|\^/| 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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 - 5 - 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 - 5 - 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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 - 6; 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 - 6; 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_m1, > array_y2_higher, > array_y2_higher_work, > array_y2_higher_work2, > array_y2_set_initial, > array_y1_higher, > array_y1_higher_work, > array_y1_higher_work2, > array_y1_set_initial, > array_poles, > array_real_pole, > array_complex_pole, > array_fact_2, > glob_last; > local kkk, order_d, adj2, adj3 , temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre add CONST FULL $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if ( not array_y2_set_initial[1,6]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[1] * expt(glob_h , (5)) * factorial_3(0,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[2,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[3,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[4,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[5,2] := temporary; > temporary := temporary / glob_h * (1.0); > array_y2_higher[6,1] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 2; > # emit pre mult FULL FULL $eq_no = 2 i = 1 > array_tmp3[1] := (array_m1[1] * (array_y2[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if ( not array_y1_set_initial[2,2]) then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[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 add CONST FULL $eq_no = 1 i = 2 > array_tmp1[2] := array_y1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if ( not array_y2_set_initial[1,7]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[2] * expt(glob_h , (5)) * factorial_3(1,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[2,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[3,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[5,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[6,2] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 3; > # emit pre mult FULL FULL $eq_no = 2 i = 2 > array_tmp3[2] := ats(2,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if ( not array_y1_set_initial[2,3]) then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[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 add CONST FULL $eq_no = 1 i = 3 > array_tmp1[3] := array_y1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if ( not array_y2_set_initial[1,8]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[3] * expt(glob_h , (5)) * factorial_3(2,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (7.0); > array_y2_higher[2,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[3,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[4,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[5,4] := temporary; > temporary := temporary / glob_h * (3.0); > array_y2_higher[6,3] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 4; > # emit pre mult FULL FULL $eq_no = 2 i = 3 > array_tmp3[3] := ats(3,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if ( not array_y1_set_initial[2,4]) then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[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 add CONST FULL $eq_no = 1 i = 4 > array_tmp1[4] := array_y1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if ( not array_y2_set_initial[1,9]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[4] * expt(glob_h , (5)) * factorial_3(3,8); > array_y2[9] := temporary; > array_y2_higher[1,9] := temporary; > temporary := temporary / glob_h * (8.0); > array_y2_higher[2,8] := temporary; > temporary := temporary / glob_h * (7.0); > array_y2_higher[3,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[4,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,5] := temporary; > temporary := temporary / glob_h * (4.0); > array_y2_higher[6,4] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 5; > # emit pre mult FULL FULL $eq_no = 2 i = 4 > array_tmp3[4] := ats(4,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if ( not array_y1_set_initial[2,5]) then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[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 add CONST FULL $eq_no = 1 i = 5 > array_tmp1[5] := array_y1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if ( not array_y2_set_initial[1,10]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp1[5] * expt(glob_h , (5)) * factorial_3(4,9); > array_y2[10] := temporary; > array_y2_higher[1,10] := temporary; > temporary := temporary / glob_h * (9.0); > array_y2_higher[2,9] := temporary; > temporary := temporary / glob_h * (8.0); > array_y2_higher[3,8] := temporary; > temporary := temporary / glob_h * (7.0); > array_y2_higher[4,7] := temporary; > temporary := temporary / glob_h * (6.0); > array_y2_higher[5,6] := temporary; > temporary := temporary / glob_h * (5.0); > array_y2_higher[6,5] := temporary; > fi;# end if 2; > fi;# end if 1; > kkk := 6; > # emit pre mult FULL FULL $eq_no = 2 i = 5 > array_tmp3[5] := ats(5,array_m1,array_y2,1); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if ( not array_y1_set_initial[2,6]) then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[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 NOT FULL - FULL add $eq_no = 1 > array_tmp1[kkk] := array_y1[kkk]; > #emit assign $eq_no = 1 > order_d := 5; > 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_tmp1[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 1; > adj3 := 2; > while (term >= 1) do # do number 2 > if (adj3 <= order_d + 1) then # if number 3 > if (adj2 > 0) then # if number 4 > temporary := temporary / glob_h * convfp(adj2); > else > temporary := temporary; > fi;# end if 4; > array_y2_higher[adj3,term] := temporary; > fi;# end if 3; > term := term - 1; > adj2 := adj2 - 1; > adj3 := adj3 + 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1; > #emit mult FULL FULL $eq_no = 2 > array_tmp3[kkk] := ats(kkk,array_m1,array_y2,1); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2 > temporary := array_tmp3[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := kkk + order_d - 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_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_m1, array_y2_higher, array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial, array_y1_higher, array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial, array_poles, array_real_pole, array_complex_pole, array_fact_2, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; if not array_y2_set_initial[1, 6] then if 1 <= glob_max_terms then temporary := array_tmp1[1]*expt(glob_h, 5)*factorial_3(0, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[3, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[4, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[5, 2] := temporary; temporary := temporary*1.0/glob_h; array_y2_higher[6, 1] := temporary end if end if; kkk := 2; array_tmp3[1] := array_m1[1]*array_y2[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*expt(glob_h, 1)*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*1.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_y1[2]; if not array_y2_set_initial[1, 7] then if 2 <= glob_max_terms then temporary := array_tmp1[2]*expt(glob_h, 5)*factorial_3(1, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[5, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[6, 2] := temporary end if end if; kkk := 3; array_tmp3[2] := ats(2, array_m1, array_y2, 1); if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[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] := array_y1[3]; if not array_y2_set_initial[1, 8] then if 3 <= glob_max_terms then temporary := array_tmp1[3]*expt(glob_h, 5)*factorial_3(2, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*7.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[4, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[5, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[6, 3] := temporary end if end if; kkk := 4; array_tmp3[3] := ats(3, array_m1, array_y2, 1); if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[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] := array_y1[4]; if not array_y2_set_initial[1, 9] then if 4 <= glob_max_terms then temporary := array_tmp1[4]*expt(glob_h, 5)*factorial_3(3, 8); array_y2[9] := temporary; array_y2_higher[1, 9] := temporary; temporary := temporary*8.0/glob_h; array_y2_higher[2, 8] := temporary; temporary := temporary*7.0/glob_h; array_y2_higher[3, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[4, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[6, 4] := temporary end if end if; kkk := 5; array_tmp3[4] := ats(4, array_m1, array_y2, 1); if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[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] := array_y1[5]; if not array_y2_set_initial[1, 10] then if 5 <= glob_max_terms then temporary := array_tmp1[5]*expt(glob_h, 5)*factorial_3(4, 9); array_y2[10] := temporary; array_y2_higher[1, 10] := temporary; temporary := temporary*9.0/glob_h; array_y2_higher[2, 9] := temporary; temporary := temporary*8.0/glob_h; array_y2_higher[3, 8] := temporary; temporary := temporary*7.0/glob_h; array_y2_higher[4, 7] := temporary; temporary := temporary*6.0/glob_h; array_y2_higher[5, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[6, 5] := temporary end if end if; kkk := 6; array_tmp3[5] := ats(5, array_m1, array_y2, 1); if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*expt(glob_h, 1)*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*5.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y1[kkk]; order_d := 5; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp1[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_tmp3[kkk] := ats(kkk, array_m1, array_y2, 1); order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp3[kkk]*expt(glob_h, order_d)* factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := kkk + order_d - 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( cos(x)); > end; exact_soln_y1 := proc(x) return cos(x) end proc > exact_soln_y2 := proc(x) > return( sin(x)); > end; exact_soln_y2 := proc(x) return sin(x) end proc > exact_soln_y2p := proc(x) > return( cos(x)); > end; exact_soln_y2p := proc(x) return cos(x) end proc > exact_soln_y2pp := proc(x) > return( -sin(x)); > end; exact_soln_y2pp := proc(x) return -sin(x) end proc > exact_soln_y2ppp := proc(x) > return( -cos(x)); > end; exact_soln_y2ppp := proc(x) return -cos(x) end proc > exact_soln_y2pppp := proc(x) > return( sin(x)); > end; exact_soln_y2pppp := proc(x) return 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_5, > array_const_0D0, > array_const_1, > #END CONST > array_y2_init, > array_y1_init, > array_norms, > array_fact_1, > array_pole, > array_1st_rel_error, > array_last_rel_error, > array_type_pole, > array_y2, > array_x, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > 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/mtest7postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 5 ) = y1 ;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * y2 ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits:=32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 5.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > 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( cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"return( sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"return( cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"return( -sin(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"return( -cos(x));"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"return( 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_m1:= Array(0..(max_terms + 1),[]); > array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work2 := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2; > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > ord := 1; > while (ord <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=6) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=3) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=2) do # do number 2 > term := 1; > while (term <= 3) do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > ord := 1; > while (ord <=max_terms) do # do number 2 > term := 1; > while (term <= max_terms) do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3; > ord := ord + 1; > od;# end do number 2; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_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_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_const_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_5[1] := 5; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms + 1) do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while (term <= max_terms) do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while (iiif <= glob_max_terms) do # do number 2 > jjjf := 0; > while (jjjf <= glob_max_terms) do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3; > iiif := iiif + 1; > od;# end do number 2; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 5.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_look_poles := true; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_desired_digits_correct:=10; > glob_display_interval:=0.001; > glob_look_poles:=true; > glob_max_iter:=10000000; > glob_max_minutes:=3; > glob_subiter_method:=3; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > if (glob_h > 0.0) then # if number 1 > glob_neg_h := false; > glob_display_interval := omniabs(glob_display_interval); > else > glob_neg_h := true; > glob_display_interval := -omniabs(glob_display_interval); > fi;# end if 1; > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := true; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > #BEGIN OPTIMIZE CODE > omniout_str(ALWAYS,"START of Optimize"); > #Start Series -- INITIALIZE FOR OPTIMIZE > glob_check_sign := check_sign(x_start,x_end); > glob_h := check_sign(x_start,x_end); > if (glob_display_interval < glob_h) then # if number 3 > glob_h := glob_display_interval; > fi;# end if 3; > 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 := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 3 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 3; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 3 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 4 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 4; > r_order := r_order + 1; > od;# end do number 3 > ; > if (glob_subiter_method = 1 ) then # if number 3 > atomall(); > elif > (glob_subiter_method = 2 ) then # if number 4 > subiter := 1; > while (subiter <= 6) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 6 + glob_max_terms) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > fi;# end if 4; > est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer); > omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,""); > value3 := test_suggested_h(); > omniout_float(ALWAYS,"value3",32,value3,32,""); > if ((value3 < est_needed_step_err) and (found_h < 0.0)) then # if number 4 > best_h := glob_h; > found_h := 1.0; > fi;# end if 4; > omniout_float(ALWAYS,"best_h",32,best_h,32,""); > opt_iter := opt_iter + 1; > glob_h := glob_h * 0.5; > od;# end do number 2; > if (found_h > 0.0) then # if number 4 > glob_h := best_h ; > else > omniout_str(ALWAYS,"No increment to obtain desired accuracy found"); > fi;# end if 4; > #END OPTIMIZE CODE > if (glob_html_log) then # if number 4 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 4; > #BEGIN SOLUTION CODE > if (found_h > 0.0) then # if number 4 > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > glob_next_display := x_start; > order_diff := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , (term_no - 1)) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > glob_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 <= 6) do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3; > else > subiter := 1; > while (subiter <= 6 + 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 := 6; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 6; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 5; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 6; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 6; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3; > array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1)); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while (ord <= order_diff) do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4; > term_no := term_no - 1; > od;# end do number 3; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1; > order_diff := 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 , 5 ) = y1 ;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * y2 ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if (glob_html_log) then # if number 6 > logstart(html_log_file); > logitem_str(html_log_file,"2013-01-28T17:54:01-06:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest7") > ; > logitem_str(html_log_file,"diff ( y2 , x , 5 ) = y1 ;") > ; > 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,"mtest7 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest7 maple results") > ; > logitem_str(html_log_file,"All Tests - All Languages") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * y2 ;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logitem_good_digits(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if (array_type_pole[2] = 1 or array_type_pole[2] = 2) then # if number 7 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 7; > logditto(html_log_file) > ; > if (glob_percent_done < 100.0) then # if number 7 > logditto(html_log_file) > ; > 0; > else > logditto(html_log_file) > ; > 0; > fi;# end if 7; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 6; > if (glob_html_log) then # if number 6 > fclose(html_log_file); > fi;# end if 6 > ; > ;; > fi;# end if 5 > #END OUTFILEMAIN > end; main := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, max_terms, opt_iter, tmp, subiter, est_needed_step_err, value3, min_value, est_answer, best_h, found_h, repeat_it; global glob_max_terms, glob_iolevel, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, MAX_UNCHANGED, glob_check_sign, glob_desired_digits_correct, glob_max_value3, glob_ratio_of_radius, glob_percent_done, glob_subiter_method, glob_total_exp_sec, glob_optimal_expect_sec, glob_html_log, glob_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag, glob_djd_debug2, glob_sec_in_minute, glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day, glob_sec_in_year, glob_almost_1, glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished, glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done, glob_disp_incr, glob_h, glob_max_h, glob_large_float, glob_last_good_h, glob_look_poles, glob_neg_h, glob_display_interval, glob_next_display, glob_dump_analytic, glob_abserr, glob_relerr, glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err, glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start, glob_small_float, glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2, glob_max_sec, glob_orig_start_sec, glob_start, glob_curr_iter_when_opt, glob_current_iter, glob_iter, glob_normmax, glob_max_minutes, array_const_5, array_const_0D0, array_const_1, array_y2_init, array_y1_init, array_norms, array_fact_1, array_pole, array_1st_rel_error, array_last_rel_error, array_type_pole, array_y2, array_x, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, 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/mtest7postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 5 ) = y1 ;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * y2 ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits:=32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 5.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_look_poles := true;"); 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(\tcos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "return(\tsin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "return(\tcos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "return( -sin(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "return(\t-cos(x));"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "return( 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_m1 := Array(0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[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_const_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.; x_end := 5.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_look_poles := true; glob_max_iter := 20; glob_desired_digits_correct := 10; glob_display_interval := 0.001; glob_look_poles := true; glob_max_iter := 10000000; glob_max_minutes := 3; glob_subiter_method := 3; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); if 0. < glob_h then glob_neg_h := false; glob_display_interval := omniabs(glob_display_interval) else glob_neg_h := true; glob_display_interval := -omniabs(glob_display_interval) end if; chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := true; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; omniout_str(ALWAYS, "START of Optimize"); glob_check_sign := check_sign(x_start, x_end); glob_h := check_sign(x_start, x_end); if glob_display_interval < glob_h then glob_h := glob_display_interval end if; 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 := 5; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 6 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 6 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; est_needed_step_err := estimated_needed_step_error(x_start, x_end, glob_h, est_answer) ; omniout_float(ALWAYS, "est_needed_step_err", 32, est_needed_step_err, 16, ""); value3 := test_suggested_h(); omniout_float(ALWAYS, "value3", 32, value3, 32, ""); if value3 < est_needed_step_err and found_h < 0. then best_h := glob_h; found_h := 1.0 end if; omniout_float(ALWAYS, "best_h", 32, best_h, 32, ""); opt_iter := opt_iter + 1; glob_h := glob_h*0.5 end do; if 0. < found_h then glob_h := best_h else omniout_str(ALWAYS, "No increment to obtain desired accuracy found") end if; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; if 0. < found_h then omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; glob_next_display := x_start; order_diff := 5; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* expt(glob_h, term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); glob_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 <= 6 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 6 + 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 := 6; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 6; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 6; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( expt(glob_h, calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum* expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1); term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 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 , 5 ) = y1 ;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * y2 ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2013-01-28T17:54:01-06:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest7"); logitem_str(html_log_file, "diff ( y2 , x , 5 ) = y1 ;"); 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, "mtest7 diffeq.mxt"); logitem_str(html_log_file, "mtest7 maple results"); logitem_str(html_log_file, "All Tests - All Languages"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * y2 ;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_good_digits(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end if end proc > # End Function number 12 > main(); ##############ECHO OF PROBLEM################# ##############temp/mtest7postode.ode################# diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; ! #BEGIN FIRST INPUT BLOCK Digits:=32; max_terms:=30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 5.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_look_poles := true; 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( cos(x)); end; exact_soln_y2 := proc(x) return( sin(x)); end; exact_soln_y2p := proc(x) return( cos(x)); end; exact_soln_y2pp := proc(x) return( -sin(x)); end; exact_soln_y2ppp := proc(x) return( -cos(x)); end; exact_soln_y2pppp := proc(x) return( 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=3.0MB, time=0.19 glob_desired_digits_correct = 10 desired_abs_gbl_error = 1.0000000000000000000000000000000e-10 range = 5 estimated_steps = 5000 step_error = 2.0000000000000000000000000000000e-14 est_needed_step_err = 2.0000000000000000000000000000000e-14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 value3 = 2.4795962632247974600749435458479e-105 max_value3 = 2.4795962632247974600749435458479e-105 value3 = 2.4795962632247974600749435458479e-105 best_h = 0.001 START of Soultion TOP MAIN SOLVE Loop x[1] = 0 y2[1] (analytic) = 0 y2[1] (numeric) = 0 absolute error = 0 relative error = -1 % Correct digits = -1 h = 0.001 y1[1] (analytic) = 1 y1[1] (numeric) = 1 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] = 0.001 y2[1] (analytic) = 0.00099999983333334166666646825397101 y2[1] (numeric) = 0.0010000000000000083333331349206349 absolute error = 1.6666666666666666666666389e-10 relative error = 1.6666669444444768518552411931143e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.99999950000004166666527777780258 y1[1] (numeric) = 0.99999949999999999999861111113591 absolute error = 4.166666666666666667e-14 relative error = 4.1666687500008680562418984579408e-12 % Correct digits = 13 h = 0.001 memory used=11.4MB, alloc=4.4MB, time=0.64 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.85 x[1] = 0.002 y2[1] (analytic) = 0.0019999986666669333333079365093474 y2[1] (numeric) = 0.0020000000000002666666412698412698 absolute error = 1.3333333333333333333319224e-09 relative error = 6.6666711111131851860529104136393e-05 % Correct digits = 6 h = 0.001 y1[1] (analytic) = 0.99999800000066666657777778412698 y1[1] (numeric) = 0.99999799999999999991111111746031 absolute error = 6.6666666666666666667e-13 relative error = 6.6666800000222222584037623948042e-11 % Correct digits = 12 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=1.05 x[1] = 0.003 y2[1] (analytic) = 0.0029999955000020249995660714828125 y2[1] (numeric) = 0.0030000000000020249995660714285714 absolute error = 4.4999999999999999999457589e-09 relative error = 0.00015000022500023625022238859585137 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.9999955000033749989875001627232 y1[1] (numeric) = 0.99999549999999999898750016272321 absolute error = 3.37499999999999999999e-12 relative error = 3.3750151875569533334391980870992e-10 % Correct digits = 11 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=1.25 x[1] = 0.004 y2[1] (analytic) = 0.0039999893333418666634158737382715 y2[1] (numeric) = 0.0040000000000085333300825396825396 absolute error = 1.06666666666666666659442681e-08 relative error = 0.00026666737777910518740656446875162 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.99999200001066666097777940317431 y1[1] (numeric) = 0.99999199999999999431111273650793 absolute error = 1.066666666666666666638e-11 relative error = 1.0666752000568892590196602984063e-09 % Correct digits = 10 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=1.46 x[1] = 0.005 y2[1] (analytic) = 0.004999979166692708317832346652129 y2[1] (numeric) = 0.0050000000000260416511656746031734 absolute error = 2.08333333333333333279510444e-08 relative error = 0.0004166684027828414484256496347327 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.99998750002604164496528746589513 y1[1] (numeric) = 0.99998749999999997829862079923114 absolute error = 2.604166666666666666399e-11 relative error = 2.6041992190890876485122095129110e-09 % Correct digits = 10 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=1.67 x[1] = 0.006 y2[1] (analytic) = 0.0059999640000647999444571706285623 y2[1] (numeric) = 0.0060000000000647999444571428571338 absolute error = 3.59999999999999999722285715e-08 relative error = 0.00060000360001512005693163741452432 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.99998200005399993520004165712619 y1[1] (numeric) = 0.99998199999999993520004165714285 absolute error = 5.399999999999999998334e-11 relative error = 5.4000972014580213437655283288958e-09 % Correct digits = 10 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=1.87 x[1] = 0.007 y2[1] (analytic) = 0.0069999428334733915032653889814512 y2[1] (numeric) = 0.007000000000140058169931944444395 absolute error = 5.71666666666666665554629438e-08 relative error = 0.00081667333614923829725365503214231 % Correct digits = 5 h = 0.001 y1[1] (analytic) = 0.99997550010004150326542075391521 y1[1] (numeric) = 0.99997549999999983659875408732638 absolute error = 1.0004166666666666658883e-10 relative error = 1.0004411773754267245297858434180e-08 % Correct digits = 9 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=2.09 x[1] = 0.008 y2[1] (analytic) = 0.0079999146669397329172321158996084 y2[1] (numeric) = 0.0080000000002730662505650793648643 absolute error = 8.53333333333333329634652559e-08 relative error = 0.0010666780445293990871943964007822 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99996800017066630257819387906919 y1[1] (numeric) = 0.9999679999999996359115272126984 absolute error = 1.7066666666666666637079e-10 relative error = 1.7067212814563934576608655038049e-08 % Correct digits = 9 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=2.29 x[1] = 0.009 y2[1] (analytic) = 0.0089998785004920740509992819119371 y2[1] (numeric) = 0.0090000000004920740509982142849283 absolute error = 1.214999999999999989323729912e-07 relative error = 0.0013500182251722277091022884687232 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99995950027337426188856762604806 y1[1] (numeric) = 0.99995949999999926188856762700892 absolute error = 2.7337499999999999903914e-10 relative error = 2.7338607206118176124012990144930e-08 % Correct digits = 9 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=45.7MB, alloc=4.5MB, time=2.51 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.5MB, time=2.72 x[1] = 0.01 y2[1] (analytic) = 0.0099998333341666646825424382690997 y2[1] (numeric) = 0.010000000000833331349206349203844 absolute error = 1.666666666666666639109347443e-07 relative error = 0.001666694444768521908103321926109 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99995000041666527778025793375221 y1[1] (numeric) = 0.99994999999999861111359126984126 absolute error = 4.1666666666666666391095e-10 relative error = 4.1668750086809085515694330209226e-08 % Correct digits = 9 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=2.92 x[1] = 0.011 y2[1] (analytic) = 0.010999778168008754466837648658227 y2[1] (numeric) = 0.011000000001342087800164484119836 absolute error = 2.21833333333333326835461609e-07 relative error = 0.0020167073366852353677434549568873 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99993950061003920617059421113112 y1[1] (numeric) = 0.9999394999999975395039275516121 absolute error = 6.1004166666666665951902e-10 relative error = 6.1007857604834573420171988133795e-08 % Correct digits = 9 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.5MB, time=3.13 x[1] = 0.012 y2[1] (analytic) = 0.0119997120020735928905285046671 y2[1] (numeric) = 0.012000000002073592890514285695671 absolute error = 2.87999999999999985781028571e-07 relative error = 0.0024000576009676945746595707352705 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99992800086399585281066421150868 y1[1] (numeric) = 0.99992799999999585281066422857144 absolute error = 8.6399999999999998293724e-10 relative error = 8.6406221173269856972679872092889e-08 % Correct digits = 9 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=3.34 x[1] = 0.013 y2[1] (analytic) = 0.012999633836427429216593310414133 y2[1] (numeric) = 0.013000000003094095883230753923356 absolute error = 3.66166666666666637443509223e-07 relative error = 0.0028167460043420490852641476605133 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99991550119003496278550915647919 y1[1] (numeric) = 0.99991549999999329611884252780262 absolute error = 1.19004166666666662867657e-09 relative error = 1.1901422322689824906093451167115e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.5MB, time=3.55 x[1] = 0.014 y2[1] (analytic) = 0.013999542671148512418012491760278 y2[1] (numeric) = 0.014000000004481845751288888787438 absolute error = 4.57333333333333276397027160e-07 relative error = 0.0032667733802179552087960992761617 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99990200160065620901437960917818 y1[1] (numeric) = 0.99990199999998954234771302222233 absolute error = 1.60066666666666658695585e-09 relative error = 1.6008235448116899860352409247426e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=3.76 x[1] = 0.015 y2[1] (analytic) = 0.014999437506328091099436296518797 y2[1] (numeric) = 0.015000000006328091099330356926162 absolute error = 5.62499999999999894060407365e-07 relative error = 0.0037501406286914931224576695995072 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99988750210935917975106359667124 y1[1] (numeric) = 0.99988749999998417975106375558062 absolute error = 2.10937499999999984109062e-09 relative error = 2.1096123269368501091876568583833e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=3.97 x[1] = 0.016 y2[1] (analytic) = 0.015999317342071413405852864078503 y2[1] (numeric) = 0.016000000008738080072330158289437 absolute error = 6.82666666666666477294210934e-07 relative error = 0.004266848716548317435724843328515 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99987200273064336508429948113164 y1[1] (numeric) = 0.9998719999999766984176331174609 absolute error = 2.73066666666666636367074e-09 relative error = 2.7310162292865836999453812939417e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=4.17 x[1] = 0.017 y2[1] (analytic) = 0.016999181178498726917256755855751 y2[1] (numeric) = 0.017000000011832060250263292792211 absolute error = 8.18833333333333006536936460e-07 relative error = 0.0048168986772670412222864602733837 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99985550348000814243828707939278 y1[1] (numeric) = 0.99985549999996647577162096827998 absolute error = 3.48004166666666611111280e-09 relative error = 3.4805445932480669321616684869418e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=80.1MB, alloc=4.5MB, time=4.39 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=4.60 x[1] = 0.018 y2[1] (analytic) = 0.017999028015746278528318051989944 y2[1] (numeric) = 0.018000000015746278527771426961372 absolute error = 9.71999999999999453374971428e-07 relative error = 0.0054002916110228535394351229689481 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99983800437395276107331153036308 y1[1] (numeric) = 0.99983799999995276107331251428812 absolute error = 4.37399999999999901607496e-09 relative error = 4.3747086836719847517662762249178e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=4.81 x[1] = 0.019 y2[1] (analytic) = 0.018998856853967314312052134696812 y2[1] (numeric) = 0.019000000020633980977829560573743 absolute error = 1.143166666666665777425876931e-06 relative error = 0.0060170286846913704561010673555568 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99981950542997632558649540967827 y1[1] (numeric) = 0.9998194999999346589198304325691 absolute error = 5.43004166666666497710917e-09 relative error = 5.4310219366359072186882474505921e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.5MB, time=5.02 x[1] = 0.02 y2[1] (analytic) = 0.019998666693333079366490294692975 y2[1] (numeric) = 0.020000000026666412698412693282039 absolute error = 1.333333333333331922398589064e-06 relative error = 0.0066671111318527196120884422872764 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99980000666657777841269559083748 y1[1] (numeric) = 0.99979999999991111174603174604029 absolute error = 6.66666666666666384479719e-09 relative error = 6.6680002222583734113208667235776e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=5.23 x[1] = 0.021 y2[1] (analytic) = 0.020998456534033817643351314104522 y2[1] (numeric) = 0.021000000034033817641162491224834 absolute error = 1.543499999999997811177120312e-06 relative error = 0.007350540252795858332441925878759 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99977950810325588132556235192481 y1[1] (numeric) = 0.99977949999988088132556694845285 absolute error = 8.10337499999999540347196e-09 relative error = 8.1051621225698194098407622788267e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=5.44 x[1] = 0.022 y2[1] (analytic) = 0.02199822537627977175771419727134 y2[1] (numeric) = 0.022000000042946438421053953615607 absolute error = 1.774666666666663339756344267e-06 relative error = 0.0080673174145231253222403088142168 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99975800976050919593877922685587 y1[1] (numeric) = 0.99975799999984252927211987939191 absolute error = 9.76066666666665934746396e-09 relative error = 9.7630292244468389570591488578661e-07 % Correct digits = 8 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=5.65 x[1] = 0.023 y2[1] (analytic) = 0.022997972220302182777692239857764 y2[1] (numeric) = 0.02300000005363551610606207930479 absolute error = 2.027833333333328369839447026e-06 relative error = 0.0088174440507550259684826088415286 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99973551165983606320750309990763 y1[1] (numeric) = 0.99973549999979439654084784927689 absolute error = 1.166004166666665525063074e-08 relative error = 1.1663126427616617715543768060525e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=5.86 x[1] = 0.024 y2[1] (analytic) = 0.02399769606635428999310864667882 y2[1] (numeric) = 0.02400000006635428998582853330739 absolute error = 2.303999999999992719886628570e-06 relative error = 0.0096009216619352512771014590699751 % Correct digits = 4 h = 0.001 y1[1] (analytic) = 0.99971201382373458193002504208987 y1[1] (numeric) = 0.99971199999973458193004251436195 absolute error = 1.382399999999998252772792e-08 relative error = 1.3827982267738734610440610797809e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=6.07 x[1] = 0.025 y2[1] (analytic) = 0.024997395914712330662173929649734 y2[1] (numeric) = 0.02500000008137899731832831328723 absolute error = 2.604166666666656154383637496e-06 relative error = 0.010417751815235930474507948845646 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99968751627570258624967338769563 y1[1] (numeric) = 0.99968749999966091958303300173653 absolute error = 1.627604166666664038595910e-08 relative error = 1.6281129254571876581690169477975e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=114.4MB, alloc=4.5MB, time=6.29 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.6MB, time=6.50 x[1] = 0.026 y2[1] (analytic) = 0.02599707076567653973516533926464 y2[1] (numeric) = 0.026000000099009873053536415987037 absolute error = 2.929333333333318371076722397e-06 relative error = 0.011267936144563117304441801189671 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99966201904023762215698154912569 y1[1] (numeric) = 0.9996619999995709554903537843262 absolute error = 1.904066666666662776479949e-08 relative error = 1.9047104225233366180134831172595e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.6MB, time=6.71 x[1] = 0.027 y2[1] (analytic) = 0.026996719619572149554108606008347 y2[1] (numeric) = 0.027000000119572149533094503591604 absolute error = 3.280499999999978985897583257e-06 relative error = 0.012151476350562510052270758984709 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99963552214283692299214406781718 y1[1] (numeric) = 0.9996354999994619229922008058937 absolute error = 2.214337499999994326192348e-08 relative error = 2.2151448712559754842328575678131e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.6MB, time=6.92 x[1] = 0.028 y2[1] (analytic) = 0.027996341476750389527462292102751 y2[1] (numeric) = 0.028000000143417056164977570008922 absolute error = 3.658666666666637515277906171e-06 relative error = 0.013068374200625405330253334630433 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99960802560999738394778539881849 y1[1] (numeric) = 0.99960799999933071728120035604035 absolute error = 2.561066666666658504277814e-08 relative error = 2.5620709328577088381677902960432e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.6MB, time=7.13 x[1] = 0.029 y2[1] (analytic) = 0.028995935337589485778805078986833 y2[1] (numeric) = 0.029000000170922819072160607051566 absolute error = 4.064833333333293355528064733e-06 relative error = 0.014018631528894885658649668290203 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99957952946921553557206692623928 y1[1] (numeric) = 0.99957949999917386890551619520789 absolute error = 2.947004166666655073103139e-08 relative error = 2.9482438163089805251870921415898e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.6MB, time=7.34 x[1] = 0.03 y2[1] (analytic) = 0.029995500202495660768526341926262 y2[1] (numeric) = 0.030000000202495660714285270497689 absolute error = 4.499999999999945758928571427e-06 relative error = 0.015002250236272240878936150139059 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99955003374898751627215870646661 y1[1] (numeric) = 0.9995499999989875162723214296809 absolute error = 3.374999999999983727678571e-08 relative error = 3.3765193197397582485415520691243e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.6MB, time=7.54 x[1] = 0.031 y2[1] (analytic) = 0.030995035071904132887520390145338 y2[1] (numeric) = 0.031000000238570799481326546007686 absolute error = 4.965166666666593806155862348e-06 relative error = 0.016019232290423623436750704977749 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99951953847880904381810343567299 y1[1] (numeric) = 0.99951949999876737715166263658981 absolute error = 3.848004166666644079908318e-08 relative error = 3.8498538733149798898547899728764e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.6MB, time=7.75 x[1] = 0.032 y2[1] (analytic) = 0.031994538946280116021884778870325 y2[1] (numeric) = 0.032000000279613449258259414868914 absolute error = 5.461333333333236374635998589e-06 relative error = 0.017069579725786937573567225843105 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99948804368917538584710113775004 y1[1] (numeric) = 0.99948799999850871918074473891485 absolute error = 4.369066666666635639883519e-08 relative error = 4.3713045836347640196850546226099e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.6MB, time=7.96 x[1] = 0.033 y2[1] (analytic) = 0.03299401082611981908762312866916 y2[1] (numeric) = 0.033000000326119818959725519536794 absolute error = 5.989499999999872102390867634e-06 relative error = 0.018153294643578962467469589335844 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99945554941158132936824406838078 y1[1] (numeric) = 0.99945549999820632936866613049092 absolute error = 4.941337499999957793788986e-08 relative error = 4.9440292796504226026713899946027e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.6MB, time=8.17 x[1] = 0.034 y2[1] (analytic) = 0.033993449711951445534352917468021 y2[1] (numeric) = 0.034000000378618112033699828936099 absolute error = 6.550666666666499346911468078e-06 relative error = 0.019270379211802709364768001861079 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99942205567852114926773233051278 y1[1] (numeric) = 0.99942199999785448260163455101379 absolute error = 5.568066666666609777949899e-08 relative error = 5.5712865600973494809385353654714e-06 % Correct digits = 7 h = 0.001 memory used=152.5MB, alloc=4.6MB, time=8.39 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.6MB, time=8.60 x[1] = 0.035 y2[1] (analytic) = 0.034992854604336192817018741620246 y2[1] (numeric) = 0.035000000437669525933157303481261 absolute error = 7.145833333333116138561861015e-06 relative error = 0.020420835665255012745573125640692 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99938756252348857581460169601424 y1[1] (numeric) = 0.99938749999744690914869521104773 absolute error = 6.252604166666590648496651e-08 relative error = 6.2564358424458938379895729299549e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.6MB, time=8.81 x[1] = 0.036 y2[1] (analytic) = 0.035992224503869251834611574397632 y2[1] (numeric) = 0.036000000503869251554739559769061 absolute error = 7.775999999999720127985371429e-06 relative error = 0.021604666305534355567816528608488 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99935206998097676116699612778233 y1[1] (numeric) = 0.999351999996976761168003667035 absolute error = 6.998399999999899246074733e-08 relative error = 7.0029374133713635045773956445284e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.6MB, time=9.02 x[1] = 0.037 y2[1] (analytic) = 0.036991558411180806334894583268148 y2[1] (numeric) = 0.037000000577847472643421534891063 absolute error = 8.442166666666308526951622915e-06 relative error = 0.022821873501048928635579505847085 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99931557808647824487901849602845 y1[1] (numeric) = 0.99931549999643657821367694630746 absolute error = 7.809004166666534154972099e-08 relative error = 7.8143524807443386693320660051542e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.6MB, time=9.23 x[1] = 0.038 y2[1] (analytic) = 0.037990855326937032284136101317525 y2[1] (numeric) = 0.038000000660270365162178150306591 absolute error = 9.145333333332878042048989066e-06 relative error = 0.024072459687024924138966244744602 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99927808687648491840819398188693 y1[1] (numeric) = 0.99927799999581825174325742210078 absolute error = 8.688066666666493655978615e-08 relative error = 8.6943432271425123015494369094806e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.6MB, time=9.44 x[1] = 0.039 y2[1] (analytic) = 0.038990114251841097200850383165022 y2[1] (numeric) = 0.039000000751841096625650975209889 absolute error = 9.886499999999424800592044867e-06 relative error = 0.025356427365515063414131664103387 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99923959638848798862358166088065 y1[1] (numeric) = 0.99923949999511298862582493857168 absolute error = 9.639337499999775672230897e-08 relative error = 9.6466728648853093828378664650578e-06 % Correct digits = 7 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.6MB, time=9.65 x[1] = 0.04 y2[1] (analytic) = 0.039989334186634159452546811715915 y2[1] (numeric) = 0.040000000853300825396814889317327 absolute error = 1.0666666666665944268077601412e-05 relative error = 0.026673779105407358973449061597588 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99920010666097794031457075812913 y1[1] (numeric) = 0.99919999999431127365079368581873 absolute error = 1.0666666666666377707231040e-07 relative error = 1.0675205692592572879597773352158e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.6MB, time=9.86 x[1] = 0.041 y2[1] (analytic) = 0.040988514132096367514488259084749 y2[1] (numeric) = 0.041000000965429699945644744992045 absolute error = 1.1486833333332431156485907296e-05 relative error = 0.028024517542434110857177967134759 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99915961773344449770039906649961 y1[1] (numeric) = 0.9991594999934028310374313249074 absolute error = 1.1774004166666296774159221e-07 relative error = 1.1783907153268640270898742358569e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.6MB, time=10.07 x[1] = 0.042 y2[1] (analytic) = 0.041987653089047859189459343014283 y2[1] (numeric) = 0.042000001089047858068782028614285 absolute error = 1.2347999999998879322685600002e-05 relative error = 0.029408645379181137359368334131075 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99911812964637658494043201817947 y1[1] (numeric) = 0.99911799999237658494513886289996 absolute error = 1.2965399999999529315527951e-07 relative error = 1.2976843893913170377549277805164e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=186.9MB, alloc=4.6MB, time=10.28 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.6MB, time=10.50 x[1] = 0.043 y2[1] (analytic) = 0.042986750058349760787545359105131 y2[1] (numeric) = 0.043000001225016426069201521095756 absolute error = 1.3251166666665281656161990625e-05 relative error = 0.030826165385097240182113419441357 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99907564244126228564524189938771 y1[1] (numeric) = 0.99907549999122061898453077789116 absolute error = 1.4245004166666071112149655e-07 relative error = 1.4258183826660116219355881948875e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.6MB, time=10.71 x[1] = 0.044 y2[1] (analytic) = 0.043985804040905186264922709160433 y2[1] (numeric) = 0.044000001374238517894877957425693 absolute error = 1.4197333333331629955248265260e-05 relative error = 0.032277080396503904073640418115596 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99903215616058880138852769714285 y1[1] (numeric) = 0.99903199998992213472935589405049 absolute error = 1.5617066666665917180309236e-07 relative error = 1.5632196191446275660074520112129e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.6MB, time=10.92 x[1] = 0.045 y2[1] (analytic) = 0.044984814037660236320661686938394 y2[1] (numeric) = 0.045000001537660234235452685124784 absolute error = 1.5187499999997914790998186390e-05 relative error = 0.033761393316605231007105144108068 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99898767084784240921991706616396 y1[1] (numeric) = 0.99898749998846740922930050667213 absolute error = 1.7085937499999061655949183e-07 relative error = 1.7103251620210887684704991383117e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.6MB, time=11.13 x[1] = 0.046 y2[1] (analytic) = 0.045983779049604997450542524593155 y2[1] (numeric) = 0.046000001716271661575900321470764 absolute error = 1.6222666666664125357796877609e-05 relative error = 0.03527910711549810895833479513085 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9989421865475084181786929030993 y1[1] (numeric) = 0.99894199998684175152371625723368 absolute error = 1.8656066666665497664586562e-07 relative error = 1.8675822202627778292906447317505e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.6MB, time=11.34 x[1] = 0.047 y2[1] (analytic) = 0.046982698077774540956885646071211 y2[1] (numeric) = 0.047000001911107871206195409346224 absolute error = 1.7303833333330249309763275013e-05 relative error = 0.036830224830182615342141121727211 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9988957033050711248084880143524 y1[1] (numeric) = 0.99889549998502945815631625846502 absolute error = 2.0332004166665217175588738e-07 relative error = 2.0354481553371596186762297832582e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.6MB, time=11.55 x[1] = 0.048 y2[1] (analytic) = 0.047981570123249921913397117716371 y2[1] (numeric) = 0.048000002123249918185979071544956 absolute error = 1.8431999999996272581953828585e-05 relative error = 0.038414749564572655168205150022844 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99884822116701376767299236280714 y1[1] (numeric) = 0.99884799998301376769088396942878 absolute error = 2.2118399999998210839337836e-07 relative error = 2.2143904880919714682240064938522e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.6MB, time=11.76 x[1] = 0.049 y2[1] (analytic) = 0.048980394187159178084030331321055 y2[1] (numeric) = 0.049000002353825840263225663357975 absolute error = 1.9608166666662179195332036920e-05 relative error = 0.040032684489506833978913997257749 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99879974018081848087271837774091 y1[1] (numeric) = 0.99879949998077681422804032061394 absolute error = 2.4020004166664467805712697e-07 relative error = 2.4048869057891412582824510728261e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.6MB, time=11.97 x[1] = 0.05 y2[1] (analytic) = 0.04997916927067832879486500084549 y2[1] (numeric) = 0.050000002604011656745909423244104 absolute error = 2.0833333333327951044422398614e-05 relative error = 0.041684032842759565632910281663028 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99875026039496624656287081115652 y1[1] (numeric) = 0.99874999997829957992311558904454 absolute error = 2.6041666666663975522211198e-07 relative error = 2.6074252692925983122301661204832e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.6MB, time=12.18 x[1] = 0.051 y2[1] (analytic) = 0.050977894375032373758004601009052 y2[1] (numeric) = 0.051000002875032367325671121372701 absolute error = 2.2108499999993567666520363649e-05 relative error = 0.043368797929052414999495176395576 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9986997818589368464723686226592 memory used=225.0MB, alloc=4.6MB, time=12.39 y1[1] (numeric) = 0.99869949997556184650517352340536 absolute error = 2.8188337499996719509925384e-07 relative error = 2.8225036204101456512891780840966e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.6MB, time=12.61 x[1] = 0.052 y2[1] (analytic) = 0.051976568501496291846493423939535 y2[1] (numeric) = 0.052000003168162950852484705807656 absolute error = 2.3434666666659005991281868121e-05 relative error = 0.045086983120065675630407303741818 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99864830462320881242406737385262 y1[1] (numeric) = 0.99864799997254214579723621918692 absolute error = 3.0465066666662683115466570e-07 relative error = 3.0506301893895658126228369899776e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.6MB, time=12.81 x[1] = 0.053 y2[1] (analytic) = 0.052975190651396039819254479046544 y2[1] (numeric) = 0.05300000348472936405932394608217 absolute error = 2.4812833333324240069467035626e-05 relative error = 0.046838591854450182476881423272686 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99859582873925937585623161202751 y1[1] (numeric) = 0.99859549996921770923775924385223 absolute error = 3.2877004166661847236817528e-07 relative error = 3.2923234025691360889419102262674e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.6MB, time=13.02 x[1] = 0.054 y2[1] (analytic) = 0.053973759826109550995049511264322 y2[1] (numeric) = 0.054000003826109540235829073892969 absolute error = 2.6243999999989240779562628647e-05 relative error = 0.048623627637839359721273249027187 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99854235425956441634530772166625 y1[1] (numeric) = 0.99854199996556441640340751202806 absolute error = 3.5429399999994190020963819e-07 relative error = 3.5481118901827327097967587240486e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.6MB, time=13.23 x[1] = 0.055 y2[1] (analytic) = 0.05497227502706773387446246378722 y2[1] (numeric) = 0.055000004193734387849973420620501 absolute error = 2.7729166666653975510956833281e-05 relative error = 0.050442094042861503793919748675498 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99848788123759840913004872098633 y1[1] (numeric) = 0.99848749996155674253318341072375 absolute error = 3.8127604166659686531026258e-07 relative error = 3.8185344943197071533049967143270e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.6MB, time=13.45 x[1] = 0.056 y2[1] (analytic) = 0.055970735255755470708907763397574 y2[1] (numeric) = 0.056000004589088789116730051358197 absolute error = 2.9269333333318407822287960623e-05 relative error = 0.0522939947091523016472879447541 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99843240972783437163704347939343 y1[1] (numeric) = 0.99843199995716770505395967458085 absolute error = 4.0977066666658308380481258e-07 relative error = 4.1041402770397214523899119471396e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.6MB, time=13.66 x[1] = 0.057 y2[1] (analytic) = 0.056969139513712616015664859460901 y2[1] (numeric) = 0.05700000501371259851273839510906 absolute error = 3.0865499999982497073535648159e-05 relative error = 0.054179333343367584360849567373278 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99837593978574380900770383031052 y1[1] (numeric) = 0.99837549995236880910747051115733 absolute error = 4.3983337499990023331915319e-07 relative error = 4.4054885286427330418226816897362e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.6MB, time=13.87 x[1] = 0.058 y2[1] (analytic) = 0.057967486802534995037940501637101 y2[1] (numeric) = 0.058000005469201641235970870781587 absolute error = 3.2518666666646198030369144486e-05 relative error = 0.056098113719196316151503911805541 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99831847146779665862676405239132 y1[1] (numeric) = 0.99831799994712999207881547625028 absolute error = 4.7152066666654794857614104e-07 relative error = 4.7231487760943233816089492772293e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.6MB, time=14.08 x[1] = 0.059 y2[1] (analytic) = 0.058965776123875402148960296328588 y2[1] (numeric) = 0.059000005957208711609399508589289 absolute error = 3.4229833333309460439212260701e-05 relative error = 0.058050339677373818865756946088734 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99826000483146123365234819061394 y1[1] (numeric) = 0.99825949994141956712653159926161 absolute error = 5.0489004166652581659135233e-07 relative error = 5.0577007916065682886758909152165e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=259.4MB, alloc=4.6MB, time=14.29 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.6MB, time=14.51 x[1] = 0.06 y2[1] (analytic) = 0.059964006479444599199091137856983 y2[1] (numeric) = 0.060000006479444571427662566428773 absolute error = 3.5999999999972228571428571790e-05 relative error = 0.06003601512569523203125110583491 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99820053993520416554766168718284 y1[1] (numeric) = 0.99819999993520416571429025861141 absolute error = 5.3999999999983337142857143e-07 relative error = 5.4097346013746516125381705564578e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.6MB, time=14.72 x[1] = 0.061 y2[1] (analytic) = 0.060962176871012313804996167329149 y2[1] (numeric) = 0.061000007037678948245731140780502 absolute error = 3.7830166666634440734973451353e-05 relative error = 0.062055144039029208546627318717527 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99814007683849034561436479054242 y1[1] (numeric) = 0.99813949992844867914427630720437 absolute error = 5.7691004166647008848333805e-07 relative error = 5.7798504944694276017891830643438e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=14.93 x[1] = 0.062 y2[1] (analytic) = 0.061960286300408237579823970120792 y2[1] (numeric) = 0.062000007633741533608575771643781 absolute error = 3.9721333333296028751801522989e-05 relative error = 0.064107730459331846090088632364572 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99807861560178286552768620912431 y1[1] (numeric) = 0.99807799992111619909230794795487 absolute error = 6.1568066666643537826116944e-07 relative error = 6.1686590318861410270172052519642e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.6MB, time=15.14 x[1] = 0.063 y2[1] (analytic) = 0.062958333769523024303433781871613 y2[1] (numeric) = 0.063000008269522981220833040983301 absolute error = 4.1674499999956917399259111688e-05 relative error = 0.06619377849566085432842338951792 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9980161562865429568733364747094 y1[1] (numeric) = 0.998015499913167957144756859377 absolute error = 6.5637337499972857961533240e-07 relative error = 6.5767810557495178522243417238679e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.6MB, time=15.35 x[1] = 0.064 y2[1] (analytic) = 0.063956318280309288031658532849996 y2[1] (numeric) = 0.064000008946975905055472164128547 absolute error = 4.3690666666617023813631278551e-05 relative error = 0.068313292324189958009635216016227 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99795269895522992968628147848646 y1[1] (numeric) = 0.99795199990456326333732907124628 absolute error = 6.9905066666634895240724018e-07 relative error = 7.0048476986754429811697826301525e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.6MB, time=15.56 x[1] = 0.065 y2[1] (analytic) = 0.064954238834782601143607621507354 y2[1] (numeric) = 0.065000009668115877400461573529536 absolute error = 4.5770833333276256853952022182e-05 relative error = 0.070466276188223536023717173420356 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99788824367130110999143764102859 y1[1] (numeric) = 0.99788749989525944369576809034045 absolute error = 7.4377604166629566955068814e-07 relative error = 7.4535003932894453474085672066197e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.6MB, time=15.77 x[1] = 0.066 y2[1] (analytic) = 0.065952094435022492326011370002533 y2[1] (numeric) = 0.066000010435022426842435494232609 absolute error = 4.7915999999934516424124230076e-05 relative error = 0.072652734398211496517498291622363 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9978227904992117763463511754871 y1[1] (numeric) = 0.99782199988521177677854277626718 absolute error = 7.9061399999956780839921992e-07 relative error = 7.9233908819022143672939287762508e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.6MB, time=15.98 x[1] = 0.067 y2[1] (analytic) = 0.066949884083173444493609177434988 y2[1] (numeric) = 0.067000011249840036186360510398328 absolute error = 5.0127166666591692751332963340e-05 relative error = 0.07487267133176438815088235054307 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99775633950441509538592490131835 y1[1] (numeric) = 0.99775549987437342922158346738749 absolute error = 8.3963004166616434143393086e-07 relative error = 8.4151812263423755339969579067150e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.6MB, time=16.19 x[1] = 0.068 y2[1] (analytic) = 0.06794760678144589264458345048173 y2[1] (numeric) = 0.068000012114779140310202122139815 absolute error = 5.2405333333247665618671658085e-05 relative error = 0.077126091433668747583191236823659 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99768889075336205636925706381129 y1[1] (numeric) = 0.99768799986269539028513085684401 absolute error = 8.9089066666608412620696728e-07 relative error = 8.9295438179467566978138017996912e-05 % Correct digits = 6 h = 0.001 memory used=297.5MB, alloc=4.6MB, time=16.41 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.6MB, time=16.62 x[1] = 0.069 y2[1] (analytic) = 0.068945261532117221650041456087275 y2[1] (numeric) = 0.069000013032117123953591291914087 absolute error = 5.4751499999902303549835826812e-05 relative error = 0.079412999215902683279718474129644 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99762044431350140472865761257148 y1[1] (numeric) = 0.99761949985012640540276311870427 absolute error = 9.4446337499932589449386721e-07 relative error = 9.4671613877083803538204027642348e-05 % Correct digits = 6 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.6MB, time=16.83 x[1] = 0.07 y2[1] (analytic) = 0.069942847337532763976547306807887 y2[1] (numeric) = 0.070000014004199319439490979651027 absolute error = 5.7166666666555462943672843140e-05 relative error = 0.081733399257651695729992627284771 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99755100025327957462090838993974 y1[1] (numeric) = 0.99754999983661290873266778422983 absolute error = 1.00041666666588824060570991e-06 relative error = 0.00010028727016582421042440829408692 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.6MB, time=17.04 x[1] = 0.071 y2[1] (analytic) = 0.070940363200106797340706356361279 y2[1] (numeric) = 0.071000015033440004327862665754466 absolute error = 5.9651833333206987156309393187e-05 relative error = 0.084087296205324734170645223686661 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9974805586421406204808346780796 y1[1] (numeric) = 0.99747949982209895471122586828291 absolute error = 1.05882004166576960880979669e-06 relative error = 0.00010614944145950370761860996671674 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.6MB, time=17.26 x[1] = 0.072 y2[1] (analytic) = 0.071937808122323542294804350880499 y2[1] (numeric) = 0.07200001612232339900033286105747 absolute error = 6.2207999999856705528510176971e-05 relative error = 0.086474694772570489907173633466318 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99740911955052614757725655115641 y1[1] (numeric) = 0.99740799980652614860897674588314 absolute error = 1.11974399999896827980527327e-06 relative error = 0.00011226526588242659093588916814763 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.6MB, time=17.47 x[1] = 0.073 y2[1] (analytic) = 0.072935181106738159742503750316011 y2[1] (numeric) = 0.073000017273404664174859602759133 absolute error = 6.4836166666504432355852443122e-05 relative error = 0.088895599740293926330286015236795 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.9973366830498752415713894766508 y1[1] (numeric) = 0.99733549978983357608903327892797 absolute error = 1.18326004166548235619772283e-06 relative error = 0.00011864198537719978553979968854466 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.6MB, time=17.68 x[1] = 0.074 y2[1] (analytic) = 0.073932481155977748383599704372739 y2[1] (numeric) = 0.074000018489310898349398935313019 absolute error = 6.7537333333149965799230940280e-05 relative error = 0.091350015956673045723912980388934 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99726324921262439707776460740017 y1[1] (numeric) = 0.99726199977195773176801769309123 absolute error = 1.24944066666530974691430894e-06 relative error = 0.00012528694581413569505355925094304 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.6MB, time=17.88 x[1] = 0.075 y2[1] (analytic) = 0.07492970727274234208683823830925 y2[1] (numeric) = 0.075000019772742135173571375177731 absolute error = 7.0312499999793086733136868481e-05 relative error = 0.093837948337175892963369068227834 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99718881811220744522774020344191 y1[1] (numeric) = 0.99718749975283244677958970491542 absolute error = 1.31835937499844815049852649e-06 relative error = 0.00013220759710224722790595020364309 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.6MB, time=18.10 x[1] = 0.076 y2[1] (analytic) = 0.07592685845980590718979927586399 y2[1] (numeric) = 0.076000021126472340747328358277869 absolute error = 7.3162666666433557529082413879e-05 relative error = 0.096359401864577796203546470155305 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99711338982305548023567662014081 y1[1] (numeric) = 0.99711199973238881534063939911449 absolute error = 1.39009066666489503722102632e-06 relative error = 0.00013941149330183762094903115823829 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=331.8MB, alloc=4.6MB, time=18.31 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.6MB, time=18.53 x[1] = 0.077 y2[1] (analytic) = 0.076923933720017339724847199508653 y2[1] (numeric) = 0.077000022553350410845618668958795 absolute error = 7.6088833333071120771469450142e-05 relative error = 0.098914381588978844658423706313168 % Correct digits = 3 h = 0.001 y1[1] (analytic) = 0.99703696442059678496784829641972 y1[1] (numeric) = 0.99703549971055512032021835610499 absolute error = 1.46471004166464762994031473e-06 relative error = 0.00014690629273868771888039434904856 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.6MB, time=18.74 x[1] = 0.078 y2[1] (analytic) = 0.077920932056301462570151722161243 y2[1] (numeric) = 0.078000024056301168068054849151079 absolute error = 7.9091999999705497903126989836e-05 relative error = 0.10150289262782160357457315565819 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99695954198125675551416717417515 y1[1] (numeric) = 0.99695799968725675781128352978468 absolute error = 1.54229399999770288364439047e-06 relative error = 0.00015469975811984340659711392165343 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.6MB, time=18.95 x[1] = 0.079 y2[1] (analytic) = 0.078917852471660022524781919421034 y2[1] (numeric) = 0.079000025638326358912579586390188 absolute error = 8.2173166666336387797666969154e-05 relative error = 0.10412494016590906650275348344308 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9968811225824578247627929771481 y1[1] (numeric) = 0.9968794996624161607053293755791 absolute error = 1.62292004166405746360156900e-06 relative error = 0.00016279975665100593030319210656063 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.6MB, time=19.16 x[1] = 0.08 y2[1] (analytic) = 0.079914693969172687306876347314497 y2[1] (numeric) = 0.080000027302505650772132079263805 absolute error = 8.5333333332963465255731949308e-05 relative error = 0.10678052945542284497307611134127 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99680170630261938497770677463351 y1[1] (numeric) = 0.99679999963595272126998472877799 absolute error = 1.70666666666370772204585552e-06 relative error = 0.00017121426015552788198870379751319 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.6MB, time=19.37 x[1] = 0.081 y2[1] (analytic) = 0.080911455551998042473892247465161 y2[1] (numeric) = 0.081000029051997628853314378783072 absolute error = 8.8573499999586379422131317911e-05 relative error = 0.10946966581594159568063894817186 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99672129322115770937932525244839 y1[1] (numeric) = 0.99671949960778271272965193318481 absolute error = 1.79361337499664967331926358e-06 relative error = 0.00017995134519501766079845151304372 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.6MB, time=19.58 x[1] = 0.082 y2[1] (analytic) = 0.081908136223374588263936919521264 y2[1] (numeric) = 0.082000030890040793016057704094979 absolute error = 9.1894666666204752120784573715e-05 relative error = 0.11219235463445968528992565636211 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99663988341848587272823411053763 y1[1] (numeric) = 0.99663799957781920984926672010424 absolute error = 1.88384066666287896739043339e-06 relative error = 0.00018901919319155526381226371949129 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.6MB, time=19.79 x[1] = 0.083 y2[1] (analytic) = 0.082904734986621736357184419592911 y2[1] (numeric) = 0.083000032819954554533288730870905 absolute error = 9.5297833332818176104311277994e-05 relative error = 0.11494860136540609296767478379384 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99655747697601367091212000347765 y1[1] (numeric) = 0.99655549954597200852125833769418 absolute error = 1.97743004166239086166578347e-06 relative error = 0.00019842609055152229786959757709504 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.6MB, time=20.00 x[1] = 0.084 y2[1] (analytic) = 0.083901250845140806556380823365096 y2[1] (numeric) = 0.084000034845140232769595850621035 absolute error = 9.8783999999426213215027255939e-05 relative error = 0.11773841153066355075533015592246 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99647407397614753953598143693918 y1[1] (numeric) = 0.9964719995121475443557904307104 absolute error = 2.07446399999518019100622878e-06 relative error = 0.00020818042879104914328934543807645 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.6MB, time=20.22 x[1] = 0.085 y2[1] (analytic) = 0.084897682802416023385441373464374 y2[1] (numeric) = 0.085000036969082051777895399095759 absolute error = 0.000102354166666028392454025631385 relative error = 0.12056179071958792189359201175277 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99638967450229047151570002989151 y1[1] (numeric) = 0.99638749947624881027436417067385 absolute error = 2.17502604166124133585921766e-06 relative error = 0.00021829070466308223966320205824217 % memory used=370.0MB, alloc=4.6MB, time=20.43 Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.6MB, time=20.65 x[1] = 0.086 y2[1] (analytic) = 0.085894029862015512605142912565098 y2[1] (numeric) = 0.086000039195348136813097851843302 absolute error = 0.000106009333332624207954939278204 relative error = 0.12341874458902781721299749273099 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99630427863884193367505454897002 y1[1] (numeric) = 0.99630199943817527310686613649248 absolute error = 2.27920066666056818841247754e-06 relative error = 0.00022876552028607450333914153903513 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.6MB, time=20.86 x[1] = 0.087 y2[1] (analytic) = 0.086890291027592297644915086625826 y2[1] (numeric) = 0.087000041527591510761773984897525 absolute error = 0.000109750499999213116858898271699 relative error = 0.1263092788633444497058692688751 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9962178864711977823462611179861 y1[1] (numeric) = 0.99621549939782278919214444557144 absolute error = 2.38707337499315411667241466e-06 relative error = 0.00023961358327430192576200065710665 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.6MB, time=21.07 x[1] = 0.088 y2[1] (analytic) = 0.087886465302885295949733886547727 y2[1] (numeric) = 0.088000043969551090486820998471058 absolute error = 0.000113578666665794537087111923331 relative error = 0.12923339933443172739638232464604 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99613049808575017797412400203214 y1[1] (numeric) = 0.99612799935508351898219763544758 absolute error = 2.49873066665899192636658456e-06 relative error = 0.00025084370686980944150239570801124 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.6MB, time=21.28 x[1] = 0.089 y2[1] (analytic) = 0.088882551691720315241121181444477 y2[1] (numeric) = 0.089000046525052683086128601426594 absolute error = 0.000117494833332367845007419982117 relative error = 0.13219111186173658462691124130751 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99604211356988749872388236202374 y1[1] (numeric) = 0.99603949930984584065006179598634 absolute error = 2.61426004165807382056603740e-06 relative error = 0.000262464810075989194584746861358 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.6MB, time=21.49 x[1] = 0.09 y2[1] (analytic) = 0.089878549198011049691253982607137 y2[1] (numeric) = 0.09000004919800998206424505419316 absolute error = 0.000121499999998932372991071586023 relative error = 0.13518242237227955188023371594402 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99595273301199425309283937182514 y1[1] (numeric) = 0.99594999926199426270148245218139 absolute error = 2.73374999999039135691964375e-06 relative error = 0.00027448591779279437162158708343749 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.6MB, time=21.70 x[1] = 0.091 y2[1] (analytic) = 0.090874456825760076009187264137752 y2[1] (numeric) = 0.091000051992425563416043167684448 absolute error = 0.000125595166665487406855903546696 relative error = 0.13820733686067556425858056312961 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99586235650145099152586108632152 y1[1] (numeric) = 0.99585949921140933559045869759987 absolute error = 2.85729004165593540238872165e-06 relative error = 0.00028691616095359181027613820422919 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.6MB, time=21.91 x[1] = 0.092 y2[1] (analytic) = 0.091870273579059849438194254111873 y2[1] (numeric) = 0.092000054912391881621386255662736 absolute error = 0.000129781333332032183192001550863 relative error = 0.14126586138915500874193806655726 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99577098412863421703483344493189 y1[1] (numeric) = 0.99576799915796756233874807851837 absolute error = 2.98497066665469608536641352e-06 relative error = 0.00029976477666365663170989743258346 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.6MB, time=22.12 x[1] = 0.093 y2[1] (analytic) = 0.092865998462093699663228199012698 y2[1] (numeric) = 0.093000057962092265549794037874424 absolute error = 0.000134059499998565886565838861726 relative error = 0.14435800208758501034942529800477 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99567861598491629482216679109816 y1[1] (numeric) = 0.99567549910154130815942172879763 absolute error = 3.11688337498666274506230053e-06 relative error = 0.0003130411083403121859282528434203 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=404.3MB, alloc=4.6MB, time=22.34 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.6MB, time=22.56 x[1] = 0.094 y2[1] (analytic) = 0.093861630479136826627509694058062 y2[1] (numeric) = 0.094000061145801914274108491161764 absolute error = 0.000138430666665087646598797103702 relative error = 0.1474837651534909573289869130324 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9955852521626653609084382842383 y1[1] (numeric) = 0.99558199904199870908456025554658 absolute error = 3.25312066665182387802869172e-06 relative error = 0.00032675460585471863931650211239494 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.6MB, time=22.77 x[1] = 0.095 y2[1] (analytic) = 0.094857168634557296257243762915944 y2[1] (numeric) = 0.095000064467888892792159645629761 absolute error = 0.000142895833331596534915882713817 relative error = 0.15064315685207826550206097991642 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99549089275524522976426357651361 y1[1] (numeric) = 0.99548749897920357959718187562908 absolute error = 3.39377604165016708170088453e-06 relative error = 0.00034091482567531357416265782276749 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.6MB, time=22.98 x[1] = 0.096 y2[1] (analytic) = 0.095852611932817036093470962174359 y2[1] (numeric) = 0.096000067932815127655431322817478 absolute error = 0.000147455999998091561960360643119 relative error = 0.15383618351625438189130161392837 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99539553785701530094649012253066 y1[1] (numeric) = 0.99539199891301531926749530306997 absolute error = 3.53894399998167899481946069e-06 relative error = 0.00035553143101290801059366455520461 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.6MB, time=23.19 x[1] = 0.097 y2[1] (analytic) = 0.096847959378472830830056878797539 y2[1] (numeric) = 0.097000071545137402503726812688942 absolute error = 0.000152112166664571673669933891403 relative error = 0.15706285154665102776085758618192 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99529918756333046473880548577688 y1[1] (numeric) = 0.99529549884328881839357088741989 absolute error = 3.68872004164634523459835699e-06 relative error = 0.00037061419196744130210971439209812 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.6MB, time=23.40 x[1] = 0.098 y2[1] (analytic) = 0.097843209976177317756824482661829 y2[1] (numeric) = 0.098000075309508353504834486120458 absolute error = 0.000156865333331035748010003458629 relative error = 0.16032316741164668120013066846547 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9952018419705410067968550011736 y1[1] (numeric) = 0.99519799876987436264652450314177 absolute error = 3.84320066664415033049803183e-06 relative error = 0.0003861729856763983967888218743452 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.6MB, time=23.61 x[1] = 0.099 y2[1] (analytic) = 0.098838362730679982106833891121925 y2[1] (numeric) = 0.099000079230677464698193339418247 absolute error = 0.000161716499997482591359448296322 relative error = 0.16361713764738929938336127568232 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99510350117599251179796414862088 y1[1] (numeric) = 0.99509949869261753672030969008518 absolute error = 4.00248337497507765445853570e-06 relative error = 0.00040221779646489299725230767382354 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.6MB, time=23.82 x[1] = 0.1 y2[1] (analytic) = 0.099833416646828152306814198410622 y2[1] (numeric) = 0.10000008331349206324155846725295 absolute error = 0.000166666666663910934744268842328 relative error = 0.1669447688578192806388139894088 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99500416527802576609556198780387 y1[1] (numeric) = 0.99499999861135912698621454511831 absolute error = 4.16666666663910934744268556e-06 relative error = 0.00041875871599742019363295020712845 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.6MB, time=24.03 x[1] = 0.101 y2[1] (analytic) = 0.10082837072956799512975211952319 y2[1] (numeric) = 0.10100008756289831455966646024539 absolute error = 0.0001717168333303194299143407222 relative error = 0.17030606771469266646276180259502 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99490383437597665937840299982896 y1[1] (numeric) = 0.99489949852593502315216086499103 absolute error = 4.33585004163622624213483793e-06 relative error = 0.00043580594343128218507291132283684 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.6MB, time=24.24 x[1] = 0.102 y2[1] (analytic) = 0.10182322398394551074864229608065 y2[1] (numeric) = 0.1020000919839422173939007232813 absolute error = 0.00017686799999670664525842720065 relative error = 0.1737010409576045836148954303637 % Correct digits = 2 h = 0.001 memory used=442.5MB, alloc=4.6MB, time=24.46 y1[1] (analytic) = 0.99480250857017608533468567645987 y1[1] (numeric) = 0.99479799843617611892690404050635 absolute error = 4.51013399996640778163595352e-06 relative error = 0.000453369785571690746699748832806 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.6MB, time=24.67 x[1] = 0.103 y2[1] (analytic) = 0.10281797541510752769040421050459 y2[1] (numeric) = 0.10300009658177059875195671047085 absolute error = 0.00018212116666307106155249996626 relative error = 0.17712969539401292643321279788728 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99470018796194984132116719282663 y1[1] (numeric) = 0.99469549834190821168923320208157 absolute error = 4.68962004162963193399074506e-06 relative error = 0.00047146065702855014058752506302207 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.6MB, time=24.88 x[1] = 0.104 y2[1] (analytic) = 0.10381262402830269768897075466946 y2[1] (numeric) = 0.10400010136163210875650707250241 absolute error = 0.00018747733332941106753631783295 relative error = 0.18059203789926227950787385776713 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99459687265361852703737449448465 y1[1] (numeric) = 0.99459199824295190116227211678455 absolute error = 4.87441066662587510237770010e-06 relative error = 0.00049008908037492421090784468895687 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.6MB, time=25.09 x[1] = 0.105 y2[1] (analytic) = 0.10480716882888249043655360002678 y2[1] (numeric) = 0.10500010632887821539186671196815 absolute error = 0.00019293749999572495531311194137 relative error = 0.18408807541660808085493721840396 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99449256274849744220501312460406 y1[1] (numeric) = 0.99448749813912248709298233693492 absolute error = 5.06460937495511203078766914e-06 relative error = 0.00050926568630719144531425217574883 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.6MB, time=25.30 x[1] = 0.106 y2[1] (analytic) = 0.10580160882230218823209061801872 y2[1] (numeric) = 0.10600011148896419914765774206235 absolute error = 0.00019850266666201091556712404363 relative error = 0.18761781495724102573232769614612 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99438725835089648325267611187222 y1[1] (numeric) = 0.99438199803022986593697110036463 absolute error = 5.26032066661731570501150759e-06 relative error = 0.00052900121380689182658444262367013 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.6MB, time=25.51 x[1] = 0.107 y2[1] (analytic) = 0.10679594301412188052588070241646 y2[1] (numeric) = 0.10700011684745014755847434387129 absolute error = 0.00020417383332826703259364145483 relative error = 0.19118126360031171124181785017105 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99428095956612003900595623439178 y1[1] (numeric) = 0.99427549791607842654870748243667 absolute error = 5.46165004161245724875195511e-06 relative error = 0.00054930651030426934066985069525522 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.6MB, time=25.72 x[1] = 0.108 y2[1] (analytic) = 0.10779017041000745835941144903159 y2[1] (numeric) = 0.10800012241000194963854751728597 absolute error = 0.00020995199999449127913606825438 relative error = 0.19477842849295552186224183325297 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99417366650046688538306596945332 y1[1] (numeric) = 0.99416799779646694487725129992599 absolute error = 5.66870399994050581466952733e-06 relative error = 0.00057019253184351404957304973935083 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.6MB, time=25.93 x[1] = 0.109 y2[1] (analytic) = 0.10878429001573160869938525305544 y2[1] (numeric) = 0.10900012818239229021040972037632 absolute error = 0.00021583816666068151102446732088 relative error = 0.1984093168503177560605965089288 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99406537926123007909607043355394 y1[1] (numeric) = 0.99405949767118847766760026687152 absolute error = 5.88159004160142847016668242e-06 relative error = 0.00059167034324970767989169448950095 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.6MB, time=26.14 x[1] = 0.11 y2[1] (analytic) = 0.10977830083717480866494949008345 y2[1] (numeric) = 0.11000013417050164412655939186693 absolute error = 0.00022183333332683546160990178348 relative error = 0.20207393595557899412912275683173 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99395609795669685035783961141985 y1[1] (numeric) = 0.9939499975400302551677619025134 absolute error = 6.10041666659519007770890645e-06 relative error = 0.00061375111829747672043516107324737 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=476.8MB, alloc=4.6MB, time=26.35 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.6MB, time=26.57 x[1] = 0.111 y2[1] (analytic) = 0.11077220188032631964713655367693 y2[1] (numeric) = 0.11100014038031927038312535115029 absolute error = 0.00022793849999295073598879747336 relative error = 0.20577229315998070739789922964194 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99384582269614849459482716707199 y1[1] (numeric) = 0.99383949740277357284165769143526 absolute error = 6.32529337492175316947563673e-06 relative error = 0.0006364461398813570650382712572472 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.6MB, time=26.78 x[1] = 0.112 y2[1] (analytic) = 0.11176599215128518131951963010521 y2[1] (numeric) = 0.11200014681794420612453107006377 absolute error = 0.00023415466665902480501143995856 relative error = 0.20950439588285110897392154816579 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99373455358986026316578412414666 y1[1] (numeric) = 0.9937279972591936820879679960367 absolute error = 6.55633066658107781612810996e-06 relative error = 0.00065976680018787427956723586216423 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.6MB, time=26.99 x[1] = 0.113 y2[1] (analytic) = 0.1127596706562612055390901996952 y2[1] (numeric) = 0.11300015348958626053815881044059 absolute error = 0.00024048283332505499906861074539 relative error = 0.21327025161163124615908204049045 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99362229074910125308651669674845 y1[1] (numeric) = 0.99361549710905967996502722146729 absolute error = 6.79364004157312148947528116e-06 relative error = 0.00068372460086934361513792563033158 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.6MB, time=27.20 x[1] = 0.114 y2[1] (analytic) = 0.11375323640157597013636336399366 y2[1] (numeric) = 0.11400016040156700863801362122359 absolute error = 0.00024692399999103850165025722993 relative error = 0.21706986790190133470090866036923 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99350903428613429576079854606851 y1[1] (numeric) = 0.99350199695213439792187973315942 absolute error = 7.03733399989783891881290909e-06 relative error = 0.00070833115321939393274749561484277 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.6MB, time=27.41 x[1] = 0.115 y2[1] (analytic) = 0.1147466883936638125937172087197 y2[1] (numeric) = 0.1150001675603207849363871887025 absolute error = 0.0002534791666569723426699799828 relative error = 0.22090325237740733503136667174371 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99339478431421584471754873184649 y1[1] (numeric) = 0.99338749678817428953560802710352 absolute error = 7.28752604155518194070474297e-06 relative error = 0.00073359817835021974785897912343068 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.6MB, time=27.62 x[1] = 0.116 y2[1] (analytic) = 0.11574002563907282361097252425083 y2[1] (numeric) = 0.11600017497239567700252153320158 absolute error = 0.00026014933332285339154900895075 relative error = 0.2247704127300877706504730753689 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99327954094759586235438762148898 y1[1] (numeric) = 0.99327199661692931725504565301597 absolute error = 7.54433066654509934196847301e-06 relative error = 0.00075953750737156564697646596726906 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.6MB, time=27.83 x[1] = 0.117 y2[1] (analytic) = 0.11673324714446584055721931814593 y2[1] (numeric) = 0.11700018264445451890727254530395 absolute error = 0.00026693549998867835005322715802 relative error = 0.22867135672010078881292159199855 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99316330430151770568768401327901 y1[1] (numeric) = 0.99315549643814283815098839055662 absolute error = 7.80786337486753669562272239e-06 relative error = 0.00078616108157144737190763265074815 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.6MB, time=28.04 x[1] = 0.118 y2[1] (analytic) = 0.11772635191662144080789666796104 y2[1] (numeric) = 0.11800019058327588455277335445231 absolute error = 0.00027383866665444374487668649127 relative error = 0.23260609217585146367736532026408 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99304607449221801110920772362005 y1[1] (numeric) = 0.99303799625155148867301817875996 absolute error = 8.07824066652243618954486009e-06 relative error = 0.00081348095259861391123245363660203 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.6MB, time=28.26 x[1] = 0.119 y2[1] (analytic) = 0.11871933896243493496613257736117 y2[1] (numeric) = 0.11900019879575508088609752251225 memory used=514.9MB, alloc=4.6MB, time=28.48 absolute error = 0.00028085983332014591996494515108 relative error = 0.23657462699401934207945496716842 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99292785163692657814950288165217 y1[1] (numeric) = 0.99291949605688506841305529885124 absolute error = 8.35558004150973644758280093e-06 relative error = 0.00084150928264675498248365640466811 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.6MB, time=28.69 x[1] = 0.12 y2[1] (analytic) = 0.11971220728891935996735061427097 y2[1] (numeric) = 0.12000020728890514099592205462441 absolute error = 0.00028799999998578102857144035344 relative error = 0.24057696913958623209118282120021 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99280863585386625224809816785763 y1[1] (numeric) = 0.9927999958538664228757553106264 absolute error = 8.63999999982937234285723123e-06 relative error = 0.00087025834464045833269766149649692 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.6MB, time=28.90 x[1] = 0.121 y2[1] (analytic) = 0.12070495590320647206615022654028 y2[1] (numeric) = 0.12100021606985781709119021940497 absolute error = 0.00029526016665134502503999286469 relative error = 0.24461312664586423453053641472584 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9926884272622528065306712264356 y1[1] (numeric) = 0.99267949564221132525586824258247 absolute error = 8.93162004148127480298385313e-06 relative error = 0.00089974052242292132931615396898508 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.6MB, time=29.11 x[1] = 0.122 y2[1] (analytic) = 0.12169758381254773970446774832719 y2[1] (numeric) = 0.12200022514586457336077417028018 absolute error = 0.00030264133331683365630642195299 relative error = 0.24868310761452401758692111723648 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99256722598229482259328547427195 y1[1] (numeric) = 0.99255799542162835722267853599318 absolute error = 9.23056066646537060693827877e-06 relative error = 0.00092996831094542135790985629421705 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.6MB, time=29.32 x[1] = 0.123 y2[1] (analytic) = 0.1226900900243153362600252291201 y2[1] (numeric) = 0.12300023452429757871313735946008 absolute error = 0.00031014449998224245311213033998 relative error = 0.25278692021562333472926772909683 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99244503213519357029381852225733 y1[1] (numeric) = 0.99243549519181878871164524313284 absolute error = 9.53694337478158217327912449e-06 relative error = 0.0009609543164585495878593155131806 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.6MB, time=29.53 x[1] = 0.124 y2[1] (analytic) = 0.12368247354600313267407433703294 y2[1] (numeric) = 0.12400024421265069939499673576854 absolute error = 0.0003177706666475667209223987356 relative error = 0.25692457268763578606519951853833 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99232184584314288655070241751501 y1[1] (numeric) = 0.99231199495247645672336297986026 absolute error = 9.85089066642982733943765475e-06 relative error = 0.00099271125670521271196439002995901 % Correct digits = 5 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.6MB, time=29.74 x[1] = 0.125 y2[1] (analytic) = 0.12467473338522768995744270871211 y2[1] (numeric) = 0.12500025421854049148798471725188 absolute error = 0.00032552083331280153054200853977 relative error = 0.26109607333747982332109307877607 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99219766722932905314909690778825 y1[1] (numeric) = 0.99218749470328764312996513278336 absolute error = 1.017252604141001913177500489e-05 relative error = 0.0010252519611154073109664441587128 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.6MB, time=29.96 x[1] = 0.126 y2[1] (analytic) = 0.12566686854972925157389023989174 y2[1] (numeric) = 0.12600026454970719328231092918569 absolute error = 0.00033339599997794170842068929395 relative error = 0.26530143054054799861432888874623 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9920724964179306735546179218037 y1[1] (numeric) = 0.99206199444393095148909182123431 absolute error = 1.050197399972206552610056939e-05 relative error = 0.0010585893710027715391568614838264 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.6MB, time=30.17 x[1] = 0.127 y2[1] (analytic) = 0.12665887804737273569978293332346 y2[1] (numeric) = 0.1270002752140157175264236977896 absolute error = 0.00034139716664298182664076446614 relative error = 0.26954065274073645719049055604174 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99194633353411854873474445187208 y1[1] (numeric) = 0.99193549417407718286554611429467 absolute error = 1.083936004136586919833757741e-05 relative error = 0.0010927365397629188726142114167872 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=549.3MB, alloc=4.6MB, time=30.38 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.6MB, time=30.59 x[1] = 0.128 y2[1] (analytic) = 0.12765076088614872735909204448972 y2[1] (numeric) = 0.12800028621945664355167128964224 absolute error = 0.00034952533330791619257924515252 relative error = 0.2738137484504746742997364162585 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9918191787040555519880280173089 y1[1] (numeric) = 0.99180799389338921066076300311982 absolute error = 1.118481066634132726501418908e-05 relative error = 0.0011277066330735587071620972024765 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.6MB, time=30.80 x[1] = 0.129 y2[1] (analytic) = 0.12864251607417447043272639018397 y2[1] (numeric) = 0.12900029757414720927096288646312 absolute error = 0.00035778149997273883823649627915 relative error = 0.27812072625075543638803347421676 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99169103205489650278122987945538 y1[1] (numeric) = 0.991679493601521854450216628822 absolute error = 1.153845337464833101325063338e-05 relative error = 0.0011635129290964086388722384025961 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.6MB, time=31.01 x[1] = 0.13 y2[1] (analytic) = 0.12963414261969485954120581070831 y2[1] (numeric) = 0.13000030928633230305042928459529 absolute error = 0.00036616666663744350922347388698 relative error = 0.28246159479116506678041161248148 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99156189371478803959451217115181 y1[1] (numeric) = 0.99154999329812175282889226618208 absolute error = 1.190041666628676561990496973e-05 relative error = 0.0012001688186809033058545671259645 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.6MB, time=31.22 x[1] = 0.131 y2[1] (analytic) = 0.13062563953108343179968390309763 y2[1] (numeric) = 0.13100032136438545545308330818121 absolute error = 0.00037468183330202365339940508358 relative error = 0.28683636278991389603486557574704 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99143176381286849177481009546157 y1[1] (numeric) = 0.99141949298282723526495056347067 absolute error = 1.227083004125650985953199090e-05 relative error = 0.0012376878055697047161799261572157 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=568.4MB, alloc=4.6MB, time=31.44 x[1] = 0.132 y2[1] (analytic) = 0.13161700581684335844432827043014 y2[1] (numeric) = 0.13200033381680983085347992467507 absolute error = 0.00038332799996647240915165424493 relative error = 0.29124503903386697714700347944899 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99130064247926775039751334026303 y1[1] (numeric) = 0.9912879926552681929617125386706 absolute error = 1.264982399955743580080159243e-05 relative error = 0.0012760835066060190330732401032746 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.6MB, time=31.65 x[1] = 0.133 y2[1] (analytic) = 0.13260824048560843632906666092685 y2[1] (numeric) = 0.13300034665223921892237605097734 absolute error = 0.00039210616663078259330939005049 relative error = 0.29568763237857504578701350151059 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99116852984510713813658584701707 y1[1] (numeric) = 0.99115549231506594872809483240427 absolute error = 1.303753004118940849101461280e-05 relative error = 0.0013153696519427248349976899606771 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.6MB, time=31.85 x[1] = 0.134 y2[1] (analytic) = 0.13359934254614407929170750017626 y2[1] (numeric) = 0.13400035987943902598039003811131 absolute error = 0.00040101733329494668868253793505 relative error = 0.30016415174830572575199501173235 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99103542604249927814325406357971 y1[1] (numeric) = 0.99102199196183312585762571788125 absolute error = 1.343408066615228562834569846e-05 relative error = 0.0013555600852533179149253700814447 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.6MB, time=32.07 x[1] = 0.135 y2[1] (analytic) = 0.13459031100734830938844345044656 y2[1] (numeric) = 0.1350003735073072662196608219871 absolute error = 0.00041006249995895683121737154054 relative error = 0.30467460613607497981817668720733 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9909013312045479619333948023605 y1[1] (numeric) = 0.99088749159517351601617336819372 absolute error = 1.383960937444591722143416678e-05 relative error = 0.0013966687639446777299590681109394 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=583.6MB, alloc=4.6MB, time=32.28 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.6MB, time=32.50 x[1] = 0.136 y2[1] (analytic) = 0.13558114487825274799574676266417 y2[1] (numeric) = 0.13600038754487555279250672741548 absolute error = 0.00041924266662280479675996475131 relative error = 0.3092190046036788061790221692645 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99076624546534801628375481642801 y1[1] (numeric) = 0.99075199121468194613851888130016 absolute error = 1.425425066607014523593512785e-05 relative error = 0.0014387097593716606595351179599345 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.6MB, time=32.71 x[1] = 0.137 y2[1] (analytic) = 0.13657184316802360677866531924609 y2[1] (numeric) = 0.13700040200131008876608391214207 absolute error = 0.00042855883328648198741859289598 relative error = 0.31379735628172518065670355078514 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99063016895998516913713519733158 y1[1] (numeric) = 0.99061549081994414433390756305052 absolute error = 1.467814004102480322763428106e-05 relative error = 0.0014816972570535252777006790636211 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.6MB, time=32.92 x[1] = 0.138 y2[1] (analytic) = 0.13756240488596267852452839957234 y2[1] (numeric) = 0.13800041688591265794204443727181 absolute error = 0.00043801199994997941751603769947 relative error = 0.31840967036966624487590445761025 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99049310182453591451667468944385 y1[1] (numeric) = 0.99047799041053660480071296861972 absolute error = 1.511141399930971596172082413e-05 relative error = 0.0015256455568921948924222492425031 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.6MB, time=33.13 x[1] = 0.139 y2[1] (analytic) = 0.13855282904150832784107133447554 y2[1] (numeric) = 0.13900043220812161554019395004384 absolute error = 0.0004476031666132876991226155683 relative error = 0.32305595613583074059039771678344 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99035504419606737644936700652949 y1[1] (numeric) = 0.99033948998602645175034920272997 absolute error = 1.555421004092469901780379952e-05 relative error = 0.0015705690733923626525476918409237 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.6MB, time=33.34 x[1] = 0.14 y2[1] (analytic) = 0.13954311464423648171798835170537 y2[1] (numeric) = 0.14000044797751287874514896449803 absolute error = 0.00045733333327639702716061279266 relative error = 0.32773622291745669035432760312037 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9902159962126371718989482270114 y1[1] (numeric) = 0.99019998954597130234056797905686 absolute error = 1.600666666586955838024795454e-05 relative error = 0.0016164823358834445709135303494612 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.6MB, time=33.55 x[1] = 0.141 y2[1] (analytic) = 0.14053326070386161995092305089768 y2[1] (numeric) = 0.14100046420380091711499372514619 absolute error = 0.00046720349993929716407067424851 relative error = 0.33245048012072432473161343701788 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.99007595801329327270829133503572 y1[1] (numeric) = 0.9900594890899191286182779392287 absolute error = 1.646892337414409001339580702e-05 relative error = 0.0016633999887433858601647270146463 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.6MB, time=33.76 x[1] = 0.142 y2[1] (analytic) = 0.14152326623023776542690608414029 y2[1] (numeric) = 0.14200048089683974285093663832337 absolute error = 0.00047721466660197742403055418308 relative error = 0.33719873722078925623837988540828 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98993492973807386655144596492939 y1[1] (numeric) = 0.98991798861740811847202473184366 absolute error = 1.694112066574807942123308573e-05 relative error = 0.0017113367916243260261376190665435 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.6MB, time=33.97 x[1] = 0.143 y2[1] (analytic) = 0.14251313023335947427024975678031 y2[1] (numeric) = 0.1430004980666239009269662554474 absolute error = 0.00048736783326442665671649866709 relative error = 0.34198100376181590021480970812948 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98979291152800721689546239699913 y1[1] (numeric) = 0.98977548812796653559427135194499 absolute error = 1.742340004068130119104505414e-05 relative error = 0.0017603076196801282121501523116131 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.6MB, time=34.18 x[1] = 0.144 y2[1] (analytic) = 0.14350285172336282584790940266096 y2[1] (numeric) = 0.14400051572328945907850679195797 absolute error = 0.00049766399992663323059738929701 relative error = 0.3467972893570111428243069080766 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98964990352511152197213984283608 y1[1] (numeric) = 0.98963198762111257845361924141042 absolute error = 1.791590399894351852060142566e-05 relative error = 0.0018103274637957783362490538377157 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=621.8MB, alloc=4.6MB, time=34.40 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.6MB, time=34.61 x[1] = 0.145 y2[1] (analytic) = 0.14449242971052641263332152850892 y2[1] (numeric) = 0.14500053387711499764907316523965 absolute error = 0.00050810416658858501575163673073 relative error = 0.35164760368865825637935229955199 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98950590587239477275984004836598 y1[1] (numeric) = 0.98948748709635423827711165072838 absolute error = 1.841877604053448272839763760e-05 relative error = 0.0018614114308186596123831625668643 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.6MB, time=34.82 x[1] = 0.146 y2[1] (analytic) = 0.14548186320527232992772886371659 y2[1] (numeric) = 0.14600055253852259929392553435659 absolute error = 0.00051868933325026936619667064 relative error = 0.35653195650815106219492941941129 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98936091871385460997550823281966 y1[1] (numeric) = 0.9893419865531891560427617626506 absolute error = 1.893216066545393274647016906e-05 relative error = 0.0019135747437917080956078396754329 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.6MB, time=35.03 x[1] = 0.147 y2[1] (analytic) = 0.14647115121816716543800259427676 y2[1] (numeric) = 0.14700057171807883853972332393965 absolute error = 0.00052942049991167310172072966289 relative error = 0.36145035763602834117189648416862 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98921494219447818007704437159081 y1[1] (numeric) = 0.98919548599110447848244907822811 absolute error = 1.945620337370159459529336270e-05 relative error = 0.0019668327421884549407792739785153 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.6MB, time=35.24 x[1] = 0.148 y2[1] (analytic) = 0.14746029275992298870997220312979 y2[1] (numeric) = 0.14800059142649577119917871406947 absolute error = 0.00054029866657278248920651093968 relative error = 0.36640281696200849231417975773271 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98906797646024199027616882059779 y1[1] (numeric) = 0.98904798540957671309532856575544 absolute error = 1.999105066527718084025484235e-05 relative error = 0.0020212008821499611137716564687972 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.6MB, time=35.45 x[1] = 0.149 y2[1] (analytic) = 0.14844928684139834041627348367598 y2[1] (numeric) = 0.14900061167463192363970957749153 absolute error = 0.00055132483323358322343609381555 relative error = 0.37138934444502443938516525289736 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98892002165811176256192726927181 y1[1] (numeric) = 0.98889948480807158217189807316639 absolute error = 2.053685004018039002919610542e-05 relative error = 0.0020766947367236503440467118467705 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.6MB, time=35.66 x[1] = 0.15 y2[1] (analytic) = 0.14943813247359922149772543868764 y2[1] (numeric) = 0.15000063247349328190509184498088 absolute error = 0.00056249999989406040736640629324 relative error = 0.37640995011325878591016915949554 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98877107793604228673498099865434 y1[1] (numeric) = 0.98874998418604387582887050444355 absolute error = 2.109374999841090611049421079e-05 relative error = 0.0021333299961040461574260445413065 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.6MB, time=35.87 x[1] = 0.151 y2[1] (analytic) = 0.1504268286676800821572469233262 y2[1] (numeric) = 0.15100065383423428068911127914546 absolute error = 0.00057382516655419853186435581926 relative error = 0.3814646440641792187333727881478 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98862114544297727245282941030121 y1[1] (numeric) = 0.98859948354293730405499826062323 absolute error = 2.166190003996839783114967798e-05 relative error = 0.0021911224678754188781642966097673 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.6MB, time=36.08 x[1] = 0.152 y2[1] (analytic) = 0.15141537443494481070532403843028 y2[1] (numeric) = 0.15200067576815879216021463641712 absolute error = 0.00058530133321398145489059798684 relative error = 0.38655343646457416033911515423855 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98847022432884920028611278075862 y1[1] (numeric) = 0.98844798287818434776799844599746 absolute error = 2.224145066485251811433476116e-05 relative error = 0.0022500880772563485398973522818002 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=656.1MB, alloc=4.6MB, time=36.30 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.6MB, time=36.51 x[1] = 0.153 y2[1] (analytic) = 0.15240376878684772225603942868975 y2[1] (numeric) = 0.15300069828672111463616019642862 absolute error = 0.00059692949987339238012076773887 relative error = 0.39167633755058867014894561743084 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98831831474457917178614418529584 y1[1] (numeric) = 0.98829548219120610888272834013522 absolute error = 2.283255337306290341584516062e-05 relative error = 0.0023102428673462096957468990906134 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.6MB, time=36.73 x[1] = 0.154 y2[1] (analytic) = 0.15339201073499454727267478975868 y2[1] (numeric) = 0.15400072140152696110766763741318 absolute error = 0.0006087106665324138349928476545 relative error = 0.39683335762776059500735025206164 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98816541684207675856382052335014 y1[1] (numeric) = 0.98814198148141215939076163636613 absolute error = 2.343536066459917305888698401e-05 relative error = 0.0023716029993735841688027221638861 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.6MB, time=36.94 x[1] = 0.155 y2[1] (analytic) = 0.15438009929114341996189803878732 y2[1] (numeric) = 0.15500074512433444761006723568964 absolute error = 0.00062064583319102764816919690232 relative error = 0.40202450707105696907057886662533 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98801153077423985038006356676048 y1[1] (numeric) = 0.9879874807482003894515169473915 absolute error = 2.405002603946092854661936898e-05 relative error = 0.0024341847529466078353793333263714 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=671.3MB, alloc=4.6MB, time=37.15 x[1] = 0.156 y2[1] (analytic) = 0.15536803346720586651554675426811 y2[1] (numeric) = 0.15600076946705508144194836671186 absolute error = 0.00063273599984921492640161244375 relative error = 0.40724979632491066331451483251288 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98785665669495450224794294033609 y1[1] (numeric) = 0.98783197999095685449509107870993 absolute error = 2.467670399764775285186162616e-05 relative error = 0.0024980045263052575848561006647807 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.6MB, time=37.36 x[1] = 0.157 y2[1] (analytic) = 0.15635581227524779319901964349465 y2[1] (numeric) = 0.15700079444175474922980728456462 absolute error = 0.00064498216650695603078764106997 relative error = 0.41250923590325728487904713612535 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98770079475909478054663393262434 y1[1] (numeric) = 0.98767547920905562133695057056728 absolute error = 2.531555003915920968336205706e-05 relative error = 0.0025630788365755846515621414570692 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.6MB, time=37.57 x[1] = 0.158 y2[1] (analytic) = 0.15734343472749047428528794932464 y2[1] (numeric) = 0.15800082006065470483769415618015 absolute error = 0.00065738533316423055240620685551 relative error = 0.41780283638957232646792334973424 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98754394512252260814736402290726 y1[1] (numeric) = 0.98751797840185861330463600916453 absolute error = 2.596672066399484272801374273e-05 relative error = 0.0026294243200259005660610797045273 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.6MB, time=37.78 x[1] = 0.159 y2[1] (analytic) = 0.15833089983631153983353886231754 y2[1] (numeric) = 0.15900084633613255712085932592967 absolute error = 0.00066994649982101728732046361213 relative error = 0.42313060843690856602458354001052 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98738610794208760855150299846715 y1[1] (numeric) = 0.98735947756871545437663460788076 absolute error = 2.663037337215417486839058639e-05 relative error = 0.0026970577323249220253285710277423 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.6MB, time=37.99 x[1] = 0.16 y2[1] (analytic) = 0.15931820661424596331146315968599 y2[1] (numeric) = 0.16000087328072325752239878561207 absolute error = 0.00068266666647729421093562592608 relative error = 0.42849256276793371690599851246917 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98722728337562694904095252401834 y1[1] (numeric) = 0.98719997670896331233357755929347 absolute error = 2.730666666363670737496472487e-05 relative error = 0.0027659959488018810336994983487734 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.6MB, time=38.20 x[1] = 0.161 y2[1] (analytic) = 0.16030535407398704906019944885553 y2[1] (numeric) = 0.16100090090712008751189882421783 absolute error = 0.0006955468331330384516993753623 relative error = 0.43388871017496832877806124116154 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98706747158196518284099201290235 y1[1] (numeric) = 0.98703947582192674092191965880349 absolute error = 2.799576003844191907235409886e-05 relative error = 0.0028362559647086067190941918770711 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=694.2MB, alloc=4.6MB, time=38.41 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.6MB, time=38.62 x[1] = 0.162 y2[1] (analytic) = 0.16129234122838741960094755077078 y2[1] (numeric) = 0.16200092922817564586507983118949 absolute error = 0.00070858799978822626413228041871 relative error = 0.43931906152002393945760786925827 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98690667272091409029573863718748 y1[1] (numeric) = 0.98687797490691752103025970069785 absolute error = 2.869781399656926547893648963e-05 relative error = 0.0029078548954835852819161910839941 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.6MB, time=38.83 x[1] = 0.163 y2[1] (analytic) = 0.16227916709046000278226371641693 y2[1] (numeric) = 0.163000958256902835783439226231 absolute error = 0.00072179116644283300117550981407 relative error = 0.44478362773484147792767430344721 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98674488695327251905638030119956 y1[1] (numeric) = 0.98671547396323450087846114751047 absolute error = 2.941299003801817791915368909e-05 relative error = 0.0029808099770180045871502237545225 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.6MB, time=39.05 x[1] = 0.164 y2[1] (analytic) = 0.1632658306733790187670505293435 y2[1] (numeric) = 0.16400098800647585185289348803621 absolute error = 0.00073515733309683308584295869271 relative error = 0.45028241982092991875412617726447 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98658211444082622328234139023756 y1[1] (numeric) = 0.98655197299016343521973357356796 absolute error = 3.014145066278806260781666960e-05 relative error = 0.0030551385659237899635805216457007 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.6MB, time=39.26 x[1] = 0.165 y2[1] (analytic) = 0.16425233099048096685825450728289 y2[1] (numeric) = 0.16500101849023116684041925361234 absolute error = 0.00074868749975019998216474632945 relative error = 0.45581544884960518813333384080297 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98641835534634770185554209329493 y1[1] (numeric) = 0.98638747198697682355583638363565 absolute error = 3.088335937087829970570965928e-05 relative error = 0.003130858139803637827698632441002 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.6MB, time=39.46 x[1] = 0.166 y2[1] (analytic) = 0.16523866705526561216228457724819 y2[1] (numeric) = 0.16600104972166851832769345916626 absolute error = 0.00076238266640290616540888191807 relative error = 0.4613827259620293218021000613815 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98625360983359603560791308551389 y1[1] (numeric) = 0.98622197095293374736556730760774 absolute error = 3.163888066228824234577790615e-05 relative error = 0.0032079862975230538037788471044923 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.6MB, time=39.68 x[1] = 0.167 y2[1] (analytic) = 0.16622483788139697208916476077408 y2[1] (numeric) = 0.16700108171445189518073249280081 absolute error = 0.00077624383305492309156773202673 relative error = 0.46698426236924987504258630651972 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98608787806731672356232834284434 y1[1] (numeric) = 0.9860554698872797063466991722148 absolute error = 3.240818003701721562917062954e-05 relative error = 0.0032865407594844020657705791393439 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.6MB, time=39.89 x[1] = 0.168 y2[1] (analytic) = 0.16721084248270430268843456923034 y2[1] (numeric) = 0.16800111448241052385453032853395 absolute error = 0.00079027199970622116609575930361 relative error = 0.47262006935223958501652384170583 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98592116021324151818711984796102 y1[1] (numeric) = 0.98588796878924645367152945075201 absolute error = 3.319142399506451559039720901e-05 relative error = 0.0033665393679029726810928616189701 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.6MB, time=40.10 x[1] = 0.169 y2[1] (analytic) = 0.16819667987318308481981077338977 y2[1] (numeric) = 0.16900114803953985453169561040588 absolute error = 0.00080446816635676971188483701611 relative error = 0.4782901582619362856645384260738 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98575345643808825966433893291046 y1[1] (numeric) = 0.98571946765805183025620809186241 absolute error = 3.398878003642940813084104805e-05 relative error = 0.0034480000870850737911189385111655 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=728.6MB, alloc=4.6MB, time=40.31 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.6MB, time=40.53 x[1] = 0.17 y2[1] (analytic) = 0.16918234906699601015762437667085 y2[1] (numeric) = 0.17000118240000254709408765467793 absolute error = 0.00081883333300653693646327800708 relative error = 0.48399454051928307540796214405139 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9855847669095607091719299902125 y1[1] (numeric) = 0.98554996649289959804401012844089 absolute error = 3.480041666111112791986177161e-05 relative error = 0.0035309410037081555181111037451406 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.6MB, time=40.74 x[1] = 0.171 y2[1] (analytic) = 0.1701678490784739670280467877005 y2[1] (numeric) = 0.17100121757812945692645133735175 absolute error = 0.00083336849965548989840454965125 relative error = 0.48973322761526873789205288495315 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98541509179634838117998327022891 y1[1] (numeric) = 0.98537946529297927230272056775731 absolute error = 3.562650336910887726270247160e-05 relative error = 0.003615380327102972543609885288651 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.6MB, time=40.95 x[1] = 0.172 y2[1] (analytic) = 0.17115317892211702607811935505273 y2[1] (numeric) = 0.17200125358842062055105083344812 absolute error = 0.00084807466630359447293147839539 relative error = 0.49550623111096841601109119100274 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98524443126812637476123446853214 y1[1] (numeric) = 0.98520796405746595293630006392998 absolute error = 3.646721066042182493440460216e-05 relative error = 0.0037013363895377923587997987633605 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.6MB, time=41.16 x[1] = 0.173 y2[1] (analytic) = 0.17213833761259542577560059521592 y2[1] (numeric) = 0.17300129044554624109230217368134 absolute error = 0.00086295283295081531670157846542 relative error = 0.50131356263758453945737565158513 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98507278549555520391597979276082 y1[1] (numeric) = 0.98503546278552015481100087391498 absolute error = 3.732271003504910497891884584e-05 relative error = 0.0037888276465046562431686384032217 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.6MB, time=41.37 x[1] = 0.174 y2[1] (analytic) = 0.17312332416475055773864561402361 y2[1] (numeric) = 0.17400132816434767357040458334743 absolute error = 0.00087800399959711583175896932382 relative error = 0.5071552338964880060376917433535 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98490015465028062691157618403252 y1[1] (numeric) = 0.98486196147628763709610359821138 absolute error = 3.819317399298981547258582114e-05 relative error = 0.0038778726770077000838510811316031 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.6MB, time=41.58 x[1] = 0.175 y2[1] (analytic) = 0.17410813759359595189433239195141 y2[1] (numeric) = 0.17500136675983841002297056741226 absolute error = 0.00089322916624245812863817546085 relative error = 0.51303125665925961700238501696598 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98472653890493347463669735339954 y1[1] (numeric) = 0.98468746012889923161944620751813 absolute error = 3.907877603424301725114588141e-05 relative error = 0.0039684901838535422044027174270311 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.6MB, time=41.79 x[1] = 0.176 y2[1] (analytic) = 0.17509277691431826146504977483591 y2[1] (numeric) = 0.17600140624720506445365470493862 absolute error = 0.00090862933288680298860493010271 relative error = 0.51894164276773176663372782647458 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98455193843312947797051727907732 y1[1] (numeric) = 0.9845119587424706702379178566147 absolute error = 3.997969065880773259942246262e-05 relative error = 0.0040606989939437454283899719452139 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.6MB, time=42.00 x[1] = 0.177 y2[1] (analytic) = 0.17607724114227824778176218370968 y2[1] (numeric) = 0.17700144664180835760678111512985 absolute error = 0.00092420549953010982501893142017 relative error = 0.52488640413403038634182940263251 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98437635340946909416699379524751 y1[1] (numeric) = 0.98433545731610241122309098677501 absolute error = 4.089609336668294390280847250e-05 relative error = 0.0041545180585693606601072359022036 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.6MB, time=42.21 x[1] = 0.178 y2[1] (analytic) = 0.17706152929301176492316623056969 y2[1] (numeric) = 0.17800148795918410156696955639063 absolute error = 0.00093995866617233664380332582094 relative error = 0.53086555274061714351790200094978 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98419978400953733225442588813777 y1[1] (numeric) = 0.98415795584887946466216621806222 absolute error = 4.182816065786759225967007555e-05 relative error = 0.0042499664537075593219474171732765 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=766.7MB, alloc=4.6MB, time=42.42 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.6MB, time=42.64 x[1] = 0.179 y2[1] (analytic) = 0.17804564038223074417975460100464 y2[1] (numeric) = 0.17900153021504418418276011891375 absolute error = 0.00095588983281344000300551790911 relative error = 0.53687910064033189539626112497573 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98402223040990357745045929980641 y1[1] (numeric) = 0.98397945433987121687440553289103 absolute error = 4.277607003236057605376691538e-05 relative error = 0.0043470633803203620454585549384573 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.6MB, time=42.85 x[1] = 0.18 y2[1] (analytic) = 0.17902957342582417834180273969921 y2[1] (numeric) = 0.18000157342527755331323647039437 absolute error = 0.00097199999945337497143373069516 relative error = 0.54292705995643539817800545012081 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98384369278812141459271602461153 y1[1] (numeric) = 0.98379995278813125384323025228408 absolute error = 4.373999999016074948577232745e-05 relative error = 0.0044458281646554710709196928671167 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.6MB, time=43.06 x[1] = 0.181 y2[1] (analytic) = 0.18001332743985910581029405091082 y2[1] (numeric) = 0.1810016176059512008966476135505 absolute error = 0.00098829016609209508635356263968 relative error = 0.54900944288265227167089206824641 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98366417132272845058522426772069 y1[1] (numeric) = 0.98361945119269718366416130628991 absolute error = 4.472013003126692106296143078e-05 relative error = 0.0045462802585492138683664249293686 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.6MB, time=43.27 x[1] = 0.182 y2[1] (analytic) = 0.18099690144058159452979950307546 y2[1] (numeric) = 0.18200166277331114684002811318982 absolute error = 0.00100476133272955231022861011436 relative error = 0.55512626168321421970149505428573 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98348366619324613586082641921602 y1[1] (numeric) = 0.98343794955259045800878030007178 absolute error = 4.571664065567785204611914424e-05 relative error = 0.0046484392397316055513930049430708 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.6MB, time=43.49 x[1] = 0.183 y2[1] (analytic) = 0.18198029444441772574232770474512 y2[1] (numeric) = 0.18300170894378342272881674960861 absolute error = 0.00102141449936569698648904486349 relative error = 0.56127752869290350655731013777053 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98330217758017958485974358137227 y1[1] (numeric) = 0.98325544786681619260489087721922 absolute error = 4.672971336339225485270415305e-05 relative error = 0.0047523248121335377137562469649211 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.6MB, time=43.70 x[1] = 0.184 y2[1] (analytic) = 0.18296350546797457756116169808868 y2[1] (numeric) = 0.18400175613397505535547355413809 absolute error = 0.00103825066600047779431185604941 relative error = 0.56746325631709668971804546040077 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98311970566501739552447617052807 y1[1] (numeric) = 0.98307194613436298673306088187809 absolute error = 4.775953065440879141528864998e-05 relative error = 0.0048579568061961013778092579461307 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.6MB, time=43.90 x[1] = 0.185 y2[1] (analytic) = 0.18394653352804120836369889620145 y2[1] (numeric) = 0.1850018043606750500660951816666 absolute error = 0.00105527083263384170239628546515 relative error = 0.57368345703180860913691803057816 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98293625063023146781122109863481 y1[1] (numeric) = 0.98288744435420274173972682133947 absolute error = 4.880627602872607149427729534e-05 relative error = 0.0049653551791820518031029746664571 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.6MB, time=44.11 x[1] = 0.186 y2[1] (analytic) = 0.18492937764158964000231077146534 y2[1] (numeric) = 0.18600185364085537392402857396315 absolute error = 0.00107247599926573392171780249781 relative error = 0.57993814338373663333435756305935 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98275181265927682121798702305087 y1[1] (numeric) = 0.98270194252529047856704313077337 absolute error = 4.987013398634265094389227750e-05 relative error = 0.0050745400154894229631131795343108 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=801.1MB, alloc=4.6MB, time=44.33 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.6MB, time=44.54 x[1] = 0.187 y2[1] (analytic) = 0.18591203682577584083223908418196 y2[1] (numeric) = 0.18700190399167193868948286660779 absolute error = 0.00108986716589609785724378242583 relative error = 0.58622732799030516256810393135546 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98256639193659141132959013645082 y1[1] (numeric) = 0.98251544064656415429965974184003 absolute error = 5.095129002725702993039461079e-05 relative error = 0.0051855315269672995579828186811918 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.6MB, time=44.75 x[1] = 0.188 y2[1] (analytic) = 0.18689451009794070855554562366427 y2[1] (numeric) = 0.18800195543046558361413949129799 absolute error = 0.00110744533252487505859386763372 relative error = 0.59255102353971038934527147854316 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98237998864759594537971395183828 y1[1] (numeric) = 0.98232793871694447772861245695921 absolute error = 5.204993065146765110149487907e-05 relative error = 0.0052983500532337544914167336685375 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.6MB, time=44.96 x[1] = 0.189 y2[1] (analytic) = 0.18787679647561105288013261791901 y2[1] (numeric) = 0.18900200797476305804976042424647 absolute error = 0.00112521149915200516962780632746 relative error = 0.59890924279096531654354294340696 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98219260297869369683021752058749 y1[1] (numeric) = 0.98213943673533472393251163106662 absolute error = 5.316624335897289770588952087e-05 relative error = 0.0054130160619959598004310566767618 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.6MB, time=45.17 x[1] = 0.19 y2[1] (analytic) = 0.18885889497650057799285115298131 y2[1] (numeric) = 0.19000206164227800386979453031536 absolute error = 0.00114316666577742587694337733405 relative error = 0.6053019985739450334102477796337 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98200423511727031896787750418991 y1[1] (numeric) = 0.98194993470062054787621566273653 absolute error = 5.430041664977109166184145338e-05 relative error = 0.0055295501493724790875452385570289 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.6MB, time=45.38 x[1] = 0.191 y2[1] (analytic) = 0.18984080461851086484571512887505 y2[1] (numeric) = 0.19100211645091193770298195144356 absolute error = 0.00116131183240107285726682256851 relative error = 0.6117293037894322497096741911327 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98181488525169365751875050294814 y1[1] (numeric) = 0.98175943261166979702717679660042 absolute error = 5.545264002386049157370634772e-05 relative error = 0.0056479730402177495662137292327963 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.6MB, time=45.59 x[1] = 0.192 y2[1] (analytic) = 0.19082252441973235325423846606677 y2[1] (numeric) = 0.19200217241875523297795648681848 absolute error = 0.00117964799902287972371802075171 relative error = 0.61819117140916308829056129247599 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98162455357131356228034302723921 y1[1] (numeric) = 0.98156793046733232298964773904359 absolute error = 5.662310398123929069528819562e-05 relative error = 0.0057683055884487618918294794327363 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.6MB, time=45.80 x[1] = 0.193 y2[1] (analytic) = 0.19180405339844532380691346415776 y2[1] (numeric) = 0.19300222956408810177784591112024 absolute error = 0.00119817616564277797093244696248 relative error = 0.62468761447587313634731744545511 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98143324026646169777177747916177 y1[1] (numeric) = 0.98137542826643979215693858921468 absolute error = 5.781200002190561483888994709e-05 relative error = 0.0058905687773739460124954699201887 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.6MB, time=46.02 x[1] = 0.194 y2[1] (analytic) = 0.1927853905731208795848484034179 y2[1] (numeric) = 0.19400228790538157650387017602517 absolute error = 0.00121689733226069691902177260727 relative error = 0.63121864610334375565011303641058 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98124094552845135290214349438516 y1[1] (numeric) = 0.98118192600780549538191458743739 absolute error = 5.901952064585752022890694777e-05 relative error = 0.0060147837200242713359562070797458 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.6MB, time=46.23 x[1] = 0.195 y2[1] (analytic) = 0.19376653496242192769058266960535 y2[1] (numeric) = 0.19500234746129849134693743899617 absolute error = 0.00123581249887656365635476939082 relative error = 0.63778427947644865202060076036975 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98104766954957724965722497583334 y1[1] (numeric) = 0.980987423690224156665926183169 absolute error = 6.024585935309299129879266434e-05 relative error = 0.0061409716594865695716113799011406 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=839.2MB, alloc=4.6MB, time=46.45 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.6MB, time=46.66 x[1] = 0.196 y2[1] (analytic) = 0.19474748558520416058509787333882 y2[1] (numeric) = 0.19600240825069446356623786220996 absolute error = 0.00125492266549030298113998887114 relative error = 0.64438452785120070433162388251651 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98085341252311535080479413246059 y1[1] (numeric) = 0.98079192131247174086636392470688 absolute error = 6.149121064360993843020775371e-05 relative error = 0.0062691539692390886694015006781557 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.6MB, time=46.87 x[1] = 0.197 y2[1] (analytic) = 0.19572824146051703723204362709306 y2[1] (numeric) = 0.19700247029261887457383512327534 absolute error = 0.00127422883210183734179149618228 relative error = 0.65101940455479905331088297128265 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98065817464332266661866481780904 y1[1] (numeric) = 0.98059541887330526042303167290195 absolute error = 6.275577001740619563314490709e-05 relative error = 0.0063993521534892863405632182940609 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.6MB, time=47.08 x[1] = 0.198 y2[1] (analytic) = 0.19670880160760476404819683567353 y2[1] (numeric) = 0.19800253360631585082425557818174 absolute error = 0.00129373199871108677605874250821 relative error = 0.65768892298567645043014425588204 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9804619561054370606216984442784 y1[1] (numeric) = 0.98039791637146258110353264119692 absolute error = 6.403973397447951816580308148e-05 relative error = 0.0065315878475138717088029871526597 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.6MB, time=47.29 x[1] = 0.199 y2[1] (analytic) = 0.1976891650459072756591735497928 y2[1] (numeric) = 0.199002598211225244508075015684 absolute error = 0.0013134331653179688489014658912 relative error = 0.66439309661354686716318807058125 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98026475710567705434795673008606 y1[1] (numeric) = 0.98019941380566222676786376436746 absolute error = 6.534330001482758009296571860e-05 relative error = 0.0066658828180011037043348058092931 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.6MB, time=47.51 x[1] = 0.2 y2[1] (analytic) = 0.19866933079506121545941262711839 y2[1] (numeric) = 0.20000266412698361404850294107649 absolute error = 0.0013333333319223985890903139581 relative error = 0.67113193897945336489731382417857 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.98006657784124163112419651674817 y1[1] (numeric) = 0.97999991117460318315241489840572 absolute error = 6.666666663844797178161834245e-05 relative error = 0.0068022589633953548774737369099951 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.6MB, time=47.72 x[1] = 0.201 y2[1] (analytic) = 0.19964929787490091597545064089029 y2[1] (numeric) = 0.2010027313734252043999643260382 absolute error = 0.00135343349852428842451368514791 relative error = 0.67790546369581622578483859201811 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97986741851031003887090287557097 y1[1] (numeric) = 0.97979940847696470067357035404833 absolute error = 6.801003334533819733252152264e-05 relative error = 0.006940738314243949373074835275006 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.6MB, time=47.93 x[1] = 0.202 y2[1] (analytic) = 0.20062906530545937903150767291479 y2[1] (numeric) = 0.20200279997058292714767875993886 absolute error = 0.00137373466512354811617108702407 relative error = 0.68471368444648134482264978542649 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97966727931204159192305770210243 y1[1] (numeric) = 0.97959790571140609625111126651512 absolute error = 6.937360063549567194643558731e-05 relative error = 0.007081343033546283872059915671717 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.6MB, time=48.14 x[1] = 0.203 y2[1] (analytic) = 0.20160863210696925571640382543065 y2[1] (numeric) = 0.20300286993868934040723693668538 absolute error = 0.00139423783172008469083311125473 relative error = 0.69155661498676888344949842561718 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97946616044657547187084197775936 y1[1] (numeric) = 0.97939540287656655415161830408986 absolute error = 7.075757000891771922367366950e-05 relative error = 0.0072240954171052403715852799181309 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=873.5MB, alloc=4.6MB, time=48.35 TOP MAIN SOLVE Loop memory used=877.3MB, alloc=4.6MB, time=48.57 x[1] = 0.204 y2[1] (analytic) = 0.20258799729986382615082648501258 y2[1] (numeric) = 0.20400294129817762852317440985721 absolute error = 0.00141494399831380237234792484463 relative error = 0.69843426914352218495234835230668 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97926406211503052742047085791098 y1[1] (numeric) = 0.97919189997106492585207521824098 absolute error = 7.216214396560156839563967000e-05 relative error = 0.0073690178938808997410751092709338 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.6MB, time=48.78 x[1] = 0.205 y2[1] (analytic) = 0.20356715990477797905396857132664 y2[1] (numeric) = 0.20500301406968258156554254752839 absolute error = 0.00143585416490460251157397620175 relative error = 0.70534666081515695197472824693346 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97906098451950507327536172556728 y1[1] (numeric) = 0.97898739699349952892387473804824 absolute error = 7.358752600554435148698751904e-05 relative error = 0.0075161330263465650573807497785431 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.6MB, time=48.99 x[1] = 0.206 y2[1] (analytic) = 0.20454611894254919110855820418075 y2[1] (numeric) = 0.20600308827404157462347661680302 absolute error = 0.00145696933149238351491841262227 relative error = 0.71229380397171068642166766345553 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9788569278630766880378363294873 y1[1] (numeric) = 0.97878189394244794493742931177052 absolute error = 7.503392062874310040701771678e-05 relative error = 0.0076654635108471037887286343559405 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.6MB, time=49.20 x[1] = 0.207 y2[1] (analytic) = 0.20552487343421850612330042392233 y2[1] (numeric) = 0.20700316393229554689476092669959 absolute error = 0.00147829049807704077146050277726 relative error = 0.71927571265489239205743535172344 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97865189234980201113155910498837 y1[1] (numeric) = 0.97857539081646681638759019846051 absolute error = 7.650153333519474396890652786e-05 relative error = 0.0078170321779596179638921770852114 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.6MB, time=49.41 x[1] = 0.208 y2[1] (analytic) = 0.20650342240103151399175180282299 y2[1] (numeric) = 0.20800324106568998057039095660738 absolute error = 0.00149981866465846657863915378439 relative error = 0.7262924009781325400939380458494 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97844587818471653874491475500107 y1[1] (numeric) = 0.97836788761409164264007941260428 absolute error = 7.799057062489610483534239679e-05 relative error = 0.0079708619928564515301687463522908 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.6MB, time=49.62 x[1] = 0.209 y2[1] (analytic) = 0.20748176486443932944664898865714 y2[1] (numeric) = 0.20900331969567587951313239610539 absolute error = 0.00152155483123655006648340744825 relative error = 0.73334388312663329806928058928843 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97823888557383441879552914797525 y1[1] (numeric) = 0.97815938433383657489914002483717 absolute error = 7.950123999784389638912313808e-05 relative error = 0.0081269760556705441712649003485034 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.6MB, time=49.83 x[1] = 0.21 y2[1] (analytic) = 0.20845989984609957060871242622764 y2[1] (numeric) = 0.21000339984391074772907702048011 absolute error = 0.00154349999781117712036459425247 relative error = 0.74043017335741902231763379525423 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97803091472414824491613856809935 y1[1] (numeric) = 0.9779498809741942101966113218623 absolute error = 8.103374995403471952724623705e-05 relative error = 0.0082853976018631409240946005326245 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=904.0MB, alloc=4.6MB, time=50.05 x[1] = 0.211 y2[1] (analytic) = 0.20943782636787733732894670811626 y2[1] (numeric) = 0.21100348153225956763119532480353 absolute error = 0.00156565516438223030224861668727 relative error = 0.74755128599938701433320481269771 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97782196584362884946201333194623 y1[1] (numeric) = 0.97773937753363538440263632877443 absolute error = 8.258830999346505937700317180e-05 relative error = 0.0084461500025938670017792781347613 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.6MB, time=50.26 x[1] = 0.212 y2[1] (analytic) = 0.21041554345184618932345921244009 y2[1] (numeric) = 0.21200356478279577809388583793586 absolute error = 0.00158802133094958877042662549577 relative error = 0.7547072354533585413327559999815 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97761203914122509554014276410505 y1[1] (numeric) = 0.97752787401060896425821019706986 absolute error = 8.416513061613128193256703519e-05 relative error = 0.0086092567650931772988086116696609 % Correct digits = 4 h = 0.001 memory used=911.7MB, alloc=4.6MB, time=50.48 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.6MB, time=50.68 x[1] = 0.213 y2[1] (analytic) = 0.2113930501202891240998188928769 y2[1] (numeric) = 0.21300364961780225229752103629933 absolute error = 0.00161059949751312819770214342243 relative error = 0.7618980361921301213227724175288 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97740113482686366806038950259663 y1[1] (numeric) = 0.97731537040354163842977896170236 absolute error = 8.576442332202963061054089427e-05 relative error = 0.0087747415330371901233798987433696 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.6MB, time=50.90 x[1] = 0.214 y2[1] (analytic) = 0.21237034539569955467397729468196 y2[1] (numeric) = 0.21400373605977227536198977572918 absolute error = 0.00163339066407272068801248104722 relative error = 0.76912370276052507297903505348672 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97718925311144886380882208290055 y1[1] (numeric) = 0.97710186671083770758609917062606 absolute error = 8.738640061115622272291227449e-05 relative error = 0.0089426280869249147713852164678746 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.6MB, time=51.11 x[1] = 0.215 y2[1] (analytic) = 0.21334742830078228707677407985706 y2[1] (numeric) = 0.21500382413141052176823615814573 absolute error = 0.00165639583062823469146207828867 relative error = 0.77638424977544533064801680889818 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97697639420686238054343572724421 y1[1] (numeric) = 0.97688736293087887349756989034877 absolute error = 8.903127598350704586583689544e-05 relative error = 0.0091129403444578826263624285386024 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.6MB, time=51.32 x[1] = 0.216 y2[1] (analytic) = 0.21432429785845449764904955504731 y2[1] (numeric) = 0.2160039138556340325667947482069 absolute error = 0.00167961599717953491774519315959 relative error = 0.78367969192592352478118110840401 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97676255832596310511247224341507 y1[1] (numeric) = 0.97667185906202402715824959110317 absolute error = 9.069926393907795422265231190e-05 relative error = 0.009285702360922191539971804689107 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.6MB, time=51.53 x[1] = 0.217 y2[1] (analytic) = 0.21530095309184671012438690713494 y2[1] (numeric) = 0.21700400525557319237232205349354 absolute error = 0.0017030521637264822479351463586 relative error = 0.79101004397317532811492878453249 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97654774568258690059555091475888 y1[1] (numeric) = 0.97645535510260903593077141532895 absolute error = 9.239057997786466477949942993e-05 relative error = 0.0094609383295729733182078858164659 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.6MB, time=51.74 x[1] = 0.218 y2[1] (analytic) = 0.21627739302430377249850706386915 y2[1] (numeric) = 0.21800409835457270614312418015024 absolute error = 0.00172670533026893364461711628109 relative error = 0.79837532075065206791060762594902 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97633195649154639246782324021503 y1[1] (numeric) = 0.97623785105094652971437133324629 absolute error = 9.410544059986275345190696874e-05 relative error = 0.0096386725820212942096095957340589 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.6MB, time=51.95 x[1] = 0.219 y2[1] (analytic) = 0.21725361667938583368433931021855 y2[1] (numeric) = 0.21900419317619257574468057425151 absolute error = 0.00175057649680674206034126403296 relative error = 0.80577553716409360457067069839208 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97611519096863075378736536021661 y1[1] (numeric) = 0.97601934690532568613624468939 absolute error = 9.584406330506765112067082661e-05 relative error = 0.0098189295886234983631938338911386 % Correct digits = 4 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.6MB, time=52.16 x[1] = 0.22 y2[1] (analytic) = 0.21822962308086931995179100545701 y2[1] (numeric) = 0.22000428974420907629616375748766 absolute error = 0.00177466666333975634437275203065 relative error = 0.81321070819158147694874425867046 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9758974493306054894060229810447 y1[1] (numeric) = 0.97579984266401201476644764406408 absolute error = 9.760666659347463957533698062e-05 relative error = 0.010001733958873004295712272888951 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=946.0MB, alloc=4.6MB, time=52.38 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.6MB, time=52.59 x[1] = 0.221 y2[1] (analytic) = 0.21920541125274791115123996129451 y2[1] (numeric) = 0.22100438808261573229895496406545 absolute error = 0.00179897682986782114771500277094 relative error = 0.82068084888359231467304380348728 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97567873179521221920392458677419 y1[1] (numeric) = 0.97557933832524714035656101376883 absolute error = 9.939346996507884736357300536e-05 relative error = 0.010187110441794564480121246269494 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.6MB, time=52.80 x[1] = 0.222 y2[1] (analytic) = 0.22018098021923351671977325764203 y2[1] (numeric) = 0.22200448821562429354615558399593 absolute error = 0.0018235079963907768263823263539 relative error = 0.82818597436305151780425754282638 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97545903858116846034787970427966 y1[1] (numeric) = 0.97535783388724858510233501474656 absolute error = 0.0001012046939198752455446895331 relative error = 0.010375083926340998239863887344394 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.6MB, time=53.01 x[1] = 0.223 y2[1] (analytic) = 0.221156329004757251469196489853 y2[1] (numeric) = 0.22300459016766571081209431619549 absolute error = 0.00184826116290845934289782634249 relative error = 0.83572609982538720415070037914247 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97523836990816740857387996288501 y1[1] (numeric) = 0.97513532934820954993053441388763 absolute error = 0.00010304055995785864334554899738 relative error = 0.010565679441792408206695536378078 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.6MB, time=53.22 x[1] = 0.224 y2[1] (analytic) = 0.22213145663397041115483765951328 y2[1] (numeric) = 0.22400469396339111132082993305562 absolute error = 0.00187323732942070016599227354234 relative error = 0.84330124053858442456522832535948 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97501672599687771849392166613751 y1[1] (numeric) = 0.97491182470629869481020459133611 absolute error = 0.0001049012905790236837170748014 relative error = 0.010758922158157890673341364727528 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.6MB, time=53.44 x[1] = 0.225 y2[1] (analytic) = 0.2231063621317454478241701400572 y2[1] (numeric) = 0.22500479962767277399264955634232 absolute error = 0.00189843749592732616847941628512 relative error = 0.85091141184323964655009322358106 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97479410706894328292736956886549 y1[1] (numeric) = 0.97468731995965991808858001923338 absolute error = 0.00010678710928336483878954963211 relative error = 0.010954837386579750246262690681303 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.6MB, time=53.65 x[1] = 0.226 y2[1] (analytic) = 0.22408104452317694494427936866789 y2[1] (numeric) = 0.22600490718560510446756234246687 absolute error = 0.00192386266242815952328297379898 relative error = 0.85855662915261550649761064956349 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9745705133469830112570825281373 y1[1] (numeric) = 0.97446181510641213485185766113927 absolute error = 0.00010869824057087640522486699803 relative error = 0.011153450579740229278229129201773 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.6MB, time=53.86 x[1] = 0.227 y2[1] (analytic) = 0.22505550283358259230719813707651 y2[1] (numeric) = 0.22700501666250560990478847332612 absolute error = 0.00194951382892301759759033624961 relative error = 0.86623690795269583089621002229467 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97434594505459060681052267197768 y1[1] (numeric) = 0.97423531014464905431105879677311 absolute error = 0.00011063490994155249946387520457 relative error = 0.011354787332270762635251100265388 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.6MB, time=54.07 x[1] = 0.228 y2[1] (analytic) = 0.2260297360885041607121355760063 y2[1] (numeric) = 0.22800512808391587355724334704166 absolute error = 0.00197539199541171284510777103536 relative error = 0.87395226380224092683313520042422 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97412040241633434326607070471358 y1[1] (numeric) = 0.97400780507243895621320377682173 absolute error = 0.00011259734389538705286692789185 relative error = 0.011558873381163768427724918438797 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.6MB, time=54.28 x[1] = 0.229 y2[1] (analytic) = 0.22700374331370847642362515111377 y2[1] (numeric) = 0.22900524147560252912001686103367 memory used=984.2MB, alloc=4.6MB, time=54.50 absolute error = 0.0020014981618940526963917099199 relative error = 0.88170271233284314212676625502576 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97389388565775684008477094261565 y1[1] (numeric) = 0.97377929988782446627802521266819 absolute error = 0.00011458576993237380674572994746 relative error = 0.011765734606186985411384327933787 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.6MB, time=54.71 x[1] = 0.23 y2[1] (analytic) = 0.22797752353518839540461721236007 y2[1] (numeric) = 0.23000535686355823485184767794609 absolute error = 0.00202783332836983944723046558602 relative error = 0.88948826924898269542323867833741 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9736663950053748369677306480716 y1[1] (numeric) = 0.97354979458882233066044610600348 absolute error = 0.00011660041655250630728454206812 relative error = 0.011975397030300367839841588221882 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.6MB, time=54.92 x[1] = 0.231 y2[1] (analytic) = 0.22895107577916377732354186380137 y2[1] (numeric) = 0.23100547427400264746859236299534 absolute error = 0.00205439849483887014505049919397 relative error = 0.89730895032808377659374503770727 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97343793068667896733939920487326 y1[1] (numeric) = 0.97331928917342318943905042339389 absolute error = 0.00011864151325577790034878147937 relative error = 0.0121878868200755486271417390197 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.6MB, time=55.13 x[1] = 0.232 y2[1] (analytic) = 0.22992439907208245933436814681645 y2[1] (numeric) = 0.23200559373338339580768927934437 absolute error = 0.00208119466130093647332113252792 relative error = 0.90516477142057091777061603049694 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97320849293013353085695365131938 y1[1] (numeric) = 0.97308778363959134913077462098914 absolute error = 0.00012070929054218172617903033024 relative error = 0.012403230286117881755849191858948 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.6MB, time=55.34 x[1] = 0.233 y2[1] (analytic) = 0.23089749244062122962868575679341 y2[1] (numeric) = 0.2330057152683770542626171261075 absolute error = 0.00210822282775582463393136931409 relative error = 0.91305574844992563536199305615835 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97297808196517626494601806172955 y1[1] (numeric) = 0.97285527798526455423204962467076 absolute error = 0.00012280397991171071396843705879 relative error = 0.012621453883491074943740048701455 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.6MB, time=55.55 x[1] = 0.234 y2[1] (analytic) = 0.2318703549116868007588357412751 y2[1] (numeric) = 0.23400583890589011598634800156904 absolute error = 0.00213548399420331522751226029394 relative error = 0.92098189741274334338662281343824 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97274669802221811536294524063099 y1[1] (numeric) = 0.97262177220835375778662377105673 absolute error = 0.00012492581386435757632146957426 relative error = 0.012842584212144423660190305171623 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1007.0MB, alloc=4.6MB, time=55.76 x[1] = 0.235 y2[1] (analytic) = 0.2328429855124167827311168565134 y2[1] (numeric) = 0.23500596467305996586279487214963 absolute error = 0.00216297916064318313167801563623 relative error = 0.92894323437879053847202607134033 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97251434133264300578389016731721 y1[1] (numeric) = 0.97238726630674289098029821489657 absolute error = 0.00012707502590011480359195242064 relative error = 0.013066648017342657661833154812153 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.6MB, time=55.97 x[1] = 0.236 y2[1] (analytic) = 0.23381538327018065586809448930743 y2[1] (numeric) = 0.23600609259725585324525332557854 absolute error = 0.00219070932707519737715883627111 relative error = 0.93693977549106225686101766875527 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97228101212880760642090560168606 y1[1] (numeric) = 0.97215176027828863176280730851187 absolute error = 0.00012925185051897465809829317419 relative error = 0.013293672190098411296011798555793 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.6MB, time=56.18 x[1] = 0.237 y2[1] (analytic) = 0.23478754721258074343903928189747 y2[1] (numeric) = 0.2370062227060798644608374846277 absolute error = 0.00221867549349912102179820273023 relative error = 0.94497153696583980377328298810869 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97204671064404110166529123524216 y1[1] (numeric) = 0.97191525412082017249707745905961 absolute error = 0.00013145652322092916821377618255 relative error = 0.013523683767607328899981337044812 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1018.5MB, alloc=4.6MB, time=56.39 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.6MB, time=56.61 x[1] = 0.238 y2[1] (analytic) = 0.23575947636745318405752282955735 y2[1] (numeric) = 0.23800635502736789507990995563339 absolute error = 0.00224687865991471102238712607604 relative error = 0.95303853509274875547044763909562 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97181143711264495675842874389526 y1[1] (numeric) = 0.97167774783213898663609896952046 absolute error = 0.0001336892805059701223297743748 relative error = 0.013756709933685816703718369085678 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.6MB, time=56.82 x[1] = 0.239 y2[1] (analytic) = 0.23673116976286890384519805337042 y2[1] (numeric) = 0.23900648958919062194950568387451 absolute error = 0.00227531982632171810430763050409 relative error = 0.96114078623481723437481189845098 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97157519176989268349033607170002 y1[1] (numeric) = 0.97143924141001859442764636944105 absolute error = 0.00013595035987408906268970225897 relative error = 0.013992778019211452724583754020981 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.6MB, time=57.03 x[1] = 0.24 y2[1] (analytic) = 0.23770262642713458836079208448982 y2[1] (numeric) = 0.24000662641985447498974958569169 absolute error = 0.00230399999271988662895750120187 relative error = 0.96927830682853445759365959729658 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97133797485202960492617524696338 y1[1] (numeric) = 0.9711997348522043276470837415882 absolute error = 0.00013823999982527727909150537518 relative error = 0.014231915502566066222956566171339 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1033.8MB, alloc=4.6MB, time=57.24 x[1] = 0.241 y2[1] (analytic) = 0.23867384538879365429333973097121 y2[1] (numeric) = 0.24100676554790260875226782501884 absolute error = 0.00233292015910895445892809404763 relative error = 0.97745111338390955920279264700106 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97109978659627261916094900419216 y1[1] (numeric) = 0.9709592281564130933584925508044 absolute error = 0.00014055843985952580245645338776 relative error = 0.014474150010081498369319553437973 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.6MB, time=57.45 x[1] = 0.242 y2[1] (analytic) = 0.23964482567662722091868583402537 y2[1] (numeric) = 0.24200690700211587373959259975833 absolute error = 0.00236208132548865282090676573296 relative error = 0.98565922248453068664468726547262 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9708606272408099621026224571645 y1[1] (numeric) = 0.97071772132033313670436048148719 absolute error = 0.00014290592047682539826197567731 relative error = 0.014719509316488055855132418314414 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1041.4MB, alloc=4.6MB, time=57.66 x[1] = 0.243 y2[1] (analytic) = 0.24061556631965508131828505726935 y2[1] (numeric) = 0.24300705081151378748456030116198 absolute error = 0.00239148449185870616627524389263 relative error = 0.99390265078762437159841622564035 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97062049702480096928390703998371 y1[1] (numeric) = 0.9704752143416238027240707902508 absolute error = 0.00014528268317716655983624973291 relative error = 0.014968021345365669262183007865523 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.6MB, time=57.88 x[1] = 0.244 y2[1] (analytic) = 0.2415860663471366733593278902572 y2[1] (numeric) = 0.24400719700535550538870290708258 absolute error = 0.00242113065821883202937501682538 relative error = 1.0021814150241151756802331148021 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97037939618837583670294490431084 y1[1] (numeric) = 0.9702317072179152972014326804665 absolute error = 0.00014768897046053950151222384434 relative error = 0.01521971416959776808796210113071 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.6MB, time=58.09 x[1] = 0.245 y2[1] (analytic) = 0.2425563247885720504352218862454 y2[1] (numeric) = 0.24500734561314079131863246763449 absolute error = 0.00245102082456874088341058138909 relative error = 1.0104955319986856113354696849449 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.97013732497263538069313293207151 y1[1] (numeric) = 0.96998719994680844654149420551823 absolute error = 0.00015012502582693415163872655328 relative error = 0.015474616011827884407969021211785 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1052.8MB, alloc=4.6MB, time=58.30 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.6MB, time=58.52 x[1] = 0.246 y2[1] (analytic) = 0.24352634067370285196545739379243 y2[1] (numeric) = 0.24600749666461098795941853944664 absolute error = 0.00248115599090813599396114565421 relative error = 1.0188450185898363382841559084304 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96989428361965079682232649379306 y1[1] (numeric) = 0.96974169252587445667688020775286 absolute error = 0.0001525910937763401454462860402 relative error = 0.015732755244918997239726910491154 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.6MB, time=58.73 x[1] = 0.247 y2[1] (analytic) = 0.24449611303251327365388728240771 y2[1] (numeric) = 0.24700765018974998692395842230668 absolute error = 0.00251153715723671327007113989897 relative error = 1.0272298917499466358845343478516 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96965027237246341782166405334813 y1[1] (numeric) = 0.96949518495265467100389880024943 absolute error = 0.0001550874198087468177652530987 relative error = 0.015994160392415629757672358873239 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1064.3MB, alloc=4.6MB, time=58.94 x[1] = 0.248 y2[1] (analytic) = 0.24546564089523103750445040405111 y2[1] (numeric) = 0.24800780621878519861734004958105 absolute error = 0.00254216532355416111288964552994 relative error = 1.0356501685053351517804059218836 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96940529147508447054425469025992 y1[1] (numeric) = 0.96924767722466032734866089867899 absolute error = 0.00015761425042414319559379158093 relative error = 0.016258860129008711592988367377262 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.6MB, time=59.16 x[1] = 0.249 y2[1] (analytic) = 0.24643492329232836159336877484025 y2[1] (numeric) = 0.24900796478218852185519738135202 absolute error = 0.00257304148986016026182860651177 relative error = 1.044105865956320927200013118484 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96915934117249483195397158086133 y1[1] (numeric) = 0.96899916933937231396345831067664 absolute error = 0.00016017183312251799051327018469 relative error = 0.016526883281003218537876596503406 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.6MB, time=59.36 x[1] = 0.25 y2[1] (analytic) = 0.24740395925452292959684870484939 y2[1] (numeric) = 0.25000812591067731323505814673903 absolute error = 0.00260416665615438363820944188964 relative error = 1.052597001277284699275939190596 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96891242171064478414459544949419 y1[1] (numeric) = 0.96874966129424092455364689029964 absolute error = 0.00016276041640385959094855919455 relative error = 0.016798258826788602059718757743978 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1075.7MB, alloc=4.6MB, time=59.58 x[1] = 0.251 y2[1] (analytic) = 0.24837274781277886007331634837941 y2[1] (numeric) = 0.25100828963521535625968377936762 absolute error = 0.00263554182243649618636743098821 relative error = 1.0611235917167304807572778861279 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9686645333364537683895529705847 y1[1] (numeric) = 0.96849915308668561233528226530016 absolute error = 0.00016538024976815605427070528454 relative error = 0.017073015897312021117062158213478 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.6MB, time=59.79 x[1] = 0.252 y2[1] (analytic) = 0.24934128799830767549921839254425 y2[1] (numeric) = 0.25200845598701383021140138741492 absolute error = 0.00266716798870615471218299487067 relative error = 1.069685654597347417487107831173 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96841567629781013822249607183617 y1[1] (numeric) = 0.96824764471409474312375664509863 absolute error = 0.00016803158371539509873942673754 relative error = 0.017351183776554388856385137462586 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.6MB, time=60.00 x[1] = 0.253 y2[1] (analytic) = 0.25030957884256927105741884845382 y2[1] (numeric) = 0.25300862499753227877642759709545 absolute error = 0.00269904615496300771900874864163 relative error = 1.0782832073160719240200888217176 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96816585084357091154896905793918 y1[1] (numeric) = 0.96799513617382534745368621750343 absolute error = 0.00017071466974556409528284043575 relative error = 0.017632791902009246856158811338824 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1087.2MB, alloc=4.6MB, time=60.21 x[1] = 0.254 y2[1] (analytic) = 0.2512776193772728831772231566772 y2[1] (numeric) = 0.25400879669847957841818410585485 absolute error = 0.00273117732120669524096094917765 relative error = 1.086916267344150097756784002546 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96791505722356152178941144311144 y1[1] (numeric) = 0.96774162746320287173029964238521 absolute error = 0.00017342976035865005911180072623 relative error = 0.01791786986516447967282656408188 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1091.0MB, alloc=4.6MB, time=60.42 TOP MAIN SOLVE Loop memory used=1094.8MB, alloc=4.6MB, time=60.64 x[1] = 0.255 y2[1] (analytic) = 0.25224540863437805782506106704299 y2[1] (numeric) = 0.25500897112181490649860477891197 absolute error = 0.00276356248743684867354371186898 relative error = 1.0955848522272004119731022409185 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96766329568857556805374534944369 y1[1] (numeric) = 0.96748711857952092841257915067897 absolute error = 0.00017617710905463964116619876472 relative error = 0.018206447411986882531976545566616 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1098.6MB, alloc=4.6MB, time=60.85 x[1] = 0.256 y2[1] (analytic) = 0.2532129456460956185448600021744 y2[1] (numeric) = 0.25600914829974870914643412013077 absolute error = 0.00279620265365309060157411795637 relative error = 1.1042889795852766881250489555495 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96741056649037456434779729644346 y1[1] (numeric) = 0.96723160952004104522840675725493 absolute error = 0.00017895697033351911939053918853 relative error = 0.018498554443409595097189509877928 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1102.4MB, alloc=4.6MB, time=61.06 x[1] = 0.257 y2[1] (analytic) = 0.25418022944488863424714086446645 y2[1] (numeric) = 0.25700932826474366887151694551317 absolute error = 0.00282909881985503462437608104672 relative error = 1.1130286671129313478107712564948 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96715686988168768781180517533403 y1[1] (numeric) = 0.96697510028199241342196909636947 absolute error = 0.00018176959969527438983607896456 relative error = 0.018794221015822414338809184084742 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1106.2MB, alloc=4.6MB, time=61.27 x[1] = 0.258 y2[1] (analytic) = 0.25514725906347338674586849749019 y2[1] (numeric) = 0.25800951104951567192407908488142 absolute error = 0.00286225198604228517821058739123 relative error = 1.1218039325792789447736845073778 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9669022061162115259912621695806 y1[1] (numeric) = 0.96671759086257163503367538858052 absolute error = 0.00018461525363989095758678100008 relative error = 0.01909347734156499961520952796508 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1110.0MB, alloc=4.6MB, time=61.48 x[1] = 0.259 y2[1] (analytic) = 0.25611403353482033804208926505403 y2[1] (numeric) = 0.25900969668703477539799893456397 absolute error = 0.00289566315221443735590966950994 relative error = 1.130614793828059977332272356593 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96664657544860982314035035077869 y1[1] (numeric) = 0.96645908125894246921284404818747 absolute error = 0.00018749418966735392750630259122 relative error = 0.019396353789422983170027318735174 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1113.9MB, alloc=4.6MB, time=61.69 x[1] = 0.26 y2[1] (analytic) = 0.25708055189215509735338846436522 y2[1] (numeric) = 0.26000988521052617407706968111163 absolute error = 0.00292933331837107672368121674641 relative error = 1.1394612687777049816239609170042 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96638997813451322555821764645006 y1[1] (numeric) = 0.96619957146823557756341444043454 absolute error = 0.00019040666627764799480320601552 relative error = 0.019702880885126999340294088335613 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1117.7MB, alloc=4.6MB, time=61.90 x[1] = 0.261 y2[1] (analytic) = 0.25804681316895938788820054391467 y2[1] (numeric) = 0.26101007665347116702325201325104 absolute error = 0.00296326348451177913505146933637 relative error = 1.148343375421398906052280123056 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96613241443051902595835284344793 y1[1] (numeric) = 0.96593906148754826852294129789754 absolute error = 0.00019335294297075743541154555039 relative error = 0.020013089311854645862443210514607 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1121.5MB, alloc=4.6MB, time=62.11 x[1] = 0.262 y2[1] (analytic) = 0.25901281639897201336400535185544 y2[1] (numeric) = 0.26201027104960812390591713642959 absolute error = 0.00299745465063611054191178457415 relative error = 1.1572611318271457673283413786761 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96587388459419090687131425757517 y1[1] (numeric) = 0.96567755131394424077513030565851 absolute error = 0.00019633328024666609618395191666 relative error = 0.020327009910735390755790573955986 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1125.3MB, alloc=4.6MB, time=62.32 TOP MAIN SOLVE Loop memory used=1129.1MB, alloc=4.6MB, time=62.54 x[1] = 0.263 y2[1] (analytic) = 0.25997856061618982426844389675928 y2[1] (numeric) = 0.26301046843293345107107990141997 absolute error = 0.00303190781674362680263600466069 relative error = 1.1662145561378335884994804476307 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96561438888405868308106866666555 y1[1] (numeric) = 0.96541504094445332569617436505959 absolute error = 0.00019934793960535738489430160596 relative error = 0.020644673681358438356295517173573 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1132.9MB, alloc=4.6MB, time=62.75 x[1] = 0.264 y2[1] (analytic) = 0.26094404485486868386238735971576 y2[1] (numeric) = 0.26401066883770255734962185553295 absolute error = 0.00306662398283387348723449581719 relative error = 1.1752036665712996193597381489797 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9653539275596180430951980707674 y1[1] (numeric) = 0.96515153037607122883515104601759 absolute error = 0.00020239718354681426004702474981 relative error = 0.02096611178228356816720730975909 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1136.7MB, alloc=4.6MB, time=62.97 x[1] = 0.265 y2[1] (analytic) = 0.26190926814952443392399335478576 y2[1] (numeric) = 0.26501087229843081960350402203374 absolute error = 0.00310160414890638567951066724798 relative error = 1.1842284814203958396386788223928 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96509250088133028964923280920166 y1[1] (numeric) = 0.96488701960575927042874273807359 absolute error = 0.00020548127557101922049007112807 relative error = 0.021291355531554960287596250591406 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1140.6MB, alloc=4.6MB, time=63.17 x[1] = 0.266 y2[1] (analytic) = 0.26287422953493386023278369383338 y2[1] (numeric) = 0.26601107884989454800896921037005 absolute error = 0.00313684931496068777618551653667 relative error = 1.1932890190530547453668777408781 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96483010911062207924537053013933 y1[1] (numeric) = 0.9646215086304441249505420105478 absolute error = 0.00020860048017795429482851959153 relative error = 0.02162043640721802127476226292834 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1144.4MB, alloc=4.6MB, time=63.39 x[1] = 0.267 y2[1] (analytic) = 0.26383892804613565779277817173887 y2[1] (numeric) = 0.26701128852713195107573365679846 absolute error = 0.00317236048099629328295548505959 relative error = 1.202385297912355418818243690293 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96456675250988516072584147395786 y1[1] (numeric) = 0.96435499744701755969520569236882 absolute error = 0.00021175506286760103063578158904 relative error = 0.021953386047839224392112584690481 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1148.2MB, alloc=4.6MB, time=63.60 x[1] = 0.268 y2[1] (analytic) = 0.26480336271843139579371914893952 y2[1] (numeric) = 0.26801150136544410040116779193968 absolute error = 0.00320813864701270460744864300016 relative error = 1.2115173365165898824311818249221 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96430243134247611288118149698917 y1[1] (numeric) = 0.96408748605233617239772218234842 absolute error = 0.00021494529013994048345931464075 relative error = 0.022290236253028978290308704632018 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.6MB, time=63.81 x[1] = 0.269 y2[1] (analytic) = 0.26576753258738648230942197015403 y2[1] (numeric) = 0.26901171740039589515846592870249 absolute error = 0.00324418481300941284904395854846 relative error = 1.2206851534593297371124446659812 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96403714587271608109367522736473 y1[1] (numeric) = 0.96381897444322112788805750087787 absolute error = 0.00021817142949495320561772648686 relative error = 0.022631018983967538266306046755276 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1155.8MB, alloc=4.6MB, time=64.02 x[1] = 0.27 y2[1] (analytic) = 0.26673143668883112873228652102054 y2[1] (numeric) = 0.2700119366678170263178046608902 absolute error = 0.00328049997898589758551813986966 relative error = 1.2298887674094930853293657533559 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9637708963658905130162327094922 y1[1] (numeric) = 0.96354946261645789378144659423011 absolute error = 0.00022143374943261923478611526209 relative error = 0.022975766363933974342353061362834 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1159.6MB, alloc=4.6MB, time=64.24 x[1] = 0.271 y2[1] (analytic) = 0.26769507405886131394300548821702 y2[1] (numeric) = 0.27101215920380294059948975964261 absolute error = 0.00331708514494162665648427142559 relative error = 1.2391281971114117393980210103302 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9635036830882488932869638582654 y1[1] (numeric) = 0.96327895056879597520459740286316 absolute error = 0.00022473251945291808236645540224 relative error = 0.023324510678838210505084387979733 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1163.5MB, alloc=4.6MB, time=64.45 TOP MAIN SOLVE Loop memory used=1167.3MB, alloc=4.6MB, time=64.67 x[1] = 0.272 y2[1] (analytic) = 0.26865844373383974821450515343617 y2[1] (numeric) = 0.27201238504471580415809135166937 absolute error = 0.0033539413108760559435861982332 relative error = 1.2484034613848987153767173547857 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96323550630700447727971600841062 y1[1] (numeric) = 0.96300743829694864855807620533472 absolute error = 0.0002280680100558287216398030759 relative error = 0.023677284377756149543540699785731 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1171.1MB, alloc=4.6MB, time=64.88 x[1] = 0.273 y2[1] (analytic) = 0.26962154475039683684915481735437 y2[1] (numeric) = 0.27301261422718546599656715999842 absolute error = 0.00339106947678862914741234264405 relative error = 1.2577145791253160129760665084187 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96296636629033402389084080840986 y1[1] (numeric) = 0.96273492579759269431514374965554 absolute error = 0.00023144049274132957569705875432 relative error = 0.024034120073467898024280850201147 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1174.9MB, alloc=4.6MB, time=65.09 x[1] = 0.274 y2[1] (analytic) = 0.27058437614543164354828121646544 y2[1] (numeric) = 0.27401284678811042110937358469438 absolute error = 0.00342847064267877756109236822894 relative error = 1.2670615693036426818987643367336 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96269626330737752736245767221169 y1[1] (numeric) = 0.96246141306736812885731268413008 absolute error = 0.00023485024000939850514498808161 relative error = 0.024395050542999106041725190065874 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1178.7MB, alloc=4.6MB, time=65.30 x[1] = 0.275 y2[1] (analytic) = 0.27154693695611285351302456334528 y2[1] (numeric) = 0.27501308276465877335356439769684 absolute error = 0.00346614580854591984053983435156 relative error = 1.2764444509665431750240624163936 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96242519762823794814248196544391 y1[1] (numeric) = 0.96218690010287793534689779995703 absolute error = 0.00023829752536001279558416548688 relative error = 0.024760108728165436482487621436956 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1182.5MB, alloc=4.6MB, time=65.51 x[1] = 0.276 y2[1] (analytic) = 0.27250922621987973627557310957138 y2[1] (numeric) = 0.27601332219426919804687682258684 absolute error = 0.00350409597438946177130371301546 relative error = 1.2858632432364359888537888926877 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96215316952398094278168706607751 y1[1] (numeric) = 0.96191138690068779363683159809002 absolute error = 0.00024178262329314914485546798749 relative error = 0.025129327736120178643723356740828 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1186.3MB, alloc=4.6MB, time=65.72 x[1] = 0.277 y2[1] (analytic) = 0.27347124297444310825981340014308 y2[1] (numeric) = 0.27701356511465190429180476671134 absolute error = 0.00354232214020879603199136656826 relative error = 1.2953179653115625916386500773602 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96188017926663459286807040245721 y1[1] (numeric) = 0.96163487345732580921801869308946 absolute error = 0.00024530580930878365005170936775 relative error = 0.025502740839905021147444758436946 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1190.2MB, alloc=4.6MB, time=65.93 x[1] = 0.278 y2[1] (analytic) = 0.27443298625778629507043365883237 y2[1] (numeric) = 0.27801381156378959702465896967977 absolute error = 0.0035808253060033019542253108474 relative error = 1.3048086364660566396054226659677 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96160622712918913299879453431011 y1[1] (numeric) = 0.96135735976928224120450356693101 absolute error = 0.0002488673599068917942909673791 relative error = 0.025880381479003999195344386494218 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1194.0MB, alloc=4.6MB, time=66.14 x[1] = 0.279 y2[1] (analytic) = 0.27539445510816609350951801544215 y2[1] (numeric) = 0.27901406157993843878861382879359 absolute error = 0.00361960647177234527909581335144 relative error = 1.3143352760500134817075289433542 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96133131338559667778997530476856 y1[1] (numeric) = 0.9610788458330092293567271859736 absolute error = 0.00025246755258744843324811879496 relative error = 0.026262283259900631311917864772355 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1197.8MB, alloc=4.6MB, time=66.35 TOP MAIN SOLVE Loop memory used=1201.6MB, alloc=4.6MB, time=66.57 x[1] = 0.28 y2[1] (analytic) = 0.27635564856411373331966955845785 y2[1] (numeric) = 0.28001431520162901122974065847902 absolute error = 0.00365866663751527791007110002117 relative error = 1.3238979034895599533233739158776 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96105543831077094792459005359648 y1[1] (numeric) = 0.96079933164492052014314899453128 absolute error = 0.0002561066658504277814410590652 relative error = 0.026648479956638260827604823099497 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1205.4MB, alloc=4.6MB, time=66.78 x[1] = 0.281 y2[1] (analytic) = 0.27731656566443583865270047004946 y2[1] (numeric) = 0.28101457246766727631502713726425 absolute error = 0.00369800680323143766232666721479 relative error = 1.3334965382869244593287139791055 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96077860218058699523877984368792 y1[1] (numeric) = 0.9605188172013911918405117987379 absolute error = 0.00025978497919580339826804495002 relative error = 0.027039005511383617458269454385181 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1209.2MB, alloc=4.6MB, time=66.99 x[1] = 0.282 y2[1] (analytic) = 0.27827720544821538926292777481407 y2[1] (numeric) = 0.28201483341713553727138269227527 absolute error = 0.0037376279689201480084549174612 relative error = 1.3431312000205073469712215196182 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96050080527188092684682061451294 y1[1] (numeric) = 0.96023730249875737867302805464171 absolute error = 0.00026350277312354817379255987123 relative error = 0.027433894034993614442628665802164 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1213.0MB, alloc=4.6MB, time=67.20 x[1] = 0.283 y2[1] (analytic) = 0.27923756695481268142411350904312 y2[1] (numeric) = 0.28301509808939339924462956761905 absolute error = 0.00377753113458071782051605857593 relative error = 1.3528019083449515689773087794864 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.96022204786244962830503913751647 y1[1] (numeric) = 0.95995478753331599399076707471887 absolute error = 0.0002672603291336343142720627976 relative error = 0.027833179807585396805210965484389 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1216.9MB, alloc=4.6MB, time=67.41 x[1] = 0.284 y2[1] (analytic) = 0.28019764922386628856908839365443 y2[1] (numeric) = 0.28401536652407872967747931937812 absolute error = 0.00381771730021244110839092572369 relative error = 1.362508682991213637323177401188 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95994233023105048581495060953123 y1[1] (numeric) = 0.9596712723013244524875236672504 absolute error = 0.00027105792972603332742694228083 relative error = 0.028236897279109656419098723305912 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1220.7MB, alloc=4.6MB, time=67.62 x[1] = 0.285 y2[1] (analytic) = 0.28115745129529402165109837124522 y2[1] (numeric) = 0.28501563876110861840549447625738 absolute error = 0.00385818746581459675439610501216 relative error = 1.3722515437666348681039673399571 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95966165265740110746589568104396 y1[1] (numeric) = 0.95938675679900039145844972326604 absolute error = 0.00027489585840071600744595777792 relative error = 0.028645081069927229650075934322073 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1224.5MB, alloc=4.6MB, time=67.83 x[1] = 0.286 y2[1] (analytic) = 0.28211697220929388922591364599979 y2[1] (numeric) = 0.28601591484068033747003510120085 absolute error = 0.00389894263138644824412145520106 relative error = 1.3820305105550129179367902989663 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95938001542217904351745567665462 y1[1] (numeric) = 0.95910124102252139109773126602143 absolute error = 0.00027877439965765241972441063319 relative error = 0.029057765971388993471878801562812 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1228.3MB, alloc=4.6MB, time=68.05 x[1] = 0.287 y2[1] (analytic) = 0.28307621100634505725374014442268 y2[1] (numeric) = 0.28701619480327230064718998553382 absolute error = 0.00393998379692724339344984111114 relative error = 1.3918456033166736123353485312607 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95909741880702150572192572529021 y1[1] (numeric) = 0.95881472496802469383659447824158 absolute error = 0.00028269383899681188533124704863 relative error = 0.029474986946419076051033093718925 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1232.1MB, alloc=4.6MB, time=68.26 x[1] = 0.288 y2[1] (analytic) = 0.28403516672720880861997359506588 y2[1] (numeric) = 0.28801647868964502269169220338317 absolute error = 0.00398131196243621407171860831729 relative error = 1.4016968420885430664957597803359 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95881386309452508568712647767644 y1[1] (numeric) = 0.95852720863160692272192522263382 absolute error = 0.00028665446291816296520125504262 relative error = 0.029896779130101397909266123145813 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1235.9MB, alloc=4.6MB, time=68.47 TOP MAIN SOLVE Loop memory used=1239.7MB, alloc=4.6MB, time=68.69 x[1] = 0.289 y2[1] (analytic) = 0.28499383841292950237383670657605 y2[1] (numeric) = 0.28901676654084207829481875028633 absolute error = 0.00402292812791257592098204371028 relative error = 1.411584246984220098935133319511 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95852934856824547227983604823229 y1[1] (numeric) = 0.9582386920093237988357875714478 absolute error = 0.00029065655892167344404847678449 relative error = 0.030323177830269559881708179323184 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.6MB, time=68.90 x[1] = 0.29 y2[1] (analytic) = 0.28595222510483553268394020550437 y2[1] (numeric) = 0.29001705839819106075527398601597 absolute error = 0.0040648332933555280713337805116 relative error = 1.421507838194048938426370518661 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95824387551269716807012477793186 y1[1] (numeric) = 0.95794917509718985775612786113792 absolute error = 0.00029470041550731031399691679394 relative error = 0.03075421852810009420005423977518 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1247.4MB, alloc=4.6MB, time=69.11 x[1] = 0.291 y2[1] (analytic) = 0.28691032584454028750980877839799 y2[1] (numeric) = 0.29101735430330454036205659772388 absolute error = 0.00410702845876425285224781932589 relative error = 1.4314676359851922246745961358981 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9579574442133532048168763737751 y1[1] (numeric) = 0.95765865789117816505895178846559 absolute error = 0.00029878632217503975792458530951 relative error = 0.031189936878709095141547711155795 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1251.2MB, alloc=4.6MB, time=69.33 x[1] = 0.292 y2[1] (analytic) = 0.28786813967394310698841324672701 y2[1] (numeric) = 0.29201765429808102248830979554239 absolute error = 0.00414951462413791549989654881538 relative error = 1.4414636607017043031825636217574 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95767005495664485799477993932263 y1[1] (numeric) = 0.95736714038722003086226306466468 absolute error = 0.00030291456942482713251687465795 relative error = 0.031630368711752245797079824036342 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1255.0MB, alloc=4.6MB, time=69.54 x[1] = 0.293 y2[1] (analytic) = 0.28882566563523024153475058819466 y2[1] (numeric) = 0.29301795842470590539515444877576 absolute error = 0.0041922927894756638604038605811 relative error = 1.4514959327646048147543191549678 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95738170802996136036307836927879 y1[1] (numeric) = 0.95707462258120472341205314458322 absolute error = 0.00030708544875663695102522469557 relative error = 0.032075550032028257624877162370831 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1258.8MB, alloc=4.6MB, time=69.75 x[1] = 0.294 y2[1] (analytic) = 0.28978290277087580965551370393053 y2[1] (numeric) = 0.29401826672565243774450486676576 absolute error = 0.00423536395477662808899116283523 relative error = 1.4615644726719525800883549220695 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95709240372164961457635953935068 y1[1] (numeric) = 0.95678110446897918171063254800839 absolute error = 0.00031129925267043286572699134229 relative error = 0.032525517020085739570181749749438 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1262.6MB, alloc=4.6MB, time=69.96 x[1] = 0.295 y2[1] (analytic) = 0.29073985012364275547489311797684 y2[1] (numeric) = 0.29501857924368267581986692442626 absolute error = 0.00427872912003992034497380644942 relative error = 1.4716693009989197799134323290988 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95680214232101390483767768056805 y1[1] (numeric) = 0.95648658604634772718759529067987 absolute error = 0.00031555627466617765008238988818 relative error = 0.032980306032833513646019287609878 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1266.5MB, alloc=4.6MB, time=70.17 x[1] = 0.296 y2[1] (analytic) = 0.29169650673658380597155308334595 y2[1] (numeric) = 0.2960188960218484404541182283095 absolute error = 0.00432238928526463448256514496355 relative error = 1.481810438397866431122210412344 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9565109241183156075942932849186 y1[1] (numeric) = 0.95619106730907177441370894279846 absolute error = 0.00031985680924383318058434212014 relative error = 0.033439953604154393985607745440592 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1270.3MB, alloc=4.6MB, time=70.39 TOP MAIN SOLVE Loop memory used=1274.1MB, alloc=4.6MB, time=70.60 x[1] = 0.297 y2[1] (analytic) = 0.29265287165304242792582485775268 y2[1] (numeric) = 0.29701921710349227366327001489244 absolute error = 0.00436634545044984573744515713976 relative error = 1.4919879055984151593597737180058 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95621874940477290127632084653473 y1[1] (numeric) = 0.95589454825286954085802383314338 absolute error = 0.00032420115190336041829701339135 relative error = 0.033904496445522446493186791559318 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1277.9MB, alloc=4.6MB, time=70.81 x[1] = 0.298 y2[1] (analytic) = 0.29360894391665378457616020190792 y2[1] (numeric) = 0.29801954253224839498521046855439 absolute error = 0.00441059861559461040905026664647 relative error = 1.5022017234075262685261173678154 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95592561847256047507857469975975 y1[1] (numeric) = 0.95559702887341575568849591722186 absolute error = 0.00032858959914471939007878253789 relative error = 0.034373971446623746337054829916393 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1281.7MB, alloc=4.6MB, time=71.03 x[1] = 0.299 y2[1] (analytic) = 0.29456472257134569198388844399979 y2[1] (numeric) = 0.29901987235204365752242914245695 absolute error = 0.00445514978069796553854069845716 relative error = 1.5124519127095731076536149403128 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95563153161480923678590417222355 y1[1] (numeric) = 0.95529850916634136761641882818939 absolute error = 0.00033302244846786916948534403416 relative error = 0.034848415675980650646391031195658 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1285.5MB, alloc=4.6MB, time=71.24 x[1] = 0.3 y2[1] (analytic) = 0.29552020666133957510532074568503 y2[1] (numeric) = 0.30002020660709850368772216123362 absolute error = 0.00449999994575892858240141554859 relative error = 1.5227384944664177356224671963361 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95533648912560601964231022756805 y1[1] (numeric) = 0.95499898912723325178496162959792 absolute error = 0.00033749999837276785734859797013 relative error = 0.035327866381579603892021126538882 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1289.3MB, alloc=4.6MB, time=71.46 x[1] = 0.301 y2[1] (analytic) = 0.29647539523115142357024549756582 y2[1] (numeric) = 0.30102054534192792065187788004946 absolute error = 0.00454515011077649708163238248364 relative error = 1.5330614897174868841791065835302 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95504049129999328826413672868155 y1[1] (numeric) = 0.95469846875163391570210978935255 absolute error = 0.000342022548359372562026939329 relative error = 0.03581236099150249355066433504847 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1293.2MB, alloc=4.6MB, time=71.66 x[1] = 0.302 y2[1] (analytic) = 0.29743028732559274716585906573658 y2[1] (numeric) = 0.30202088860134239549234267019985 absolute error = 0.00459060127574964832648360446327 relative error = 1.543420919579848219724513888742 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95474353843396884359763040822611 y1[1] (numeric) = 0.95439694803504120421830789458486 absolute error = 0.00034659039892763937932251364125 relative error = 0.036301937114561573772381141798905 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1297.0MB, alloc=4.6MB, time=71.87 x[1] = 0.303 y2[1] (analytic) = 0.2983848819897715310251764055494 y2[1] (numeric) = 0.30302123643044887004186649698219 absolute error = 0.00463635444067733901669009143279 relative error = 1.5538168052482869043413893909838 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95444563082448552692116458887338 y1[1] (numeric) = 0.9540944269729080035491036274832 absolute error = 0.00035120385157752337206096139018 relative error = 0.036796632540937974891934306796869 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1300.8MB, alloc=4.6MB, time=72.08 x[1] = 0.304 y2[1] (analytic) = 0.29933917826909319051896635426711 y2[1] (numeric) = 0.3040215888746516954361279510946 absolute error = 0.00468241060555850491716159682749 relative error = 1.5642491679953824565311114216098 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95414676876945092289242265100057 y1[1] (numeric) = 0.9537909055606419443430935224565 absolute error = 0.00035586320880897854932912854407 relative error = 0.037296485242823816746585098210359 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1304.6MB, alloc=4.6MB, time=72.30 x[1] = 0.305 y2[1] (analytic) = 0.30029317520926152585025671074844 y2[1] (numeric) = 0.30502194597965358635933839029075 absolute error = 0.00472877077039206050908167954231 relative error = 1.5747180291715859121334103838682 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95384695256772706164083820063833 y1[1] (numeric) = 0.95348638379360510379547202534951 absolute error = 0.00036056877412195784536617528882 relative error = 0.037801533375067943885479992386803 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1308.4MB, alloc=4.6MB, time=72.51 TOP MAIN SOLVE Loop memory used=1312.2MB, alloc=4.6MB, time=72.72 x[1] = 0.306 y2[1] (analytic) = 0.30124687185627967635045450773953 y2[1] (numeric) = 0.30602230779145657498682484345055 absolute error = 0.00477543593517689863637033571102 relative error = 1.5852234102052972859036860428138 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95354618251913011990558984520543 y1[1] (numeric) = 0.95318086166711370680748637577261 absolute error = 0.00036532085201641309810346943282 relative error = 0.03831181527582530087924671292761 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1316.0MB, alloc=4.6MB, time=72.94 x[1] = 0.307 y2[1] (analytic) = 0.30220026725645107447612718073115 y2[1] (numeric) = 0.30702267435636296462359132461093 absolute error = 0.00482240709991189014746414387978 relative error = 1.5957653326029433342249002891653 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95324445892443012121944943901075 y1[1] (numeric) = 0.95287433917643782619210083395971 absolute error = 0.00037011974799229502734860505104 relative error = 0.03882736946720996606271929272144 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1319.9MB, alloc=4.6MB, time=73.15 x[1] = 0.308 y2[1] (analytic) = 0.30315336045638039950549063667997 y2[1] (numeric) = 0.30802304572097628303785819984031 absolute error = 0.00486968526459588353236756316034 relative error = 1.6063438179490556194329866292822 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95294178208535063513878361464923 y1[1] (numeric) = 0.95256681631680108192617477392235 absolute error = 0.00037496576854955321260884072688 relative error = 0.039348234655951862168856695683049 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1323.7MB, alloc=4.6MB, time=73.36 x[1] = 0.309 y2[1] (analytic) = 0.3041061505029745309336505261852 y2[1] (numeric) = 0.30902342193220223548857924513328 absolute error = 0.00491727142922770455492871894808 relative error = 1.6169588879063488762367313790043 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95263815230456847552000937026516 y1[1] (numeric) = 0.95225829308338033944946016502781 absolute error = 0.00037985922118813607054920523735 relative error = 0.039874449734057162437915346804817 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1327.5MB, alloc=4.6MB, time=73.57 x[1] = 0.31 y2[1] (analytic) = 0.30505863644344350156564332395896 y2[1] (numeric) = 0.31002380303724965744593602874905 absolute error = 0.00496516659380615588029270479009 relative error = 1.6276105642157996807150999633535 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95233356988571339784280543620221 y1[1] (numeric) = 0.95194876947130540701072496449298 absolute error = 0.00038480041440799083208047170923 relative error = 0.040406053779472410912789666878618 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1331.3MB, alloc=4.6MB, time=73.78 x[1] = 0.311 y2[1] (analytic) = 0.30601081732530145030632412462842 y2[1] (numeric) = 0.3110241890836314670038092466172 absolute error = 0.00501337175833001669748512198878 relative error = 1.638298868696725422377004868732 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95202803513336779558038209780341 y1[1] (numeric) = 0.95163824547565873206130994365485 absolute error = 0.00038978965770906351907215414856 relative error = 0.040943086056752375759153428148601 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1335.1MB, alloc=4.6MB, time=73.99 x[1] = 0.312 y2[1] (analytic) = 0.30696269219636757464614836406167 y2[1] (numeric) = 0.31202458011916561698322663458784 absolute error = 0.00506188792279804233707827052617 relative error = 1.6490238232468635797705396806294 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95172154835306639561711310406623 y1[1] (numeric) = 0.95132672109147509669642747125235 absolute error = 0.00039482726159129892068563281388 relative error = 0.041485586017731654577625535980282 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1338.9MB, alloc=4.6MB, time=74.20 x[1] = 0.313 y2[1] (analytic) = 0.30791426010476708284189498051468 y2[1] (numeric) = 0.31302497619197604672578707640914 absolute error = 0.00511071608720896388389209589446 relative error = 1.659785449842451300130736290195 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95141410985129595271383424449514 y1[1] (numeric) = 0.95101419631374131214451177733272 absolute error = 0.00039991353755464056932246716242 relative error = 0.042033593302200050804653856546405 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1342.7MB, alloc=4.6MB, time=74.42 TOP MAIN SOLVE Loop memory used=1346.6MB, alloc=4.6MB, time=74.63 x[1] = 0.314 y2[1] (analytic) = 0.30886552009893214579137883495571 y2[1] (numeric) = 0.31402537735049363357606052137393 absolute error = 0.00515985725156148778468168641822 relative error = 1.6705837705383052835569397886509 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95110571993549494302111412882791 y1[1] (numeric) = 0.95070067113739591230493122177938 absolute error = 0.00040504879809903071618290704853 relative error = 0.042587147738581740429167170390666 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1350.4MB, alloc=4.6MB, time=74.84 x[1] = 0.315 y2[1] (analytic) = 0.30981647122760284860120051593398 y2[1] (numeric) = 0.31502578364345714405196332058785 absolute error = 0.00520931241585429545076280465387 relative error = 1.6814188074679019722129378117399 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95079637891405325664080365633916 y1[1] (numeric) = 0.95038614555732884633437409184672 absolute error = 0.00041023335672441030642956449244 relative error = 0.043146289344618248383295516995263 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1354.2MB, alloc=4.6MB, time=75.05 x[1] = 0.316 y2[1] (analytic) = 0.31076711253982814184658196132219 y2[1] (numeric) = 0.31602619511991418470210858577408 absolute error = 0.00525908258008604285552662445189 relative error = 1.6922905828434580450450281687792 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95048608709631188923617161314611 y1[1] (numeric) = 0.95007061956838117028222045348078 absolute error = 0.00041546752793071895395115966533 relative error = 0.043711058328055254097610449459239 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1358.0MB, alloc=4.6MB, time=75.26 x[1] = 0.317 y2[1] (analytic) = 0.3117174430849667925223366371764 y2[1] (numeric) = 0.31702661182922215264913116944394 absolute error = 0.00530916874425536012679453226754 relative error = 1.7031991189560112185152605148357 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.95017484479256263269093478735519 y1[1] (numeric) = 0.94975409316534473777521358160348 absolute error = 0.00042075162721789491572120575171 relative error = 0.044281495087333245844396447304309 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1361.8MB, alloc=4.6MB, time=75.48 x[1] = 0.318 y2[1] (analytic) = 0.31266746191268833468402332282246 y2[1] (numeric) = 0.31802703382104918581798686012818 absolute error = 0.00535957190836085113396353730572 relative error = 1.7141444381755013538491446217815 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94986265231404776481749194299381 y1[1] (numeric) = 0.94943656634296188975174549494175 absolute error = 0.00042608597108587506574644805206 relative error = 0.044857640212282043626440409420909 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1365.6MB, alloc=4.6MB, time=75.69 x[1] = 0.319 y2[1] (analytic) = 0.3136171680729740197783328610944 y2[1] (numeric) = 0.31902746114537511284822538118015 absolute error = 0.00541029307240109306989252008575 relative error = 1.7251265629508518712991794969628 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94954950997295973811467194446714 y1[1] (numeric) = 0.94911803909592514324607212139178 absolute error = 0.00043147087703459486859982307536 relative error = 0.045439534484819210503725302575953 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1369.4MB, alloc=4.6MB, time=75.89 x[1] = 0.32 y2[1] (analytic) = 0.31456656061611776666175754341715 y2[1] (numeric) = 0.32002789385249240268923677642907 absolute error = 0.00546133323637463602747923301192 relative error = 1.7361455158100514719276242090252 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94923541808244086757530727376609 y1[1] (numeric) = 0.94879851141887687922277462032277 absolute error = 0.00043690666356398835253265344332 relative error = 0.046027218879652372386244273368636 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1373.3MB, alloc=4.6MB, time=76.11 x[1] = 0.321 y2[1] (analytic) = 0.31551563859272711130659311114346 y2[1] (numeric) = 0.32102833199300711387747076067919 absolute error = 0.00551269340028000257087764953573 relative error = 1.7472013193602361674140028314139 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94892037695658301754394513282693 y1[1] (numeric) = 0.94847798330640902946178438864389 absolute error = 0.00044239365017398808216074418304 relative error = 0.046620734564985466457920507951122 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1377.1MB, alloc=4.6MB, time=76.32 x[1] = 0.322 y2[1] (analytic) = 0.31646440105372415619332366722217 y2[1] (numeric) = 0.32202877561783984349462860771782 absolute error = 0.00556437456411568730130494049565 relative error = 1.75829399628777161839491242754 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94860438691042728762500927330517 y1[1] (numeric) = 0.94815645475306276249429027788282 absolute error = 0.00044793215736452513071899542235 relative error = 0.04722012290322893853433357568744 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1380.9MB, alloc=4.6MB, time=76.53 TOP MAIN SOLVE Loop memory used=1384.7MB, alloc=4.6MB, time=76.74 x[1] = 0.323 y2[1] (analytic) = 0.31741284705034651938844010589189 y2[1] (numeric) = 0.32302922477822667580582714311253 absolute error = 0.00561637772788015641738703722064 relative error = 1.7694235693583357818457845002278 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94828744825996369764172664557596 y1[1] (numeric) = 0.94783392575332816858984754995423 absolute error = 0.00045352250663552905187909562173 relative error = 0.047825425451713909795622718553408 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1388.5MB, alloc=4.6MB, time=76.96 x[1] = 0.324 y2[1] (analytic) = 0.31836097563414828330674298266094 y2[1] (numeric) = 0.32402967952572013057673440364428 absolute error = 0.00566870389157184726999142098334 relative error = 1.7805900614170018680163368339608 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9479695613221308716461339080079 y1[1] (numeric) = 0.94751039630164394379500909973215 absolute error = 0.00045916502048692785112480827575 relative error = 0.048436683963410333475569413163776 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1392.3MB, alloc=4.6MB, time=77.17 x[1] = 0.325 y2[1] (analytic) = 0.31930878585700094315718106234965 y2[1] (numeric) = 0.32503013991219011106867651973878 absolute error = 0.00572135405518916791149545738913 relative error = 1.7917934953883216074335441946542 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94765072641481572098047978647747 y1[1] (numeric) = 0.94718586639239707302380047298078 absolute error = 0.00046486002241864795667931349669 relative error = 0.049053940387649162228463471186791 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1396.2MB, alloc=4.6MB, time=77.38 x[1] = 0.326 y2[1] (analytic) = 0.32025627677109435507127709943546 y2[1] (numeric) = 0.3260306059898248517107153717229 absolute error = 0.00577432921873049663943827228744 relative error = 1.8030338942764088284880529406295 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94733094385685312639034022269541 y1[1] (numeric) = 0.94686033601992251220036120864504 absolute error = 0.00047060783693061418997901405037 relative error = 0.049677236870848547036936959350206 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1400.0MB, alloc=4.6MB, time=77.59 x[1] = 0.327 y2[1] (analytic) = 0.32120344742893768391319272235417 y2[1] (numeric) = 0.32703107781113186544769656514555 absolute error = 0.00582763038219418153450384279138 relative error = 1.8143112811650233461220662627774 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94701021396802561918976419820327 y1[1] (numeric) = 0.94653380517850286945407603495382 absolute error = 0.00047640878952274973568816324945 relative error = 0.050306615757244088666516384946327 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1403.8MB, alloc=4.6MB, time=77.80 x[1] = 0.328 y2[1] (analytic) = 0.32215029688336035077048461177134 y2[1] (numeric) = 0.32803155542893889076326726476363 absolute error = 0.00588125854557853999278265299229 relative error = 1.8256256792176551621388335348012 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94668853706906306147876906886782 y1[1] (numeric) = 0.94620627386236808536752044924665 absolute error = 0.00048226320669497611124861962117 relative error = 0.050942119589623162816204049478561 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1407.6MB, alloc=4.6MB, time=78.01 x[1] = 0.329 y2[1] (analytic) = 0.32309682418751298012460448214665 y2[1] (numeric) = 0.3290320388963948383768634211022 absolute error = 0.00593521470888185825225893895555 relative error = 1.8369771116776089776559891383028 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9463659134816423254135051923513 y1[1] (numeric) = 0.9458777420656951122775462118977 absolute error = 0.0004881714159472131359589804536 relative error = 0.051583791110063340258962435595703 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1411.4MB, alloc=4.6MB, time=78.22 x[1] = 0.33 y2[1] (analytic) = 0.32404302839486834670019569617022 y2[1] (numeric) = 0.33003252826697073761366591775441 absolute error = 0.00598949987210239091347022158419 relative error = 1.8483656018680890182271031556766 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94604234352838697152941057836621 y1[1] (numeric) = 0.94554820978260759262983328517994 absolute error = 0.00049413374577937889957729318627 relative error = 0.052231673260674923411549246141878 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1415.2MB, alloc=4.6MB, time=78.44 TOP MAIN SOLVE Loop memory used=1419.0MB, alloc=4.6MB, time=78.65 x[1] = 0.331 y2[1] (analytic) = 0.32498890855922232199223966285307 y2[1] (numeric) = 0.33103302359446068244652516179005 absolute error = 0.00604411503523836045428549893698 relative error = 1.8597911731922841721579285191692 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94571782753286692611767723853306 y1[1] (numeric) = 0.94521767700717553638723574838707 absolute error = 0.00050015052569138973044149014599 relative error = 0.052885809184347620919743616656686 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1422.9MB, alloc=4.6MB, time=78.87 x[1] = 0.332 y2[1] (analytic) = 0.32593446373469482047010549220433 y2[1] (numeric) = 0.33203352493298277720885363379196 absolute error = 0.00609906119828795673874814158763 relative error = 1.8712538491334534425459565901357 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94539236581959815765535185934806 y1[1] (numeric) = 0.94488614373341499749225022101134 absolute error = 0.00050622208618316016310163833672 relative error = 0.053546242225501381992624504838589 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1426.7MB, alloc=4.6MB, time=79.08 x[1] = 0.333 y2[1] (analytic) = 0.32687969297573074545755670252426 y2[1] (numeric) = 0.33303403233698008197748590813621 absolute error = 0.00615433936124933651992920561195 relative error = 1.8827536532550117135740257417913 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94506595871404235228939436813284 y1[1] (numeric) = 0.94455360995528774938393632626192 absolute error = 0.00051234875875460290545804187092 relative error = 0.054213015930841412368218826664915 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1430.5MB, alloc=4.6MB, time=79.29 x[1] = 0.334 y2[1] (analytic) = 0.32782459533710093468776910038533 y2[1] (numeric) = 0.33403454586122155762450564817508 absolute error = 0.00620995052412062293673654778975 relative error = 1.894290609200615831590865354725 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94473860654260658837501890788084 y1[1] (numeric) = 0.94422007566670095956961972770057 absolute error = 0.00051853087590562880539918018027 relative error = 0.05488617405011739394253813826928 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1434.3MB, alloc=4.6MB, time=79.50 x[1] = 0.335 y2[1] (analytic) = 0.32876916987390310553241427836219 y2[1] (numeric) = 0.33503506556080301053703907497065 absolute error = 0.00626589568689990500462479660846 relative error = 1.9058647406942510015136007306124 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9444103096326430100686426826321 y1[1] (numeric) = 0.94388554086150686325170927227009 absolute error = 0.00052476877113614681693341036201 relative error = 0.055565760536886930244777209177562 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1438.1MB, alloc=4.6MB, time=79.71 x[1] = 0.336 y2[1] (analytic) = 0.32971341564156279990386350150578 y2[1] (numeric) = 0.33603559149114803700401440216139 absolute error = 0.00632217584958523710015090065561 relative error = 1.9174760715403174990893928092691 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94408106831244849997576908040049 y1[1] (numeric) = 0.94355000553350243600996077349502 absolute error = 0.00053106277894606396580830690547 relative error = 0.056251819549283240093264426547683 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1441.9MB, alloc=4.6MB, time=79.92 x[1] = 0.337 y2[1] (analytic) = 0.33065733169583432882956708043654 y2[1] (numeric) = 0.33703612370800896726888672342366 absolute error = 0.00637879201217463843931964298712 relative error = 1.9291246256237176995555402608121 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94375088291126435085413242574299 y1[1] (numeric) = 0.94321346967642906553952096914483 absolute error = 0.00053741323483528531461145659816 relative error = 0.056944395450787121919641418202858 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1445.7MB, alloc=4.6MB, time=80.13 x[1] = 0.338 y2[1] (analytic) = 0.33160091709280171669766465675598 y2[1] (numeric) = 0.33803666226746780924732783281472 absolute error = 0.00643574517466609254966317605874 relative error = 1.9408104269099434232395305421182 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9434197537592759363724326587988 y1[1] (numeric) = 0.94287593328397222244508618816631 absolute error = 0.00054382047530371392734647063249 relative error = 0.057643532811003211402716468906539 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1449.6MB, alloc=4.6MB, time=80.34 x[1] = 0.339 y2[1] (analytic) = 0.33254417088887964517288215524501 y2[1] (numeric) = 0.33903720722593719190888045205297 absolute error = 0.00649303633705754673599829680796 relative error = 1.9525334994451635986426908783137 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94308768118761238092498918203633 y1[1] (numeric) = 0.94253739634976113009151126221469 absolute error = 0.00055028483785125083347791982164 relative error = 0.058349276406440555208492191954746 % Correct digits = 3 h = 0.001 memory used=1453.4MB, alloc=4.6MB, time=80.56 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1457.2MB, alloc=4.6MB, time=80.78 x[1] = 0.34 y2[1] (analytic) = 0.33348709214081439678177148703079 y2[1] (numeric) = 0.34003775864016130832157633250452 absolute error = 0.00655066649934691153980484547373 relative error = 1.9642938673563122435532598795789 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94275466552834622850264406002658 y1[1] (numeric) = 0.94219785886736843351120521764224 absolute error = 0.00055680666097779499143884238434 relative error = 0.059061671221297523789021548103082 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1461.0MB, alloc=4.6MB, time=80.99 x[1] = 0.341 y2[1] (analytic) = 0.33442967990568479816634941856096 y2[1] (numeric) = 0.34103831656721685835851769330254 absolute error = 0.00660863666153206019216827474158 relative error = 1.9760915548511767647368756549632 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9424207071144931106202457013121 y1[1] (numeric) = 0.94185732083030986736865128433826 absolute error = 0.00056338628418324325159441697384 relative error = 0.059780762448251086350006797460173 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1464.8MB, alloc=4.6MB, time=81.20 x[1] = 0.342 y2[1] (analytic) = 0.33537193324090316300519235282508 y2[1] (numeric) = 0.34203888106451399106542145062673 absolute error = 0.00666694782361082806022909780165 relative error = 1.9879265862184865767546568618959 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94208580628001141330104509486035 y1[1] (numeric) = 0.94151578223204392298238975835641 absolute error = 0.00057002404796749031865533650394 relative error = 0.060506595489250471255432528879553 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1468.6MB, alloc=4.6MB, time=81.41 x[1] = 0.343 y2[1] (analytic) = 0.33631385120421623460104410180696 y2[1] (numeric) = 0.34303945218979724668812568671442 absolute error = 0.00672560098558101208708158490746 relative error = 1.9997989858280020404612391568352 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94174996335980194311833761667723 y1[1] (numeric) = 0.94117324306597151440480325581332 absolute error = 0.00057672029383042871353436086391 relative error = 0.061239215956315235297025818674946 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1472.4MB, alloc=4.6MB, time=81.62 x[1] = 0.344 y2[1] (analytic) = 0.33725543285370612813399406263873 y2[1] (numeric) = 0.34404003000114649835905780066189 absolute error = 0.00678459714744037022506373802316 relative error = 2.0117087781306037217373210128207 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94141317868970759229468436491135 y1[1] (numeric) = 0.94082970332543564356004489609719 absolute error = 0.00058347536427194873463946881416 relative error = 0.061978669672337765416973191455745 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1476.3MB, alloc=4.6MB, time=81.83 x[1] = 0.345 y2[1] (analytic) = 0.33819667724779127257928354435702 y2[1] (numeric) = 0.34504061455697789344166377650416 absolute error = 0.00684393730918662086238023214714 relative error = 2.0236559876583819710134698679037 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9410754526065130028590479241997 y1[1] (numeric) = 0.94048516300372106444045095298631 absolute error = 0.00059028960279193841859697121339 relative error = 0.062725002671890236634104838559587 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1480.1MB, alloc=4.6MB, time=82.05 x[1] = 0.346 y2[1] (analytic) = 0.33913758344522735228879832753336 y2[1] (numeric) = 0.3460412059160447945317979974335 absolute error = 0.00690362247081744224299966990014 relative error = 2.0356406390247268241441420886922 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94073678544794422986217840209091 y1[1] (numeric) = 0.94013962209405394636178051284521 absolute error = 0.0005971633538902835003978892457 relative error = 0.063478261202036050086691025984522 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1483.9MB, alloc=4.6MB, time=82.26 x[1] = 0.347 y2[1] (analytic) = 0.34007815050510824823530587536464 y2[1] (numeric) = 0.34704180413743872011507302833064 absolute error = 0.006963653632330471879767152966 relative error = 2.047662756924418225193078299749 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94039717755266840365058652213218 y1[1] (numeric) = 0.93979308058960153627762567964067 absolute error = 0.00060409696306686737296084249151 relative error = 0.064238491723145775269093410389571 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1487.7MB, alloc=4.6MB, time=82.47 TOP MAIN SOLVE Loop memory used=1491.5MB, alloc=4.6MB, time=82.68 x[1] = 0.348 y2[1] (analytic) = 0.34101837748686697891849595206509 y2[1] (numeric) = 0.34804240928059028487916878203819 absolute error = 0.0070240317937233059606728299731 relative error = 2.0597223661337165716934492667219 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.94005662926029339119944149961845 y1[1] (numeric) = 0.93944553848347182015333686710102 absolute error = 0.00061109077682157104610463251743 relative error = 0.065005740909717620704784780520342 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1495.3MB, alloc=4.6MB, time=82.89 x[1] = 0.349 y2[1] (analytic) = 0.34195826345027664093188374259728 y2[1] (numeric) = 0.34904302140527013968010047800245 absolute error = 0.00708475795499349874821673540517 relative error = 2.0718194915104535829483467535812 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93971514091136745650473236707785 y1[1] (numeric) = 0.93909699576871318339980871893006 absolute error = 0.00061814514265427310492364814779 relative error = 0.065780055651202457464704340703822 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1499.2MB, alloc=4.6MB, time=83.10 x[1] = 0.35 y2[1] (analytic) = 0.34289780745545134918963490691763 y2[1] (numeric) = 0.35004364057158991116144479504733 absolute error = 0.0071458331161385619718098881297 relative error = 2.0839541579941234919394386261612 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93937271284737892003503235730367 y1[1] (numeric) = 0.93874745243831407036747319858179 absolute error = 0.00062526040906484966755915872188 relative error = 0.066561483052833420107561928050108 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1503.0MB, alloc=4.6MB, time=83.31 x[1] = 0.351 y2[1] (analytic) = 0.34383700856284717681237234198958 y2[1] (numeric) = 0.35104426684000314102552361312229 absolute error = 0.00720725827715596421315127113271 relative error = 2.0961263906059745614138379706022 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93902934541075581724320689214026 y1[1] (numeric) = 0.93839690848520264290084739070386 absolute error = 0.0006324369255531743423595014364 relative error = 0.067350070436460109787553469204974 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1506.8MB, alloc=4.6MB, time=83.52 x[1] = 0.352 y2[1] (analytic) = 0.34477586583326309467102476583608 y2[1] (numeric) = 0.35204490027130622495554473188459 absolute error = 0.00726903443804313028451996604851 relative error = 2.1083362144491009247214721604567 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93868503894486555613840666528628 y1[1] (numeric) = 0.9380453639022464379539845569662 absolute error = 0.00063967504261911818442210832008 relative error = 0.068145865341387424445011588033224 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1510.6MB, alloc=4.6MB, time=83.73 x[1] = 0.353 y2[1] (analytic) = 0.34571437832784191058777757986105 y2[1] (numeric) = 0.35304554092663935118769894693447 absolute error = 0.00733116259879744059992136707342 relative error = 2.1205836547085347519774796652942 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93833979379401457391868824709369 y1[1] (numeric) = 0.937692818682252024267177989607 absolute error = 0.00064697511176254965151025748669 relative error = 0.068948915525219041166799714549247 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1514.4MB, alloc=4.6MB, time=83.95 x[1] = 0.354 y2[1] (analytic) = 0.34665254510807120819318680856723 y2[1] (numeric) = 0.35404618886748743873221285741952 absolute error = 0.00739364375941623053902604885229 relative error = 2.1328687366513387421264099711823 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93799361030344799266460557871336 y1[1] (numeric) = 0.93733927281796465810526820665097 absolute error = 0.00065433748548333455933737206239 relative error = 0.069759268964705575975775550344142 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1518.2MB, alloc=4.6MB, time=84.16 x[1] = 0.355 y2[1] (analytic) = 0.34759036523578428543851725963473 y2[1] (numeric) = 0.3550468441556810752423567715618 absolute error = 0.00745647891989678980383951192707 relative error = 2.1451914856266989414872553047015 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93764648881934927409411666196697 y1[1] (numeric) = 0.93698472630206793805790503338459 absolute error = 0.00066176251728133603621162858238 relative error = 0.070576973856597446482410640844068 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1522.0MB, alloc=4.6MB, time=84.37 x[1] = 0.356 y2[1] (analytic) = 0.34852783777316109276236639210034 y2[1] (numeric) = 0.35604750685339745453040706943693 absolute error = 0.00751966908023636176804067733659 memory used=1525.9MB, alloc=4.6MB, time=84.59 relative error = 2.1575519270660178893606019418844 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93729842968883987337915069000988 y1[1] (numeric) = 0.93662917912718345890211711531022 absolute error = 0.00066925056165641447703357469966 relative error = 0.07140207861850246300666750666447 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1529.7MB, alloc=4.6MB, time=84.80 x[1] = 0.357 y2[1] (analytic) = 0.34946496178272917091063572609188 y2[1] (numeric) = 0.35704817702316131372956237504883 absolute error = 0.00758321524043214281892664895695 relative error = 2.1699500864830080912814537670213 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9369494332599788920241818021889 y1[1] (numeric) = 0.93627263128587046452754240844512 absolute error = 0.00067680197410842749663939374378 relative error = 0.072234631889748173954514805042564 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1533.5MB, alloc=4.6MB, time=85.01 x[1] = 0.358 y2[1] (analytic) = 0.35040173632736458840891197422432 y2[1] (numeric) = 0.3580488547278458701008128823964 absolute error = 0.00764711840048128169190090817208 relative error = 2.1823859894737858205035514487388 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93659949988176272980715658449232 y1[1] (numeric) = 0.93591508277062549992467419348313 absolute error = 0.00068441711113722988248239100919 relative error = 0.073074682532248991411014932199249 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1537.3MB, alloc=4.6MB, time=85.22 x[1] = 0.359 y2[1] (analytic) = 0.35133816047029287868632042235473 y2[1] (numeric) = 0.35904954003067375748376217281881 absolute error = 0.00771137956038087879744175046408 relative error = 2.1948596617169652483032871473982 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93624862990412473578312337463565 y1[1] (numeric) = 0.93555653357388206223647816099585 absolute error = 0.0006920963302426735466452136398 relative error = 0.073922279631378123090758038023344 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1541.1MB, alloc=4.6MB, time=85.43 x[1] = 0.36 y2[1] (analytic) = 0.35227423327508997684991343592073 y2[1] (numeric) = 0.36005023299521796239040085343387 absolute error = 0.00777599972012798554048741751314 relative error = 2.2073711289737529036935970841464 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93589682367793485835091236812474 y1[1] (numeric) = 0.93519698368801025087373711551633 absolute error = 0.00069983998992460747717525260841 relative error = 0.074777472496844336966552401530298 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1544.9MB, alloc=4.6MB, time=85.64 x[1] = 0.361 y2[1] (analytic) = 0.35320995380568315610865731755197 y2[1] (numeric) = 0.36105093368540275974083133894903 absolute error = 0.00784097987971960363217402139706 relative error = 2.2199204170880424631405026133035 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93554408155499929438321645858698 y1[1] (numeric) = 0.93483643310531641669448084702258 absolute error = 0.0007076484496828776887356115644 relative error = 0.075640310663573585078724401897365 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1548.7MB, alloc=4.6MB, time=85.85 x[1] = 0.362 y2[1] (analytic) = 0.35414532112635196384608109204584 y2[1] (numeric) = 0.36205164216550464823994309152626 absolute error = 0.00790632103915268439386199948042 relative error = 2.2325075519865098708772646716754 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93519040388806013742042368226048 y1[1] (numeric) = 0.93447488181804281024785971901948 absolute error = 0.000715522070017327172563963241 relative error = 0.076510843892595513210142906728303 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1552.6MB, alloc=4.6MB, time=86.06 x[1] = 0.363 y2[1] (analytic) = 0.35508033430172915734065114613672 y2[1] (numeric) = 0.36305235850015328539403762572034 absolute error = 0.00797202419842412805338647958362 relative error = 2.2451325596787087904134166565774 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93483579103079502492855307277957 y1[1] (numeric) = 0.93411232981836722908282152310685 absolute error = 0.00072346121242779584573154967272 relative error = 0.077389122171934883296173876618288 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1556.4MB, alloc=4.6MB, time=86.28 x[1] = 0.364 y2[1] (analytic) = 0.35601499239680163913293600276189 y2[1] (numeric) = 0.36405308275433242216640257778418 absolute error = 0.00803809035753078303346657502229 relative error = 2.2577954662571663878382469345587 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93448024333781678462164666829116 y1[1] (numeric) = 0.93374877709840266412195215061837 absolute error = 0.00073146623941412049969451767279 relative error = 0.078275195717507935624202543300132 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1560.2MB, alloc=4.6MB, time=86.49 TOP MAIN SOLVE Loop memory used=1564.0MB, alloc=4.6MB, time=86.71 x[1] = 0.365 y2[1] (analytic) = 0.35694929447691139203862586273754 y2[1] (numeric) = 0.36505381499338083727083413084511 absolute error = 0.00810452051646944523220826810757 relative error = 2.2704962978974794475206143307286 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93412376116467307984897134848078 y1[1] (numeric) = 0.93338422365019694510084163262055 absolute error = 0.00073953751447613474812971586023 relative error = 0.079169114974023718064143949179366 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1567.8MB, alloc=4.6MB, time=86.92 x[1] = 0.366 y2[1] (analytic) = 0.35788323960775641380647190090305 y2[1] (numeric) = 0.36605455528299327110210707960103 absolute error = 0.00817131567523685729563517869798 relative error = 2.2832350808584108208092981202569 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93376634486784605404738511427659 y1[1] (numeric) = 0.93301866946573238507333810027343 absolute error = 0.00074767540211366897404701400316 relative error = 0.08007093061589040975950933214648 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1571.6MB, alloc=4.6MB, time=87.13 x[1] = 0.367 y2[1] (analytic) = 0.35881682685539165142021065887221 y2[1] (numeric) = 0.36705530368922135930239181026606 absolute error = 0.00823847683382970788218115139385 relative error = 2.2960118414819862083404082649846 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93340799480475197425922335783568 y1[1] (numeric) = 0.93265211453692542398305321827491 absolute error = 0.00075588026782655027617013956077 relative error = 0.080980693548126666898117298090434 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1575.4MB, alloc=4.6MB, time=87.34 x[1] = 0.368 y2[1] (analytic) = 0.35975005528622993504353923254485 y2[1] (numeric) = 0.36805606027847456596261746351016 absolute error = 0.00830600499224463091907823096531 relative error = 2.3088266061935912765607119351564 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93304871133374087371606160489668 y1[1] (numeric) = 0.93228455885562627130148364483893 absolute error = 0.00076415247811460241457796005775 relative error = 0.081898454907278018372446545087404 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1579.3MB, alloc=4.6MB, time=87.55 x[1] = 0.369 y2[1] (analytic) = 0.36068292396704291160720730948157 y2[1] (numeric) = 0.36905682511752111645778054008658 absolute error = 0.00837390115047820485057323060501 relative error = 2.3216794015020691090780687553375 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9326884948140961934887121457059 y1[1] (numeric) = 0.93191600241361854773311407239408 absolute error = 0.00077249240047764575559807331182 relative error = 0.082824266062338339331932793919606 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1583.1MB, alloc=4.6MB, time=87.76 x[1] = 0.37 y2[1] (analytic) = 0.36161543196496197803729246912715 y2[1] (numeric) = 0.37005759827348892991519820072435 absolute error = 0.0084421663085269518779057315972 relative error = 2.3345702539998179934525097409232 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93232734560603442320381290449088 y1[1] (numeric) = 0.93154644520261892598786840393333 absolute error = 0.00078090040341549721594450055755 relative error = 0.083758178615676430823228351827242 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1586.9MB, alloc=4.6MB, time=87.98 x[1] = 0.371 y2[1] (analytic) = 0.36254757834747921412372551768536 y2[1] (numeric) = 0.37105837981386655131470550367984 absolute error = 0.00851080146638733719097998599448 relative error = 2.3474991903628895440438435733288 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93196526407070474082736783086223 y1[1] (numeric) = 0.93117588721427677062127662069835 absolute error = 0.00078937685642797020609121016388 relative error = 0.084700244403967733909580309537719 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1590.7MB, alloc=4.6MB, time=88.19 x[1] = 0.372 y2[1] (analytic) = 0.36347936218244831502813298919735 y2[1] (numeric) = 0.37205916980650408321979581509157 absolute error = 0.00857980762405576819166282589422 relative error = 2.3604662373510871615340287249263 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93160225057018865151559902957351 y1[1] (numeric) = 0.93080432844017377694272589764243 absolute error = 0.00079792213001487457287313193108 relative error = 0.085650515499131206857054774099516 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1594.5MB, alloc=4.6MB, time=88.40 x[1] = 0.373 y2[1] (analytic) = 0.36441078253808552343006430505902 y2[1] (numeric) = 0.37305996831961411713870361896538 memory used=1598.3MB, alloc=4.6MB, time=88.62 absolute error = 0.00864918578152859370863931390636 relative error = 2.3734714218080648297449110150299 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93123830546749962553347177775691 y1[1] (numeric) = 0.93043176887182360899216552388517 absolute error = 0.00080653659567601654130625387174 relative error = 0.086609044209271394173351909198563 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1602.1MB, alloc=4.6MB, time=88.83 x[1] = 0.374 y2[1] (analytic) = 0.3653418384829705613106714458277 y2[1] (numeric) = 0.37406077542177266451442894523275 absolute error = 0.00871893693880210320375749940505 relative error = 2.3865147706614262503742934829464 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93087342912658273524125451107944 y1[1] (numeric) = 0.93005820850067153658563618614929 absolute error = 0.00081522062591119865561832493015 relative error = 0.087575883079625716484432138830918 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1606.0MB, alloc=4.6MB, time=89.04 x[1] = 0.375 y2[1] (analytic) = 0.36627252908604756137290935171626 y2[1] (numeric) = 0.37506159118192008734270262587242 absolute error = 0.00878906209587252596979327415616 relative error = 2.3995963109228243162756790293766 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93050762191231429114947679222956 y1[1] (numeric) = 0.92968364731809407142999517395583 absolute error = 0.00082397459422021971948161827373 relative error = 0.088551084893517010435120029374927 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1609.8MB, alloc=4.6MB, time=89.25 x[1] = 0.376 y2[1] (analytic) = 0.36720285341662599809732563165185 y2[1] (numeric) = 0.37606241566936202841689158056516 absolute error = 0.00885956225273603031956594891331 relative error = 2.4127160696880609239094061307402 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.93014088419050147704264920674576 y1[1] (numeric) = 0.92930808531539860230721006614825 absolute error = 0.00083279887510287473543914059751 relative error = 0.089534702673311348002281572035995 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1613.6MB, alloc=4.6MB, time=89.46 x[1] = 0.377 y2[1] (analytic) = 0.36813281054438161843250852518704 y2[1] (numeric) = 0.37706324895377034119884332476229 absolute error = 0.00893043840938872276633479957525 relative error = 2.4258740741371871255952840987744 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92977321632788198417211006243701 y1[1] (numeric) = 0.9289315224838230293285944591187 absolute error = 0.00084169384405895484351560331831 relative error = 0.090526789681381164813095429313342 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1617.4MB, alloc=4.6MB, time=89.67 x[1] = 0.378 y2[1] (analytic) = 0.3690623995393573721192624268931 y2[1] (numeric) = 0.3780640911051840193146688843904 absolute error = 0.0090016915658266471954064574973 relative error = 2.4390703515346036221992268670857 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92940461869212364451836469951764 y1[1] (numeric) = 0.92855395881453539725936029792124 absolute error = 0.0008506598775882472590044015964 relative error = 0.091527399421073727266371887376614 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1621.2MB, alloc=4.6MB, time=89.88 x[1] = 0.379 y2[1] (analytic) = 0.36999161947196434164758064913733 y2[1] (numeric) = 0.3790649421940101256744632926875 absolute error = 0.00907332272204578402688264355017 relative error = 2.4523049292291615968887831645883 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92903509165182406312328414908702 y1[1] (numeric) = 0.92817539429863352791386237227684 absolute error = 0.00085969735319053520942177681018 relative error = 0.092536585637684968461827589611924 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1625.0MB, alloc=4.6MB, time=90.09 x[1] = 0.38 y2[1] (analytic) = 0.3709204694129826718454854663492 y2[1] (numeric) = 0.38006580229102472121496283586865 absolute error = 0.00914533287804204936947736951945 relative error = 2.4655778346542638905948662097571 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92866463557651024949253080772456 y1[1] (numeric) = 0.92779582892714465162191154030406 absolute error = 0.0008688066493655978706192674205 relative error = 0.093554402319438723150712550699811 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1628.9MB, alloc=4.6MB, time=90.31 x[1] = 0.381 y2[1] (analytic) = 0.37184894843356249909880585201274 y2[1] (numeric) = 0.38106667146737379326413820545202 absolute error = 0.00921772303381129416533235343928 relative error = 2.4788890953279665198193977569026 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92829325083663824806857972574377 y1[1] (numeric) = 0.92741526269102503776653424364677 absolute error = 0.000877988145613210302045482097 relative error = 0.094580903698471392131221520217857 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1632.7MB, alloc=4.6MB, time=90.52 TOP MAIN SOLVE Loop memory used=1636.5MB, alloc=4.6MB, time=90.73 x[1] = 0.382 y2[1] (analytic) = 0.3727770556052248802009636886848 y2[1] (numeric) = 0.38206754979457418352672270613892 absolute error = 0.00929049418934930332575901745412 relative error = 2.4922387388530805374309994735913 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9279209378035927677747050360532 y1[1] (numeric) = 0.92703369558115962439355687851719 absolute error = 0.00088724222243314338114815753601 relative error = 0.095616144251822066723717654116208 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1640.3MB, alloc=4.6MB, time=90.94 x[1] = 0.383 y2[1] (analytic) = 0.37370478999986272083183960133056 y2[1] (numeric) = 0.38306843734451451568967465913295 absolute error = 0.00936364734465179485783505780239 relative error = 2.5056267929172742370932892541805 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92754769684968681063030197960704 y1[1] (numeric) = 0.92665112758836164689339458802792 absolute error = 0.00089656926132516373690739157912 relative error = 0.096660178702428144173965957271153 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1644.1MB, alloc=4.6MB, time=91.15 x[1] = 0.384 y2[1] (analytic) = 0.37463215068974170366478993518755 y2[1] (numeric) = 0.38406933418945612264657313170407 absolute error = 0.00943718349971441898178319651652 relative error = 2.5190532852931757019727712061846 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92717352834816129943791591209232 y1[1] (numeric) = 0.92626755870337226575542504205138 absolute error = 0.00090596964478903368249087004094 relative error = 0.09771306202012646504733049841881 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1647.9MB, alloc=4.6MB, time=91.36 x[1] = 0.385 y2[1] (analytic) = 0.3755591367475012161008867712188 y2[1] (numeric) = 0.3850702404020339733399461146524 absolute error = 0.0095111036545327572390593434336 relative error = 2.5325182438384756983757457109607 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92679843267318470454235060479278 y1[1] (numeric) = 0.92588298891686019339532877171884 absolute error = 0.00091544375632451114702183307394 relative error = 0.098774849422660003893246511726717 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1651.7MB, alloc=4.6MB, time=91.57 x[1] = 0.386 y2[1] (analytic) = 0.37648574724615527762945324499228 y2[1] (numeric) = 0.38607115605525759922053026010376 absolute error = 0.00958540880910232159107701511148 relative error = 2.546021696496030914966110186354 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92642241019985266966222908048989 y1[1] (numeric) = 0.92549741821942132005577862655411 absolute error = 0.00092499198043134960645045393578 relative error = 0.099845596376690144677249853334998 % Correct digits = 3 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1655.6MB, alloc=4.6MB, time=91.78 x[1] = 0.387 y2[1] (analytic) = 0.37741198125909346681396680852865 y2[1] (numeric) = 0.38707208122251202032246128277382 absolute error = 0.00966009996341855350849447424517 relative error = 2.559563671293967548218371993889 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92604546130418763679438115280913 y1[1] (numeric) = 0.92511084660157833878086192312926 absolute error = 0.00093461470260929801351922967987 relative error = 0.10092535859881457269744566892749 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1659.4MB, alloc=4.6MB, time=92.00 x[1] = 0.388 y2[1] (analytic) = 0.37833783786008184790240344929121 y2[1] (numeric) = 0.3880730159775586709533941184701 absolute error = 0.00973517811747682305099066917889 relative error = 2.5731441963457852347626523651213 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92566758636313847019143276459259 y1[1] (numeric) = 0.92472327405378036946461985503123 absolute error = 0.00094431230935810072681290956136 relative error = 0.1020141920565908149235394695732 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1663.2MB, alloc=4.6MB, time=92.21 x[1] = 0.389 y2[1] (analytic) = 0.37926331612326389706109625605126 y2[1] (numeric) = 0.38907396039453632499855192416015 absolute error = 0.00981064427127242793745566810889 relative error = 2.5867632998504613312809242986101 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92528878575458007941297314767738 y1[1] (numeric) = 0.92433470056640258197408973483906 absolute error = 0.00095408518817749743888341283832 relative error = 0.10311215296956546091945115638692 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1667.0MB, alloc=4.6MB, time=92.42 x[1] = 0.39 y2[1] (analytic) = 0.38018841512316142823118209784716 y2[1] (numeric) = 0.39007491454796202083770299442028 absolute error = 0.00988649942480059260652089657312 relative error = 2.6004210100925555426161981293277 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9249090598573130414506767528811 y1[1] (numeric) = 0.9239451261297458183472366397321 absolute error = 0.000963933727567223103440113149 relative error = 0.10421929781030909673510005841922 % Correct digits = 2 h = 0.001 memory used=1670.8MB, alloc=4.6MB, time=92.64 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1674.6MB, alloc=4.6MB, time=92.85 x[1] = 0.391 y2[1] (analytic) = 0.38111313393467551860671055966795 y2[1] (numeric) = 0.39107587851273198587406465949127 absolute error = 0.00996274457805646726735409982332 relative error = 2.6141173554423148987588459237309 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92452840905106322192775782504114 y1[1] (numeric) = 0.92355455073403621406616203327929 absolute error = 0.00097385831702700786159579176185 relative error = 0.10533568330545698437920106275821 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1678.4MB, alloc=4.6MB, time=93.06 x[1] = 0.392 y2[1] (analytic) = 0.38203747163308743373348965682936 y2[1] (numeric) = 0.3920768523641225606741332205054 absolute error = 0.01003938073103512694064356367604 relative error = 2.6278523643557790813767400353526 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92414683371648139537313642362145 y1[1] (numeric) = 0.92316297436942481840597793689937 absolute error = 0.00098385934705657696715848672208 relative error = 0.10646136643675551971286286347541 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1682.3MB, alloc=4.6MB, time=93.27 x[1] = 0.393 y2[1] (analytic) = 0.3829614272940595522277432292739 y2[1] (numeric) = 0.3930778361777911227174389677127 absolute error = 0.0101164088837315704896957384388 relative error = 2.6416260653748861005583720953604 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92376433423514286457069561468935 y1[1] (numeric) = 0.92277039702598721385973622543112 absolute error = 0.00099393720915565071095938925823 relative error = 0.1075964044421145018334438136843 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1686.1MB, alloc=4.6MB, time=93.49 x[1] = 0.394 y2[1] (analytic) = 0.38388499999363629011365529721442 y2[1] (numeric) = 0.3940788300297770097552253177228 absolute error = 0.01019383003614071964157002050838 relative error = 2.6554384871275783224406164392857 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92338091098954707898401048497331 y1[1] (numeric) = 0.92237681869372313463980362221178 absolute error = 0.00100409229582394434420686276153 relative error = 0.10874085481666524724951354446838 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1689.9MB, alloc=4.6MB, time=93.69 x[1] = 0.395 y2[1] (analytic) = 0.38480818880824502477887704065397 y2[1] (numeric) = 0.39507983399650244277705109589206 absolute error = 0.01027164518825741799817405523809 relative error = 2.6692896583279088483953065131796 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92299656436311725225693055324085 y1[1] (numeric) = 0.92198223936255608425607397003072 absolute error = 0.00101432500056116800085658321013 relative error = 0.10989477531382458238090426480628 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1693.7MB, alloc=4.6MB, time=93.91 x[1] = 0.396 y2[1] (analytic) = 0.38573099281469701854707244735207 y2[1] (numeric) = 0.39608084815477344858431498002338 absolute error = 0.01034985534007643003724253267131 relative error = 2.6831796077761482464513041889824 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92261129474019997879039807838253 y1[1] (numeric) = 0.92158665902233295217141035530442 absolute error = 0.00102463571786702661898772307811 relative error = 0.11105822394636474815272946491005 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1697.5MB, alloc=4.6MB, time=94.12 x[1] = 0.397 y2[1] (analytic) = 0.38665341109018834186657905676835 y2[1] (numeric) = 0.3970818725817807819697011115075 absolute error = 0.01042846149159244010312205473915 relative error = 2.6971083643588916356312601786681 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92222510250606484939588568735141 y1[1] (numeric) = 0.92119007766282362953471066380734 absolute error = 0.00103502484324121986117502354407 relative error = 0.11223125898748925068891473826031 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1701.3MB, alloc=4.6MB, time=94.33 x[1] = 0.398 y2[1] (analytic) = 0.38757544271230079611426061140022 y2[1] (numeric) = 0.39808290735510084750154486991993 absolute error = 0.01050746464280005138728425851971 relative error = 2.7110759570491661238847888984327 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92183798804690406602583766948861 y1[1] (numeric) = 0.92079249527372062399199114729258 absolute error = 0.00104549277318344203384652219603 relative error = 0.11341393897191469234924088293932 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1705.1MB, alloc=4.6MB, time=94.54 TOP MAIN SOLVE Loop memory used=1709.0MB, alloc=4.6MB, time=94.76 x[1] = 0.399 y2[1] (analytic) = 0.3884970867590028360136288117384 y2[1] (numeric) = 0.39908395255269662091211779689592 absolute error = 0.01058686579369378489848898515752 relative error = 2.7250824149065386003023132275816 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92144995174983205558150020676146 y1[1] (numeric) = 0.92039391184463867357588358134501 absolute error = 0.00105603990519338200561662541645 relative error = 0.11460632269695861759415875080985 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1712.8MB, alloc=4.6MB, time=94.97 x[1] = 0.4 y2[1] (analytic) = 0.38941834230865049166631175679571 y2[1] (numeric) = 0.40008500825291857008883064483703 absolute error = 0.01066666594426807842251888804132 relative error = 2.7391277670772238822963736602195 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9210609940028850827985267320518 y1[1] (numeric) = 0.91999432736511435967394259582895 absolute error = 0.00106666663777072312458413622285 relative error = 0.11580846922363340840371403795517 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1716.6MB, alloc=4.6MB, time=95.18 x[1] = 0.401 y2[1] (analytic) = 0.39033920843998829019594703881735 y2[1] (numeric) = 0.4010860745345055756673535156566 absolute error = 0.01074686609451728547140647683925 relative error = 2.7532120427941932184397423914236 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92067111519502086221074552985688 y1[1] (numeric) = 0.91959374182460571907616076032216 absolute error = 0.00107737337041514313458476953472 relative error = 0.1170204378777462642208340512798 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1720.4MB, alloc=4.6MB, time=95.39 x[1] = 0.402 y2[1] (analytic) = 0.39125968423215017700357784835651 y2[1] (numeric) = 0.40208715147658585122565204434678 absolute error = 0.01082746724443567422207419599027 relative error = 2.767335271377283147652235942019 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.92028031571611816919247761560285 y1[1] (numeric) = 0.91919215521249185510209000796777 absolute error = 0.00108816050362631409038760763508 relative error = 0.11824228825100530163499329091471 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1724.2MB, alloc=4.6MB, time=95.60 x[1] = 0.403 y2[1] (analytic) = 0.39217976876466043663363083439577 y2[1] (numeric) = 0.40308823915867786307793857164738 absolute error = 0.01090847039401742644430773725161 relative error = 2.7814974822333047154306800375324 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91988859595697645007979385122064 y1[1] (numeric) = 0.91878956751807254780796898222637 absolute error = 0.00109902843890390227182486899427 relative error = 0.11947408020213180926990645120395 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1728.0MB, alloc=4.6MB, time=95.81 x[1] = 0.404 y2[1] (analytic) = 0.39309946111743461324955485361347 y2[1] (numeric) = 0.404089337660691249667537239515 absolute error = 0.01098987654325663641798238590153 relative error = 2.7956987048561530478190476462542 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91949595630931543137110117569449 y1[1] (numeric) = 0.91838597873056786327425689207138 absolute error = 0.00110997757874756809684428362311 relative error = 0.12071587385797869358841230966893 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1731.9MB, alloc=4.6MB, time=96.02 x[1] = 0.405 y2[1] (analytic) = 0.39401876037078043071820013323271 y2[1] (numeric) = 0.40509044706292774055766193243066 absolute error = 0.01107168669214730983946179919795 relative error = 2.8099389688269172838183653791995 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91910239716577472800744874996453 y1[1] (numeric) = 0.9179813888391177619739754622425 absolute error = 0.00112100832665696603347328772203 relative error = 0.12196772961465515157912624017945 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1735.7MB, alloc=4.6MB, time=96.23 x[1] = 0.406 y2[1] (analytic) = 0.39493766560539871230201776315066 y2[1] (numeric) = 0.40609156744608207501910597684369 absolute error = 0.01115390184068336271708821369303 relative error = 2.8242183038139908669385648900101 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9187079189199134507329457358444 y1[1] (numeric) = 0.9175757978327817062222615662544 absolute error = 0.00113212108713174451068416959 relative error = 0.12322970813865760654276920326588 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1739.5MB, alloc=4.6MB, time=96.45 x[1] = 0.407 y2[1] (analytic) = 0.39585617590238429995815982522535 y2[1] (numeric) = 0.40709269889124292021384250022991 absolute error = 0.01123652298885862025568267500456 relative error = 2.8385367395731821965970445162194 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91831252196620981253568334850355 y1[1] (numeric) = 0.91716920570053826670753413095076 absolute error = 0.00114331626567154582814921755279 relative error = 0.12450187036800694345134363774889 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1743.3MB, alloc=4.6MB, time=96.66 TOP MAIN SOLVE Loop memory used=1747.1MB, alloc=4.6MB, time=96.88 x[1] = 0.408 y2[1] (analytic) = 0.39677429034322697324356086069621 y2[1] (numeric) = 0.40809384147989378897353434034165 absolute error = 0.01131955113666681572997347964544 relative error = 2.8528943059478256400713022044311 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91791620670006073416955474155938 y1[1] (numeric) = 0.91676161243128472810467990249798 absolute error = 0.0011545942687760060648748390614 relative error = 0.12578427751339208061053846421792 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1750.9MB, alloc=4.6MB, time=97.09 x[1] = 0.409 y2[1] (analytic) = 0.39769200800981236782508177073383 y2[1] (numeric) = 0.40909499529391395717195238424617 absolute error = 0.01140298728410158934687061351234 relative error = 2.8672910328688929057156037909384 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91751897351778144875736720292634 y1[1] (numeric) = 0.91635301801383669377066366482755 absolute error = 0.00116595550394475498670353809879 relative error = 0.12707699105931991461492333120348 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1754.7MB, alloc=4.6MB, time=97.30 x[1] = 0.41 y2[1] (analytic) = 0.39860932798442289359379764005114 y2[1] (numeric) = 0.41009616041557938069030120568695 absolute error = 0.01148683243115648709650356563581 relative error = 2.8817269503551047781542609969075 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91712082281660510547564205827702 y1[1] (numeric) = 0.91594342243692768952296950266214 absolute error = 0.00117740037967741595267255561488 relative error = 0.12838007276527167584665336736613 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1758.6MB, alloc=4.6MB, time=97.51 x[1] = 0.411 y2[1] (analytic) = 0.3995262493497386523825113693651 y2[1] (numeric) = 0.41109733692756361197445085815879 absolute error = 0.01157108757782495959193948879369 relative error = 2.8962020885130432161667110730788 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91672175499468237232149859728209 y1[1] (numeric) = 0.91553282568920876650128070239746 absolute error = 0.00118892930547360582021789488463 relative error = 0.12969358466686573203156728707176 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1762.4MB, alloc=4.6MB, time=97.72 x[1] = 0.412 y2[1] (analytic) = 0.40044277118883835528557539927145 y2[1] (numeric) = 0.41209852491293871618307366986203 absolute error = 0.01165575372410036089749827059058 relative error = 2.9107164775372638139822149242541 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91632177045108103796201925571231 y1[1] (numeric) = 0.91512122775924810311280688526014 absolute error = 0.00120054269183293484921237045217 relative error = 0.13101758907702687763174113482963 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1766.2MB, alloc=4.6MB, time=97.93 x[1] = 0.413 y2[1] (analytic) = 0.40135889258520023958010420578745 y2[1] (numeric) = 0.41309972445517618692568487539361 absolute error = 0.01174083186997594734558066960616 relative error = 2.9252701477104086267046227886475 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91592086958578561266649420400396 y1[1] (numeric) = 0.91470862863553060606166796832142 absolute error = 0.00121224095025500660482623568254 relative error = 0.1323521485871621471207748129591 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1770.0MB, alloc=4.6MB, time=98.14 x[1] = 0.414 y2[1] (analytic) = 0.40227461262270298524766064642639 y2[1] (numeric) = 0.41410093563814786158958590764225 absolute error = 0.01182632301544487634192526121586 relative error = 2.939863129403319360590296172618 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91551905279969692832194441001016 y1[1] (numeric) = 0.91429502830645751046274555011713 absolute error = 0.00122402449323941785919885989303 relative error = 0.13369732606834319045735655000168 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1773.8MB, alloc=4.6MB, time=98.35 x[1] = 0.415 y2[1] (analytic) = 0.4031899303856266310954996351939 y2[1] (numeric) = 0.41510215854612683625470916188146 absolute error = 0.01191222816050020515920952668756 relative error = 2.9544954530751509289049217778707 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91511632049463173753232316038139 y1[1] (numeric) = 0.91388042676034597904041331880691 absolute error = 0.00123589373428575849190984157448 relative error = 0.13505318467249524934398953573061 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1777.6MB, alloc=4.6MB, time=98.57 TOP MAIN SOLVE Loop memory used=1781.4MB, alloc=4.6MB, time=98.78 x[1] = 0.416 y2[1] (analytic) = 0.40410484495865349047645302533885 y2[1] (numeric) = 0.41610339326378838019536303249716 absolute error = 0.01199854830513488971891000715831 relative error = 2.9691671492734853740876076370168 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9147126730733223118017969413405 y1[1] (numeric) = 0.91346482398542870041255908199925 absolute error = 0.00124784908789361138923785934125 relative error = 0.13641978783359277313119314347012 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1785.3MB, alloc=4.6MB, time=98.99 x[1] = 0.417 y2[1] (analytic) = 0.40501935542686906660653998005014 y2[1] (numeric) = 0.41710463987621084996787601114592 absolute error = 0.01208528444934178336133603109578 relative error = 2.9838782486344461569533136255507 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91430811093941603880250749553771 y1[1] (numeric) = 0.91304821996985348646031201857427 absolute error = 0.00125989096956255234219547696344 relative error = 0.13779719926886171350302672410696 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1789.1MB, alloc=4.6MB, time=99.20 x[1] = 0.418 y2[1] (analytic) = 0.40593346087576296747938751356535 y2[1] (numeric) = 0.41810589846887660308313862341467 absolute error = 0.01217243759311363560375110984932 relative error = 2.9986287818828128136673379747429 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91390263449747501872721778719006 y1[1] (numeric) = 0.91263061470168286878388975405341 absolute error = 0.00127201979579214994332803313665 relative error = 0.13918548297998853735744530468398 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1792.9MB, alloc=4.6MB, time=99.41 x[1] = 0.419 y2[1] (analytic) = 0.40684716039122982037654628834693 y2[1] (numeric) = 0.41910716912767291126304196924287 absolute error = 0.01226000873644309088649568089594 relative error = 3.0134187798321359812282584021523 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91349624415297565972724552282569 y1[1] (numeric) = 0.91221200816889369424498086229385 absolute error = 0.00128423598408196548226466053184 relative error = 0.14058470325433599757480224880714 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1796.7MB, alloc=4.6MB, time=99.63 x[1] = 0.42 y2[1] (analytic) = 0.40776045305957018597278715808634 y2[1] (numeric) = 0.42010845193889287327981162047347 absolute error = 0.01234799887932268730702446238713 relative error = 3.0282482733848527921984110358001 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91308894031230827243608878966567 y1[1] (numeric) = 0.91179240035937671959607939752622 absolute error = 0.00129653995293155284000939213945 relative error = 0.14199492466616570164978280424769 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1800.5MB, alloc=4.6MB, time=99.84 x[1] = 0.421 y2[1] (analytic) = 0.40867333796749147203546435131582 y2[1] (numeric) = 0.42110974698923632737723561691841 absolute error = 0.01243640902174485534177126560259 relative error = 3.0431172935324026394236824658645 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91268072338277666357914928798398 y1[1] (numeric) = 0.91137179126093620519718906200676 absolute error = 0.00130893212184045838196022597722 relative error = 0.14341621207786751844620342194388 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1804.3MB, alloc=4.6MB, time=100.05 x[1] = 0.422 y2[1] (analytic) = 0.40958581420210884671703159634065 y2[1] (numeric) = 0.42211105436581076327278529025834 absolute error = 0.01252524016370191655575369391769 relative error = 3.0580258713553433114870900459497 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91227159377259772866995954768862 y1[1] (numeric) = 0.9109501808612895078203156158198 absolute error = 0.00132141291130822084964393186882 relative error = 0.1448486306411958636204639075922 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1808.1MB, alloc=4.6MB, time=100.26 x[1] = 0.423 y2[1] (analytic) = 0.41049788085094615143979789505198 y2[1] (numeric) = 0.42311237415613223373962763294372 absolute error = 0.01261449330518608229982973789174 relative error = 3.0729740380234674996433330160117 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91186155189090104379332143286255 y1[1] (numeric) = 0.91052756914806667254216713664308 absolute error = 0.00133398274283437125115429621947 relative error = 0.14629224579851290454801217228059 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1812.0MB, alloc=4.6MB, time=100.47 x[1] = 0.424 y2[1] (analytic) = 0.41140953700193681337201006094047 y2[1] (numeric) = 0.42411370644812626576752791702504 absolute error = 0.01270416944618945239551785608457 relative error = 3.0879618247959196769842121629171 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.911450598147728456475764151092 y1[1] (numeric) = 0.91010395610881002372548273857746 absolute error = 0.00134664203891843275028141251454 relative error = 0.14774712328403872587799407681152 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1815.8MB, alloc=4.6MB, time=100.69 TOP MAIN SOLVE Loop memory used=1819.6MB, alloc=4.6MB, time=100.90 x[1] = 0.425 y2[1] (analytic) = 0.41232078174342475749434954530431 y2[1] (numeric) = 0.42511505133012877130164125551385 absolute error = 0.01279426958670401380729171020954 relative error = 3.1029892630213133505875386043515 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91103873295403367564373089709014 y1[1] (numeric) = 0.90967934173097375508941136044369 absolute error = 0.00135939122305992055431953664645 relative error = 0.14921332912510849713433329652849 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1823.4MB, alloc=4.6MB, time=101.11 x[1] = 0.426 y2[1] (analytic) = 0.41323161416416531825593148523067 y2[1] (numeric) = 0.4261164088908869575581917864622 absolute error = 0.01288479472672163930226030123153 relative error = 3.1180563841378486874048829093795 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91062595672168186066990417239512 y1[1] (numeric) = 0.90925372600192351886936323526266 absolute error = 0.00137223071975834180054093713246 relative error = 0.15069092964343668407683813899431 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1827.2MB, alloc=4.6MB, time=101.33 x[1] = 0.427 y2[1] (analytic) = 0.41414203335332615081889431742766 y2[1] (numeric) = 0.42711777921956023691603814744647 absolute error = 0.01297574586623408609714383001881 relative error = 3.1331632196734305146462541866273 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.91021226986344920950808073478303 y1[1] (numeric) = 0.90882710890893601406675765396146 absolute error = 0.00138516095451319544132308082157 relative error = 0.1521799914563883458335838857735 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1831.0MB, alloc=4.6MB, time=101.53 x[1] = 0.428 y2[1] (analytic) = 0.41505203840048814189066871339302 y2[1] (numeric) = 0.42811916240572113638312389555139 absolute error = 0.01306712400523299449245518215837 relative error = 3.148309801245786695422545011251 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90979767279302254591700804248653 y1[1] (numeric) = 0.90839949043919857378909163768631 absolute error = 0.00139818235382397212791640480022 relative error = 0.15368058147825756011579075390722 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1834.9MB, alloc=4.6MB, time=101.75 x[1] = 0.429 y2[1] (analytic) = 0.41596162839564632014301500372652 y2[1] (numeric) = 0.42912055853935620663681151527114 absolute error = 0.01315893014370988649379651154462 relative error = 3.16349616056258688040933215685 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90938216592499890577359496934819 y1[1] (numeric) = 0.90797087057980875168075513445449 absolute error = 0.0014112953451901540928398348937 relative error = 0.1551927669215530191287294291798 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1838.7MB, alloc=4.6MB, time=101.96 x[1] = 0.43 y2[1] (analytic) = 0.41687080242921076621691867262457 y2[1] (numeric) = 0.43012196771086693063709864397658 absolute error = 0.01325116528165616442017997135201 relative error = 3.1787223294215616362983850810183 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90896574967488512247591047766345 y1[1] (numeric) = 0.90754124931777390744501935724159 absolute error = 0.00142450035711121503089112042186 relative error = 0.15671661529829083909685895503003 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1842.5MB, alloc=4.6MB, time=102.17 x[1] = 0.431 y2[1] (analytic) = 0.41777955959200752231243391773727 y2[1] (numeric) = 0.43112339001107063181171513173982 absolute error = 0.01334383041906310949928121400255 relative error = 3.1939883397106219518060040158752 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90854842445909741143638484567998 y1[1] (numeric) = 0.90711062664001079145762588197693 absolute error = 0.00143779781908661997875896370305 relative error = 0.15825219442129462662845640961742 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1846.3MB, alloc=4.6MB, time=102.38 x[1] = 0.432 y2[1] (analytic) = 0.41868789897527950136256568562034 y2[1] (numeric) = 0.43212482553120138181209953936002 absolute error = 0.01343692655592188044953385373968 relative error = 3.2092942234079791220100873705413 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90813019069496095366562895651753 y1[1] (numeric) = 0.90667900253334512847240512530984 absolute error = 0.00145118816161582519322383120769 relative error = 0.15979957240550284545445531132 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1850.1MB, alloc=4.6MB, time=102.59 TOP MAIN SOLVE Loop memory used=1853.9MB, alloc=4.6MB, time=102.81 x[1] = 0.433 y2[1] (analytic) = 0.41959581967068739579028100897533 y2[1] (numeric) = 0.43312627436291090783925366539613 absolute error = 0.0135304546922235120489726564208 relative error = 3.2246400125822650117906139941704 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90771104880070947844728806465426 y1[1] (numeric) = 0.90624637698451120041935382341211 absolute error = 0.00146467181619827802793424124215 relative error = 0.16135881766928352738809130490597 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1857.7MB, alloc=4.6MB, time=103.02 x[1] = 0.434 y2[1] (analytic) = 0.42050332077031058584774088874292 y2[1] (numeric) = 0.43412773659826949953847367988353 absolute error = 0.01362441582795891369073279114061 relative error = 3.240025739392652699151019708509 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90729099919548484510434736509116 y1[1] (numeric) = 0.90581274998015142829560213449766 absolute error = 0.0014782492153334168087452305935 relative error = 0.16292999893575637166628084667442 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1861.6MB, alloc=4.6MB, time=103.23 x[1] = 0.435 y2[1] (analytic) = 0.42141040136664804753684438189271 y2[1] (numeric) = 0.43512921232976691546195642919165 absolute error = 0.01371881096311886792511204729894 relative error = 3.2554514360889774992007494318969 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90687004229933662385730759885391 y1[1] (numeric) = 0.90537812150681595314970198916937 absolute error = 0.00149192079252067070760560968454 relative error = 0.16451318523412227715045298390157 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1865.4MB, alloc=4.6MB, time=103.44 x[1] = 0.436 y2[1] (analytic) = 0.4223170605526192601101769744414 y2[1] (numeric) = 0.43613070165031328909827946316768 absolute error = 0.01381364109769402898810248872628 relative error = 3.2709171350118583695820762145403 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90644817853322167577464983662187 y1[1] (numeric) = 0.90494249155096221615966931414536 absolute error = 0.00150568698225945961498052247651 relative error = 0.16610844590100035218383777831944 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1869.2MB, alloc=4.6MB, time=103.65 x[1] = 0.437 y2[1] (analytic) = 0.42322329742156511315145573882644 y2[1] (numeric) = 0.43713220465324003446775332230804 absolute error = 0.0139089072316749213162975834816 relative error = 3.2864228685928196981270966221682 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90602540831900373181600948998423 y1[1] (numeric) = 0.90450586009895453780521375637225 absolute error = 0.00151954822004919401079573361198 relative error = 0.16771585058177244722400953268304 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1873.0MB, alloc=4.6MB, time=103.86 x[1] = 0.438 y2[1] (analytic) = 0.42412911106724881323456419526555 y2[1] (numeric) = 0.43813372143230075128264460920278 absolute error = 0.01400461036505193804808041393723 relative error = 3.3019686693544134735336381746206 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90560173207945297096848050711436 y1[1] (numeric) = 0.90406822713706369613459053600235 absolute error = 0.00153350494238927483388997111201 relative error = 0.1693354692319352556938110352181 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1876.8MB, alloc=4.6MB, time=104.07 x[1] = 0.439 y2[1] (analytic) = 0.42503450058385679016027021814296 y2[1] (numeric) = 0.43913525208167212967126835490908 absolute error = 0.01410075149781533951099813676612 relative error = 3.3175545699103418398516490016053 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90517715023824559747647161652294 y1[1] (numeric) = 0.90362959265146650412651005819384 absolute error = 0.0015475575867790933499615583291 relative error = 0.17096737211846002882066904633753 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1880.6MB, alloc=4.6MB, time=104.28 x[1] = 0.44 y2[1] (analytic) = 0.42593946506599960276972075077992 y2[1] (numeric) = 0.44013679669595485446494817722746 absolute error = 0.01419733162995525169522742644754 relative error = 3.3331806029655800355744825535413 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90475166321996341716553738899837 y1[1] (numeric) = 0.90318995662824538614754191518951 absolute error = 0.00156170659171803101799547380886 relative error = 0.17261162982115995056377394107657 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1884.4MB, alloc=4.6MB, time=104.49 x[1] = 0.441 y2[1] (analytic) = 0.42684400360871284433380751517007 y2[1] (numeric) = 0.44113835537017450904684271407814 absolute error = 0.01429435176146166471303519890807 relative error = 3.3488468013164997181323411349995 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90432527145009341286060779386822 y1[1] (numeric) = 0.90274931905338795350545091163938 absolute error = 0.00157595239670545935515688222884 relative error = 0.17426831323406521906066073565797 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1888.3MB, alloc=4.6MB, time=104.70 TOP MAIN SOLVE Loop memory used=1892.1MB, alloc=4.6MB, time=104.92 x[1] = 0.442 y2[1] (analytic) = 0.42774811530745804751749832738978 y2[1] (numeric) = 0.44213992819978247876163680130445 absolute error = 0.01439181289232443124413847391467 relative error = 3.3645531978509926745880012456047 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90389797535502731889904083131662 y1[1] (numeric) = 0.90230767991278657909890374765619 absolute error = 0.00159029544224073980013708366043 relative error = 0.17593749356680588135941783659962 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1895.9MB, alloc=4.6MB, time=105.13 x[1] = 0.443 y2[1] (analytic) = 0.42865179925812358891822905442715 y2[1] (numeric) = 0.44314151528065685388509585026534 absolute error = 0.01448971602253326496686679583819 relative error = 3.3802998255485949193378112531547 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90346977536206119473892372766962 y1[1] (numeric) = 0.90186503919223797116398599563064 absolute error = 0.00160473616982322357493773203898 relative error = 0.17761924234600246854008715050956 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1899.7MB, alloc=4.6MB, time=105.34 x[1] = 0.444 y2[1] (analytic) = 0.42955505455702559317745167411342 y2[1] (numeric) = 0.44414311670910333215248186651884 absolute error = 0.01458806215207773897503019240542 relative error = 3.3960867174806111796238278196543 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9030406718993949976630490853117 y1[1] (numeric) = 0.9014213968774427461179700083846 absolute error = 0.0016192750219522515450790769271 relative error = 0.17931363141666447866882830449273 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1903.5MB, alloc=4.6MB, time=105.55 x[1] = 0.445 y2[1] (analytic) = 0.43045788030090883666443432668387 y2[1] (numeric) = 0.44514473258185612084482953674293 absolute error = 0.01468685228094728418039521005906 relative error = 3.4119139068102397696658417881911 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9026106653961321545789932832218 y1[1] (numeric) = 0.90097675295400500050077539780661 absolute error = 0.00163391244212715407821788541519 relative error = 0.18102073294359675537112450339615 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1907.3MB, alloc=4.6MB, time=105.75 x[1] = 0.446 y2[1] (analytic) = 0.43136027558694765073140967424357 y2[1] (numeric) = 0.44614636299607883843208079678885 absolute error = 0.01478608740913118770067112254528 relative error = 3.4277814267926978542249369510951 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90217975628227913291572532801462 y1[1] (numeric) = 0.9005311074074318820145647246936 absolute error = 0.00164864887484725090116060332102 relative error = 0.18274061941281381015573207612545 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1911.1MB, alloc=4.6MB, time=105.97 x[1] = 0.447 y2[1] (analytic) = 0.43226223951274682453916831306481 y2[1] (numeric) = 0.44714800804936541577207627941422 absolute error = 0.01488576853661859123290796634941 relative error = 3.4436893107753471024131262926971 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.9017479449887450106171752588427 y1[1] (numeric) = 0.90008446022313315966191804211741 absolute error = 0.00166348476561185095525721672529 relative error = 0.18447336363296213696924435918865 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1915.0MB, alloc=4.6MB, time=106.18 x[1] = 0.448 y2[1] (analytic) = 0.43316377117634250745219441319813 y2[1] (numeric) = 0.44814966783974099686440202579894 absolute error = 0.01498589666339848941220761260081 relative error = 3.4596375921978197325665199678578 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90131523194734104523319211255506 y1[1] (numeric) = 0.89963681138642079298303093624307 absolute error = 0.00167842056092025225016117631199 relative error = 0.18621903873675056781207778939949 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1918.8MB, alloc=4.6MB, time=106.39 x[1] = 0.449 y2[1] (analytic) = 0.43406486967620311100244119033643 y2[1] (numeric) = 0.44915134246566283915808983040526 absolute error = 0.01508647278945972815564864006883 relative error = 3.4756263045921449490023974754263 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90088161759078024210832235811838 y1[1] (numeric) = 0.89918816088250850039238171014905 absolute error = 0.00169345670827174171594064796933 relative error = 0.18797771818238871860041872728428 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1922.6MB, alloc=4.6MB, time=106.61 TOP MAIN SOLVE Loop memory used=1926.4MB, alloc=4.6MB, time=106.82 x[1] = 0.45 y2[1] (analytic) = 0.4349655341112302104208442462319 y2[1] (numeric) = 0.45015303202602121341216957410418 absolute error = 0.01518749791479100299132532787228 relative error = 3.4916554815828757714834832488446 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90044710235267692166884061148645 y1[1] (numeric) = 0.89873850869651132661531435783752 absolute error = 0.00170859365616559505352625364893 relative error = 0.18974947575503357481521864910429 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1930.2MB, alloc=4.6MB, time=107.03 x[1] = 0.451 y2[1] (analytic) = 0.43586576358075944573567124622747 y2[1] (numeric) = 0.45115473662014030310807188575322 absolute error = 0.01528897303938085737240063952575 relative error = 3.5077251568872162582156602496628 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.90001168666754628580846534385106 y1[1] (numeric) = 0.89828785481344520922498497727497 absolute error = 0.00172383185410107658348036657609 relative error = 0.19153438556824426683871821462164 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1934.0MB, alloc=4.6MB, time=107.25 x[1] = 0.452 y2[1] (analytic) = 0.43676555718456142243680683562839 y2[1] (numeric) = 0.45215645634777910341287945757494 absolute error = 0.01539089916321768097607262194655 relative error = 3.5238353643151491232083001489325 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89957537097080398337319319752249 y1[1] (numeric) = 0.89783619921822654428012027297085 absolute error = 0.00173917175257743909307292455164 relative error = 0.19333252206544508524124287401214 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1937.8MB, alloc=4.6MB, time=107.46 x[1] = 0.453 y2[1] (analytic) = 0.43766491402284261170507213070383 y2[1] (numeric) = 0.45315819130913231969242532475097 absolute error = 0.01549327728628970798735319404714 relative error = 3.5399861377695637488293413520934 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89913815569876567474568642456905 y1[1] (numeric) = 0.89738354189567175106403780028395 absolute error = 0.0017546138030939236816486242851 relative error = 0.19514396002139678664616990549484 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1941.7MB, alloc=4.6MB, time=107.67 x[1] = 0.454 y2[1] (analytic) = 0.43856383319624625020567855507421 y2[1] (numeric) = 0.45415994160483126557323640461253 absolute error = 0.01559610840858501536755784953832 relative error = 3.5561775112463845943902075003631 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89870004128864659552964886379195 y1[1] (numeric) = 0.8969298828304968359253786053434 absolute error = 0.00177015845814975960427025844855 relative error = 0.19696877454367624116904511348476 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1945.5MB, alloc=4.6MB, time=107.88 x[1] = 0.455 y2[1] (analytic) = 0.43946231380585323944491622810532 y2[1] (numeric) = 0.45516170733594476055232057567472 absolute error = 0.0156993935300915211074043475694 relative error = 3.5724095188347000015986292018878 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89826102817856111933462677162328 y1[1] (numeric) = 0.89647522200731695522100391618327 absolute error = 0.00178580617124416411362285544001 relative error = 0.19880704107416447279785315969151 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1949.3MB, alloc=4.6MB, time=108.09 x[1] = 0.456 y2[1] (analytic) = 0.44036035495318304468917754869582 y2[1] (numeric) = 0.45616348860398002715379556152813 absolute error = 0.01580313365079698246461801283231 relative error = 3.5886821947168913977204106447129 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89782111680752231966167172210963 y1[1] (numeric) = 0.89601955941064597736150854241714 absolute error = 0.00180155739687634230016317969249 relative error = 0.20065883539054314445544519961971 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1953.1MB, alloc=4.6MB, time=108.30 x[1] = 0.457 y2[1] (analytic) = 0.44125795574019459344541705550947 y2[1] (numeric) = 0.45716528551088358763135786926671 absolute error = 0.01590732977068899418594081375724 relative error = 3.6049955731687628972941704571022 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89738030761544153089030369028207 y1[1] (numeric) = 0.89556289502489604395980464252168 absolute error = 0.00181741259054548693049904776039 relative error = 0.20252423360779953986212796927399 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1956.9MB, alloc=4.6MB, time=108.51 x[1] = 0.458 y2[1] (analytic) = 0.44215511526928717350214908326701 y2[1] (numeric) = 0.45816709815904216021559001669548 absolute error = 0.01601198288975498671344093342847 relative error = 3.6213496885596713032460827451631 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89693860104312790836721333191287 y1[1] (numeric) = 0.89510522883437713008323051955631 absolute error = 0.00183337220875077828398281235656 relative error = 0.20440331217974009469644679064099 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1960.7MB, alloc=4.6MB, time=108.72 TOP MAIN SOLVE Loop memory used=1964.6MB, alloc=4.6MB, time=108.93 x[1] = 0.459 y2[1] (analytic) = 0.44305183264330133053008517417501 y2[1] (numeric) = 0.45916892665128355490510426702457 absolute error = 0.01611709400798222437501909284956 relative error = 3.6377445753526565082546496892323 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89649599753228798759714337091984 y1[1] (numeric) = 0.89464656082329660360964010791946 absolute error = 0.00184943670899138398750326300038 relative error = 0.20629614790051252993527848629689 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1968.4MB, alloc=4.6MB, time=109.15 x[1] = 0.46 y2[1] (analytic) = 0.4439481069655197652415136439289 y2[1] (numeric) = 0.460170771090877568800521074117 absolute error = 0.0162226641253578035590074301881 relative error = 3.6541802681045722972185514557664 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89605249752552524253638990350041 y1[1] (numeric) = 0.89418689097575878368792981553113 absolute error = 0.00186560654976645884846008796928 relative error = 0.20820281790613664064051653009917 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1972.2MB, alloc=4.6MB, time=109.36 x[1] = 0.461 y2[1] (analytic) = 0.44484393733966823010752414298558 y2[1] (numeric) = 0.46117263158153688098028042561645 absolute error = 0.01632869424186865087275628263087 relative error = 3.6706568014662175516836425169482 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89560810146633964298936532545704 y1[1] (numeric) = 0.89372621927576449830346038763621 absolute error = 0.00188188219057514468590493782083 relative error = 0.21012339967604379384890780211528 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1976.0MB, alloc=4.6MB, time=109.57 x[1] = 0.462 y2[1] (analytic) = 0.44573932286991642563218049595565 y2[1] (numeric) = 0.46217450822741794691728425543687 absolute error = 0.01643518535750152128510375948122 relative error = 3.6871742101824678570881958027889 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89516280979912721110866548611451 y1[1] (numeric) = 0.89326454570721064094883246024365 absolute error = 0.00189826409191657015983302587086 relative error = 0.2120579710346251896140162279379 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1979.8MB, alloc=4.6MB, time=109.78 x[1] = 0.463 y2[1] (analytic) = 0.44663426266087889618274554501705 y2[1] (numeric) = 0.46317640113312189243536808114845 absolute error = 0.0165421384722429962526225361314 relative error = 3.7037325290924075136885374769682 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8947166229691795769990845687246 y1[1] (numeric) = 0.89280187025388972640047547305293 absolute error = 0.00191475271528985059860909567167 relative error = 0.21400661015278893964487181016715 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1983.6MB, alloc=4.6MB, time=109.99 x[1] = 0.464 y2[1] (analytic) = 0.44752875581761592537506216720012 y2[1] (numeric) = 0.46417831040369540720460000574326 absolute error = 0.01664955458607948182953783854314 relative error = 3.7203317931294619520302655649866 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89426954142268353342602209330656 y1[1] (numeric) = 0.89233819289948944560151061357198 absolute error = 0.00193134852319408782451147973458 relative error = 0.21596939554952601838464283057763 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1987.4MB, alloc=4.6MB, time=110.21 x[1] = 0.465 y2[1] (analytic) = 0.44842280144563443101319508023752 y2[1] (numeric) = 0.46518023614463163777440520710849 absolute error = 0.01675743469899720676121012687097 relative error = 3.7369720373215305538333052087879 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89382156560672058962872733347906 y1[1] (numeric) = 0.89187351362759221965134946599899 absolute error = 0.00194805197912836997737786748007 relative error = 0.21794640609348514177467332753626 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=1991.3MB, alloc=4.6MB, time=110.43 x[1] = 0.466 y2[1] (analytic) = 0.44931639865088885958243849741175 y2[1] (numeric) = 0.46618217846187108014351402227535 absolute error = 0.0168657798109822205610755248636 relative error = 3.7536532967911198791621220129435 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89337269596926652423882733400213 y1[1] (numeric) = 0.8914078324216747529024910403257 absolute error = 0.00196486354759177133633629367643 relative error = 0.21993772100455662935448663538278 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=1995.1MB, alloc=4.6MB, time=110.64 TOP MAIN SOLVE Loop memory used=1998.9MB, alloc=4.6MB, time=110.86 x[1] = 0.467 y2[1] (analytic) = 0.45020954653978208029479513846738 y2[1] (numeric) = 0.4671841374618024718657317171467 absolute error = 0.01697459092202039157093657867932 relative error = 3.7703756067554773007554928212693 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89292293295919093730458561046372 y1[1] (numeric) = 0.8909411492651075851649808590205 absolute error = 0.00198178369408335213960475144322 relative error = 0.22194341985546530575689840284779 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2002.7MB, alloc=4.6MB, time=111.06 x[1] = 0.468 y2[1] (analytic) = 0.45110224421916627868603255118318 y2[1] (numeric) = 0.46818611325126368369052801593594 absolute error = 0.01708386903209740500449546475276 relative error = 3.7871390025267250463933203571913 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.892472277026256801421339506815 y1[1] (numeric) = 0.89047346414115464301899678056748 absolute error = 0.00199881288510215840234272624752 relative error = 0.2239635825733724980692389728374 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2006.5MB, alloc=4.6MB, time=111.28 x[1] = 0.469 y2[1] (analytic) = 0.45199449079634384976342314662252 y2[1] (numeric) = 0.46918810593754261073744444797339 absolute error = 0.01719361514119876097402130135087 relative error = 3.803943519511994650181074513661 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89202072862112001196856508027942 y1[1] (numeric) = 0.89000477703297279023602724107146 absolute error = 0.00201595158814722173253783920796 relative error = 0.22599828944148718594688549058964 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2010.3MB, alloc=4.6MB, time=111.49 x[1] = 0.47 y2[1] (analytic) = 0.45288628537906829070327480039641 y2[1] (numeric) = 0.47019011562837806320331755285343 absolute error = 0.01730383024930977250004275245702 relative error = 3.8207891932135618136355487271686 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89156828819532893645401927653339 y1[1] (numeric) = 0.88953508792361137730910859708975 absolute error = 0.00203320027171755914491067944364 relative error = 0.22804762110068636178387909698707 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2014.1MB, alloc=4.6MB, time=111.70 x[1] = 0.471 y2[1] (analytic) = 0.45377762707554509309735932248279 y2[1] (numeric) = 0.47119214243196065660131596810623 absolute error = 0.01741451535641556350395664562344 relative error = 3.8376760592289816774587348533826 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89111495620132396296541005097869 y1[1] (numeric) = 0.88906439679601179009258925481884 absolute error = 0.00205055940531217287282079615985 relative error = 0.23011165855114465866738284847538 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2018.0MB, alloc=4.6MB, time=111.92 x[1] = 0.472 y2[1] (analytic) = 0.45466851499443263474734654924825 y2[1] (numeric) = 0.47219418645693370153078940668073 absolute error = 0.01752567146250106678344285743248 relative error = 3.854604153251224504889744317054 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89066073309243704773004598439895 y1[1] (numeric) = 0.88859270363300699755188927274838 absolute error = 0.00206802945943005017815671165057 relative error = 0.23219048315397330426815268238777 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2021.8MB, alloc=4.6MB, time=112.13 x[1] = 0.473 y2[1] (analytic) = 0.45555894824484307100635226331207 y2[1] (numeric) = 0.4731962478123940929769275145211 absolute error = 0.01763729956755102197057525120903 relative error = 3.8715735110688117775278370749898 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.89020561932289126178291783331278 y1[1] (numeric) = 0.88812000841732109862372512689614 absolute error = 0.00208561090557016315919270641664 relative error = 0.23428417663286845924807822501667 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2025.6MB, alloc=4.6MB, time=112.34 x[1] = 0.474 y2[1] (analytic) = 0.45644892593634322566670859977923 y2[1] (numeric) = 0.47419832660789319913922658140586 absolute error = 0.01774940067154997347251798162663 relative error = 3.8885841685659527045227631458753 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88974961534780033674366534690441 y1[1] (numeric) = 0.88764631113156886818727032975578 absolute error = 0.00210330421623146855639501714863 relative error = 0.23639282107576899919823424277902 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2029.4MB, alloc=4.6MB, time=112.55 x[1] = 0.475 y2[1] (analytic) = 0.45733844717895548139306605114609 y2[1] (numeric) = 0.47520042295343774978776206099748 absolute error = 0.01786197577448226839469600985139 relative error = 3.9056361617226811460317741638274 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88929272162316820970288357352693 y1[1] (numeric) = 0.8871716117582553021467235961248 absolute error = 0.00212110986491290755615997740213 relative error = 0.23851649893652379955679910511679 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2033.2MB, alloc=4.6MB, time=112.77 TOP MAIN SOLVE Loop memory used=2037.0MB, alloc=4.6MB, time=112.98 x[1] = 0.476 y2[1] (analytic) = 0.45822751108315866969993663785086 y2[1] (numeric) = 0.47620253695949072414626483871951 absolute error = 0.01797502587633205444632820086865 relative error = 3.9227295266149929518458246420912 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88883493860588856721822377043406 y1[1] (numeric) = 0.88669591027977516162575725103271 absolute error = 0.00213902832611340559246651940135 relative error = 0.2406552930365685833956761239766 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2040.8MB, alloc=4.6MB, time=113.19 x[1] = 0.477 y2[1] (analytic) = 0.45911611675988896047278826700008 y2[1] (numeric) = 0.47720466873697223830099916863834 absolute error = 0.01808855197708327782821090163826 relative error = 3.9398642994149837160906544283735 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88837626675374438842074492060154 y1[1] (numeric) = 0.88621920667841251627431957705948 absolute error = 0.00215706007533187214642534354206 relative error = 0.24280928656661239240772974596738 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2044.7MB, alloc=4.6MB, time=113.40 x[1] = 0.478 y2[1] (analytic) = 0.46000426332054075103180075825063 y2[1] (numeric) = 0.47820681839726043213444018297641 absolute error = 0.01820255507671968110263942472578 relative error = 3.9570405163909869489116252331187 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88791670652540748723197275024844 y1[1] (numeric) = 0.88574150093634028668826580042203 absolute error = 0.00217520558906720054370694982641 relative error = 0.24497856308833374187325431544989 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2048.5MB, alloc=4.6MB, time=113.61 x[1] = 0.479 y2[1] (analytic) = 0.46089194987696755473739447316549 y2[1] (numeric) = 0.47920898605219235578274886022303 absolute error = 0.01831703617522480104535438705754 relative error = 3.9742582139077126660543751555126 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88745625838043805369212402996133 y1[1] (numeric) = 0.88526279303561978594229341731172 absolute error = 0.00219346534481826774983061264961 relative error = 0.24716320653608652083466184782844 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2052.3MB, alloc=4.6MB, time=113.82 x[1] = 0.48 y2[1] (analytic) = 0.46177917554148288913664294258864 y2[1] (numeric) = 0.48021117181406485561604232003753 absolute error = 0.01843199627258196647939937744889 relative error = 3.9915174284263863972565558588869 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88699492277928419439995483115874 y1[1] (numeric) = 0.88478308295820026023665856408853 absolute error = 0.00221183982108393416329626707021 relative error = 0.24936330121861569916244063578458 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2056.1MB, alloc=4.6MB, time=114.03 x[1] = 0.481 y2[1] (analytic) = 0.46266593942686116364968134570045 y2[1] (numeric) = 0.48121337579563545974045729525651 absolute error = 0.01854743636877429609077594955606 relative error = 4.0088181965048886143691274967989 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88653270018328147206469229800935 y1[1] (numeric) = 0.88430237068591842865815113707863 absolute error = 0.00223032949736304340654116093072 relative error = 0.25157893182078290365323258021704 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2059.9MB, alloc=4.6MB, time=114.25 x[1] = 0.482 y2[1] (analytic) = 0.4635522406463385667952231544191 y2[1] (numeric) = 0.48221559811012326302100461332212 absolute error = 0.01866335746378469622578145890302 relative error = 4.0261605547978945801289067031111 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88606959105465244417051038283381 y1[1] (numeric) = 0.88382065620049802205580736988047 absolute error = 0.00224893485415442211470301295334 relative error = 0.25381018340530192576243825863743 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2063.7MB, alloc=4.6MB, time=114.46 x[1] = 0.483 y2[1] (analytic) = 0.46443807831361395295429771770524 y2[1] (numeric) = 0.48321783887120981162421250134138 absolute error = 0.01877976055759585866991478363614 relative error = 4.0435445400570146185072929738682 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88560559585650620075401088047591 y1[1] (numeric) = 0.88333793948354932103183957826137 absolute error = 0.00226765637295687972217130221454 relative error = 0.25605714141448422403911962989826 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2067.6MB, alloc=4.6MB, time=114.67 x[1] = 0.484 y2[1] (analytic) = 0.46532345154284972867132202210636 y2[1] (numeric) = 0.48422009819303998707955651076663 absolute error = 0.01889664665019025840823448866027 relative error = 4.0609701891309348075633386254468 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88514071505283790129517198412375 y1[1] (numeric) = 0.88285422051656869304826378492153 absolute error = 0.00228649453626920824690819920222 relative error = 0.25831989167199448480016598965073 % Correct digits = 2 memory used=2071.4MB, alloc=4.6MB, time=114.88 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2075.2MB, alloc=4.6MB, time=115.10 x[1] = 0.485 y2[1] (analytic) = 0.46620835944867273849162032754275 y2[1] (numeric) = 0.48522237619022288985867383935418 absolute error = 0.01901401674155015136705351181143 relative error = 4.0784375389655580957325772527895 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88467494910852831072222747159347 y1[1] (numeric) = 0.88236949928093812864970693861539 absolute error = 0.00230544982759018207252053297808 relative error = 0.26059852038461630505375475455414 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2079.0MB, alloc=4.6MB, time=115.31 x[1] = 0.486 y2[1] (analytic) = 0.46709280114617515033450584088946 y2[1] (numeric) = 0.48622467297783272247135980961156 absolute error = 0.0191318718316575721368539687221 relative error = 4.095946626604145842486285273517 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88420829848934333453094051715798 y1[1] (numeric) = 0.88188377575792477680287644435193 absolute error = 0.00232452273141855772806407280605 relative error = 0.26289311414402806215911064261195 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2082.8MB, alloc=4.6MB, time=115.52 x[1] = 0.487 y2[1] (analytic) = 0.46797677575091534040103905434617 y2[1] (numeric) = 0.48722698867140967207734424438293 absolute error = 0.01925021292049433167630519003676 relative error = 4.1134974891874597842991207691741 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88374076366193355301873700960789 y1[1] (numeric) = 0.88139704992868047935317572364561 absolute error = 0.00234371373325307366556128596228 relative error = 0.26520375992858903519048097195183 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2086.6MB, alloc=4.6MB, time=115.73 x[1] = 0.488 y2[1] (analytic) = 0.46886028237891877761557784091055 y2[1] (numeric) = 0.4882293233869607926128454615466 absolute error = 0.01936904100804201499726762063605 relative error = 4.1310901639539044268663634640487 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88327234509383375463416414237277 y1[1] (numeric) = 0.8809093217742413045989505260582 absolute error = 0.00236302331959245003521361631457 relative error = 0.26753054510513584345813762785729 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2090.4MB, alloc=4.6MB, time=115.94 x[1] = 0.489 y2[1] (analytic) = 0.46974332014667890760023486547853 y2[1] (numeric) = 0.48923167724096088643089959100826 absolute error = 0.01948835709428197883066472552973 relative error = 4.1487246882396698645152693561498 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88280304325346246844214092620495 y1[1] (numeric) = 0.88042059127552707998385171555924 absolute error = 0.00238245197793538845828921064571 relative error = 0.26987355743078926812812462501068 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2094.3MB, alloc=4.6MB, time=116.16 x[1] = 0.49 y2[1] (analytic) = 0.47062588817115803618135833718796 y2[1] (numeric) = 0.4902340503503533854544628982673 absolute error = 0.01960816217919534927310456107934 relative error = 4.1664010994788750277583532745097 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88233285861012149570546815913666 y1[1] (numeric) = 0.87993085841334092390780125753911 absolute error = 0.00240200019678057179766690159755 relative error = 0.27223288505477152337543137122261 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2098.1MB, alloc=4.6MB, time=116.37 x[1] = 0.491 y2[1] (analytic) = 0.47150798556978821242715259659826 y2[1] (numeric) = 0.49123644283255123184128477981153 absolute error = 0.01972845726276301941413218321327 relative error = 4.1841194352037113599397225235928 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88186179163399544058306627216136 y1[1] (numeric) = 0.87944012316836877665704913463395 absolute error = 0.00242166846562666392601713752741 relative error = 0.27460861652023404400232335133899 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2101.9MB, alloc=4.6MB, time=116.58 x[1] = 0.492 y2[1] (analytic) = 0.47238961146047211121555550015936 y2[1] (numeric) = 0.49223885480543775815954907645712 absolute error = 0.01984924334496564694399357629776 relative error = 4.2018797330445869239289048300547 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88138984279615123994541035236238 y1[1] (numeric) = 0.87894838552117893045380992186591 absolute error = 0.00244145727497230949160043049647 relative error = 0.27700084076609585695474201013808 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2105.7MB, alloc=4.6MB, time=116.79 TOP MAIN SOLVE Loop memory used=2109.5MB, alloc=4.6MB, time=117.01 x[1] = 0.493 y2[1] (analytic) = 0.47327076496158391533149003416583 y2[1] (numeric) = 0.49324128638736756707328133149493 absolute error = 0.0199705214257836517417912973291 relative error = 4.219682030730270939819944071279 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88091701256853769230763252801455 y1[1] (numeric) = 0.87845564545222155862596875396576 absolute error = 0.00246136711631613368166377404879 relative error = 0.27940964712889260467503252259053 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2113.3MB, alloc=4.6MB, time=117.22 x[1] = 0.494 y2[1] (analytic) = 0.47415144519197019709260806101824 y2[1] (numeric) = 0.49424373769716741053651960113169 absolute error = 0.02009229250519721344391154011345 relative error = 4.2375263660880387545968777802719 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.88044330142398498588076278251734 y1[1] (numeric) = 0.87796190294182824389734742012766 absolute error = 0.00248139848215674198341536238968 relative error = 0.28183512534463628873881069264556 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2117.1MB, alloc=4.6MB, time=117.43 x[1] = 0.495 y2[1] (analytic) = 0.47503165127095079950264457212144 y2[1] (numeric) = 0.49524620885413706849524640522339 absolute error = 0.02021455758318626899260183310195 relative error = 4.2554127770438172447300612295582 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87996870983620422574158014587922 y1[1] (numeric) = 0.87746715797021150579902232384827 absolute error = 0.00250155186599271994255782203095 relative error = 0.28427736555068580273757760741363 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2121.0MB, alloc=4.6MB, time=117.64 x[1] = 0.496 y2[1] (analytic) = 0.47591138231831971693150129413895 y2[1] (numeric) = 0.49624869997805022709607938668941 absolute error = 0.02033731765973051016457809255046 relative error = 4.2733413016223306526711640396762 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87949323827978696012154709386275 y1[1] (numeric) = 0.87697141051746432720218704792389 absolute error = 0.00252182776232263291936004593886 relative error = 0.28673645828762832388677248286753 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2124.8MB, alloc=4.6MB, time=117.85 x[1] = 0.497 y2[1] (analytic) = 0.47679063745434597532117896859318 y2[1] (numeric) = 0.49725121118915535640071822826764 absolute error = 0.02046057373480938107953925967446 relative error = 4.2913119779472468582180367776278 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8790168872302047058153008658165 y1[1] (numeric) = 0.87647466056355967997305326712118 absolute error = 0.00254222666664502584224759869532 relative error = 0.28921249450117163336136036525078 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2128.6MB, alloc=4.6MB, time=118.06 x[1] = 0.498 y2[1] (analytic) = 0.47766941579977451191667809895267 y2[1] (numeric) = 0.49825374260817658760514535542371 absolute error = 0.02058432680840207568846725647104 relative error = 4.3093248442413240857240269496068 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87853965716380847270917629266282 y1[1] (numeric) = 0.87597690808835004975028475349787 absolute error = 0.00256274907545842295889153916495 relative error = 0.2917055655440474358878224045896 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2132.4MB, alloc=4.6MB, time=118.28 x[1] = 0.499 y2[1] (analytic) = 0.47854771647582705452098843437875 y2[1] (numeric) = 0.49925629435631458976257793426043 absolute error = 0.02070857788048753524158949988168 relative error = 4.3273799388265580481297161929725 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87806154855782828743023560647926 y1[1] (numeric) = 0.87547815307156695984546022183137 absolute error = 0.00258339548626132758477538464789 relative error = 0.29421576317792574965259311223191 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2136.2MB, alloc=4.6MB, time=118.49 x[1] = 0.5 y2[1] (analytic) = 0.47942553860420300027328793521557 y2[1] (numeric) = 0.50025886655524744600916865318602 absolute error = 0.02083332795104444573588071797045 relative error = 4.34547730012432952879845337709 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87758256189037271611628158260383 y1[1] (numeric) = 0.87497839549282049426706176511409 absolute error = 0.00260416639755222184921981748974 relative error = 0.29674317957534043812261259133 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2140.0MB, alloc=4.6MB, time=118.70 x[1] = 0.501 y2[1] (analytic) = 0.4803028813070802939494724420977 y2[1] (numeric) = 0.50126145932713152929145275689193 absolute error = 0.02095857802005123534198031479423 relative error = 4.3636169666555524021404717744915 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87710269764042838630733124421144 y1[1] (numeric) = 0.87447763533159881986848663259583 absolute error = 0.00262506230882956643884461161561 relative error = 0.29928790732162595591377384943196 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2143.8MB, alloc=4.6MB, time=118.92 TOP MAIN SOLVE Loop memory used=2147.7MB, alloc=4.6MB, time=119.13 x[1] = 0.502 y2[1] (analytic) = 0.48117974370711630578413774821874 y2[1] (numeric) = 0.50226407279460237759453878086163 absolute error = 0.02108432908748607181040103264289 relative error = 4.3817989770408220940138025054052 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87662195628785950795902823784783 y1[1] (numeric) = 0.87397587256726770762058110539508 absolute error = 0.00264608372059180033844713245275 relative error = 0.30185003941686538138768805570177 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2151.5MB, alloc=4.6MB, time=119.35 x[1] = 0.503 y2[1] (analytic) = 0.48205612492744870881313625285219 y2[1] (numeric) = 0.5032667070807755686700404141809 absolute error = 0.02121058215332685985690416132871 relative error = 4.4000233700005644828936311332833 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87614033831340739357847286646878 y1[1] (numeric) = 0.87347310717907005300919622726315 absolute error = 0.00266723113433734056927663920563 relative error = 0.30442966927784980920640651496721 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2155.3MB, alloc=4.6MB, time=119.56 x[1] = 0.504 y2[1] (analytic) = 0.48293202409169635573583085364091 y2[1] (numeric) = 0.50426936230924759426274689784708 absolute error = 0.02133733821755123852691604420617 relative error = 4.4182901843551852428051896399288 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87565784419868997748294964411447 y1[1] (numeric) = 0.87296933914612539555826615066744 absolute error = 0.00268850505256458192468349344703 relative error = 0.30702689074004917662857015782448 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2159.1MB, alloc=4.6MB, time=119.77 x[1] = 0.505 y2[1] (analytic) = 0.48380744032396015529616921547434 y2[1] (numeric) = 0.50527203860409673383502934507908 absolute error = 0.02146459828013657853886012960474 relative error = 4.4365994590252196290187320794295 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87517447442620133418203311345153 y1[1] (numeric) = 0.87246456844742943747891086096346 absolute error = 0.00270990597877189670312225248807 relative error = 0.30964179805959459788894889447155 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2162.9MB, alloc=4.6MB, time=119.98 x[1] = 0.506 y2[1] (analytic) = 0.48468237274882394818170203495237 y2[1] (numeric) = 0.506274736089883927787980349311 absolute error = 0.02159236334105997960627831435863 relative error = 4.4549512330314827075086090440221 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87469022947931119588355354403665 y1[1] (numeric) = 0.87195879506185356144506604404889 absolute error = 0.00273143441745763443848749998776 relative error = 0.3122744859152722815665281016936 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2166.7MB, alloc=4.6MB, time=120.19 x[1] = 0.507 y2[1] (analytic) = 0.48555682049135538243966940149045 y2[1] (numeric) = 0.5072774548916536501782842246099 absolute error = 0.02172063440029826773861482311945 relative error = 4.4733455454952200291819337161908 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87420510984226446912390500529606 y1[1] (numeric) = 0.87145201896814434749614386553803 absolute error = 0.00275309087412012162776113975803 relative error = 0.31492504941052910641424211244788 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2170.5MB, alloc=4.6MB, time=120.40 x[1] = 0.508 y2[1] (analytic) = 0.48643078267710678840927983905261 y2[1] (numeric) = 0.50828019513493478092981520219175 absolute error = 0.02184941245782799252053536313914 relative error = 4.4917824356382587498858207734653 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87371911600018075052317918387225 y1[1] (numeric) = 0.87094424014492308906722943216052 absolute error = 0.00277487585525766145594975171173 relative error = 0.31759358407548993169618961873345 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2174.4MB, alloc=4.6MB, time=120.61 x[1] = 0.509 y2[1] (analytic) = 0.48730425843211605316930709630622 y2[1] (numeric) = 0.5092829569457414775389608855185 absolute error = 0.02197869851362542436965378921228 relative error = 4.5102619427831591972056787998511 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87323224843905384166560919016402 y1[1] (numeric) = 0.87043545857068530814731870877522 absolute error = 0.0027967898683685335182904813888 relative error = 0.32028018586898671865573860727871 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2178.2MB, alloc=4.6MB, time=120.83 TOP MAIN SOLVE Loop memory used=2182.0MB, alloc=4.6MB, time=121.04 x[1] = 0.51 y2[1] (analytic) = 0.48817724688290749450013023767457 y2[1] (numeric) = 0.51028574045057404627266824514312 absolute error = 0.02210849356766655177253800746855 relative error = 4.5287841063533668850705471848384 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87274450764575126310580847357551 y1[1] (numeric) = 0.86992567422380026956610466709833 absolute error = 0.00281883342195099353970380647718 relative error = 0.322984951180599540320384518658 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2185.8MB, alloc=4.6MB, time=121.25 x[1] = 0.511 y2[1] (analytic) = 0.48904974715649273435934307332011 y2[1] (numeric) = 0.51128854577641981285820941302778 absolute error = 0.02223879861992707849886633970767 relative error = 4.547348965873364977184989801971 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87225589410801376750129084019472 y1[1] (numeric) = 0.86941488708251049440981944497436 absolute error = 0.00284100702550327309147139522036 relative error = 0.32570797683270955743661092252336 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2189.6MB, alloc=4.6MB, time=121.46 x[1] = 0.512 y2[1] (analytic) = 0.48992175838037157187005945252148 y2[1] (numeric) = 0.51229137305075399266366451449283 absolute error = 0.02236961467038242079360506197135 relative error = 4.5659565609688272003105900988621 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87176640831445485187175844034113 y1[1] (numeric) = 0.86890309712493127256664129776957 absolute error = 0.00286331118952357930511714257156 relative error = 0.32844936008256403892036378249931 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2193.4MB, alloc=4.6MB, time=121.67 x[1] = 0.513 y2[1] (analytic) = 0.49079327968253285582104143221207 y2[1] (numeric) = 0.51329422240154056036811875425991 absolute error = 0.02250094271900770454707732204784 relative error = 4.5846069313667712084236356437718 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87127605075456026898564546665356 y1[1] (numeric) = 0.8683903043290501744021761262402 absolute error = 0.00288574642551009458346934041336 relative error = 0.33120919862435350580613547627084 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2197.3MB, alloc=4.6MB, time=121.89 x[1] = 0.514 y2[1] (analytic) = 0.49166431019145535667777782062445 y2[1] (numeric) = 0.51429709395723311912057095123152 absolute error = 0.02263278376577776244279313060707 relative error = 4.6033001168957123987791347059852 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87078482191868753787440617613407 y1[1] (numeric) = 0.86787650867272656156552436802227 absolute error = 0.0029083132459609763088818081118 relative error = 0.33398759059130107828011076227089 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2201.1MB, alloc=4.6MB, time=122.10 x[1] = 0.515 y2[1] (analytic) = 0.4925348490361086381036410850348 y2[1] (numeric) = 0.51529998784677576918655069470077 absolute error = 0.02276513881066713108290960966597 relative error = 4.6220361574858181809148731429898 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.87029272229806545347503672181887 y1[1] (numeric) = 0.86736171013369109692644504270605 absolute error = 0.00293101216437435654859167911282 relative error = 0.33678463455776410599040196225328 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2204.9MB, alloc=4.6MB, time=122.32 x[1] = 0.516 y2[1] (analytic) = 0.49340489534595392799025110252325 y2[1] (numeric) = 0.51630290419960397608144127260825 absolute error = 0.022898008853650048091190170085 relative error = 4.6408150931690626996327967723863 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86979975238479359540132115151374 y1[1] (numeric) = 0.86684590868954525364412974329655 absolute error = 0.00295384369524834175719140821719 relative error = 0.33960042954134816244014337878188 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2208.7MB, alloc=4.6MB, time=122.53 x[1] = 0.517 y2[1] (analytic) = 0.49427444825094498899617472345866 y2[1] (numeric) = 0.51730584314564543818950550025833 absolute error = 0.02303139489470044919333077679967 relative error = 4.6596369640793820129985925664483 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86930591267184183584429280230693 y1[1] (numeric) = 0.86632910431776082336810036972197 absolute error = 0.00297680835408101247619243258496 relative error = 0.34243507500503348488717451479701 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2212.5MB, alloc=4.6MB, time=122.74 x[1] = 0.518 y2[1] (analytic) = 0.49514350688152898859309060908113 y2[1] (numeric) = 0.51830880481532095386761155557276 absolute error = 0.02316529793379196527452094649163 relative error = 4.6785018104528297264039414673474 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86881120365304984660240319035711 y1[1] (numeric) = 0.86581129699567942357174540293478 absolute error = 0.00299990665737042303065778742233 relative error = 0.34528867085931394179726764867329 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2216.3MB, alloc=4.6MB, time=122.95 TOP MAIN SOLVE Loop memory used=2220.1MB, alloc=4.6MB, time=123.17 x[1] = 0.519 y2[1] (analytic) = 0.49601207036864736861854929708972 y2[1] (numeric) = 0.5193117893395452880326559044964 absolute error = 0.02329971897089791941410660740668 relative error = 4.6974096726277330837395264280455 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8683156258231266052418913657465 y1[1] (numeric) = 0.86529248670051200401901052105511 absolute error = 0.00302313912261460122288084469139 relative error = 0.34816131746434861052639790080754 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2224.0MB, alloc=4.6MB, time=123.38 x[1] = 0.52 y2[1] (analytic) = 0.49688013784373671433445894254775 y2[1] (numeric) = 0.52031479684972803823168037757638 absolute error = 0.02343465900599132389722143502863 relative error = 4.7163605910448495167305014831727 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86781917967764990038784757198851 y1[1] (numeric) = 0.86477267340933835236476036193399 absolute error = 0.00304650626831154802308721005452 relative error = 0.35105311563212604854146378958232 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2227.8MB, alloc=4.6MB, time=123.59 x[1] = 0.521 y2[1] (analytic) = 0.49774770843872962299042767569256 y2[1] (numeric) = 0.52131782747777450019368043601232 absolute error = 0.02357011903904487720325276031976 relative error = 4.7353546062475236534897612924791 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86732186571306583614646591908526 y1[1] (numeric) = 0.86425185709910659888932923946417 absolute error = 0.00307000861395923725713667962109 relative error = 0.35396416662864134212819462928181 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2231.6MB, alloc=4.6MB, time=123.80 x[1] = 0.522 y2[1] (analytic) = 0.49861478128605557189109401337953 y2[1] (numeric) = 0.52232088135608653286210164262047 absolute error = 0.02370610007003096097100762924094 relative error = 4.7543917588818447873479957232058 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8668236844266883356589816478407 y1[1] (numeric) = 0.86373003774663272036777962393943 absolute error = 0.00309364668005561529120202390127 relative error = 0.35689457217608601717977972018792 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2235.4MB, alloc=4.6MB, time=124.02 x[1] = 0.523 y2[1] (analytic) = 0.49948135551864178596657725690241 y2[1] (numeric) = 0.52332395861756342290702133016871 absolute error = 0.0238426030989216369404440732663 relative error = 4.7734720896968048070231706934477 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86632463631669864378778943145095 y1[1] (numeric) = 0.86320721532860004307438819975932 absolute error = 0.00311742098809860071340123169163 relative error = 0.35984443445505089731007541503048 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2239.2MB, alloc=4.6MB, time=124.23 x[1] = 0.524 y2[1] (analytic) = 0.50034743026991410484518030581186 y2[1] (numeric) = 0.52432705939560274871601243642114 absolute error = 0.02397962912568864387083213060928 relative error = 4.7925956395444565891957447332658 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86582472188214482893524002821195 y1[1] (numeric) = 0.86268338982155874492288031679536 absolute error = 0.00314133206058608401235971141659 relative error = 0.36281385610674199519114265813366 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2243.0MB, alloc=4.6MB, time=124.44 x[1] = 0.525 y2[1] (analytic) = 0.5012130046737978494274778151016 y2[1] (numeric) = 0.52533018382410124386268645198083 absolute error = 0.02411717915030339443520863687923 relative error = 4.8117624493800728545596105810705 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86532394162294128399561346650638 y1[1] (numeric) = 0.86215856120192535674293465477699 absolute error = 0.00316538042101592725267881172939 relative error = 0.36580294023520952367639288175017 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2246.8MB, alloc=4.6MB, time=124.65 x[1] = 0.526 y2[1] (analytic) = 0.50207807786471868796092312174618 y2[1] (numeric) = 0.52633333203745566005191240363585 absolute error = 0.02425525417273697209098928188967 relative error = 4.8309725602623054884224426667171 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86482229603986822644076781005499 y1[1] (numeric) = 0.86163272944598226269348092312117 absolute error = 0.00318956659388596374728688693382 relative error = 0.36881179040959011393782816738442 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2250.7MB, alloc=4.6MB, time=124.86 TOP MAIN SOLVE Loop memory used=2254.5MB, alloc=4.6MB, time=125.08 x[1] = 0.527 y2[1] (analytic) = 0.50294264897760350161410786605581 y2[1] (numeric) = 0.52733650417056362954070877239709 absolute error = 0.02439385519296012792660090634128 relative error = 4.8502260133533453269328345873497 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86431978563457119753996341774188 y1[1] (numeric) = 0.8611058945298771998133144217186 absolute error = 0.00321389110469399772664899602328 relative error = 0.37184051066636232851880686601409 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2258.3MB, alloc=4.6MB, time=125.29 x[1] = 0.528 y2[1] (analytic) = 0.50380671714788124954980873366049 y2[1] (numeric) = 0.52833970035882452703380522176574 absolute error = 0.02453298321094327748399648810525 relative error = 4.8695228499190824100153257050623 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86381641090956056071436347814793 y1[1] (numeric) = 0.86057805642962275670955229130204 absolute error = 0.00323835447993780400481118684589 relative error = 0.37488920551161555788250352234833 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2262.1MB, alloc=4.6MB, time=125.50 x[1] = 0.529 y2[1] (analytic) = 0.50467028151148383349595624514904 y2[1] (numeric) = 0.52934292073814033105287098798337 absolute error = 0.02467263922665649755691474283433 relative error = 4.8888631113292667020981428344144 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86331217236821099902671246424977 y1[1] (numeric) = 0.86004921512109587138445728515874 absolute error = 0.00326295724711512764225517909103 relative error = 0.37795797992333238972081764815917 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2265.9MB, alloc=4.6MB, time=125.72 x[1] = 0.53 y2[1] (analytic) = 0.50553334120484696181366102246608 y2[1] (numeric) = 0.5303461654449164847784067600977 absolute error = 0.02481282424006952296474573763162 relative error = 4.9082468390576692817222216911596 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8628070705147610118066950185642 y1[1] (numeric) = 0.85951937058003732820115589710901 absolute error = 0.00328769993472368360553912145519 relative error = 0.38104693935368454097897591035484 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2269.7MB, alloc=4.6MB, time=125.93 x[1] = 0.531 y2[1] (analytic) = 0.50639589536491101306143346411287 y2[1] (numeric) = 0.5313494346160627563632968536217 absolute error = 0.02495353925115174330186338950883 relative error = 4.9276740746822440011238233889965 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86230110585431241041247864333708 y1[1] (numeric) = 0.85898852278205125398877868385721 absolute error = 0.00331258307226115642369995947987 relative error = 0.38415618973134244324752350722199 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2273.5MB, alloc=4.6MB, time=126.14 x[1] = 0.532 y2[1] (analytic) = 0.50725794312912189905473326500416 y2[1] (numeric) = 0.53235272838899409871701845737275 absolute error = 0.02509478525987219966228519236859 relative error = 4.9471448598852896168868238475894 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86179427889282981312894443419202 y1[1] (numeric) = 0.85845667170260461328755162302985 absolute error = 0.00333760719022519984139281116217 relative error = 0.38728583746379857287587036977776 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2277.4MB, alloc=4.6MB, time=126.35 x[1] = 0.533 y2[1] (analytic) = 0.50811948363543192741998572150358 y2[1] (numeric) = 0.53335604690163150875950470875077 absolute error = 0.02523656326619958133951898724719 relative error = 4.9666592364536123927645285606755 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86128659013714013920311095896611 y1[1] (numeric) = 0.8579238173170267027343683514478 absolute error = 0.00336277282011343646874260751831 relative error = 0.39043598943970461787010442155772 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2281.2MB, alloc=4.6MB, time=126.56 x[1] = 0.534 y2[1] (analytic) = 0.508980516022300663642202267693 y2[1] (numeric) = 0.53435939029240288614365832824979 absolute error = 0.02537887427010222250145606055679 relative error = 4.986217246278689175774651816963 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86077804009493210201725724626652 y1[1] (numeric) = 0.85738995960050864458937413143688 absolute error = 0.00338808049442345742788311482964 relative error = 0.39360675303122257435246615222856 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2285.0MB, alloc=4.6MB, time=126.77 x[1] = 0.535 y2[1] (analytic) = 0.50984103942869579260534319532731 y2[1] (numeric) = 0.53536275870024389144551251939568 absolute error = 0.02552171927154809884016932406837 relative error = 5.0058189313568309466748982174513 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.86026862927475570140025171058284 y1[1] (numeric) = 0.85685509852810287940409339626235 absolute error = 0.00341353074665282199615831432049 relative error = 0.3967982360963898660807555241804 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2288.8MB, alloc=4.6MB, time=126.99 TOP MAIN SOLVE Loop memory used=2292.6MB, alloc=4.6MB, time=127.20 x[1] = 0.536 y2[1] (analytic) = 0.51070105299409397962456101718358 y2[1] (numeric) = 0.53636615226459880382103581556262 absolute error = 0.02566509927050482419647479837904 relative error = 5.0254643337893468459303952400918 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85975835818602171507759470258392 y1[1] (numeric) = 0.85631923407472265783163372907911 absolute error = 0.00343912411129905724596097350481 relative error = 0.40001054698149858125307368248088 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2296.4MB, alloc=4.6MB, time=127.41 x[1] = 0.537 y2[1] (analytic) = 0.51156055585848173096946344163303 y2[1] (numeric) = 0.53736957112542137812857753024296 absolute error = 0.02580901526693964715911408860993 relative error = 5.0451534957827086762880487157553 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85924722733900118926068323451424 y1[1] (numeric) = 0.85578236621514153157950013312038 absolute error = 0.00346486112385965768118310139386 relative error = 0.40324379452348892155674866076205 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2300.3MB, alloc=4.6MB, time=127.63 x[1] = 0.538 y2[1] (analytic) = 0.51241954716235625387753543524462 y2[1] (numeric) = 0.53837301542317570151595044232768 absolute error = 0.02595346826081944763841500708306 relative error = 5.0648864596487158830767284477453 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85873523724482492837580729138267 y1[1] (numeric) = 0.8552444949239928435055544542035 absolute error = 0.00349074232083208487025283717917 relative error = 0.40649808805235695916011749700349 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2304.1MB, alloc=4.6MB, time=127.84 x[1] = 0.539 y2[1] (analytic) = 0.51327802604672631605686036006966 y2[1] (numeric) = 0.53937648529883704947114732279814 absolute error = 0.02609845925211073341428696272848 relative error = 5.0846632678046610133560388806216 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85822238841548298393338799890475 y1[1] (numeric) = 0.85470562017576921685765582001257 absolute error = 0.00351676823971376707573217889218 relative error = 0.40977353739357679809209877432747 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2307.9MB, alloc=4.6MB, time=128.06 x[1] = 0.54 y2[1] (analytic) = 0.51413599165311310467728068295824 y2[1] (numeric) = 0.54037998089389274133568788393314 absolute error = 0.0262439892407796366584072009749 relative error = 5.104483962773495655040289752521 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8577086813638241425379687789178 y1[1] (numeric) = 0.85416574194482204365751896402385 absolute error = 0.00354293941900209888044981489395 relative error = 0.41307025287053723720725212345728 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2311.7MB, alloc=4.6MB, time=128.27 x[1] = 0.541 y2[1] (analytic) = 0.514993443123551084849139265818 y2[1] (numeric) = 0.54138350235034299527959270669836 absolute error = 0.02639005922679191043045344088036 relative error = 5.1243485871839968571281540991742 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85719411660355541303947148223492 y1[1] (numeric) = 0.85362486020536097222932830537143 absolute error = 0.00356925639819444081014317686349 relative error = 0.41638834530699303269334787353934 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2315.5MB, alloc=4.6MB, time=128.48 x[1] = 0.542 y2[1] (analytic) = 0.51585037960058885758874275814576 y2[1] (numeric) = 0.54238704981070178273698067640711 absolute error = 0.02653667021011292514823791826135 relative error = 5.1442571837709340321723858672318 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85667869464924151282623034763916 y1[1] (numeric) = 0.8530829749314533938736466594078 absolute error = 0.00359571971778811895258368823136 relative error = 0.41972792602953085884442470032054 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2319.3MB, alloc=4.6MB, time=128.69 x[1] = 0.543 y2[1] (analytic) = 0.51670680022729001726968912644003 y2[1] (numeric) = 0.54339062341799768230128643102179 absolute error = 0.02668382319070766503159730458176 relative error = 5.164209795375236342127866790464 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85616241601630435326031749394093 y1[1] (numeric) = 0.85254008609702392868715845719675 absolute error = 0.00362232991928042457315903674418 relative error = 0.42308910687005006659496036204239 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2323.1MB, alloc=4.6MB, time=128.90 TOP MAIN SOLVE Loop memory used=2327.0MB, alloc=4.6MB, time=129.12 x[1] = 0.544 y2[1] (analytic) = 0.51756270414723400855920186923829 y2[1] (numeric) = 0.5443942233157747330790943006041 absolute error = 0.02683151916854072451989243136581 relative error = 5.1842064649441605687201621354439 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85564528122102252425567450973039 y1[1] (numeric) = 0.8519961936758539105287883556845 absolute error = 0.00364908754516861372688615404589 relative error = 0.42647200016825834009018569228977 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2330.8MB, alloc=4.6MB, time=129.33 x[1] = 0.545 y2[1] (analytic) = 0.5184180905045169828386139815162 y2[1] (numeric) = 0.54539784964809328750158519041771 absolute error = 0.02697975914357630466297120890151 relative error = 5.2042472355314594694806874844386 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85512729078053077799956556265031 y1[1] (numeric) = 0.85145129764158087113273712382952 absolute error = 0.00367599313894990686682843882079 relative error = 0.42987671877418235235380089294638 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2334.6MB, alloc=4.6MB, time=129.54 x[1] = 0.546 y2[1] (analytic) = 0.51927295844375265410714524803636 y2[1] (numeric) = 0.54640150255953086359259283404042 absolute error = 0.02712854411577820948544758600406 relative error = 5.2243321502975506205985239438332 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85460844521281951181786830669308 y1[1] (numeric) = 0.85090539796769802336897769353203 absolute error = 0.00370304724512148844889061316105 relative error = 0.43330337605069352190747250468231 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2338.4MB, alloc=4.6MB, time=129.75 x[1] = 0.547 y2[1] (analytic) = 0.52012730711007315436811696194029 y2[1] (numeric) = 0.54740518219518299669226581655182 absolute error = 0.02727787508510984232414885461153 relative error = 5.2444612525096857477428670978481 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8540887450367342501847197221881 y1[1] (numeric) = 0.85035849462755374365175526779088 absolute error = 0.00373025040918050653296445439722 relative error = 0.43675208587604897299656660827161 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2342.2MB, alloc=4.6MB, time=129.97 x[1] = 0.548 y2[1] (analytic) = 0.52098113564912988849674868244063 y2[1] (numeric) = 0.5484088887006640906353317414281 absolute error = 0.02742775305153420213858305898747 relative error = 5.2646345855421205460140557210982 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8535681907719751258770348787904 y1[1] (numeric) = 0.8498105875943510534966363821288 absolute error = 0.0037576031776240723803984966616 relative error = 0.44022296264644780288367693275627 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2346.0MB, alloc=4.6MB, time=130.18 x[1] = 0.549 y2[1] (analytic) = 0.52183444320709438858868216388758 y2[1] (numeric) = 0.54941262222210826838295988819628 absolute error = 0.0275781790150138797942777243087 relative error = 5.2848521928762849901850997719321 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85304678293909636027441746690851 y1[1] (numeric) = 0.84926167684114710022665281896648 absolute error = 0.00378510609794926004776464794203 relative error = 0.44371612127860276048570445450339 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2349.8MB, alloc=4.6MB, time=130.39 x[1] = 0.55 y2[1] (analytic) = 0.52268722893065916778837810775729 y2[1] (numeric) = 0.5504163829061702221072186811758 absolute error = 0.02772915397551105431884057341851 relative error = 5.3051141181009541363996135629685 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85252452205950574280498179761777 y1[1] (numeric) = 0.84871176234085263682808727829237 absolute error = 0.0038127597186531059768945193254 relative error = 0.44723167721232744145160734404713 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2353.7MB, alloc=4.6MB, time=130.60 x[1] = 0.551 y2[1] (analytic) = 0.52353949196703857359653190923621 y2[1] (numeric) = 0.55142017090002606272712426276542 absolute error = 0.02788067893298748913059235352921 relative error = 5.3254204049124194164960592987765 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8520014086554641095376068251937 y1[1] (numeric) = 0.84816084406623150095644871166817 absolute error = 0.00384056458923260858115811352553 relative error = 0.45076974641313910560653708513709 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2357.5MB, alloc=4.6MB, time=130.81 x[1] = 0.552 y2[1] (analytic) = 0.52439123146396964065565509105708 y2[1] (numeric) = 0.55242398635137416889527643771738 absolute error = 0.0280327548874045282396213466603 relative error = 5.3457710971146604261322184351061 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85147744325008482092114359996793 y1[1] (numeric) = 0.84760892198990009309318623032989 absolute error = 0.00386852126018472782795736963804 relative error = 0.45433044537487722352397934141076 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2361.3MB, alloc=4.6MB, time=131.03 TOP MAIN SOLVE Loop memory used=2365.1MB, alloc=4.6MB, time=131.24 x[1] = 0.553 y2[1] (analytic) = 0.52524244656971294301296963907598 y2[1] (numeric) = 0.55342782940843603543407822767793 absolute error = 0.02818538283872309242110858860195 relative error = 5.3661662386195172078878336026816 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85095262636733323867109841225574 y1[1] (numeric) = 0.84705599608432685385369150189167 absolute error = 0.00389663028300638481740691036407 relative error = 0.45791389112233785983079853724232 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2368.9MB, alloc=4.6MB, time=131.45 x[1] = 0.554 y2[1] (analytic) = 0.52609313643305344585976297676717 y2[1] (numeric) = 0.55443170021995712122053524796347 absolute error = 0.0283385637869036753607722711963 relative error = 5.3866058734468630305274022039147 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.85042695853202620180431474062843 y1[1] (numeric) = 0.84650206632183174044714055393379 absolute error = 0.00392489221019446135717418669464 relative error = 0.46152020121392400170081578434892 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2372.7MB, alloc=4.6MB, time=131.66 x[1] = 0.555 y2[1] (analytic) = 0.52694330020330135674635183935189 y2[1] (numeric) = 0.55543559893520769651863109108384 absolute error = 0.02849229873190633977227925173195 relative error = 5.4070900457247776656091542862584 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84990044026983150182217796980501 y1[1] (numeric) = 0.84594713267458570228872690655811 absolute error = 0.0039533075952457995334510632469 relative error = 0.46514949374431194185080414452503 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2376.5MB, alloc=4.6MB, time=131.87 x[1] = 0.556 y2[1] (analytic) = 0.52779293703029297627180383266784 y2[1] (numeric) = 0.55643952570398368975827487391862 absolute error = 0.02864658867369071348647104125078 relative error = 5.427618799689721162630311974857 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84937307210726735704286769491463 y1[1] (numeric) = 0.84539119511461015576483895982338 absolute error = 0.00398187699265720127802873509125 relative error = 0.4688018873471338262186374867545 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2380.4MB, alloc=4.6MB, time=132.08 x[1] = 0.557 y2[1] (analytic) = 0.52864204606439154824756598712908 y2[1] (numeric) = 0.55744348067660753375981707769746 absolute error = 0.02880143461221598551225109056838 relative error = 5.4481921796867081239028056627237 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8488448545717018860831832798337 y1[1] (numeric) = 0.84483425361377645815173556582995 absolute error = 0.00401060095792542793144771400375 relative error = 0.4724775011976764773768543942231 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2384.2MB, alloc=4.6MB, time=132.29 x[1] = 0.558 y2[1] (analytic) = 0.52949062645648810933415014321829 y2[1] (numeric) = 0.55844746400392901140312978203188 absolute error = 0.02895683754744090206897963881359 relative error = 5.4688102301694824803577133634602 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84831578819135258049046918772829 y1[1] (numeric) = 0.84427630814380538068827471910802 absolute error = 0.00403948004754719980219446862027 relative error = 0.47617645501559660561617253809293 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2388.0MB, alloc=4.6MB, time=132.51 x[1] = 0.559 y2[1] (analytic) = 0.53033867735800233815002553189701 y2[1] (numeric) = 0.5594514758373261007402473661921 absolute error = 0.02911279847932376259022183429509 relative error = 5.4894729957006927694807941827726 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8477858734952857765251674518325 y1[1] (numeric) = 0.84371735867626658080325130287655 absolute error = 0.00406851481901919572191614895595 relative error = 0.47989886906765252052258831902482 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2391.8MB, alloc=4.6MB, time=132.72 x[1] = 0.56 y2[1] (analytic) = 0.53118619792088340385186944111203 y2[1] (numeric) = 0.56045551632870581955056372261857 absolute error = 0.02926931840782241569869428150654 relative error = 5.5101805209520679165856048155779 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84725511101341612609452550386632 y1[1] (numeric) = 0.84315740518257807349790083268068 absolute error = 0.00409770583083805259662467118564 relative error = 0.48364486417045245676869887710705 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2395.6MB, alloc=4.6MB, time=132.93 TOP MAIN SOLVE Loop memory used=2399.4MB, alloc=4.6MB, time=133.15 x[1] = 0.561 y2[1] (analytic) = 0.53203318729761081418532738821783 y2[1] (numeric) = 0.56145958563050506933758199930306 absolute error = 0.02942639833289425515225461108523 relative error = 5.5309328507045935206348193795634 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84672350127650606683798842634102 y1[1] (numeric) = 0.84259644763400570188412714288467 absolute error = 0.00412705364250036495386128345635 relative error = 0.48741456169321962874486712243479 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2403.2MB, alloc=4.6MB, time=133.36 x[1] = 0.562 y2[1] (analytic) = 0.53287964464119526300543474762577 y2[1] (numeric) = 0.56246368389569147876621285916792 absolute error = 0.02958403925449621576077811154215 relative error = 5.5517300298486886458245178082873 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84619104481616529136480554331576 y1[1] (numeric) = 0.84203448600166260687901296549521 absolute error = 0.00415655881450268448579257782055 relative error = 0.49120808356057412956889443238296 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2407.1MB, alloc=4.6MB, time=133.57 x[1] = 0.563 y2[1] (analytic) = 0.53372556910517947726585231332886 y2[1] (numeric) = 0.56346781127776424653961721591404 absolute error = 0.02974224217258476927376490258518 relative error = 5.5725721033843831201503665024831 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8456577421648502156443821119545 y1[1] (numeric) = 0.84147152025650869605617335481578 absolute error = 0.00418622190834151958820875713872 relative error = 0.4950255522553317909340501519425 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2410.9MB, alloc=4.6MB, time=133.78 x[1] = 0.564 y2[1] (analytic) = 0.53457095984363906347606880713726 y2[1] (numeric) = 0.56447196793075498371458937699742 absolute error = 0.02990100808711592023852056986016 relative error = 5.5934591164214953421787870320049 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84512359385586344654990772448725 y1[1] (numeric) = 0.84090755036935011165451291548802 absolute error = 0.00421604348651333489539480899923 relative error = 0.49886709082132012118471294884509 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2414.7MB, alloc=4.6MB, time=133.99 x[1] = 0.565 y2[1] (analytic) = 0.53541581601118335362572387549242 y2[1] (numeric) = 0.56547615400922855545447649543086 absolute error = 0.03006033799804520182875261993844 relative error = 5.6143911141798105972503944485028 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84458860042335324855579387690292 y1[1] (numeric) = 0.84034257631083869774494879555959 absolute error = 0.00424602411251455081084508134333 relative error = 0.50273282286621143994658822900249 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2418.5MB, alloc=4.6MB, time=134.20 x[1] = 0.566 y2[1] (analytic) = 0.53626013676295625057520565060748 y2[1] (numeric) = 0.56648036966828392221863020299011 absolute error = 0.03022023290532767164342455238263 relative error = 5.6353681419892598843471862657724 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84405276240231300958945400689171 y1[1] (numeric) = 0.83977659805147146655566241033108 absolute error = 0.00427616435084154303379159656063 relative error = 0.50662287256437332858456091850896 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2422.3MB, alloc=4.6MB, time=134.41 x[1] = 0.567 y2[1] (analytic) = 0.5371039212546370729116774854067 y2[1] (numeric) = 0.56748461506355498038738626813295 absolute error = 0.03038069380891790747570878272625 relative error = 5.656390245290099254859176446923 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84351608032858070603796014921248 y1[1] (numeric) = 0.83920961556159006395644386687634 absolute error = 0.00430646476699064208151628233614 relative error = 0.51053736465973651671580758085431 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2426.1MB, alloc=4.6MB, time=134.63 x[1] = 0.568 y2[1] (analytic) = 0.53794716864244139926968900630767 y2[1] (numeric) = 0.56848889035121140232156809251383 absolute error = 0.03054172170877000305187908620616 relative error = 5.6774574696330896644903958608235 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84297855473883836691011120178398 y1[1] (numeric) = 0.83864162881138023410269406330224 absolute error = 0.00433692592745813280741713848174 relative error = 0.51447642446868032596891059341952 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2430.0MB, alloc=4.6MB, time=134.84 x[1] = 0.569 y2[1] (analytic) = 0.53878987808312191211552716330558 y2[1] (numeric) = 0.5694931956879594758555098303962 absolute error = 0.03070331760483756373998266709062 relative error = 5.6985698606796773395484216913085 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84244018617061153715444864038683 y1[1] (numeric) = 0.83807263777087128323965044101458 absolute error = 0.00436754839974025391479819937225 relative error = 0.51844017788293579315147541511889 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2433.8MB, alloc=4.6MB, time=135.05 TOP MAIN SOLVE Loop memory used=2437.6MB, alloc=4.6MB, time=135.27 x[1] = 0.57 y2[1] (analytic) = 0.53963204873396924099446349307883 y2[1] (numeric) = 0.57049753123104294322259488552818 absolute error = 0.03086548249707370222813139244935 relative error = 5.7197274642021746588658532576823 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84190097516226874013375636391601 y1[1] (numeric) = 0.83750264240993554266740337248746 absolute error = 0.00439833275233319746635299142855 relative error = 0.52242875137250659596923623552831 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2441.4MB, alloc=4.6MB, time=135.48 x[1] = 0.571 y2[1] (analytic) = 0.54047367975281280524005434793895 y2[1] (numeric) = 0.57150189713824383941230551015474 absolute error = 0.03102821738543103417225116221579 relative error = 5.7409303260839415526064206910514 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84136092225302093925658219563904 y1[1] (numeric) = 0.83693164269828783086727117129389 absolute error = 0.00442927955473310838931102434515 relative error = 0.52644227198860790542893285333319 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2445.2MB, alloc=4.6MB, time=135.69 x[1] = 0.572 y2[1] (analytic) = 0.54131477029802165614465138139488 y2[1] (numeric) = 0.57250629356788332995777920079032 absolute error = 0.03119152326986167381312781939544 relative error = 5.7621784923195674192126959648795 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84082002798292099876631940889362 y1[1] (numeric) = 0.83635963860548491479010271544561 absolute error = 0.00446038937743608397621669344801 relative error = 0.53048086736662329005544079879522 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2449.0MB, alloc=4.6MB, time=135.90 x[1] = 0.573 y2[1] (analytic) = 0.54215531952850531859028011989125 y2[1] (numeric) = 0.5735107206788225481528675551694 absolute error = 0.03135540115031722956258743527815 relative error = 5.7834720090150535617566729572244 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.84027829289286314368838748809822 y1[1] (numeric) = 0.83578663010092497030707767941067 absolute error = 0.00449166279193817338130980868755 relative error = 0.5345446657290797980608267743314 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2452.8MB, alloc=4.6MB, time=136.11 x[1] = 0.574 y2[1] (analytic) = 0.54299532660371463213904498991224 y2[1] (numeric) = 0.57451517863046343169769322442819 absolute error = 0.03151985202674879955864823451595 relative error = 5.8048109223879961449587945837638 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83973571752458241893605217784984 y1[1] (numeric) = 0.83521261715384704182357537452798 absolute error = 0.00452310037073537711247680332186 relative error = 0.53863379588864134461927270766043 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2456.7MB, alloc=4.6MB, time=136.32 x[1] = 0.575 y2[1] (analytic) = 0.54383479068364259158221971011618 y2[1] (numeric) = 0.57551966758274955877170056404812 absolute error = 0.03168487689910696718948085393194 relative error = 5.8261952787677696741453306427594 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83919230242065414757542571424383 y1[1] (numeric) = 0.83463759973333050105668420191937 absolute error = 0.00455470268732364651874151232446 relative error = 0.54274838725112053242725535832544 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2460.5MB, alloc=4.6MB, time=136.53 x[1] = 0.576 y2[1] (analytic) = 0.54467371092882518694718249948034 y2[1] (numeric) = 0.5765241876961669835331955564103 absolute error = 0.03185047676734179658601305692996 relative error = 5.8476251245957109974183499135254 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83864804812449338825018897337042 y1[1] (numeric) = 0.8340615778082945049769247264113 absolute error = 0.00458647031619888327326424695912 relative error = 0.54688856981850903476307676475368 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2464.3MB, alloc=4.6MB, time=136.74 x[1] = 0.577 y2[1] (analytic) = 0.54551208650034224296135609459091 y2[1] (numeric) = 0.57752873913174507104437054696939 absolute error = 0.03201665263140282808301445237848 relative error = 5.8691005064253038323168843068251 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83810295518035439176657811222054 y1[1] (numeric) = 0.83348455134749745291476038442111 absolute error = 0.00461840383285693885181772779943 relative error = 0.55105447419202667130390716022165 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2468.1MB, alloc=4.6MB, time=136.95 x[1] = 0.578 y2[1] (analytic) = 0.54634991655981825797231311220796 y2[1] (numeric) = 0.57853332205105733162080930505442 absolute error = 0.03218340549123907364849619284646 relative error = 5.890621470922363818252251537567 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83755702413333005683917911696904 y1[1] (numeric) = 0.83290652031953644283247084323608 memory used=2471.9MB, alloc=4.6MB, time=137.17 absolute error = 0.00465050381379361400670827373296 relative error = 0.55524623157518930801202065058976 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2475.7MB, alloc=4.6MB, time=137.38 x[1] = 0.579 y2[1] (analytic) = 0.54718720026942324232320783707006 y2[1] (numeric) = 0.57953793661622225460446788914289 absolute error = 0.03235073634679901228126005207283 relative error = 5.9121880648652240960048859357169 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83701025552935138499807451279544 y1[1] (numeric) = 0.83232748469284672676196403361813 absolute error = 0.00468277083650465823611047917731 relative error = 0.55946397377689571346497030855455 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2479.5MB, alloc=4.6MB, time=137.59 x[1] = 0.58 y2[1] (analytic) = 0.54802393679187355618269605957646 y2[1] (numeric) = 0.58054258298990414155912676513217 absolute error = 0.03251864619803058537643070555571 relative error = 5.9338003351449214155744246896089 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83646264991518693465788732805002 y1[1] (numeric) = 0.8317474444357011654091038822028 absolute error = 0.00471520547948576924878344584722 relative error = 0.56370783321453350507715983116873 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2483.4MB, alloc=4.6MB, time=137.80 x[1] = 0.581 y2[1] (analytic) = 0.54886012529043274682850513349703 y2[1] (numeric) = 0.58154726133531393888730959464841 absolute error = 0.03268713604488119205880446115138 relative error = 5.9554583287653827736792090857894 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83591420783844227434926824367577 y1[1] (numeric) = 0.83116639951620968192513177472838 absolute error = 0.00474780832223259242413646894739 relative error = 0.56797794291710431974272103360657 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2487.2MB, alloc=4.6MB, time=138.01 x[1] = 0.582 y2[1] (analytic) = 0.54969576492891238538381697020945 y2[1] (numeric) = 0.5825519718162100698676640787871 absolute error = 0.03285620688729768448384710857765 relative error = 5.9771620928436125822057872308549 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83536492984755943511337269635362 y1[1] (numeric) = 0.83058434990231871484576078572984 absolute error = 0.00478057994524072026761191062378 relative error = 0.57227443652836834452189880106837 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2491.0MB, alloc=4.6MB, time=138.22 x[1] = 0.583 y2[1] (analytic) = 0.55053085487167290300562723315059 y2[1] (numeric) = 0.58355671459689926611180021087073 absolute error = 0.03302585972522636310617297772014 relative error = 5.9989116746098803689134463728307 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83481481649181636205987554084799 y1[1] (numeric) = 0.83000129556181067019852271496261 absolute error = 0.00481352093000569186135282588538 relative error = 0.57659744831000834409537737826425 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2494.8MB, alloc=4.6MB, time=138.44 x[1] = 0.584 y2[1] (analytic) = 0.55136539428362442652424454419241 y2[1] (numeric) = 0.58456148984223739843958125983732 absolute error = 0.03319609555861297191533671564491 relative error = 6.0207071214079090117032593427653 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8342638683213263650890717134926 y1[1] (numeric) = 0.82941723646230337277894897548377 absolute error = 0.00484663185902299231012273800883 relative error = 0.58094711314481332282325483912752 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2498.6MB, alloc=4.6MB, time=138.64 x[1] = 0.585 y2[1] (analytic) = 0.5521993823302276135330940625129 y2[1] (numeric) = 0.58556629771763030717186277373776 absolute error = 0.03336691538740269363876871122486 relative error = 6.0425484806950635077656008711873 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83371208588703756877861217466974 y1[1] (numeric) = 0.82883217257124951659616738301256 absolute error = 0.00487991331578805218244479165718 relative error = 0.58532356653988196036778816941009 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2502.4MB, alloc=4.6MB, time=138.86 x[1] = 0.586 y2[1] (analytic) = 0.55303281817749448692799034622804 y2[1] (numeric) = 0.58657113838903463183967486052009 absolute error = 0.03353832021154014491168451429205 relative error = 6.064435800042540278924575659638 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83315946974073236143542524350155 y1[1] (numeric) = 0.82824610385593611448849790091885 absolute error = 0.0049133658847962469469273425827 relative error = 0.5897269446298459609716926713201 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2506.2MB, alloc=4.6MB, time=139.07 TOP MAIN SOLVE Loop memory used=2510.1MB, alloc=4.6MB, time=139.29 x[1] = 0.587 y2[1] (analytic) = 0.55386570099198926889504495758147 y2[1] (numeric) = 0.58757601202295864030884297081404 absolute error = 0.03371031103096937141379801323257 relative error = 6.0863691271355570145023011651496 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83260602043502684331337427278583 y1[1] (numeric) = 0.8276590302834839469096313999472 absolute error = 0.00494699015154289640374287283863 relative error = 0.59415738418011345762679057355606 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2513.9MB, alloc=4.6MB, time=139.51 x[1] = 0.588 y2[1] (analytic) = 0.55469802994082921434637482385373 y2[1] (numeric) = 0.58858091878646305731904237479889 absolute error = 0.03388288884563384297266755094516 relative error = 6.1083485097735430530305041462986 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83205173852337027399720344647288 y1[1] (numeric) = 0.82707095182084700988597649657571 absolute error = 0.00498078670252326411122694989717 relative error = 0.59861502259013261352127017975756 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2517.7MB, alloc=4.6MB, time=139.72 x[1] = 0.589 y2[1] (analytic) = 0.55552980419168544380277791835226 y2[1] (numeric) = 0.58958585884716189243628149244169 absolute error = 0.03405605465547644863350357408943 relative error = 6.130373995870330304141421184509 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83149662456004451895332431569136 y1[1] (numeric) = 0.82648186843481196214576053873324 absolute error = 0.00501475612523255680756377695812 relative error = 0.6030999978966755643178451711945 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2521.5MB, alloc=4.6MB, time=139.93 x[1] = 0.59 y2[1] (analytic) = 0.55636102291278377572254337887577 y2[1] (numeric) = 0.59059083237322326741780920343014 absolute error = 0.03422980946043949169526582455437 relative error = 6.1524456334543447119745396950975 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83094067910016349524799652249068 y1[1] (numeric) = 0.82589178009199757142047181245567 absolute error = 0.00504889900816592382752471003501 relative error = 0.60761244877714284598980154829276 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2525.3MB, alloc=4.6MB, time=140.14 x[1] = 0.591 y2[1] (analytic) = 0.55719168527290555827556373491228 y2[1] (numeric) = 0.59159583953337024298844122999465 absolute error = 0.03440415426046468471287749508237 relative error = 6.1745634706687982614402774407497 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.83038390269967261643345699307291 y1[1] (numeric) = 0.8253006867588541599192310479522 absolute error = 0.00508321594081845651422594512071 relative error = 0.61215251455288845412739611220856 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2529.1MB, alloc=4.6MB, time=140.35 x[1] = 0.592 y2[1] (analytic) = 0.55802179044138850056191746952789 y2[1] (numeric) = 0.59260088049688164502730065251696 absolute error = 0.03457909005549314446538318298907 relative error = 6.1967275557718815286862753178319 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82982629591534823660255271433876 y1[1] (numeric) = 0.82470858840166304897668130847602 absolute error = 0.00511770751368518762587140586274 relative error = 0.61672033519256568182343553857207 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2533.0MB, alloc=4.6MB, time=140.57 x[1] = 0.593 y2[1] (analytic) = 0.55885133758812750327409069743309 y2[1] (numeric) = 0.59360595543359289016396758435696 absolute error = 0.03475461784546538688987688692387 relative error = 6.2189379371369567771165702651965 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82926785930479709361243303906856 y1[1] (numeric) = 0.82411548498653600287498635035055 absolute error = 0.00515237431826109073744668871801 relative error = 0.62131605131549388445423040618634 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2536.8MB, alloc=4.6MB, time=140.78 x[1] = 0.594 y2[1] (analytic) = 0.55968032588357548880200729707396 y2[1] (numeric) = 0.59461106451389681078303299869529 absolute error = 0.03493073863032132198102570162133 relative error = 6.2411946632527516003185226086892 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82870859342645575147785829599953 y1[1] (numeric) = 0.82352137647941467184052854749285 absolute error = 0.00518721694704107963732974850668 relative error = 0.62593980419504632089059669395981 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2540.6MB, alloc=4.6MB, time=140.99 x[1] = 0.595 y2[1] (analytic) = 0.56050875449874423078003739178746 y2[1] (numeric) = 0.59561620790874447943605166638581 absolute error = 0.03510745341000024865601427459835 relative error = 6.2634977827235531132569950648751 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82814849883959004193468231144419 y1[1] (numeric) = 0.82292626284607003421589847879986 absolute error = 0.00522223599352000771878383264433 relative error = 0.630591735762059221903282199651 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2544.4MB, alloc=4.6MB, time=141.21 TOP MAIN SOLVE Loop memory used=2548.2MB, alloc=4.6MB, time=141.43 x[1] = 0.596 y2[1] (analytic) = 0.56133662260520518307515463308144 y2[1] (numeric) = 0.59662138578964603265988912983851 absolute error = 0.03528476318444084958473449675707 relative error = 6.2858473442694026930999190477978 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.827587576104294505174067278921 y1[1] (numeric) = 0.82233014405210183780776928182109 absolute error = 0.00525743205219266736629799709991 relative error = 0.63527198860826223776824229966569 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2552.0MB, alloc=4.6MB, time=141.64 x[1] = 0.597 y2[1] (analytic) = 0.56216392937509030821541329795109 y2[1] (numeric) = 0.59762659832867149420045760380992 absolute error = 0.03546266895358118598504430585883 relative error = 6.3082433967262912710440379161403 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82702582578149182974799024253562 y1[1] (numeric) = 0.82173302006293804041124988123348 absolute error = 0.00529280571855378933674036130214 relative error = 0.63998070598973041832969499699144 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2555.8MB, alloc=4.6MB, time=141.85 x[1] = 0.598 y2[1] (analytic) = 0.56299067398109290525791677182386 y2[1] (numeric) = 0.59863184569845159764083565966325 absolute error = 0.03564117171735869238291888783939 relative error = 6.3306859890463551765142864283747 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82646324843293229164660128855966 y1[1] (numeric) = 0.82113489084383424951131220576029 absolute error = 0.00532835758909804213528908279937 relative error = 0.64471803183035788004296714890453 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2559.7MB, alloc=4.6MB, time=142.06 x[1] = 0.599 y2[1] (analytic) = 0.56381685559646843709544954923328 y2[1] (numeric) = 0.59963712807217860843276651517434 absolute error = 0.03582027247571017133731696594106 relative error = 6.3531751702980725351149510043795 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82589984462119319254799436780206 y1[1] (numeric) = 0.82053575635987316116188851233677 absolute error = 0.00536408826132003138610585546529 relative error = 0.64948411072535331579492131531162 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2563.5MB, alloc=4.6MB, time=142.28 x[1] = 0.6 y2[1] (analytic) = 0.56464247339503535720094544565866 y2[1] (numeric) = 0.60064244562360714533052971730126 absolute error = 0.0359999722285717881295842716426 relative error = 6.3757109896664602217154564875232 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82533561490967829724095249895538 y1[1] (numeric) = 0.8199356165759639980432359415203 absolute error = 0.00539999833371429919771655743508 relative error = 0.65427908794475750458734636089807 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2567.3MB, alloc=4.6MB, time=142.49 x[1] = 0.601 y2[1] (analytic) = 0.56546752655117593580896527613138 y2[1] (numeric) = 0.60164779852705500122618097050445 absolute error = 0.03618027197587906541721569437307 relative error = 6.3982934964532713700583420257778 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82477055986261727022122993012494 y1[1] (numeric) = 0.81933447145684194669816643337295 absolute error = 0.00543608840577532352306349675199 relative error = 0.65910310943698297946822668480796 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2571.1MB, alloc=4.6MB, time=142.70 x[1] = 0.602 y2[1] (analytic) = 0.56629201423983708553335781919889 y2[1] (numeric) = 0.60265318695740396338515482820027 absolute error = 0.03636117271756687785179700900138 relative error = 6.4209227400771934402817215086978 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82420468004506511146193466221171 y1[1] (numeric) = 0.81873232096706759394774113830917 absolute error = 0.00547235907799751751419352390254 relative error = 0.6639563218323760134073980295369 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2574.9MB, alloc=4.6MB, time=142.91 x[1] = 0.603 y2[1] (analytic) = 0.56711593563653118642027844865423 y2[1] (numeric) = 0.60365861109010063308122492975289 absolute error = 0.03654267545356944666094648109866 relative error = 6.4435987700740468457532727739031 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82363797602290159135857556371942 y1[1] (numeric) = 0.81812916507102636248702946270129 absolute error = 0.00550881095187522887154610101813 relative error = 0.66883887244680108413687692613225 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2578.7MB, alloc=4.6MB, time=143.13 TOP MAIN SOLVE Loop memory used=2582.5MB, alloc=4.6MB, time=143.34 x[1] = 0.604 y2[1] (analytic) = 0.56793928991733691043574038008136 y2[1] (numeric) = 0.60466407110115724462981643005748 absolute error = 0.03672478118382033419407604997612 relative error = 6.4663216360969841406175645972921 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82307044836283068484933913189164 y1[1] (numeric) = 0.81752500373292794566153389437085 absolute error = 0.00554544462990273918780523752079 relative error = 0.67375090928524798031224207416709 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2586.4MB, alloc=4.6MB, time=143.55 x[1] = 0.605 y2[1] (analytic) = 0.5687620762589000453868740447335 y2[1] (numeric) = 0.60566956716715248381866523324032 absolute error = 0.03690749090825243843179118850682 relative error = 6.489091387916689769463311371042 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82250209763238000471116177985496 y1[1] (numeric) = 0.81691983691680574142488275846445 absolute error = 0.00558226071557426328627902139051 relative error = 0.67869258104546171269997687687512 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2590.2MB, alloc=4.6MB, time=143.77 x[1] = 0.606 y2[1] (analytic) = 0.56958429383843431827607066955397 y2[1] (numeric) = 0.60667509946523230573481860629924 absolute error = 0.03709080562679798745874793674527 relative error = 6.5119080754215803805219424181811 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8219329243999002340321643536487 y1[1] (numeric) = 0.81631366458651628547839405961904 absolute error = 0.00561925981338394855377029402966 relative error = 0.68366403712159539545678195268722 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2594.0MB, alloc=4.6MB, time=143.98 x[1] = 0.607 y2[1] (analytic) = 0.57040594183372221808718670926455 y2[1] (numeric) = 0.60768066817311075198697171262918 absolute error = 0.03727472633938853389978500336463 relative error = 6.5347717486180057038136861582686 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82136292923456455786101640665948 y1[1] (numeric) = 0.81570648670573868359311457176387 absolute error = 0.00565644252882587426790183489561 relative error = 0.68866542760788626394066519464724 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2597.8MB, alloc=4.6MB, time=144.19 x[1] = 0.608 y2[1] (analytic) = 0.57122701942311581800298634438536 y2[1] (numeric) = 0.60868627346907076732213456932259 absolute error = 0.03745925404595494931914822493723 relative error = 6.5576824576304499956621988917369 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82079211270636809403379858204876 y1[1] (numeric) = 0.8150983032379740431149393423841 absolute error = 0.00569380946839405091885923966466 relative error = 0.69369690330235499688024680956618 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2601.6MB, alloc=4.6MB, time=144.41 x[1] = 0.609 y2[1] (analytic) = 0.57204752578553759705299982781237 y2[1] (numeric) = 0.60969191553196501563562389590206 absolute error = 0.03764438974642741858262406808969 relative error = 6.580640252701734051003613877225 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.82022047538612732317893227626382 y1[1] (numeric) = 0.81448911414654490365341778358555 absolute error = 0.00573136123958241952551449267827 relative error = 0.69875861571052851212831120907544 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2605.4MB, alloc=4.6MB, time=144.62 x[1] = 0.61 y2[1] (analytic) = 0.57286746010048126119097603216272 y2[1] (numeric) = 0.61069759454121669537337428573292 absolute error = 0.0378301344407354341823982535702 relative error = 6.6036451841932177849207487038204 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81964801784547951790074657865482 y1[1] (numeric) = 0.81387891939459466695485352785048 absolute error = 0.00576909845088485094589305080434 relative error = 0.70385071704918640663833164235016 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2609.2MB, alloc=4.6MB, time=144.83 x[1] = 0.611 y2[1] (analytic) = 0.57368682154801256380110812050361 y2[1] (numeric) = 0.61170331067682035432556309477494 absolute error = 0.03801648912880779052445497427133 relative error = 6.6266973025850033848380877754624 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81907474065688217114225330358349 y1[1] (numeric) = 0.81326771894508702596030623196126 absolute error = 0.00580702171179514518194707162223 relative error = 0.70897336025013121272862359974951 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2613.1MB, alloc=4.6MB, time=145.04 x[1] = 0.612 y2[1] (analytic) = 0.57450560930877012563221183430752 y2[1] (numeric) = 0.61270906411934270381054340556554 absolute error = 0.03820345481057257817833157125802 relative error = 6.6497966584761390348180520954263 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81850064439361242372770175220081 y1[1] (numeric) = 0.81265551276080539304910451819268 absolute error = 0.00584513163280703067859723400813 relative error = 0.71412669896398264413808738847417 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2616.9MB, alloc=4.6MB, time=145.26 TOP MAIN SOLVE Loop memory used=2620.7MB, alloc=4.6MB, time=145.47 x[1] = 0.613 y2[1] (analytic) = 0.57532382256396625415903646452381 y2[1] (numeric) = 0.61371485504992343224807938738016 absolute error = 0.03839103248595717808904292285635 relative error = 6.6729433025848232134039805323903 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81792572962976649108548566129119 y1[1] (numeric) = 0.81204230080435232746848024753404 absolute error = 0.00588342882541416361700541375715 relative error = 0.71931088756399600683031858221212 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2624.5MB, alloc=4.6MB, time=145.68 x[1] = 0.614 y2[1] (analytic) = 0.57614146049538776236988914452402 y2[1] (numeric) = 0.61472068365027601812087833638905 absolute error = 0.03857922315488825575098919186503 relative error = 6.6961372857486095664601754342094 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81734999694025908915197561622843 y1[1] (numeric) = 0.81142808303814896194993532539982 absolute error = 0.00592191390211012720204029082861 relative error = 0.72452608114990495096933857887931 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2628.3MB, alloc=4.6MB, time=145.89 x[1] = 0.615 y2[1] (analytic) = 0.5769585222853967869797536773647 y2[1] (numeric) = 0.61572655010268854232341364232276 absolute error = 0.03876802781729175534365996495806 relative error = 6.7193786589246123564643108994375 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8167734469008228594568510241632 y1[1] (numeric) = 0.81081285942443442851295324602262 absolute error = 0.00596058747638843094389777814058 relative error = 0.7297724355517887419704691922174 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2632.1MB, alloc=4.6MB, time=146.10 x[1] = 0.616 y2[1] (analytic) = 0.57777500711693160606808568431733 y2[1] (numeric) = 0.61673245459002449989703289067019 absolute error = 0.03895744747309289382894720635286 relative error = 6.7426674731897124897124642882819 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81619608008800779339050656206213 y1[1] (numeric) = 0.8101966299252652834566685874942 absolute error = 0.00599945016274250993383797456793 relative error = 0.73505010733396423002408962881719 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2635.9MB, alloc=4.6MB, time=146.32 x[1] = 0.617 y2[1] (analytic) = 0.57859091417350745614046643693812 y2[1] (numeric) = 0.61773839729572361115034527176341 absolute error = 0.03914748312221615500987883482529 relative error = 6.7660037797407641229020107232762 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8156178970791806556541088321442 y1[1] (numeric) = 0.8095793945025149315401086752302 absolute error = 0.006038502576665724114000156914 relative error = 0.74035925379890269899831760379149 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2639.8MB, alloc=4.6MB, time=146.53 x[1] = 0.618 y2[1] (analytic) = 0.57940624263921734861329831109204 y2[1] (numeric) = 0.618744378403802632163882430251 absolute error = 0.03933813576458528355058411915896 relative error = 6.7893876298948018505626164642358 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81503889845252440689287977460952 y1[1] (numeric) = 0.80896115311787304935162263748183 absolute error = 0.00607774533465135754125713712769 relative error = 0.74570003299117177714919665550383 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2643.6MB, alloc=4.6MB, time=146.74 x[1] = 0.619 y2[1] (analytic) = 0.58022099169873288572072537830366 y2[1] (numeric) = 0.6197503980988561646780268504268 absolute error = 0.03952940640012327895730147212314 relative error = 6.812819075089248474810580211876 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81445908478703762551318420432926 y1[1] (numeric) = 0.80834190573284500786811408240318 absolute error = 0.00611717905419261764507012192608 relative error = 0.75107260370140259360389857183438 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2647.4MB, alloc=4.6MB, time=146.96 x[1] = 0.62 y2[1] (analytic) = 0.58103516053730507584296322758221 y2[1] (numeric) = 0.62075645656605746536320183466233 absolute error = 0.03972129602875238952023860708012 relative error = 6.8362981668821233589068016693276 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8138784566625339286839996543607 y1[1] (numeric) = 0.80772165230875129420469463210649 absolute error = 0.00615680435378263447930502225421 relative error = 0.75647712547028236613391460722449 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2651.2MB, alloc=4.6MB, time=147.17 TOP MAIN SOLVE Loop memory used=2655.0MB, alloc=4.6MB, time=147.38 x[1] = 0.621 y2[1] (analytic) = 0.58184874834076514825522268945897 y2[1] (numeric) = 0.62176255399115925447131709378866 absolute error = 0.03991380565039410621609440432969 relative error = 6.8598249569522513661037041408816 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81329701465964139252334752476951 y1[1] (numeric) = 0.80710039280672693255537655509966 absolute error = 0.00619662185291445996797096966985 relative error = 0.76191375859257260730136497439102 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2658.8MB, alloc=4.6MB, time=147.59 x[1] = 0.622 y2[1] (analytic) = 0.58266175429552536729641271338109 y2[1] (numeric) = 0.62276869056049452386746392968639 absolute error = 0.0401069362649691565710512163053 relative error = 6.8833994970994723852715026429296 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81271475935980197147026535027979 y1[1] (numeric) = 0.80647812718772090432542374450065 absolute error = 0.00623663217208106714484160577914 relative error = 0.76738266412115313764255783480339 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2662.7MB, alloc=4.6MB, time=147.81 x[1] = 0.623 y2[1] (analytic) = 0.58347417758857984595680822982696 y2[1] (numeric) = 0.62377486646097734444085395157007 absolute error = 0.04030068887239749848404572174311 relative error = 6.907021839244851444799291013866 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81213169134527091684290081473111 y1[1] (numeric) = 0.80585485541249556745598129546263 absolute error = 0.00627683593277534938691951926848 relative error = 0.77288400387109209614893338318786 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2666.5MB, alloc=4.6MB, time=148.02 x[1] = 0.624 y2[1] (analytic) = 0.58428601740750535888386940954296 y2[1] (numeric) = 0.62478108188010367289399522849542 absolute error = 0.04049506447259831401012581895246 relative error = 6.9306920354308894162715209087906 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81154781119911619458330895420011 y1[1] (numeric) = 0.80523057744162607494160494132166 absolute error = 0.00631723375749011964170401287845 relative error = 0.77841794042374213991669413910624 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2670.3MB, alloc=4.6MB, time=148.23 x[1] = 0.625 y2[1] (analytic) = 0.58509727294046215480539931415008 y2[1] (numeric) = 0.62578733700595215790909974147324 absolute error = 0.04069006406549000310370042732316 relative error = 6.9544101378217343094255624222735 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81096311950521790218953480394108 y1[1] (numeric) = 0.80460529323549979254131261409571 absolute error = 0.00635782626971810964822218984537 relative error = 0.78398463713086302646290958191728 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2674.1MB, alloc=4.6MB, time=148.44 x[1] = 0.626 y2[1] (analytic) = 0.58590794337619476836922751503053 y2[1] (numeric) = 0.62679363202718494569071595924271 absolute error = 0.04088568865099017732148844421218 relative error = 6.978176198703393159901170469921 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.81037761684826768483556455701403 y1[1] (numeric) = 0.80397900275431571568378140112006 absolute error = 0.00639861409395196915178315589397 relative error = 0.78958425811877077384785401979555 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2677.9MB, alloc=4.6MB, time=148.66 x[1] = 0.627 y2[1] (analytic) = 0.5867180279040328313986078408783 y2[1] (numeric) = 0.62779996713304848488358032223788 absolute error = 0.04108193922901565348497248135958 relative error = 7.0019902704839445112978330488455 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80979130381376815067972911460066 y1[1] (numeric) = 0.80335170595808388556731417579992 absolute error = 0.00643959785568426511241493880074 relative error = 0.79521696829251359540095518526682 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2681.7MB, alloc=4.6MB, time=148.87 x[1] = 0.628 y2[1] (analytic) = 0.58752752571389188356251899858354 y2[1] (numeric) = 0.62880634251337433086468137957434 absolute error = 0.0412788167994824473021623809908 relative error = 7.0258524056937514930611471605827 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80920418098803228536214471955587 y1[1] (numeric) = 0.80272340280662480445520118669631 absolute error = 0.00648077818140748090694353285956 relative error = 0.80088293334007480752116352947955 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2685.5MB, alloc=4.6MB, time=149.08 x[1] = 0.629 y2[1] (analytic) = 0.5883364359962741824600573972178 y2[1] (numeric) = 0.62981275835857994940853028398759 absolute error = 0.04147632236230576694847288676979 relative error = 7.0497626569856754957245555900044 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80861624895818286569177617570531 y1[1] (numeric) = 0.80209409325956885016710289543641 absolute error = 0.0065221556986140155246732802689 relative error = 0.80658231973660291071196651492188 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2689.4MB, alloc=4.6MB, time=149.30 TOP MAIN SOLVE Loop memory used=2693.2MB, alloc=4.6MB, time=149.51 x[1] = 0.63 y2[1] (analytic) = 0.58914475794226951311811209079462 y2[1] (numeric) = 0.6308192148596695197246313095697 absolute error = 0.04167445691740000660651921877508 relative error = 7.0737210771352904450379829632093 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80802750831215187252370896577706 y1[1] (numeric) = 0.80146377727635568976708136025457 absolute error = 0.00656373103579618275662760552249 relative error = 0.81231529474866904571683831489351 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2697.0MB, alloc=4.6MB, time=149.72 x[1] = 0.631 y2[1] (analytic) = 0.58995249074355599690151234219815 y2[1] (numeric) = 0.63182571220823473686614601687639 absolute error = 0.04187322146467873996463367467824 relative error = 7.0977277190410976765201326292365 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.8074379596386799028272173906462 y1[1] (numeric) = 0.80083245481623369244890846832568 absolute error = 0.00660550482244621037830892232052 relative error = 0.81808202643855202834280513968636 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2700.8MB, alloc=4.6MB, time=149.94 x[1] = 0.632 y2[1] (analytic) = 0.59075963359240089983483889819962 y2[1] (numeric) = 0.63283225059645561350874464951152 absolute error = 0.0420726170040547136739057513119 relative error = 7.1217826357247414119764469983124 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80684760352731558094521666177536 y1[1] (numeric) = 0.80020012583825934161928032644795 absolute error = 0.00664747768905623932593633532741 relative error = 0.82388268366855116829819386067935 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2704.6MB, alloc=4.6MB, time=150.15 x[1] = 0.633 y2[1] (analytic) = 0.59156618568166144033509065381761 y2[1] (numeric) = 0.63383883021710128109863830564011 absolute error = 0.0422726445354398407635476518225 relative error = 7.1458858803312248395299930969279 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80625644056841496904568768734982 y1[1] (numeric) = 0.79956679030129664617956812606857 absolute error = 0.00668965026711832286611956128125 relative error = 0.82971743610532707912569267031149 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2708.4MB, alloc=4.6MB, time=150.36 x[1] = 0.634 y2[1] (analytic) = 0.59237214620478559635439897342298 y2[1] (numeric) = 0.63484545126353079036878538703313 absolute error = 0.04247330505874519401438641361015 relative error = 7.1700375061291267987178123412365 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80566447135314097676566410063355 y1[1] (numeric) = 0.79893244816401655100673680512265 absolute error = 0.0067320231891244257589272955109 relative error = 0.83558645422427068808376524082406 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2712.2MB, alloc=4.6MB, time=150.57 x[1] = 0.635 y2[1] (analytic) = 0.59317751435581291193198252594122 y2[1] (numeric) = 0.63585211392969391122226578720776 absolute error = 0.04267459957388099929028326126654 relative error = 7.1942375665108190722105689598316 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80507169647346277004837188650966 y1[1] (numeric) = 0.79829709938489634663406383567357 absolute error = 0.00677459708856642341430805083609 relative error = 0.84148990931390065661840436237281 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2716.1MB, alloc=4.6MB, time=150.79 x[1] = 0.636 y2[1] (analytic) = 0.59398228932937530315453608226469 y2[1] (numeric) = 0.6368588184101319319818162389941 absolute error = 0.04287652908075662882728015672941 relative error = 7.2184861149926842857186451891936 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80447811652215517917411276901668 y1[1] (numeric) = 0.7976607439222190781322914729022 absolute error = 0.00681737259993610104182129611448 relative error = 0.84742797348028942387336960617677 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2719.9MB, alloc=4.6MB, time=151.00 x[1] = 0.637 y2[1] (analytic) = 0.59478647032069786352424731455312 y2[1] (numeric) = 0.6378655648999784580045202004334 absolute error = 0.04307909457928059448027288588028 relative error = 7.2427832052153344176531633953135 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80388373209279810598548332894764 y1[1] (numeric) = 0.79702338173407295319184680759251 absolute error = 0.00686035035872515279363652135513 relative error = 0.85340081965151808751061057165661 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2723.7MB, alloc=4.6MB, time=151.21 TOP MAIN SOLVE Loop memory used=2727.5MB, alloc=4.6MB, time=151.43 x[1] = 0.638 y2[1] (analytic) = 0.59559005652559966873363622947259 y2[1] (numeric) = 0.63887235359496020966064561629302 absolute error = 0.04328229706936054092700938682043 relative error = 7.2671288909438299201157657184564 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80328854377977593030752262624373 y1[1] (numeric) = 0.79638501277835074940676497090316 absolute error = 0.00690353100142518090075765534057 relative error = 0.85940862158216033795371931352764 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2731.3MB, alloc=4.6MB, time=151.64 x[1] = 0.639 y2[1] (analytic) = 0.59639304714049458084641246060074 y2[1] (numeric) = 0.63987918469139781967562385066892 absolute error = 0.04348613755090323882921139006818 relative error = 7.2915232260678994527963507703529 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80269255217827691556338190698517 y1[1] (numeric) = 0.7957456370127492207609518468983 absolute error = 0.00694691516552769480243006008687 relative error = 0.86545155385779566402617138297348 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2735.1MB, alloc=4.6MB, time=151.85 x[1] = 0.64 y2[1] (analytic) = 0.59719544136239205188354623920793 y2[1] (numeric) = 0.64088605838620662983416304413685 absolute error = 0.04369061702381457795061680492892 relative error = 7.3159662646021602313633544103969 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80209575788429261358611077926032 y1[1] (numeric) = 0.79510525439476850331742365503616 absolute error = 0.00699050348952411026868712422416 relative error = 0.87152979189955204983299556496824 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2738.9MB, alloc=4.6MB, time=152.06 x[1] = 0.641 y2[1] (analytic) = 0.59799723838889792681374945741014 y2[1] (numeric) = 0.64189297487689748704548910670824 absolute error = 0.0438957364879995602317396492981 relative error = 7.340458060686338991936567766033 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80149816149461726862715504607705 y1[1] (numeric) = 0.79446386488171152011116177158174 absolute error = 0.00703429661290574851599327449531 relative error = 0.8776435119686783846295511190411 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2742.8MB, alloc=4.6MB, time=152.28 x[1] = 0.642 y2[1] (analytic) = 0.59879843741821524594756383327983 y2[1] (numeric) = 0.6428999343615775387687075154451 absolute error = 0.04410149694336229282114368216527 relative error = 7.3649986685854935732379105188674 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80089976360684722056216218676894 y1[1] (numeric) = 0.79382146843068338524622216571987 absolute error = 0.00707829517616383531594002104907 relative error = 0.88379289117114680933448369006308 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2746.6MB, alloc=4.6MB, time=152.48 x[1] = 0.643 y2[1] (analytic) = 0.59959903764914504673425378389305 y2[1] (numeric) = 0.6439069370389510277972790429897 absolute error = 0.04430789938980598106302525909665 relative error = 7.3895881426902351180210211295668 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.80030056481938030729469128104118 y1[1] (numeric) = 0.7931780649985908071977398329973 absolute error = 0.00712249982078950009695144804388 relative error = 0.88997810746228522527587492365334 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2750.4MB, alloc=4.6MB, time=152.69 x[1] = 0.644 y2[1] (analytic) = 0.6003990382810871649607022094871 y2[1] (numeric) = 0.64491398310832008640160250046888 absolute error = 0.04451494482723292144090029098178 relative error = 7.4142265375169508953859881981294 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79970056573141526635842497189628 y1[1] (numeric) = 0.79253365454214149131946961561751 absolute error = 0.00716691118927377503895535627877 relative error = 0.89619933965144019271029642065424 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2754.2MB, alloc=4.6MB, time=152.91 x[1] = 0.645 y2[1] (analytic) = 0.60119843851404103535150798989947 y2[1] (numeric) = 0.6459210727695855298286975352386 absolute error = 0.04472263425554449447718954533913 relative error = 7.4389139077080277455910286297634 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79909976694295113571848186517791 y1[1] (numeric) = 0.79188823701784354155750580605016 absolute error = 0.00721152992510759416097605912775 relative error = 0.9024567674066704486241285987126 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2758.0MB, alloc=4.6MB, time=153.12 x[1] = 0.646 y2[1] (analytic) = 0.6019972375486064915694845932574 y2[1] (numeric) = 0.64692820622324764915798048074153 absolute error = 0.04493096867464115758849588748413 relative error = 7.4636503080320761489784187780118 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79849816905478665377242856437044 y1[1] (numeric) = 0.79124181238200486137082393739799 absolute error = 0.00725635667278179240160462697245 relative error = 0.90875057125947127531531430774272 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2761.8MB, alloc=4.6MB, time=153.34 TOP MAIN SOLVE Loop memory used=2765.7MB, alloc=4.6MB, time=153.55 x[1] = 0.647 y2[1] (analytic) = 0.60279543458598456561575979648616 y2[1] (numeric) = 0.64793538367040700351212621235834 absolute error = 0.04513994908442243789636641587218 relative error = 7.4884357933841549206375043445032 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79789577266851965855159133959223 y1[1] (numeric) = 0.79059438059073255385928917098861 absolute error = 0.00730139207778710469230216860362 relative error = 0.91508093260952995326189312231774 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2769.5MB, alloc=4.6MB, time=153.76 x[1] = 0.648 y2[1] (analytic) = 0.60359302882797828662867711760275 y2[1] (numeric) = 0.64894260531276521162200891954132 absolute error = 0.04534957648478692499333180193857 relative error = 7.5132704187859965324331536073983 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79729257838654648612326822942085 y1[1] (numeric) = 0.78994594159993232109977669872625 absolute error = 0.0073466367866141650234915306946 relative error = 0.92144803372951253381141503289032 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2773.3MB, alloc=4.6MB, time=153.98 x[1] = 0.649 y2[1] (analytic) = 0.60439001947699347908070016096041 y2[1] (numeric) = 0.64994987135262574274471466072632 absolute error = 0.04555985187563226366401449976591 relative error = 7.5381542393862330640335766071113 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79668858681206136819444317328799 y1[1] (numeric) = 0.78929649536530786269105058485044 absolute error = 0.00739209144675350550339258843755 relative error = 0.92785205776988216927287420899726 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2777.1MB, alloc=4.6MB, time=154.19 x[1] = 0.65 y2[1] (analytic) = 0.60518640573603956037252167860594 y2[1] (numeric) = 0.65095718199289470693361852352556 absolute error = 0.04577077625685514656109684491962 relative error = 7.5630873104606227845770103179034 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79608379854905582891760457067991 y1[1] (numeric) = 0.7886460418423602735080484789038 absolute error = 0.00743775670669555540955609177611 relative error = 0.93429318876374924006034957875197 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2780.9MB, alloc=4.6MB, time=154.40 x[1] = 0.651 y2[1] (analytic) = 0.60598218680873033782357975370724 y2[1] (numeric) = 0.65196453743708164465951916850822 absolute error = 0.04598235062835130683593941480098 relative error = 7.5880696874122773666223666567975 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79547821420231808089927146127429 y1[1] (numeric) = 0.78799458098638744066622063891086 absolute error = 0.00748363321593064023305082236343 relative error = 0.94077161163175352062530669771352 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2784.7MB, alloc=4.6MB, time=154.61 x[1] = 0.652 y2[1] (analytic) = 0.60677736189928480505818411560141 y2[1] (numeric) = 0.65297193788930031578182349047832 absolute error = 0.04619457599001551072363937487691 relative error = 7.6131014257718897340345565072852 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7948718343774324204118313174373 y1[1] (numeric) = 0.78734211275248343969657271101366 absolute error = 0.00752972162494898071525860642364 relative error = 0.94728751218697862802272490908923 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2788.5MB, alloc=4.6MB, time=154.82 x[1] = 0.653 y2[1] (analytic) = 0.60757193021252793778645620040338 y2[1] (numeric) = 0.65397938355426948786877408655876 absolute error = 0.04640745334174155008231788615538 relative error = 7.6381825811979625454608388447961 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7942646596807786218092942371924 y1[1] (numeric) = 0.78668863709553792993206271909827 absolute error = 0.00757602258524069187723151809413 relative error = 0.95384107713989899908508790620868 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2792.4MB, alloc=4.6MB, time=155.03 x[1] = 0.654 y2[1] (analytic) = 0.60836589095389148897928717630129 y2[1] (numeric) = 0.65498687463731372386571217558619 absolute error = 0.0466209836834222348864249992849 relative error = 7.6633132094770373150601996245624 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79365669071953133114756912185648 y1[1] (numeric) = 0.78603415397023554910600372527935 absolute error = 0.00762253674929578204156539657713 relative error = 0.96043249410335964432803995075087 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2796.2MB, alloc=4.6MB, time=155.25 x[1] = 0.655 y2[1] (analytic) = 0.60915924332941478343651875864697 y2[1] (numeric) = 0.65599441134436416911036856831346 absolute error = 0.04683516801494938567384980966649 relative error = 7.6884933665239241721534404115578 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7930479281016594590098682180164 y1[1] (numeric) = 0.78537866333105530716312462948804 absolute error = 0.00766926477060415184674358852836 relative error = 0.96706195159758892888239233688244 % Correct digits = 2 h = 0.001 memory used=2800.0MB, alloc=4.6MB, time=155.46 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2803.8MB, alloc=4.6MB, time=155.68 x[1] = 0.656 y2[1] (analytic) = 0.60995198654574551174755224672681 y2[1] (numeric) = 0.65700199388195933769417524270323 absolute error = 0.04705000733621382594662299597642 relative error = 7.7137231083819322614673518779898 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79243837243592557253784719839097 y1[1] (numeric) = 0.78472216513226997928394258383139 absolute error = 0.00771620730365559325390461455958 relative error = 0.97372963905524463293939612680423 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2807.6MB, alloc=4.6MB, time=155.88 x[1] = 0.657 y2[1] (analytic) = 0.61074411981014052364359182167023 y2[1] (numeric) = 0.65800962245724589816859003317828 absolute error = 0.04726550264710537452499821150805 relative error = 7.7390024912231007856520623482228 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79182802433188528666908875038748 y1[1] (numeric) = 0.78406465932794549812310150486001 absolute error = 0.00776336500393978854598724552747 relative error = 0.98043574682649354641001140045557 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2811.4MB, alloc=4.6MB, time=156.09 x[1] = 0.658 y2[1] (analytic) = 0.61153564233046662074072875331851 y2[1] (numeric) = 0.65901729727797945859542689706982 absolute error = 0.04748165494751283785469814375131 relative error = 7.7643315713484306917563866161795 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79121688439988665458153843481859 y1[1] (numeric) = 0.7834061458719403452623321743946 absolute error = 0.00781073852794630931920626042399 relative error = 0.98718046618412485473453676088738 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2815.2MB, alloc=4.6MB, time=156.30 x[1] = 0.659 y2[1] (analytic) = 0.61232655331520134867307377303585 y2[1] (numeric) = 0.66002501855252535094018417567439 absolute error = 0.04769846523732400226711040263854 relative error = 7.789710405188117003351755378701 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.79060495325106955734550237029284 y1[1] (numeric) = 0.78274662471790494187869042712154 absolute error = 0.0078583285331646154668119431713 relative error = 0.99396398932869757503665496929891 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2819.1MB, alloc=4.6MB, time=156.52 x[1] = 0.66 y2[1] (analytic) = 0.6131168519734337886151454793963 y2[1] (numeric) = 0.66103278648985941480736322129216 absolute error = 0.04791593451642562619221774189586 relative error = 7.8151390493017818000010809029778 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78999223149736509278381709123024 y1[1] (numeric) = 0.78208609581928103862873093077354 absolute error = 0.0079061356780840541550861604567 relative error = 1.0007865093937223040959435928116 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2822.9MB, alloc=4.6MB, time=156.73 x[1] = 0.661 y2[1] (analytic) = 0.61390653751486534819272325442414 y2[1] (numeric) = 0.66204060129956878051676971537379 absolute error = 0.04813406378470343232404646094965 relative error = 7.8406175603787078457747100601873 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7893787197514949635408027192822 y1[1] (numeric) = 0.78142455912930110474927507236277 absolute error = 0.00795416062219385879152764691943 relative error = 1.0076482204508775419154386052863 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2826.7MB, alloc=4.6MB, time=156.94 x[1] = 0.662 y2[1] (analytic) = 0.61469560914981055178137377960066 y2[1] (numeric) = 0.66304846319185265151978995644908 absolute error = 0.04835285404204209973841617684842 relative error = 7.8661459952380728685214316945623 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78876441862697086436061137915158 y1[1] (numeric) = 0.78076201460098771637543247163229 absolute error = 0.00800240402598314798517890751929 relative error = 1.0145493175152608569861721255186 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2830.5MB, alloc=4.6MB, time=157.16 x[1] = 0.663 y2[1] (analytic) = 0.61548406608919783019186085317667 y2[1] (numeric) = 0.66405637237752308615463434984763 absolute error = 0.04857230628832525596277349667096 relative error = 7.8917244108291844916083415411733 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78814932873809386857558358041344 y1[1] (numeric) = 0.78009846218715294407653665063604 absolute error = 0.0080508665509409244990469297774 relative error = 1.0214899965506751616989840535129 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2834.3MB, alloc=4.6MB, time=157.37 TOP MAIN SOLVE Loop memory used=2838.1MB, alloc=4.6MB, time=157.58 x[1] = 0.664 y2[1] (analytic) = 0.61627190754457030974164882344686 y2[1] (numeric) = 0.66506432906800577873954028434931 absolute error = 0.04879242152343546899789146090245 relative error = 7.9173528642317158198492246411265 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78753345069995381380522607692892 y1[1] (numeric) = 0.77943390184039773961065639614907 absolute error = 0.00809954885955607419456968077985 relative error = 1.0284704544749503687255854657546 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2841.9MB, alloc=4.6MB, time=157.80 x[1] = 0.665 y2[1] (analytic) = 0.61705913272808660071171056654808 y2[1] (numeric) = 0.66607233347534084000292653381951 absolute error = 0.04901320074725423929121596727143 relative error = 7.943031412655941681346992514426 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78691678512842868686642550482327 y1[1] (numeric) = 0.77876833351311132189834535944822 absolute error = 0.00814845161531736496808014537505 relative error = 1.0354908891653007015860865329242 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2845.8MB, alloc=4.6MB, time=158.01 x[1] = 0.666 y2[1] (analytic) = 0.61784574085252158518785155203961 y2[1] (numeric) = 0.66708038581218357684949127459066 absolute error = 0.04923464495966199166163972255105 relative error = 7.9687601134429755269816103232901 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78629933264018400789551288876302 y1[1] (numeric) = 0.77810175715747056221629344588883 absolute error = 0.00819757548271344567921944287419 relative error = 1.0425514994637179350392538342877 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2849.6MB, alloc=4.6MB, time=158.22 x[1] = 0.667 y2[1] (analytic) = 0.61863173113126720428576215500663 y2[1] (numeric) = 0.66808848629180527146124576184654 absolute error = 0.04945675516053806717548360683991 relative error = 7.9945390240650069892808679780867 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78568109385267221368279489441666 y1[1] (numeric) = 0.77743417272543936861154455463623 absolute error = 0.00824692112723284507125033978043 relative error = 1.0496524851824008433748948372303 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2853.4MB, alloc=4.6MB, time=158.43 x[1] = 0.668 y2[1] (analytic) = 0.61941710277833324475901098970051 y2[1] (numeric) = 0.66909663512809395973247566054884 absolute error = 0.04967953234976071497346467084833 relative error = 8.0203682021255401024172886895988 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78506206938413204022016849251592 y1[1] (numeric) = 0.77676558016876806953694623689118 absolute error = 0.00829648921536397068322225562474 relative error = 1.0567940471092211371552477744223 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2857.2MB, alloc=4.6MB, time=158.64 x[1] = 0.669 y2[1] (analytic) = 0.62020185500834812498919265678791 y2[1] (numeric) = 0.67010483253555520903762197851586 absolute error = 0.04990297752720708404842932172795 relative error = 8.0462477053596321850804289417697 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78444225985358790446243648685181 y1[1] (numeric) = 0.77609597943899279670849784897693 absolute error = 0.00834628041459510775393863787488 relative error = 1.063976387013226171444353225523 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2861.0MB, alloc=4.6MB, time=158.85 x[1] = 0.67 y2[1] (analytic) = 0.62098598703655968035744391412659 y2[1] (numeric) = 0.67111307872931289533107350112024 absolute error = 0.05012709169275321497362958699365 relative error = 8.0721775916341333879798053345518 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78382166588084928530294214483812 y1[1] (numeric) = 0.77542537048743486718526478473205 absolute error = 0.00839629539341441811767736010607 relative error = 1.0711997076501787110813727327162 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2864.8MB, alloc=4.6MB, time=159.07 x[1] = 0.671 y2[1] (analytic) = 0.62176949807883594799654289961709 y2[1] (numeric) = 0.67212137392510997957786257871577 absolute error = 0.05035187584627403158131967909868 relative error = 8.0981579189479269077396863142748 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78320028808651010376414195495638 y1[1] (numeric) = 0.77475375326520016467252737977772 absolute error = 0.00844653482130993909161457517866 relative error = 1.0784642127681340410959764291581 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2868.7MB, alloc=4.6MB, time=159.28 x[1] = 0.672 y2[1] (analytic) = 0.62255238735166595092280665409653 y2[1] (numeric) = 0.67312971833930928351425606933207 absolute error = 0.05057733098764333259144941523554 relative error = 8.1241887454321698689530105562125 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78257812709194810240373632045772 y1[1] (numeric) = 0.77408112772317852004883408840149 absolute error = 0.00849699936876958235490223205623 relative error = 1.0857701071130547129315260014135 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2872.5MB, alloc=4.6MB, time=159.49 TOP MAIN SOLVE Loop memory used=2876.3MB, alloc=4.6MB, time=159.70 x[1] = 0.673 y2[1] (analytic) = 0.62333465407216048154700281244236 y2[1] (numeric) = 0.67413811218889426473723319038947 absolute error = 0.05080345811673378319023037794711 relative error = 8.150270129350534876167738778598 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78195518351932422393697878313928 y1[1] (numeric) = 0.7734074938120430911176295420213 absolute error = 0.00854768970728113281934924111798 relative error = 1.0931175964344632197351148377153 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2880.1MB, alloc=4.6MB, time=159.92 x[1] = 0.674 y2[1] (analytic) = 0.62411629745805288456349195203955 y2[1] (numeric) = 0.67514655569146979112184198418414 absolute error = 0.05103025823341690655835003214459 relative error = 8.1764021290994522375850121372914 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78133145799158198907578515483418 y1[1] (numeric) = 0.77273285148224974158412910646421 absolute error = 0.00859860650933224749165604836997 relative error = 1.1005068874911328965928809067078 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2883.9MB, alloc=4.6MB, time=160.12 x[1] = 0.675 y2[1] (analytic) = 0.6248973167276998392168177095343 y2[1] (numeric) = 0.67615504906526291456542605267509 absolute error = 0.05125773233756307534860834314079 relative error = 8.2025848032083528622545781641166 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78070695113244687358526471745402 y1[1] (numeric) = 0.77205720068403641925811256361426 absolute error = 0.00864975044841045432715215383976 relative error = 1.1079381880568173442346702633756 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2887.7MB, alloc=4.6MB, time=160.34 x[1] = 0.676 y2[1] (analytic) = 0.62567771110008214094496239934914 y2[1] (numeric) = 0.677163592529123644057713167669 absolute error = 0.05148588142904150311275076831986 relative error = 8.2288182103399118325590545585561 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.78008166356642568455829643500084 y1[1] (numeric) = 0.77138054136742253348331055135293 absolute error = 0.00870112219900315107498588364791 relative error = 1.1154117069260186774043941582952 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2891.5MB, alloc=4.6MB, time=160.55 x[1] = 0.677 y2[1] (analytic) = 0.62645747979480548239848649076909 y2[1] (numeric) = 0.67817218630252571807575731284576 absolute error = 0.05171470650772023567727082207667 relative error = 8.255102409290292653784732111143 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77945559591880593590877390292041 y1[1] (numeric) = 0.77070287348220833179405840413449 absolute error = 0.00875272243659760411471549878592 relative error = 1.1229276539197949017915882201002 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2895.4MB, alloc=4.6MB, time=160.76 x[1] = 0.678 y2[1] (analytic) = 0.62723662203210123383477092452439 y2[1] (numeric) = 0.67918083060556737630272566419628 absolute error = 0.05194420857346614246795473967189 relative error = 8.2814374589893921825827707173897 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77882874881565522308414354149961 y1[1] (numeric) = 0.77002419697797427579989304500688 absolute error = 0.00880455183768094728425049649273 relative error = 1.1304862398916067261460494437077 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2899.2MB, alloc=4.6MB, time=160.97 x[1] = 0.679 y2[1] (analytic) = 0.6280151370328272228865818746926 y2[1] (numeric) = 0.68018952565897213066952196535372 absolute error = 0.05217438862614490778294009066112 relative error = 8.3078234185010862361308169232991 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77820112288382059699786132071801 y1[1] (numeric) = 0.76934451180408041629876958840734 absolute error = 0.00885661107974018069909173231067 relative error = 1.13808767673320411895130081998 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2903.0MB, alloc=4.6MB, time=161.18 x[1] = 0.68 y2[1] (analytic) = 0.62879302401846851370417818742025 y2[1] (numeric) = 0.68119827168408953571823770398982 absolute error = 0.05240524766562102201405951656957 relative error = 8.3342603470234758838112678181305 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77757271875092793718239408404432 y1[1] (numeric) = 0.76866381790966576761957532163059 absolute error = 0.00890890084126216956281876241373 relative error = 1.1457321773805529218143232242649 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2906.8MB, alloc=4.6MB, time=161.40 TOP MAIN SOLVE Loop memory used=2910.6MB, alloc=4.6MB, time=161.62 x[1] = 0.681 y2[1] (analytic) = 0.62957028221113818547018235442143 y2[1] (numeric) = 0.68220706890289595828642244491805 absolute error = 0.05263678669175777281624009049662 relative error = 8.360748303889134423228624447799 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77694353704538132416339231812446 y1[1] (numeric) = 0.76798211524364768119461974148643 absolute error = 0.00896142180173364296877257663803 relative error = 1.1534199558198018345388122982502 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2914.4MB, alloc=4.6MB, time=161.83 x[1] = 0.682 y2[1] (analytic) = 0.63034691083357811028643650644746 y2[1] (numeric) = 0.68321591753799534651116462479486 absolute error = 0.0528690067044172362247281183474 relative error = 8.3872873485653550423946183544037 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77631357839636241105566199413604 y1[1] (numeric) = 0.76729940375472121836278033133343 absolute error = 0.00901417464164119269288166280261 relative error = 1.1611512270932900896874810369432 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2918.2MB, alloc=4.6MB, time=162.04 x[1] = 0.683 y2[1] (analytic) = 0.63112290910915973043206553993625 y2[1] (numeric) = 0.68422481781261999815197406233842 absolute error = 0.05310190870346026771990852240217 relative error = 8.4138775406543991699160574457239 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77568284343382979438156388478507 y1[1] (numeric) = 0.76661568339135852240398477239583 absolute error = 0.00906716004247127197757911238924 relative error = 1.1689262073055961373059570777986 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2922.1MB, alloc=4.6MB, time=162.25 x[1] = 0.684 y2[1] (analytic) = 0.63189827626188483499197011884303 y2[1] (numeric) = 0.68523376995063132823145738679036 absolute error = 0.05333549368874649323948726794733 relative error = 8.4405189398937455150266222549225 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77505133278851838411246953849312 y1[1] (numeric) = 0.7659309541018081898057112920425 absolute error = 0.00912037868671019430675824645062 relative error = 1.1767451136296276633769417037275 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2925.9MB, alloc=4.6MB, time=162.46 x[1] = 0.685 y2[1] (analytic) = 0.63267301151638633585497292322433 y2[1] (numeric) = 0.68624277417652063599277753592966 absolute error = 0.05356976266013430013780461270533 relative error = 8.4672116061563397993101508578151 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77441904709193877293390386926657 y1[1] (numeric) = 0.76524521583409464076218986052985 absolute error = 0.00917383125784413217171400873672 relative error = 1.1846081643127532684988337664308 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2929.7MB, alloc=4.6MB, time=162.67 x[1] = 0.686 y2[1] (analytic) = 0.63344711409792904308084214649343 y2[1] (numeric) = 0.68725183071540987117288842330805 absolute error = 0.05380471661748082809204627681462 relative error = 8.4939555994508451819692803657972 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77378598697637660473500509705261 y1[1] (numeric) = 0.76455846853601748890698795658488 absolute error = 0.00922751844035911582801714046773 relative error = 1.1925155786829761362383086447019 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2933.5MB, alloc=4.6MB, time=162.89 x[1] = 0.687 y2[1] (analytic) = 0.63422058323241043963541687438845 y2[1] (numeric) = 0.68826093979305239959053582251282 absolute error = 0.05404035656064195995511894812437 relative error = 8.5207509799218933804996651000518 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77315215307489194232293354906961 y1[1] (numeric) = 0.76387071215515091027966563113098 absolute error = 0.00928144091974103204326791793863 relative error = 1.2004675771551500235917166463108 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2937.3MB, alloc=4.6MB, time=163.10 x[1] = 0.688 y2[1] (analytic) = 0.63499341814636145549305961059239 y2[1] (numeric) = 0.68927010163583376804801546417481 absolute error = 0.05427668348947231255495585358242 relative error = 8.5475978078503364886363663707874 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77251754602131863436286160765029 y1[1] (numeric) = 0.76318194663884301152718560743723 absolute error = 0.00933559938247562283567600021306 relative error = 1.208464381237237909005967808774 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2941.1MB, alloc=4.6MB, time=163.31 x[1] = 0.689 y2[1] (analytic) = 0.63576561806694724110566184661687 y2[1] (numeric) = 0.69027931647077246854567928912637 absolute error = 0.0545136984038252274400174425095 relative error = 8.574496143653499493445406328219 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77188216645026368154417786455494 y1[1] (numeric) = 0.76249217193421519734076516500238 absolute error = 0.00938999451604848420341269955256 relative error = 1.2165062135366136364561459728431 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2944.9MB, alloc=4.6MB, time=163.52 TOP MAIN SOLVE Loop memory used=2948.8MB, alloc=4.6MB, time=163.73 x[1] = 0.69 y2[1] (analytic) = 0.63653718222196794023742920700872 y2[1] (numeric) = 0.6912885845255207018081807485749 absolute error = 0.05475140230355276157075154156618 relative error = 8.6014460478854334934398987140305 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77124601499710660197353931549777 y1[1] (numeric) = 0.76180138798816153712885756356754 absolute error = 0.00944462700894506484468175193023 relative error = 1.2245932977664068971547937218219 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2952.6MB, alloc=4.6MB, time=163.94 x[1] = 0.691 y2[1] (analytic) = 0.63730810983985946216467333515846 y2[1] (numeric) = 0.69229790602836514012144998939256 absolute error = 0.0549897961885056779567766542341 relative error = 8.6284475812371696196066126185791 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.77060909229799879579540620178138 y1[1] (numeric) = 0.76110959474734813092695177278713 absolute error = 0.00949949755065066486845442899425 relative error = 1.2327258587518918935769850974212 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2956.4MB, alloc=4.6MB, time=164.16 x[1] = 0.692 y2[1] (analytic) = 0.63807840014969425323983831998321 y2[1] (numeric) = 0.69330728120822768947938970963026 absolute error = 0.05522888105853343623955138964705 relative error = 8.6555008045369736612352916350596 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76997139898986290904069487845139 y1[1] (numeric) = 0.76041679215821247454488028227592 absolute error = 0.00955460683165043449581459617547 relative error = 1.240904122436920033626313144724 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2960.2MB, alloc=4.6MB, time=164.37 x[1] = 0.693 y2[1] (analytic) = 0.63884805238118206781899009952198 y2[1] (numeric) = 0.69431671029466625103928241614403 absolute error = 0.05546865791348418322029231662205 relative error = 8.6826057787506013984495401933257 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7693329357103921967041848602655 y1[1] (numeric) = 0.75972298016696282395232577599166 absolute error = 0.00960995554342937275185908427384 relative error = 1.2491283158903970059401270198362 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2964.0MB, alloc=4.6MB, time=164.58 x[1] = 0.694 y2[1] (analytic) = 0.63961706576467073855199791401804 y2[1] (numeric) = 0.69532619351787548188489976277387 absolute error = 0.05570912775320474333290184875583 relative error = 8.7097625649815546433446014493174 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76869370309804988505131696801677 y1[1] (numeric) = 0.7590281587195775589032184642074 absolute error = 0.00966554437847232614809850380937 relative error = 1.2573986673128045905381258790049 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2967.8MB, alloc=4.6MB, time=164.79 x[1] = 0.695 y2[1] (analytic) = 0.64038543953114694603463751837122 y2[1] (numeric) = 0.69633573110868755509630459383761 absolute error = 0.05595029157754060906166707546639 relative error = 8.7369712244713379916438869974792 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76805370179206853315502026835991 y1[1] (numeric) = 0.75833232776180454579971687567617 absolute error = 0.00972137403026398735530339268374 relative error = 1.265715406042767562257125935215 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2971.7MB, alloc=4.6MB, time=165.00 x[1] = 0.696 y2[1] (analytic) = 0.64115317291223698782184650192101 y2[1] (numeric) = 0.697345323298572919125336263796 absolute error = 0.05619215038633593130348976187499 relative error = 8.7642318185997162867926779606409 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76741293243244939366320627026033 y1[1] (numeric) = 0.75763548723916049979646592199269 absolute error = 0.00977744519328889386674034826764 relative error = 1.2740787625636660476868394712553 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2975.5MB, alloc=4.6MB, time=165.21 x[1] = 0.697 y2[1] (analytic) = 0.64192026514020754680136270236923 y2[1] (numeric) = 0.69835497031964105647576974980797 absolute error = 0.05643470517943350967440704743874 relative error = 8.7915444088849727984139997917474 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76677139565996177279756961051859 y1[1] (numeric) = 0.75693763709693034614582705561313 absolute error = 0.00983375856303142665174255490546 relative error = 1.2824889685102936996272215308585 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=2979.3MB, alloc=4.6MB, time=165.43 TOP MAIN SOLVE Loop memory used=2983.1MB, alloc=4.6MB, time=165.64 x[1] = 0.698 y2[1] (analytic) = 0.64268671544796645892697734026787 y2[1] (numeric) = 0.69936467240464124168713901952743 absolute error = 0.05667795695667478276016167925956 relative error = 8.8189090569841681170582794927906 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76612909211614238958433522951618 y1[1] (numeric) = 0.75623877728016658078477635250427 absolute error = 0.00989031483597580879955887701191 relative error = 1.2909462566755620564277375709578 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2986.9MB, alloc=4.6MB, time=165.85 x[1] = 0.699 y2[1] (analytic) = 0.64345252306906348031063514088304 y2[1] (numeric) = 0.7003744297869632986212150618937 absolute error = 0.05692190671789981831057992101066 relative error = 8.846325824693399767185024016546 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76548602244329473431759280638201 y1[1] (numeric) = 0.75553890773368863016416735995839 absolute error = 0.00994711470960610415342544642362 relative error = 1.2994508610172514569431745190499 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2990.7MB, alloc=4.6MB, time=166.06 x[1] = 0.7 y2[1] (analytic) = 0.64421768723769105367261435139872 y2[1] (numeric) = 0.70138424270063835705012893383634 absolute error = 0.05716655546294730337751458243762 relative error = 8.8737947739480625403214124652227 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76484218728448842625585999019186 y1[1] (numeric) = 0.75483802840208221032105655972992 absolute error = 0.01000415888240621593480343046194 relative error = 1.3080030166648088852497543494207 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2994.5MB, alloc=4.6MB, time=166.27 x[1] = 0.701 y2[1] (analytic) = 0.64498220718868507414902020334415 y2[1] (numeric) = 0.70239411138033960854513012075097 absolute error = 0.05741190419165453439610991740682 relative error = 8.9013159668231095503493724360333 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76419758728355857055251673058384 y1[1] (numeric) = 0.75413613922969868519479030632428 absolute error = 0.01006144805385988535772642425956 relative error = 1.3166029599261931227097143865245 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=2998.4MB, alloc=4.6MB, time=166.49 x[1] = 0.702 y2[1] (analytic) = 0.64574608215752565445582601281535 y2[1] (numeric) = 0.70340403606138306166497045330526 absolute error = 0.05765795390385740720914444048991 relative error = 8.928889465533314012879412586791 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76355222308510511442075377730208 y1[1] (numeric) = 0.75343324016065442418755310999935 absolute error = 0.01011898292445069023320066730273 relative error = 1.3252509282947675884525980551053 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3002.2MB, alloc=4.6MB, time=166.70 x[1] = 0.703 y2[1] (analytic) = 0.64650931138033788940869675451334 y2[1] (numeric) = 0.70441401697972829644290376760285 absolute error = 0.05790470559939040703420701308951 relative error = 8.9565153324335317506762093051585 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7629060953344922025336791836665 y1[1] (numeric) = 0.75272933113883015897007814382505 absolute error = 0.01017676419566204356360103984145 relative error = 1.333947160456241252857664862655 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3006.0MB, alloc=4.6MB, time=166.91 x[1] = 0.704 y2[1] (analytic) = 0.64727189409389261979783058983915 y2[1] (numeric) = 0.7054240543719792181712914399665 absolute error = 0.05815216027808659837346085012735 relative error = 8.9841936300189644271076953635482 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7622592046778475316602274138083 y1[1] (numeric) = 0.75202441210787033953322186398742 absolute error = 0.01023479256997719212700554982088 relative error = 1.3426918962956580121744953758309 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3009.8MB, alloc=4.6MB, time=167.12 x[1] = 0.705 y2[1] (analytic) = 0.64803382953560719561705447426787 y2[1] (numeric) = 0.70643414847538481048280387160059 absolute error = 0.05840031893977761486574939733272 relative error = 9.0119244209254235095961727291466 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76161155176206170453751641770848 y1[1] (numeric) = 0.75131848301118248948610564242017 absolute error = 0.01029306875087921505141077528831 relative error = 1.3514853769044349160084574835991 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3013.6MB, alloc=4.6MB, time=167.34 x[1] = 0.706 y2[1] (analytic) = 0.64879511694354623864641061496962 y2[1] (numeric) = 0.70744429952783988772720794215538 absolute error = 0.05864918258429364908079732718576 relative error = 9.0397077679295949650567703765204 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76096313723478758298029880162827 y1[1] (numeric) = 0.75061154379193656060152832079977 absolute error = 0.0103515934428510223787704808285 relative error = 1.3603278445874496430246413339032 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=3017.4MB, alloc=4.6MB, time=167.55 TOP MAIN SOLVE Loop memory used=3021.2MB, alloc=4.6MB, time=167.77 x[1] = 0.707 y2[1] (analytic) = 0.64955575555642240438747119615466 y2[1] (numeric) = 0.70845450776788584664273039474151 absolute error = 0.05889875221146344225525919858685 relative error = 9.0675437339493046893153911207355 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.76031396174443964022815398442661 y1[1] (numeric) = 0.74990359439306428660935460494903 absolute error = 0.01041036735137535361879937947758 relative error = 1.3692195428701776238885944334694 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3025.1MB, alloc=4.6MB, time=167.98 x[1] = 0.708 y2[1] (analytic) = 0.6503157446135971433506194368912 y2[1] (numeric) = 0.70946477343471141732098705823182 absolute error = 0.05914902882111427397036762134062 relative error = 9.0954323820437846725051392543735 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7596640259401933125310689925183 y1[1] (numeric) = 0.74919463475725853623858522876018 absolute error = 0.01046939118293477629248376375812 relative error = 1.3781607165058792141651334703273 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3028.9MB, alloc=4.6MB, time=168.19 x[1] = 0.709 y2[1] (analytic) = 0.65107508335508146169353569417858 y2[1] (numeric) = 0.71047509676815341346446775573846 absolute error = 0.05940001341307195177093206155988 relative error = 9.123373775413939902447093234988 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75901333047198434997405630783822 y1[1] (numeric) = 0.74848466482697266550881582687093 absolute error = 0.01052866564501168446524048096729 relative error = 1.3871516114828373236381190047953 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3032.7MB, alloc=4.6MB, time=168.40 x[1] = 0.71 y2[1] (analytic) = 0.65183377102153668121012797285284 y2[1] (numeric) = 0.71148547800869748193556669096542 absolute error = 0.05965170698716080072543871811258 relative error = 9.1513679774026160080281849339862 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75836187599050816654145794413955 y1[1] (numeric) = 0.74777368454441986927179246550667 absolute error = 0.01058819144608829726966547863288 relative error = 1.3961924750316459122948024933159 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3036.5MB, alloc=4.6MB, time=168.62 x[1] = 0.711 y2[1] (analytic) = 0.6525918068542751986691468534576 y2[1] (numeric) = 0.71249591739747885159614804670964 absolute error = 0.05990411054320365292700119325204 relative error = 9.1794150514948676445958691271768 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7577096631472191894215856872678 y1[1] (numeric) = 0.74706169385157253200377279113904 absolute error = 0.01064796929564665741781289612876 relative error = 1.4052835556325497670386471243444 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3040.3MB, alloc=4.6MB, time=168.83 x[1] = 0.712 y2[1] (analytic) = 0.65334919009526124450172549952873 y2[1] (numeric) = 0.71350641517628308143663647211724 absolute error = 0.06015722508102183693491097258851 relative error = 9.207515061318227623396214085783 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7570566925943302075523481947161 y1[1] (numeric) = 0.74634869269016157784940276690563 absolute error = 0.01070799990416862970294542781047 relative error = 1.4144251030228359770548454472431 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3044.1MB, alloc=4.6MB, time=169.04 x[1] = 0.713 y2[1] (analytic) = 0.65410591998711164083708605681577 y2[1] (numeric) = 0.71451697158754680799362207739394 absolute error = 0.06041105160043516715653602057817 relative error = 9.2356680706429767870890164192472 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75640296498481171940851640878051 y1[1] (numeric) = 0.74563468100167581991781997708779 absolute error = 0.01076828398313589949069643169272 relative error = 1.4236173682042775296535744635242 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3047.9MB, alloc=4.6MB, time=169.25 x[1] = 0.714 y2[1] (analytic) = 0.65486199577309655888565440879708 y2[1] (numeric) = 0.71552758687435849205496949652054 absolute error = 0.06066559110126193316931508772346 relative error = 9.263874143382414633380540832764 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75574848097239128003127949599547 y1[1] (numeric) = 0.74491965872736130883169549035402 absolute error = 0.01082882224502997119958400564145 relative error = 1.4328606034506294523578154158555 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3051.8MB, alloc=4.6MB, time=169.46 x[1] = 0.715 y2[1] (analytic) = 0.655617416697140275668825905437 y2[1] (numeric) = 0.71653826128045916465142052013395 memory used=3055.6MB, alloc=4.6MB, time=169.68 absolute error = 0.06092084458331888898259461469695 relative error = 9.292133343593130688821508298994 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75509324121155284730074428323906 y1[1] (numeric) = 0.74420362580822068052992728294502 absolute error = 0.01088961540333216677081700029404 relative error = 1.4421550623151779309857997209338 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3059.4MB, alloc=4.6MB, time=169.89 x[1] = 0.716 y2[1] (analytic) = 0.65637218200382193009462533548235 y2[1] (numeric) = 0.71754899505024317233367974210182 absolute error = 0.06117681304642124223905440661947 relative error = 9.3204457354752766348250044109177 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75443724635753612745203191795418 y1[1] (numeric) = 0.74348658218501250332469923350344 absolute error = 0.01095066417252362412733268445074 relative error = 1.4515009996383428375033092752103 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3063.2MB, alloc=4.6MB, time=170.10 x[1] = 0.717 y2[1] (analytic) = 0.65712629093837627837850506670131 y2[1] (numeric) = 0.71855978842875892173397260444294 absolute error = 0.06143349749038264335546753774163 relative error = 9.3488113833728391879660534878697 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75378049706633591983562623633442 y1[1] (numeric) = 0.74276852779825062421362071183755 absolute error = 0.01101196926808529562200552449687 relative error = 1.4608986715553341054886498925557 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3067.0MB, alloc=4.6MB, time=170.31 x[1] = 0.718 y2[1] (analytic) = 0.6578797427466944488085259333295 y2[1] (numeric) = 0.71957064166170962341106516612631 absolute error = 0.06169089891501517460253923279681 relative error = 9.3772303517739137366317034566683 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75312299399470146092262907907173 y1[1] (numeric) = 0.74204946258820351444766279455265 absolute error = 0.01107353140649794647496628451908 relative error = 1.4703483355038623951636284209146 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3070.8MB, alloc=4.6MB, time=170.53 x[1] = 0.719 y2[1] (analytic) = 0.65863253667532469585416610560527 y2[1] (numeric) = 0.72058155499545403497773486191773 absolute error = 0.06194901832012933912356875631246 relative error = 9.4057027053109787360975917318834 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75246473780013576755557854935575 y1[1] (numeric) = 0.74132938649489361435560815118841 absolute error = 0.01113535130524215319997039816734 relative error = 1.4798502502319044940978010657139 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3074.7MB, alloc=4.6MB, time=170.74 x[1] = 0.72 y2[1] (analytic) = 0.65938467197147315361800383264817 y2[1] (numeric) = 0.72159252867700720350968145783404 absolute error = 0.06220785670553404989167762518587 relative error = 9.4342285087611708641141133818704 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75180572914089497944548696225195 y1[1] (numeric) = 0.74060829945809667742573265526376 absolute error = 0.01119742968279830201975430698819 relative error = 1.4894046758055239038911330718362 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3078.5MB, alloc=4.6MB, time=170.95 x[1] = 0.721 y2[1] (analytic) = 0.6601361478830045886295206070606 y2[1] (numeric) = 0.72260356295404120723486734991043 absolute error = 0.06246741507103661860534674284983 relative error = 9.4628078270465609390924898986975 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75114596867598770091575598836582 y1[1] (numeric) = 0.73988620141734111364543778545438 absolute error = 0.01125976725864658727031820291144 relative error = 1.4990118736167470673825352407221 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3082.3MB, alloc=4.6MB, time=171.16 x[1] = 0.722 y2[1] (analytic) = 0.66088696365844315198027195751232 y2[1] (numeric) = 0.72361465807488589650227629288537 absolute error = 0.06272769441644274452200433537305 relative error = 9.4914407252344306029882399995911 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.75048545706517434189362724782304 y1[1] (numeric) = 0.73916309231190733209955389301118 absolute error = 0.01132236475326700979407335481186 relative error = 1.5086721063914956952190445429827 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3086.1MB, alloc=4.6MB, time=171.37 x[1] = 0.723 y2[1] (analytic) = 0.66163711854697313079967373419959 y2[1] (numeric) = 0.72462581428852963402907958505963 absolute error = 0.06298869574155650322940585086004 relative error = 9.5201272685375497709867831846003 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74982419496896645814982736306022 y1[1] (numeric) = 0.73843897208082708282803542247169 absolute error = 0.01138522288813937532179194058853 relative error = 1.5183856381975756549532248835469 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=3089.9MB, alloc=4.6MB, time=171.59 TOP MAIN SOLVE Loop memory used=3093.7MB, alloc=4.6MB, time=171.80 x[1] = 0.724 y2[1] (analytic) = 0.66238661179843969907065241145532 y2[1] (numeric) = 0.72563703184462003442519867499029 absolute error = 0.06325042004618033535454626353497 relative error = 9.5488675223144548501031623697971 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74916218304862609078706723072606 y1[1] (numeric) = 0.73771384066288279794377018372028 absolute error = 0.01144834238574329284329704700578 relative error = 1.5281527344527228902152173313067 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3097.5MB, alloc=4.6MB, time=172.01 x[1] = 0.725 y2[1] (analytic) = 0.66313544266334966778440859192254 y2[1] (numeric) = 0.7266483109934647029942530948367 absolute error = 0.06351286833011503520984450291416 relative error = 9.5776615520697277288151539180681 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7484994219661651049780560241387 y1[1] (numeric) = 0.73698769799660693201122578451784 absolute error = 0.01151172396955817296683023962086 relative error = 1.537973661932706841931311273693 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3101.4MB, alloc=4.6MB, time=172.22 x[1] = 0.726 y2[1] (analytic) = 0.66388361039287223443354355759009 y2[1] (numeric) = 0.72765965198603197380988256408227 absolute error = 0.06377604159315973937633900649218 relative error = 9.6065094234542755398563419114323 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74783591238434452795369118823017 y1[1] (numeric) = 0.73626054402028130168665734374743 absolute error = 0.01157536836406322626703384448274 relative error = 1.5478486887794918480334905225019 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3105.2MB, alloc=4.6MB, time=172.43 x[1] = 0.727 y2[1] (analytic) = 0.66463111423883973184279937462657 y2[1] (numeric) = 0.72867105507395164706643204601342 absolute error = 0.06403994083511191522363267138685 relative error = 9.6354112022656111983030686613212 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.7471716549666738862420864387327 y1[1] (numeric) = 0.73553237867193642462060161680905 absolute error = 0.01163927629473746162148482192365 relative error = 1.5577780845094570026246900944038 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3109.0MB, alloc=4.6MB, time=172.64 x[1] = 0.728 y2[1] (analytic) = 0.66537795345374837633666372133474 y2[1] (numeric) = 0.72968252050951572570298847774418 absolute error = 0.06430456705576734936632475640944 relative error = 9.6643669544481347170965353485393 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74650665037741054215910052652369 y1[1] (numeric) = 0.73480320188935085762338367584538 absolute error = 0.01170344848805968453571685067831 relative error = 1.5677621200216749601330462235266 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3112.8MB, alloc=4.6MB, time=172.86 x[1] = 0.729 y2[1] (analytic) = 0.66612412729075901524309127168396 y2[1] (numeric) = 0.73069404854567915129975783273088 absolute error = 0.06456992125492013605666656104692 relative error = 9.6933767460934153021487154350344 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74584089928155902955103027654531 y1[1] (numeric) = 0.73407301361005053409436329879021 absolute error = 0.0117678856715084954566669777551 relative error = 1.5778010676062501746058075361731 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3116.6MB, alloc=4.6MB, time=173.07 x[1] = 0.73 y2[1] (analytic) = 0.66686963500369787373259413076153 y2[1] (numeric) = 0.73170563943606053924577111262598 absolute error = 0.06483600443236266551317698186445 relative error = 9.7224406434404742291881592083944 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74517440234487038879013215855033 y1[1] (numeric) = 0.73334181377130810071564923260352 absolute error = 0.01183258857356228807448292594681 relative error = 1.5878952009527170689603801322927 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3120.4MB, alloc=4.6MB, time=173.28 x[1] = 0.731 y2[1] (analytic) = 0.66761447584705730099195448311474 y2[1] (numeric) = 0.73271729343494291317690780297222 absolute error = 0.06510281758788561218495331985748 relative error = 9.7515587128760685045092106205597 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74450716023384150102363739409716 y1[1] (numeric) = 0.73260960231014225341101050749137 absolute error = 0.01189755792369924761262688660579 relative error = 1.5980447951584986337267920869341 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3124.2MB, alloc=4.6MB, time=173.49 x[1] = 0.732 y2[1] (analytic) = 0.66835864907599651573181328033319 y2[1] (numeric) = 0.73372901079727443868322526463758 absolute error = 0.06537036172127792295141198430439 relative error = 9.780731020934975311795627578756 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74383917361571442167692635072351 y1[1] (numeric) = 0.7318763791633170725707149904056 absolute error = 0.01196279445239734910621136031791 relative error = 1.6082501267374259595832798371763 % Correct digits = 2 h = 0.001 memory used=3128.1MB, alloc=4.6MB, time=173.71 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3131.9MB, alloc=4.6MB, time=173.92 x[1] = 0.733 y2[1] (analytic) = 0.66910215394634235102738946034485 y2[1] (numeric) = 0.73474079177866915628458247003695 absolute error = 0.0656386378323268052571930096921 relative error = 9.8099576343002772471970941536282 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74317044315847571321152872006884 y1[1] (numeric) = 0.73114214426734135754302637767786 absolute error = 0.01202829889113435566850234239098 relative error = 1.6185114736283192128053241138167 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3135.7MB, alloc=4.6MB, time=174.13 x[1] = 0.734 y2[1] (analytic) = 0.66984498971458999849158485776852 y2[1] (numeric) = 0.7357526366354077136735464300781 absolute error = 0.06590764692081771518196157230958 relative error = 9.8392386198036483448446379022715 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74250096953085577713861672188964 y1[1] (numeric) = 0.73040689755846796039309183826488 absolute error = 0.01209407197238781674552488362476 relative error = 1.6288291152036305676189085105609 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3139.5MB, alloc=4.6MB, time=174.35 x[1] = 0.735 y2[1] (analytic) = 0.67058715563790375177973063228011 y2[1] (numeric) = 0.73676454562443809722456959440552 absolute error = 0.06617738998653434544483896212541 relative error = 9.8685740444256408949985177775726 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74183075340232818528865932041883 y1[1] (numeric) = 0.72967063897269311892995353076773 absolute error = 0.0121601144296350663587057896511 relative error = 1.6392033322781496143716595093459 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3143.3MB, alloc=4.6MB, time=174.57 x[1] = 0.736 y2[1] (analytic) = 0.67132865097411774942523171030799 y2[1] (numeric) = 0.7377765190033763627684264438968 absolute error = 0.06644786802925861334319473358881 relative error = 9.8979639752959730570297280266835 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74115979544310901033790618335927 y1[1] (numeric) = 0.72893336844575578900241822913697 absolute error = 0.0122264269973532213354879542223 relative error = 1.6496344071177717674114810214699 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3147.1MB, alloc=4.6MB, time=174.78 x[1] = 0.737 y2[1] (analytic) = 0.67206947498173671700536640447498 y2[1] (numeric) = 0.7387885570305073656308974304905 absolute error = 0.06671908204877064862553102601552 relative error = 9.9274084796938172694438711866861 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.74048809632415615559237085697158 y1[1] (numeric) = 0.72819508591313697606452030378854 absolute error = 0.01229301041101917952785055318304 relative error = 1.6601226234483302015919557710967 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3150.9MB, alloc=4.6MB, time=175.00 x[1] = 0.738 y2[1] (analytic) = 0.67280962691993670863649904504927 y2[1] (numeric) = 0.7398006599647854899346883552921 absolute error = 0.06699103304484878129818931024283 relative error = 9.9569076250480894591637888821517 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.73981565671716868402998337321739 y1[1] (numeric) = 0.72745579131005906601131431673227 absolute error = 0.01235986540710961801866905648512 relative error = 1.6706682664644918514077950582777 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3154.8MB, alloc=4.6MB, time=175.21 x[1] = 0.739 y2[1] (analytic) = 0.67354910604856584779796412825327 y2[1] (numeric) = 0.74081282806583537716357321151453 absolute error = 0.06726372201726952936560908326126 relative error = 9.9864614789377390522950027349764 % Correct digits = 2 h = 0.001 y1[1] (analytic) = 0.73914247729458614660158324674932 y1[1] (numeric) = 0.72671548457148515528573450125604 absolute error = 0.01242699272310099131584874549328 relative error = 1.6812716228387180119026310391386 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3158.6MB, alloc=4.6MB, time=175.42 x[1] = 0.74 y2[1] (analytic) = 0.67428791162814506748388115760817 y2[1] (numeric) = 0.7418250615939526539877484541614 absolute error = 0.06753714996580758650386729655323 relative error = 10.016070109092039788605709429767 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73846855872958790979142456069883 y1[1] (numeric) = 0.72597416563211838025725940871443 absolute error = 0.0124943930974695295341651519844 relative error = 1.6919329807302900856861237494346 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=3162.4MB, alloc=4.6MB, time=175.64 TOP MAIN SOLVE Loop memory used=3166.2MB, alloc=4.6MB, time=175.87 x[1] = 0.741 y2[1] (analytic) = 0.67502604291986884968216002656091 y2[1] (numeric) = 0.74283736081010465934938659345374 absolute error = 0.06781131789023580966722656689283 relative error = 10.045733583390881341960793957173 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73779390169609248243786558070087 y1[1] (numeric) = 0.7252318344264012458731210170412 absolute error = 0.01256206726969123656474456365967 relative error = 1.7026526297944010256483695489959 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3170.0MB, alloc=4.6MB, time=176.09 x[1] = 0.742 y2[1] (analytic) = 0.67576349918560596417995746344981 y2[1] (numeric) = 0.74384972597593117080737694383412 absolute error = 0.06808622679032520662741948038431 relative error = 10.075451969865061748957073402079 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73711850686875684181491607640942 y1[1] (numeric) = 0.72448849088851495358279860774044 absolute error = 0.01263001598024188823211746866898 relative error = 1.7134308611913130282676282573446 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3173.8MB, alloc=4.6MB, time=176.31 x[1] = 0.743 y2[1] (analytic) = 0.67650027968790020669484573341403 y2[1] (numeric) = 0.74486215735374513014024129495484 absolute error = 0.06836187766584492344539556154081 relative error = 10.105225336696580648014760473477 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73644237492297575897531626890064 y1[1] (numeric) = 0.72374413495237872853653873031226 absolute error = 0.01269823997059703043877753858838 relative error = 1.7242679675955820377731217966729 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3177.6MB, alloc=4.6MB, time=176.53 x[1] = 0.744 y2[1] (analytic) = 0.67723638368997113633095546613973 y2[1] (numeric) = 0.74587465520653336820621220536854 absolute error = 0.06863827151656223187525673922881 relative error = 10.135053752218933331187941408541 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73576550653488112335582206082836 y1[1] (numeric) = 0.72299876655164914605864358533506 absolute error = 0.0127667399832319772971784754933 relative error = 1.7351642432053496268487956330213 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3181.5MB, alloc=4.6MB, time=176.75 x[1] = 0.745 y2[1] (analytic) = 0.67797181045571481235935515336133 y2[1] (numeric) = 0.74688721979795732905946155368992 absolute error = 0.06891540934224251670010640032859 relative error = 10.164937284917405610964697046033 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73508790238134126664537194399042 y1[1] (numeric) = 0.72225238561971945739627116975888 absolute error = 0.01283551676162180924910077423154 relative error = 1.7461199837517028250471829828052 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3185.3MB, alloc=4.6MB, time=176.97 x[1] = 0.746 y2[1] (analytic) = 0.67870655924970453032193053580006 y2[1] (numeric) = 0.74789985139235379332146691578495 absolute error = 0.06919329214264926299953637998489 relative error = 10.1948760034293695043353588749 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73440956313996028591681171608261 y1[1] (numeric) = 0.72150499208971891474449154036252 absolute error = 0.01290457105024137117232017572009 relative error = 1.7571354865081024716255873352454 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3189.1MB, alloc=4.6MB, time=177.20 x[1] = 0.747 y2[1] (analytic) = 0.67944062933719155745802777572154 y2[1] (numeric) = 0.74891255025473560080650327006889 absolute error = 0.06947192091754404334847549434735 relative error = 10.224869976544579736415283845358 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73373048948907736602285387485905 y1[1] (numeric) = 0.72075658589451209554834456379179 absolute error = 0.01297390359456527047450931106726 relative error = 1.7682110502998806751204276069763 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3192.9MB, alloc=4.6MB, time=177.42 x[1] = 0.748 y2[1] (analytic) = 0.68017401998410586745312498853057 y2[1] (numeric) = 0.74992531665079237240024746625557 absolute error = 0.069751296666686504947122477725 relative error = 10.254919273205471065916452804087 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73305068210776610125694929368327 y1[1] (numeric) = 0.72000716696669822608264553412762 absolute error = 0.01304351514106787517430375955565 relative error = 1.7793469755138079676405081779242 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3196.7MB, alloc=4.6MB, time=177.64 x[1] = 0.749 y2[1] (analytic) = 0.6809067304570568745087973847929 y2[1] (numeric) = 0.75093815084689123119048282589736 absolute error = 0.07003142038983435668168544110446 relative error = 10.285023962507456434770147705873 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73237014167583381627974951754159 y1[1] (numeric) = 0.71925673523861050431028605153068 absolute error = 0.01311340643722331196946346601091 relative error = 1.7905435641077307475869289933988 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 memory used=3200.5MB, alloc=4.6MB, time=177.94 TOP MAIN SOLVE Loop memory used=3204.4MB, alloc=4.6MB, time=178.50 x[1] = 0.75 y2[1] (analytic) = 0.68163876002333416673324195277989 y2[1] (numeric) = 0.75195105311007752284889117578696 absolute error = 0.07031229308674335611564922300707 relative error = 10.31518411369922594421094238485 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73168886887382088631183875300008 y1[1] (numeric) = 0.71850529064231542201977856817469 absolute error = 0.01318357823150546429206018482539 relative error = 1.8018011196202796102970946875263 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3208.2MB, alloc=4.6MB, time=179.04 x[1] = 0.751 y2[1] (analytic) = 0.68237010795090823885162829107258 y2[1] (numeric) = 0.75296402370807553526291954775837 absolute error = 0.07059391575716729641129125668579 relative error = 10.345399796183046659640250763656 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73100686438300005659341535931644 y1[1] (numeric) = 0.71775283310961208624279402041309 absolute error = 0.01325403127338797035062133890335 relative error = 1.8131199471806491719635822604486 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3212.0MB, alloc=4.6MB, time=179.58 x[1] = 0.752 y2[1] (analytic) = 0.6831007735084312242355428809353 y2[1] (numeric) = 0.75397706290928921741670871062421 absolute error = 0.07087628940085799318116582968891 relative error = 10.375671079515063246595715063377 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.73032412888537576111160338096846 y1[1] (numeric) = 0.71699936257203153995244297892414 absolute error = 0.01332476631334422115916040204432 relative error = 1.8245003535184499980962604891458 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3215.8MB, alloc=4.6MB, time=180.10 x[1] = 0.753 y2[1] (analytic) = 0.68383075596523762625079476907575 y2[1] (numeric) = 0.75499017098280289752007063191925 absolute error = 0.0711594150175652712692758628435 relative error = 10.40599803340559944016078497644 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.72964066306368344059607539423096 y1[1] (numeric) = 0.71624487896083608204305176144786 absolute error = 0.0133957841028473585530236327831 relative error = 1.8359426469736332537788076736216 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 TOP MAIN SOLVE Loop memory used=3219.6MB, alloc=4.6MB, time=180.63 x[1] = 0.754 y2[1] (analytic) = 0.68456005459134504892285131304652 y2[1] (numeric) = 0.75600334819838200038450189878504 absolute error = 0.07144329360703695146165058573852 relative error = 10.436380727719460350156937004865 % Correct digits = 1 h = 0.001 y1[1] (analytic) = 0.72895646760138885978366867212136 y1[1] (numeric) = 0.71548938220701858659218596566449 absolute error = 0.01346708539437027319148270645687 relative error = 1.847447137506488699019444815246 % Correct digits = 2 h = 0.001 NO POLE for equation 1 NO POLE for equation 2 Finished! Maximum Time Reached before Solution Completed! diff ( y2 , x , 5 ) = y1 ; diff ( y1 , x , 1 ) = m1 * y2 ; Iterations = 755 Total Elapsed Time = 3 Minutes 0 Seconds Elapsed Time(since restart) = 3 Minutes 0 Seconds Expected Time Remaining = 16 Minutes 55 Seconds Optimized Time Remaining = 16 Minutes 54 Seconds Expected Total Time = 19 Minutes 55 Seconds Time to Timeout Unknown Percent Done = 15.12 % > quit memory used=3222.3MB, alloc=4.6MB, time=181.00