 1.3061682810108837316876431526351 y2[1] (numeric) = 1.3061569702612032197823403022196 absolute error = 1.13107496805119053028504155e-05 relative error = 0.00086594888613878824925552875827629 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7201371714643037335426253304078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2407116328601007332693373951922 relative error = 8.849246111015823958442401263151 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.805 y2[1] (analytic) = 1.3068887649781557644157513731752 y2[1] (numeric) = 1.3068772639199121588571456934101 absolute error = 1.15010582436055586056797651e-05 relative error = 0.00088003344674845339151780683078528 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7208306429990985093239598806256 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.24140510439489550905067194541 relative error = 8.8724781535392129003583777250567 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.4MB, time=82.23 NO POLE NO POLE x[1] = 0.806 y2[1] (analytic) = 1.3076099420566050597204353332294 y2[1] (numeric) = 1.3075982481177616722166336281111 absolute error = 1.16939388433875038017051183e-05 relative error = 0.00089429870998038690981760962398342 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7215233937033103552250327244533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2420978550991073549517447892377 relative error = 8.8956742263998300657043245416278 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.807 y2[1] (analytic) = 1.3083318115250545992504875956188 y2[1] (numeric) = 1.3083199221072247485990922412758 absolute error = 1.18894178298506513953543430e-05 relative error = 0.00090874636885820066559113570976522 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7222154228841886247632213874979 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2427898842799856244899334522823 relative error = 8.9188343523066818363415780619723 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.4MB, time=82.86 NO POLE NO POLE x[1] = 0.808 y2[1] (analytic) = 1.3090543726616349747121556625597 y2[1] (numeric) = 1.3090422851398967941809192951413 absolute error = 1.20875217381805312363674184e-05 relative error = 0.00092337812627321018596331363110439 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7229067298497041947293528157898 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2434811912455011944560648805742 relative error = 8.941958553936240888855964304158 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.809 y2[1] (analytic) = 1.3097776247437851097384901136346 y2[1] (numeric) = 1.3097653364664956325766221792286 absolute error = 1.22882772894771618679344060e-05 relative error = 0.00093819569500440648757671028875521 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7235973139085501572167689158648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2441717753043471569434809806492 relative error = 8.9650468539324487745050408544903 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.4MB, time=83.51 NO POLE NO POLE x[1] = 0.81 y2[1] (analytic) = 1.3105015670482529824503607593199 y2[1] (numeric) = 1.3104890753368615048388179103425 absolute error = 1.24917113914776115428489774e-05 relative error = 0.00095320079773835659436488025465196 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7242871743701425109281768525145 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2448616357659395106548889172989 relative error = 8.9880992749067185643928716046333 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.811 y2[1] (analytic) = 1.311226198851096348708418249117 y2[1] (numeric) = 1.3112135009999570694582331325717 absolute error = 1.26978511392792501851165453e-05 relative error = 0.00096839516708903296919583052011538 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7249763105446208517595927974149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2455507719404178514863048621993 relative error = 9.0111158394379375594833845055669 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.812 y2[1] (analytic) = 1.3119515194276834660552778823829 y2[1] (numeric) = 1.3119386127038674023637041172888 absolute error = 1.29067238160636915737650941e-05 relative error = 0.00098378054561757208025995186710734 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7256647217428490626606885447446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.246239183138646062387400609529 relative error = 9.0340965700724700650647578958337 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.4MB, time=84.14 NO POLE NO POLE x[1] = 0.813 y2[1] (analytic) = 1.3126775280526938183472016797382 y2[1] (numeric) = 1.3126644096957999969221767631503 absolute error = 1.31183568938214250249165879e-05 relative error = 0.00099935868585196232401388172310267 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 2.7263524072764160027708511335054 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2469268686722130024975631982898 relative error = 9.0570414893241602292786719256079 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.814 y2[1] (analytic) = 1.3134042240001188410745540834314 y2[1] (numeric) = 1.3133908912220847639387065960966 absolute error = 1.33327780340771358474873348e-05 relative error = 0.0010151313503066615274173577643777 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7270393664576361958302663405423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2476138278534331955569784053267 relative error = 9.0799506196743349453296481587468 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.4MB, time=84.78 NO POLE NO POLE x[1] = 0.815 y2[1] (analytic) = 1.3141316065432626473703059662622 y2[1] (numeric) = 1.314118056528174031656458769352 absolute error = 1.35500150886157138471969102e-05 relative error = 0.0010311003115021442531142417327365 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7277255985995505178653376332361 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2483000599953475175920496980205 relative error = 9.1028239835718068169910826039731 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.816 y2[1] (analytic) = 1.314859674954742754705860940622 y2[1] (numeric) = 1.3148459048586425457567080634246 absolute error = 1.37700961002089491528771974e-05 relative error = 0.0010472673519843791321115846498105 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7284111030159268841477528965088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2489855644117238838744649612932 relative error = 9.1256616034328771870259552151183 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=511.1MB, alloc=4.4MB, time=85.41 x[1] = 0.817 y2[1] (analytic) = 1.315588428506490812273477271886 y2[1] (numeric) = 1.3155744354571874693588388861064 absolute error = 1.39930493033429146383857796e-05 relative error = 0.0010636342643442364494019121885474 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.72909587902126093542651197513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2496703404170579351532240399144 relative error = 9.1484635016413392281415723200789 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.818 y2[1] (analytic) = 1.316317866469753329054558013794 y2[1] (numeric) = 1.3163036475666283830203452724733 absolute error = 1.42189031249460342127413207e-05 relative error = 0.0010802028512368262088538783602124 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7297799259307767234322287993561 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2503543873265737231589408641405 relative error = 9.1712297005484810960990675007284 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.819 y2[1] (analytic) = 1.3170479881150924025730812975917 y2[1] (numeric) = 1.3170335404289072847368308848851 absolute error = 1.44476861851178362504127066e-05 relative error = 0.001096974925400766904565112756269 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7304632430604273956530225896556 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.25103770445622439537973465444 relative error = 9.1939602224730891445997511623412 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.4MB, time=86.05 NO POLE NO POLE x[1] = 0.82 y2[1] (analytic) = 1.3177787927123864483334420215631 y2[1] (numeric) = 1.3177641132850885899420090129855 absolute error = 1.46794272978583914330085776e-05 relative error = 0.0011139523096773852267285166343301 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7311458297268958793813133646877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2517202911226928791080254294721 relative error = 9.2166550897014512015717594130151 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.821 y2[1] (analytic) = 1.3185102795308309299419755031717 y2[1] (numeric) = 1.318495365375359131507702573702 absolute error = 1.49141554717984342729294697e-05 relative error = 0.001131136837029846930909492387598 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7318276852475955650308377057945 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2524021466433925647575497705789 relative error = 9.239314324487359906481808932105 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.4MB, time=86.69 NO POLE NO POLE x[1] = 0.822 y2[1] (analytic) = 1.3192424478389390899114329723498 y2[1] (numeric) = 1.3192272959390281597438441112461 absolute error = 1.51518999109301675888611037e-05 relative error = 0.0011485303505622191004666659340663 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7325088089406709887232014610491 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2530832703364679884499135258335 relative error = 9.2619379490521161082982162534957 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.823 y2[1] (analytic) = 1.3199752969045426811476781015192 y2[1] (numeric) = 1.3199599042145273423984757971132 absolute error = 1.53926900153387492023044060e-05 relative error = 0.0011661347035384640326726278354 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7331892001249985141432868023628 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2537636615207955138699988671472 relative error = 9.2845259855845323237326873357101 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.824 y2[1] (analytic) = 1.3207088259947926991178730857087 y2[1] (numeric) = 1.3206931894394107646577494300824 absolute error = 1.56365553819344601236556263e-05 relative error = 0.001183951759401364979904123901153 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7338688581201870136628317803018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2544433195159840133895438450862 relative error = 9.3070784562409362553897264479548 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.4MB, time=87.34 NO POLE NO POLE x[1] = 0.825 y2[1] (analytic) = 1.3214430343761601146994221046441 y2[1] (numeric) = 1.3214271508503549291459264362168 absolute error = 1.58835258051855534956684273e-05 relative error = 0.0012019833917913839780730156809441 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7345477822465785487315012530908 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2551222436423755484582133178752 relative error = 9.3295953831451743694538522803886 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.826 y2[1] (analytic) = 1.3221779213144366077089393179268 y2[1] (numeric) = 1.3221617876831587559253778688634 absolute error = 1.61336312778517835614490634e-05 relative error = 0.0012202314845654519952602526243579 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7352259718252490495347687987877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2558004332210460492614808635721 relative error = 9.3520767883886155325461437994853 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.4MB, time=87.97 NO POLE NO POLE x[1] = 0.827 y2[1] (analytic) = 1.3229134860747353011105078643946 y2[1] (numeric) = 1.3228970991727435824965844086531 absolute error = 1.63869019917186139234557415e-05 relative error = 0.0012386979318156916342950978852693 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.735903426178008993917929952807 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2564778875738059936446420175914 relative error = 9.3745226940301547073829687268813 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.828 y2[1] (analytic) = 1.3236497279214914959024956574681 y2[1] (numeric) = 1.3236330845531531637981363635006 absolute error = 1.66433683383321043592939675e-05 relative error = 0.0012573846378880726237909758506475 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7365801446274040855755678468317 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2571546060232010853022799116161 relative error = 9.3969331220962167068710736332696 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.4MB, time=88.61 NO POLE NO POLE x[1] = 0.829 y2[1] (analytic) = 1.3243866461184634066821930897261 y2[1] (numeric) = 1.3243697430575536722067336686046 absolute error = 1.69030609097344754594211215e-05 relative error = 0.0012762935174010003329076082852042 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7372561264967159315057930597084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2578305878925129312325051244928 relative error = 9.4193080945807600062745365197812 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.83 y2[1] (analytic) = 1.3251242399287328978875370821356 y2[1] (numeric) = 1.3251070739182336975371858864475 absolute error = 1.71660104992003503511956881e-05 relative error = 0.0012954264952638375458566260027273 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7379313711099627187285802261381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2585058325057597184552922909225 relative error = 9.441647633445280613090400418174 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.831 y2[1] (analytic) = 1.3258625086147062207151852362717 y2[1] (numeric) = 1.3258450763666042470424122067958 absolute error = 1.74322481019736727730294759e-05 relative error = 0.0013147855066953597329046302090574 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7386058777918998902675246848866 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.259180339187696889994236749671 relative error = 9.4639517606188159942711199902844 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.4MB, time=89.25 NO POLE NO POLE x[1] = 0.832 y2[1] (analytic) = 1.3266014514381147507142031715169 y2[1] (numeric) = 1.3265837496331987454134414466997 absolute error = 1.77018049160053007617248172e-05 relative error = 0.0013343724972421440553537816220958 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7392796458680208203943431848106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.259854107263817820121055249595 relative error = 9.4862204979979490604332623567348 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.833 y2[1] (analytic) = 1.3273410676600157260546274536119 y2[1] (numeric) = 1.3273230929476730347794120504934 absolute error = 1.79747123426912752154031185e-05 relative error = 0.0013541894227968923426954619192962 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.739952674664557489135443404258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2605271360603544888621554690424 relative error = 9.508453867446812206693208447026 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.4MB, time=89.89 NO POLE NO POLE x[1] = 0.834 y2[1] (analytic) = 1.3280813565407929864701658460576 y2[1] (numeric) = 1.328063105538805374707572089795 absolute error = 1.82510019876117625937562626e-05 relative error = 0.001374238249616688280837430986313 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7406249635084811560398877773265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2611994249042781557665998421109 relative error = 9.5306518907970914097719020481735 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.835 y2[1] (analytic) = 1.3288223173401577128742959417292 y2[1] (numeric) = 1.3288037866344964422032792635063 absolute error = 1.85307056612706710166782229e-05 relative error = 0.001394520954341189050999241265765 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.741296511727503033208077859075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2618709731233000329347899238594 relative error = 9.5528145898480303810119904488806 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.836 y2[1] (analytic) = 1.3295639493171491676490225586661 y2[1] (numeric) = 1.3295451354617693317100008978132 absolute error = 1.88138553798359390216608529e-05 relative error = 0.0014150395240107516595545163428926 % Correct digits = 4 h = 0.001 memory used=541.6MB, alloc=4.4MB, time=90.52 y1[1] (analytic) = 2.7419673186500749575804862010582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2625417800458719573071982658426 relative error = 9.5749419863664347749519931413972 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.837 y2[1] (analytic) = 1.3303062517301354356055536113409 y2[1] (numeric) = 1.3302871512467695551093139461854 absolute error = 1.91004833658804962396651555e-05 relative error = 0.0014357959560844941997721027429336 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7426373836053900624857634485088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2632118450011870622124755132932 relative error = 9.5970341020866764531034234652651 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.838 y2[1] (analytic) = 1.3310492238368141656161534967937 y2[1] (numeric) = 1.3310298332147650417209049893765 absolute error = 1.93906220491238952485074172e-05 relative error = 0.0014567922584582922870711100879532 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.743306705923383448447549111117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2638811673191804481742611759014 relative error = 9.6190909587106978025780723670068 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.4MB, time=91.15 NO POLE NO POLE x[1] = 0.839 y2[1] (analytic) = 1.3317928648942133129164323638407 y2[1] (numeric) = 1.331773180590146138302570235424 absolute error = 1.96843040671746138621284167e-05 relative error = 0.0014780304494827109100575141103406 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7439752849347328532493152006504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2645497463305298529760272654348 relative error = 9.6411125779080161092139436184842 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.84 y2[1] (analytic) = 1.3325371741586918820773289631291 y2[1] (numeric) = 1.3325171925964256090502155196492 absolute error = 1.99815622662730271134434799e-05 relative error = 0.0014995125579808719402523576805615 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7446431199708593212565726706296 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.265217581366656320983284735414 relative error = 9.6630989813157279848496058955976 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.4MB, time=91.80 NO POLE NO POLE x[1] = 0.841 y2[1] (analytic) = 1.3332821508859406706460441061175 y2[1] (numeric) = 1.3332618684562386355978563046573 absolute error = 2.02824297020350481878014602e-05 relative error = 0.0015212406232662575440536961245456 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7453102103639278719957713359055 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2658846717597248717224834006899 relative error = 9.6850501905385138483979990786157 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.842 y2[1] (analytic) = 1.3340277943309830134551810921098 y2[1] (numeric) = 1.3340072073913428170176176803374 absolute error = 2.05869396401964375634117724e-05 relative error = 0.0015432166951604497410963433087149 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7459765554468481679892246932965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2665510168426451677159367580809 relative error = 9.7069662271486424603720000075688 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.843 y2[1] (analytic) = 1.334774103748175527599348794266 y2[1] (numeric) = 1.3347532086226181698197343638626 absolute error = 2.08951255573577796144304034e-05 relative error = 0.0015654428340108063537852333485864 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7466421545532751818453918084153 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2672166159490721815721038731997 relative error = 9.7288471126859755105153167211015 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.4MB, time=92.44 NO POLE NO POLE x[1] = 0.844 y2[1] (analytic) = 1.3355210783912088580784824280462 y2[1] (numeric) = 1.3354998713700671279525506996897 absolute error = 2.12070211417301259317283565e-05 relative error = 0.0015879211107080735933798677970695 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7473070070176098626038491784596 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.267881468413406862330561243244 relative error = 9.7506928686579722581935399364642 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.845 y2[1] (analytic) = 1.3362687175131084241071363588314 y2[1] (numeric) = 1.3362471948528145428025206595595 absolute error = 2.15226602938813046156992719e-05 relative error = 0.0016106536067039355285989198485158 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7479711121749998013342862260498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2685455735707968010609982908342 relative error = 9.7725035165396942252014362026548 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.4MB, time=93.09 NO POLE NO POLE x[1] = 0.846 y2[1] (analytic) = 1.3370170203662351660890026394896 y2[1] (numeric) = 1.3369951782891076831942078424967 absolute error = 2.18420771274828947947969929e-05 relative error = 0.0016336424140285006832956637505567 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7486344693613398959888588251738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2692089307571368957155708899582 relative error = 9.7942790777738099406438187892222 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.847 y2[1] (analytic) = 1.3377659862022862932559083034306 y2[1] (numeric) = 1.3377438208963162353902854748098 absolute error = 2.21653059700578656228286208e-05 relative error = 0.001656889635307726010326538871626 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7492970779132730155072360069414 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2698715393090700152339480717258 relative error = 9.8160195737705997375485799708115 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=560.7MB, alloc=4.4MB, time=93.74 x[1] = 0.848 y2[1] (analytic) = 1.3385156142722960319705437742155 y2[1] (numeric) = 1.3384931218909323030915364100912 absolute error = 2.24923813637288790073641243e-05 relative error = 0.0016803973837807784892968932181899 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7499589371681906631736757401562 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2705333985639876629003878049406 relative error = 9.837725025907960600871711943055 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.849 y2[1] (analytic) = 1.3392659038266363746921740890535 y2[1] (numeric) = 1.3392430804885704074368531292172 absolute error = 2.28233380659672553209598363e-05 relative error = 0.0017041677833173345964198296212868 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7506200464642336392254664296844 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2711945078600306389521784944688 relative error = 9.8593954555314110665553831699381 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.85 y2[1] (analytic) = 1.3400168541150178296045839705385 y2[1] (numeric) = 1.339993695903967487003237740348 absolute error = 2.31582110503426013462301905e-05 relative error = 0.0017282029684348178952661493577926 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7512804051402927027120715242355 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2718548665360897024387835890199 relative error = 9.8810308839540961713013725271652 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.4MB, time=94.38 NO POLE NO POLE x[1] = 0.851 y2[1] (analytic) = 1.3407684643864901709055071187424 y2[1] (numeric) = 1.3407449673509828978058019789277 absolute error = 2.34970355072730997051398147e-05 relative error = 0.0017525050843155749977157015873884 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7519400125360092326043153744632 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2725144739318062323310274392476 relative error = 9.9026313324567924527233951810239 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.852 y2[1] (analytic) = 1.3415207338894431897567894342973 y2[1] (numeric) = 1.3414968940425984132977672076843 absolute error = 2.38398468447764590222266130e-05 relative error = 0.0017770762868239901449430526736172 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7525988679917758881529492322585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2731733293875728878796612970429 relative error = 9.9241968222879129995430817391055 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=568.3MB, alloc=4.4MB, time=95.02 NO POLE NO POLE x[1] = 0.853 y2[1] (analytic) = 1.3422736618716074458945352223685 y2[1] (numeric) = 1.3422494751909182243704644166295 absolute error = 2.41866806892215240708057390e-05 relative error = 0.0018019187425235386587833371292129 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7532569708487372684959370327215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2738314322445342682226490975059 relative error = 9.9457273746635125514955958382273 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.854 y2[1] (analytic) = 1.3430272475800550198984847674316 y2[1] (numeric) = 1.3430027100071689393533342230591 absolute error = 2.45375728860805451505443725e-05 relative error = 0.0018270346286937795143274902189557 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7539143204487905715138013515826 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.274488781844587571240513416367 relative error = 9.9672230107672926486120950074975 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.855 y2[1] (analytic) = 1.3437814902612002661198710095412 y2[1] (numeric) = 1.3437565977016995840139268715527 absolute error = 2.48925595006821059441379885e-05 relative error = 0.0018524261333472872850898428062521 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7545709161345862519323706827818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2751453775303832516590827475662 relative error = 9.9886837517506068295474553709929 % Correct digits = 2 h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.4MB, time=95.65 NO POLE NO POLE x[1] = 0.856 y2[1] (analytic) = 1.3445363891608005662670023942965 y2[1] (numeric) = 1.3445111374839816015579022339738 absolute error = 2.52516768189647091001603227e-05 relative error = 0.001878095455246523712575329639678 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7552267572495286786722699335127 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2758012186453256783989819982971 relative error = 10.010109618732465878622892546008 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.857 y2[1] (analytic) = 1.3452919435239570836478183109831 y2[1] (numeric) = 1.3452663285626088526290298094698 absolute error = 2.56149613482310187885015133e-05 relative error = 0.0019040448039206491525483743625248 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7558818431377767914444967872976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.276456304533573791171208852082 relative error = 10.03150063279954312125431896016 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.4MB, time=96.28 NO POLE NO POLE x[1] = 0.858 y2[1] (analytic) = 1.3460481525951155180686628763995 y2[1] (numeric) = 1.3460221701452976153091887244719 absolute error = 2.59824498179027594741519276e-05 relative error = 0.001930276399682274150770917453403 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7565361731442447565914273395692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2771106345400417563181394043536 relative error = 10.052856815006179767438481764173 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.859 y2[1] (analytic) = 1.3468050156180668613885221656564 y2[1] (numeric) = 1.3467786614388865851183677326953 absolute error = 2.63541791802762701544329611e-05 relative error = 0.0019567924736441514014330968114988 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.757189746614602622172595164811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2777642080103996218993072295954 relative error = 10.074178186374390302970125568308 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.4MB, time=96.92 NO POLE NO POLE x[1] = 0.86 y2[1] (analytic) = 1.3475625318359481537279693357761 y2[1] (numeric) = 1.347535801649336875014665215139 absolute error = 2.67301866112787133041206371e-05 relative error = 0.0019835952677358083419468255496377 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7578425628952769722945887295286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.278417024291073972021300794313 relative error = 10.095464767893867928064620389059 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.861 y2[1] (analytic) = 1.3483207004912432403320614332074 y2[1] (numeric) = 1.3482935899817320153942891800859 absolute error = 2.71105095112249377722531215e-05 relative error = 0.0020106870347201206382099866715791 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7584946213334515806844128212126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.279069082729248580411124885997 relative error = 10.116716580521990043061687470593 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.862 y2[1] (analytic) = 1.3490795208257835290864310224247 y2[1] (numeric) = 1.3490520256402779540915572631028 absolute error = 2.74951855055749948737593219e-05 relative error = 0.0020380700382098268148772313163247 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7591459212770680635056604199826 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.279720382672865063232372484767 relative error = 10.13793364518382378088704405207 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.4MB, time=97.55 NO POLE NO POLE x[1] = 0.863 y2[1] (analytic) = 1.3498389920807487486858151195816 y2[1] (numeric) = 1.3498111078283030563788967270404 absolute error = 2.78842524456923069183925412e-05 relative error = 0.0020657465526839842855924746691808 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7597964620748265314168421967984 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2803709234706235311435542615828 relative error = 10.159115982772131585949972699269 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.864 y2[1] (analytic) = 1.3505991134966677074542632627533 y2[1] (numeric) = 1.3505708357482581049668444620332 absolute error = 2.82777484096024874188007201e-05 relative error = 0.0020937188635043670385481827917166 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7604462430761862408712215799592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2810207044719832405979336447436 relative error = 10.180263614147376839156001516383 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.4MB, time=98.18 NO POLE NO POLE x[1] = 0.865 y2[1] (analytic) = 1.3513598843134190528162658986232 y2[1] (numeric) = 1.3513312086017163000040469854997 absolute error = 2.86757117027528122189131235e-05 relative error = 0.0021219892669318052331374841443351 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7610952636313662446575040901144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2816697250271632443842161548988 relative error = 10.201376560137729528715058413238 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.866 y2[1] (analytic) = 1.3521213037702320314180436145485 y2[1] (numeric) = 1.3520922255893732590772604421422 absolute error = 2.90781808587723407831724063e-05 relative error = 0.0021505600701424669638570718799273 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7617435230913460416807304031469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2823179844871430414074424679313 relative error = 10.222454841539071966426635633953 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=591.2MB, alloc=4.4MB, time=98.82 x[1] = 0.867 y2[1] (analytic) = 1.3528833711056872498982370947791 y2[1] (numeric) = 1.3528538859110470172113506039469 absolute error = 2.94851946402326868864908322e-05 relative error = 0.0021794335912440824480018370787399 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7623910208078662259827233600927 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2829654822036632257094354248771 relative error = 10.24349847911500454912466996698 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.868 y2[1] (analytic) = 1.3536460855577174363072370302028 y2[1] (numeric) = 1.3536161887656780268692928701839 absolute error = 2.98967920394094379441600189e-05 relative error = 0.0022086121592921108940662394679352 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.763037756133429135001439903703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2836122175292261347281519684874 relative error = 10.264507493596851564966009463156 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.869 y2[1] (analytic) = 1.3544094463636082021743925623504 y2[1] (numeric) = 1.3543791333513291579521722674072 absolute error = 3.03130122790442222202949432e-05 relative error = 0.0022380981143058503081326309255771 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7636837284212994970685796823498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2842581898170964967952917471342 relative error = 10.28548190568366704424749909902 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=595.0MB, alloc=4.4MB, time=99.46 NO POLE NO POLE x[1] = 0.87 y2[1] (analytic) = 1.3551734527599988052223361945172 y2[1] (numeric) = 1.3551427188651856977991834494546 absolute error = 3.07338948131074231527450626e-05 relative error = 0.0022678938072844904958831486239993 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7643289370255050781448028237228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2849033984213020778715148885072 relative error = 10.306421736042240654437875647675 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.871 y2[1] (analytic) = 1.3559381039828829127276624557362 y2[1] (numeric) = 1.3559069445035553511876306974479 absolute error = 3.11594793275615400317582883e-05 relative error = 0.002298001600223109518219438671039 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7649733813008373277919101431513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2855478426966343275186222079357 relative error = 10.327327005307103639111816069062 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.4MB, time=100.10 NO POLE NO POLE x[1] = 0.872 y2[1] (analytic) = 1.3567033992676093655271969569926 y2[1] (numeric) = 1.3566718094618682403329279197928 absolute error = 3.15898057411251942690371998e-05 relative error = 0.0023284238661286138588134094002523 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7656170606028520243813398144258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2861915219986490241080518792102 relative error = 10.348197734080534800474634016756 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.873 y2[1] (analytic) = 1.3574693378488829426690918334692 y2[1] (numeric) = 1.3574373129346769048885986521787 absolute error = 3.20249142060377804931812905e-05 relative error = 0.0023591629890356225622424938330489 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7662599742878699195383352946765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2868344356836669192650473594609 relative error = 10.369033942932566525167265589351 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.874 y2[1] (analytic) = 1.3582359189607651267079829217956 y2[1] (numeric) = 1.358203454115656301946276057579 absolute error = 3.24648451088247617068642166e-05 relative error = 0.0023902213640222956016845764598603 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7669021217129773818211400591947 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2874765831087743815478521239791 relative error = 10.389835652400990853042328241819 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.4MB, time=100.74 NO POLE NO POLE x[1] = 0.875 y2[1] (analytic) = 1.359003141836674869643443377204 y2[1] (numeric) = 1.3589702321976038060357029262511 absolute error = 3.29096390710636077404509529e-05 relative error = 0.0024216013972261067354608579910966 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7675435022360270396345754670545 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2881179636318240393612875318389 relative error = 10.410602882991365588603175826304 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.876 y2[1] (analytic) = 1.3597710057093893595009677922045 y2[1] (numeric) = 1.359737646372439209124731675736 absolute error = 3.33593369501503762361164685e-05 relative error = 0.0024533055058595611120195455306458 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.768184115215638423377358844013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2887585766114354231040709087974 relative error = 10.431335655177020454799008063334 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.4MB, time=101.38 NO POLE NO POLE x[1] = 0.877 y2[1] (analytic) = 1.3605395098110447875547202358586 y2[1] (numeric) = 1.3605056958312047206193243508589 absolute error = 3.38139798400669353958849997e-05 relative error = 0.0024853361182258578832494132351562 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7688239600111986068225196354215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2893984214069956065492317002059 relative error = 10.452033989399063288870224363298 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.878 y2[1] (analytic) = 1.3613086533731371161912789909656 y2[1] (numeric) = 1.3612743797640649673635526237286 absolute error = 3.42736090721488277263672370e-05 relative error = 0.0025176956737344980863000316551577 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.769463035982862847730272248788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2900374973786598474569843135724 relative error = 10.472697906066386279939339835383 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.4MB, time=102.02 NO POLE NO POLE x[1] = 0.879 y2[1] (analytic) = 1.3620784356265228474136101254846 y2[1] (numeric) = 1.362043697360306993639597793738 absolute error = 3.47382662158537740123317466e-05 relative error = 0.0025503866229168380543648619668533 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7701013424915552276927049731688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2906758038873522274194170379532 relative error = 10.493327425555672248043905546588 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.88 y2[1] (analytic) = 1.3628488558014197919845013942779 y2[1] (numeric) = 1.3628136478083402611677507875638 absolute error = 3.52079930795308167506067141e-05 relative error = 0.0025834114274415886171545043734306 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.770738878898969291209645130756 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2913133402947662909363571955404 relative error = 10.513922568211400964308995638046 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.881 y2[1] (analytic) = 1.3636199131274078392086873278103 y2[1] (numeric) = 1.3635842302956966491064121591666 absolute error = 3.56828317111901022751686437e-05 relative error = 0.0026167725601302603520502293126728 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.771375644567568683995061384847 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2919501059633656837217734496314 relative error = 10.534483354345855511957940779423 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.4MB, time=102.64 NO POLE NO POLE x[1] = 0.882 y2[1] (analytic) = 1.3643916068334297273528957257406 y2[1] (numeric) = 1.3643554440090304540520920897908 absolute error = 3.61628243992733008036359498e-05 relative error = 0.0026504725049725551471825544073256 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.772011638860587790513364897848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2925861002563847902400769626324 relative error = 10.555009804239128687861100655412 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.883 y2[1] (analytic) = 1.3651639361477918147030451354242 y2[1] (numeric) = 1.3651272881341183900394103879648 absolute error = 3.66480136734246636347474594e-05 relative error = 0.0026845137571417043379261109216032 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7726468611420323707449718030637 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2932213225378293704716838678481 relative error = 10.575501938139129444323577741384 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.4MB, time=103.29 NO POLE NO POLE x[1] = 0.884 y2[1] (analytic) = 1.3659369002981648512578222581931 y2[1] (numeric) = 1.3658997618558595885410964895008 absolute error = 3.71384423052627167257686923e-05 relative error = 0.0027188988230097536785404201457215 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7732813107766801961804902247626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.293855772172477195907202289547 relative error = 10.59595977626158937081388054835 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.885 y2[1] (analytic) = 1.3667104985115847510578675899006 y2[1] (numeric) = 1.3666728643582755984679894574949 absolute error = 3.76341533091525898781324057e-05 relative error = 0.0027536302201627954109165229781706 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7739149871300816850428958523849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2944894485258786847696079171693 relative error = 10.616383338790069215336646811076 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.886 y2[1] (analytic) = 1.3674847300144533651497969666091 y2[1] (numeric) = 1.3674465948245103861690379823271 absolute error = 3.81351899429789807589842820e-05 relative error = 0.0027887104774161476926117251709544 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7745478895685605367370608467703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2951223509643575364637729115547 relative error = 10.636772645875965445153635767425 % Correct digits = 1 h = 0.001 memory used=621.8MB, alloc=4.4MB, time=103.94 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.887 y2[1] (analytic) = 1.3682595940325392551842860514642 y2[1] (numeric) = 1.3682209524368303354313003816613 absolute error = 3.86415957089197529856698029e-05 relative error = 0.0028241421348294816465690862185784 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7751800174592143655260016289292 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2957544788550113652527136937136 relative error = 10.65712771763851684655829374219 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.888 y2[1] (analytic) = 1.3690350897909784676474441647341 y2[1] (numeric) = 1.3689959363766242474799446004453 absolute error = 3.91534143542201674995642888e-05 relative error = 0.0028599277437218962951247416456214 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7758113701699153334332118751625 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2963858315657123331599239399469 relative error = 10.677448574164811163410288715048 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.4MB, time=104.60 NO POLE NO POLE x[1] = 0.889 y2[1] (analytic) = 1.369811216514275308724703225707 y2[1] (numeric) = 1.3697715458244033409782482109108 absolute error = 3.96706898719677464550147962e-05 relative error = 0.0028960698666869416411047568716082 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7764419470693107823704478162497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2970164084651077820971598810341 relative error = 10.697735235509791774137497429935 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.89 y2[1] (analytic) = 1.3705879734263031197964469426198 y2[1] (numeric) = 1.3705477799598012520275984125733 absolute error = 4.01934665018677688485300465e-05 relative error = 0.0029325710776075901590040150150705 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7770717475268238654903337129732 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2976462089226208652170457777576 relative error = 10.717987721696264406914012902407 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.4MB, time=105.22 NO POLE NO POLE x[1] = 0.891 y2[1] (analytic) = 1.3713653597503050535646047550548 y2[1] (numeric) = 1.3713246379615740341674920322322 absolute error = 4.07217887310193971127228226e-05 relative error = 0.0029694339616711569594226919176601 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7777007709126541777631561554249 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2982752323084511774898682202093 relative error = 10.738206052714903892723820912406 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.892 y2[1] (analytic) = 1.3721433747088948508094344022757 y2[1] (numeric) = 1.3721021190076001583755355239708 absolute error = 4.12557012946924338988783049e-05 relative error = 0.0030066611153841688901112183991739 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7783290165977783857772166093547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2989034779935753855039286741391 relative error = 10.758390248524260956020871242713 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.893 y2[1] (analytic) = 1.3729220175240576177757163607833 y2[1] (numeric) = 1.3728802222748805130674449691562 absolute error = 4.17952491771047082713916271e-05 relative error = 0.0030442551465871828371423221673176 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7789564839539508567621124092591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2995309453497478564888244740435 relative error = 10.77854032905076904269734304801 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.4MB, time=105.86 NO POLE NO POLE x[1] = 0.894 y2[1] (analytic) = 1.373701287417150604187582764963 y2[1] (numeric) = 1.3736589469395384040970460764396 absolute error = 4.23404776122000905366885234e-05 relative error = 0.0030822186744695534898888302642356 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7795831723537042868343171749836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.300157633749501286561029239768 relative error = 10.798656314188751185072973826444 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.895 y2[1] (analytic) = 1.3744811836089039818912027960585 y2[1] (numeric) = 1.3744382921768195547562741817559 absolute error = 4.28914320844271349286143026e-05 relative error = 0.0031205543295841508336384463977891 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.780209081170350328464432406308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3007835425661473281911444710924 relative error = 10.818738223800426903619388024426 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.4MB, time=106.49 NO POLE NO POLE x[1] = 0.896 y2[1] (analytic) = 1.3752617053194216241245458968532 y2[1] (numeric) = 1.375218257161092105775174248324 absolute error = 4.34481583295183493716485292e-05 relative error = 0.0031592647538620276338217461811062 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7808342097779802171654827883184 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3014086711737772168921948531028 relative error = 10.838786077715919145134424346859 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.897 y2[1] (analytic) = 1.3760428517681818854134435423582 y2[1] (numeric) = 1.3759988410658466153219008666465 absolute error = 4.40107023352700915426757117e-05 relative error = 0.003198352600627037175967206373929 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7814585575514653974016285193201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3020330189472623971283405841045 relative error = 10.858799895733261257082520378351 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=640.8MB, alloc=4.4MB, time=107.13 x[1] = 0.898 y2[1] (analytic) = 1.3768246221740383820931696705131 y2[1] (numeric) = 1.3767800430636960590027182545101 absolute error = 4.45791103423230904514160030e-05 relative error = 0.0032378205346104015256272518532279 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7820821238664581477166687526331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3026565852622551474433808174175 relative error = 10.878779697618403997818269157053 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.899 y2[1] (analytic) = 1.3776070157552207734547592513822 y2[1] (numeric) = 1.3775618623263758298620002569853 absolute error = 4.51534288449435927589943969e-05 relative error = 0.0032776712319652305726421149445733 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7827049080993922050817110238177 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3032793694951892048084230886021 relative error = 10.898725503105222582411314890871 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9 y2[1] (analytic) = 1.3783900317293355435152838485929 y2[1] (numeric) = 1.3783442980247437383822303464265 absolute error = 4.57337045918051330535021664e-05 relative error = 0.0033179073802809921242238059049881 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7833269096274833884613823157136 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.303901371023280388188094380498 relative error = 10.91863733189552376379180407652 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.4MB, time=107.76 NO POLE NO POLE x[1] = 0.901 y2[1] (analytic) = 1.3791736693133667834113024028072 y2[1] (numeric) = 1.3791273493287800124840016224719 absolute error = 4.63199845867709273007803353e-05 relative error = 0.003358531678597933311450740195672 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7839481278287302215979581951327 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3045225892245272213246702599171 relative error = 10.938515203659052948936653884742 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.902 y2[1] (analytic) = 1.3799579277236769744147048438388 y2[1] (numeric) = 1.3799110154075872975260168120436 absolute error = 4.69123160896768886880317952e-05 relative error = 0.0033995468374214535738646063045143 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7845685620819145550127872371293 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3051430234777115547394993019137 relative error = 10.958359138033501349817941820303 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.4MB, time=108.40 NO POLE NO POLE x[1] = 0.903 y2[1] (analytic) = 1.380742806176007771570165515639 y2[1] (numeric) = 1.3806952954293906563050882693477 absolute error = 4.75107466171152650772462913e-05 relative error = 0.0034409555787364294869549376219319 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7851882117666021872243887354735 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3057626731623991869511008002579 relative error = 10.978169154624513168835759362738 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.904 y2[1] (analytic) = 1.3815283038854807879534227767624 y2[1] (numeric) = 1.3814801885615375690561379758741 absolute error = 4.81153239432188972848008883e-05 relative error = 0.0034827606360214916974036213404125 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7858070762631434851826024812843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3063815376589404849093145460687 relative error = 10.997945273005692818458907553547 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.905 y2[1] (analytic) = 1.3823144200665983795496005180982 y2[1] (numeric) = 1.3822656939704979334521975403965 absolute error = 4.87260961004460974029777017e-05 relative error = 0.003524964754263254231041286282557 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7864251549526740039181701757212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3069996163484710036448822405056 relative error = 11.017687512718612174797844327024 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.4MB, time=109.02 NO POLE NO POLE x[1] = 0.906 y2[1] (analytic) = 1.3831011539332444307507867196122 y2[1] (numeric) = 1.3830518108218640646044081989727 absolute error = 4.93431113803661463785206395e-05 relative error = 0.0035675706899704964385402089163683 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.787042447217115105407128827208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3076169086129121051338408919924 relative error = 11.037395893272817864835321795661 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.907 y2[1] (analytic) = 1.3838885046986851404720835485838 y2[1] (numeric) = 1.3838385382803506950620208149442 absolute error = 4.99664183344454100627336396e-05 relative error = 0.0036105812111882978439341111283062 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7876589524391745766493972688437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3082334138349715763761093336281 relative error = 11.057070434145838587041176706266 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.4MB, time=109.64 NO POLE NO POLE x[1] = 0.908 y2[1] (analytic) = 1.3846764715755698088853428833566 y2[1] (numeric) = 1.3846258755097949748123958789364 absolute error = 5.05960657748340729470044202e-05 relative error = 0.0036539990975121261611140442286045 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7882746700023472469609377174681 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3088491313981442466876497822525 relative error = 11.076711154783192465098758890113 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.909 y2[1] (analytic) = 1.3854650537759316247698005289301 y2[1] (numeric) = 1.3854138216731564712810035088587 absolute error = 5.12321027751534887970200714e-05 relative error = 0.0036978271401018787435015089859226 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.78888959929091560447887508227 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3094640606867126042055871470544 relative error = 11.096318074598394434471500748796 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.4MB, time=110.28 NO POLE NO POLE x[1] = 0.91 y2[1] (analytic) = 1.3862542505111884534788217738253 y2[1] (numeric) = 1.3862023759325171693314234499043 absolute error = 5.18745786712841473983239210e-05 relative error = 0.0037420681416958777321451009872436 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7895037396899504118789575178716 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.310078201085747411605669582656 relative error = 11.115891212972963661539145657316 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.911 y2[1] (analytic) = 1.3870440609921436255219703215436 y2[1] (numeric) = 1.3869915374490814712653450745503 absolute error = 5.25235430621542566252469933e-05 relative error = 0.0037867249166248191675253419518873 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7901170905853113213047425044789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3106915519811083210314545692633 relative error = 11.135430589256430995034164636675 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.912 y2[1] (analytic) = 1.387834484428986725761612014616 y2[1] (numeric) = 1.3877813053831761968225673825577 absolute error = 5.31790458105289390446320583e-05 relative error = 0.0038318002908256763303840101555054 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7907296513636474885078935259636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.311304112759444488234605590748 relative error = 11.154936222766346449509898759956 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.4MB, time=110.90 NO POLE NO POLE x[1] = 0.913 y2[1] (analytic) = 1.3886255200312943832232641547054 y2[1] (numeric) = 1.3885716788942505831809990009713 absolute error = 5.38411370438000422651537341e-05 relative error = 0.0038772971018555575769192648285204 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7913414214123981861989732056309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3119158828081951859256852704153 relative error = 11.174408132788286720572969518052 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.914 y2[1] (analytic) = 1.3894171670080310615189006084766 y2[1] (numeric) = 1.3893626571408762849566581841199 absolute error = 5.45098671547765622424243567e-05 relative error = 0.0039232181989055189337062185612165 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7919524001197934166081195489314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3125268615155904163348316137158 relative error = 11.193846338575862731613500793778 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.4MB, time=111.54 NO POLE NO POLE x[1] = 0.915 y2[1] (analytic) = 1.390209424567549849882422275997 y2[1] (numeric) = 1.3901542392807473742036728136161 absolute error = 5.51852868024756787494623809e-05 relative error = 0.0039695664428143317177143974916586 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7925625868748545232549927324916 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.313137048270651522981704797276 relative error = 11.213250859350727211767694185639 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.916 y2[1] (analytic) = 1.3910022919175932548165018862618 y2[1] (numeric) = 1.3909464244706803404142803983564 absolute error = 5.58674469129144022214879054e-05 relative error = 0.0040163447060822054467987882157857 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7931719810673948019273806695674 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3137464424631918016540927343518 relative error = 11.232621714302582304848294194797 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=671.3MB, alloc=4.4MB, time=112.16 x[1] = 0.917 y2[1] (analytic) = 1.3917957682652939923500114730661 y2[1] (numeric) = 1.3917392118666140905188280745212 absolute error = 5.65563986799018311833985449e-05 relative error = 0.0040635558728844663060399524737788 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7937805820880201108678523733656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.31435504348381711059456443815 relative error = 11.251958922589187208979471250428 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.918 y2[1] (analytic) = 1.3925898528171757809052402738607 y2[1] (numeric) = 1.3925326006236099488857726055748 absolute error = 5.72521935658320194676682859e-05 relative error = 0.0041112028390851914353010425416041 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7943883893281294801678489316321 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3149628507239264798945609964165 relative error = 11.271262503336365846673638709412 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.919 y2[1] (analytic) = 1.3933845447791541347741101844421 y2[1] (numeric) = 1.3933265898958516573216803822653 absolute error = 5.79548833024774524298021768e-05 relative error = 0.00415928851225079930335552090107 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7949954021799157203686026984643 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3155698635757127200953147632487 relative error = 11.290532475638014565088704835516 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.4MB, time=112.79 NO POLE NO POLE x[1] = 0.92 y2[1] (analytic) = 1.3941798433565371582025952933256 y2[1] (numeric) = 1.3941211788366453750712274226249 absolute error = 5.86645198917831313678707007e-05 relative error = 0.0042078158116635964339190237932363 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7956016200363660302682761024816 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.316176081432163029994988167266 relative error = 11.309768858556109866205242351083 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.921 y2[1] (analytic) = 1.3949757477540263400825514114488 y2[1] (numeric) = 1.3949163665984196788171993719694 absolute error = 5.93811556066612653520394794e-05 relative error = 0.0042567876683352807488921586776386 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7962070422912626039347122642647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3167815036870596036614243290491 relative error = 11.328971671120716166664036469614 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.4MB, time=113.41 NO POLE NO POLE x[1] = 0.922 y2[1] (analytic) = 1.3957722571757173492501609054418 y2[1] (numeric) = 1.3957121523327255626804915028986 absolute error = 6.01048429917865696694025432e-05 relative error = 0.0043062070250204017940881368280621 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7968116683391832369231904103635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3173861297349802366499024751479 relative error = 11.348140932329993587005447370691 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.923 y2[1] (analytic) = 1.3965693708251008303901975360864 y2[1] (numeric) = 1.3965085351902364382201087152963 absolute error = 6.08356348643921700888207901e-05 relative error = 0.0043560768362297781126800629817708 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.797415497575501931698579866169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3179899589712989314252919309534 relative error = 11.367276661150205770052994878714 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.924 y2[1] (analytic) = 1.3973670879050632005453153977649 y2[1] (numeric) = 1.39730551432074813443316553633 absolute error = 6.15735843150661121498614349e-05 relative error = 0.0044064000682438720315574804165989 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7980185293963895022612872055464 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3185929907921865019879992703308 relative error = 11.386378876515727728184541663484 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.4MB, time=114.03 NO POLE NO POLE x[1] = 0.925 y2[1] (analytic) = 1.3981654076178874462295654496762 y2[1] (numeric) = 1.3981030888731788977548861204512 absolute error = 6.23187447085484746793292250e-05 relative error = 0.0044571796991261221257304501497589 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7986207631988141779763919313308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3191952245946111777031039961152 relative error = 11.40544759732905371923541660328 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.926 y2[1] (analytic) = 1.3989643291652539211453425253694 y2[1] (numeric) = 1.3989012579955693920586042493953 absolute error = 6.30711696845290867382759741e-05 relative error = 0.004508418718736233625862074197712 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7992221983805422066053668576022 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3197966597763392063320789223866 relative error = 11.424482842460805150778782049361 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.4MB, time=114.65 NO POLE NO POLE x[1] = 0.927 y2[1] (analytic) = 1.3997638517482411445029651037137 y2[1] (numeric) = 1.3997000208350826986557633321815 absolute error = 6.38309131584458472017715322e-05 relative error = 0.0045601201287434270339470016790272 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.7998228343401384565397801620681 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3203972957359354562664922268525 relative error = 11.443484630749738512529507614047 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.928 y2[1] (analytic) = 1.4005639745673265999420895217925 y2[1] (numeric) = 1.4004993765380043162959164051129 absolute error = 6.45980293222836461731166796e-05 relative error = 0.0046122869426396452120841305883115 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8004226704769670182363768749028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3209971318727640179630889396872 relative error = 11.462452981002753336618768782354 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=690.4MB, alloc=4.4MB, time=115.28 x[1] = 0.929 y2[1] (analytic) = 1.4013646968223875350541597083728 y2[1] (numeric) = 1.4012993242497421611667261317765 absolute error = 6.53725726453738874335765963e-05 relative error = 0.0046649221857527192092164835975168 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8010217061911918048529383690117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3215961675869888045796504337961 relative error = 11.481387911994900185487541128929 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.93 y2[1] (analytic) = 1.402166017712701761505092915567 y2[1] (numeric) = 1.4020998631148265668939648030432 absolute error = 6.61545978751946111281125238e-05 relative error = 0.004718028895259493090630140504899 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8016199408837771520843192159106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.322194402279574151811031280695 relative error = 11.500289442469388667148110217096 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.931 y2[1] (analytic) = 1.4029679364369484557574013260696 y2[1] (numeric) = 1.4029009922769102845415143370677 absolute error = 6.69441600381712158869890019e-05 relative error = 0.0047716101201989080349171994183979 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8022173739564884171980615712348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3227918353522854169247736360192 relative error = 11.519157591137595477563663374874 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.4MB, time=115.90 NO POLE NO POLE x[1] = 0.932 y2[1] (analytic) = 1.4037704521932089603909488139114 y2[1] (numeric) = 1.4037027108787684826113662792888 absolute error = 6.77413144404777795825346226e-05 relative error = 0.0048256689214850459630150594826382 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.802814004811892577268988054311 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3233884662076895769957001190954 relative error = 11.537992376679072469896972492766 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.933 y2[1] (analytic) = 1.4045735641789675860215415380431 y2[1] (numeric) = 1.4045050180622987470436218024289 absolute error = 6.85461166688389779197356142e-05 relative error = 0.0048802083719201329638359175642019 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8034098328533588266121748872515 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3239842942491558263388869520359 relative error = 11.556793817741554750380116779881 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=698.0MB, alloc=4.4MB, time=116.53 NO POLE NO POLE x[1] = 0.934 y2[1] (analytic) = 1.4053772715911124138165504502244 y2[1] (numeric) = 1.4053079129685210812164917064945 absolute error = 6.93586225913326000587437299e-05 relative error = 0.0049352315562075027808962945319309 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8040048574850591734137078606457 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3245793188808561731404199254301 relative error = 11.575561932940968800558131057383 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.935 y2[1] (analytic) = 1.4061815736259360986067632016613 y2[1] (numeric) = 1.4061113947375779059462964187759 absolute error = 7.01788883581926604667828854e-05 relative error = 0.0049907415709645206242467010835705 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8045990781119690355586244951433 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3251735395077660352853365599277 relative error = 11.594296740861440625660398671 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.936 y2[1] (analytic) = 1.4069864694791366725936623366093 y2[1] (numeric) = 1.4069154625087340594874659938472 absolute error = 7.10069704026131061963427621e-05 relative error = 0.0050467415247354675718862639832572 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8051924941398678356554465710368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3257669555356648353821586358212 relative error = 11.612998260055303928854538476572 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.4MB, time=117.15 NO POLE NO POLE x[1] = 0.937 y2[1] (analytic) = 1.4077919583458183496513260657285 y2[1] (numeric) = 1.4077201154203767975325401135666 absolute error = 7.18429254415521187859521619e-05 relative error = 0.0051032345380043858247263066516295 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8057851049753395952567080013595 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3263595663711365949834200661439 relative error = 11.631666509043108311138462603602 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.938 y2[1] (analytic) = 1.4085980394204923302221473173594 y2[1] (numeric) = 1.4085253526100157932121680870759 absolute error = 7.26868104765370099792302835e-05 relative error = 0.0051602237432078850790405602837944 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8063769100257735282748838280223 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3269513714215705280015958928067 relative error = 11.650301506313627496627205840977 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.4MB, time=117.79 NO POLE NO POLE x[1] = 0.939 y2[1] (analytic) = 1.409404711897077606805566171065 y2[1] (numeric) = 1.4093311732142831370951088508011 absolute error = 7.35386827944697104573202639e-05 relative error = 0.0052177122847479102802079169546533 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8069679086993646335931269251073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3275423700951616333198389898917 relative error = 11.668903270323867582992048525319 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.94 y2[1] (analytic) = 1.410211974968901770039010184776 y2[1] (numeric) = 1.4101375763689333371882309684518 absolute error = 7.43985999684328507792163242e-05 relative error = 0.0052757033190044710214164722786123 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8075581004051142868702197986342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3281325618009112865969318634186 relative error = 11.687471819499075316810372755571 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.4MB, time=118.42 NO POLE NO POLE x[1] = 0.941 y2[1] (analytic) = 1.4110198278287018153702365346646 y2[1] (numeric) = 1.4109445612088433189365126310217 absolute error = 7.52666198584964337239036429e-05 relative error = 0.0053342000143483328508550851750378 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8081474845528308315391496778929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3287219459486278312658617426773 relative error = 11.706007172232746393585606615963 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.942 y2[1] (analytic) = 1.4118282696686249503202692954725 y2[1] (numeric) = 1.4117521268680124252230416567882 absolute error = 7.61428006125250972276386843e-05 relative error = 0.0053932055511536707507708536609158 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8087360605531301689987158998209 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3293105219489271687254279646053 relative error = 11.724509346886633782197522873436 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.943 y2[1] (analytic) = 1.4126372996802294023361245984231 y2[1] (numeric) = 1.4125602724795624163690154913127 absolute error = 7.70272006669859671091071104e-05 relative error = 0.0054527231218106850516178117851727 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8093238278174363479975793948635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3298982892132333477242914596479 relative error = 11.742978361790756073544067333187 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.4MB, time=119.05 NO POLE NO POLE x[1] = 0.944 y2[1] (analytic) = 1.41344691705448522723251581406 y2[1] (numeric) = 1.4133689971757374701337412074405 absolute error = 7.79198787477570987746066195e-05 relative error = 0.0055127559307381800443638400887794 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8099107857579821532101648903185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3304852471537791529368769551029 relative error = 11.761414235243405853136797697275 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.945 y2[1] (analytic) = 1.4142571209817751182217303183736 y2[1] (numeric) = 1.4141783000879041817146355053007 absolute error = 7.88208938709365070948130729e-05 relative error = 0.0055733071943961055538592944418141 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8104969337878096930038272553123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3310713951836066927305393200967 relative error = 11.779816985511158097412916384683 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.4MB, time=119.68 NO POLE NO POLE x[1] = 0.946 y2[1] (analytic) = 1.4150679106518952155308688124071 y2[1] (numeric) = 1.4149881803465515637472247123064 absolute error = 7.97303053436517836441001007e-05 relative error = 0.0056343801412980617360022410806168 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8110822713207709863966942202884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3316567327165679861234062850728 relative error = 11.798186630828878593527780346215 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.947 y2[1] (analytic) = 1.4158792852540559166056375781701 y2[1] (numeric) = 1.4157986370812910463051447831544 absolute error = 8.06481727648703004927950157e-05 relative error = 0.005695978012023767361261483538656 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8116667977715285492055985132169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3322412591673255489323105780013 relative error = 11.816523189399732382392667453412 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=720.9MB, alloc=4.4MB, time=120.30 x[1] = 0.948 y2[1] (analytic) = 1.4166912439768826868998834671338 y2[1] (numeric) = 1.4166096694208564769001412998256 absolute error = 8.15745560262099997421673082e-05 relative error = 0.0057581040592314918469398242224018 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8122505125555559793835132646391 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3328249739513529791102253294235 relative error = 11.834826679395192224723472565874 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.949 y2[1] (analytic) = 1.4175037860084168712500608318425 y2[1] (numeric) = 1.4174212764931041204820694715846 absolute error = 8.25095153127507679913602579e-05 relative error = 0.005820761547670451300376264939532 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8128334150891385415459053441629 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3334078764849355412726174089473 relative error = 11.853097118955047089866896895646 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.95 y2[1] (analytic) = 1.4183169105361165058338190262395 y2[1] (numeric) = 1.41823345742501265943889413498 absolute error = 8.34531111038463949248912595e-05 relative error = 0.005883953754193168835097159343248 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8134155047893737506854221021026 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.333989966185170750412134166887 relative error = 11.871334526187410667171581799125 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=724.7MB, alloc=4.4MB, time=120.93 NO POLE NO POLE x[1] = 0.951 y2[1] (analytic) = 1.4191306167468571307118985161905 y2[1] (numeric) = 1.4190462113426831935966897538442 absolute error = 8.44054041739371152087623463e-05 relative error = 0.0059476839677677994217327322152883 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8139967810741719550743278016264 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3345712424699689548010398664108 relative error = 11.889538919168729899672522645768 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.952 y2[1] (analytic) = 1.419944903826932602952523058373 y2[1] (numeric) = 1.4198595373713392402196404192936 absolute error = 8.53664555933627328826390794e-05 relative error = 0.0060119554894904195353169174550268 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8145772433622569183541068390228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3351517047580539180808189038072 relative error = 11.907710315943793539857979947351 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.4MB, time=121.57 NO POLE NO POLE x[1] = 0.953 y2[1] (analytic) = 1.4207597709620559103374748232099 y2[1] (numeric) = 1.4206734346353267340100398497283 absolute error = 8.63363267291763274349734816e-05 relative error = 0.0060767716325972818603851846564342 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.815156891073166400811651662531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3357313524689634005383637273154 relative error = 11.925848734525740727288983490874 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.954 y2[1] (analytic) = 1.4215752173373599856490387558386 y2[1] (numeric) = 1.4214879022581140271082913908325 absolute error = 8.73150792459585407473650061e-05 relative error = 0.0061421357224770353150769648552144 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8157357236272527398414541135974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3363101850230497395681661783818 relative error = 11.943954192896069587842400811363 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.955 y2[1] (analytic) = 1.4223912421373985215370018882395 y2[1] (numeric) = 1.4223029393622918890929080155741 absolute error = 8.83027751066324440938726654e-05 relative error = 0.006208051096682910655236494663955 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8163137404456834295932197284128 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3368882018414804293199317931972 relative error = 11.962026709004645854349413976456 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.4MB, time=122.19 NO POLE NO POLE x[1] = 0.956 y2[1] (analytic) = 1.4232078445461467859648927355918 y2[1] (numeric) = 1.423118545069573506980512324205 absolute error = 8.92994765732789843804113868e-05 relative error = 0.0062745211049448719192884166295848 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8168909409504416998043253521668 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3374654023462386995310374169512 relative error = 11.980066300769711508402118342213 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.957 y2[1] (analytic) = 1.4240250237470024382346453306867 y2[1] (numeric) = 1.423934718500794485225836544261 absolute error = 9.03052462079530088087864257e-05 relative error = 0.0063415491091817339744423467327191 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8174673245643270938165412336083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3380417859601240935432532983927 relative error = 11.998072986077893443101823687374 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.4MB, time=122.82 NO POLE NO POLE x[1] = 0.958 y2[1] (analytic) = 1.4248427789227863455888718718004 y2[1] (numeric) = 1.4247514587759128457217225305616 absolute error = 9.13201468734998671493412388e-05 relative error = 0.0064091384835132464245538893255963 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8180428907109560457764395832387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3386173521067530455031516480231 relative error = 12.016046782784212146523501950666 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.959 y2[1] (analytic) = 1.4256611092557434003899273818234 y2[1] (numeric) = 1.4255687650140090277991217652104 absolute error = 9.23442417343725908056166130e-05 relative error = 0.0064772926142721441397382895727333 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8186176388147624570189123947776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.339192100210559456745624459562 relative error = 12.033987708712090405671686691323 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.4MB, time=123.45 NO POLE NO POLE x[1] = 0.96 y2[1] (analytic) = 1.4264800139275433378749491996481 y2[1] (numeric) = 1.4263866363332858882270953575948 absolute error = 9.33775942574496478538420533e-05 relative error = 0.0065460149000161646675971057595336 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8191915683009982716332221464304 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3397660296967952713599342112148 relative error = 12.051895781653362030703987375677 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.961 y2[1] (analytic) = 1.4272994921192815544860535488458 y2[1] (numeric) = 1.4272050718510687012128140443861 absolute error = 9.44202682128532732395044597e-05 relative error = 0.0066153087515400327856780016780926 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8197646785957340512110098159569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3403391399915310509377218807413 relative error = 12.069771019368280599199236671347 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.962 y2[1] (analytic) = 1.4281195430114799267748708535018 y2[1] (numeric) = 1.4280240706838051584015581895394 absolute error = 9.54723276747683733126639624e-05 relative error = 0.0066851775918874124545430447052243 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.820336969125859548775685461578 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3409114305216565485023975263624 relative error = 12.087613439585528220248141113821 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.4MB, time=124.07 NO POLE NO POLE x[1] = 0.963 y2[1] (analytic) = 1.4289401657840876308806008967442 y2[1] (numeric) = 1.4288436319470653688767177842938 absolute error = 9.65338370222620038831124504e-05 relative error = 0.0067556248563628264305717914629204 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8209084393190842818926274393802 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3414829007148812816193395041646 relative error = 12.105423060002224318145154807288 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.964 y2[1] (analytic) = 1.4297613596164819625807683439772 y2[1] (numeric) = 1.4296637547555418591597924471722 absolute error = 9.76048609401034209758968050e-05 relative error = 0.0068266539925435437973719911640222 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8214790886039381049596171470655 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3420535499997351046863292118499 relative error = 12.123199898283934435461142240683 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.4MB, time=124.70 NO POLE NO POLE x[1] = 0.965 y2[1] (analytic) = 1.4305831236874691579138585801337 y2[1] (numeric) = 1.4304844382230495732103914239814 absolute error = 9.86854644195847034671561523e-05 relative error = 0.006898268460291435674412980022335 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8220489164097717806769370036593 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3426233778055687804036490684437 relative error = 12.140943972064679055277239850195 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.966 y2[1] (analytic) = 1.4314054571752852143730132383785 y2[1] (numeric) = 1.4313056814625258724262335878121 absolute error = 9.97757127593419467796505664e-05 relative error = 0.0069704717317647993612348195432425 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8226179221667575506965601951263 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3431923835625545504232722599107 relative error = 12.158655298946942442361166649562 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=751.5MB, alloc=4.4MB, time=125.32 x[1] = 0.967 y2[1] (analytic) = 1.4322283592575967126699642266353 y2[1] (numeric) = 1.432127483586030535643147439039 absolute error = 0.0001008756715661770268167875963 relative error = 0.0070432672914301511753199894470781 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8231861053058897054498615367527 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3437605667016867051765736015371 relative error = 12.176333896501681503068072088021 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.968 y2[1] (analytic) = 1.4330518291115016390683844880724 y2[1] (numeric) = 1.4329498437047457591350711053204 absolute error = 0.000101985406755879933313382752 relative error = 0.0071166586360739882414440238142973 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8237534652589851531532796246302 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3443279266547821528799916894146 relative error = 12.193979782268334663748844291454 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.969 y2[1] (analytic) = 1.4338758659135302082858331622636 y2[1] (numeric) = 1.4337727609289761566140523415988 absolute error = 0.0001031049845540516717808206648 relative error = 0.0071906492748145194900469179093747 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8243200014586839879913612706282 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3448944628544809877180733354126 relative error = 12.211592973754830767449634003948 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.4MB, time=125.95 NO POLE NO POLE x[1] = 0.97 y2[1] (analytic) = 1.4347004688396456869634722451501 y2[1] (numeric) = 1.4345962343681487592302485301003 absolute error = 0.0001042344714969277332237150498 relative error = 0.0072652427291133661218884754605367 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8248857133384500574766200378563 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3454601747342470572033321026407 relative error = 12.229173488437597988687178882994 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.971 y2[1] (analytic) = 1.4355256370652452177027312781524 y2[1] (numeric) = 1.4354202631308130155719266803351 absolute error = 0.0001053739344322021308045978173 relative error = 0.0073404425327872317959680511183883 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8254506003325715289856415168064 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3460250617283685287123535815908 relative error = 12.246721343761572766085339320889 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.4MB, time=126.58 NO POLE NO POLE x[1] = 0.972 y2[1] (analytic) = 1.4363513697651606436680960298383 y2[1] (numeric) = 1.4362448463246407916654634290972 absolute error = 0.0001065234405198520026326007411 relative error = 0.0074162522320195427974024139229138 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8260146618761614554708688061158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3465891232719584551975808709002 relative error = 12.264236557140208752659080675839 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.973 y2[1] (analytic) = 1.4371776661136593337551965674268 y2[1] (numeric) = 1.4370699830564263709753450404644 absolute error = 0.0001076830572329627798515269624 relative error = 0.0074926753853720584416647533602899 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8265778974051583403475024862134 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3471523588009553400742145509978 relative error = 12.281719145955485783532957707705 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.974 y2[1] (analytic) = 1.4380045252844450083233695501071 y2[1] (numeric) = 1.4378956724320864544041674057986 absolute error = 0.0001088528523585539192021443085 relative error = 0.0075697155637964519712932120588079 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8271403063563267015549501989961 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3477147677521237012816622637805 relative error = 12.299169127557918860881975133604 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.4MB, time=127.21 NO POLE NO POLE x[1] = 0.975 y2[1] (analytic) = 1.4388319464506585654918690116816 y2[1] (numeric) = 1.4387219135566601602926360437453 absolute error = 0.0001100328939984051992329679363 relative error = 0.0076473763506458622008787988780274 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8277018881672576347922617721328 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3482763495630546345189738369172 relative error = 12.316586519266567155883513556413 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.976 y2[1] (analytic) = 1.4396599287848789079988993363884 y2[1] (numeric) = 1.4395487055343090244195661002342 absolute error = 0.0001112232505698835793332361542 relative error = 0.0077256613416864161658401521999133 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8282626422763693759269866526067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3488371036721663756536987173911 relative error = 12.333971338369043027469822583032 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.4MB, time=127.84 NO POLE NO POLE x[1] = 0.977 y2[1] (analytic) = 1.4404884714591237706226435689417 y2[1] (numeric) = 1.4403760474683170000018823484786 absolute error = 0.0001124239908067706207612204631 relative error = 0.0078045741451087230301864279431046 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8288225681229078625768912406878 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3493970295187048623036033054722 relative error = 12.351323602121521057671392747765 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.978 y2[1] (analytic) = 1.4413175736448505481634596378282 y2[1] (numeric) = 1.4412039384610904576946191889758 absolute error = 0.0001136351837600904688404488524 relative error = 0.007884118381539339508159617741207 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8293816651469472948639745426626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.349956126542744294590686607447 relative error = 12.368643327748747103342324897523 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=770.5MB, alloc=4.4MB, time=128.47 x[1] = 0.979 y2[1] (analytic) = 1.4421472345129571239864165097351 y2[1] (numeric) = 1.4420323776141581855909206495071 absolute error = 0.000114856898798938395495860228 relative error = 0.0079642976840522070543339023341458 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8299399327893906953402213883531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3505143941851876950669334531375 relative error = 12.385930532444047364059619988651 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.98 y2[1] (analytic) = 1.4429774532337826991233417326401 y2[1] (numeric) = 1.4428613640281713892220403851375 absolute error = 0.0001160892056113099013013475026 relative error = 0.0080451156981800610764322508676532 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8304973704919704680845332877192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3510718318877674678112453525036 relative error = 12.403185233369337465989113798188 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.981 y2[1] (analytic) = 1.4438082289771086219335512655861 y2[1] (numeric) = 1.4436908968029036915573416782159 absolute error = 0.0001173321742049303762095873702 relative error = 0.008126576081925812424799429825064 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8310539776972489569702778296585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3516284390930459566969898944429 relative error = 12.420407447655131561511579873773 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.4MB, time=129.09 NO POLE NO POLE x[1] = 0.982 y2[1] (analytic) = 1.4446395609121592183224319344801 y2[1] (numeric) = 1.4445209750372511330042974383752 absolute error = 0.0001185858749080853181344961049 relative error = 0.0082086825057739014121459242838527 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.831609753848619003102898355503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3521842152444160028296104202874 relative error = 12.437597192400551444403320144884 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.983 y2[1] (analytic) = 1.4454714482076026225170462954026 y2[1] (numeric) = 1.4453515978292321714084902025322 absolute error = 0.0001198503783704511085560928704 relative error = 0.0082914386527016246168490384093322 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8321646983903045014270264696466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.352739159786101501153738534431 relative error = 12.454754484673335680366356001541 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.4MB, time=129.72 NO POLE NO POLE x[1] = 0.984 y2[1] (analytic) = 1.4463038900315516083979291298914 y2[1] (numeric) = 1.4461827642759876820536121348874 absolute error = 0.000121125755563926344316995004 relative error = 0.0083748482181904347227656708230527 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8327188107673609565025407802402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3532932721631579562292528450246 relative error = 12.471879341509848752704123324131 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.985 y2[1] (analytic) = 1.4471368855515644213862442404742 y2[1] (numeric) = 1.4470144734737809576614650269253 absolute error = 0.0001224120777834637247792135489 relative error = 0.0084589149102372136481759926993707 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8332720904256760374490160939396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.353846551821473037175728158724 relative error = 12.488971779915090222939362927146 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.986 y2[1] (analytic) = 1.4479704339346456108854696593607 y2[1] (numeric) = 1.4478467245179977083919602974143 absolute error = 0.0001237094166479024935093619464 relative error = 0.0085436424493655192161385305371951 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8338245368119701320580081203051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3543989982077671317847201850895 relative error = 12.506031816862703906171683169521 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.4MB, time=130.35 NO POLE NO POLE x[1] = 0.987 y2[1] (analytic) = 1.4488045343472468632767788286789 y2[1] (numeric) = 1.4486795165031460618431189924066 absolute error = 0.0001250178441008014336598362723 relative error = 0.0086290345686368056181950105715254 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8343761493737969000726195736126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.354950610769593899799331638397 relative error = 12.523059469294987060973054092611 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.988 y2[1] (analytic) = 1.4496391859552678354672847569453 y2[1] (numeric) = 1.4495128485228565630510717852384 absolute error = 0.0001263374324112724162129717069 relative error = 0.0087150950136616179230177959482156 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8349269275595438256337943925575 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3555013889553408253605064573419 relative error = 12.540054754122899593620272382406 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.4MB, time=130.98 NO POLE NO POLE x[1] = 0.989 y2[1] (analytic) = 1.4504743879240569889903136035916 y2[1] (numeric) = 1.4503467196698821744900589765297 absolute error = 0.0001276682541748145002546270619 relative error = 0.0088018275426107608812438790632536 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8354768708184327688927876316028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3560513322142297686194996963872 relative error = 12.557017688226073276464213723396 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.99 y2[1] (analytic) = 1.4513101394184124246568735913464 y2[1] (numeric) = 1.4511811290360982760724304941845 absolute error = 0.0001290103823141485844430971619 relative error = 0.0088892359262264422773872187332914 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8360259786005205167892594115471 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3566004399963175165159714763315 relative error = 12.573948288452820980236463725889 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.4MB, time=131.61 NO POLE NO POLE x[1] = 0.991 y2[1] (analytic) = 1.4521464396025827177574845950707 y2[1] (numeric) = 1.4520160757125026651486458933905 absolute error = 0.0001303638900800526088387016802 relative error = 0.0089773239478333910793657721214363 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8365742503566993329944421512648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3571487117524963327211542160492 relative error = 12.590846571620145920094690574926 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.992 y2[1] (analytic) = 1.4529832876402677538135332052885 y2[1] (numeric) = 1.4528515587892155565072743566194 absolute error = 0.0001317288510521973062588486691 relative error = 0.0090660954033499506358209030733355 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8371216855386975070188311374976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.357696146934494506745543202282 relative error = 12.607712554513750915208891875328 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.993 y2[1] (analytic) = 1.4538206826946195648773175151265 y2[1] (numeric) = 1.4536875773554795823749946936267 absolute error = 0.0001331053391399825023228214998 relative error = 0.0091555541012991471710449890027902 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8376682835990799024838493250508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3582427449948769022105613898352 relative error = 12.624546253888047661691414862026 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.4MB, time=132.24 NO POLE NO POLE x[1] = 0.994 y2[1] (analytic) = 1.4546586239282431663799453306873 y2[1] (numeric) = 1.4545241304996597924165953414519 absolute error = 0.0001344934285833739633499892354 relative error = 0.00924570386281973382696803503813 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8382140439912485045569380957782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3587885053870455042836501605626 relative error = 12.641347686466166018674413216221 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.995 y2[1] (analytic) = 1.4554971105031973945262489570286 y2[1] (numeric) = 1.4553612173092436537349743644183 absolute error = 0.0001358931939537407912745926103 relative error = 0.009336548521677210501285974573171 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8387589661694429665495265413068 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3593334275652399662762386060912 relative error = 12.658116868939963307339165183617 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.4MB, time=132.88 NO POLE NO POLE x[1] = 0.996 y2[1] (analytic) = 1.4563361415809957442358791649033 y2[1] (numeric) = 1.4561988368708410508711394541332 absolute error = 0.0001373047101546933647397107701 relative error = 0.0094280919242748197304421260053838 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8393030495887411556773326715804 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3598775109845381554040447363648 relative error = 12.674853817970033622702436539963 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.997 y2[1] (analytic) = 1.4571757163226072076297403972349 y2[1] (numeric) = 1.4570369882701842858042079294876 absolute error = 0.0001387280524229218255324677473 relative error = 0.0095203379296645188657990238303342 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.839846293705059697982450788966 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3604207551008566977091628537504 relative error = 12.691558550185717157965828198815 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=801.0MB, alloc=4.4MB, time=133.51 x[1] = 0.998 y2[1] (analytic) = 1.4580158338884571130609287289657 y2[1] (numeric) = 1.4578756705921280779514067366565 absolute error = 0.0001401632963290351095219923092 relative error = 0.0096132904095579287909605850859721 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8403886979751545224166801058793 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3609631593709515221433921706637 relative error = 12.708231082185109541234801915319 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.999 y2[1] (analytic) = 1.4588564934384279646893335494061 y2[1] (numeric) = 1.4587148829206495641680724490988 absolute error = 0.0001416105177784005212611003073 relative error = 0.0097069532483372594278243454047017 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8409302618566214040855505226477 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3615047232524184038122625874321 relative error = 12.724871430535071184414828616052 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1 y2[1] (analytic) = 1.459697694131860282599063392557 y2[1] (numeric) = 1.4595546243388482987476512675572 absolute error = 0.0001430697930119838514121249998 relative error = 0.0098013303430662122785603402326044 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8414709848078965066525023216303 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3620454462036935063792143864147 relative error = 12.74147961177123664409285238639 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.4MB, time=134.16 NO POLE NO POLE x[1] = 1.001 y2[1] (analytic) = 1.4605394351275534434578557980464 y2[1] (numeric) = 1.4603948939289462534216990200583 absolute error = 0.0001445411986071900361567779881 relative error = 0.0098964256035008602503271507962476 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.8420108662882569239026773734589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3625853276840539236293894382433 relative error = 12.758055642398023994213009081703 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.002 y2[1] (analytic) = 1.4613817155837665217176305433427 y2[1] (numeric) = 1.4612356907722878173598811619127 absolute error = 0.00014602481147870435774938143 relative error = 0.0099922429521005050091467189388908 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 2.842549905757821220465780291656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3631243671536182201924923564404 relative error = 12.774599538888644210356281905063 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.4MB, time=134.80 NO POLE NO POLE x[1] = 1.003 y2[1] (analytic) = 1.4622245346582191313553450467597 y2[1] (numeric) = 1.4620770139493397971699727757147 absolute error = 0.000147520708879334185372271045 relative error = 0.010088786324038512108967794409226 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8430881026775499716974688128113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3636625640733469714241808775957 relative error = 12.791111317685110565434517119844 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.004 y2[1] (analytic) = 1.4630678915080922681533102004696 y2[1] (numeric) = 1.4629188625396914168978585713426 absolute error = 0.000149028968400851255451629127 relative error = 0.01018605966721312414155334939681 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8436254565092463027187335209743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3641999179050433024454455857587 relative error = 12.807590995198248036609961348992 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.005 y2[1] (analytic) = 1.4639117852900291525181243532775 y2[1] (numeric) = 1.4637612356220543180275328859586 absolute error = 0.0001505496679748344905914673189 relative error = 0.010284066942258252152430013069202 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.844161966715556426612727876925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3647364281113534263394399417094 relative error = 12.82403858780770272325221766133 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.4MB, time=135.44 NO POLE NO POLE x[1] = 1.006 y2[1] (analytic) = 1.4647562151601360728373826242936 y2[1] (numeric) = 1.4646041322742625594810996840088 absolute error = 0.0001520828858735133562829402848 relative error = 0.01038281212255424556773757913369 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8446976327599701817785103555398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3652720941557671815052224203242 relative error = 12.840454111861951275745250867654 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.007 y2[1] (analytic) = 1.4656011802739832293733181908644 y2[1] (numeric) = 1.4654475515732726176187725572231 absolute error = 0.0001536287007106117545456336413 relative error = 0.010482299194238640876413957400618 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8452324541068215684411613375549 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3658069155026185681678734023393 relative error = 12.856837583678310334957803152915 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.4MB, time=136.08 NO POLE NO POLE x[1] = 1.008 y2[1] (analytic) = 1.4664466797866055786925316571923 y2[1] (numeric) = 1.4662914925951633862388747246153 absolute error = 0.000155187191442192453656932577 relative error = 0.010582532156216889311745610805217 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8457664302212892843177382456532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3663408916170862840444503104376 relative error = 12.873189019542945982191309363741 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.009 y2[1] (analytic) = 1.467292712852503678630964073983 y2[1] (numeric) = 1.467135954415136176577839032483 absolute error = 0.0001567584373675020531250415 relative error = 0.010683515020173063775905577300329 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8462995605693972594385332589671 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3668740219651942591652453237515 relative error = 12.889508435710883199420126960964 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.4MB, time=136.70 NO POLE NO POLE x[1] = 1.01 y2[1] (analytic) = 1.4681392786256445337932686442208 y2[1] (numeric) = 1.4679809361075147173102079544079 absolute error = 0.0001583425181298164830606898129 relative error = 0.010785251810580545250690656555261 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.846831844618015190123098784782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3674063060138121898498108495664 relative error = 12.905795848406015339639618842126 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.011 y2[1] (analytic) = 1.4689863762594624415857356157674 y2[1] (numeric) = 1.4688264367457451545486335912555 absolute error = 0.0001599395137172870371020245119 relative error = 0.010887746564712688937256278213614 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8473632818348590721105067114598 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3679377432306560718372187762442 relative error = 12.922051273821113607138347947521 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.012 y2[1] (analytic) = 1.4698340049068598387819243279326 y2[1] (numeric) = 1.469672455402396051843877671175 absolute error = 0.0001615495044637869380466567576 relative error = 0.010991003332653470367231997048317 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8478938716884917328433083123683 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3684683330842887325700203771527 relative error = 12.938274728117836547511360792789 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.4MB, time=137.33 NO POLE NO POLE x[1] = 1.013 y2[1] (analytic) = 1.4706821637202081486201558464534 y2[1] (numeric) = 1.4705189911491583901848115495998 absolute error = 0.0001631725710497584353442968536 relative error = 0.011095026177308111727182513763293 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8484236136483233629046625169003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3689980750441203626313745816847 relative error = 12.95446622742673954723225282928 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.014 y2[1] (analytic) = 1.4715308518513486284320190894609 y2[1] (numeric) = 1.4713660430568455679984162092469 absolute error = 0.000164808794503060433602880214 relative error = 0.011199819174413688637958633727481 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8489525071846120466081011114986 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.369526968580409046334813176283 relative error = 12.970625787847284342602421828244 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=827.7MB, alloc=4.4MB, time=137.96 NO POLE NO POLE x[1] = 1.015 y2[1] (analytic) = 1.472380068451593217801042815998 y2[1] (numeric) = 1.4722136101953934011497822601174 absolute error = 0.0001664582561998166512605558806 relative error = 0.011305386412549717630059681937467 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8494805517684642917394002809662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3700550131642612914661123457506 relative error = 12.98675342544784853789662632419 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.016 y2[1] (analytic) = 1.4732298126717253872506853184886 y2[1] (numeric) = 1.4730616916338601229421099394961 absolute error = 0.0001681210378652643085753789925 relative error = 0.011411731993148724555703626522903 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.850007746871835558450028748234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3705822082676325581767408130184 relative error = 13.002849156265735132524674544174 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=831.6MB, alloc=4.4MB, time=138.60 x[1] = 1.017 y2[1] (analytic) = 1.4740800836620009874607931312371 y2[1] (numeric) = 1.4739102864404263841167091119518 absolute error = 0.0001697972215746033440840192853 relative error = 0.011518860030506794177873556610766 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8505340919675307873016436191816 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.371108553363327787028355683966 relative error = 13.018912996307182057029775201237 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.018 y2[1] (analytic) = 1.4749308805721490990116795385718 y2[1] (numeric) = 1.4747593936823952528529992693371 absolute error = 0.0001714868897538461586802692347 relative error = 0.011626774651794101176179248742506 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8510595865292049264611058880601 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3716340479250019261878179528445 relative error = 13.034944961547371717744785049455 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.019 y2[1] (analytic) = 1.4757822025513728826549731386242 y2[1] (numeric) = 1.4756090124261922147685095307886 absolute error = 0.0001731901251806678864636078356 relative error = 0.01173547999706542280894037077996 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8515842300313634580454884085451 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3721586914271604577722004733295 relative error = 13.050945067930440549928289192668 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.4MB, time=139.23 NO POLE NO POLE x[1] = 1.02 y2[1] (analytic) = 1.4766340487483504301103861919662 y2[1] (numeric) = 1.4764591417373651729188786427267 absolute error = 0.0001749070109852571915075492395 relative error = 0.011844980219270633470463447451055 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8521080219493629236165499854554 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3726824833451599233432620502398 relative error = 13.066913331369488579203148816855 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.021 y2[1] (analytic) = 1.4774864183112356153875519584076 y2[1] (numeric) = 1.4773097806805844477978549788557 absolute error = 0.0001766376306511675896969795519 relative error = 0.01195527948426518138204807962034 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8526309617594114488241500927072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3732054231552084485508621574916 relative error = 13.082849767746588991120847284876 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.4MB, time=139.86 NO POLE NO POLE x[1] = 1.022 y2[1] (analytic) = 1.4783393103876589466320797001881 y2[1] (numeric) = 1.4781609283196427773372965401638 absolute error = 0.0001783820680161692947831600243 relative error = 0.012066381970820547654819103114101 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8531530489385692671980795741338 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3737275103343662669247916389182 relative error = 13.098754392912797708675659399691 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.023 y2[1] (analytic) = 1.4791927241247284184949755055798 y2[1] (numeric) = 1.4790125837174553169071709549231 absolute error = 0.0001801404072731015878045506567 relative error = 0.012178291870634687962040424563909 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8536742829647492430877835353817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3742487443605462428144956001661 relative error = 13.114627222688162977593360115685 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.024 y2[1] (analytic) = 1.4800466586690303650245765635492 y2[1] (numeric) = 1.4798647459360596393155554786895 absolute error = 0.0001819127329707257090210848597 relative error = 0.012291013388342457058123213780321 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.854194663316717393749453487206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3747691247125143934761655519904 relative error = 13.130468272861734959219878065323 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.4MB, time=140.49 NO POLE NO POLE x[1] = 1.025 y2[1] (analytic) = 1.4809011131666303130801459976169 y2[1] (numeric) = 1.4807174140366157348086369943029 absolute error = 0.000183699130014578271509003314 relative error = 0.012404550741526016381095996987481 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8547141894740934105799666531149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3752886508698904103066787178993 relative error = 13.146277559191575330835985977277 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.026 y2[1] (analytic) = 1.4817560867630738362662748453913 y2[1] (numeric) = 1.481570587079406011070712011887 absolute error = 0.0001854996836678251955628335043 relative error = 0.012518908160725224974857014443542 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8552328609173511794971512074687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3758073223131481792238632722531 relative error = 13.162055097404766893224804400418 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.4MB, time=141.11 NO POLE NO POLE x[1] = 1.027 y2[1] (analytic) = 1.4826115786033874093872372494439 y2[1] (numeric) = 1.4824242641238352932241866688494 absolute error = 0.0001873144795521161630505805945 relative error = 0.012634089889448013967080011325927 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8557506771278193004658570638093 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3763251385236163001925691285937 relative error = 13.177800903197423185319577122801 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.028 y2[1] (analytic) = 1.4834675878320792634204444052437 y2[1] (numeric) = 1.4832784442284308238295767298815 absolute error = 0.0001891436036484395908676753622 relative error = 0.012750100184180744838193454581701 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8562676375876816061693126873962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3768420989834786058960247521806 relative error = 13.193514992234698105759856294169 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.4MB, time=141.74 NO POLE NO POLE x[1] = 1.029 y2[1] (analytic) = 1.4843241135931402410081422927682 y2[1] (numeric) = 1.4841331264508422628855075869588 absolute error = 0.0001909871422979781226347058094 relative error = 0.012866943314398551716400041252571 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8567837417799776798252492606312 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3773582031757746795519613254156 relative error = 13.209197380150795541184912531271 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.03 y2[1] (analytic) = 1.4851811550300446524664977001626 y2[1] (numeric) = 1.4849883098478416878287142593405 absolute error = 0.0001928451822029646377834408221 relative error = 0.012984623562575667933248317451119 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8572989891886033721462743852944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3778734505844003718729864500788 relative error = 13.224848082548979001093860215981 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.031 y2[1] (analytic) = 1.4860387112857511323112165304354 y2[1] (numeric) = 1.4858439934753235935340413935698 absolute error = 0.0001947178104275387771751368656 relative error = 0.013103145224195737073811292865519 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8578133792983113174439783612591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3783878406941083171706904260435 relative error = 13.240467115001581259102660793387 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.4MB, time=142.36 NO POLE NO POLE x[1] = 1.032 y2[1] (analytic) = 1.4868967815027034962988378656402 y2[1] (numeric) = 1.4867001763883048923144432634736 absolute error = 0.0001966051143986039843946021666 relative error = 0.013222512607762108755068143769417 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8583269115947114488762569376219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3789013729905084486029690024063 relative error = 13.256054493050014000428837148847 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.033 y2[1] (analytic) = 1.4877553648228315989828467473245 y2[1] (numeric) = 1.4875568576409249139209837701629 absolute error = 0.0001985071819066850618629771616 relative error = 0.013342730034808119365624479686882 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.85883958556427151283733528897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3794140469600685125640473537544 relative error = 13.27161023220477747543540009674 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.4MB, time=143.00 NO POLE NO POLE x[1] = 1.034 y2[1] (analytic) = 1.4886144603875521917837481172009 y2[1] (numeric) = 1.4884140362864454055428364420325 absolute error = 0.0002004241011067862409116751684 relative error = 0.013463801839907357999444234652874 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8593514006943175824899788268026 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.379925862090114582216690891587 relative error = 13.287134347945470159066153656605 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.035 y2[1] (analytic) = 1.489474067337769781572243848041 y2[1] (numeric) = 1.489271711377250531807284434761 absolute error = 0.00020235596051924976495941328 relative error = 0.013585732370683917815802064910257 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8598623564730345704393773139402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3804368178688315701660893787246 relative error = 13.302626855720798416005209132335 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=862.1MB, alloc=4.4MB, time=143.63 x[1] = 1.036 y2[1] (analytic) = 1.4903341848138774897646542816844 y2[1] (numeric) = 1.4901298819648468747797205313111 absolute error = 0.0002043028490306149849337503733 relative error = 0.013708525987822633057199220136702 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8603724523894667405481896080782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3809469137852637402749016728626 relative error = 13.318087770948586171394199054106 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.037 y2[1] (analytic) = 1.4911948119557579119297251788145 y2[1] (numeric) = 1.4909885470998634339636471419291 absolute error = 0.0002062648558944779660780368854 relative error = 0.013832187065079301956518236073867 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8608816879335182188922372194854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3814561493293152186189492842698 relative error = 13.33351710901578458694134079869 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.038 y2[1] (analytic) = 1.4920559479027839779059604737648 y2[1] (numeric) = 1.4918477058320516263006763041454 absolute error = 0.0002082420707323516052841696194 relative error = 0.013956719989290895764222501368698 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8613900625959535038563357271943 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3819645239917505035830477919787 relative error = 13.348914885278481742257156178489 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.4MB, time=144.25 NO POLE NO POLE x[1] = 1.039 y2[1] (analytic) = 1.4929175917938198124286207170946 y2[1] (numeric) = 1.4927073572102852861705296827742 absolute error = 0.0002102345835345262580910343204 relative error = 0.0140821291603857541259358116528 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.861897575868397975369753957895 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3824720372641949750964660226794 relative error = 13.364281115061912321252307491061 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.04 y2[1] (analytic) = 1.4937797427672215962655265790078 y2[1] (numeric) = 1.4935675002825606653910385699136 absolute error = 0.0002122424846609308744880090942 relative error = 0.014208418991393767040264467797972 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8624042272433384032807916921162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3829786886391354030075037569006 relative error = 13.379615813660467303433662455958 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.4MB, time=144.88 NO POLE NO POLE x[1] = 1.041 y2[1] (analytic) = 1.4946423999608384278608062778836 y2[1] (numeric) = 1.4944281340959964332181438849456 absolute error = 0.000214265864841994642662392938 relative error = 0.014335593908456543626250333067601 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8629100162141234548699675231574 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3834844776099204545966795879418 relative error = 13.394918996337703659935350141982 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.042 y2[1] (analytic) = 1.4955055625120131854857252902416 y2[1] (numeric) = 1.495289257696833676345896174536 absolute error = 0.0002163048151795091398291157056 relative error = 0.014463658350837567929367564155147 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.863414942274964201501309355628 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3839894036707612012280214204124 relative error = 13.410190678326354054122217412702 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.043 y2[1] (analytic) = 1.4963692295575833898957361913855 y2[1] (numeric) = 1.4961508701304358989064556126346 absolute error = 0.0002183594271474909892805787509 memory used=873.5MB, alloc=4.4MB, time=145.50 relative error = 0.014592616770932341994498503672624 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8639190049209346244112408923424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3844934663167316241379529571268 relative error = 13.425430874828336546603740598504 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.044 y2[1] (analytic) = 1.4972334002338820674928859697464 y2[1] (numeric) = 1.497012970441289022470092000475 absolute error = 0.0002204297925930450227939692714 relative error = 0.014722473634278516433845494609232 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8644222036479721196345583207306 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.384996665043769119361270385515 relative error = 13.440639601014764304497090047191 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.045 y2[1] (analytic) = 1.4980980736767386139927176525903 y2[1] (numeric) = 1.4978755576730013860451847665747 absolute error = 0.0002225160037372279475328860156 relative error = 0.014853233419566008717255179824994 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8649245379528780020669922728253 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3854989993486750017937043376097 relative error = 13.455816872025955314778685918841 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.4MB, time=146.13 NO POLE NO POLE x[1] = 1.046 y2[1] (analytic) = 1.4989632490214796585948025762604 y2[1] (numeric) = 1.4987386308683037460782229667351 absolute error = 0.0002246181531759125165796095253 relative error = 0.014984900618647109411950210331118 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8654260073333180086638509963099 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3860004687291150083905630610943 relative error = 13.470962702971442101564222082398 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.047 y2[1] (analytic) = 1.499828925402929928656039130494 y2[1] (numeric) = 1.4996021890690492764538052840415 absolute error = 0.0002267363338806522022338464525 relative error = 0.01511747973654657659818023306293 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8659266112878228007742415380223 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3865010726836198005009536028067 relative error = 13.486077108929981447157771247582 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.4MB, time=146.77 NO POLE NO POLE x[1] = 1.048 y2[1] (analytic) = 1.5006951019554131148658533035871 y2[1] (numeric) = 1.500466231316213568494640028863 absolute error = 0.0002288706391995463712132747241 relative error = 0.015250975291471718686819590462199 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8664263493157884656103666057382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3870008107115854653370786705226 relative error = 13.501160104949564116711218534308 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.049 y2[1] (analytic) = 1.5015617778127527369224358532785 y2[1] (numeric) = 1.5013307566498946309615451388527 absolute error = 0.0002310211628581059608907144258 relative error = 0.015385391814822465864453368452831 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8669252209174770168513956389767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3874996823132740165781077037611 relative error = 13.516211706047424586335902549331 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.05 y2[1] (analytic) = 1.5024289521082730097091504271879 y2[1] (numeric) = 1.5021957641093128900534481789476 absolute error = 0.0002331879989601196557022482403 relative error = 0.01552073385120143039100630420733 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8674232255940168943814094850003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3879976869898138941081215497847 relative error = 13.531231927210050774508972714008 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.4MB, time=147.39 NO POLE NO POLE x[1] = 1.051 y2[1] (analytic) = 1.5032966239747997099702464564727 y2[1] (numeric) = 1.5030612527328111894073863413684 absolute error = 0.0002353712419885205628601151043 relative error = 0.015657005958423955974480638141708 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8679203628474034631609189421053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3884948242432004628876310068897 relative error = 13.546220783393193776617599074756 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.052 y2[1] (analytic) = 1.5041647925446610434850101470624 y2[1] (numeric) = 1.5039272215578547900985064456199 absolute error = 0.0002375709868062533865037014425 relative error = 0.015794212707528156446879293249514 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8684166321804995112314582987262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3889910935762965109581703635106 relative error = 13.561178289521877602484796136266 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.4MB, time=148.03 NO POLE NO POLE x[1] = 1.053 y2[1] (analytic) = 1.5050334569496885127394863943916 y2[1] (numeric) = 1.5047936696210313706400649384906 absolute error = 0.000239787328657142099421455901 relative error = 0.015932358682784943964899816933694 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8689120330970357468527558638018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3894864944928327465794679285862 relative error = 13.576104460490408916721245393888 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.054 y2[1] (analytic) = 1.5059026163212177850949039499833 y2[1] (numeric) = 1.505660595958051026983427894053 absolute error = 0.0002420203631667581114760559303 relative error = 0.016071448481708046958492352619998 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8694065651016112947719843512738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3899810264974082944986964160582 relative error = 13.590999311162386781748122213001 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.4MB, time=148.65 NO POLE NO POLE x[1] = 1.055 y2[1] (analytic) = 1.5067722697900895614519356715277 y2[1] (numeric) = 1.5065279996037462725180710136635 absolute error = 0.0002442701863432889338646578642 relative error = 0.016211486715064018049881547944149 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8699002276996941916245948495095 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3904746890954911913513069142939 relative error = 13.605862856370712403336551516647 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.056 y2[1] (analytic) = 1.5076424164866504454099251922705 y2[1] (numeric) = 1.5073958795920720380715796259623 absolute error = 0.0002465368945784073383455663082 relative error = 0.016352478006882232165157780214086 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8703930203976218804662389748547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3909674817934188801929510396391 relative error = 13.620695110917598878509933405366 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.057 y2[1] (analytic) = 1.508513055540753812920210850555 y2[1] (numeric) = 1.5082642349561056719096486868735 absolute error = 0.0002488205846481410105621636815 relative error = 0.016494426994464875060047414284513 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8708849427026017044352846774374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3914594040983987041619967422218 relative error = 13.635496089574580945655994352151 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.4MB, time=149.28 NO POLE NO POLE x[1] = 1.058 y2[1] (analytic) = 1.5093841860817606824326772262677 y2[1] (numeric) = 1.5091330647280469397360827796051 absolute error = 0.0002511213537137426965944466626 relative error = 0.016637338328396922480975030243789 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8713759941227113995454320367466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.391950455518508399272144101531 relative error = 13.650265807082524736696031997584 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.059 y2[1] (analytic) = 1.5102558072385405855346641377078 y2[1] (numeric) = 1.5100023679392180246927961146489 absolute error = 0.0002534392993225608418680230589 relative error = 0.016781216672556110182032694001708 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.871866174166899586607936254411 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3924406355626965863346483191954 relative error = 13.665004278151637531159431822814 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.4MB, time=149.91 NO POLE NO POLE x[1] = 1.06 y2[1] (analytic) = 1.5111279181394724380813624600436 y2[1] (numeric) = 1.5108721436200635273598125297808 absolute error = 0.0002557745194089107215499302628 relative error = 0.016926066704122895017972419615052 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8723554823449862622829459219974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3929299437407832620096579867818 relative error = 13.679711517461477512012142107955 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.061 y2[1] (analytic) = 1.5120005179124454118168256350344 y2[1] (numeric) = 1.5117423908001504657552654900604 absolute error = 0.000258127112294946061560144974 relative error = 0.017071893113590407332838014209345 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8728439181676632892594655125299 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3934183795634602889861775773143 relative error = 13.694387539660963523088399597656 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=904.0MB, alloc=4.4MB, time=150.54 x[1] = 1.062 y2[1] (analytic) = 1.5128736056848598064847252510766 y2[1] (numeric) = 1.5126131085081682753353980878313 absolute error = 0.0002604971766915311493271632453 relative error = 0.017218700604774394863351529499555 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8733314811464948855634519158083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3939059425422918852901639805927 relative error = 13.70903235936838482797560220115 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.063 y2[1] (analytic) = 1.513747180583627922427978582893 y2[1] (numeric) = 1.5134842957719288089945630427208 absolute error = 0.0002628848116991134334155401722 relative error = 0.01736649389482315837566759549161 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8738181707939181129935557094709 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3943926321897151127202677742553 relative error = 13.723645991171410870202826857969 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.064 y2[1] (analytic) = 1.5146212417351749336763754913097 y2[1] (numeric) = 1.5143559516183663370652227016403 absolute error = 0.0002652901168085966111527896694 relative error = 0.01751527771422747925360600575625 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8743039866232433646840187301006 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.394878448019040364410730794885 relative error = 13.738228449627101034584090409494 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.4MB, time=151.17 NO POLE NO POLE x[1] = 1.065 y2[1] (analytic) = 1.5154957882654397615213315955666 y2[1] (numeric) = 1.515228075073537547317949038785 absolute error = 0.0002677131919022142033825567816 relative error = 0.017665056806830539255969086468695 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8747889281486548517942403815169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3953633895444518515209524463013 relative error = 13.752779749261914409568048937689 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.066 y2[1] (analytic) = 1.5163708192998759485768941434805 y2[1] (numeric) = 1.5161006651626215449614236556339 absolute error = 0.0002701541372544036154704878466 relative error = 0.017815835929837832660045637356512 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.875272994885211089324525990729 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3958474562810080890512380555134 relative error = 13.767299904571719550446426572701 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.4MB, time=151.80 NO POLE NO POLE x[1] = 1.067 y2[1] (analytic) = 1.5172463339634525333261265185295 y2[1] (numeric) = 1.51697372090991985264243778095 absolute error = 0.0002726130535326806836887375795 relative error = 0.017967619853827071007897607707898 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8757561863488453810575313958413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3963306477446423807842434606257 relative error = 13.781788930021804243274058237107 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.068 y2[1] (analytic) = 1.5181223313806549251519968375448 y2[1] (numeric) = 1.5178472413388564104458922707801 absolute error = 0.0002750900417985147061045667647 relative error = 0.018120413362758080671519188629006 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8762385020563663036249188245075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3968129634521633033516308892919 relative error = 13.796246840046885269354022193669 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.069 y2[1] (analytic) = 1.5189988106754857798518956081959 y2[1] (numeric) = 1.5187212254719775758947976084549 absolute error = 0.000277585203508203957097999741 relative error = 0.018274221253982693452450689366429 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.876719941525458189698739996318 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3972944029212551894254520611024 relative error = 13.810673649051118170141927602206 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.4MB, time=152.42 NO POLE NO POLE x[1] = 1.07 y2[1] (analytic) = 1.5198757709714658756349069318241 y2[1] (numeric) = 1.5195956723309521239502739045891 absolute error = 0.000280098640513751684633027235 relative error = 0.018429048338254630430921444611716 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8772005042746816103070632577768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3977749656704786100337753225612 relative error = 13.825069371408107012424009576331 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.071 y2[1] (analytic) = 1.5207532113916349896009572544251 y2[1] (numeric) = 1.5204705809365712470115508970811 absolute error = 0.000282630455063742589406357344 relative error = 0.018584899439739379279087095935184 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8776801898234738562733624342827 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3982546512192708560000744990671 relative error = 13.839434021460914153624269469556 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.4MB, time=153.06 NO POLE NO POLE x[1] = 1.072 y2[1] (analytic) = 1.521631131058552774700965186707 y2[1] (numeric) = 1.5213459503087485549159679511133 absolute error = 0.0002851807498042197849972355937 relative error = 0.018741779396024065252416928163622 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8781589976921494187791859597638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3987334590879464185058980245482 relative error = 13.853767613522070007096481318876 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.073 y2[1] (analytic) = 1.5225095290942996371771154331449 y2[1] (numeric) = 1.522221779466520074938974059152 absolute error = 0.0002877496277795622381413739929 relative error = 0.01889969305812731607277654428543 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8786369274019004690496257213382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3992113887976974687763377861226 relative error = 13.868070161873582807257466539809 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.4MB, time=153.70 NO POLE NO POLE x[1] = 1.074 y2[1] (analytic) = 1.5233884046204776144823793898327 y2[1] (numeric) = 1.5230980674280442517941278409473 absolute error = 0.0002903371924333626882515488854 relative error = 0.019058645290509120916240054734183 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8791139784747973371611059335712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3996884398705943368878179983556 relative error = 13.882341680766948374418618106245 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.075 y2[1] (analytic) = 1.5242677567582112536784044916836 y2[1] (numeric) = 1.5239748132106019476330975435333 absolute error = 0.0002929435476093060453069481503 relative error = 0.019218640971080683718154161823735 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8795901504337889899710132345797 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4001646118295859896977252993641 relative error = 13.89658218442315987917323256844 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.076 y2[1] (analytic) = 1.5251475846281484903108939111643 y2[1] (numeric) = 1.5248520158305964420456610412278 absolute error = 0.0002955687975520482652328699365 relative error = 0.019379684991214271007464061908228 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8800654428027035081686900743944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4006399041985005078954021391788 relative error = 13.910791687032717606197783369688 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.4MB, time=154.33 NO POLE NO POLE x[1] = 1.077 y2[1] (analytic) = 1.5260278873504615277615977332555 y2[1] (numeric) = 1.5257296743035534320597058356326 absolute error = 0.0002982130469080957018918976229 relative error = 0.019541782255753054481797989063643 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8805398551062485624473143446251 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4011143165020455621740264094095 relative error = 13.924970202755638717325842023343 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.078 y2[1] (analytic) = 1.5269086640448477170760362547213 y2[1] (numeric) = 1.5266077876441210321412290556335 absolute error = 0.0003008764007266849348071990878 relative error = 0.019704937683020948534293508936517 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8810133868700118887961890775899 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4015878482658088885229011423743 relative error = 13.939117745721467013753924813691 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=930.7MB, alloc=4.4MB, time=154.97 NO POLE NO POLE x[1] = 1.079 y2[1] (analytic) = 1.527789913830530437266075580037 y2[1] (numeric) = 1.5274863548660697741943374573999 absolute error = 0.0003035589644606630717381226371 relative error = 0.01986915620483244294263436212321 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8814860376204617629129669226588 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4020604990162587626396789874432 relative error = 13.953234330029282697239111793402 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.08 y2[1] (analytic) = 1.528671635826259976086475211474 y2[1] (numeric) = 1.5283653749822926075612474243853 absolute error = 0.0003062608439673685252277870887 relative error = 0.020034442766502430930251776412814 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8819578068849474737353349876248 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4025322682807444734620470524092 relative error = 13.96731996974771213014885197341 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=934.6MB, alloc=4.4MB, time=155.60 x[1] = 1.081 y2[1] (analytic) = 1.5295538291503144112845268568664 y2[1] (numeric) = 1.5292448470048048990222849673271 absolute error = 0.0003089821455095122622418895393 relative error = 0.020200802326856032809128739126094 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8824286941916997960916865134587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4030031555874967958183985782431 relative error = 13.981374678914937594223933745115 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.082 y2[1] (analytic) = 1.5304364929205004923219032054952 y2[1] (numeric) = 1.5301247699447444327958857242464 absolute error = 0.0003117229757560595260174812488 relative error = 0.020368239858238415413129767124144 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8828986990698314624703067318156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4034731604656284621970187966 relative error = 13.995398471538707047916162746046 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.083 y2[1] (analytic) = 1.5313196262541545225678349503138 y2[1] (numeric) = 1.5310051428123714105385949604484 absolute error = 0.0003144834417831120292399898654 relative error = 0.020536760346524607530262255164836 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8833678210493376339066011361452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4039422824451346336333132009296 relative error = 14.009391361596343882162850585282 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.4MB, time=156.24 NO POLE NO POLE x[1] = 1.084 y2[1] (analytic) = 1.5322032282681432419627338634115 y2[1] (numeric) = 1.531885964617068451345067568522 absolute error = 0.0003172636510747906176662948895 relative error = 0.02070636879112931154175854593591 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8838360596610963699878952792174 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4044105210568933697146073440018 relative error = 14.023353363034756674460777090851 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.085 y2[1] (analytic) = 1.533087298078864710151379261166 y2[1] (numeric) = 1.5327672343673405917480680683401 absolute error = 0.0003200637115241184033111928259 relative error = 0.020877070205016711475350468679832 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8843034144368690979753360923033 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4048778758326660977020481570877 relative error = 14.037284489770448941102846034278 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.4MB, time=156.87 NO POLE NO POLE x[1] = 1.086 y2[1] (analytic) = 1.5339718348022491900847847259714 y2[1] (numeric) = 1.5336489510708152857184706070594 absolute error = 0.000322883731433904366314118912 relative error = 0.021048869614710277679590260458839 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8847698849093010810424256041483 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4053443463050980807691376689327 relative error = 14.051184755689528887441209634203 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.087 y2[1] (analytic) = 1.5348568375537600320898614827493 y2[1] (numeric) = 1.5345311137342424046652589591206 absolute error = 0.0003257238195176274246025236287 relative error = 0.021221772060302568325553536170262 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8852354706119218856297188212437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4058099320077188853564308860281 relative error = 14.065054174647719156041190548065 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.088 y2[1] (analytic) = 1.5357423054483945584059943606521 y2[1] (numeric) = 1.5354137213634942374355265262482 absolute error = 0.0003285840849003209704678344039 relative error = 0.021395782595465027941741332251773 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8857001710791458479152184147362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4062746324749428476419304795206 relative error = 14.078892760470366572590881534724 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.4MB, time=157.49 NO POLE NO POLE x[1] = 1.089 y2[1] (analytic) = 1.5366282376006849481876458034578 y2[1] (numeric) = 1.5362967729635654903144763374505 absolute error = 0.0003314646371194578731694660073 relative error = 0.021570906287457783187479236164922 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8861639858462725393999997436219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4067384472420695391267118084063 relative error = 14.092700526952451889431852518305 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.09 y2[1] (analytic) = 1.5375146331246991229721029261249 y2[1] (numeric) = 1.5371802675385732870254210490199 absolute error = 0.000334365586125835946681877105 relative error = 0.021747148217139436069592250218144 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.886626914449487231608600628636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4072013758452842313353126934204 relative error = 14.106477487858599526576942410629 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.4MB, time=158.12 NO POLE NO POLE x[1] = 1.091 y2[1] (analytic) = 1.5384014911340416326114821498343 y2[1] (numeric) = 1.5380642040917571687297829445325 absolute error = 0.0003372870422844638816992053018 relative error = 0.021924513478976854806614345796483 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8870889564258613599037111764894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4076634178216583596304232412738 relative error = 14.12022365692308731008165876332 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.092 y2[1] (analytic) = 1.5392888107418545416681054835882 y2[1] (numeric) = 1.5389485816254790940270939348484 absolute error = 0.0003402291163754476410115487398 relative error = 0.022103007181054962544271663057497 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8875501113133529864146998397988 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4081245727091499861414119045832 relative error = 14.13393904784985620763625212706 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.4MB, time=158.76 NO POLE NO POLE x[1] = 1.093 y2[1] (analytic) = 1.5401765910608183162723620570624 y2[1] (numeric) = 1.5398333991412234389549955581115 absolute error = 0.0003431919195948773173664989509 relative error = 0.022282634445086524125458022926257 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8880103786508072620795127842255 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4085848400466042618062248490099 relative error = 14.147623674312520061246073901432 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.094 y2[1] (analytic) = 1.5410648312031527114421680469252 y2[1] (numeric) = 1.5407186556395969969892389797496 absolute error = 0.0003461755635557144529290671756 relative error = 0.022463400406421931117400863298683 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8884697579779568877994845209589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4090442193737538875261965857433 relative error = 14.16127754995437531686836647022 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.095 y2[1] (analytic) = 1.5419535302806176588631376772364 y2[1] (numeric) = 1.5416043501203289790436849924744 absolute error = 0.000349180160288679819452684762 relative error = 0.022645310214058985298194910331249 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.888928248835422574706598649776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4095027102312195744333107145604 relative error = 14.174900688388410750874172541114 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=957.4MB, alloc=4.4MB, time=159.38 NO POLE NO POLE x[1] = 1.096 y2[1] (analytic) = 1.5428426874045141551285775138303 y2[1] (numeric) = 1.5424904815822710134703040162815 absolute error = 0.0003522058222431416582734975488 relative error = 0.022828369030652680804359869044236 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8893858507647135035427384454507 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4099603121605105032694505102351 relative error = 14.188493103197317193204586851 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.097 y2[1] (analytic) = 1.5437323016856851504384158127608 y2[1] (numeric) = 1.5433770490233971460591760984503 absolute error = 0.0003552526622880043792397143105 relative error = 0.023012582032524985140557185166805 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8898425633082277831504679083043 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4104170247040247828771799730887 relative error = 14.202054807933497247091107765787 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.4MB, time=160.01 NO POLE NO POLE x[1] = 1.098 y2[1] (analytic) = 1.5446223722345164377561782239551 y2[1] (numeric) = 1.5442640514408038400384909135442 absolute error = 0.0003583207937125977176873104109 relative error = 0.023197954409674619252079512861524 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8902983860092529080748847881513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4108728474050499078015968529357 relative error = 14.215585816119075005210378802466 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.099 y2[1] (analytic) = 1.5455128981609375424231206931733 y2[1] (numeric) = 1.5451514878307099760745477634105 absolute error = 0.0003614103302275663485729297628 relative error = 0.023384491365786836860204939980751 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8907533184119662152760879798278 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4113277798077632150028000446122 relative error = 14.229086141245905762144140737992 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=965.1MB, alloc=4.4MB, time=160.64 x[1] = 1.1 y2[1] (analytic) = 1.5464038785744226122286299482153 y2[1] (numeric) = 1.5460393571884568522717555771802 absolute error = 0.0003645213859657599568743710351 relative error = 0.023572198118243203259986294089633 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8912073600614353399518025778717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4117818214572323396785146426561 relative error = 14.242555796775585723015743750369 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.101 y2[1] (analytic) = 1.5472953125839913079360014990487 y2[1] (numeric) = 1.5469276585085081841726329112684 absolute error = 0.0003676540754831237633685877803 relative error = 0.023761079898131373779523998063482 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8916605105036186704697067677687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4122349718994156701964188325531 relative error = 14.255994796139461708175095968752 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.102 y2[1] (analytic) = 1.5481871992982096942627046261544 y2[1] (numeric) = 1.5478163907844501047578079493739 absolute error = 0.0003708085137595895048966767805 relative error = 0.023951141950254872099248983408796 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8921127692853658024090056214744 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4126872306811628021357176862588 relative error = 14.269403152738640853804449897538 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.4MB, time=161.27 NO POLE NO POLE x[1] = 1.103 y2[1] (analytic) = 1.5490795378251911313142433768984 y2[1] (numeric) = 1.5487055530089911644460185024795 absolute error = 0.0003739848161999668682248744189 relative error = 0.024142389533142868629220121269976 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8925641359544179917107977556764 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4131385973502149914375098204608 relative error = 14.282780879944000308317951430671 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.104 y2[1] (analytic) = 1.5499723272725971664707221361436 y2[1] (numeric) = 1.5495951441739623310941120088519 absolute error = 0.0003771830986348353766101272917 relative error = 0.02433482791905995914191851551882 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8930146100594086069367817024688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4135890714552056066634937672532 relative error = 14.296127991096196924428397593169 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.4MB, time=161.90 NO POLE NO POLE x[1] = 1.105 y2[1] (analytic) = 1.5508655667476384267252238846103 y2[1] (numeric) = 1.5504851632703169899970455340416 absolute error = 0.0003804034773214367281783505687 relative error = 0.024528462394015943857498837526301 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8934641911498635806358497337686 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.414038652545660580362561798553 relative error = 14.309444499505676946755168743109 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.106 y2[1] (analytic) = 1.551759255357075511473108806681 y2[1] (numeric) = 1.551375609288130943887885770883 absolute error = 0.000383646068944567585223035798 relative error = 0.024723298257775607177935687586828 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8939128787762018598181177729194 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4144873401719988595448298377038 relative error = 14.322730418452685694847818745712 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.107 y2[1] (analytic) = 1.5526533922072198857513404584262 y2[1] (numeric) = 1.5522664812166024129378090394945 absolute error = 0.0003869109906174728135314189317 relative error = 0.024919340823868498265980762270422 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8943606724897358555359409194884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4149351338855328552626529842728 relative error = 14.335985761187277241500322597552 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.4MB, time=162.53 NO POLE NO POLE x[1] = 1.108 y2[1] (analytic) = 1.5535479764039347739269462565986 y2[1] (numeric) = 1.5531577780440520347561012872782 absolute error = 0.0003901983598827391708449693204 relative error = 0.025116595419598712664324408470116 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8948075718426718915714650062808 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4153820332384688912981770710652 relative error = 14.349210540929324086231495139864 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.109 y2[1] (analytic) = 1.5544430070526360538337186002104 y2[1] (numeric) = 1.5540494987579228643901580889202 absolute error = 0.0003935082947131894435605112902 relative error = 0.025315067386054675149832972379014 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8952535763881106522302655010551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4158280377839076519569775658395 relative error = 14.362404770868526823807606861294 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.4MB, time=163.16 NO POLE NO POLE x[1] = 1.11 y2[1] (analytic) = 1.5553384832582931513562624880664 y2[1] (numeric) = 1.5549416423447803743254846463904 absolute error = 0.000396840913512777030777841676 relative error = 0.025514762078118924017211223302891 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8956986856800476292406259593394 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4162731470758446289673380241238 relative error = 14.375568464164423807683733358837 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.111 y2[1] (analytic) = 1.5562344041254299354604950482804 y2[1] (numeric) = 1.5558342077903124544856957889427 absolute error = 0.0004001963351174809747992593377 relative error = 0.02571568486447789698591706612784 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8961428992733735677580091291065 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4167173606691705674847211938909 relative error = 14.38870163394640080824088380689 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.4MB, time=163.78 NO POLE NO POLE x[1] = 1.112 y2[1] (analytic) = 1.5571307687581256136697019493493 y2[1] (numeric) = 1.5567271940793294122325159731148 absolute error = 0.0004035746787962014371859762345 relative error = 0.025917841127631718923633770607425 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.896586216723874911474274702875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4171606781196719112009867676594 relative error = 14.401804293313700665696460784858 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.113 y2[1] (analytic) = 1.5580275762600156279852552168044 y2[1] (numeric) = 1.5576206001957639723657792827283 absolute error = 0.0004069760642516556194759340761 relative error = 0.026121236263903991579083058202155 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8970286375882342468311986080539 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4176030989840312465579106728383 relative error = 14.414876455335432937566109039389 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.114 y2[1] (analytic) = 1.5589248257342925512510965347952 y2[1] (numeric) = 1.5585144251226712771234294288887 absolute error = 0.0004104006116212741276671059065 relative error = 0.026325875683451585516440615586819 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8974701614240307463378496220504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4180446228198277460645616868348 relative error = 14.427918133050583540555514214601 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.4MB, time=164.40 NO POLE NO POLE x[1] = 1.115 y2[1] (analytic) = 1.5598225162837069839610896681975 y2[1] (numeric) = 1.5594086678422288861815197499853 absolute error = 0.0004138484414780977795699182122 relative error = 0.026531764810274434443093966072687 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8979107877897406109913799948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4184852491855376107180920595844 relative error = 14.44092933946802438676121427829 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.116 y2[1] (analytic) = 1.5607206470105684515083451979695 y2[1] (numeric) = 1.5603033273357367766542132116915 absolute error = 0.000417319674831674854131986278 relative error = 0.026738909082225332121961143233096 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8983505162447375118007876579656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.41892497764053451152749972275 relative error = 14.453910087566523014059986310554 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.4MB, time=165.03 NO POLE NO POLE x[1] = 1.117 y2[1] (analytic) = 1.5616192170167463018756203205038 y2[1] (numeric) = 1.5611984025836173430937824069643 absolute error = 0.0004208144331289587818379135395 relative error = 0.026947313951019732059067292190918 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8987893463492930304132084970801 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4193638077450900301399205618645 relative error = 14.466860390294752210566869509386 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.118 y2[1] (analytic) = 1.5625182254036706037658960206517 y2[1] (numeric) = 1.5620938925654153974906095560448 absolute error = 0.0004243328382552062752864646069 relative error = 0.027156984882245550156555190778672 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8992272776645770988422980603767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4198017390603740985690101251611 relative error = 14.479780260571299633042381711744 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=995.6MB, alloc=4.4MB, time=165.66 x[1] = 1.119 y2[1] (analytic) = 1.5634176712723330451722334879172 y2[1] (numeric) = 1.5629897962597981692731865064579 absolute error = 0.0004278750125348758990469814593 relative error = 0.027367927355372970520784752068917 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.8996643097526584382982629759624 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4202387711484554380249750407468 relative error = 14.49266971128467741912998143446 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.12 y2[1] (analytic) = 1.5643175537232878323860112060389 y2[1] (numeric) = 1.5638861126445553053081147330124 absolute error = 0.0004314410787325270778964730265 relative error = 0.027580146863764254614655858059695 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9001004421765049971191032473392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4206749035723019968458153121236 relative error = 14.505528755293331793305320413083 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.121 y2[1] (analytic) = 1.5652178718566525894426437077979 y2[1] (numeric) = 1.564782840696598869900105337801 absolute error = 0.0004350311600537195425383699969 relative error = 0.027793648914683553942768398969026 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9005356744999843878026274960677 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4211101358957813875293395608521 relative error = 14.518357405425652666419322864492 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.4MB, time=166.29 NO POLE NO POLE x[1] = 1.122 y2[1] (analytic) = 1.5661186247721092580038825494078 y2[1] (numeric) = 1.5656799793919633447919790502002 absolute error = 0.0004386453801459132119034992076 relative error = 0.02800843902930672645751316969979 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9009700062878643231388041195943 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4215444676836613228655161843787 relative error = 14.531155674479983228717617226753 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.123 y2[1] (analytic) = 1.5670198115689049976757996222608 y2[1] (numeric) = 1.5665775277058056291646662268705 absolute error = 0.0004422838630993685111333953903 relative error = 0.028224522742731156873667321267166 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9014034371058130514420122319265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4219778985016100511687242967109 relative error = 14.543923575224629536219333943342 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.4MB, time=166.91 NO POLE NO POLE x[1] = 1.124 y2[1] (analytic) = 1.5679214313458530867615524841214 y2[1] (numeric) = 1.5674754846124050396372068517562 absolute error = 0.0004459467334480471243456323652 relative error = 0.02844190560398558107854839668852 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9018359665203997908827571549424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4224104279161967906094692197268 relative error = 14.55666112039787009033876896442 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.125 y2[1] (analytic) = 1.5688234832013338234480309570783 y2[1] (numeric) = 1.5683738490851633102667505360855 absolute error = 0.0004496341161705131812804209928 relative error = 0.02866059317603991482426161403701 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9022675940990951629184161286548 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4228420554948921626451281934392 relative error = 14.569368322707965410633897041327 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.126 y2[1] (analytic) = 1.5697259662332954274254838056815 y2[1] (numeric) = 1.5692726200966045925485565183705 absolute error = 0.000453346136690834876927287311 relative error = 0.0288805910358150868880560101069 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9026983194102716248225808097203 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4232727808060686245492928745047 relative error = 14.58204519483316760056620159781 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.4MB, time=167.54 NO POLE NO POLE x[1] = 1.127 y2[1] (analytic) = 1.5706288795392549419392238757145 y2[1] (numeric) = 1.5701717966183754554159936644072 absolute error = 0.0004570829208794865232302113073 relative error = 0.029101904774192876886286342624529 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9031281420232039013125640288867 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4237026034190009010392760936711 relative error = 14.594691749421729906156768978598 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.128 y2[1] (analytic) = 1.571532222216299136272509641971 y2[1] (numeric) = 1.5710713776212448852405404672754 absolute error = 0.0004608445950542510319691746956 relative error = 0.02932453999602575792695928241131 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.903557061508069415274639179909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4241315229038664150013512446934 relative error = 14.607307999091916267424074208877 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.4MB, time=168.17 NO POLE NO POLE x[1] = 1.129 y2[1] (analytic) = 1.5724359933610854086597006822295 y2[1] (numeric) = 1.5719713620751042858317850473389 absolute error = 0.0004646312859811228279156348906 relative error = 0.029548502320146744285324425374179 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9039850774359487175865815147284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4245595388317457173132935795128 relative error = 14.619893956432010862489363052576 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.13 y2[1] (analytic) = 1.5733401920698426896287841643465 y2[1] (numeric) = 1.5728717489489674784374251522453 absolute error = 0.0004684431208752111913590121012 relative error = 0.029773797379379244286453033193492 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9044121893788259160370815224114 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4249866507746229157637935871958 relative error = 14.632449634000327644236011139538 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.4MB, time=168.79 NO POLE NO POLE x[1] = 1.131 y2[1] (analytic) = 1.5742448174383723457723690040154 y2[1] (numeric) = 1.5737725372109707017432681569261 absolute error = 0.0004722802274016440291008470893 relative error = 0.030000430820546918578230185894548 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9048383969095891033416014724691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4254128583053861030683135372535 relative error = 14.644975044325219869409715246907 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.132 y2[1] (analytic) = 1.5751498685620490839462439222745 y2[1] (numeric) = 1.5746737258283726118732310635967 absolute error = 0.0004761427336764720730128586778 relative error = 0.030228408304483543977669215321047 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9052636996020307842542471067375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4258381609978277839809591715219 relative error = 14.657470199905089620046844474831 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.133 y2[1] (analytic) = 1.5760553445358218558945952042796 y2[1] (numeric) = 1.5755753137675542823893405017564 absolute error = 0.0004800307682675735052547025232 relative error = 0.030457735506042883072940899774257 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9056880970308483017752273679812 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4262625584266453015019394327656 relative error = 14.669935113208397317118750056306 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.4MB, time=169.42 NO POLE NO POLE x[1] = 1.134 y2[1] (analytic) = 1.5769612444542147633009795341995 y2[1] (numeric) = 1.5764772999940192042917327281884 absolute error = 0.0004839444601955590092468060111 relative error = 0.030688418114108559762993952749086 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9061115887716442624534759577981 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4266860501674412621801880225825 relative error = 14.68236979667367122628030189174 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.135 y2[1] (analytic) = 1.5778675674113279632641468553367 y2[1] (numeric) = 1.5773796834723932860186536269597 absolute error = 0.000487883938934677245493228377 relative error = 0.030920461831603940916127846933443 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.906534174400926960784009421237 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4271086357967239605107214860214 relative error = 14.694774262709516955611387606256 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.4MB, time=170.05 NO POLE NO POLE x[1] = 1.136 y2[1] (analytic) = 1.578774312500838574197807779727 y2[1] (numeric) = 1.5782824631664248534464587094213 absolute error = 0.0004918493344137207513490703057 relative error = 0.031153872375502024328363993451378 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9069558534961108026995973608071 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4275303148919078024263094255915 relative error = 14.707148523694626945240575997864 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.137 y2[1] (analytic) = 1.5796814788160015821534396475239 y2[1] (numeric) = 1.5791856380389846498896131142079 absolute error = 0.000495840777016932263826533316 relative error = 0.031388655476835333161946759974443 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9073766256355167281563212882432 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4279510870313137278830333530276 relative error = 14.719492591977789948740611182977 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1026.1MB, alloc=4.4MB, time=170.68 x[1] = 1.138 y2[1] (analytic) = 1.5805890654496507475652249134399 y2[1] (numeric) = 1.5800892070520658361006916072383 absolute error = 0.0004998583975849114645333062016 relative error = 0.031624816880705817043791774717272 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9077964903983726328125995285035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4283709517941696325393115932879 relative error = 14.731806479877900506185866558341 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.139 y2[1] (analytic) = 1.5814970714941995124162151153795 y2[1] (numeric) = 1.580993169166783990270378581715 absolute error = 0.0005039023274155221458365336645 relative error = 0.031862362346294760003185440125322 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9082154473648137888012564970109 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4287899087606107885279685617953 relative error = 14.744090199683968408762348890875 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.14 y2[1] (analytic) = 1.5824054960416419078248132591774 y2[1] (numeric) = 1.5818975233433771080274680581246 absolute error = 0.0005079726982647997973452010528 relative error = 0.032101297646872695427526584955837 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9086334961158832645942155781022 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4292079575116802643209276428866 relative error = 14.756343763655128154821302424947 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.4MB, time=171.30 NO POLE NO POLE x[1] = 1.141 y2[1] (analytic) = 1.5833143381835534620506670330335 y2[1] (numeric) = 1.5828022685412056024388636842373 absolute error = 0.0005120696423478596118033487962 relative error = 0.03234162856980932821438873016967 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.909050636233532343959395740028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4296250976293293436861078048124 relative error = 14.768567184020648397267920866119 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.142 y2[1] (analytic) = 1.5842235970110921089190648458288 y2[1] (numeric) = 1.5837074037187523040095787351074 absolute error = 0.0005161932923398049094861107214 relative error = 0.032583360916583464297669546570712 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9094668673006209440093929296424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4300413286964179437361049944268 relative error = 14.780760472979941382177131466925 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1033.7MB, alloc=4.4MB, time=171.94 NO POLE NO POLE x[1] = 1.143 y2[1] (analytic) = 1.5851332716149990966629262650005 y2[1] (numeric) = 1.584612927833622460682736113073 absolute error = 0.0005203437813766359801901519275 relative error = 0.032826500502792947725082754289463 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9098821889009180323415281981339 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4304566502967150320682402629183 relative error = 14.792923642702572378528870209505 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.144 y2[1] (analytic) = 1.5860433610855998971814780120622 y2[1] (numeric) = 1.5855188398425437378395683477561 absolute error = 0.0005245212430561593419096643061 relative error = 0.033071053158164605463736969477035 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.910296600619102043268845417787 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4308710620148990429955574825714 relative error = 14.805056705328269098955720257866 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.145 memory used=1037.6MB, alloc=4.4MB, time=172.56 y2[1] (analytic) = 1.5869538645128051157147062571694 y2[1] (numeric) = 1.5864251387013662182994175960626 absolute error = 0.0005287258114388974152886611068 relative error = 0.033317024726564200110035855740131 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9107101020407612931416423588084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4312845634365582928683544235928 relative error = 14.817159672966931111396237444335 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.146 y2[1] (analytic) = 1.5878647809861114009326755383524 y2[1] (numeric) = 1.5873318233650624023197356421823 absolute error = 0.0005329576210489986129398961701 relative error = 0.033564421066006390679624399881673 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9111226927523943947591198047236 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.431697154148191394485831869508 relative error = 14.829232557698639241547736566725 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.147 y2[1] (analytic) = 1.5887761095946023554388042161757 y2[1] (numeric) = 1.5882388927877272075960838975888 absolute error = 0.0005372168068751478427203185869 relative error = 0.033813248048664701652597217318582 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9115343723414106708707342947284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4321088337372076705974463595128 relative error = 14.841275371573664966012760709851 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.4MB, time=173.19 NO POLE NO POLE x[1] = 1.148 y2[1] (analytic) = 1.5896878494269494466861859606218 y2[1] (numeric) = 1.5891463459225779692621334010397 absolute error = 0.0005415035043714774240525595821 relative error = 0.03406351156088150044867651430305 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9119451403961305667668409916768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4325196017919275664935530564612 relative error = 14.853288126612479796033902673448 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.149 y2[1] (analytic) = 1.590599999571412918306046353956 y2[1] (numeric) = 1.5900541817219544398896648185763 absolute error = 0.0005458178494584784163815353797 relative error = 0.034315217503177983506559706051594 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9123549965057860619582140850978 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4329294579015830616849261498822 relative error = 14.86527083480576465171209289358 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.4MB, time=173.82 NO POLE NO POLE x[1] = 1.15 y2[1] (analytic) = 1.5915125591158427018474232811901 y2[1] (numeric) = 1.590962399137318789488568443524 absolute error = 0.0005501599785239123588548376661 relative error = 0.034568371790264171141129723547208 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9127639402605210809440330497537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4333384016563180806707451145381 relative error = 14.877223508114419226603911991951 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.151 y2[1] (analytic) = 1.5924255271476793289271593685416 y2[1] (numeric) = 1.591870997119255605506844196492 absolute error = 0.0005545300284237234203151720496 relative error = 0.034822980351048911351714751281698 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.913171971251391903067923991789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4337464326471889027946360565734 relative error = 14.889146158469571342593928282896 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.152 y2[1] (analytic) = 1.5933389027539548437892943199711 y2[1] (numeric) = 1.5927799746174718928306016253733 absolute error = 0.0005589281364829509586926945978 relative error = 0.035079049128649892754078534925146 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9135790890703675714616462264618 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4341535504661645711883582912462 relative error = 14.901038797772586294938501216469 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.4MB, time=174.44 NO POLE NO POLE x[1] = 1.153 y2[1] (analytic) = 1.594252685021293716272944592482 y2[1] (numeric) = 1.5936893305807970737840599053449 absolute error = 0.0005633544404966424888846871371 relative error = 0.035336584080403666808317495367488 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9139852933103303010760151438061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4345597547061273008027272085905 relative error = 14.912901437895076187377930843948 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.154 y2[1] (analytic) = 1.5951668730359137551877574423796 y2[1] (numeric) = 1.5945990639571829881295478388676 absolute error = 0.000567809078730767058209603512 relative error = 0.035595591177875679514336695647964 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9143905835650758857986533313354 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4349650449608728855253653961198 relative error = 14.924734090678909257214270964383 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.4MB, time=175.07 NO POLE NO POLE x[1] = 1.155 y2[1] (analytic) = 1.5960814658836270220960259671097 y2[1] (numeric) = 1.5955091736937038930675038556862 absolute error = 0.0005722921899231290285221114235 relative error = 0.035856076406870312746073242034829 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9147949594293141046581628360706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.435369420825111104384874900855 relative error = 14.93653676793621919025255965335 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.156 y2[1] (analytic) = 1.5969964626498407455005513606404 y2[1] (numeric) = 1.5964196587365564632364760128292 absolute error = 0.0005768039132842822640753478112 relative error = 0.036118045767440935395132973041468 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9151984204986691271143123617542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4357728818944661268410244265386 relative error = 14.948309481449414425503655393232 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.4MB, time=175.70 NO POLE NO POLE x[1] = 1.157 y2[1] (analytic) = 1.5979118624195582354373381945989 y2[1] (numeric) = 1.5973305180310597907131219946092 absolute error = 0.0005813443884984447242161999897 relative error = 0.03638150527389996449400431102567 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9156009663696799174338341110968 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4361754277654769171605461758812 relative error = 14.96005224297118744954730002363 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.158 y2[1] (analytic) = 1.5988276642773797984722081325456 y2[1] (numeric) = 1.5982417505216553850122091126225 absolute error = 0.0005859137557244134599990199231 relative error = 0.036646460954828936488511933760471 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9160025966398006381514258972928 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4365770580355976378781379620772 relative error = 14.97176506422452408045446121643 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.159 y2[1] (analytic) = 1.5997438673075036531004170808466 y2[1] (numeric) = 1.5991533551519071730866143057494 absolute error = 0.0005905121555964800138027750972 relative error = 0.036912918853088588828672478208547 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9164033109074010526155550638374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4369777723031980523422671286218 relative error = 14.983447956902712741168437158156 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1060.4MB, alloc=4.4MB, time=176.33 NO POLE NO POLE x[1] = 1.16 y2[1] (analytic) = 1.600660470593726845548360376606 y2[1] (numeric) = 1.600065330864501499327324140154 absolute error = 0.000595139729225346221036236452 relative error = 0.037180885025828952046614828862738 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9168031087717669266186616668743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4373775701675639263453737316587 relative error = 14.995100932669353722244634597836 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.161 y2[1] (analytic) = 1.6015774732194461659764502110262 y2[1] (numeric) = 1.6009776766012471255634348092843 absolute error = 0.0005997966181990404130154017419 relative error = 0.037450365544499452489728678368839 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9172019898331004291113592899035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4377764512288974288380713546879 relative error = 15.006724003158368433849358397253 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.4MB, time=176.96 NO POLE NO POLE x[1] = 1.162 y2[1] (analytic) = 1.602494874267659065082249085398 y2[1] (numeric) = 1.6018903913030752310621521338723 absolute error = 0.0006044829645838340200969515257 relative error = 0.037721366494859025876706991889488 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9175999536925205320002327766828 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4381744150883175317269448414672 relative error = 15.018317179974008646918376207668 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.163 y2[1] (analytic) = 1.6034126728209645711029426966612 y2[1] (numeric) = 1.6028034739100394125287915619337 absolute error = 0.0006091989109251585741511347275 relative error = 0.037993893976986241843650768489919 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.917996999952063409028833084559 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4385714613478604087555451493434 relative error = 15.0298804746908657233764458981 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1068.1MB, alloc=4.4MB, time=177.59 x[1] = 1.164 y2[1] (analytic) = 1.6043308679615642072162352501407 y2[1] (numeric) = 1.6037169233613156841067781687682 absolute error = 0.0006139446002485231094570813725 relative error = 0.038267954105289439646908085127627 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9183931282146828337414703772652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4389675896104798334681824420496 relative error = 15.041413898853879835319415880521 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.165 y2[1] (analytic) = 1.6052494587712629093387497986382 y2[1] (numeric) = 1.6046307385952024773776466569594 absolute error = 0.0006187201760604319611031416788 relative error = 0.038543553008516875188823842060965 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9187883380842505765294073934265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4393627994800475762561194582109 relative error = 15.052917463978349173060929522482 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.166 y2[1] (analytic) = 1.6061684443314699443210158095567 y2[1] (numeric) = 1.6055449185491206413610413563747 absolute error = 0.000623525782349302959974453182 relative error = 0.038820696829766879532081913874335 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9191826291655568007590560446127 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4397570905613538004857681093971 relative error = 15.064391181549939141946184412708 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.4MB, time=178.21 NO POLE NO POLE x[1] = 1.167 y2[1] (analytic) = 1.6070878237231998285381257651454 y2[1] (numeric) = 1.6064594621596134425147162241655 absolute error = 0.0006283615635863860234095409799 relative error = 0.039099391726498029067827558442191 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9195760010643104579817811147742 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4401504624601074577084931795586 relative error = 15.075835063024691547835615355781 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.168 y2[1] (analytic) = 1.6080075960270732468751422052864 y2[1] (numeric) = 1.6073743683623465647345348447669 absolute error = 0.0006332276647266821406073605195 relative error = 0.039379643870539327502264958332697 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9199684533871396822249158512909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4405429147829366819516279160753 relative error = 15.087249119829033771161786623443 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1075.7MB, alloc=4.4MB, time=178.85 NO POLE NO POLE x[1] = 1.169 y2[1] (analytic) = 1.6089277603233179721063362274918 y2[1] (numeric) = 1.6082896360921081093544704298981 absolute error = 0.0006381242312098627518657975937 relative error = 0.039661459448100399825932675107402 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9203599857415921833635951566516 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.440934447137389183090307221436 relative error = 15.098633363359787929463194187547 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.17 y2[1] (analytic) = 1.6098483156917697846673380649495 y2[1] (numeric) = 1.609205264282808595146605818562 absolute error = 0.0006430514089611895207322463875 relative error = 0.0399448446597816984293685982461 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.920750597736135639573013008962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4413250591319326392997250737464 relative error = 15.109987804984180028299092408644 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.171 y2[1] (analytic) = 1.6107692612118733928192799705438 y2[1] (numeric) = 1.6101212518674809583211334770455 absolute error = 0.0006480093443924344981464934983 relative error = 0.040229805720584721528385676470059 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9211402889801580888607116590592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4417147503759550885874237238436 relative error = 15.121312456039849100449871960091 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.4MB, time=179.46 NO POLE NO POLE x[1] = 1.172 y2[1] (analytic) = 1.6116905959626833532040112427848 y2[1] (numeric) = 1.6110375977782805525263554989193 absolute error = 0.0006529981844028006776557438655 relative error = 0.040516348859922244061690341149749 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9215290590839683196785110719728 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4421035204797653194052231367572 relative error = 15.132607327834856333307926635294 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.173 y2[1] (analytic) = 1.6126123190228649917894648385082 y2[1] (numeric) = 1.6119543009464851488486836050381 absolute error = 0.0006580180763798429407812334701 relative error = 0.040804480321628561223087078739329 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9219169076587962606136880008392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4424913690545932603404000656236 relative error = 15.143872431647694184364356121143 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.4MB, time=180.10 NO POLE NO POLE x[1] = 1.174 y2[1] (analytic) = 1.6135344294706953252042546270552 y2[1] (numeric) = 1.6128713603024949358126391435404 absolute error = 0.0006630691682003893916154835148 relative error = 0.04109420636396974479002509240594 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9223038343167933691590150021193 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4428782957125903688857270669037 relative error = 15.155107778727295484697259828446 % Correct digits = 1 h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.175 y2[1] (analytic) = 1.6144569263840639824605819514124 y2[1] (numeric) = 1.6137887747758325193808530898485 absolute error = 0.0006681516082314630797288615639 relative error = 0.041385533259653912409756421819244 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 2.9226898386710330195612706221156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4432643000668300192879826869 relative error = 15.166313380293042530367783456191 % Correct digits = 1 h = 0.001 Finished! Maximum Time Reached before Solution Completed! diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); Iterations = 675 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 39 Minutes 14 Seconds Optimized Time Remaining = 39 Minutes 11 Seconds Expected Total Time = 42 Minutes 11 Seconds Time to Timeout Unknown Percent Done = 7.116 % > quit memory used=1085.9MB, alloc=4.4MB, time=180.49