|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > # Begin Function number 3 > check_sign := proc( x0 ,xf) > local ret; > if (xf > x0) then # if number 1 > ret := 1.0; > else > ret := -1.0; > fi;# end if 1; > ret;; > end; check_sign := proc(x0, xf) local ret; if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret end proc > # End Function number 3 > # Begin Function number 4 > est_size_answer := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local min_size; > min_size := glob_large_float; > if (omniabs(array_y2[1]) < min_size) then # if number 1 > min_size := omniabs(array_y2[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (omniabs(array_y1[1]) < min_size) then # if number 1 > min_size := omniabs(array_y1[1]); > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > if (min_size < 1.0) then # if number 1 > min_size := 1.0; > omniout_float(ALWAYS,"min_size",32,min_size,32,""); > fi;# end if 1; > min_size; > end; est_size_answer := proc() local min_size; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; min_size := glob_large_float; if omniabs(array_y2[1]) < min_size then min_size := omniabs(array_y2[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if omniabs(array_y1[1]) < min_size then min_size := omniabs(array_y1[1]); omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; if min_size < 1.0 then min_size := 1.0; omniout_float(ALWAYS, "min_size", 32, min_size, 32, "") end if; min_size end proc > # End Function number 4 > # Begin Function number 5 > test_suggested_h := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local max_value3,hn_div_ho,hn_div_ho_2,hn_div_ho_3,value3,no_terms; > max_value3 := 0.0; > no_terms := glob_max_terms; > hn_div_ho := 0.5; > hn_div_ho_2 := 0.25; > hn_div_ho_3 := 0.125; > omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,""); > omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,""); > omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,""); > value3 := omniabs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > value3 := omniabs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3); > if (value3 > max_value3) then # if number 1 > max_value3 := value3; > omniout_float(ALWAYS,"value3",32,value3,32,""); > fi;# end if 1; > omniout_float(ALWAYS,"max_value3",32,max_value3,32,""); > max_value3; > end; test_suggested_h := proc() local max_value3, hn_div_ho, hn_div_ho_2, hn_div_ho_3, value3, no_terms; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; max_value3 := 0.; no_terms := glob_max_terms; hn_div_ho := 0.5; hn_div_ho_2 := 0.25; hn_div_ho_3 := 0.125; omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, ""); omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, ""); omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, ""); value3 := omniabs(array_y2[no_terms - 3] + array_y2[no_terms - 2]*hn_div_ho + array_y2[no_terms - 1]*hn_div_ho_2 + array_y2[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; value3 := omniabs(array_y1[no_terms - 3] + array_y1[no_terms - 2]*hn_div_ho + array_y1[no_terms - 1]*hn_div_ho_2 + array_y1[no_terms]*hn_div_ho_3); if max_value3 < value3 then max_value3 := value3; omniout_float(ALWAYS, "value3", 32, value3, 32, "") end if; omniout_float(ALWAYS, "max_value3", 32, max_value3, 32, ""); max_value3 end proc > # End Function number 5 > # Begin Function number 6 > reached_interval := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local ret; > if (glob_check_sign * (array_x[1]) >= glob_check_sign * glob_next_display) then # if number 1 > ret := true; > else > ret := false; > fi;# end if 1; > return(ret); > end; reached_interval := proc() local ret; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if glob_check_sign*glob_next_display <= glob_check_sign*array_x[1] then ret := true else ret := false end if; return ret end proc > # End Function number 6 > # Begin Function number 7 > display_alot := proc(iter) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (reached_interval()) then # if number 1 > if (iter >= 0) then # if number 2 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := omniabs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (omniabs(analytic_val_y) <> 0.0) then # if number 3 > relerr := abserr*100.0/omniabs(analytic_val_y); > if (relerr > 0.0000000000000000000000000000000001) then # if number 4 > glob_good_digits := -trunc(log10(relerr)) + 2; > else > glob_good_digits := Digits; > fi;# end if 4; > else > relerr := -1.0 ; > glob_good_digits := -1; > fi;# end if 3; > if (glob_iter = 1) then # if number 3 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 3; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ") > ; > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > fi;# end if 2; > #BOTTOM DISPLAY ALOT > fi;# end if 1; > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if reached_interval() then if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := omniabs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if omniabs(analytic_val_y) <> 0. then relerr := abserr*100.0/omniabs(analytic_val_y); if 0.1*10^(-33) < relerr then glob_good_digits := -trunc(log10(relerr)) + 2 else glob_good_digits := Digits end if else relerr := -1.0; glob_good_digits := -1 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_int(INFO, "Correct digits ", 32, glob_good_digits, 4, " "); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end if end proc > # End Function number 7 > # Begin Function number 8 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > hnew := h_param; > glob_normmax := glob_small_float; > if (omniabs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (omniabs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := omniabs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1; > if (glob_look_poles and (omniabs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > return(hnew); > fi;# end if 2 > fi;# end if 1; > if ( not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1; > hnew := sz2; > ;#END block > return(hnew); > #BOTTOM ADJUST FOR POLE > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < omniabs(array_y2_higher[1, 1]) then tmp := omniabs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < omniabs(array_y1_higher[1, 1]) then tmp := omniabs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < omniabs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2; return hnew end proc > # End Function number 8 > # Begin Function number 9 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if (convfloat(percent_done) < convfloat(100.0)) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > omniout_str_noeol(INFO,"Expected Total Time "); > omniout_timestr(convfloat(glob_total_exp_sec)); > fi;# end if 1; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec; percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)); omniout_str_noeol(INFO, "Expected Total Time "); omniout_timestr(convfloat(glob_total_exp_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # End Function number 9 > # Begin Function number 10 > check_for_pole := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local cnt, dr1, dr2, ds1, ds2, hdrc,hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y2_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y2_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y2_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((omniabs(array_y1_higher[1,m]) < glob_small_float * glob_small_float) or (omniabs(array_y1_higher[1,m-1]) < glob_small_float * glob_small_float) or (omniabs(array_y1_higher[1,m-2]) < glob_small_float * glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m)*rm0-convfloat(m-1)*rm1; > if (omniabs(hdrc) > glob_small_float * glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := (rm1*convfloat((m-2)*(m-2))-rm0*convfloat(m-3))/hdrc; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 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 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y2_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y2_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y2_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y2_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y2_higher[1,m-5]) <= (glob_small_float)))) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (omniabs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2; > n := n - 1; > od;# end do number 2; > m := n + cnt; > if (m <= 10) then # if number 2 > rad_c := glob_large_float; > ord_no := glob_large_float; > elif > (((omniabs(array_y1_higher[1,m]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (omniabs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (omniabs(array_y1_higher[1,m-5]) >= (glob_large_float))) or ((omniabs(array_y1_higher[1,m]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-1]) <=(glob_small_float)) or (omniabs(array_y1_higher[1,m-2]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-3]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-4]) <= (glob_small_float)) or (omniabs(array_y1_higher[1,m-5]) <= (glob_small_float)))) then # if number 3 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((omniabs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (omniabs(dr1) <= glob_small_float)) then # if number 4 > rad_c := glob_large_float; > ord_no := glob_large_float; > else > if (omniabs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (omniabs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * omniabs(glob_h); > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3; > #BOTTOM RADII COMPLEX EQ = 2 > found_sing := 0; > #TOP WHICH RADII EQ = 1 > if (1 <> found_sing and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0)))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float)))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found_sing := 1; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > -1.0 * glob_smallish_float))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found_sing := 1; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0))) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found_sing := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 1"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (1 <> found_sing ) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 1"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 1 > #TOP WHICH RADII EQ = 2 > if (2 <> found_sing and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0)))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float)))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found_sing := 2; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 2"); > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > -1.0 * glob_smallish_float))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found_sing := 2; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Real estimate of pole used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0))) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found_sing := 2; > if (glob_display_flag) then # if number 4 > if (reached_interval()) then # if number 5 > omniout_str(ALWAYS,"Complex estimate of poles used for equation 2"); > fi;# end if 5; > fi;# end if 4; > fi;# end if 3; > if (2 <> found_sing ) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (reached_interval()) then # if number 4 > omniout_str(ALWAYS,"NO POLE for equation 2"); > fi;# end if 4; > fi;# end if 3; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if (array_pole[1] > array_poles[1,1]) then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if (array_pole[1] > array_poles[2,1]) then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3; > #BOTTOM WHICH RADIUS EQ = 2 > #START ADJUST ALL SERIES > if (array_pole[1] * glob_ratio_of_radius < omniabs(glob_h)) then # if number 3 > h_new := array_pole[1] * glob_ratio_of_radius; > term := 1; > ratio := 1.0; > while (term <= glob_max_terms) do # do number 2 > array_y2[term] := array_y2[term]* ratio; > array_y2_higher[1,term] := array_y2_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > array_y1[term] := array_y1[term]* ratio; > array_y1_higher[1,term] := array_y1_higher[1,term]* ratio; > array_x[term] := array_x[term]* ratio; > ratio := ratio * h_new / omniabs(glob_h); > term := term + 1; > od;# end do number 2; > glob_h := h_new; > fi;# end if 3; > #BOTTOM ADJUST ALL SERIES > if (reached_interval()) then # if number 3 > display_pole(); > fi;# end if 3 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, hdrc_BBB, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y2_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y2_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y2_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and ( omniabs(array_y1_higher[1, m]) < glob_small_float*glob_small_float or omniabs(array_y1_higher[1, m - 1]) < glob_small_float*glob_small_float or omniabs(array_y1_higher[1, m - 2]) < glob_small_float*glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m)*rm0 - convfloat(m - 1)*rm1; if glob_small_float*glob_small_float < omniabs(hdrc) then rcs := glob_h/hdrc; ord_no := ( rm1*convfloat((m - 2)*(m - 2)) - rm0*convfloat(m - 3))/hdrc ; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 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 rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y2_higher[1, m]) or glob_large_float <= omniabs(array_y2_higher[1, m - 1]) or glob_large_float <= omniabs(array_y2_higher[1, m - 2]) or glob_large_float <= omniabs(array_y2_higher[1, m - 3]) or glob_large_float <= omniabs(array_y2_higher[1, m - 4]) or glob_large_float <= omniabs(array_y2_higher[1, m - 5]) or omniabs(array_y2_higher[1, m]) <= glob_small_float or omniabs(array_y2_higher[1, m - 1]) <= glob_small_float or omniabs(array_y2_higher[1, m - 2]) <= glob_small_float or omniabs(array_y2_higher[1, m - 3]) <= glob_small_float or omniabs(array_y2_higher[1, m - 4]) <= glob_small_float or omniabs(array_y2_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < omniabs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then rad_c := glob_large_float; ord_no := glob_large_float elif glob_large_float <= omniabs(array_y1_higher[1, m]) or glob_large_float <= omniabs(array_y1_higher[1, m - 1]) or glob_large_float <= omniabs(array_y1_higher[1, m - 2]) or glob_large_float <= omniabs(array_y1_higher[1, m - 3]) or glob_large_float <= omniabs(array_y1_higher[1, m - 4]) or glob_large_float <= omniabs(array_y1_higher[1, m - 5]) or omniabs(array_y1_higher[1, m]) <= glob_small_float or omniabs(array_y1_higher[1, m - 1]) <= glob_small_float or omniabs(array_y1_higher[1, m - 2]) <= glob_small_float or omniabs(array_y1_higher[1, m - 3]) <= glob_small_float or omniabs(array_y1_higher[1, m - 4]) <= glob_small_float or omniabs(array_y1_higher[1, m - 5]) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if omniabs(nr1*dr2 - nr2*dr1) <= glob_small_float or omniabs(dr1) <= glob_small_float then rad_c := glob_large_float; ord_no := glob_large_float else if glob_small_float < omniabs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < omniabs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*omniabs(glob_h) else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found_sing := 0; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found_sing := 1; array_type_pole[1] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found_sing := 1; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 1 <> found_sing and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and -1.0*glob_smallish_float < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found_sing := 1; array_type_pole[1] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 1") end if end if end if; if 1 <> found_sing and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found_sing := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 1") end if end if end if; if 1 <> found_sing then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 1") end if end if; if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found_sing := 2; array_type_pole[2] := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 2") end if end if end if; if 2 <> found_sing and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and -1.0*glob_smallish_float < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found_sing := 2; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 2") end if end if end if; if 2 <> found_sing and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found_sing := 2; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 2") end if end if; if 2 <> found_sing and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and -1.0*glob_smallish_float < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found_sing := 2; array_type_pole[2] := 1; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Real estimate of pole used for equation 2") end if end if end if; if 2 <> found_sing and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found_sing := 2; if glob_display_flag then if reached_interval() then omniout_str(ALWAYS, "Complex estimate of poles used for equation 2") end if end if end if; if 2 <> found_sing then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if reached_interval() then omniout_str(ALWAYS, "NO POLE for equation 2") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; if array_pole[1]*glob_ratio_of_radius < omniabs(glob_h) then h_new := array_pole[1]*glob_ratio_of_radius; term := 1; ratio := 1.0; while term <= glob_max_terms do array_y2[term] := array_y2[term]*ratio; array_y2_higher[1, term] := array_y2_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; array_y1[term] := array_y1[term]*ratio; array_y1_higher[1, term] := array_y1_higher[1, term]*ratio; array_x[term] := array_x[term]*ratio; ratio := ratio*h_new/omniabs(glob_h); term := term + 1 end do; glob_h := h_new end if; if reached_interval() then display_pole() end if end proc > # End Function number 10 > # Begin Function number 11 > get_norms := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local iii; > if ( not glob_initial_pass) then # if number 3 > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > array_norms[iii] := 0.0; > iii := iii + 1; > od;# end do number 2; > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y2[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (omniabs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := omniabs(array_y1[iii]); > fi;# end if 4; > iii := iii + 1; > od;# end do number 2 > #BOTTOM GET NORMS > ; > fi;# end if 3; > end; get_norms := proc() local iii; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; if not glob_initial_pass then iii := 1; while iii <= glob_max_terms do array_norms[iii] := 0.; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y2[iii]) then array_norms[iii] := omniabs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < omniabs(array_y1[iii]) then array_norms[iii] := omniabs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # End Function number 11 > # Begin Function number 12 > atomall := proc() > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult FULL FULL $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_y1[1])); > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add FULL - CONST $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y2_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #emit pre sub FULL - CONST $eq_no = 2 i = 1 > array_tmp5[1] := array_y2[1] - array_const_1D0[1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * expt(glob_h , (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y1_higher[2,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult FULL FULL $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_y1,1); > #emit pre add CONST FULL $eq_no = 1 i = 2 > array_tmp2[2] := array_tmp1[2]; > #emit pre add FULL CONST $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #emit pre sub FULL CONST $eq_no = 2 i = 2 > array_tmp5[2] := array_y2[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_tmp5[2] * expt(glob_h , (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult FULL FULL $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_y1,1); > #emit pre add CONST FULL $eq_no = 1 i = 3 > array_tmp2[3] := array_tmp1[3]; > #emit pre add FULL CONST $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #emit pre sub FULL CONST $eq_no = 2 i = 3 > array_tmp5[3] := array_y2[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_tmp5[3] * expt(glob_h , (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y1_higher[2,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult FULL FULL $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_y1,1); > #emit pre add CONST FULL $eq_no = 1 i = 4 > array_tmp2[4] := array_tmp1[4]; > #emit pre add FULL CONST $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #emit pre sub FULL CONST $eq_no = 2 i = 4 > array_tmp5[4] := array_y2[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_tmp5[4] * expt(glob_h , (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y1_higher[2,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult FULL FULL $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_y1,1); > #emit pre add CONST FULL $eq_no = 1 i = 5 > array_tmp2[5] := array_tmp1[5]; > #emit pre add FULL CONST $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #emit pre sub FULL CONST $eq_no = 2 i = 5 > array_tmp5[5] := array_y2[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_tmp5[5] * expt(glob_h , (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y1_higher[2,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult FULL FULL $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_y1,1); > #emit NOT FULL - FULL add $eq_no = 1 > array_tmp2[kkk] := array_tmp1[kkk]; > #emit FULL - NOT FULL add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y2_set_initial[1,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y2_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > #emit FULL - NOT FULL sub $eq_no = 2 > array_tmp5[kkk] := array_y2[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_tmp5[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y1_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > kkk := kkk + 1; > od;# end do number 1; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > #BOTTOM ATOMALL ??? > end; atomall := proc() local kkk, order_d, adj2, adj3, temporary, term; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_m1[1]*array_y1[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_y2[1] - array_const_1D0[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y1, 1); array_tmp2[2] := array_tmp1[2]; array_tmp3[2] := array_tmp2[2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := array_y2[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*expt(glob_h, 1)*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y1, 1); array_tmp2[3] := array_tmp1[3]; array_tmp3[3] := array_tmp2[3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := array_y2[3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*expt(glob_h, 1)*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*3.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y1, 1); array_tmp2[4] := array_tmp1[4]; array_tmp3[4] := array_tmp2[4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := array_y2[4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*expt(glob_h, 1)*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*4.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y1, 1); array_tmp2[5] := array_tmp1[5]; array_tmp3[5] := array_tmp2[5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := array_y2[5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_y1, 1); array_tmp2[kkk] := array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y2_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; array_tmp5[kkk] := array_y2[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_tmp5[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 1; adj3 := 2; while 1 <= term do if adj3 <= order_d + 1 then if 0 < adj2 then temporary := temporary*convfp(adj2)/glob_h else temporary := temporary end if; array_y1_higher[adj3, term] := temporary end if; term := term - 1; adj2 := adj2 - 1; adj3 := adj3 + 1 end do end if end if; kkk := kkk + 1 end do end proc > # End Function number 12 > #BEGIN ATS LIBRARY BLOCK > # Begin Function number 2 > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s\n",str); > fi;# end if 1; > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > # End Function number 2 > # Begin Function number 3 > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > printf("%s",str); > fi;# end if 1; > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > # End Function number 3 > # Begin Function number 4 > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > print(label,str); > fi;# end if 1; > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > # End Function number 4 > # Begin Function number 5 > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 1 > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 5 > # Begin Function number 6 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > if vallen = 5 then # if number 1 > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi;# end if 1; > fi;# end if 0; > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > # End Function number 6 > # Begin Function number 7 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then # if number 0 > print(prelabel,"[",elemnt,"]",value, postlabel); > fi;# end if 0; > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > # End Function number 7 > # Begin Function number 8 > dump_series := proc(iolevel,dump_label,series_name,arr_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then # if number 0 > i := 1; > while (i <= numb) do # do number 1 > print(dump_label,series_name > ,i,arr_series[i]); > i := i + 1; > od;# end do number 1 > fi;# end if 0 > end; dump_series := proc(iolevel, dump_label, series_name, arr_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, arr_series[i]); i := i + 1 end do end if end proc > # End Function number 8 > # Begin Function number 9 > dump_series_2 := proc(iolevel,dump_label,series_name2,arr_series2,numb,subnum,arr_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then # if number 0 > sub := 1; > while (sub <= subnum) do # do number 1 > i := 1; > while (i <= numb) do # do number 2 > print(dump_label,series_name2,sub,i,arr_series2[sub,i]); > od;# end do number 2; > sub := sub + 1; > od;# end do number 1; > fi;# end if 0; > end; dump_series_2 := proc( iolevel, dump_label, series_name2, arr_series2, numb, subnum, arr_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, arr_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > # End Function number 9 > # Begin Function number 10 > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then # if number 0 > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi;# end if 0; > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # End Function number 10 > # Begin Function number 11 > logitem_time := proc(fd,secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > fprintf(fd,""); > if (secs_in >= 0) then # if number 0 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 1 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 2 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 3 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 4 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 4 > else > fprintf(fd," Unknown"); > fi;# end if 3 > fprintf(fd,"\n"); > end; logitem_time := proc(fd, secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; fprintf(fd, ""); if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, " Unknown") end if; fprintf(fd, "\n") end proc > # End Function number 11 > # Begin Function number 12 > omniout_timestr := proc(secs_in) > global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; > local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int; > if (secs_in >= 0) then # if number 3 > years_int := trunc(secs_in / glob_sec_in_year); > sec_temp := (trunc(secs_in) mod trunc(glob_sec_in_year)); > days_int := trunc(sec_temp / glob_sec_in_day) ; > sec_temp := (sec_temp mod trunc(glob_sec_in_day)) ; > hours_int := trunc(sec_temp / glob_sec_in_hour); > sec_temp := (sec_temp mod trunc(glob_sec_in_hour)); > minutes_int := trunc(sec_temp / glob_sec_in_minute); > sec_int := (sec_temp mod trunc(glob_sec_in_minute)); > if (years_int > 0) then # if number 4 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif > (days_int > 0) then # if number 5 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif > (hours_int > 0) then # if number 6 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif > (minutes_int > 0) then # if number 7 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 7 > else > printf(" Unknown\n"); > fi;# end if 6 > end; omniout_timestr := proc(secs_in) local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int; global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year; if 0 <= secs_in then years_int := trunc(secs_in/glob_sec_in_year); sec_temp := trunc(secs_in) mod trunc(glob_sec_in_year); days_int := trunc(sec_temp/glob_sec_in_day); sec_temp := sec_temp mod trunc(glob_sec_in_day); hours_int := trunc(sec_temp/glob_sec_in_hour); sec_temp := sec_temp mod trunc(glob_sec_in_hour); minutes_int := trunc(sec_temp/glob_sec_in_minute); sec_int := sec_temp mod trunc(glob_sec_in_minute); if 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > # End Function number 12 > # Begin Function number 13 > ats := proc(mmm_ats,arr_a,arr_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 6 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 6; > ret_ats; > end; ats := proc(mmm_ats, arr_a, arr_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + arr_a[iii_ats]*arr_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > # End Function number 13 > # Begin Function number 14 > att := proc(mmm_att,arr_aa,arr_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 6 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 7 > ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* convfp(al_att); > fi;# end if 7; > iii_att := iii_att + 1; > od;# end do number 1; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 6; > ret_att; > end; att := proc(mmm_att, arr_aa, arr_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # End Function number 14 > # Begin Function number 15 > display_pole_debug := proc(typ,radius,order2) > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if (typ = 1) then # if number 6 > omniout_str(ALWAYS,"Real"); > else > omniout_str(ALWAYS,"Complex"); > fi;# end if 6; > omniout_float(ALWAYS,"DBG Radius of convergence ",4, radius,4," "); > omniout_float(ALWAYS,"DBG Order of pole ",4, order2,4," "); > end; display_pole_debug := proc(typ, radius, order2) global ALWAYS, glob_display_flag, glob_large_float, array_pole; if typ = 1 then omniout_str(ALWAYS, "Real") else omniout_str(ALWAYS, "Complex") end if; omniout_float(ALWAYS, "DBG Radius of convergence ", 4, radius, 4, " "); omniout_float(ALWAYS, "DBG Order of pole ", 4, order2, 4, " ") end proc > # End Function number 15 > # Begin Function number 16 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 6 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 6 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # End Function number 16 > # Begin Function number 17 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # End Function number 17 > # Begin Function number 18 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # End Function number 18 > # Begin Function number 19 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # End Function number 19 > # Begin Function number 20 > logitem_good_digits := proc(file,rel_error) > global glob_small_float; > local good_digits; > fprintf(file,""); > if (rel_error <> -1.0) then # if number 6 > if (rel_error > + 0.0000000000000000000000000000000001) then # if number 7 > good_digits := 1-trunc(log10(rel_error)); > fprintf(file,"%d",good_digits); > else > good_digits := Digits; > fprintf(file,"%d",good_digits); > fi;# end if 7; > else > fprintf(file,"Unknown"); > fi;# end if 6; > fprintf(file,""); > end; logitem_good_digits := proc(file, rel_error) local good_digits; global glob_small_float; fprintf(file, ""); if rel_error <> -1.0 then if 0.1*10^(-33) < rel_error then good_digits := 1 - trunc(log10(rel_error)); fprintf(file, "%d", good_digits) else good_digits := Digits; fprintf(file, "%d", good_digits) end if else fprintf(file, "Unknown") end if; fprintf(file, "") end proc > # End Function number 20 > # Begin Function number 21 > log_revs := proc(file,revs) > fprintf(file,revs); > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # End Function number 21 > # Begin Function number 22 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # End Function number 22 > # Begin Function number 23 > logitem_pole := proc(file,pole) > fprintf(file,""); > if (pole = 0) then # if number 6 > fprintf(file,"NA"); > elif > (pole = 1) then # if number 7 > fprintf(file,"Real"); > elif > (pole = 2) then # if number 8 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 8 > fprintf(file,""); > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # End Function number 23 > # Begin Function number 24 > logstart := proc(file) > fprintf(file,""); > end; logstart := proc(file) fprintf(file, "") end proc > # End Function number 24 > # Begin Function number 25 > logend := proc(file) > fprintf(file,"\n"); > end; logend := proc(file) fprintf(file, "\n") end proc > # End Function number 25 > # Begin Function number 26 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 8 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 8; > if (glob_max_iter < 2) then # if number 8 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 8; > if (errflag) then # if number 8 > quit; > fi;# end if 8 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > # End Function number 26 > # Begin Function number 27 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 8 > sec_left := 0.0; > else > if (sub2 > 0.0) then # if number 9 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 9 > fi;# end if 8; > sec_left; > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec2; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > # End Function number 27 > # Begin Function number 28 > comp_percent := proc(t_end2,t_start2, t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub2 > glob_small_float) then # if number 8 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 8; > rrr; > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < sub2 then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # End Function number 28 > # Begin Function number 29 > factorial_2 := proc(nnn) > nnn!; > end; factorial_2 := proc(nnn) nnn! end proc > # End Function number 29 > # Begin Function number 30 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 8 > if (array_fact_1[nnn] = 0) then # if number 9 > ret := factorial_2(nnn); > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 9; > else > ret := factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := factorial_2(nnn); array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := factorial_2(nnn) end if; ret end proc > # End Function number 30 > # Begin Function number 31 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if ((nnn <= glob_max_terms) and (mmm <= glob_max_terms)) then # if number 8 > if (array_fact_2[mmm,nnn] = 0) then # if number 9 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 9; > else > ret := factorial_2(mmm)/factorial_2(nnn); > fi;# end if 8; > ret; > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := factorial_2(mmm)/factorial_2(nnn) end if; ret end proc > # End Function number 31 > # Begin Function number 32 > convfp := proc(mmm) > (mmm); > end; convfp := proc(mmm) mmm end proc > # End Function number 32 > # Begin Function number 33 > convfloat := proc(mmm) > (mmm); > end; convfloat := proc(mmm) mmm end proc > # End Function number 33 > # Begin Function number 34 > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > # End Function number 34 > # Begin Function number 35 > omniabs := proc(x) > abs(x); > end; omniabs := proc(x) abs(x) end proc > # End Function number 35 > # Begin Function number 36 > expt := proc(x,y) > (x^y); > end; expt := proc(x, y) x^y end proc > # End Function number 36 > # Begin Function number 37 > estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer) > local desired_abs_gbl_error,range,estimated_steps,step_error; > global glob_desired_digits_correct,ALWAYS; > omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,""); > desired_abs_gbl_error := expt(10.0,- glob_desired_digits_correct) * omniabs(estimated_answer); > omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,""); > range := (x_end - x_start); > omniout_float(ALWAYS,"range",32,range,32,""); > estimated_steps := range / estimated_h; > omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,""); > step_error := omniabs(desired_abs_gbl_error / estimated_steps); > omniout_float(ALWAYS,"step_error",32,step_error,32,""); > (step_error);; > end; estimated_needed_step_error := proc( x_start, x_end, estimated_h, estimated_answer) local desired_abs_gbl_error, range, estimated_steps, step_error; global glob_desired_digits_correct, ALWAYS; omniout_float(ALWAYS, "glob_desired_digits_correct", 32, glob_desired_digits_correct, 32, ""); desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*omniabs(estimated_answer); omniout_float(ALWAYS, "desired_abs_gbl_error", 32, desired_abs_gbl_error, 32, ""); range := x_end - x_start; omniout_float(ALWAYS, "range", 32, range, 32, ""); estimated_steps := range/estimated_h; omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, ""); step_error := omniabs(desired_abs_gbl_error/estimated_steps); omniout_float(ALWAYS, "step_error", 32, step_error, 32, ""); step_error end proc > # End Function number 37 > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > return(1.0 + cos(x)); > end; exact_soln_y1 := proc(x) return 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > return(1.0 - sin(x)); > end; exact_soln_y2 := proc(x) return 1.0 - sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > main := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, max_terms, opt_iter, tmp,subiter, est_needed_step_err,value3,min_value,est_answer,best_h,found_h,repeat_it; > global > glob_max_terms, > glob_iolevel, > ALWAYS, > INFO, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_check_sign, > glob_desired_digits_correct, > glob_max_value3, > glob_ratio_of_radius, > glob_percent_done, > glob_subiter_method, > glob_total_exp_sec, > glob_optimal_expect_sec, > glob_html_log, > glob_good_digits, > glob_max_opt_iter, > glob_dump, > glob_djd_debug, > glob_display_flag, > glob_djd_debug2, > glob_sec_in_minute, > glob_min_in_hour, > glob_hours_in_day, > glob_days_in_year, > glob_sec_in_hour, > glob_sec_in_day, > glob_sec_in_year, > glob_almost_1, > glob_clock_sec, > glob_clock_start_sec, > glob_not_yet_finished, > glob_initial_pass, > glob_not_yet_start_msg, > glob_reached_optimal_h, > glob_optimal_done, > glob_disp_incr, > glob_h, > glob_max_h, > glob_large_float, > glob_last_good_h, > glob_look_poles, > glob_neg_h, > glob_display_interval, > glob_next_display, > glob_dump_analytic, > glob_abserr, > glob_relerr, > glob_max_hours, > glob_max_iter, > glob_max_rel_trunc_err, > glob_max_trunc_err, > glob_no_eqs, > glob_optimal_clock_start_sec, > glob_optimal_start, > glob_small_float, > glob_smallish_float, > glob_unchanged_h_cnt, > glob_warned, > glob_warned2, > glob_max_sec, > glob_orig_start_sec, > glob_start, > glob_curr_iter_when_opt, > glob_current_iter, > glob_iter, > glob_normmax, > glob_max_minutes, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_1, > array_const_0D0, > array_const_1D0, > #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_tmp5, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > glob_iolevel := 5; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > MAX_UNCHANGED := 10; > glob_check_sign := 1.0; > glob_desired_digits_correct := 8.0; > glob_max_value3 := 0.0; > glob_ratio_of_radius := 0.01; > glob_percent_done := 0.0; > glob_subiter_method := 3; > glob_total_exp_sec := 0.1; > glob_optimal_expect_sec := 0.1; > glob_html_log := true; > glob_good_digits := 0; > glob_max_opt_iter := 10; > glob_dump := false; > glob_djd_debug := true; > glob_display_flag := true; > glob_djd_debug2 := true; > glob_sec_in_minute := 60; > glob_min_in_hour := 60; > glob_hours_in_day := 24; > glob_days_in_year := 365; > glob_sec_in_hour := 3600; > glob_sec_in_day := 86400; > glob_sec_in_year := 31536000; > glob_almost_1 := 0.9990; > glob_clock_sec := 0.0; > glob_clock_start_sec := 0.0; > glob_not_yet_finished := true; > glob_initial_pass := true; > glob_not_yet_start_msg := true; > glob_reached_optimal_h := false; > glob_optimal_done := false; > glob_disp_incr := 0.1; > glob_h := 0.1; > glob_max_h := 0.1; > glob_large_float := 9.0e100; > glob_last_good_h := 0.1; > glob_look_poles := false; > glob_neg_h := false; > glob_display_interval := 0.0; > glob_next_display := 0.0; > glob_dump_analytic := false; > glob_abserr := 0.1e-10; > glob_relerr := 0.1e-10; > glob_max_hours := 0.0; > glob_max_iter := 1000; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_trunc_err := 0.1e-10; > glob_no_eqs := 0; > glob_optimal_clock_start_sec := 0.0; > glob_optimal_start := 0.0; > glob_small_float := 0.1e-200; > glob_smallish_float := 0.1e-100; > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_max_sec := 10000.0; > glob_orig_start_sec := 0.0; > glob_start := 0; > glob_curr_iter_when_opt := 0; > glob_current_iter := 0; > glob_iter := 0; > glob_normmax := 0.0; > glob_max_minutes := 0.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest3postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = y2 - 1.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 0.5;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_desired_digits_correct:=10;"); > omniout_str(ALWAYS,"glob_display_interval:=0.001;"); > omniout_str(ALWAYS,"glob_look_poles:=true;"); > omniout_str(ALWAYS,"glob_max_iter:=10000000;"); > omniout_str(ALWAYS,"glob_max_minutes:=3;"); > omniout_str(ALWAYS,"glob_subiter_method:=3;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 + cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return(1.0 - sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits:=32; > max_terms:=30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y2_init:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_y2_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1D0[1] := 1.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 0.5; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := false; > array_y2_set_initial[1,3] := false; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 3 > glob_h := glob_display_interval; > fi;# end if 3; > if (glob_max_h < glob_h) then # if number 3 > glob_h := glob_max_h; > fi;# end if 3; > found_h := -1.0; > best_h := 0.0; > min_value := glob_large_float; > est_answer := est_size_answer(); > opt_iter := 1; > while ((opt_iter <= 20) and (found_h < 0.0)) do # do number 2 > omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,""); > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 2) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 2 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 4; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 4 > best_h := glob_h; > found_h := 1.0; > fi;# end if 4; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 4 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 4; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 4 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 4; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 4 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_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; > display_alot(current_iter); > if (glob_look_poles) then # if number 6 > #left paren 0004C > check_for_pole(); > fi;# end if 6;#was right paren 0004C > if (reached_interval()) then # if number 6 > glob_next_display := glob_next_display + glob_display_interval; > fi;# end if 6; > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1; > order_diff := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > ; > od;# end do number 2;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 6 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!"); > fi;# end if 6; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 6 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!"); > fi;# end if 6; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = y2 - 1.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T16:42:51-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest3") > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if (array_type_pole[1] = 1 or array_type_pole[1] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if (glob_percent_done < 100.0) then # if number 7 > logitem_time(html_log_file,convfloat(glob_total_exp_sec)) > ; > 0; > else > logitem_str(html_log_file,"Done") > ; > 0; > fi;# end if 7; > log_revs(html_log_file," 165 ") > ; > logitem_str(html_log_file,"mtest3 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest3 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = y2 - 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 7 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 7; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_1, array_const_0D0, array_const_1D0, 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_tmp5, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; glob_iolevel := 5; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; MAX_UNCHANGED := 10; glob_check_sign := 1.0; glob_desired_digits_correct := 8.0; glob_max_value3 := 0.; glob_ratio_of_radius := 0.01; glob_percent_done := 0.; glob_subiter_method := 3; glob_total_exp_sec := 0.1; glob_optimal_expect_sec := 0.1; glob_html_log := true; glob_good_digits := 0; glob_max_opt_iter := 10; glob_dump := false; glob_djd_debug := true; glob_display_flag := true; glob_djd_debug2 := true; glob_sec_in_minute := 60; glob_min_in_hour := 60; glob_hours_in_day := 24; glob_days_in_year := 365; glob_sec_in_hour := 3600; glob_sec_in_day := 86400; glob_sec_in_year := 31536000; glob_almost_1 := 0.9990; glob_clock_sec := 0.; glob_clock_start_sec := 0.; glob_not_yet_finished := true; glob_initial_pass := true; glob_not_yet_start_msg := true; glob_reached_optimal_h := false; glob_optimal_done := false; glob_disp_incr := 0.1; glob_h := 0.1; glob_max_h := 0.1; glob_large_float := 0.90*10^101; glob_last_good_h := 0.1; glob_look_poles := false; glob_neg_h := false; glob_display_interval := 0.; glob_next_display := 0.; glob_dump_analytic := false; glob_abserr := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_max_hours := 0.; glob_max_iter := 1000; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_trunc_err := 0.1*10^(-10); glob_no_eqs := 0; glob_optimal_clock_start_sec := 0.; glob_optimal_start := 0.; glob_small_float := 0.1*10^(-200); glob_smallish_float := 0.1*10^(-100); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_max_sec := 10000.0; glob_orig_start_sec := 0.; glob_start := 0; glob_curr_iter_when_opt := 0; glob_current_iter := 0; glob_iter := 0; glob_normmax := 0.; glob_max_minutes := 0.; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest3postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 0.5;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_desired_digits_correct:=10;"); omniout_str(ALWAYS, "glob_display_interval:=0.001;"); omniout_str(ALWAYS, "glob_look_poles:=true;"); omniout_str(ALWAYS, "glob_max_iter:=10000000;"); omniout_str(ALWAYS, "glob_max_minutes:=3;"); omniout_str(ALWAYS, "glob_subiter_method:=3;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "return(1.0 + cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(1.0 - sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y2_init := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 0.5; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_max_iter := 20; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := false; array_y2_set_initial[1, 3] := false; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; if glob_max_h < glob_h then glob_h := glob_max_h end if; found_h := -1.0; best_h := 0.; min_value := glob_large_float; est_answer := est_size_answer(); opt_iter := 1; while opt_iter <= 20 and found_h < 0. do omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, ""); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_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; display_alot(current_iter); if glob_look_poles then check_for_pole() end if; if reached_interval() then glob_next_display := glob_next_display + glob_display_interval end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 2; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T16:42:51-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest3"); logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_good_digits(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_total_exp_sec)); 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 165 "); logitem_str(html_log_file, "mtest3 diffeq.mxt"); logitem_str(html_log_file, "mtest3 maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = y2 - 1.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 0.5; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_desired_digits_correct:=10; glob_display_interval:=0.001; glob_look_poles:=true; glob_max_iter:=10000000; glob_max_minutes:=3; glob_subiter_method:=3; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) return(1.0 + cos(x)); end; exact_soln_y2 := proc(x) return(1.0 - sin(x)); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 opt_iter = 1 memory used=3.8MB, alloc=3.1MB, time=0.20 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 0.4 estimated_steps = 400 step_error = 2.5000000000000000000000000000000e-13 est_needed_step_err = 2.5000000000000000000000000000000e-13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.4759225582891422933370225621906e-106 value3 = 2.4672040251049429538467757202074e-105 max_value3 = 2.4672040251049429538467757202074e-105 value3 = 2.4672040251049429538467757202074e-105 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 0.90016658335317184769318580158938 y2[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.44 x[1] = 0.101 y2[1] (analytic) = 0.89917162927043200487024788047681 y2[1] (numeric) = 0.89917162927043200487024788047681 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.994903834375976659378402999829 y1[1] (numeric) = 1.994903834375976659378402999829 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.69 x[1] = 0.102 y2[1] (analytic) = 0.89817677601605448925135770391935 y2[1] (numeric) = 0.89817677601605448925135770391935 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.9948025085701760853346856764599 y1[1] (numeric) = 1.9948025085701760853346856764599 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.103 y2[1] (analytic) = 0.89718202458489247230959578949541 y2[1] (numeric) = 0.89718202458489247230959578949541 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.9947001879619498413211671928266 y1[1] (numeric) = 1.9947001879619498413211671928267 absolute error = 1e-31 relative error = 5.0132847333900969580736126213353e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=15.2MB, alloc=4.3MB, time=0.92 TOP MAIN SOLVE Loop x[1] = 0.104 y2[1] (analytic) = 0.89618737597169730231102924533054 y2[1] (numeric) = 0.89618737597169730231102924533054 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 y1[1] (analytic) = 1.9945968726536185270373744944846 y1[1] (numeric) = 1.9945968726536185270373744944847 absolute error = 1e-31 relative error = 5.0135444094504999744422042989207e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=1.16 x[1] = 0.105 y2[1] (analytic) = 0.89519283117111750956344639997322 y2[1] (numeric) = 0.89519283117111750956344639997321 absolute error = 1e-32 relative error = 1.1170777570814219760206128377360e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9944925627484974422050131246041 y1[1] (numeric) = 1.9944925627484974422050131246041 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.40 x[1] = 0.106 y2[1] (analytic) = 0.89419839117769781176790938198128 y2[1] (numeric) = 0.89419839117769781176790938198127 absolute error = 1e-32 relative error = 1.1183200617068399222589756982068e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9943872583508964832526761118722 y1[1] (numeric) = 1.9943872583508964832526761118723 absolute error = 1e-31 relative error = 5.0140713435307056092197789941372e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.107 y2[1] (analytic) = 0.89320405698587811947411929758354 y2[1] (numeric) = 0.89320405698587811947411929758352 absolute error = 2e-32 relative error = 2.2391299998670076868448853850700e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9942809595661200390059562343918 y1[1] (numeric) = 1.9942809595661200390059562343919 absolute error = 1e-31 relative error = 5.0143386026087422693494546616177e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.64 x[1] = 0.108 y2[1] (analytic) = 0.89220982958999254164058855096841 y2[1] (numeric) = 0.8922098295899925416405885509684 absolute error = 1e-32 relative error = 1.1208125788745698046855410005165e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9941736665004668853830659694533 y1[1] (numeric) = 1.9941736665004668853830659694534 absolute error = 1e-31 relative error = 5.0146083904260896791060449451647e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.89 x[1] = 0.109 y2[1] (analytic) = 0.89121570998426839130061474694456 y2[1] (numeric) = 0.89121570998426839130061474694454 absolute error = 2e-32 relative error = 2.2441256113352217567953267159562e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9940653792612300790960704335539 y1[1] (numeric) = 1.994065379261230079096070433554 absolute error = 1e-31 relative error = 5.0148807075246665300616373141045e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=2.13 x[1] = 0.11 y2[1] (analytic) = 0.89022169916282519133505050991655 y2[1] (numeric) = 0.89022169916282519133505050991653 absolute error = 2e-32 relative error = 2.2466313749494347211081974406268e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9939560979566968503578396114198 y1[1] (numeric) = 1.9939560979566968503578396114199 absolute error = 1e-31 relative error = 5.0151555544515163299513758223921e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.111 y2[1] (analytic) = 0.88922779811967368035286344632307 y2[1] (numeric) = 0.88922779811967368035286344632305 absolute error = 2e-32 relative error = 2.2491424629651949362687953771165e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.993845822696148494594827167072 y1[1] (numeric) = 1.993845822696148494594827167072 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.37 x[1] = 0.112 y2[1] (analytic) = 0.88823400784871481868048036989479 y2[1] (numeric) = 0.88823400784871481868048036989477 absolute error = 2e-32 relative error = 2.2516588898053570398915774345620e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9937345535898602631657841241467 y1[1] (numeric) = 1.9937345535898602631657841241467 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=2.62 x[1] = 0.113 y2[1] (analytic) = 0.8872403293437387944609098003048 y2[1] (numeric) = 0.88724032934373879446090980030478 absolute error = 2e-32 relative error = 2.2541806699424172072513032681368e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9936222907491012530865166967484 y1[1] (numeric) = 1.9936222907491012530865166967485 absolute error = 1e-31 relative error = 5.0159952797490600140029164077157e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.114 y2[1] (analytic) = 0.88624676359842402986363663600634 y2[1] (numeric) = 0.88624676359842402986363663600631 absolute error = 3e-32 relative error = 3.3850617268480761944203721174969e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9935090342861342957607985460685 y1[1] (numeric) = 1.9935090342861342957607985460686 absolute error = 1e-31 relative error = 5.0162802515620153356578675886210e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.86 x[1] = 0.115 y2[1] (analytic) = 0.8852533116063361874062827912803 y2[1] (numeric) = 0.88525331160633618740628279128028 absolute error = 2e-32 relative error = 2.2592403482466509755981957994363e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9933947843142158447175487318465 y1[1] (numeric) = 1.9933947843142158447175487318466 absolute error = 1e-31 relative error = 5.0165677560154160235631469102881e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=3.10 x[1] = 0.116 y2[1] (analytic) = 0.88425997436092717638902747574917 y2[1] (numeric) = 0.88425997436092717638902747574914 absolute error = 3e-32 relative error = 3.3926674134133025114734768757084e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.993279540947595862354387621489 y1[1] (numeric) = 1.9932795409475958623543876214891 absolute error = 1e-31 relative error = 5.0168577936871043750751276314026e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=3.34 x[1] = 0.117 y2[1] (analytic) = 0.88326675285553415944278068185407 y2[1] (numeric) = 0.88326675285553415944278068185404 absolute error = 3e-32 relative error = 3.3964824219877272885762939066605e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.993163304301517705687684013279 y1[1] (numeric) = 1.9931633043015177056876840132791 absolute error = 1e-31 relative error = 5.0171503651600643420268444514782e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.118 y2[1] (analytic) = 0.88227364808337855919210333203896 y2[1] (numeric) = 0.88227364808337855919210333203893 absolute error = 3e-32 relative error = 3.4003055701789332154524433289617e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.99304607449221801110920772362 y1[1] (numeric) = 1.9930460744922180111092077236201 absolute error = 1e-31 relative error = 5.0174454710224240252081801655507e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=3.58 x[1] = 0.119 y2[1] (analytic) = 0.88128066103756506503386742263883 y2[1] (numeric) = 0.8812806610375650650338674226388 absolute error = 3e-32 relative error = 3.4041368801489261055202243212795e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9929278516369265781495028816522 y1[1] (numeric) = 1.9929278516369265781495028816522 absolute error = 0 relative error = 0 % Correct digits = 32 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.4MB, time=3.83 x[1] = 0.12 y2[1] (analytic) = 0.88028779271108064003264938572903 y2[1] (numeric) = 0.880287792711080640032649385729 absolute error = 3e-32 relative error = 3.4079763741363506023300343931569e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9928086358538662522480981678576 y1[1] (numeric) = 1.9928086358538662522480981678577 absolute error = 1e-31 relative error = 5.0180432882935908112451694551819e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=4.07 x[1] = 0.121 y2[1] (analytic) = 0.87929504409679352793384977345972 y2[1] (numeric) = 0.87929504409679352793384977345968 absolute error = 4e-32 relative error = 4.5490987659424095213311720332303e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9926884272622528065306712264356 y1[1] (numeric) = 1.9926884272622528065306712264357 absolute error = 1e-31 relative error = 5.0183460009043976231818861055706e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.122 y2[1] (analytic) = 0.87830241618745226029553225167281 y2[1] (numeric) = 0.87830241618745226029553225167277 absolute error = 4e-32 relative error = 4.5542400046708939227102223691582e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.992567225982294822593285474272 y1[1] (numeric) = 1.9925672259822948225932854742721 absolute error = 1e-31 relative error = 5.0186512503086087147802678879264e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=4.31 x[1] = 0.123 y2[1] (analytic) = 0.8773099099756846637399747708799 y2[1] (numeric) = 0.87730990997568466373997477087986 absolute error = 4e-32 relative error = 4.5593922449945460613552099494721e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9924450321351935702938185222573 y1[1] (numeric) = 1.9924450321351935702938185222575 absolute error = 2e-31 relative error = 1.0037918074240222260358253667455e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=4.56 x[1] = 0.124 y2[1] (analytic) = 0.87631752645399686732592566296706 y2[1] (numeric) = 0.87631752645399686732592566296703 absolute error = 3e-32 relative error = 3.4234166377334093976771369684560e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.992321845843142886550702417515 y1[1] (numeric) = 1.9923218458431428865507024175152 absolute error = 2e-31 relative error = 1.0038538723915902996870739417277e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.125 y2[1] (analytic) = 0.87532526661477231004255729128789 y2[1] (numeric) = 0.87532526661477231004255729128786 absolute error = 3e-32 relative error = 3.4272973880922939879124629753081e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9921976672293290531490969077882 y1[1] (numeric) = 1.9921976672293290531490969077884 absolute error = 2e-31 relative error = 1.0039164450892677369081925000522e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=4.80 x[1] = 0.126 y2[1] (analytic) = 0.87433313145027074842610976010826 y2[1] (numeric) = 0.87433313145027074842610976010823 absolute error = 3e-32 relative error = 3.4311864575277510624030639187458e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9920724964179306735546179218037 y1[1] (numeric) = 1.9920724964179306735546179218039 absolute error = 2e-31 relative error = 1.0039795256429292925758083279198e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=5.05 x[1] = 0.127 y2[1] (analytic) = 0.87334112195262726430021706667654 y2[1] (numeric) = 0.8733411219526272643002170666765 absolute error = 4e-32 relative error = 4.5801118250984778739937092177196e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9919463335341185487347444518721 y1[1] (numeric) = 1.9919463335341185487347444518723 absolute error = 2e-31 relative error = 1.0040431141794832426277726888305e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=5.29 x[1] = 0.128 y2[1] (analytic) = 0.87234923911385127264090795551028 y2[1] (numeric) = 0.87234923911385127264090795551025 absolute error = 3e-32 relative error = 3.4389896448439117080901317646250e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9918191787040555519880280173089 y1[1] (numeric) = 1.9918191787040555519880280173091 absolute error = 2e-31 relative error = 1.0041072108268719277418903648233e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.129 y2[1] (analytic) = 0.87135748392582552956727360981603 y2[1] (numeric) = 0.871357483925825529567273609816 absolute error = 3e-32 relative error = 3.4429038085307540283301055523704e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9916910320548965027812298794554 y1[1] (numeric) = 1.9916910320548965027812298794556 absolute error = 2e-31 relative error = 1.0041718157140723015143946141587e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=5.53 x[1] = 0.13 y2[1] (analytic) = 0.87036585738030514045879418929169 y2[1] (numeric) = 0.87036585738030514045879418929165 absolute error = 4e-32 relative error = 4.5957685105428091385734511947828e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9915618937147880395945121711518 y1[1] (numeric) = 1.991561893714788039594512171152 absolute error = 2e-31 relative error = 1.0042369289710964831422071099758e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=5.78 x[1] = 0.131 y2[1] (analytic) = 0.86937436046891656820031609690237 y2[1] (numeric) = 0.86937436046891656820031609690233 absolute error = 4e-32 relative error = 4.6010098547678703667386917818045e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9914317638128684917748100954616 y1[1] (numeric) = 1.9914317638128684917748100954618 absolute error = 2e-31 relative error = 1.0043025507289923146130562707447e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.132 y2[1] (analytic) = 0.86838299418315664155567172956986 y2[1] (numeric) = 0.86838299418315664155567172956982 absolute error = 4e-32 relative error = 4.6062624749608263689261729132492e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.991300642479267750397513340263 y1[1] (numeric) = 1.9913006424792677503975133402633 absolute error = 3e-31 relative error = 1.5065530216797658836113419283996e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=95.3MB, alloc=4.4MB, time=6.02 TOP MAIN SOLVE Loop x[1] = 0.133 y2[1] (analytic) = 0.86739175951439156367093333907315 y2[1] (numeric) = 0.86739175951439156367093333907311 absolute error = 4e-32 relative error = 4.6115264021408228794262602231311e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9911685298451071381365858470171 y1[1] (numeric) = 1.9911685298451071381365858470173 absolute error = 2e-31 relative error = 1.0044353202767722837174230762644e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=6.26 x[1] = 0.134 y2[1] (analytic) = 0.86640065745385592070829249982374 y2[1] (numeric) = 0.8664006574538559207082924998237 absolute error = 4e-32 relative error = 4.6168016674352974648062542205788e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9910354260424992781432540635797 y1[1] (numeric) = 1.9910354260424992781432540635799 absolute error = 2e-31 relative error = 1.0045024683339357971838974226552e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.4MB, time=6.51 x[1] = 0.135 y2[1] (analytic) = 0.86540968899265169061155654955344 y2[1] (numeric) = 0.8654096889926516906115565495534 absolute error = 4e-32 relative error = 4.6220883020804317975048604800521e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9909013312045479619333948023605 y1[1] (numeric) = 1.9909013312045479619333948023607 absolute error = 2e-31 relative error = 1.0045701254265308581607595117831e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.136 y2[1] (analytic) = 0.86441885512174725200425323733583 y2[1] (numeric) = 0.86441885512174725200425323733578 absolute error = 5e-32 relative error = 5.7842329217770076716120643201105e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.990766245465348016283754816428 y1[1] (numeric) = 1.9907662454653480162837548164282 absolute error = 2e-31 relative error = 1.0046382916907924385060032496373e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=6.75 x[1] = 0.137 y2[1] (analytic) = 0.86342815683197639322133468075391 y2[1] (numeric) = 0.86342815683197639322133468075386 absolute error = 5e-32 relative error = 5.7908697561423200411247680794535e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9906301689599851691371351973316 y1[1] (numeric) = 1.9906301689599851691371351973318 absolute error = 2e-31 relative error = 1.0047069672639946709065528037444e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=6.99 x[1] = 0.138 y2[1] (analytic) = 0.86243759511403732147547160042766 y2[1] (numeric) = 0.86243759511403732147547160042761 absolute error = 5e-32 relative error = 5.7975209201529140703423883308995e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9904931018245359145166746894438 y1[1] (numeric) = 1.9904931018245359145166746894441 absolute error = 3e-31 relative error = 1.5071642284266771566104470306467e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=7.24 x[1] = 0.139 y2[1] (analytic) = 0.86144717095849167215892866552446 y2[1] (numeric) = 0.86144717095849167215892866552441 absolute error = 5e-32 relative error = 5.8041864534034462273004264759941e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9903550441960673764493670065295 y1[1] (numeric) = 1.9903550441960673764493670065297 absolute error = 2e-31 relative error = 1.0048458468915169644797995858842e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (analytic) = 0.86045688535576351828201164829463 y2[1] (numeric) = 0.86045688535576351828201164829458 absolute error = 5e-32 relative error = 5.8108663956273715292834160742387e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9902159962126371718989482270114 y1[1] (numeric) = 1.9902159962126371718989482270116 absolute error = 2e-31 relative error = 1.0049160512255864176420440742915e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=7.48 x[1] = 0.141 y2[1] (analytic) = 0.85946673929613838004907694910232 y2[1] (numeric) = 0.85946673929613838004907694910227 absolute error = 5e-32 relative error = 5.8175607866975256767794024678851e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9900759580132932727082913350357 y1[1] (numeric) = 1.9900759580132932727082913350359 absolute error = 2e-31 relative error = 1.0049867654280965072886633500590e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=7.72 x[1] = 0.142 y2[1] (analytic) = 0.85847673376976223457309391585971 y2[1] (numeric) = 0.85847673376976223457309391585966 absolute error = 5e-32 relative error = 5.8242696666267100411457918037568e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9899349297380738665514459649294 y1[1] (numeric) = 1.9899349297380738665514459649296 absolute error = 2e-31 relative error = 1.0050579896415260940810671647313e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.143 y2[1] (analytic) = 0.85748686976664052572975024321969 y2[1] (numeric) = 0.85748686976664052572975024321964 absolute error = 5e-32 relative error = 5.8309930755682795219804128555278e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9897929115280072168954623969991 y1[1] (numeric) = 1.9897929115280072168954623969993 absolute error = 2e-31 relative error = 1.0051297240093968008949722131981e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=7.96 x[1] = 0.144 y2[1] (analytic) = 0.85649714827663717415209059733904 y2[1] (numeric) = 0.85649714827663717415209059733899 absolute error = 5e-32 relative error = 5.8377310538167332902925591359729e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9896499035251115219721398428361 y1[1] (numeric) = 1.9896499035251115219721398428362 absolute error = 1e-31 relative error = 5.0260098433813681449942269421877e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=8.21 x[1] = 0.145 y2[1] (analytic) = 0.85550757028947358736667847149108 y2[1] (numeric) = 0.85550757028947358736667847149103 absolute error = 5e-32 relative error = 5.8444836418083084336704109618459e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.989505905872394772759840048366 y1[1] (numeric) = 1.9895059058723947727598400483661 absolute error = 1e-31 relative error = 5.0263736189388278940040674992332e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=8.46 x[1] = 0.146 y2[1] (analytic) = 0.85451813679472767007227113628341 y2[1] (numeric) = 0.85451813679472767007227113628336 absolute error = 5e-32 relative error = 5.8512508801215765197435828628824e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9893609187138546099755082328197 y1[1] (numeric) = 1.9893609187138546099755082328198 absolute error = 1e-31 relative error = 5.0267399474526313758431314876131e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.147 y2[1] (analytic) = 0.85352884878183283456199740572324 y2[1] (numeric) = 0.85352884878183283456199740572319 absolute error = 5e-32 relative error = 5.8580328094780430943426065257114e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9892149421944781800770443715908 y1[1] (numeric) = 1.989214942194478180077044371591 absolute error = 2e-31 relative error = 1.0054217659322545973272942741022e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=8.70 x[1] = 0.148 y2[1] (analytic) = 0.85253970724007701129002779687021 y2[1] (numeric) = 0.85253970724007701129002779687017 absolute error = 4e-32 relative error = 4.6918635765942001046887591155860e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9890679764602419902761688205978 y1[1] (numeric) = 1.989067976460241990276168820598 absolute error = 2e-31 relative error = 1.0054960532616953133390573973376e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=8.95 x[1] = 0.149 y2[1] (analytic) = 0.85155071315860165958372651632402 y2[1] (numeric) = 0.85155071315860165958372651632397 absolute error = 5e-32 relative error = 5.8716409049248814474296847209873e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9889200216581117625619272692718 y1[1] (numeric) = 1.988920021658111762561927269272 absolute error = 2e-31 relative error = 1.0055708516286397191703756608917e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (analytic) = 0.85056186752640077850227456131236 y2[1] (numeric) = 0.85056186752640077850227456131231 absolute error = 5e-32 relative error = 5.8784671531783711086201984236119e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9887710779360422867349809986543 y1[1] (numeric) = 1.9887710779360422867349809986545 memory used=144.9MB, alloc=4.4MB, time=9.19 absolute error = 2e-31 relative error = 1.0056461611839262823506671282776e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.151 y2[1] (analytic) = 0.8495731713323199178427530766738 y2[1] (numeric) = 0.84957317133231991784275307667375 absolute error = 5e-32 relative error = 5.8853082568025148284962872800144e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9886211454429772724528294103012 y1[1] (numeric) = 1.9886211454429772724528294103014 absolute error = 2e-31 relative error = 1.0057219820794412902275539858543e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=9.43 x[1] = 0.152 y2[1] (analytic) = 0.84858462556505518929467596156972 y2[1] (numeric) = 0.84858462556505518929467596156966 absolute error = 6e-32 relative error = 7.0705971086911012703325389936195e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9884702243288492002861127807586 y1[1] (numeric) = 1.9884702243288492002861127807588 absolute error = 2e-31 relative error = 1.0057983144681195028234120157272e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=9.68 x[1] = 0.153 y2[1] (analytic) = 0.84759623121315227774396057131025 y2[1] (numeric) = 0.8475962312131522777439605713102 absolute error = 5e-32 relative error = 5.8990351960904451113133023498748e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9883183147445791717861441852958 y1[1] (numeric) = 1.988318314744579171786144185296 absolute error = 2e-31 relative error = 1.0058751585039448102980538486994e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.154 y2[1] (analytic) = 0.84660798926500545272732521024132 y2[1] (numeric) = 0.84660798926500545272732521024127 absolute error = 5e-32 relative error = 5.9059211150851763355200083163966e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9881654168420767585638205233501 y1[1] (numeric) = 1.9881654168420767585638205233503 absolute error = 2e-31 relative error = 1.0059525143419508950224113614814e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=9.92 x[1] = 0.155 y2[1] (analytic) = 0.84561990070885658003810196121268 y2[1] (numeric) = 0.84561990070885658003810196121262 absolute error = 6e-32 relative error = 7.0953864673364340346239078820797e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9880115307742398503800635667605 y1[1] (numeric) = 1.9880115307742398503800635667606 absolute error = 1e-31 relative error = 5.0301519106911094913405882080405e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=10.16 x[1] = 0.156 y2[1] (analytic) = 0.84463196653279413348445324573189 y2[1] (numeric) = 0.84463196653279413348445324573183 absolute error = 6e-32 relative error = 7.1036856734536589242305957156056e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9878566566949545022479429403361 y1[1] (numeric) = 1.9878566566949545022479429403362 absolute error = 1e-31 relative error = 5.0305438102494654575896202916916e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=10.40 x[1] = 0.157 y2[1] (analytic) = 0.84364418772475220680098035650535 y2[1] (numeric) = 0.84364418772475220680098035650529 absolute error = 6e-32 relative error = 7.1120030070752566281204038530042e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9877007947590947805466339326243 y1[1] (numeric) = 1.9877007947590947805466339326245 absolute error = 2e-31 relative error = 1.0061876542351515524019231486357e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.158 y2[1] (analytic) = 0.84265656527250952571471205067536 y2[1] (numeric) = 0.8426565652725095257147120506753 absolute error = 6e-32 relative error = 7.1203385190022698360612620737539e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9875439451225226081473640229073 y1[1] (numeric) = 1.9875439451225226081473640229074 absolute error = 1e-31 relative error = 5.0313352942661842263229162728394e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.4MB, time=10.65 x[1] = 0.159 y2[1] (analytic) = 0.84166910016368846016646113768246 y2[1] (numeric) = 0.8416691001636884601664611376824 absolute error = 6e-32 relative error = 7.1286922602161768097755335524334e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9873861079420876085515029984672 y1[1] (numeric) = 1.9873861079420876085515029984673 absolute error = 1e-31 relative error = 5.0317348803222085318381806625831e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=10.89 x[1] = 0.16 y2[1] (analytic) = 0.84068179338575403668853684031401 y2[1] (numeric) = 0.84068179338575403668853684031395 absolute error = 6e-32 relative error = 7.1370642818796584109670951466707e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9872272833756269490409525240183 y1[1] (numeric) = 1.9872272833756269490409525240185 absolute error = 2e-31 relative error = 1.0064274060301127337338940958891e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.161 y2[1] (analytic) = 0.83969464592601295093980055114447 y2[1] (numeric) = 0.83969464592601295093980055114441 absolute error = 6e-32 relative error = 7.1454546353373689400207697384388e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9870674715819651828409920129024 y1[1] (numeric) = 1.9870674715819651828409920129025 absolute error = 1e-31 relative error = 5.0325417445632554081855432598379e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=11.13 x[1] = 0.162 y2[1] (analytic) = 0.83870765877161258039905244922922 y2[1] (numeric) = 0.83870765877161258039905244922915 absolute error = 7e-32 relative error = 8.3461739341361626081896158726682e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9869066727209140902957386371875 y1[1] (numeric) = 1.9869066727209140902957386371876 absolute error = 1e-31 relative error = 5.0329490243775657987150902527648e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=11.38 x[1] = 0.163 y2[1] (analytic) = 0.83772083290953999721773628358307 y2[1] (numeric) = 0.837720832909539997217736283583 absolute error = 7e-32 relative error = 8.3560056345833818996751916970906e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9867448869532725190563803011996 y1[1] (numeric) = 1.9867448869532725190563803011997 absolute error = 1e-31 relative error = 5.0333588704160566845338333877699e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.5MB, time=11.63 x[1] = 0.164 y2[1] (analytic) = 0.8367341693266209812329494706565 y2[1] (numeric) = 0.83673416932662098123294947065643 absolute error = 7e-32 relative error = 8.3658589031130327321541650727921e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9865821144408262232823413902376 y1[1] (numeric) = 1.9865821144408262232823413902377 absolute error = 1e-31 relative error = 5.0337712835065732481595740054154e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.165 y2[1] (analytic) = 0.83574766900951903314174549271711 y2[1] (numeric) = 0.83574766900951903314174549271704 absolute error = 7e-32 relative error = 8.3757338004855040910281504549655e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9864183553463477018555420932949 y1[1] (numeric) = 1.9864183553463477018555420932951 absolute error = 2e-31 relative error = 1.0068372528964495151962928113393e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=11.87 x[1] = 0.166 y2[1] (analytic) = 0.83476133294473438783771542275181 y2[1] (numeric) = 0.83476133294473438783771542275174 absolute error = 7e-32 relative error = 8.3856303876780514422098696494668e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9862536098335960356079130855139 y1[1] (numeric) = 1.9862536098335960356079130855141 absolute error = 2e-31 relative error = 1.0069207628363004494499897890260e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=12.11 x[1] = 0.167 y2[1] (analytic) = 0.83377516211860302791083523922592 y2[1] (numeric) = 0.83377516211860302791083523922585 absolute error = 7e-32 relative error = 8.3955487258857232546548302355625e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9860878780673167235623283428443 y1[1] (numeric) = 1.9860878780673167235623283428445 absolute error = 2e-31 relative error = 1.0070047866896107892908019906781e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=12.36 x[1] = 0.168 y2[1] (analytic) = 0.83278915751729569731156543076966 y2[1] (numeric) = 0.83278915751729569731156543076959 absolute error = 7e-32 relative error = 8.4054888765222921488815616077521e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.985921160213241518187119847961 y1[1] (numeric) = 1.9859211602132415181871198479612 absolute error = 2e-31 relative error = 1.0070893246261834198225026534807e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.169 y2[1] (analytic) = 0.83180332012681691518018922661023 y2[1] (numeric) = 0.83180332012681691518018922661016 absolute error = 7e-32 relative error = 8.4154509012211906978885168114016e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9857534564380882596643389329105 y1[1] (numeric) = 1.9857534564380882596643389329106 absolute error = 1e-31 relative error = 5.0358718840844075310066519868860e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=12.60 x[1] = 0.17 y2[1] (analytic) = 0.83081765093300398984237562332915 y2[1] (numeric) = 0.83081765093300398984237562332908 absolute error = 7e-32 relative error = 8.4254348618364519070454817149844e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9855847669095607091719299902125 y1[1] (numeric) = 1.9855847669095607091719299902126 absolute error = 1e-31 relative error = 5.0362997171681461508806471945451e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=12.85 x[1] = 0.171 y2[1] (analytic) = 0.8298321509215260329719532122995 y2[1] (numeric) = 0.82983215092152603297195321229943 absolute error = 7e-32 relative error = 8.4354408204436543997082794139332e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9854150917963483811799832702289 y1[1] (numeric) = 1.985415091796348381179983270229 absolute error = 1e-31 relative error = 5.0367301232470626566380541486165e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.172 y2[1] (analytic) = 0.82884682107788297392188064494727 y2[1] (numeric) = 0.8288468210778829739218806449472 absolute error = 7e-32 relative error = 8.4454688393408723354777266396802e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9852444312681263747612344685321 y1[1] (numeric) = 1.9852444312681263747612344685322 absolute error = 1e-31 relative error = 5.0371631031913992650611999673230e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.5MB, time=13.09 x[1] = 0.173 y2[1] (analytic) = 0.82786166238740457422439940478408 y2[1] (numeric) = 0.82786166238740457422439940478401 absolute error = 7e-32 relative error = 8.4555189810496300881971999765540e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9850727854955552039159797927608 y1[1] (numeric) = 1.9850727854955552039159797927609 absolute error = 1e-31 relative error = 5.0375986578767144650814597912235e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=13.34 x[1] = 0.174 y2[1] (analytic) = 0.82687667583524944226135438597639 y2[1] (numeric) = 0.82687667583524944226135438597632 absolute error = 7e-32 relative error = 8.4655913083158617109578125756920e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9849001546502806269115761840325 y1[1] (numeric) = 1.9849001546502806269115761840326 absolute error = 1e-31 relative error = 5.0380367881838867946282593425039e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=13.58 x[1] = 0.175 y2[1] (analytic) = 0.82589186240640404810566760804859 y2[1] (numeric) = 0.82589186240640404810566760804852 absolute error = 7e-32 relative error = 8.4756858841108752155560965893498e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9847265389049334746366973533995 y1[1] (numeric) = 1.9847265389049334746366973533996 absolute error = 1e-31 relative error = 5.0384774949991186410848730511387e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.176 y2[1] (analytic) = 0.82490722308568173853495022516409 y2[1] (numeric) = 0.82490722308568173853495022516402 absolute error = 7e-32 relative error = 8.4858027716323216940262426055857e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9845519384331294779705172790773 y1[1] (numeric) = 1.9845519384331294779705172790774 absolute error = 1e-31 relative error = 5.0389207792139400653792684886860e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.5MB, time=13.82 x[1] = 0.177 y2[1] (analytic) = 0.82392275885772175221823781629032 y2[1] (numeric) = 0.82392275885772175221823781629025 absolute error = 7e-32 relative error = 8.4959420343051693100473749019003e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9843763534094690941669937952475 y1[1] (numeric) = 1.9843763534094690941669937952476 absolute error = 1e-31 relative error = 5.0393666417252126497384297434273e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.5MB, time=14.07 x[1] = 0.178 y2[1] (analytic) = 0.82293847070698823507683376943031 y2[1] (numeric) = 0.82293847070698823507683376943023 absolute error = 8e-32 relative error = 9.7212614123230653579497718886167e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9841997840095373322544258881378 y1[1] (numeric) = 1.9841997840095373322544258881379 absolute error = 1e-31 relative error = 5.0398150834351333691347745877695e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.179 y2[1] (analytic) = 0.82195435961776925582024539899536 y2[1] (numeric) = 0.82195435961776925582024539899529 absolute error = 7e-32 relative error = 8.5162879399474042292751699499598e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9840222304099035774504592998064 y1[1] (numeric) = 1.9840222304099035774504592998065 absolute error = 1e-31 relative error = 5.0402661052512384864534628324771e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=225.0MB, alloc=4.5MB, time=14.31 TOP MAIN SOLVE Loop x[1] = 0.18 y2[1] (analytic) = 0.82097042657417582165819726030079 y2[1] (numeric) = 0.82097042657417582165819726030072 absolute error = 7e-32 relative error = 8.5264947109121478798527931059974e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9838436927881214145927160246115 y1[1] (numeric) = 1.9838436927881214145927160246116 absolute error = 1e-31 relative error = 5.0407197080864074714095761345369e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.5MB, time=14.56 x[1] = 0.181 y2[1] (analytic) = 0.81998667256014089418970594908918 y2[1] (numeric) = 0.81998667256014089418970594908911 absolute error = 7e-32 relative error = 8.5367241130209878848879624904715e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9836641713227284505852242677207 y1[1] (numeric) = 1.9836641713227284505852242677208 absolute error = 1e-31 relative error = 5.0411758928588669432443327284863e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=232.6MB, alloc=4.5MB, time=14.81 x[1] = 0.182 y2[1] (analytic) = 0.81900309855941840547020049692454 y2[1] (numeric) = 0.81900309855941840547020049692447 absolute error = 7e-32 relative error = 8.5469762108502600518055810412083e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.983483666193246135860826419216 y1[1] (numeric) = 1.9834836661932461358608264192161 absolute error = 1e-31 relative error = 5.0416346604921946372296840869981e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.183 y2[1] (analytic) = 0.81801970555558227425767229525488 y2[1] (numeric) = 0.81801970555558227425767229525481 absolute error = 7e-32 relative error = 8.5572510692095650551286560267459e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9833021775801795848597435813723 y1[1] (numeric) = 1.9833021775801795848597435813724 absolute error = 1e-31 relative error = 5.0420960119153233950108243876294e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.5MB, time=15.05 x[1] = 0.184 y2[1] (analytic) = 0.81703649453202542243883830191132 y2[1] (numeric) = 0.81703649453202542243883830191125 absolute error = 7e-32 relative error = 8.5675487531427773106838377389049e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9831197056650173955244761705281 y1[1] (numeric) = 1.9831197056650173955244761705282 absolute error = 1e-31 relative error = 5.0425599480625451788163278710881e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.5MB, time=15.30 x[1] = 0.185 y2[1] (analytic) = 0.81605346647195879163630110379855 y2[1] (numeric) = 0.81605346647195879163630110379848 absolute error = 7e-32 relative error = 8.5778693279290589486651492063135e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9829362506302314678112210986348 y1[1] (numeric) = 1.9829362506302314678112210986349 absolute error = 1e-31 relative error = 5.0430264698735151095658137243275e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.5MB, time=15.54 x[1] = 0.186 y2[1] (analytic) = 0.81507062235841035999768922853466 y2[1] (numeric) = 0.81507062235841035999768922853459 absolute error = 7e-32 relative error = 8.5882128590838789150211367636360e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9827518126592768212179870230509 y1[1] (numeric) = 1.982751812659276821217987023051 absolute error = 1e-31 relative error = 5.0434955782932555289052230114821e-30 % Correct digits = 31 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.187 y2[1] (analytic) = 0.81408796317422415916776091581804 y2[1] (numeric) = 0.81408796317422415916776091581797 absolute error = 7e-32 relative error = 8.5985794123600372308223807398312e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9825663919365914113295901364508 y1[1] (numeric) = 1.982566391936591411329590136451 absolute error = 2e-31 relative error = 1.0087934548544320170399954818566e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.5MB, time=15.78 x[1] = 0.188 y2[1] (analytic) = 0.81310548990205929144445437633573 y2[1] (numeric) = 0.81310548990205929144445437633566 absolute error = 7e-32 relative error = 8.6089690537486944394594018416325e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9823799886475959453797139518383 y1[1] (numeric) = 1.9823799886475959453797139518385 absolute error = 2e-31 relative error = 1.0088883117531995687032950166730e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.5MB, time=16.03 x[1] = 0.189 y2[1] (analytic) = 0.81212320352438894711986738208099 y2[1] (numeric) = 0.81212320352438894711986738208093 absolute error = 6e-32 relative error = 7.3880415852689196614704226143903e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9821926029786936968302175205875 y1[1] (numeric) = 1.9821926029786936968302175205877 absolute error = 2e-31 relative error = 1.0089836865471834839245129940049e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.19 y2[1] (analytic) = 0.81114110502349942200714884701869 y2[1] (numeric) = 0.81114110502349942200714884701863 absolute error = 6e-32 relative error = 7.3969867423081401933899229936576e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9820042351172703189678775041899 y1[1] (numeric) = 1.9820042351172703189678775041901 absolute error = 2e-31 relative error = 1.0090795794296902276075654013421e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.5MB, time=16.27 x[1] = 0.191 y2[1] (analytic) = 0.81015919538148913515428487112495 y2[1] (numeric) = 0.81015919538148913515428487112488 absolute error = 7e-32 relative error = 8.6402771700984374248641777030803e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9818148852516936575187505029481 y1[1] (numeric) = 1.9818148852516936575187505029483 absolute error = 2e-31 relative error = 1.0091759905951038428329344972188e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.5MB, time=16.52 x[1] = 0.192 y2[1] (analytic) = 0.80917747558026764674576153393323 y2[1] (numeric) = 0.80917747558026764674576153393316 absolute error = 7e-32 relative error = 8.6507598286522297863830222779011e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9816245535713135622803430272392 y1[1] (numeric) = 1.9816245535713135622803430272394 absolute error = 2e-31 relative error = 1.0092729202388867921062931390297e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.5MB, time=16.76 x[1] = 0.193 y2[1] (analytic) = 0.80819594660155467619308653584224 y2[1] (numeric) = 0.80819594660155467619308653584217 absolute error = 7e-32 relative error = 8.6612659088861291946616436022755e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9814332402664616977717774791618 y1[1] (numeric) = 1.981433240266461697771777479162 absolute error = 2e-31 relative error = 1.0093703685575808034358110689189e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.194 y2[1] (analytic) = 0.8072146094268791204151515965821 y2[1] (numeric) = 0.80721460942687912041515159658203 absolute error = 7e-32 relative error = 8.6717954782433720470826866027180e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9812409455284513529021434943852 y1[1] (numeric) = 1.9812409455284513529021434943854 absolute error = 2e-31 relative error = 1.0094683357488077212444583994990e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.5MB, time=17.01 x[1] = 0.195 y2[1] (analytic) = 0.80623346503757807230941733039465 y2[1] (numeric) = 0.80623346503757807230941733039458 absolute error = 7e-32 relative error = 8.6823486044129092015893970037079e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9810476695495772496572249758333 y1[1] (numeric) = 1.9810476695495772496572249758336 absolute error = 3e-31 relative error = 1.5143502330169055431854887313091e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.5MB, time=17.25 x[1] = 0.196 y2[1] (analytic) = 0.80525251441479583941490212666118 y2[1] (numeric) = 0.80525251441479583941490212666111 absolute error = 7e-32 relative error = 8.6929253553304780247660400705220e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9808534125231153508047941324606 y1[1] (numeric) = 1.9808534125231153508047941324609 absolute error = 3e-31 relative error = 1.5144987413171300631520281044339e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.5MB, time=17.50 x[1] = 0.197 y2[1] (analytic) = 0.80427175853948296276795637290694 y2[1] (numeric) = 0.80427175853948296276795637290687 absolute error = 7e-32 relative error = 8.7035257991796799053227491424915e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.980658174643322666618664817809 y1[1] (numeric) = 1.9806581746433226666186648178093 absolute error = 3e-31 relative error = 1.5146480288251861631463304393383e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.198 y2[1] (analytic) = 0.80329119839239523595180316432647 y2[1] (numeric) = 0.8032911983923952359518031643264 absolute error = 7e-32 relative error = 8.7141500043930632648445593440009e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9804619561054370606216984442784 y1[1] (numeric) = 1.9804619561054370606216984442787 absolute error = 3e-31 relative error = 1.5147980958440002173608341602801e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.5MB, time=17.75 x[1] = 0.199 y2[1] (analytic) = 0.8023108349540927243408264502072 y2[1] (numeric) = 0.80231083495409272434082645020713 absolute error = 7e-32 relative error = 8.7247980396532120978734844175872e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9802647571056770543479567300861 y1[1] (numeric) = 1.9802647571056770543479567300864 absolute error = 3e-31 relative error = 1.5149489426781252655753970838099e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.5MB, time=17.99 x[1] = 0.2 y2[1] (analytic) = 0.80133066920493878454058737288161 y2[1] (numeric) = 0.80133066920493878454058737288154 absolute error = 7e-32 relative error = 8.7354699738938400736031231398581e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9800665778412416311241965167482 y1[1] (numeric) = 1.9800665778412416311241965167485 absolute error = 3e-31 relative error = 1.5151005696337423332428237405056e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.201 y2[1] (analytic) = 0.80035070212509908402454935910971 y2[1] (numeric) = 0.80035070212509908402454935910964 absolute error = 7e-32 relative error = 8.7461658763008902316774485151913e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.979867418510310038870902875571 y1[1] (numeric) = 1.9798674185103100388709028755713 absolute error = 3e-31 relative error = 1.5152529770186617588947844467261e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.5MB, time=18.24 x[1] = 0.202 y2[1] (analytic) = 0.79937093469454062096849232708521 y2[1] (numeric) = 0.79937093469454062096849232708513 absolute error = 8e-32 relative error = 1.0007869504358446062627600297492e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9796672793120415919230577021024 y1[1] (numeric) = 1.9796672793120415919230577021028 absolute error = 4e-31 relative error = 2.0205415535230993718374045891190e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.5MB, time=18.48 x[1] = 0.203 y2[1] (analytic) = 0.79839136789303074428359617456935 y2[1] (numeric) = 0.79839136789303074428359617456927 absolute error = 8e-32 relative error = 1.0020148415572358515506493107896e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9794661604465754718708419777594 y1[1] (numeric) = 1.9794661604465754718708419777597 absolute error = 3e-31 relative error = 1.5155601343158036194310507188101e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.5MB, time=18.73 x[1] = 0.204 y2[1] (analytic) = 0.79741200270013617384917351498742 y2[1] (numeric) = 0.79741200270013617384917351498734 absolute error = 8e-32 relative error = 1.0032454957927652776214875850103e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.979264062115030527420470857911 y1[1] (numeric) = 1.9792640621150305274204708579113 absolute error = 3e-31 relative error = 1.5157148848518053461107296031697e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.205 y2[1] (analytic) = 0.79643284009522202094603142867336 y2[1] (numeric) = 0.79643284009522202094603142867328 absolute error = 8e-32 relative error = 1.0044789211659723714166366201908e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9790609845195050732753617255673 y1[1] (numeric) = 1.9790609845195050732753617255676 absolute error = 3e-31 relative error = 1.5158704170646707205799096779146e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.5MB, time=18.97 x[1] = 0.206 y2[1] (analytic) = 0.79545388105745080889144179581925 y2[1] (numeric) = 0.79545388105745080889144179581917 absolute error = 8e-32 relative error = 1.0057151257298609528218033809172e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9788569278630766880378363294873 y1[1] (numeric) = 1.9788569278630766880378363294876 absolute error = 3e-31 relative error = 1.5160267312703768147652123105131e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.5MB, time=19.22 x[1] = 0.207 y2[1] (analytic) = 0.79447512656578149387669957607767 y2[1] (numeric) = 0.79447512656578149387669957607759 absolute error = 8e-32 relative error = 1.0069541175670287695043994205744e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9786518923498020111315591049884 y1[1] (numeric) = 1.9786518923498020111315591049887 absolute error = 3e-31 relative error = 1.5161838277865381323958138136096e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.208 y2[1] (analytic) = 0.79349657759896848600824819717701 y2[1] (numeric) = 0.79349657759896848600824819717693 absolute error = 8e-32 relative error = 1.0081959047897977577644155233324e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9784458781847165387449147550011 y1[1] (numeric) = 1.9784458781847165387449147550014 absolute error = 3e-31 relative error = 1.5163417069324079879332891639242e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.5MB, time=19.46 x[1] = 0.209 y2[1] (analytic) = 0.79251823513556067055335101134286 y2[1] (numeric) = 0.79251823513556067055335101134278 absolute error = 8e-32 relative error = 1.0094404955403449733126252978759e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9782388855738344187955291479752 y1[1] (numeric) = 1.9782388855738344187955291479756 absolute error = 4e-31 relative error = 2.0220004920385065238705029532612e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.5MB, time=19.70 x[1] = 0.21 y2[1] (analytic) = 0.79154010015390042939128757377236 y2[1] (numeric) = 0.79154010015390042939128757377228 absolute error = 8e-32 relative error = 1.0106878979908341959158263286153e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9780309147241482449161385680994 y1[1] (numeric) = 1.9780309147241482449161385680997 absolute error = 3e-31 relative error = 1.5166598143984889496365564690110e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.5MB, time=19.95 x[1] = 0.211 y2[1] (analytic) = 0.79056217363212266267105329188374 y2[1] (numeric) = 0.79056217363212266267105329188366 absolute error = 8e-32 relative error = 1.0119381203435482118749128956175e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9778219658436288494620133319462 y1[1] (numeric) = 1.9778219658436288494620133319466 absolute error = 4e-31 relative error = 2.0224267244872176699178382986142e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.212 y2[1] (analytic) = 0.78958445654815381067654078755991 y2[1] (numeric) = 0.78958445654815381067654078755983 absolute error = 8e-32 relative error = 1.0131911708310217783278517242668e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.977612039141225095540142764105 y1[1] (numeric) = 1.9776120391412250955401427641054 absolute error = 4e-31 relative error = 2.0226414083406337282434217059670e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.5MB, time=20.19 x[1] = 0.213 y2[1] (analytic) = 0.7886069498797108759001811071231 y2[1] (numeric) = 0.78860694987971087590018110712303 absolute error = 7e-32 relative error = 8.8764117550165336422159036658806e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9774011348268636680603895025966 y1[1] (numeric) = 1.977401134826863668060389502597 absolute error = 4e-31 relative error = 2.0228571378615245231399158388189e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.5MB, time=20.44 x[1] = 0.214 y2[1] (analytic) = 0.78762965460430044532602270531804 y2[1] (numeric) = 0.78762965460430044532602270531796 absolute error = 8e-32 relative error = 1.0157057892924490362196973135299e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9771892531114488638088220829006 y1[1] (numeric) = 1.9771892531114488638088220829009 absolute error = 3e-31 relative error = 1.5173054351165330925482791767462e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.5MB, time=20.68 x[1] = 0.215 y2[1] (analytic) = 0.78665257169921771292322592014294 y2[1] (numeric) = 0.78665257169921771292322592014286 absolute error = 8e-32 relative error = 1.0169673738839384009530344473092e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9769763942068623805434357272442 y1[1] (numeric) = 1.9769763942068623805434357272446 absolute error = 4e-31 relative error = 2.0232917356632114925631470015457e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.216 y2[1] (analytic) = 0.78567570214154550235095044495269 y2[1] (numeric) = 0.78567570214154550235095044495262 absolute error = 7e-32 relative error = 8.9095284236483825021797836668276e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9767625583259631051124722434151 y1[1] (numeric) = 1.9767625583259631051124722434155 absolute error = 4e-31 relative error = 2.0235106048282457401857407345363e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.5MB, time=20.92 x[1] = 0.217 y2[1] (analytic) = 0.78469904690815328987561309286506 y2[1] (numeric) = 0.78469904690815328987561309286499 absolute error = 7e-32 relative error = 8.9206174361765592456378501992139e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9765477456825869005955509147589 y1[1] (numeric) = 1.9765477456825869005955509147593 absolute error = 4e-31 relative error = 2.0237305214292347163802008447365e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.5MB, time=21.17 x[1] = 0.218 y2[1] (analytic) = 0.78372260697569622750149293613085 y2[1] (numeric) = 0.78372260697569622750149293613078 absolute error = 7e-32 relative error = 8.9317316327166695774787889836935e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.976331956491546392467823240215 y1[1] (numeric) = 1.9763319564915463924678232402155 absolute error = 5e-31 relative error = 2.5299393573922545204807052838998e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.219 y2[1] (analytic) = 0.78274638332061416631566068978145 y2[1] (numeric) = 0.78274638332061416631566068978137 absolute error = 8e-32 relative error = 1.0220424099645040771654154339040e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9761151909686307537873653602166 y1[1] (numeric) = 1.9761151909686307537873653602171 absolute error = 5e-31 relative error = 2.5302168734147294939111215318674e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.5MB, time=21.41 x[1] = 0.22 y2[1] (analytic) = 0.78177037691913068004820899454299 y2[1] (numeric) = 0.78177037691913068004820899454291 absolute error = 8e-32 relative error = 1.0233183855759669721224204264164e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9758974493306054894060229810447 y1[1] (numeric) = 1.9758974493306054894060229810452 absolute error = 5e-31 relative error = 2.5304957004190171564532112113104e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.5MB, time=21.66 x[1] = 0.221 y2[1] (analytic) = 0.78079458874725208884876003870549 y2[1] (numeric) = 0.78079458874725208884876003870542 absolute error = 7e-32 relative error = 8.9652260669879490691883504238521e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9756787317952122192039245867742 y1[1] (numeric) = 1.9756787317952122192039245867747 absolute error = 5e-31 relative error = 2.5307758389729287057768418451278e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.5MB, time=21.90 x[1] = 0.222 y2[1] (analytic) = 0.77981901978076648328022674235797 y2[1] (numeric) = 0.7798190197807664832802267423579 absolute error = 7e-32 relative error = 8.9764417415311784657753618179398e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9754590385811684603478797042797 y1[1] (numeric) = 1.9754590385811684603478797042802 absolute error = 5e-31 relative error = 2.5310572896470401690624942535257e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.223 y2[1] (analytic) = 0.778843670995242748530803510147 y2[1] (numeric) = 0.77884367099524274853080351014693 absolute error = 7e-32 relative error = 8.9876829724443593353990716366432e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.975238369908167408573879962885 y1[1] (numeric) = 1.9752383699081674085738799628855 absolute error = 5e-31 relative error = 2.5313400530146948881157424609929e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.5MB, time=22.15 x[1] = 0.224 y2[1] (analytic) = 0.77786854336602958884516234048672 y2[1] (numeric) = 0.77786854336602958884516234048665 absolute error = 7e-32 relative error = 8.9989498350315961958692336179813e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9750167259968777184939216661375 y1[1] (numeric) = 1.975016725996877718493921666138 absolute error = 5e-31 relative error = 2.5316241296520060170874492718091e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.5MB, time=22.39 x[1] = 0.225 y2[1] (analytic) = 0.7768936378682545521758298599428 y2[1] (numeric) = 0.77689363786825455217582985994273 absolute error = 7e-32 relative error = 9.0102424048773822249203416004664e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9747941070689432829273695688655 y1[1] (numeric) = 1.974794107068943282927369568866 absolute error = 5e-31 relative error = 2.5319095201378590328184704602865e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.226 y2[1] (analytic) = 0.77591895547682305505572063133211 y2[1] (numeric) = 0.77591895547682305505572063133204 absolute error = 7e-32 relative error = 9.0215607578478500220067260327423e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9745705133469830112570825281373 y1[1] (numeric) = 1.9745705133469830112570825281378 absolute error = 5e-31 relative error = 2.5321962250539142578277607380671e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=354.7MB, alloc=4.5MB, time=22.64 TOP MAIN SOLVE Loop x[1] = 0.227 y2[1] (analytic) = 0.77494449716641740769280186292349 y2[1] (numeric) = 0.77494449716641740769280186292342 absolute error = 7e-32 relative error = 9.0329049700920288888016435712117e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9743459450545906068105226719777 y1[1] (numeric) = 1.9743459450545906068105226719782 absolute error = 5e-31 relative error = 2.5324842449846093959628750955369e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.5MB, time=22.88 x[1] = 0.228 y2[1] (analytic) = 0.7739702639114958392878644239937 y2[1] (numeric) = 0.77397026391149583928786442399362 absolute error = 8e-32 relative error = 1.0336314420620695619714116779233e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9741204024163343432660707047136 y1[1] (numeric) = 1.9741204024163343432660707047141 absolute error = 5e-31 relative error = 2.5327735805171620807319597690100e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.5MB, time=23.13 x[1] = 0.229 y2[1] (analytic) = 0.77299625668629152357637484888623 y2[1] (numeric) = 0.77299625668629152357637484888615 absolute error = 8e-32 relative error = 1.0349338603908240199181536019696e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9738938856577568400847709426156 y1[1] (numeric) = 1.9738938856577568400847709426162 absolute error = 6e-31 relative error = 3.0396770786898869236037135532063e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.23 y2[1] (analytic) = 0.77202247646481160459538278763993 y2[1] (numeric) = 0.77202247646481160459538278763985 absolute error = 8e-32 relative error = 1.0362392603688185454373180720842e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9736663950053748369677306480716 y1[1] (numeric) = 1.9736663950053748369677306480722 absolute error = 6e-31 relative error = 3.0400274409007507817083398467313e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.5MB, time=23.37 x[1] = 0.231 y2[1] (analytic) = 0.77104892422083622267645813619863 y2[1] (numeric) = 0.77104892422083622267645813619855 absolute error = 8e-32 relative error = 1.0375476508295754990820320901213e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9734379306866789673393992048733 y1[1] (numeric) = 1.9734379306866789673393992048739 absolute error = 6e-31 relative error = 3.0403793839678734786945855109978e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.5MB, time=23.61 x[1] = 0.232 y2[1] (analytic) = 0.77007560092791754066563185318355 y2[1] (numeric) = 0.77007560092791754066563185318348 absolute error = 7e-32 relative error = 9.0900166055971831164687038687941e-30 % Correct digits = 31 h = 0.001 y1[1] (analytic) = 1.9732084929301335308569536513194 y1[1] (numeric) = 1.97320849293013353085695365132 absolute error = 6e-31 relative error = 3.0407329086092907222914515314984e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.5MB, time=23.86 x[1] = 0.233 y2[1] (analytic) = 0.76910250755937877037131424320659 y2[1] (numeric) = 0.76910250755937877037131424320651 absolute error = 8e-32 relative error = 1.0401734386989185316590020402005e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9729780819651762649460180617296 y1[1] (numeric) = 1.9729780819651762649460180617302 absolute error = 6e-31 relative error = 3.0410880155463896548898545640705e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.234 y2[1] (analytic) = 0.7681296450883131992411642587249 y2[1] (numeric) = 0.76812964508831319924116425872482 absolute error = 8e-32 relative error = 1.0414908539404472674767121851664e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.972746698022218115362945240631 y1[1] (numeric) = 1.9727466980222181153629452406316 absolute error = 6e-31 relative error = 3.0414447055039120033357141473492e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.5MB, time=24.10 x[1] = 0.235 y2[1] (analytic) = 0.7671570144875832172688831434866 y2[1] (numeric) = 0.76715701448758321726888314348651 absolute error = 9e-32 relative error = 1.1731627072472879102432275613040e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9725143413326430057838901673172 y1[1] (numeric) = 1.9725143413326430057838901673178 absolute error = 6e-31 relative error = 3.0418029792099572441046236479964e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.5MB, time=24.35 x[1] = 0.236 y2[1] (analytic) = 0.76618461672981934413190551069257 y2[1] (numeric) = 0.76618461672981934413190551069248 absolute error = 9e-32 relative error = 1.1746516183544939857015372627874e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9722810121288076064209056016861 y1[1] (numeric) = 1.9722810121288076064209056016867 absolute error = 6e-31 relative error = 3.0421628373959857838819940014039e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.237 y2[1] (analytic) = 0.76521245278741925656096071810253 y2[1] (numeric) = 0.76521245278741925656096071810244 absolute error = 9e-32 relative error = 1.1761439541680139857425552861063e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9720467106440411016652912352422 y1[1] (numeric) = 1.9720467106440411016652912352428 absolute error = 6e-31 relative error = 3.0425242807968221555726825378280e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.5MB, time=24.59 x[1] = 0.238 y2[1] (analytic) = 0.76424052363254681594247717044265 y2[1] (numeric) = 0.76424052363254681594247717044256 absolute error = 9e-32 relative error = 1.1776397248894478495140004241396e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9718114371126449567584287438953 y1[1] (numeric) = 1.9718114371126449567584287438959 absolute error = 6e-31 relative error = 3.0428873101506582297642426900502e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.5MB, time=24.84 x[1] = 0.239 y2[1] (analytic) = 0.76326883023713109615480194662958 y2[1] (numeric) = 0.7632688302371310961548019466295 absolute error = 8e-32 relative error = 1.0481235028966888702274104850782e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9715751917698926834903360717 y1[1] (numeric) = 1.9715751917698926834903360717007 absolute error = 7e-31 relative error = 3.5504605805655658486127298594102e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.5MB, time=25.08 x[1] = 0.24 y2[1] (analytic) = 0.76229737357286541163920791551018 y2[1] (numeric) = 0.7622973735728654116392079155101 absolute error = 8e-32 relative error = 1.0494592107151353350592167892287e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9713379748520296049261752469634 y1[1] (numeric) = 1.9713379748520296049261752469641 absolute error = 7e-31 relative error = 3.5508878179681118724898367705815e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.241 y2[1] (analytic) = 0.76132615461120634570666026902879 y2[1] (numeric) = 0.76132615461120634570666026902871 absolute error = 8e-32 relative error = 1.0507979991946337296542918682897e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9710997865962726191609490041922 y1[1] (numeric) = 1.9710997865962726191609490041929 absolute error = 7e-31 relative error = 3.5513169082564381982249223134855e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.5MB, time=25.33 x[1] = 0.242 y2[1] (analytic) = 0.76035517432337277908131416597463 y2[1] (numeric) = 0.76035517432337277908131416597454 absolute error = 9e-32 relative error = 1.1836573622332415788816331685131e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9708606272408099621026224571645 y1[1] (numeric) = 1.9708606272408099621026224571652 absolute error = 7e-31 relative error = 3.5517478523075207460054227492605e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.5MB, time=25.57 x[1] = 0.243 y2[1] (analytic) = 0.75938443368034491868171494273065 y2[1] (numeric) = 0.75938443368034491868171494273057 absolute error = 8e-32 relative error = 1.0534848549934219312566315117634e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9706204970248009692839070399837 y1[1] (numeric) = 1.9706204970248009692839070399844 absolute error = 7e-31 relative error = 3.5521806510022830016182478925237e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.5MB, time=25.82 x[1] = 0.244 y2[1] (analytic) = 0.7584139336528633266406721097428 y2[1] (numeric) = 0.75841393365286332664067210974272 absolute error = 8e-32 relative error = 1.0548329408280243939042358740000e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9703793961883758367029449043108 y1[1] (numeric) = 1.9703793961883758367029449043115 absolute error = 7e-31 relative error = 3.5526153052255998719316894591292e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.245 y2[1] (analytic) = 0.7574436752114279495647781137546 y2[1] (numeric) = 0.75744367521142794956477811375452 absolute error = 8e-32 relative error = 1.0561841443546190441108024012494e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9701373249726353806931329320715 y1[1] (numeric) = 1.9701373249726353806931329320722 absolute error = 7e-31 relative error = 3.5530518158663015586077250173530e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.5MB, time=26.07 x[1] = 0.246 y2[1] (analytic) = 0.75647365932629714803454260620757 y2[1] (numeric) = 0.75647365932629714803454260620749 absolute error = 8e-32 relative error = 1.0575384749185671403493930180178e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9698942836196507968223264937931 y1[1] (numeric) = 1.9698942836196507968223264937938 absolute error = 7e-31 relative error = 3.5534901838171774500740406235301e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.5MB, time=26.31 x[1] = 0.247 y2[1] (analytic) = 0.75550388696748672634611271759229 y2[1] (numeric) = 0.75550388696748672634611271759221 absolute error = 8e-32 relative error = 1.0588959419005982871005465532089e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9696502723724634178216640533481 y1[1] (numeric) = 1.9696502723724634178216640533489 absolute error = 8e-31 relative error = 4.0616347542571200363259912261665e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.248 y2[1] (analytic) = 0.75453435910476896249554959594889 y2[1] (numeric) = 0.75453435910476896249554959594881 absolute error = 8e-32 relative error = 1.0602565547169708421233035642242e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9694052914750844705442546902599 y1[1] (numeric) = 1.9694052914750844705442546902607 absolute error = 8e-31 relative error = 4.0621399945604900740604275880829e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.5MB, time=26.55 x[1] = 0.249 y2[1] (analytic) = 0.75356507670767163840663122515975 y2[1] (numeric) = 0.75356507670767163840663122515967 absolute error = 8e-32 relative error = 1.0616203228196331736377515469281e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9691593411724948319539715808613 y1[1] (numeric) = 1.9691593411724948319539715808621 absolute error = 8e-31 relative error = 4.0626473605922448945417233921748e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.5MB, time=26.80 x[1] = 0.25 y2[1] (analytic) = 0.75259604074547707040315129515061 y2[1] (numeric) = 0.75259604074547707040315129515053 absolute error = 8e-32 relative error = 1.0629872556963857725687379856705e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9689124217106447841445954494942 y1[1] (numeric) = 1.968912421710644784144595449495 absolute error = 8e-31 relative error = 4.0631568533908592651295073313858e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.5MB, time=27.04 x[1] = 0.251 y2[1] (analytic) = 0.75162725218722113992668365162059 y2[1] (numeric) = 0.75162725218722113992668365162051 absolute error = 8e-32 relative error = 1.0643573628710442250355289438266e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9686645333364537683895529705847 y1[1] (numeric) = 1.9686645333364537683895529705855 absolute error = 8e-31 relative error = 4.0636684739993552921070949963022e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.252 y2[1] (analytic) = 0.75065871200169232450078160745575 y2[1] (numeric) = 0.75065871200169232450078160745566 absolute error = 9e-32 relative error = 1.1989469856415534315960360758547e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9684156762978101382224960718362 y1[1] (numeric) = 1.968415676297810138222496071837 absolute error = 8e-31 relative error = 4.0641822234653069945722102173436e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.5MB, time=27.29 x[1] = 0.253 y2[1] (analytic) = 0.74969042115743072894258115154618 y2[1] (numeric) = 0.74969042115743072894258115154609 absolute error = 9e-32 relative error = 1.2004955306892004606676018473445e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9681658508435709115489690579392 y1[1] (numeric) = 1.96816585084357091154896905794 absolute error = 8e-31 relative error = 4.0646981028408448994352703009504e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.5MB, time=27.53 x[1] = 0.254 y2[1] (analytic) = 0.7487223806227271168227768433228 y2[1] (numeric) = 0.74872238062272711682277684332271 absolute error = 9e-32 relative error = 1.2020476792098191514485771961473e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9679150572235615217894114431114 y1[1] (numeric) = 1.9679150572235615217894114431123 absolute error = 9e-31 relative error = 4.5733681273304932397551161825195e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.255 y2[1] (analytic) = 0.74775459136562194217493893295701 y2[1] (numeric) = 0.74775459136562194217493893295692 absolute error = 9e-32 relative error = 1.2036034420816229691295541449292e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9676632956885755680537453494437 y1[1] (numeric) = 1.9676632956885755680537453494445 absolute error = 8e-31 relative error = 4.0657362555520116810821365590172e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=434.8MB, alloc=4.5MB, time=27.78 TOP MAIN SOLVE Loop x[1] = 0.256 y2[1] (analytic) = 0.7467870543539043814551399978256 y2[1] (numeric) = 0.74678705435390438145513999782551 absolute error = 9e-32 relative error = 1.2051628302242738048546198820295e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9674105664903745643477972964435 y1[1] (numeric) = 1.9674105664903745643477972964443 absolute error = 8e-31 relative error = 4.0662585310147258019392682440068e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.5MB, time=28.02 x[1] = 0.257 y2[1] (analytic) = 0.74581977055511136575285913553355 y2[1] (numeric) = 0.74581977055511136575285913553346 absolute error = 9e-32 relative error = 1.2067258545990712511740248536306e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.967156869881687687811805175334 y1[1] (numeric) = 1.9671568698816876878118051753349 absolute error = 9e-31 relative error = 4.5751308082213566956071547353065e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.5MB, time=28.27 x[1] = 0.258 y2[1] (analytic) = 0.74485274093652661325413150250981 y2[1] (numeric) = 0.74485274093652661325413150250972 absolute error = 9e-32 relative error = 1.2082925262091428872357675518884e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9669022061162115259912621695806 y1[1] (numeric) = 1.9669022061162115259912621695815 absolute error = 9e-31 relative error = 4.5757231711947392201775190876811e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.259 y2[1] (analytic) = 0.74388596646517966195791073494597 y2[1] (numeric) = 0.74388596646517966195791073494588 absolute error = 9e-32 relative error = 1.2098628560996355798761488142652e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9666465754486098231403503507787 y1[1] (numeric) = 1.9666465754486098231403503507796 absolute error = 9e-31 relative error = 4.5763179375262272629805618744130e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.5MB, time=28.51 x[1] = 0.26 y2[1] (analytic) = 0.74291944810784490264661153563478 y2[1] (numeric) = 0.74291944810784490264661153563469 absolute error = 9e-32 relative error = 1.2114368553579078068116601684141e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9663899781345132255582176464501 y1[1] (numeric) = 1.966389978134513225558217646451 absolute error = 9e-31 relative error = 4.5769151084354969112124928792545e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.5MB, time=28.76 x[1] = 0.261 y2[1] (analytic) = 0.74195318683104061211179945608533 y2[1] (numeric) = 0.74195318683104061211179945608524 absolute error = 9e-32 relative error = 1.2130145351137230081772056390046e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9661324144305190259583528434479 y1[1] (numeric) = 1.9661324144305190259583528434489 absolute error = 1.0e-30 relative error = 5.0861274279415472643861018365973e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.5MB, time=29.00 x[1] = 0.262 y2[1] (analytic) = 0.74098718360102798663599464814456 y2[1] (numeric) = 0.74098718360102798663599464814446 absolute error = 1.0e-31 relative error = 1.3495510072660488585540191055455e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9658738845941909068713142575752 y1[1] (numeric) = 1.9658738845941909068713142575761 absolute error = 9e-31 relative error = 4.5781166688919321870132857776241e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.263 y2[1] (analytic) = 0.74002143938381017573155610324072 y2[1] (numeric) = 0.74002143938381017573155610324062 absolute error = 1.0e-31 relative error = 1.3513122009446980720341260000518e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9656143888840586830810686666656 y1[1] (numeric) = 1.9656143888840586830810686666665 absolute error = 9e-31 relative error = 4.5787210609043129820137333389625e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.5MB, time=29.25 x[1] = 0.264 y2[1] (analytic) = 0.73905595514513131613761264028424 y2[1] (numeric) = 0.73905595514513131613761264028414 absolute error = 1.0e-31 relative error = 1.3530775214491385547064128916372e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9653539275596180430951980707674 y1[1] (numeric) = 1.9653539275596180430951980707684 absolute error = 1.0e-30 relative error = 5.0881420693610183994884272638175e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.5MB, time=29.49 x[1] = 0.265 y2[1] (analytic) = 0.73809073185047556607600664521424 y2[1] (numeric) = 0.73809073185047556607600664521413 absolute error = 1.1e-31 relative error = 1.4903316794700532843592920579860e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9650925008813302896492328092017 y1[1] (numeric) = 1.9650925008813302896492328092027 absolute error = 1.0e-30 relative error = 5.0888189718881272517875497956842e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.266 y2[1] (analytic) = 0.73712577046506613976721630616662 y2[1] (numeric) = 0.73712577046506613976721630616652 absolute error = 1.0e-31 relative error = 1.3566205932117685935553328035733e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9648301091106220792453705301393 y1[1] (numeric) = 1.9648301091106220792453705301404 absolute error = 1.1e-30 relative error = 5.5984484098623348184619508822390e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=465.3MB, alloc=4.5MB, time=29.73 x[1] = 0.267 y2[1] (analytic) = 0.73616107195386434220722182826113 y2[1] (numeric) = 0.73616107195386434220722182826103 absolute error = 1.0e-31 relative error = 1.3583983697288880854217183325161e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9645667525098851607258414739579 y1[1] (numeric) = 1.9645667525098851607258414739589 absolute error = 1.0e-30 relative error = 5.0901808183530698046296009585882e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.5MB, time=29.98 x[1] = 0.268 y2[1] (analytic) = 0.73519663728156860420628085106048 y2[1] (numeric) = 0.73519663728156860420628085106038 absolute error = 1.0e-31 relative error = 1.3601803235901035885966479327048e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9643024313424761128811814969892 y1[1] (numeric) = 1.9643024313424761128811814969902 absolute error = 1.0e-30 relative error = 5.0908657650877285309294985431725e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.5MB, time=30.22 x[1] = 0.269 y2[1] (analytic) = 0.73423246741261351769057802984597 y2[1] (numeric) = 0.73423246741261351769057802984587 absolute error = 1.0e-31 relative error = 1.3619664675466254270787734059393e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9640371458727160810936752273647 y1[1] (numeric) = 1.9640371458727160810936752273658 absolute error = 1.1e-30 relative error = 5.6007087356345143975828083854236e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.27 y2[1] (analytic) = 0.73326856331116887126771347897946 y2[1] (numeric) = 0.73326856331116887126771347897936 absolute error = 1.0e-31 relative error = 1.3637568143987666513120147986682e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9637708963658905130162327094922 y1[1] (numeric) = 1.9637708963658905130162327094933 absolute error = 1.1e-30 relative error = 5.6014680838565987023130090620512e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.5MB, time=30.46 x[1] = 0.271 y2[1] (analytic) = 0.73230492594113868605699451178298 y2[1] (numeric) = 0.73230492594113868605699451178288 absolute error = 1.0e-31 relative error = 1.3655513769961696916219774096800e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9635036830882488932869638582654 y1[1] (numeric) = 1.9635036830882488932869638582665 absolute error = 1.1e-30 relative error = 5.6022303878233211179242761750288e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.5MB, time=30.71 x[1] = 0.272 y2[1] (analytic) = 0.73134155626616025178549484656383 y2[1] (numeric) = 0.73134155626616025178549484656372 absolute error = 1.1e-31 relative error = 1.5040851850618376572014576961615e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9632355063070044772797160084106 y1[1] (numeric) = 1.9632355063070044772797160084117 absolute error = 1.1e-30 relative error = 5.6029956491016392862380455200351e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.273 y2[1] (analytic) = 0.73037845524960316315084518264563 y2[1] (numeric) = 0.73037845524960316315084518264552 absolute error = 1.1e-31 relative error = 1.5060685211806809569586583129631e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9629663662903340238908408084099 y1[1] (numeric) = 1.9629663662903340238908408084109 absolute error = 1.0e-30 relative error = 5.0943307902408259819559099334717e-29 % Correct digits = 30 h = 0.001 memory used=484.4MB, alloc=4.5MB, time=30.95 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.274 y2[1] (analytic) = 0.72941562385456835645171878353456 y2[1] (numeric) = 0.72941562385456835645171878353445 absolute error = 1.1e-31 relative error = 1.5080565373512195850506182811150e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9626962633073775273624576722117 y1[1] (numeric) = 1.9626962633073775273624576722127 absolute error = 1.0e-30 relative error = 5.0950318635389900388027846286740e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.5MB, time=31.20 x[1] = 0.275 y2[1] (analytic) = 0.72845306304388714648697543665472 y2[1] (numeric) = 0.72845306304388714648697543665461 absolute error = 1.1e-31 relative error = 1.5100492479276296864903882305940e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9624251976282379481424819654439 y1[1] (numeric) = 1.9624251976282379481424819654449 absolute error = 1.0e-30 relative error = 5.0957356296106839601371289578471e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.5MB, time=31.44 x[1] = 0.276 y2[1] (analytic) = 0.72749077378012026372442689042862 y2[1] (numeric) = 0.72749077378012026372442689042851 absolute error = 1.1e-31 relative error = 1.5120466673196166504877167537258e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9621531695239809427816870660775 y1[1] (numeric) = 1.9621531695239809427816870660785 absolute error = 1.0e-30 relative error = 5.0964420899037171286702841213958e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.277 y2[1] (analytic) = 0.72652875702555689174018659985692 y2[1] (numeric) = 0.72652875702555689174018659985681 absolute error = 1.1e-31 relative error = 1.5140488099926726210421137044400e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9618801792666345928680704024572 y1[1] (numeric) = 1.9618801792666345928680704024582 absolute error = 1.0e-30 relative error = 5.0971512458717404437215687212819e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.5MB, time=31.69 x[1] = 0.278 y2[1] (analytic) = 0.72556701374221370492956634116763 y2[1] (numeric) = 0.72556701374221370492956634116752 absolute error = 1.1e-31 relative error = 1.5160556904683354025328945666618e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9616062271291891329987945343101 y1[1] (numeric) = 1.9616062271291891329987945343111 absolute error = 1.0e-30 relative error = 5.0978630989742527393072801447340e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.5MB, time=31.93 x[1] = 0.279 y2[1] (analytic) = 0.72460554489183390649048198455785 y2[1] (numeric) = 0.72460554489183390649048198455774 absolute error = 1.1e-31 relative error = 1.5180673233244487689484297896225e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9613313133855966777899753047686 y1[1] (numeric) = 1.9613313133855966777899753047696 absolute error = 1.0e-30 relative error = 5.0985776506766072298183325934940e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.5MB, time=32.18 x[1] = 0.28 y2[1] (analytic) = 0.72364435143588626668033044154215 y2[1] (numeric) = 0.72364435143588626668033044154204 absolute error = 1.1e-31 relative error = 1.5200837231954241854571040974414e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9610554383107709479245900535965 y1[1] (numeric) = 1.9610554383107709479245900535975 absolute error = 1.0e-30 relative error = 5.0992949024500179833358581186582e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.281 y2[1] (analytic) = 0.72268343433556416134729952995054 y2[1] (numeric) = 0.72268343433556416134729952995043 absolute error = 1.1e-31 relative error = 1.5221049047725039510832394392794e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9607786021805869952387798436879 y1[1] (numeric) = 1.9607786021805869952387798436889 absolute error = 1.0e-30 relative error = 5.1000148557715664226343253735826e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.5MB, time=32.43 x[1] = 0.282 y2[1] (analytic) = 0.72172279455178461073707222518593 y2[1] (numeric) = 0.72172279455178461073707222518582 absolute error = 1.1e-31 relative error = 1.5241308828040257713124554468255e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9605008052718809268468206145129 y1[1] (numeric) = 1.9605008052718809268468206145139 absolute error = 1.0e-30 relative error = 5.1007375121242078539219597347593e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.5MB, time=32.67 x[1] = 0.283 y2[1] (analytic) = 0.72076243304518731857588649095688 y2[1] (numeric) = 0.72076243304518731857588649095677 absolute error = 1.1e-31 relative error = 1.5261616720956887695126370371844e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9602220478624496283050391375165 y1[1] (numeric) = 1.9602220478624496283050391375174 absolute error = 9e-31 relative error = 4.5913165856971002210316301693582e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.284 y2[1] (analytic) = 0.71980235077613371143091160634557 y2[1] (numeric) = 0.71980235077613371143091160634546 absolute error = 1.1e-31 relative error = 1.5281972875108209461188542083226e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9599423302310504858149506095312 y1[1] (numeric) = 1.9599423302310504858149506095322 absolute error = 1.0e-30 relative error = 5.1021909398839997014703807171879e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.5MB, time=32.91 x[1] = 0.285 y2[1] (analytic) = 0.71884254870470597834890162875478 y2[1] (numeric) = 0.71884254870470597834890162875467 absolute error = 1.1e-31 relative error = 1.5302377439706480945932382260050e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.959661652657401107465895681044 y1[1] (numeric) = 1.9596616526574011074658956810449 absolute error = 9e-31 relative error = 4.5926295428578403657738491742749e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.5MB, time=33.16 x[1] = 0.286 y2[1] (analytic) = 0.71788302779070611077408635400021 y2[1] (numeric) = 0.7178830277907061107740863540001 absolute error = 1.1e-31 relative error = 1.5322830564545641832339654388605e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9593800154221790435174556766546 y1[1] (numeric) = 1.9593800154221790435174556766556 absolute error = 1.0e-30 relative error = 5.1036551977107634887189449698404e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.5MB, time=33.41 x[1] = 0.287 y2[1] (analytic) = 0.71692378899365494274625985557732 y2[1] (numeric) = 0.71692378899365494274625985557721 absolute error = 1.1e-31 relative error = 1.5343332400004032119711390638666e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9590974188070215057219257252902 y1[1] (numeric) = 1.9590974188070215057219257252912 absolute error = 1.0e-30 relative error = 5.1043913916692459105170691646961e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.288 y2[1] (analytic) = 0.71596483327279119138002640493412 y2[1] (numeric) = 0.71596483327279119138002640493401 absolute error = 1.1e-31 relative error = 1.5363883097047125533514946792627e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9588138630945250856871264776764 y1[1] (numeric) = 1.9588138630945250856871264776774 absolute error = 1.0e-30 relative error = 5.1051302976802738306778190357374e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.5MB, time=33.65 x[1] = 0.289 y2[1] (analytic) = 0.71500616158707049762616329342395 y2[1] (numeric) = 0.71500616158707049762616329342384 absolute error = 1.1e-31 relative error = 1.5384482807230277869784911063637e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9585293485682454722798360482323 y1[1] (numeric) = 1.9585293485682454722798360482333 absolute error = 1.0e-30 relative error = 5.1058719172681048846716764997670e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.5MB, time=33.90 x[1] = 0.29 y2[1] (analytic) = 0.71404777489516446731605979449563 y2[1] (numeric) = 0.71404777489516446731605979449552 absolute error = 1.1e-31 relative error = 1.5405131682701490367394891565550e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9582438755126971680701247779319 y1[1] (numeric) = 1.9582438755126971680701247779329 absolute error = 1.0e-30 relative error = 5.1066162519629238259191461445522e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.5MB, time=34.14 x[1] = 0.291 y2[1] (analytic) = 0.71308967415545971249019122160201 y2[1] (numeric) = 0.7130896741554597124901912216019 absolute error = 1.1e-31 relative error = 1.5425829876204188202173707058413e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9579574442133532048168763737751 y1[1] (numeric) = 1.9579574442133532048168763737761 absolute error = 1.0e-30 relative error = 5.1073633033008493064452199655655e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.292 y2[1] (analytic) = 0.71213186032605689301158675327299 y2[1] (numeric) = 0.71213186032605689301158675327288 absolute error = 1.1e-31 relative error = 1.5446577541080014197501141184002e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9576700549566448579947799393226 y1[1] (numeric) = 1.9576700549566448579947799393236 absolute error = 1.0e-30 relative error = 5.1081130728239406857817023459649e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.5MB, time=34.39 x[1] = 0.293 y2[1] (analytic) = 0.71117433436476975846524941180534 y2[1] (numeric) = 0.71117433436476975846524941180523 absolute error = 1.1e-31 relative error = 1.5467374831271637846685235955069e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9573817080299613603630783692788 y1[1] (numeric) = 1.9573817080299613603630783692798 absolute error = 1.0e-30 relative error = 5.1088655620802048681697367000869e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.5MB, time=34.63 x[1] = 0.294 y2[1] (analytic) = 0.71021709722912419034448629606947 y2[1] (numeric) = 0.71021709722912419034448629606936 absolute error = 1.1e-31 relative error = 1.5488221901325579743095140413936e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9570924037216496145763595393507 y1[1] (numeric) = 1.9570924037216496145763595393517 absolute error = 1.0e-30 relative error = 5.1096207726236031681151113904122e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.295 y2[1] (analytic) = 0.70926014987635724452510688202316 y2[1] (numeric) = 0.70926014987635724452510688202305 absolute error = 1.1e-31 relative error = 1.5509118906395051514700840195485e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.956802142321013904837677680568 y1[1] (numeric) = 1.9568021423210139048376776805691 absolute error = 1.1e-30 relative error = 5.6214165766154640247840752758266e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.5MB, time=34.88 x[1] = 0.296 y2[1] (analytic) = 0.70830349326341619402844691665405 y2[1] (numeric) = 0.70830349326341619402844691665393 absolute error = 1.2e-31 relative error = 1.6941890184264885120385874951074e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9565109241183156075942932849186 y1[1] (numeric) = 1.9565109241183156075942932849196 absolute error = 1.0e-30 relative error = 5.1111393638174608222483032164338e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.5MB, time=35.12 x[1] = 0.297 y2[1] (analytic) = 0.70734712834695757207417514224732 y2[1] (numeric) = 0.7073471283469575720741751422472 absolute error = 1.2e-31 relative error = 1.6964796376629856675450785460380e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9562187494047729012763208465347 y1[1] (numeric) = 1.9562187494047729012763208465357 absolute error = 1.0e-30 relative error = 5.1119027476056770447655360877536e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.5MB, time=35.37 x[1] = 0.298 y2[1] (analytic) = 0.70639105608334621542383979809208 y2[1] (numeric) = 0.70639105608334621542383979809196 absolute error = 1.2e-31 relative error = 1.6987757555333677241838120339354e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9559256184725604750785746997598 y1[1] (numeric) = 1.9559256184725604750785746997607 absolute error = 9e-31 relative error = 4.6014019730608995467346296232009e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.299 y2[1] (analytic) = 0.70543527742865430801611155600021 y2[1] (numeric) = 0.70543527742865430801611155600008 absolute error = 1.3e-31 relative error = 1.8428338383339189546092109836442e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9556315316148092367859041722236 y1[1] (numeric) = 1.9556315316148092367859041722245 absolute error = 9e-31 relative error = 4.6020939295085389700549947208734e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.5MB, time=35.61 x[1] = 0.3 y2[1] (analytic) = 0.70447979333866042489467925431497 y2[1] (numeric) = 0.70447979333866042489467925431485 absolute error = 1.2e-31 relative error = 1.7033845560182463068885016686102e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.955336489125606019642310227568 y1[1] (numeric) = 1.955336489125606019642310227569 absolute error = 1.0e-30 relative error = 5.1142092706876420030287293303903e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.5MB, time=35.86 x[1] = 0.301 y2[1] (analytic) = 0.70352460476884857642975450243418 y2[1] (numeric) = 0.70352460476884857642975450243406 absolute error = 1.2e-31 relative error = 1.7056972732236910930578500289110e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9550404912999932882641367286816 y1[1] (numeric) = 1.9550404912999932882641367286825 absolute error = 9e-31 relative error = 4.6034852168281691779694066047728e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.302 y2[1] (analytic) = 0.70256971267440725283414093426342 y2[1] (numeric) = 0.70256971267440725283414093426329 absolute error = 1.3e-31 relative error = 1.8503501880993560577270904947907e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9547435384339688435976304082261 y1[1] (numeric) = 1.9547435384339688435976304082271 absolute error = 1.0e-30 relative error = 5.1157606117534172829147181954506e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=564.5MB, alloc=4.5MB, time=36.10 TOP MAIN SOLVE Loop x[1] = 0.303 y2[1] (analytic) = 0.7016151180102284689748235944506 y2[1] (numeric) = 0.70161511801022846897482359445048 absolute error = 1.2e-31 relative error = 1.7103394285504917615225243466929e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9544456308244855269211645888734 y1[1] (numeric) = 1.9544456308244855269211645888744 absolute error = 1.0e-30 relative error = 5.1165403847951945866249120314287e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=568.3MB, alloc=4.5MB, time=36.34 x[1] = 0.304 y2[1] (analytic) = 0.70066082173090680948103364573289 y2[1] (numeric) = 0.70066082173090680948103364573277 absolute error = 1.2e-31 relative error = 1.7126689016741791494859958702460e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9541467687694509228924226510006 y1[1] (numeric) = 1.9541467687694509228924226510016 absolute error = 1.0e-30 relative error = 5.1173228949927425183599670247306e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.5MB, time=36.59 x[1] = 0.305 y2[1] (analytic) = 0.69970682479073847414974328925156 y2[1] (numeric) = 0.69970682479073847414974328925144 absolute error = 1.2e-31 relative error = 1.7150039952216906743468985878332e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9538469525677270616408382006383 y1[1] (numeric) = 1.9538469525677270616408382006394 absolute error = 1.1e-30 relative error = 5.6299189583625804138689588181426e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.306 y2[1] (analytic) = 0.69875312814372032364954549226047 y2[1] (numeric) = 0.69875312814372032364954549226035 absolute error = 1.2e-31 relative error = 1.7173447268678025295891328248236e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9535461825191301199055898452054 y1[1] (numeric) = 1.9535461825191301199055898452065 absolute error = 1.1e-30 relative error = 5.6307857466749611349428242894647e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.5MB, time=36.83 x[1] = 0.307 y2[1] (analytic) = 0.69779973274354892552387281926885 y2[1] (numeric) = 0.69779973274354892552387281926873 absolute error = 1.2e-31 relative error = 1.7196911143573289874617729620330e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9532444589244301212194494390108 y1[1] (numeric) = 1.9532444589244301212194494390118 absolute error = 1.0e-30 relative error = 5.1196868647494236233558366378330e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.5MB, time=37.08 x[1] = 0.308 y2[1] (analytic) = 0.69684663954361960049450936332003 y2[1] (numeric) = 0.69684663954361960049450936331992 absolute error = 1.1e-31 relative error = 1.5785395775466672595794914374929e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9529417820853506351387836146492 y1[1] (numeric) = 1.9529417820853506351387836146503 absolute error = 1.1e-30 relative error = 5.6325283738126609069895302046525e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.5MB, time=37.32 x[1] = 0.309 y2[1] (analytic) = 0.6958938494970254690663494738148 y2[1] (numeric) = 0.69589384949702546906634947381468 absolute error = 1.2e-31 relative error = 1.7244009281980718007523370767769e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9526381523045684755200093702652 y1[1] (numeric) = 1.9526381523045684755200093702662 absolute error = 1.0e-30 relative error = 5.1212765602257988685123627472396e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.31 y2[1] (analytic) = 0.69494136355655649843435667604104 y2[1] (numeric) = 0.69494136355655649843435667604092 absolute error = 1.2e-31 relative error = 1.7267643903921114812995092166152e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9523335698857133978428054362022 y1[1] (numeric) = 1.9523335698857133978428054362032 absolute error = 1.0e-30 relative error = 5.1220755275879339656289087204656e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.5MB, time=37.57 x[1] = 0.311 y2[1] (analytic) = 0.69398918267469854969367587537158 y2[1] (numeric) = 0.69398918267469854969367587537146 absolute error = 1.2e-31 relative error = 1.7291335801158872837720651212833e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9520280351333677955803820978034 y1[1] (numeric) = 1.9520280351333677955803820978044 absolute error = 1.0e-30 relative error = 5.1228772435723614773779875479121e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.5MB, time=37.81 x[1] = 0.312 y2[1] (analytic) = 0.69303730780363242535385163593833 y2[1] (numeric) = 0.69303730780363242535385163593821 absolute error = 1.2e-31 relative error = 1.7315085154694328918608309651923e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9517215483530663956171131040662 y1[1] (numeric) = 1.9517215483530663956171131040672 absolute error = 1.0e-30 relative error = 5.1236817098414287561152445723890e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.313 y2[1] (analytic) = 0.69208573989523291715810501948532 y2[1] (numeric) = 0.6920857398952329171581050194852 absolute error = 1.2e-31 relative error = 1.7338892146248447699374203806172e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9514141098512959527138342444951 y1[1] (numeric) = 1.9514141098512959527138342444961 absolute error = 1.0e-30 relative error = 5.1244889280635734687171030518765e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.5MB, time=38.06 x[1] = 0.314 y2[1] (analytic) = 0.69113447990106785420862116504429 y2[1] (numeric) = 0.69113447990106785420862116504417 absolute error = 1.2e-31 relative error = 1.7362756958266262164688231399390e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9511057199354949430211141288279 y1[1] (numeric) = 1.9511057199354949430211141288289 absolute error = 1.0e-30 relative error = 5.1252988999133310406023157435978e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.5MB, time=38.30 x[1] = 0.315 y2[1] (analytic) = 0.69018352877239715139879948406602 y2[1] (numeric) = 0.69018352877239715139879948406589 absolute error = 1.3e-31 relative error = 1.8835569755080361141569501174454e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9507963789140532566408036563392 y1[1] (numeric) = 1.9507963789140532566408036563402 absolute error = 1.0e-30 relative error = 5.1261116270713421292661180597210e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.5MB, time=38.55 x[1] = 0.316 y2[1] (analytic) = 0.68923288746017185815341803867781 y2[1] (numeric) = 0.68923288746017185815341803867768 absolute error = 1.3e-31 relative error = 1.8861549175207081882024134629991e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9504860870963118892361716131461 y1[1] (numeric) = 1.9504860870963118892361716131471 absolute error = 1.0e-30 relative error = 5.1269271112243601273849199863454e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.317 y2[1] (analytic) = 0.6882825569150332074776633628236 y2[1] (numeric) = 0.68828255691503320747766336282347 absolute error = 1.3e-31 relative error = 1.8887591831859859404259487646677e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9501748447925626326909347873552 y1[1] (numeric) = 1.9501748447925626326909347873562 absolute error = 1.0e-30 relative error = 5.1277453540652586955497252956420e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.5MB, time=38.79 x[1] = 0.318 y2[1] (analytic) = 0.68733253808731166531597667717754 y2[1] (numeric) = 0.68733253808731166531597667717741 absolute error = 1.3e-31 relative error = 1.8913697925862799087811531812464e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9498626523140477648174919429938 y1[1] (numeric) = 1.9498626523140477648174919429948 absolute error = 1.0e-30 relative error = 5.1285663572930393246867186166926e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.5MB, time=39.04 x[1] = 0.319 y2[1] (analytic) = 0.6863828319270259802216671389056 y2[1] (numeric) = 0.68638283192702598022166713890547 absolute error = 1.3e-31 relative error = 1.8939867658843364364823510872486e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9495495099729597381146719444671 y1[1] (numeric) = 1.9495495099729597381146719444681 absolute error = 1.0e-30 relative error = 5.1293901226128389282237136670064e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.32 y2[1] (analytic) = 0.68543343938388223333824245658285 y2[1] (numeric) = 0.68543343938388223333824245658272 absolute error = 1.3e-31 relative error = 1.8966101233236230689448580102761e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9492354180824408675753072737661 y1[1] (numeric) = 1.9492354180824408675753072737671 absolute error = 1.0e-30 relative error = 5.1302166517359374640614093872705e-29 % Correct digits = 30 h = 0.001 memory used=614.1MB, alloc=4.5MB, time=39.29 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.321 y2[1] (analytic) = 0.68448436140727288869340688885654 y2[1] (numeric) = 0.6844843614072728886934068888564 absolute error = 1.4e-31 relative error = 2.0453352610155404264959056933236e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9489203769565830175439451328269 y1[1] (numeric) = 1.9489203769565830175439451328279 absolute error = 1.0e-30 relative error = 5.1310459463797655864086548699288e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.5MB, time=39.53 x[1] = 0.322 y2[1] (analytic) = 0.68353559894627584380667633277783 y2[1] (numeric) = 0.68353559894627584380667633277769 absolute error = 1.4e-31 relative error = 2.0481742313907434575596653774170e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9486043869104272876250092733052 y1[1] (numeric) = 1.9486043869104272876250092733061 absolute error = 9e-31 relative error = 4.6186902074411210947870609479681e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.5MB, time=39.77 x[1] = 0.323 y2[1] (analytic) = 0.68258715294965348061155989410811 y2[1] (numeric) = 0.68258715294965348061155989410797 absolute error = 1.4e-31 relative error = 2.0510201429227041508525712343220e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.948287448259963697641726645576 y1[1] (numeric) = 1.9482874482599636976417266455769 absolute error = 9e-31 relative error = 4.6194415552171195285891454534450e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.324 y2[1] (analytic) = 0.68163902436585171669325701733906 y2[1] (numeric) = 0.68163902436585171669325701733892 absolute error = 1.4e-31 relative error = 2.0538730177639991318646694035178e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9479695613221308716461339080079 y1[1] (numeric) = 1.9479695613221308716461339080088 absolute error = 9e-31 relative error = 4.6201953966321203874845556098588e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.5MB, time=40.02 x[1] = 0.325 y2[1] (analytic) = 0.68069121414299905684281893765035 y2[1] (numeric) = 0.68069121414299905684281893765021 absolute error = 1.4e-31 relative error = 2.0567328781562459512604203953597e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9476507264148157209804797864775 y1[1] (numeric) = 1.9476507264148157209804797864784 absolute error = 9e-31 relative error = 4.6209517332540231729178297576778e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.5MB, time=40.26 x[1] = 0.326 y2[1] (analytic) = 0.67974372322890564492872290056454 y2[1] (numeric) = 0.6797437232289056449287229005644 absolute error = 1.4e-31 relative error = 2.0595997464305323077595890507731e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9473309438568531263903402226954 y1[1] (numeric) = 1.9473309438568531263903402226963 absolute error = 9e-31 relative error = 4.6217105666562978513145725157266e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.5MB, time=40.51 x[1] = 0.327 y2[1] (analytic) = 0.67879655257106231608680727764583 y2[1] (numeric) = 0.67879655257106231608680727764569 absolute error = 1.4e-31 relative error = 2.0624736450078476877911703636575e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9470102139680256191897641982033 y1[1] (numeric) = 1.9470102139680256191897641982042 absolute error = 9e-31 relative error = 4.6224718984179919031306275914817e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.328 y2[1] (analytic) = 0.67784970311663964922951538822866 y2[1] (numeric) = 0.67784970311663964922951538822852 absolute error = 1.4e-31 relative error = 2.0653545963995174374833250613670e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9466885370690630614787690688678 y1[1] (numeric) = 1.9466885370690630614787690688687 absolute error = 9e-31 relative error = 4.6232357301237373991582827719637e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.5MB, time=40.76 x[1] = 0.329 y2[1] (analytic) = 0.67690317581248701987539551785335 y2[1] (numeric) = 0.67690317581248701987539551785321 absolute error = 1.4e-31 relative error = 2.0682426232076392826651383619391e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9463659134816423254135051923513 y1[1] (numeric) = 1.9463659134816423254135051923522 absolute error = 9e-31 relative error = 4.6240020633637581041446410510263e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.5MB, time=41.00 x[1] = 0.33 y2[1] (analytic) = 0.67595697160513165329980430382978 y2[1] (numeric) = 0.67595697160513165329980430382964 absolute error = 1.4e-31 relative error = 2.0711377481255223126697646272715e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9460423435283869715294105783662 y1[1] (numeric) = 1.9460423435283869715294105783671 absolute error = 9e-31 relative error = 4.6247708997338766077775264504044e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.331 y2[1] (analytic) = 0.67501109144077767800776033714693 y2[1] (numeric) = 0.67501109144077767800776033714679 absolute error = 1.4e-31 relative error = 2.0740399939381284438431877843736e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9457178275328669261176772385331 y1[1] (numeric) = 1.945717827532866926117677238534 absolute error = 9e-31 relative error = 4.6255422408355214830945283609599e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.5MB, time=41.25 x[1] = 0.332 y2[1] (analytic) = 0.67406553626530517952989450779567 y2[1] (numeric) = 0.67406553626530517952989450779553 absolute error = 1.4e-31 relative error = 2.0769493835225163787784205455945e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9453923658195981576553518593481 y1[1] (numeric) = 1.945392365819598157655351859349 absolute error = 9e-31 relative error = 4.6263160882757344723710241703554e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.5MB, time=41.50 x[1] = 0.333 y2[1] (analytic) = 0.67312030702426925454244329747574 y2[1] (numeric) = 0.6731203070242692545424432974756 absolute error = 1.4e-31 relative error = 2.0798659398482880774114928558608e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9450659587140423522893943681328 y1[1] (numeric) = 1.9450659587140423522893943681338 absolute error = 1.0e-30 relative error = 5.1412138262968641117147295077744e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.5MB, time=41.74 x[1] = 0.334 y2[1] (analytic) = 0.67217540466289906531223089961467 y2[1] (numeric) = 0.67217540466289906531223089961452 absolute error = 1.5e-31 relative error = 2.2315603778336118816782677959266e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9447386065426065883750189078808 y1[1] (numeric) = 1.9447386065426065883750189078818 absolute error = 1.0e-30 relative error = 5.1420792318090454624697545785867e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.335 y2[1] (analytic) = 0.67123083012609689446758572163781 y2[1] (numeric) = 0.67123083012609689446758572163766 absolute error = 1.5e-31 relative error = 2.2347006911440751057012156121542e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9444103096326430100686426826321 y1[1] (numeric) = 1.9444103096326430100686426826331 absolute error = 1.0e-30 relative error = 5.1429474275361652892875799906416e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.5MB, time=41.99 x[1] = 0.336 y2[1] (analytic) = 0.67028658435843720009613649849422 y2[1] (numeric) = 0.67028658435843720009613649849407 absolute error = 1.5e-31 relative error = 2.2378487575366296710929732998316e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9440810683124484999757690804005 y1[1] (numeric) = 1.9440810683124484999757690804015 absolute error = 1.0e-30 relative error = 5.1438184152888534028948530134037e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.5MB, time=42.23 x[1] = 0.337 y2[1] (analytic) = 0.66934266830416567117043291956346 y2[1] (numeric) = 0.66934266830416567117043291956331 absolute error = 1.5e-31 relative error = 2.2410046020230154087975168552408e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.943750882911264350854132425743 y1[1] (numeric) = 1.943750882911264350854132425744 absolute error = 1.0e-30 relative error = 5.1446921968840168504999633659405e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.5MB, time=42.48 x[1] = 0.338 y2[1] (analytic) = 0.66839908290719828330233534324402 y2[1] (numeric) = 0.66839908290719828330233534324387 absolute error = 1.5e-31 relative error = 2.2441682497165584324000187292031e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9434197537592759363724326587988 y1[1] (numeric) = 1.9434197537592759363724326587998 absolute error = 1.0e-30 relative error = 5.1455687741448480846239602934521e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.339 y2[1] (analytic) = 0.66745582911112035482711784475499 y2[1] (numeric) = 0.66745582911112035482711784475484 absolute error = 1.5e-31 relative error = 2.2473397258326660178862508920657e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9430876811876123809249891820363 y1[1] (numeric) = 1.9430876811876123809249891820373 absolute error = 1.0e-30 relative error = 5.1464481489008331629053807184733e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.5MB, time=42.73 x[1] = 0.34 y2[1] (analytic) = 0.66651290785918560321822851296921 y2[1] (numeric) = 0.66651290785918560321822851296906 absolute error = 1.5e-31 relative error = 2.2505190556893242992869002225079e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9427546655283462285026440600266 y1[1] (numeric) = 1.9427546655283462285026440600275 absolute error = 9e-31 relative error = 4.6325972906889839810488414304234e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=671.3MB, alloc=4.5MB, time=42.97 x[1] = 0.341 y2[1] (analytic) = 0.66557032009431520183365058143904 y2[1] (numeric) = 0.66557032009431520183365058143888 absolute error = 1.6e-31 relative error = 2.4039533490214387184337828447604e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9424207071144931106202457013121 y1[1] (numeric) = 1.942420707114493110620245701313 absolute error = 9e-31 relative error = 4.6333937684229538718178387131858e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.342 y2[1] (analytic) = 0.66462806675909683699480764717492 y2[1] (numeric) = 0.66462806675909683699480764717476 absolute error = 1.6e-31 relative error = 2.4073614703062803285038117116300e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9420858062800114133010450948604 y1[1] (numeric) = 1.9420858062800114133010450948612 absolute error = 8e-31 relative error = 4.1192824612233193450602104149994e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.5MB, time=43.22 x[1] = 0.343 y2[1] (analytic) = 0.66368614879578376539895589819304 y2[1] (numeric) = 0.66368614879578376539895589819289 absolute error = 1.5e-31 relative error = 2.2601044224316786441691507525808e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9417499633598019431183376166772 y1[1] (numeric) = 1.9417499633598019431183376166781 absolute error = 9e-31 relative error = 4.6349942937180939432714298071154e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.5MB, time=43.46 x[1] = 0.344 y2[1] (analytic) = 0.66274456714629387186600593736127 y2[1] (numeric) = 0.66274456714629387186600593736112 absolute error = 1.5e-31 relative error = 2.2633154224995567916718881939262e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9414131786897075922946843649114 y1[1] (numeric) = 1.9414131786897075922946843649122 absolute error = 8e-31 relative error = 4.1207096396653362347172264617922e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.5MB, time=43.71 x[1] = 0.345 y2[1] (analytic) = 0.66180332275220872742071645564298 y2[1] (numeric) = 0.66180332275220872742071645564282 absolute error = 1.6e-31 relative error = 2.4176366980844991527078433300136e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9410754526065130028590479241997 y1[1] (numeric) = 1.9410754526065130028590479242005 absolute error = 8e-31 relative error = 4.1214265984650148353438824984369e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.346 y2[1] (analytic) = 0.66086241655477264771120167246664 y2[1] (numeric) = 0.66086241655477264771120167246649 absolute error = 1.5e-31 relative error = 2.2697613942397330424748419159145e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9407367854479442298621784020909 y1[1] (numeric) = 1.9407367854479442298621784020917 absolute error = 8e-31 relative error = 4.1221458056474714430219008162702e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.5MB, time=43.95 x[1] = 0.347 y2[1] (analytic) = 0.65992184949489175176469412463536 y2[1] (numeric) = 0.65992184949489175176469412463521 absolute error = 1.5e-31 relative error = 2.2729964179063160871151403135282e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9403971775526684036505865221322 y1[1] (numeric) = 1.940397177552668403650586522133 absolute error = 8e-31 relative error = 4.1228672627168131215287969763994e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.5MB, time=44.20 x[1] = 0.348 y2[1] (analytic) = 0.65898162251313302108150404793491 y2[1] (numeric) = 0.65898162251313302108150404793476 absolute error = 1.5e-31 relative error = 2.2762395016108451471099901627448e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9400566292602933911994414996184 y1[1] (numeric) = 1.9400566292602933911994414996193 absolute error = 9e-31 relative error = 4.6390398425800222285498671195137e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.349 y2[1] (analytic) = 0.65804173654972335906811625740272 y2[1] (numeric) = 0.65804173654972335906811625740257 absolute error = 1.5e-31 relative error = 2.2794906716173861820734940919544e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9397151409113674565047323670778 y1[1] (numeric) = 1.9397151409113674565047323670787 absolute error = 9e-31 relative error = 4.6398565491278197366003722221219e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=694.2MB, alloc=4.5MB, time=44.44 TOP MAIN SOLVE Loop x[1] = 0.35 y2[1] (analytic) = 0.65710219254454865081036509308237 y2[1] (numeric) = 0.65710219254454865081036509308222 absolute error = 1.5e-31 relative error = 2.2827499542977199385902429468145e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9393727128473789200350323573037 y1[1] (numeric) = 1.9393727128473789200350323573045 absolute error = 8e-31 relative error = 4.1250451483636858024863402852388e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=698.0MB, alloc=4.5MB, time=44.68 x[1] = 0.351 y2[1] (analytic) = 0.65616299143715282318762765801042 y2[1] (numeric) = 0.65616299143715282318762765801027 absolute error = 1.5e-31 relative error = 2.2860173761318718601244295254951e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9390293454107558172432068921403 y1[1] (numeric) = 1.9390293454107558172432068921411 absolute error = 8e-31 relative error = 4.1257756201236416375091089051730e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.5MB, time=44.93 x[1] = 0.352 y2[1] (analytic) = 0.65522413416673690532897523416392 y2[1] (numeric) = 0.65522413416673690532897523416377 absolute error = 1.5e-31 relative error = 2.2892929637086450418198767311851e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9386850389448655561384066652863 y1[1] (numeric) = 1.9386850389448655561384066652871 absolute error = 8e-31 relative error = 4.1265083493675801471600478076042e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.353 y2[1] (analytic) = 0.65428562167215808941222242013895 y2[1] (numeric) = 0.6542856216721580894122224201388 absolute error = 1.5e-31 relative error = 2.2925767437261562502015194704945e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9383397937940145739186882470937 y1[1] (numeric) = 1.9383397937940145739186882470945 absolute error = 8e-31 relative error = 4.1272433376302813383002901515126e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.5MB, time=45.18 x[1] = 0.354 y2[1] (analytic) = 0.65334745489192879180681319143277 y2[1] (numeric) = 0.65334745489192879180681319143262 absolute error = 1.5e-31 relative error = 2.2958687429923750279369482803084e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9379936103034479926646055787134 y1[1] (numeric) = 1.9379936103034479926646055787142 absolute error = 8e-31 relative error = 4.1279805864516615084622399676628e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.5MB, time=45.42 x[1] = 0.355 y2[1] (analytic) = 0.65240963476421571456148274036527 y2[1] (numeric) = 0.65240963476421571456148274036512 absolute error = 1.5e-31 relative error = 2.2991689884256659039659096926995e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.937646488819349274094116661967 y1[1] (numeric) = 1.9376464888193492740941166619678 absolute error = 8e-31 relative error = 4.1287200973767802092889012463146e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.5MB, time=45.67 x[1] = 0.356 y2[1] (analytic) = 0.65147216222683890723763360789966 y2[1] (numeric) = 0.65147216222683890723763360789951 absolute error = 1.5e-31 relative error = 2.3024775070553337294561747846112e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9372984296888398733791506900099 y1[1] (numeric) = 1.9372984296888398733791506900107 absolute error = 8e-31 relative error = 4.1294618719558472356547312362800e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.357 y2[1] (analytic) = 0.65053503821727082908936427390812 y2[1] (numeric) = 0.65053503821727082908936427390797 absolute error = 1.5e-31 relative error = 2.3057943260221721601959443522657e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9369494332599788920241818021889 y1[1] (numeric) = 1.9369494332599788920241818021897 absolute error = 8e-31 relative error = 4.1302059117442296405230985543782e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.5MB, time=45.91 x[1] = 0.358 y2[1] (analytic) = 0.64959826367263541159108802577568 y2[1] (numeric) = 0.64959826367263541159108802577553 absolute error = 1.5e-31 relative error = 2.3091194725790153061859679560464e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9365994998817627298071565844923 y1[1] (numeric) = 1.9365994998817627298071565844931 absolute error = 8e-31 relative error = 4.1309522183024587755956529447573e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.5MB, time=46.16 x[1] = 0.359 y2[1] (analytic) = 0.64866183952970712131367957764527 y2[1] (numeric) = 0.64866183952970712131367957764512 absolute error = 1.5e-31 relative error = 2.3124529740912925693488260678829e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9362486299041247357831233746356 y1[1] (numeric) = 1.9362486299041247357831233746364 absolute error = 8e-31 relative error = 4.1317007931962373578091404436683e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.36 y2[1] (analytic) = 0.64772576672491002315008656407927 y2[1] (numeric) = 0.64772576672491002315008656407912 absolute error = 1.5e-31 relative error = 2.3157948580375866904283712005704e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9358968236779348583509123681247 y1[1] (numeric) = 1.9358968236779348583509123681255 absolute error = 8e-31 relative error = 4.1324516379964465617354253002022e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.5MB, time=46.41 x[1] = 0.361 y2[1] (analytic) = 0.64679004619431684389134268244803 y2[1] (numeric) = 0.64679004619431684389134268244788 absolute error = 1.5e-31 relative error = 2.3191451520101950263091568015476e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.935544081554999294383216458587 y1[1] (numeric) = 1.9355440815549992943832164585877 absolute error = 7e-31 relative error = 3.6165541599942589956981197453045e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.5MB, time=46.66 x[1] = 0.362 y2[1] (analytic) = 0.64585467887364803615391890795416 y2[1] (numeric) = 0.645854678873648036153918907954 absolute error = 1.6e-31 relative error = 2.4773374759634070177534011329665e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9351904038880601374204236822605 y1[1] (numeric) = 1.9351904038880601374204236822612 absolute error = 7e-31 relative error = 3.6172151256724144876901399506773e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.5MB, time=46.90 x[1] = 0.363 y2[1] (analytic) = 0.64491966569827084265934885386328 y2[1] (numeric) = 0.64491966569827084265934885386312 absolute error = 1.6e-31 relative error = 2.4809291530405411187581583503053e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9348357910307950249285530727796 y1[1] (numeric) = 1.9348357910307950249285530727803 absolute error = 7e-31 relative error = 3.6178780816695091590263649902181e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.364 y2[1] (analytic) = 0.64398500760319836086706399723811 y2[1] (numeric) = 0.64398500760319836086706399723795 absolute error = 1.6e-31 relative error = 2.4845298898415745926245378075512e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9344802433378167846216466682912 y1[1] (numeric) = 1.9344802433378167846216466682919 absolute error = 7e-31 relative error = 3.6185430293782511527052935933073e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.5MB, time=47.15 x[1] = 0.365 y2[1] (analytic) = 0.64305070552308860796137413726246 y2[1] (numeric) = 0.6430507055230886079613741372623 absolute error = 1.6e-31 relative error = 2.4881397162895303246618805909746e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9341237611646730798489713484808 y1[1] (numeric) = 1.9341237611646730798489713484815 absolute error = 7e-31 relative error = 3.6192099701959111331075444616641e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.5MB, time=47.39 x[1] = 0.366 y2[1] (analytic) = 0.64211676039224358619352809909695 y2[1] (numeric) = 0.64211676039224358619352809909679 absolute error = 1.6e-31 relative error = 2.4917586624317727609523424595834e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9337663448678460540473851142766 y1[1] (numeric) = 1.9337663448678460540473851142773 absolute error = 7e-31 relative error = 3.6198789055243286288735534135592e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.367 y2[1] (analytic) = 0.64118317314460834857978934112779 y2[1] (numeric) = 0.64118317314460834857978934112763 absolute error = 1.6e-31 relative error = 2.4953867584406277639385697329250e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9334079948047519742592233578357 y1[1] (numeric) = 1.9334079948047519742592233578364 absolute error = 7e-31 relative error = 3.6205498367699183987937412546215e-29 % Correct digits = 30 h = 0.001 memory used=743.8MB, alloc=4.5MB, time=47.64 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.368 y2[1] (analytic) = 0.64024994471377006495646076745515 y2[1] (numeric) = 0.64024994471377006495646076745498 absolute error = 1.7e-31 relative error = 2.6552130367773814569301500553064e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9330487113337408737160616048967 y1[1] (numeric) = 1.9330487113337408737160616048974 absolute error = 7e-31 relative error = 3.6212227653436768207615584332622e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.5MB, time=47.88 x[1] = 0.369 y2[1] (analytic) = 0.63931707603295708839279269051843 y2[1] (numeric) = 0.63931707603295708839279269051826 absolute error = 1.7e-31 relative error = 2.6590874289620323242539738551970e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9326884948140961934887121457059 y1[1] (numeric) = 1.9326884948140961934887121457066 absolute error = 7e-31 relative error = 3.6218976926611883038400171538870e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.5MB, time=48.13 x[1] = 0.37 y2[1] (analytic) = 0.63838456803503802196270753087285 y2[1] (numeric) = 0.63838456803503802196270753087268 absolute error = 1.7e-31 relative error = 2.6629716398575203985767477246961e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9323273456060344232038129044909 y1[1] (numeric) = 1.9323273456060344232038129044916 absolute error = 7e-31 relative error = 3.6225746201426317234925268579095e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.371 y2[1] (analytic) = 0.63745242165252078587627448231464 y2[1] (numeric) = 0.63745242165252078587627448231447 absolute error = 1.7e-31 relative error = 2.6668657020596909714545236121616e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9319652640707047408273678308622 y1[1] (numeric) = 1.9319652640707047408273678308629 absolute error = 7e-31 relative error = 3.6232535492127868800290548439675e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.5MB, time=48.38 x[1] = 0.372 y2[1] (analytic) = 0.63652063781755168497186701080265 y2[1] (numeric) = 0.63652063781755168497186701080247 absolute error = 1.8e-31 relative error = 2.8278737452593654943437466578091e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9316022505701886515155990295735 y1[1] (numeric) = 1.9316022505701886515155990295742 absolute error = 7e-31 relative error = 3.6239344813010409803188402875072e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.5MB, time=48.62 x[1] = 0.373 y2[1] (analytic) = 0.63558921746191447656993569494098 y2[1] (numeric) = 0.6355892174619144765699356949408 absolute error = 1.8e-31 relative error = 2.8320178356516233405644108541358e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9312383054674996255334717777569 y1[1] (numeric) = 1.9312383054674996255334717777576 absolute error = 7e-31 relative error = 3.6246174178413951428210970389125e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.5MB, time=48.87 x[1] = 0.374 y2[1] (analytic) = 0.6346581615170294386893285541723 y2[1] (numeric) = 0.63465816151702943868932855417212 absolute error = 1.8e-31 relative error = 2.8361724612466069656914651398097e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9308734291265827352412545110794 y1[1] (numeric) = 1.9308734291265827352412545110801 absolute error = 7e-31 relative error = 3.6253023602724709259853483314666e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.375 y2[1] (analytic) = 0.63372747091395243862709064828374 y2[1] (numeric) = 0.63372747091395243862709064828356 absolute error = 1.8e-31 relative error = 2.8403376571384328214997087573487e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9305076219123142911494767922296 y1[1] (numeric) = 1.9305076219123142911494767922302 absolute error = 6e-31 relative error = 3.1079908371750144686342099301732e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.5MB, time=49.11 x[1] = 0.376 y2[1] (analytic) = 0.63279714658337400190267436834815 y2[1] (numeric) = 0.63279714658337400190267436834797 absolute error = 1.8e-31 relative error = 2.8445134585682609892950061844809e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9301408841905014770426492067458 y1[1] (numeric) = 1.9301408841905014770426492067464 absolute error = 6e-31 relative error = 3.1085813730723558192462233025772e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.5MB, time=49.36 x[1] = 0.377 y2[1] (analytic) = 0.63186718945561838156749147481296 y2[1] (numeric) = 0.63186718945561838156749147481278 absolute error = 1.8e-31 relative error = 2.8486999009250343612462246934049e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.929773216327881984172110062437 y1[1] (numeric) = 1.9297732163278819841721100624376 absolute error = 6e-31 relative error = 3.1091736320277325169358869635125e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.378 y2[1] (analytic) = 0.6309376004606426278807375731069 y2[1] (numeric) = 0.63093760046064262788073757310672 absolute error = 1.8e-31 relative error = 2.8528970197462221616701489222190e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9294046186921236445183646995176 y1[1] (numeric) = 1.9294046186921236445183646995182 absolute error = 6e-31 relative error = 3.1097676152901466230968665829421e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.5MB, time=49.60 x[1] = 0.379 y2[1] (analytic) = 0.63000838052803565835241935086267 y2[1] (numeric) = 0.63000838052803565835241935086249 absolute error = 1.8e-31 relative error = 2.8571048507185678374134169807661e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.929035091651824063123284149087 y1[1] (numeric) = 1.9290350916518240631232841490876 absolute error = 6e-31 relative error = 3.1103633241125888571444799942848e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.5MB, time=49.85 x[1] = 0.38 y2[1] (analytic) = 0.6290795305870173281545145336508 y2[1] (numeric) = 0.62907953058701732815451453365062 absolute error = 1.8e-31 relative error = 2.8613234296788413466958853345073e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9286646355765102494925308077246 y1[1] (numeric) = 1.9286646355765102494925308077251 absolute error = 5e-31 relative error = 2.5924672997933702611780904299166e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.5MB, time=50.09 x[1] = 0.381 y2[1] (analytic) = 0.62815105156643750090119414798726 y2[1] (numeric) = 0.62815105156643750090119414798709 absolute error = 1.7e-31 relative error = 2.7063554152471183273352650171172e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9282932508366382480685797257438 y1[1] (numeric) = 1.9282932508366382480685797257443 absolute error = 5e-31 relative error = 2.5929666028912484986693435674535e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.382 y2[1] (analytic) = 0.6272229443947751197990363113152 y2[1] (numeric) = 0.62722294439477511979903631131502 absolute error = 1.8e-31 relative error = 2.8697929756649290148311997185643e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9279209378035927677747050360532 y1[1] (numeric) = 1.9279209378035927677747050360537 absolute error = 5e-31 relative error = 2.5934673471082846570092162805357e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.5MB, time=50.34 x[1] = 0.383 y2[1] (analytic) = 0.62629521000013727916816039866944 y2[1] (numeric) = 0.62629521000013727916816039866926 absolute error = 1.8e-31 relative error = 2.8740440151212484183430810252598e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.927547696849686810630301979607 y1[1] (numeric) = 1.9275476968496868106303019796075 absolute error = 5e-31 relative error = 2.5939695335019810063400524528633e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.5MB, time=50.59 x[1] = 0.384 y2[1] (analytic) = 0.62536784931025829633521006481245 y2[1] (numeric) = 0.62536784931025829633521006481227 absolute error = 1.8e-31 relative error = 2.8783059474280419881634704680006e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9271735283481612994379159120923 y1[1] (numeric) = 1.9271735283481612994379159120928 absolute error = 5e-31 relative error = 2.5944731631331876888289996180427e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.385 memory used=793.4MB, alloc=4.5MB, time=50.84 y2[1] (analytic) = 0.6244408632524987838991132287812 y2[1] (numeric) = 0.62444086325249878389911322878102 absolute error = 1.8e-31 relative error = 2.8825788091836526018441777635526e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9267984326731847045423506047928 y1[1] (numeric) = 1.9267984326731847045423506047933 absolute error = 5e-31 relative error = 2.5949782370661075679071460507444e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.386 y2[1] (analytic) = 0.62351425275384472237054675500772 y2[1] (numeric) = 0.62351425275384472237054675500754 absolute error = 1.8e-31 relative error = 2.8868626371410574217034819451156e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9264224101998526696622290804899 y1[1] (numeric) = 1.9264224101998526696622290804904 absolute error = 5e-31 relative error = 2.5954847563683010946556496898321e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.5MB, time=51.08 x[1] = 0.387 y2[1] (analytic) = 0.62258801874090653318603319147135 y2[1] (numeric) = 0.62258801874090653318603319147118 absolute error = 1.7e-31 relative error = 2.7305376088637267132286756370451e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9260454613041876367943811528091 y1[1] (numeric) = 1.9260454613041876367943811528096 absolute error = 5e-31 relative error = 2.5959927221106911913777180698096e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=801.0MB, alloc=4.5MB, time=51.32 x[1] = 0.388 y2[1] (analytic) = 0.62166216213991815209759655070879 y2[1] (numeric) = 0.62166216213991815209759655070861 absolute error = 1.8e-31 relative error = 2.8954633394510379096832900802494e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9256675863631384701914327645926 y1[1] (numeric) = 1.9256675863631384701914327645931 absolute error = 5e-31 relative error = 2.5965021353675681523954533819911e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.389 y2[1] (analytic) = 0.62073668387673610293890374394874 y2[1] (numeric) = 0.62073668387673610293890374394856 absolute error = 1.8e-31 relative error = 2.8997802880898178380108422135832e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9252887857545800794129731476774 y1[1] (numeric) = 1.9252887857545800794129731476779 absolute error = 5e-31 relative error = 2.5970129972165945621107322157865e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.5MB, time=51.57 x[1] = 0.39 y2[1] (analytic) = 0.61981158487683857176881790215284 y2[1] (numeric) = 0.61981158487683857176881790215266 absolute error = 1.8e-31 relative error = 2.9041083515043916649434435576127e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9249090598573130414506767528811 y1[1] (numeric) = 1.9249090598573130414506767528816 absolute error = 5e-31 relative error = 2.5975253087388102303694454455841e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.5MB, time=51.82 x[1] = 0.391 y2[1] (analytic) = 0.61888686606532448139328944033205 y2[1] (numeric) = 0.61888686606532448139328944033187 absolute error = 1.8e-31 relative error = 2.9084475672327600679943103307167e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9245284090510632219277578250411 y1[1] (numeric) = 1.9245284090510632219277578250416 absolute error = 5e-31 relative error = 2.5980390710186371451685801321093e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.5MB, time=52.06 x[1] = 0.392 y2[1] (analytic) = 0.61796252836691256626651034317064 y2[1] (numeric) = 0.61796252836691256626651034317045 absolute error = 1.9e-31 relative error = 3.0746200825819057676023407624978e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9241468337164813953731364236214 y1[1] (numeric) = 1.9241468337164813953731364236219 absolute error = 5e-31 relative error = 2.5985542851438844427457822010188e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.393 y2[1] (analytic) = 0.6170385727059404477722567707261 y2[1] (numeric) = 0.61703857270594044777225677072591 absolute error = 1.9e-31 relative error = 3.0792240291685544903952260533862e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9237643342351428645706956146894 y1[1] (numeric) = 1.9237643342351428645706956146898 absolute error = 4e-31 relative error = 2.0792567617646027160729568384690e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.5MB, time=52.30 x[1] = 0.394 y2[1] (analytic) = 0.61611500000636370988634470278558 y2[1] (numeric) = 0.6161150000063637098863447027854 absolute error = 1.8e-31 relative error = 2.9215325060766386384162091155548e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9233809109895470789840104849733 y1[1] (numeric) = 1.9233809109895470789840104849738 absolute error = 5e-31 relative error = 2.5995890732988424149215351018451e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.5MB, time=52.55 x[1] = 0.395 y2[1] (analytic) = 0.61519181119175497522112295934603 y2[1] (numeric) = 0.61519181119175497522112295934584 absolute error = 1.9e-31 relative error = 3.0884676379539307044074158891491e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9229965643631172522569305532408 y1[1] (numeric) = 1.9229965643631172522569305532413 absolute error = 5e-31 relative error = 2.6001086495211520781564957532072e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.396 y2[1] (analytic) = 0.61426900718530298145292755264793 y2[1] (numeric) = 0.61426900718530298145292755264775 absolute error = 1.8e-31 relative error = 2.9303122556157296121670552620689e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9226112947401999787903980783825 y1[1] (numeric) = 1.922611294740199978790398078383 absolute error = 5e-31 relative error = 2.6006296819740901639377859396193e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.5MB, time=52.80 x[1] = 0.397 y2[1] (analytic) = 0.61334658890981165813342094323165 y2[1] (numeric) = 0.61334658890981165813342094323147 absolute error = 1.8e-31 relative error = 2.9347191825088595331122261122609e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9222251025060648493958856873514 y1[1] (numeric) = 1.9222251025060648493958856873519 absolute error = 5e-31 relative error = 2.6011521717624767122311990509709e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.5MB, time=53.05 x[1] = 0.398 y2[1] (analytic) = 0.61242455728769920388573938859978 y2[1] (numeric) = 0.6124245572876992038857393885996 absolute error = 1.8e-31 relative error = 2.9391375289910402348522716935286e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9218379880469040660258376694886 y1[1] (numeric) = 1.9218379880469040660258376694891 absolute error = 5e-31 relative error = 2.6016761199945490990523237080029e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.5MB, time=53.29 x[1] = 0.399 y2[1] (analytic) = 0.6115029132409971639863711882616 y2[1] (numeric) = 0.61150291324099716398637118826142 absolute error = 1.8e-31 relative error = 2.9435673338985526967187563690628e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9214499517498320555815002067615 y1[1] (numeric) = 1.921449951749832055581500206762 absolute error = 5e-31 relative error = 2.6022015277819671293566403536325e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.4 y2[1] (analytic) = 0.61058165769134950833368824320429 y2[1] (numeric) = 0.61058165769134950833368824320411 absolute error = 1.8e-31 relative error = 2.9480086362337211168077230824998e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9210609940028850827985267320518 y1[1] (numeric) = 1.9210609940028850827985267320523 absolute error = 5e-31 relative error = 2.6027283962398181476349164956869e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.5MB, time=53.53 x[1] = 0.401 y2[1] (analytic) = 0.60966079156001170980405296118265 y2[1] (numeric) = 0.60966079156001170980405296118246 absolute error = 1.9e-31 relative error = 3.1164871126749739158616674176345e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9206711151950208622107455298569 y1[1] (numeric) = 1.9206711151950208622107455298574 absolute error = 5e-31 relative error = 2.6032567264866221662549738482904e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.5MB, time=53.78 x[1] = 0.402 y2[1] (analytic) = 0.60874031576784982299642215164349 y2[1] (numeric) = 0.6087403157678498229964221516433 absolute error = 1.9e-31 relative error = 3.1211995505889690869968875307353e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9202803157161181691924776156028 y1[1] (numeric) = 1.9202803157161181691924776156034 absolute error = 6e-31 relative error = 3.1245438235732044139092750490653e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.5MB, time=54.03 x[1] = 0.403 y2[1] (analytic) = 0.60782023123533956336636916560423 y2[1] (numeric) = 0.60782023123533956336636916560404 absolute error = 1.9e-31 relative error = 3.1259242492445868457222076121952e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9198885959569764500797938512206 y1[1] (numeric) = 1.9198885959569764500797938512212 absolute error = 6e-31 relative error = 3.1251813322060361855786880010576e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.404 y2[1] (analytic) = 0.60690053888256538675044514638653 y2[1] (numeric) = 0.60690053888256538675044514638634 absolute error = 1.9e-31 relative error = 3.1306612505210643636787229018820e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9194959563093154313711011756945 y1[1] (numeric) = 1.9194959563093154313711011756951 absolute error = 6e-31 relative error = 3.1258205990370606714735780845361e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.5MB, time=54.27 x[1] = 0.405 y2[1] (analytic) = 0.60598123962921956928179986676729 y2[1] (numeric) = 0.6059812396292195692817998667671 absolute error = 1.9e-31 relative error = 3.1354105964774567797516639594851e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9191023971657747280074487499645 y1[1] (numeric) = 1.9191023971657747280074487499651 absolute error = 6e-31 relative error = 3.1264616254250406599952976710700e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.5MB, time=54.52 x[1] = 0.406 y2[1] (analytic) = 0.60506233439460128769798223684934 y2[1] (numeric) = 0.60506233439460128769798223684914 absolute error = 2.0e-31 relative error = 3.3054445572142775645144676158960e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9187079189199134507329457358444 y1[1] (numeric) = 1.918707918919913450732945735845 absolute error = 6e-31 relative error = 3.1271044127328892322216737175451e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.407 y2[1] (analytic) = 0.60414382409761570004184017477465 y2[1] (numeric) = 0.60414382409761570004184017477446 absolute error = 1.9e-31 relative error = 3.1449464915708611905485293422738e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9183125219662098125356833485036 y1[1] (numeric) = 1.9183125219662098125356833485042 absolute error = 6e-31 relative error = 3.1277489623276760447369764152206e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.5MB, time=54.76 x[1] = 0.408 y2[1] (analytic) = 0.60322570965677302675643913930379 y2[1] (numeric) = 0.60322570965677302675643913930359 absolute error = 2.0e-31 relative error = 3.3155085534036206207919448092281e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9179162067000607341695547415594 y1[1] (numeric) = 1.91791620670006073416955474156 absolute error = 6e-31 relative error = 3.1283952755806336341080247848297e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.5MB, time=55.01 x[1] = 0.409 y2[1] (analytic) = 0.60230799199018763217491822926617 y2[1] (numeric) = 0.60230799199018763217491822926597 absolute error = 2.0e-31 relative error = 3.3205602890831017878006892715868e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9175189735177814487573672029263 y1[1] (numeric) = 1.917518973517781448757367202927 absolute error = 7e-31 relative error = 3.6505505795116910335668372039443e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.5MB, time=55.26 x[1] = 0.41 y2[1] (analytic) = 0.60139067201557710640620235994886 y2[1] (numeric) = 0.60139067201557710640620235994866 absolute error = 2.0e-31 relative error = 3.3256252433995124914681303394039e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.917120822816605105475642058277 y1[1] (numeric) = 1.9171208228166051054756420582777 absolute error = 7e-31 relative error = 3.6513087316613176131147236089912e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.411 y2[1] (analytic) = 0.6004737506502613476174886306349 y2[1] (numeric) = 0.60047375065026134761748863063471 absolute error = 1.9e-31 relative error = 3.1641682886928257305270718787422e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9167217549946823723214985972821 y1[1] (numeric) = 1.9167217549946823723214985972828 absolute error = 7e-31 relative error = 3.6520689462406714024656775733182e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.5MB, time=55.50 x[1] = 0.412 y2[1] (analytic) = 0.59955722881116164471442460072855 y2[1] (numeric) = 0.59955722881116164471442460072836 absolute error = 1.9e-31 relative error = 3.1690052403628507287691968960335e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9163217704510810379620192557123 y1[1] (numeric) = 1.916321770451081037962019255713 absolute error = 7e-31 relative error = 3.6528312248690245269123077650111e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.5MB, time=55.75 x[1] = 0.413 y2[1] (analytic) = 0.59864110741479976041989579421255 y2[1] (numeric) = 0.59864110741479976041989579421235 absolute error = 2.0e-31 relative error = 3.3408998734431972993610369974950e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.915920869585785612666494204004 y1[1] (numeric) = 1.9159208695857856126664942040047 absolute error = 7e-31 relative error = 3.6535955691705429620631398258279e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.414 y2[1] (analytic) = 0.59772538737729701475233935357361 y2[1] (numeric) = 0.59772538737729701475233935357341 absolute error = 2.0e-31 relative error = 3.3460181585654439292974824631816e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9155190527996969283219444100102 y1[1] (numeric) = 1.9155190527996969283219444100109 absolute error = 7e-31 relative error = 3.6543619807742940418419292138193e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=873.5MB, alloc=4.5MB, time=55.99 TOP MAIN SOLVE Loop x[1] = 0.415 y2[1] (analytic) = 0.5968100696143733689045003648061 y2[1] (numeric) = 0.5968100696143733689045003648059 absolute error = 2.0e-31 relative error = 3.3511498914425030444493367401644e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9151163204946317375323231603814 y1[1] (numeric) = 1.9151163204946317375323231603821 absolute error = 7e-31 relative error = 3.6551304613142539921610655201482e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.5MB, time=56.24 x[1] = 0.416 y2[1] (analytic) = 0.59589515504134650952354697466115 y2[1] (numeric) = 0.59589515504134650952354697466095 absolute error = 2.0e-31 relative error = 3.3562951184948448052398054443799e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9147126730733223118017969413405 y1[1] (numeric) = 1.9147126730733223118017969413412 absolute error = 7e-31 relative error = 3.6559010124293154903300483949382e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.5MB, time=56.48 x[1] = 0.417 y2[1] (analytic) = 0.59498064457313093339346001994986 y2[1] (numeric) = 0.59498064457313093339346001994966 absolute error = 2.0e-31 relative error = 3.3614538863443208020736986298913e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9143081109394160388025074955377 y1[1] (numeric) = 1.9143081109394160388025074955384 absolute error = 7e-31 relative error = 3.6566736357632952502602530732324e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.418 y2[1] (analytic) = 0.59406653912423703252061248643465 y2[1] (numeric) = 0.59406653912423703252061248643445 absolute error = 2.0e-31 relative error = 3.3666262418152124641224003568403e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9139026344974750187272177871901 y1[1] (numeric) = 1.9139026344974750187272177871908 absolute error = 7e-31 relative error = 3.6574483329649416335274421196241e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.5MB, time=56.72 x[1] = 0.419 y2[1] (analytic) = 0.59315283960877017962345371165307 y2[1] (numeric) = 0.59315283960877017962345371165287 absolute error = 2.0e-31 relative error = 3.3718122319352858427576331133281e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9134962441529756597272455228257 y1[1] (numeric) = 1.9134962441529756597272455228264 absolute error = 7e-31 relative error = 3.6582251056879422863537194122608e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.5MB, time=56.97 x[1] = 0.42 y2[1] (analytic) = 0.59223954694042981402721284191366 y2[1] (numeric) = 0.59223954694042981402721284191345 absolute error = 2.1e-31 relative error = 3.5458624991336954546659581337707e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9130889403123082724360887896657 y1[1] (numeric) = 1.9130889403123082724360887896664 absolute error = 7e-31 relative error = 3.6590039555909318025708625671599e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.5MB, time=57.22 x[1] = 0.421 y2[1] (analytic) = 0.59132666203250852796453564868418 y2[1] (numeric) = 0.59132666203250852796453564868397 absolute error = 2.1e-31 relative error = 3.5513365705207306816578967309148e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.912680723382776663579149287984 y1[1] (numeric) = 1.9126807233827766635791492879847 absolute error = 7e-31 relative error = 3.6597848843374994126272109655865e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.422 y2[1] (analytic) = 0.59041418579789115328296840365935 y2[1] (numeric) = 0.59041418579789115328296840365914 absolute error = 2.1e-31 relative error = 3.5568251077199994996317225597356e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9122715937725977286699595476886 y1[1] (numeric) = 1.9122715937725977286699595476893 absolute error = 7e-31 relative error = 3.6605678935961966987005282940820e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.5MB, time=57.46 x[1] = 0.423 y2[1] (analytic) = 0.58950211914905384856020210494802 y2[1] (numeric) = 0.58950211914905384856020210494781 absolute error = 2.1e-31 relative error = 3.5623281609765024063841662704058e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9118615518909010437933214328626 y1[1] (numeric) = 1.9118615518909010437933214328632 absolute error = 6e-31 relative error = 3.1383025586061817165538580360963e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.5MB, time=57.71 x[1] = 0.424 y2[1] (analytic) = 0.58859046299806318662798993905953 y2[1] (numeric) = 0.58859046299806318662798993905932 absolute error = 2.1e-31 relative error = 3.5678457807545384088519202971251e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.911450598147728456475764151092 y1[1] (numeric) = 1.9114505981477284564757641510927 absolute error = 7e-31 relative error = 3.6621401603490448601767777297078e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.425 y2[1] (analytic) = 0.58767921825657524250565045469569 y2[1] (numeric) = 0.58767921825657524250565045469548 absolute error = 2.1e-31 relative error = 3.5733780177388536964298320662527e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9110387329540336756437308970901 y1[1] (numeric) = 1.9110387329540336756437308970908 absolute error = 7e-31 relative error = 3.6629294212051804613366977604212e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=904.0MB, alloc=4.5MB, time=57.96 x[1] = 0.426 y2[1] (analytic) = 0.58676838583583468174406851476933 y2[1] (numeric) = 0.58676838583583468174406851476912 absolute error = 2.1e-31 relative error = 3.5789249228357973412893170139994e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9106259567216818606699041723951 y1[1] (numeric) = 1.9106259567216818606699041723958 absolute error = 7e-31 relative error = 3.6637207692974308040011037169770e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.5MB, time=58.20 x[1] = 0.427 y2[1] (analytic) = 0.58585796664667384918110568257234 y2[1] (numeric) = 0.58585796664667384918110568257213 absolute error = 2.1e-31 relative error = 3.5844865471744840748666809557717e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.910212269863449209508080734783 y1[1] (numeric) = 1.9102122698634492095080807347837 absolute error = 7e-31 relative error = 3.6645142063192758737968766416440e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=911.7MB, alloc=4.5MB, time=58.45 x[1] = 0.428 y2[1] (analytic) = 0.58494796159951185810933128660698 y2[1] (numeric) = 0.58494796159951185810933128660677 absolute error = 2.1e-31 relative error = 3.5900629421079641900784431511984e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9097976727930225459170080424865 y1[1] (numeric) = 1.9097976727930225459170080424872 absolute error = 7e-31 relative error = 3.6653097339692048505090803742320e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.429 y2[1] (analytic) = 0.58403837160435367985698499627348 y2[1] (numeric) = 0.58403837160435367985698499627327 absolute error = 2.1e-31 relative error = 3.5956541592144006192115476086837e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9093821659249989057735949693482 y1[1] (numeric) = 1.9093821659249989057735949693489 absolute error = 7e-31 relative error = 3.6661073539507240077038483612368e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.5MB, time=58.69 x[1] = 0.43 y2[1] (analytic) = 0.58312919757078923378308132737543 y2[1] (numeric) = 0.58312919757078923378308132737523 absolute error = 2.0e-31 relative error = 3.4297716669507173693624509670906e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9089657496748851224759104776634 y1[1] (numeric) = 1.9089657496748851224759104776642 absolute error = 8e-31 relative error = 4.1907509348255595873890222898837e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.5MB, time=58.94 x[1] = 0.431 y2[1] (analytic) = 0.58222044040799247768756608226273 y2[1] (numeric) = 0.58222044040799247768756608226252 absolute error = 2.1e-31 relative error = 3.6068812673914704454417392527214e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.90854842445909741143638484568 y1[1] (numeric) = 1.9085484244590974114363848456807 absolute error = 7e-31 relative error = 3.6677088777476910108117785818848e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.432 y2[1] (analytic) = 0.58131210102472049863743431437966 y2[1] (numeric) = 0.58131210102472049863743431437946 absolute error = 2.0e-31 relative error = 3.4404926311949410229092111422243e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9081301906949609536656289565175 y1[1] (numeric) = 1.9081301906949609536656289565182 absolute error = 7e-31 relative error = 3.6685127849953083423543065878650e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=923.1MB, alloc=4.5MB, time=59.18 TOP MAIN SOLVE Loop x[1] = 0.433 y2[1] (analytic) = 0.58040418032931260420971899102467 y2[1] (numeric) = 0.58040418032931260420971899102447 absolute error = 2.0e-31 relative error = 3.4458745608366054058929687914527e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9077110488007094784472880646543 y1[1] (numeric) = 1.9077110488007094784472880646549 absolute error = 6e-31 relative error = 3.1451303926618892672277402085502e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.5MB, time=59.43 x[1] = 0.434 y2[1] (analytic) = 0.57949667922968941415225911125708 y2[1] (numeric) = 0.57949667922968941415225911125688 absolute error = 2.0e-31 relative error = 3.4512708556993811850190829864171e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9072909991954848451043473650912 y1[1] (numeric) = 1.9072909991954848451043473650918 absolute error = 6e-31 relative error = 3.1458230561203625053906240802957e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=930.7MB, alloc=4.5MB, time=59.68 x[1] = 0.435 y2[1] (analytic) = 0.57858959863335195246315561810729 y2[1] (numeric) = 0.57858959863335195246315561810709 absolute error = 2.0e-31 relative error = 3.4566815662156165845794215192102e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9068700422993366238573075988539 y1[1] (numeric) = 1.9068700422993366238573075988546 absolute error = 7e-31 relative error = 3.6709371088337408991866695089977e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.436 y2[1] (analytic) = 0.5776829394473807398898230255586 y2[1] (numeric) = 0.57768293944738073988982302555839 absolute error = 2.1e-31 relative error = 3.6352120801921002030964178040802e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9064481785332216757746498366219 y1[1] (numeric) = 1.9064481785332216757746498366226 absolute error = 7e-31 relative error = 3.6717494232576741036943826998590e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.5MB, time=59.92 x[1] = 0.437 y2[1] (analytic) = 0.57677670257843488684854426117356 y2[1] (numeric) = 0.57677670257843488684854426117335 absolute error = 2.1e-31 relative error = 3.6409237589037753426703394543572e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9060254083190037318160094899842 y1[1] (numeric) = 1.906025408319003731816009489985 absolute error = 8e-31 relative error = 4.1972158215117940808166496833238e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.5MB, time=60.17 x[1] = 0.438 y2[1] (analytic) = 0.57587088893275118676543580473445 y2[1] (numeric) = 0.57587088893275118676543580473424 absolute error = 2.1e-31 relative error = 3.6466507343197772481323623171922e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9056017320794529709684805071144 y1[1] (numeric) = 1.9056017320794529709684805071151 absolute error = 7e-31 relative error = 3.6733803722781980636472229087095e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.5MB, time=60.42 x[1] = 0.439 y2[1] (analytic) = 0.57496549941614320983972978185704 y2[1] (numeric) = 0.57496549941614320983972978185682 absolute error = 2.2e-31 relative error = 3.8263165393993568185062609609989e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9051771502382455974764716165229 y1[1] (numeric) = 1.9051771502382455974764716165237 absolute error = 8e-31 relative error = 4.1990845832890587547725193712747e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.44 y2[1] (analytic) = 0.57406053493400039723027924922008 y2[1] (numeric) = 0.57406053493400039723027924921987 absolute error = 2.1e-31 relative error = 3.6581507910858852178079235939356e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9047516632199634171655373889984 y1[1] (numeric) = 1.9047516632199634171655373889991 absolute error = 7e-31 relative error = 3.6750197598812281994924040423398e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.5MB, time=60.66 x[1] = 0.441 y2[1] (analytic) = 0.57315599639128715566619248482993 y2[1] (numeric) = 0.57315599639128715566619248482971 absolute error = 2.2e-31 relative error = 3.8383965514653444034775540774152e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9043252714500934128606077938682 y1[1] (numeric) = 1.904325271450093412860607793869 absolute error = 8e-31 relative error = 4.2009629972027894321252582649955e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.5MB, time=60.91 x[1] = 0.442 y2[1] (analytic) = 0.57225188469254195248250167261022 y2[1] (numeric) = 0.57225188469254195248250167261 absolute error = 2.2e-31 relative error = 3.8444609075984265991671863026723e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9038979753550273188990408313166 y1[1] (numeric) = 1.9038979753550273188990408313174 absolute error = 8e-31 relative error = 4.2019058287554555749504898863915e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.443 y2[1] (analytic) = 0.57134820074187641108177094557285 y2[1] (numeric) = 0.57134820074187641108177094557263 absolute error = 2.2e-31 relative error = 3.8505415736732417054996251521254e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9034697753620611947389237276696 y1[1] (numeric) = 1.9034697753620611947389237276704 absolute error = 8e-31 relative error = 4.2028510794075050216544381603657e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.5MB, time=61.15 x[1] = 0.444 y2[1] (analytic) = 0.57044494544297440682254832588658 y2[1] (numeric) = 0.57044494544297440682254832588636 absolute error = 2.2e-31 relative error = 3.8566386074147923259298818814658e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9030406718993949976630490853117 y1[1] (numeric) = 1.9030406718993949976630490853125 absolute error = 8e-31 relative error = 4.2037987511929136442480796405939e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.5MB, time=61.40 x[1] = 0.445 y2[1] (analytic) = 0.56954211969909116333556567331613 y2[1] (numeric) = 0.56954211969909116333556567331591 absolute error = 2.2e-31 relative error = 3.8627520668047101252938845537424e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9026106653961321545789932832218 y1[1] (numeric) = 1.9026106653961321545789932832226 absolute error = 8e-31 relative error = 4.2047488461515397739612978566835e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.5MB, time=61.65 x[1] = 0.446 y2[1] (analytic) = 0.56863972441305234926859032575643 y2[1] (numeric) = 0.56863972441305234926859032575621 absolute error = 2.2e-31 relative error = 3.8688820100826251749735052065926e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9021797562822791329157253280146 y1[1] (numeric) = 1.9021797562822791329157253280154 absolute error = 8e-31 relative error = 4.2057013663291337566995591733307e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.447 y2[1] (analytic) = 0.56773776048725317546083168693519 y2[1] (numeric) = 0.56773776048725317546083168693497 absolute error = 2.2e-31 relative error = 3.8750284957475438315848488763392e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9017479449887450106171752588427 y1[1] (numeric) = 1.9017479449887450106171752588435 absolute error = 8e-31 relative error = 4.2066563137773475402118847613498e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.5MB, time=61.89 x[1] = 0.448 y2[1] (analytic) = 0.56683622882365749254780558680187 y2[1] (numeric) = 0.56683622882365749254780558680165 absolute error = 2.2e-31 relative error = 3.8811915825592352100183881562062e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9013152319473410452331921125551 y1[1] (numeric) = 1.9013152319473410452331921125559 absolute error = 8e-31 relative error = 4.2076136905537442930489662329141e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.5MB, time=62.14 x[1] = 0.449 y2[1] (analytic) = 0.56593513032379688899755880966357 y2[1] (numeric) = 0.56593513032379688899755880966334 absolute error = 2.3e-31 relative error = 4.0640700263368820536090252844992e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9008816175907802421083223581184 y1[1] (numeric) = 1.9008816175907802421083223581192 absolute error = 8e-31 relative error = 4.2085734987218080553905745623625e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.45 y2[1] (analytic) = 0.5650344658887697895791557537681 y2[1] (numeric) = 0.56503446588876978957915575376788 absolute error = 2.2e-31 relative error = 3.8935677959742058730166624527440e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9004471023526769216688406114864 y1[1] (numeric) = 1.9004471023526769216688406114873 absolute error = 9e-31 relative error = 4.7357277078948225995494293730509e-29 % Correct digits = 30 h = 0.001 memory used=972.7MB, alloc=4.5MB, time=62.38 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.451 y2[1] (analytic) = 0.56413423641924055426432875377253 y2[1] (numeric) = 0.56413423641924055426432875377231 absolute error = 2.2e-31 relative error = 3.8997810414134369868101915231804e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.9000116866675462858084653438511 y1[1] (numeric) = 1.9000116866675462858084653438519 absolute error = 8e-31 relative error = 4.2105004175165352561372847766060e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.5MB, time=62.63 x[1] = 0.452 y2[1] (analytic) = 0.56323444281543857756319316437161 y2[1] (numeric) = 0.56323444281543857756319316437139 absolute error = 2.2e-31 relative error = 3.9060111256741785754185836719084e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8995753709708039833731931975225 y1[1] (numeric) = 1.8995753709708039833731931975233 absolute error = 8e-31 relative error = 4.2114675322998584382552955733283e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.5MB, time=62.87 x[1] = 0.453 y2[1] (analytic) = 0.56233508597715738829492786929617 y2[1] (numeric) = 0.56233508597715738829492786929595 absolute error = 2.2e-31 relative error = 3.9122581088411157629070248496676e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.899138155698765674745686424569 y1[1] (numeric) = 1.8991381556987656747456864245699 absolute error = 9e-31 relative error = 4.7389917226367110987339073908685e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.454 y2[1] (analytic) = 0.56143616680375374979432144492579 y2[1] (numeric) = 0.56143616680375374979432144492557 absolute error = 2.2e-31 relative error = 3.9185220512681992197158324405799e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.898700041288646595529648863792 y1[1] (numeric) = 1.8987000412886465955296488637928 absolute error = 8e-31 relative error = 4.2134090830747571530687989719032e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.5MB, time=63.12 x[1] = 0.455 y2[1] (analytic) = 0.56053768619414676055508377189468 y2[1] (numeric) = 0.56053768619414676055508377189446 absolute error = 2.2e-31 relative error = 3.9248030135800935409302602676563e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8982610281785611193346267716233 y1[1] (numeric) = 1.8982610281785611193346267716241 absolute error = 8e-31 relative error = 4.2143835232587806995643088337900e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.5MB, time=63.36 x[1] = 0.456 y2[1] (analytic) = 0.55963964504681695531082245130418 y2[1] (numeric) = 0.55963964504681695531082245130396 absolute error = 2.2e-31 relative error = 3.9311010566736347234788620572167e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8978211168075223196616717221096 y1[1] (numeric) = 1.8978211168075223196616717221104 absolute error = 8e-31 relative error = 4.2153604094454613413388887449742e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.5MB, time=63.61 x[1] = 0.457 y2[1] (analytic) = 0.55874204425980540655458294449053 y2[1] (numeric) = 0.55874204425980540655458294449031 absolute error = 2.2e-31 relative error = 3.9374162417192968076436719013723e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8973803076154415308903036902821 y1[1] (numeric) = 1.8973803076154415308903036902828 absolute error = 7e-31 relative error = 3.6892972757777512005588207477881e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.458 y2[1] (analytic) = 0.55784488473071282649785091673299 y2[1] (numeric) = 0.55784488473071282649785091673276 absolute error = 2.3e-31 relative error = 4.1230099315336981010124324672754e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8969386010431279083672133319129 y1[1] (numeric) = 1.8969386010431279083672133319136 absolute error = 7e-31 relative error = 3.6901563372429107290999220741487e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.5MB, time=63.85 x[1] = 0.459 y2[1] (analytic) = 0.55694816735669866946991482582499 y2[1] (numeric) = 0.55694816735669866946991482582476 absolute error = 2.3e-31 relative error = 4.1296482057134770669658773067565e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8964959975322879875971433709198 y1[1] (numeric) = 1.8964959975322879875971433709206 absolute error = 8e-31 relative error = 4.2183057651635246310470748777093e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.5MB, time=64.10 x[1] = 0.46 y2[1] (analytic) = 0.5560518930344802347584863560711 y2[1] (numeric) = 0.55605189303448023475848635607087 absolute error = 2.3e-31 relative error = 4.1363045946098042445568083182261e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8960524975255252425363899035004 y1[1] (numeric) = 1.8960524975255252425363899035012 absolute error = 8e-31 relative error = 4.2192924565329982571935800869880e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.461 y2[1] (analytic) = 0.55515606266033176989247585701442 y2[1] (numeric) = 0.55515606266033176989247585701418 absolute error = 2.4e-31 relative error = 4.3231086921740467023111874984078e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.895608101466339642989365325457 y1[1] (numeric) = 1.8956081014663396429893653254578 absolute error = 8e-31 relative error = 4.2202816045213321143286969510917e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.5MB, time=64.35 x[1] = 0.462 y2[1] (analytic) = 0.55426067713008357436781950404435 y2[1] (numeric) = 0.55426067713008357436781950404412 absolute error = 2.3e-31 relative error = 4.1496719772891192076039236200940e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8951628097991272111086654861145 y1[1] (numeric) = 1.8951628097991272111086654861153 absolute error = 8e-31 relative error = 4.2212732112698744455733907136123e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.5MB, time=64.59 x[1] = 0.463 y2[1] (analytic) = 0.55336573733912110381725445498295 y2[1] (numeric) = 0.55336573733912110381725445498272 absolute error = 2.3e-31 relative error = 4.1563831021769292783343675560966e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8947166229691795769990845687246 y1[1] (numeric) = 1.8947166229691795769990845687254 absolute error = 8e-31 relative error = 4.2222672789260328685887211505412e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.5MB, time=64.84 x[1] = 0.464 y2[1] (analytic) = 0.55247124418238407462493783279988 y2[1] (numeric) = 0.55247124418238407462493783279964 absolute error = 2.4e-31 relative error = 4.3441174998199583211851988428678e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8942695414226835334260220933066 y1[1] (numeric) = 1.8942695414226835334260220933074 absolute error = 8e-31 relative error = 4.2232638096432845141491579012118e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.465 y2[1] (analytic) = 0.55157719855436556898680491976248 y2[1] (numeric) = 0.55157719855436556898680491976224 absolute error = 2.4e-31 relative error = 4.3511588337773661146903463990661e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8938215656067205896287273334791 y1[1] (numeric) = 1.8938215656067205896287273334799 absolute error = 8e-31 relative error = 4.2242628055811861978935067903440e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.5MB, time=65.09 x[1] = 0.466 y2[1] (analytic) = 0.55068360134911114041756150258825 y2[1] (numeric) = 0.550683601349111140417561502588 absolute error = 2.5e-31 relative error = 4.5398119607616589786504487934958e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8933726959692665242388273340021 y1[1] (numeric) = 1.893372695969266524238827334003 absolute error = 9e-31 relative error = 4.7534223025185577035051273691963e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.5MB, time=65.33 x[1] = 0.467 y2[1] (analytic) = 0.54979045346021791970520486153262 y2[1] (numeric) = 0.54979045346021791970520486153237 absolute error = 2.5e-31 relative error = 4.5471869950919338001095276159535e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8929229329591909373045856104637 y1[1] (numeric) = 1.8929229329591909373045856104646 absolute error = 9e-31 relative error = 4.7545517270110799590149959493848e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.468 memory used=1022.3MB, alloc=4.5MB, time=65.58 y2[1] (analytic) = 0.54889775578083372131396744881682 y2[1] (numeric) = 0.54889775578083372131396744881658 absolute error = 2.4e-31 relative error = 4.3723990027721709584983190086431e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.892472277026256801421339506815 y1[1] (numeric) = 1.8924722770262568014213395068159 absolute error = 9e-31 relative error = 4.7556839322064906271646267091554e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.469 y2[1] (analytic) = 0.54800550920365615023657685337748 y2[1] (numeric) = 0.54800550920365615023657685337724 absolute error = 2.4e-31 relative error = 4.3795180152250699748486073596932e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8920207286211200119685650802794 y1[1] (numeric) = 1.8920207286211200119685650802803 absolute error = 9e-31 relative error = 4.7568189205617648894639275675040e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.5MB, time=65.82 x[1] = 0.47 y2[1] (analytic) = 0.54711371462093170929672519960359 y2[1] (numeric) = 0.54711371462093170929672519960335 absolute error = 2.4e-31 relative error = 4.3866566234093444872570581529678e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8915682881953289364540192765334 y1[1] (numeric) = 1.8915682881953289364540192765343 absolute error = 9e-31 relative error = 4.7579566945407753522039746130520e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.5MB, time=66.07 x[1] = 0.471 y2[1] (analytic) = 0.54622237292445490690264067751721 y2[1] (numeric) = 0.54622237292445490690264067751696 absolute error = 2.5e-31 relative error = 4.5768905191764483443588386915254e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8911149562013239629654100509787 y1[1] (numeric) = 1.8911149562013239629654100509796 absolute error = 9e-31 relative error = 4.7590972566143037156333490204689e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.472 y2[1] (analytic) = 0.54533148500556736525265345075175 y2[1] (numeric) = 0.5453314850055673652526534507515 absolute error = 2.5e-31 relative error = 4.5843676162847577946608135263850e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.890660733092437047730045984399 y1[1] (numeric) = 1.8906607330924370477300459843999 absolute error = 9e-31 relative error = 4.7602406092600524811319098528164e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1033.7MB, alloc=4.5MB, time=66.31 x[1] = 0.473 y2[1] (analytic) = 0.54444105175515692899364773668793 y2[1] (numeric) = 0.54444105175515692899364773668768 absolute error = 2.5e-31 relative error = 4.5918653487655931089476746763029e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8902056193228912617829178333128 y1[1] (numeric) = 1.8902056193228912617829178333137 absolute error = 9e-31 relative error = 4.7613867549626566964795564760217e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.5MB, time=66.56 x[1] = 0.474 y2[1] (analytic) = 0.54355107406365677433329140022077 y2[1] (numeric) = 0.54355107406365677433329140022051 absolute error = 2.6e-31 relative error = 4.7833591433498055905905456014791e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8897496153478003367436653469044 y1[1] (numeric) = 1.8897496153478003367436653469053 absolute error = 9e-31 relative error = 4.7625356962136957393179042575935e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.5MB, time=66.81 x[1] = 0.475 y2[1] (analytic) = 0.54266155282104451860693394885391 y2[1] (numeric) = 0.54266155282104451860693394885365 absolute error = 2.6e-31 relative error = 4.7911999412595413626779102435504e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8892927216231682097028835735269 y1[1] (numeric) = 1.8892927216231682097028835735278 absolute error = 9e-31 relative error = 4.7636874355117051389031684424808e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.476 y2[1] (analytic) = 0.54177248891684133030006336214914 y2[1] (numeric) = 0.54177248891684133030006336214887 absolute error = 2.7e-31 relative error = 4.9836417596583296037282506644920e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8888349386058885672182237704341 y1[1] (numeric) = 1.8888349386058885672182237704349 absolute error = 8e-31 relative error = 4.2354150892108341655545987557524e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.5MB, time=67.05 x[1] = 0.477 y2[1] (analytic) = 0.54088388324011103952721173299992 y2[1] (numeric) = 0.54088388324011103952721173299965 absolute error = 2.7e-31 relative error = 4.9918292699459242065286713390704e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8883762667537443884207449206015 y1[1] (numeric) = 1.8883762667537443884207449206024 absolute error = 9e-31 relative error = 4.7659993182776290827577798248870e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.5MB, time=67.30 x[1] = 0.478 y2[1] (analytic) = 0.53999573667945924896819924174937 y2[1] (numeric) = 0.5399957366794592489681992417491 absolute error = 2.7e-31 relative error = 5.0000394755018527278966556395156e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8879167065254074872319727502484 y1[1] (numeric) = 1.8879167065254074872319727502493 absolute error = 9e-31 relative error = 4.7671594667775023774413919484385e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.479 y2[1] (analytic) = 0.53910805012303244526260552683451 y2[1] (numeric) = 0.53910805012303244526260552683424 absolute error = 2.7e-31 relative error = 5.0082724592664123505391736488419e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8874562583804380536921240299613 y1[1] (numeric) = 1.8874562583804380536921240299622 absolute error = 9e-31 relative error = 4.7683224233882874428285944046580e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1052.8MB, alloc=4.5MB, time=67.54 x[1] = 0.48 y2[1] (analytic) = 0.53822082445851711086335705741136 y2[1] (numeric) = 0.53822082445851711086335705741109 absolute error = 2.7e-31 relative error = 5.0165283045604269210302760644521e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8869949227792841943999548311587 y1[1] (numeric) = 1.8869949227792841943999548311596 absolute error = 9e-31 relative error = 4.7694881906434792396618320604904e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.5MB, time=67.79 x[1] = 0.481 y2[1] (analytic) = 0.53733406057313883635031865429955 y2[1] (numeric) = 0.53733406057313883635031865429928 absolute error = 2.7e-31 relative error = 5.0248070950873427019251588589409e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8865327001832814720646922980094 y1[1] (numeric) = 1.8865327001832814720646922980102 absolute error = 8e-31 relative error = 4.2405837965187561070954989512688e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.5MB, time=68.04 x[1] = 0.482 y2[1] (analytic) = 0.5364477593536614332047768455809 y2[1] (numeric) = 0.53644775935366143320477684558063 absolute error = 2.7e-31 relative error = 5.0331089149353376041752263774543e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8860695910546524441705103828338 y1[1] (numeric) = 1.8860695910546524441705103828347 absolute error = 9e-31 relative error = 4.7718281672562144222056761107191e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.483 y2[1] (analytic) = 0.53556192168638604704570228229476 y2[1] (numeric) = 0.53556192168638604704570228229448 absolute error = 2.8e-31 relative error = 5.2281536207490530360286420642499e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8856055958565062007540108804759 y1[1] (numeric) = 1.8856055958565062007540108804768 absolute error = 9e-31 relative error = 4.7730023817159355977868949807309e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.5MB, time=68.28 x[1] = 0.484 y2[1] (analytic) = 0.53467654845715027132867797789364 y2[1] (numeric) = 0.53467654845715027132867797789336 absolute error = 2.8e-31 relative error = 5.2368109431386365134667965573386e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8851407150528379012951719841238 y1[1] (numeric) = 1.8851407150528379012951719841246 absolute error = 8e-31 relative error = 4.2437150373550607885159364395646e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.5MB, time=68.53 x[1] = 0.485 y2[1] (analytic) = 0.53379164055132726150837967245725 y2[1] (numeric) = 0.53379164055132726150837967245697 absolute error = 2.8e-31 relative error = 5.2454924118107526624684342565940e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8846749491085283107222274715935 y1[1] (numeric) = 1.8846749491085283107222274715943 absolute error = 8e-31 relative error = 4.2447638006671053573274492309867e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.5MB, time=68.78 x[1] = 0.486 y2[1] (analytic) = 0.53290719885382484966549415911054 y2[1] (numeric) = 0.53290719885382484966549415911026 absolute error = 2.8e-31 relative error = 5.2541981155860369591912122944866e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.884208298489343334530940517158 y1[1] (numeric) = 1.8842082984893433345309405171588 absolute error = 8e-31 relative error = 4.2458150759732715564770858203023e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.487 y2[1] (analytic) = 0.53202322424908465959896094565383 y2[1] (numeric) = 0.53202322424908465959896094565355 absolute error = 2.8e-31 relative error = 5.2629281436952559327257408564244e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8837407636619335530187370096079 y1[1] (numeric) = 1.8837407636619335530187370096087 absolute error = 8e-31 relative error = 4.2468688655695109585569448230878e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1075.7MB, alloc=4.5MB, time=69.02 x[1] = 0.488 y2[1] (analytic) = 0.53113971762108122238442215908945 y2[1] (numeric) = 0.53113971762108122238442215908917 absolute error = 2.8e-31 relative error = 5.2716825857815805847562036180166e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8832723450938337546341641423728 y1[1] (numeric) = 1.8832723450938337546341641423736 absolute error = 8e-31 relative error = 4.2479251717580981266567481239489e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.5MB, time=69.27 x[1] = 0.489 y2[1] (analytic) = 0.53025667985332109239976513452147 y2[1] (numeric) = 0.53025667985332109239976513452118 absolute error = 2.9e-31 relative error = 5.4690494437565486172128612928248e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.882803043253462468442140926205 y1[1] (numeric) = 1.8828030432534624684421409262058 absolute error = 8e-31 relative error = 4.2489839968476416084631550163386e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.49 y2[1] (analytic) = 0.52937411182884196381864166281204 y2[1] (numeric) = 0.52937411182884196381864166281176 absolute error = 2.8e-31 relative error = 5.2892650725339969451652535265374e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8823328586101214957054681591367 y1[1] (numeric) = 1.8823328586101214957054681591375 absolute error = 8e-31 relative error = 4.2500453431530949657466873062150e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.5MB, time=69.51 x[1] = 0.491 y2[1] (analytic) = 0.52849201443021178757284740340174 y2[1] (numeric) = 0.52849201443021178757284740340146 absolute error = 2.8e-31 relative error = 5.2980932985691205000778973692830e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8818617916339954405830662721614 y1[1] (numeric) = 1.8818617916339954405830662721622 absolute error = 8e-31 relative error = 4.2511092129957678393290764513930e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.5MB, time=69.76 x[1] = 0.492 y2[1] (analytic) = 0.52761038853952788878444449984064 y2[1] (numeric) = 0.52761038853952788878444449984036 absolute error = 2.8e-31 relative error = 5.3069463013240642755392662223678e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8813898427961512399454103523624 y1[1] (numeric) = 1.8813898427961512399454103523632 absolute error = 8e-31 relative error = 4.2521756087033370496241938272228e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.5MB, time=70.01 x[1] = 0.493 y2[1] (analytic) = 0.52672923503841608466850996583417 y2[1] (numeric) = 0.52672923503841608466850996583389 absolute error = 2.8e-31 relative error = 5.3158241725386418859109720843588e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8809170125685376923076325280146 y1[1] (numeric) = 1.8809170125685376923076325280154 absolute error = 8e-31 relative error = 4.2532445326098577328460764542696e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.494 y2[1] (analytic) = 0.52584855480802980290739193898176 y2[1] (numeric) = 0.52584855480802980290739193898148 absolute error = 2.8e-31 relative error = 5.3247270043790248553501756936015e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8804433014239849858807627825173 y1[1] (numeric) = 1.8804433014239849858807627825182 absolute error = 9e-31 relative error = 4.7861054854377463271001521254031e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1094.8MB, alloc=4.5MB, time=70.25 x[1] = 0.495 y2[1] (analytic) = 0.52496834872904920049735542787856 y2[1] (numeric) = 0.52496834872904920049735542787828 absolute error = 2.8e-31 relative error = 5.3336548894401213825654663058728e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8799687098362042257415801458792 y1[1] (numeric) = 1.8799687098362042257415801458801 absolute error = 9e-31 relative error = 4.7873137211864242982957346559727e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1098.6MB, alloc=4.5MB, time=70.50 x[1] = 0.496 y2[1] (analytic) = 0.52408861768168028306849870586105 y2[1] (numeric) = 0.52408861768168028306849870586077 absolute error = 2.8e-31 relative error = 5.3426079207479706056285517404878e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8794932382797869601215470938628 y1[1] (numeric) = 1.8794932382797869601215470938636 absolute error = 8e-31 relative error = 4.2564664969595895816447018551466e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop x[1] = 0.497 y2[1] (analytic) = 0.52320936254565402467882103140682 y2[1] (numeric) = 0.52320936254565402467882103140653 absolute error = 2.9e-31 relative error = 5.5427142700393722138868816637830e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8790168872302047058153008658165 y1[1] (numeric) = 1.8790168872302047058153008658173 absolute error = 8e-31 relative error = 4.2575455571304256072529640589527e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1102.4MB, alloc=4.5MB, time=70.74 TOP MAIN SOLVE Loop x[1] = 0.498 y2[1] (analytic) = 0.52233058420022548808332190104733 y2[1] (numeric) = 0.52233058420022548808332190104704 absolute error = 2.9e-31 relative error = 5.5520394319631495958454714840017e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8785396571638084727091762926628 y1[1] (numeric) = 1.8785396571638084727091762926636 absolute error = 8e-31 relative error = 4.2586271572665557996949671946829e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1106.2MB, alloc=4.5MB, time=70.99 x[1] = 0.499 y2[1] (analytic) = 0.52145228352417294547901156562125 y2[1] (numeric) = 0.52145228352417294547901156562096 absolute error = 2.9e-31 relative error = 5.5613909299633257819697074880329e-29 % Correct digits = 30 h = 0.001 y1[1] (analytic) = 1.8780615485578282874302356064793 y1[1] (numeric) = 1.87806154855782828743023560648 absolute error = 7e-31 relative error = 3.7272473872729734271353587670508e-29 % Correct digits = 30 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; Iterations = 400 Total Elapsed Time = 1 Minutes 11 Seconds Elapsed Time(since restart) = 1 Minutes 10 Seconds Time to Timeout = 1 Minutes 48 Seconds Percent Done = 100.2 % > quit memory used=1108.0MB, alloc=4.5MB, time=71.09