|\^/| 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 > display_alot := proc(iter) > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > 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 := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > 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 := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_max_terms, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, glob_last; 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 := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 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_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 := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 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_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(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 (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(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 (abs(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"); > newline(); > 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 > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_max_terms, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(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 < abs(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"); newline(); 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 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > 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)); > 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)); > 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 Function number 5 > 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, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, 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)); 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)) 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 > # Begin Function number 6 > check_for_pole := proc() > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(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 (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * 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 (abs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(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 (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_max_terms, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or abs(array_y2_higher[1, m - 1]) < glob_small_float or abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or abs(array_y1_higher[1, m - 1]) < glob_small_float or abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y2_higher[1, m]) or glob_large_float <= abs(array_y2_higher[1, m - 1]) or glob_large_float <= abs(array_y2_higher[1, m - 2]) or glob_large_float <= abs(array_y2_higher[1, m - 3]) or glob_large_float <= abs(array_y2_higher[1, m - 4]) or glob_large_float <= abs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(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 < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*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 < abs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_y1_higher[1, m]) or glob_large_float <= abs(array_y1_higher[1, m - 1]) or glob_large_float <= abs(array_y1_higher[1, m - 2]) or glob_large_float <= abs(array_y1_higher[1, m - 3]) or glob_large_float <= abs(array_y1_higher[1, m - 4]) or glob_large_float <= abs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(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 < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(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 (abs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global glob_max_terms, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y2[iii]) then array_norms[iii] := abs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y1[iii]) then array_norms[iii] := abs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_m1[1] * (array_y1[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre add $eq_no = 1 i = 1 > array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre sub $eq_no = 2 i = 1 > array_tmp5[1] := (array_y2[1] - (array_const_1D0[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_m1,array_y1,1); > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre add $eq_no = 1 i = 2 > array_tmp3[2] := array_tmp2[2] + array_const_1D0[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre sub $eq_no = 2 i = 2 > array_tmp5[2] := (array_y2[2] - (array_const_1D0[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_m1,array_y1,1); > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre add $eq_no = 1 i = 3 > array_tmp3[3] := array_tmp2[3] + array_const_1D0[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre sub $eq_no = 2 i = 3 > array_tmp5[3] := (array_y2[3] - (array_const_1D0[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_m1,array_y1,1); > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre add $eq_no = 1 i = 4 > array_tmp3[4] := array_tmp2[4] + array_const_1D0[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre sub $eq_no = 2 i = 4 > array_tmp5[4] := (array_y2[4] - (array_const_1D0[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_m1,array_y1,1); > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre add $eq_no = 1 i = 5 > array_tmp3[5] := array_tmp2[5] + array_const_1D0[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp3[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre sub $eq_no = 2 i = 5 > array_tmp5[5] := (array_y2[5] - (array_const_1D0[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_m1,array_y1,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit add $eq_no = 1 > array_tmp3[kkk] := array_tmp2[kkk] + array_const_1D0[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp3[kkk] * (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 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit sub $eq_no = 2 > array_tmp5[kkk] := (array_y2[kkk] - (array_const_1D0[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp5[kkk] * (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 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 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 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_max_terms, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, glob_last; array_tmp1[1] := array_m1[1]*array_y1[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; array_tmp3[1] := array_tmp2[1] + array_const_1D0[1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp3[1]*glob_h*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp5[1] := array_y2[1] - array_const_1D0[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*glob_h*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_m1, array_y1, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; array_tmp3[2] := array_tmp2[2] + array_const_1D0[2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp3[2]*glob_h*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp5[2] := array_y2[2] - array_const_1D0[2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*glob_h*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_m1, array_y1, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; array_tmp3[3] := array_tmp2[3] + array_const_1D0[3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp3[3]*glob_h*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp5[3] := array_y2[3] - array_const_1D0[3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*glob_h*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_m1, array_y1, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; array_tmp3[4] := array_tmp2[4] + array_const_1D0[4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp3[4]*glob_h*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp5[4] := array_y2[4] - array_const_1D0[4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*glob_h*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_m1, array_y1, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; array_tmp3[5] := array_tmp2[5] + array_const_1D0[5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp3[5]*glob_h*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp5[5] := array_y2[5] - array_const_1D0[5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*glob_h*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_m1, array_y1, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; array_tmp3[kkk] := array_tmp2[kkk] + array_const_1D0[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp3[kkk]*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 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp5[kkk] := array_y2[kkk] - array_const_1D0[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp5[kkk]*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 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= 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); > fi; > fi; > # End Function number 1 > 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 > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > 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 > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > 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 > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_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, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= 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) > fi; > # End Function number 1 > 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 > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > 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 5 > 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 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 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, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > 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 10 > 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 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 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 > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > 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 + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_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 + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_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 11 > 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 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_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 + array_aa[iii_att]*array_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 > # Begin Function number 5 > 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 11 > 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 11 > # End Function number 5 > 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 > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > 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 > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > 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 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > 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 > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > 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 (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > 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 < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > 1.0 + cos(x); > end; exact_soln_y1 := proc(x) 1.0 + cos(x) end proc > exact_soln_y2 := proc(x) > 1.0 - sin(x); > end; exact_soln_y2 := proc(x) 1.0 - sin(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > glob_max_terms, > DEBUGL, > glob_iolevel, > DEBUGMASSIVE, > INFO, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_unchanged_h_cnt, > glob_large_float, > glob_not_yet_start_msg, > glob_current_iter, > glob_hmin, > glob_clock_start_sec, > glob_clock_sec, > glob_display_flag, > glob_html_log, > glob_iter, > glob_orig_start_sec, > glob_optimal_clock_start_sec, > glob_abserr, > glob_not_yet_finished, > hours_in_day, > glob_max_minutes, > djd_debug2, > glob_dump, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_start, > glob_warned2, > glob_optimal_start, > glob_max_iter, > glob_relerr, > glob_initial_pass, > glob_subiter_method, > glob_small_float, > glob_reached_optimal_h, > years_in_century, > min_in_hour, > glob_optimal_expect_sec, > MAX_UNCHANGED, > glob_curr_iter_when_opt, > glob_no_eqs, > glob_max_hours, > glob_log10_abserr, > glob_last_good_h, > glob_hmax, > glob_disp_incr, > glob_almost_1, > glob_log10relerr, > glob_max_trunc_err, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > centuries_in_millinium, > sec_in_min, > djd_debug, > glob_hmin_init, > glob_optimal_done, > glob_log10normmin, > glob_warned, > glob_smallish_float, > glob_max_rel_trunc_err, > glob_max_sec, > glob_h, > days_in_year, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1D0, > array_const_1, > #END CONST > array_x, > array_1st_rel_error, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_type_pole, > array_y1_init, > array_pole, > array_norms, > array_y2_init, > array_y2, > array_y1, > array_m1, > array_last_rel_error, > array_poles, > array_y1_set_initial, > array_y1_higher_work2, > array_y2_set_initial, > array_y2_higher_work2, > array_y1_higher_work, > array_y2_higher_work, > array_complex_pole, > array_y1_higher, > array_real_pole, > array_y2_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > DEBUGL := 3; > glob_iolevel := 5; > DEBUGMASSIVE := 4; > INFO := 2; > ALWAYS := 1; > glob_normmax := 0.0; > glob_unchanged_h_cnt := 0; > glob_large_float := 9.0e100; > glob_not_yet_start_msg := true; > glob_current_iter := 0; > glob_hmin := 0.00000000001; > glob_clock_start_sec := 0.0; > glob_clock_sec := 0.0; > glob_display_flag := true; > glob_html_log := true; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_not_yet_finished := true; > hours_in_day := 24.0; > glob_max_minutes := 0.0; > djd_debug2 := true; > glob_dump := false; > glob_max_opt_iter := 10; > glob_percent_done := 0.0; > glob_log10abserr := 0.0; > glob_start := 0; > glob_warned2 := false; > glob_optimal_start := 0.0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_initial_pass := true; > glob_subiter_method := 3; > glob_small_float := 0.1e-50; > glob_reached_optimal_h := false; > years_in_century := 100.0; > min_in_hour := 60.0; > glob_optimal_expect_sec := 0.1; > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_no_eqs := 0; > glob_max_hours := 0.0; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > glob_hmax := 1.0; > glob_disp_incr := 0.1; > glob_almost_1 := 0.9990; > glob_log10relerr := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_look_poles := false; > centuries_in_millinium := 10.0; > sec_in_min := 60.0; > djd_debug := true; > glob_hmin_init := 0.001; > glob_optimal_done := false; > glob_log10normmin := 0.1; > glob_warned := false; > glob_smallish_float := 0.1e-100; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_sec := 10000.0; > glob_h := 0.1; > days_in_year := 365.0; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest3postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = y2 - 1.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 0.5;"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > 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,"1.0 + cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"1.0 - sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_x:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_y1_init:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_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_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1_init[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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2[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_m1[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 > ; > 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 <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_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_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_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 <=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_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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 <=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 <= 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 <= 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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > 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_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_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_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_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_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > array_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 > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 0.5; > glob_h := 0.00001; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := false; > array_y2_set_initial[1,3] := false; > array_y2_set_initial[1,4] := false; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * 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]* (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] * 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]* (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(); > start_array_y2(); > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_y1(); > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > 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 3 > atomall(); > elif glob_subiter_method = 2 then # if number 4 > subiter := 1; > while subiter <= 2 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 2 + glob_max_terms do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(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] / (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 * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = y2 - 1.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-15T21:12:27-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest3") > ; > logitem_str(html_log_file,"diff ( y2 , x , 1 ) = m1 * y1 + 1.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_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 5 > 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 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 5 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"mtest3 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest3 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = y2 - 1.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > 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 5 > 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 5 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 5 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if glob_html_log then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `subiter` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global glob_max_terms, DEBUGL, glob_iolevel, DEBUGMASSIVE, INFO, ALWAYS, glob_normmax, glob_unchanged_h_cnt, glob_large_float, glob_not_yet_start_msg, glob_current_iter, glob_hmin, glob_clock_start_sec, glob_clock_sec, glob_display_flag, glob_html_log, glob_iter, glob_orig_start_sec, glob_optimal_clock_start_sec, glob_abserr, glob_not_yet_finished, hours_in_day, glob_max_minutes, djd_debug2, glob_dump, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_start, glob_warned2, glob_optimal_start, glob_max_iter, glob_relerr, glob_initial_pass, glob_subiter_method, glob_small_float, glob_reached_optimal_h, years_in_century, min_in_hour, glob_optimal_expect_sec, MAX_UNCHANGED, glob_curr_iter_when_opt, glob_no_eqs, glob_max_hours, glob_log10_abserr, glob_last_good_h, glob_hmax, glob_disp_incr, glob_almost_1, glob_log10relerr, glob_max_trunc_err, glob_log10_relerr, glob_dump_analytic, glob_look_poles, centuries_in_millinium, sec_in_min, djd_debug, glob_hmin_init, glob_optimal_done, glob_log10normmin, glob_warned, glob_smallish_float, glob_max_rel_trunc_err, glob_max_sec, glob_h, days_in_year, array_const_0D0, array_const_1D0, array_const_1, array_x, array_1st_rel_error, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_type_pole, array_y1_init, array_pole, array_norms, array_y2_init, array_y2, array_y1, array_m1, array_last_rel_error, array_poles, array_y1_set_initial, array_y1_higher_work2, array_y2_set_initial, array_y2_higher_work2, array_y1_higher_work, array_y2_higher_work, array_complex_pole, array_y1_higher, array_real_pole, array_y2_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; DEBUGL := 3; glob_iolevel := 5; DEBUGMASSIVE := 4; INFO := 2; ALWAYS := 1; glob_normmax := 0.; glob_unchanged_h_cnt := 0; glob_large_float := 0.90*10^101; glob_not_yet_start_msg := true; glob_current_iter := 0; glob_hmin := 0.1*10^(-10); glob_clock_start_sec := 0.; glob_clock_sec := 0.; glob_display_flag := true; glob_html_log := true; glob_iter := 0; glob_orig_start_sec := 0.; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_not_yet_finished := true; hours_in_day := 24.0; glob_max_minutes := 0.; djd_debug2 := true; glob_dump := false; glob_max_opt_iter := 10; glob_percent_done := 0.; glob_log10abserr := 0.; glob_start := 0; glob_warned2 := false; glob_optimal_start := 0.; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_initial_pass := true; glob_subiter_method := 3; glob_small_float := 0.1*10^(-50); glob_reached_optimal_h := false; years_in_century := 100.0; min_in_hour := 60.0; glob_optimal_expect_sec := 0.1; MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_no_eqs := 0; glob_max_hours := 0.; glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_hmax := 1.0; glob_disp_incr := 0.1; glob_almost_1 := 0.9990; glob_log10relerr := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_look_poles := false; centuries_in_millinium := 10.0; sec_in_min := 60.0; djd_debug := true; glob_hmin_init := 0.001; glob_optimal_done := false; glob_log10normmin := 0.1; glob_warned := false; glob_smallish_float := 0.1*10^(-100); glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_sec := 10000.0; glob_h := 0.1; days_in_year := 365.0; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest3postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = y2 - 1.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 0.5;"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); 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, "1.0 + cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "1.0 - sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_x := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_y1_init := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y2_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y2_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_y2_higher := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_x[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_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[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_pole[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_y2_init[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_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[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; 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 <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_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_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_y2_higher_work2[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_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[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 <= 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 <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[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_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[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_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_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; x_start := 0.1; x_end := 0.5; glob_h := 0.00001; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); glob_max_iter := 20; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := false; array_y2_set_initial[1, 3] := false; array_y2_set_initial[1, 4] := false; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]*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]* 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]*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]* 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(); start_array_y2(); if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_y1(); if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( 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*glob_h^(calc_term - 1)/convfp(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]/( 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*glob_h^(calc_term - 1)/convfp(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]/( 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*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( 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*glob_h^(calc_term - 1)/convfp(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]/( 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*glob_h^(calc_term - 1)/convfp(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]/( 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*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = y2 - 1.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-15T21:12:27-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest3") ; logitem_str(html_log_file, "diff ( y2 , x , 1 ) = m1 * y1 + 1.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_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_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "mtest3 diffeq.mxt"); logitem_str(html_log_file, "mtest3 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = y2 - 1.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); 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 proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/mtest3postode.ode################# diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 0.5; glob_h := 0.00001; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) 1.0 + cos(x); end; exact_soln_y2 := proc(x) 1.0 - sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 0.90016658335317184769318580158938 y2[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % h = 0.001 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % h = 0.001 x[1] = 0.1 y2[1] (analytic) = 0.90016658335317184769318580158938 y2[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % h = 0.001 y1[1] (analytic) = 1.9950041652780257660955619878039 y1[1] (numeric) = 1.9950041652780257660955619878039 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 0.89917162927043200487024788047681 y2[1] (numeric) = 0.89917162927043200487544864324514 absolute error = 5.20076276833e-21 relative error = 5.7839489136793428556970217920601e-19 % h = 0.001 y1[1] (analytic) = 1.994903834375976659378402999829 y1[1] (numeric) = 1.994903834375976659330072446903 absolute error = 4.83305529260e-20 relative error = 2.4227008887933798081809577766315e-18 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.20 NO POLE NO POLE x[1] = 0.102 y2[1] (analytic) = 0.89817677601605448925135770391935 y2[1] (numeric) = 0.89817677601605448926185588534498 absolute error = 1.049818142563e-20 relative error = 1.1688324287559122908516395294583e-18 % h = 0.001 y1[1] (analytic) = 1.9948025085701760853346856764599 y1[1] (numeric) = 1.9948025085701760852380350204623 absolute error = 9.66506559976e-20 relative error = 4.8451240452307603269412816161354e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 0.89718202458489247230959578949541 y2[1] (numeric) = 0.89718202458489247232548802972006 absolute error = 1.589224022465e-20 relative error = 1.7713507169298237074883038868396e-18 % h = 0.001 y1[1] (analytic) = 1.9947001879619498413211671928266 y1[1] (numeric) = 1.9947001879619498411762070285878 absolute error = 1.449601642388e-19 relative error = 7.2672657832809712535180716324922e-18 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.43 NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 0.89618737597169730231102924533054 y2[1] (numeric) = 0.89618737597169730233241216855535 absolute error = 2.138292322481e-20 relative error = 2.3859879973901014836205913977127e-18 % h = 0.001 y1[1] (analytic) = 1.9945968726536185270373744944846 y1[1] (numeric) = 1.9945968726536185268441155617897 absolute error = 1.932589326949e-19 relative error = 9.6891224158888634205388013077512e-18 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 0.89519283117111750956344639997322 y2[1] (numeric) = 0.89519283117111750959041661426551 absolute error = 2.697021429229e-20 relative error = 3.0127826489636623734907626015951e-18 % h = 0.001 y1[1] (analytic) = 1.9944925627484974422050131246041 y1[1] (numeric) = 1.9944925627484974419634663081717 absolute error = 2.415468164324e-19 relative error = 1.2110690254945748612340991454953e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.67 NO POLE NO POLE x[1] = 0.106 y2[1] (analytic) = 0.89419839117769781176790938198128 y2[1] (numeric) = 0.89419839117769781180056347908131 absolute error = 3.265409710003e-20 relative error = 3.6517731883886692157452248993452e-18 % h = 0.001 y1[1] (analytic) = 1.9943872583508964832526761118722 y1[1] (numeric) = 1.9943872583508964829628524413332 absolute error = 2.898236705390e-19 relative error = 1.4531965611264843115167125080392e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.107 y2[1] (analytic) = 0.89320405698587811947411929758354 y2[1] (numeric) = 0.89320405698587811951255385271129 absolute error = 3.843455512775e-20 relative error = 4.3029982709043678554236377897802e-18 % h = 0.001 y1[1] (analytic) = 1.9942809595661200390059562343918 y1[1] (numeric) = 1.994280959566120038667866884267 absolute error = 3.380893501248e-19 relative error = 1.6952944794616874357674530846156e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.90 NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 0.89220982958999254164058855096841 y2[1] (numeric) = 0.89220982958999254168490012263042 absolute error = 4.431157166201e-20 relative error = 4.9664966908482735335533439117671e-18 % h = 0.001 y1[1] (analytic) = 1.9941736665004668853830659694533 y1[1] (numeric) = 1.9941736665004668849967222591317 absolute error = 3.863437103216e-19 relative error = 1.9373624113670420257795693283422e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 0.89121570998426839130061474694456 y2[1] (numeric) = 0.89121570998426839135089987674073 absolute error = 5.028512979617e-20 relative error = 5.6423073822450488130411568308369e-18 % h = 0.001 y1[1] (analytic) = 1.9940653792612300790960704335539 y1[1] (numeric) = 1.9940653792612300786614838272702 absolute error = 4.345866062837e-19 relative error = 2.1793999876007451453060318257181e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.14 NO POLE NO POLE x[1] = 0.11 y2[1] (analytic) = 0.89022169916282519133505050991655 y2[1] (numeric) = 0.89022169916282519139140572234706 absolute error = 5.635521243051e-20 relative error = 6.3304694194162078108847241744334e-18 % h = 0.001 y1[1] (analytic) = 1.9939560979566968503578396114198 y1[1] (numeric) = 1.993956097956696849875021718232 absolute error = 4.828178931878e-19 relative error = 2.4214068388093740982082108337834e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=22.8MB, alloc=4.3MB, time=1.37 x[1] = 0.111 y2[1] (analytic) = 0.88922779811967368035286344632307 y2[1] (numeric) = 0.88922779811967368041538524859526 absolute error = 6.252180227219e-20 relative error = 7.0310220175748168845648326524798e-18 % h = 0.001 y1[1] (analytic) = 1.993845822696148494594827167072 y1[1] (numeric) = 1.9938458226961484940637897408385 absolute error = 5.310374262335e-19 relative error = 2.6633825955279355675241193226084e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.112 y2[1] (analytic) = 0.88823400784871481868048036989479 y2[1] (numeric) = 0.88823400784871481874926525173009 absolute error = 6.878488183530e-20 relative error = 7.7440045334332133902934571080033e-18 % h = 0.001 y1[1] (analytic) = 1.9937345535898602631657841241467 y1[1] (numeric) = 1.9937345535898602625865390635034 absolute error = 5.792450606433e-19 relative error = 2.9053268881774067930080390019212e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=26.7MB, alloc=4.3MB, time=1.61 x[1] = 0.113 y2[1] (analytic) = 0.8872403293437387944609098003048 y2[1] (numeric) = 0.88724032934373879453605423374568 absolute error = 7.514443344088e-20 relative error = 8.4694564658103128726277785464072e-18 % h = 0.001 y1[1] (analytic) = 1.9936222907491012530865166967484 y1[1] (numeric) = 1.9936222907491012524590760450855 absolute error = 6.274406516629e-19 relative error = 3.1472393470637806027697108700383e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.114 y2[1] (analytic) = 0.88624676359842402986363663600634 y2[1] (numeric) = 0.8862467635984240299452370752233 absolute error = 8.160043921696e-20 relative error = 9.2074174562441365342370108824184e-18 % h = 0.001 y1[1] (analytic) = 1.9935090342861342957607985460685 y1[1] (numeric) = 1.9935090342861342950851744915067 absolute error = 6.756240545618e-19 relative error = 3.3891196023786148788148794727919e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=1.84 NO POLE NO POLE x[1] = 0.115 y2[1] (analytic) = 0.8852533116063361874062827912803 y2[1] (numeric) = 0.88525331160633618749443567237892 absolute error = 8.815288109862e-20 relative error = 9.9579272896095932622263188667949e-18 % h = 0.001 y1[1] (analytic) = 1.9933947843142158447175487318465 y1[1] (numeric) = 1.9933947843142158439937536072134 absolute error = 7.237951246331e-19 relative error = 3.6309672841955688330198347242800e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.116 y2[1] (analytic) = 0.88425997436092717638902747574917 y2[1] (numeric) = 0.88425997436092717648382921657709 absolute error = 9.480174082792e-20 relative error = 1.0721025894724587404906566232201e-17 % h = 0.001 y1[1] (analytic) = 1.993279540947595862354387621489 y1[1] (numeric) = 1.9932795409475958615824339042952 absolute error = 7.719537171938e-19 relative error = 3.8727820224694463977227677572002e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=2.08 NO POLE NO POLE x[1] = 0.117 y2[1] (analytic) = 0.88326675285553415944278068185407 y2[1] (numeric) = 0.88326675285553415954432768180813 absolute error = 1.0154699995406e-19 relative error = 1.1496753344985111350231357523415e-17 % h = 0.001 y1[1] (analytic) = 1.993163304301517705687684013279 y1[1] (numeric) = 1.9931633043015177048675843256939 absolute error = 8.200996875851e-19 relative error = 4.1145634470352391504512297267748e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.118 y2[1] (analytic) = 0.88227364808337855919210333203896 y2[1] (numeric) = 0.88227364808337855930049197187228 absolute error = 1.0838863983332e-19 relative error = 1.2285149858978539847876424291721e-17 % h = 0.001 y1[1] (analytic) = 1.99304607449221801110920772362 y1[1] (numeric) = 1.9930460744922180102409748324471 absolute error = 8.682328911729e-19 relative error = 4.3563111876081722591741322559435e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=2.32 NO POLE NO POLE x[1] = 0.119 y2[1] (analytic) = 0.88128066103756506503386742263883 y2[1] (numeric) = 0.88128066103756506514919406426794 absolute error = 1.1532664162911e-19 relative error = 1.3086255801112392672578331026117e-17 % h = 0.001 y1[1] (analytic) = 1.9929278516369265781495028816522 y1[1] (numeric) = 1.9929278516369265772331496983044 absolute error = 9.163531833478e-19 relative error = 4.5980248737812414418891143286486e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.12 y2[1] (analytic) = 0.88028779271108064003264938572903 y2[1] (numeric) = 0.88028779271108064015501037204105 absolute error = 1.2236098631202e-19 relative error = 1.3900111682246184880027367356654e-17 % h = 0.001 y1[1] (analytic) = 1.9928086358538662522480981678576 y1[1] (numeric) = 1.9928086358538662512836377483326 absolute error = 9.644604195250e-19 relative error = 4.8397041350222471151822012203744e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.3MB, time=2.55 NO POLE NO POLE x[1] = 0.121 y2[1] (analytic) = 0.87929504409679352793384977345972 y2[1] (numeric) = 0.87929504409679352806334142811954 absolute error = 1.2949165465982e-19 relative error = 1.4726758160320695635166059967657e-17 % h = 0.001 y1[1] (analytic) = 1.9926884272622528065306712264356 y1[1] (numeric) = 1.9926884272622528055181167712902 absolute error = 1.0125544551454e-18 relative error = 5.0813486006768493509757294659088e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.122 y2[1] (analytic) = 0.87830241618745226029553225167281 y2[1] (numeric) = 0.87830241618745226043225087893036 absolute error = 1.3671862725755e-19 relative error = 1.5566236041000567929464361274250e-17 % h = 0.001 y1[1] (analytic) = 1.992567225982294822593285474272 y1[1] (numeric) = 1.992567225982294821532650328597 absolute error = 1.0606351456750e-18 relative error = 5.3229578999630920929075439569264e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.3MB, time=2.79 NO POLE NO POLE x[1] = 0.123 y2[1] (analytic) = 0.8773099099756846637399747708799 y2[1] (numeric) = 0.87730990997568466388401665537737 absolute error = 1.4404188449747e-19 relative error = 1.6418586278304121112995521586997e-17 % h = 0.001 y1[1] (analytic) = 1.9924450321351935702938185222573 y1[1] (numeric) = 1.992445032135193569185116175652 absolute error = 1.1087023466053e-18 relative error = 5.5645316619709441989791125878824e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.124 y2[1] (analytic) = 0.87631752645399686732592566296706 y2[1] (numeric) = 0.87631752645399686747738706954622 absolute error = 1.5146140657916e-19 relative error = 1.7283849975253360681849122868520e-17 % h = 0.001 y1[1] (analytic) = 1.992321845843142886550702417515 y1[1] (numeric) = 1.9923218458431428853939465040607 absolute error = 1.1567559134543e-18 relative error = 5.8060695156648517243198215245480e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=3.03 NO POLE NO POLE x[1] = 0.125 y2[1] (analytic) = 0.87532526661477231004255729128789 y2[1] (numeric) = 0.87532526661477231020153446479739 absolute error = 1.5897717350950e-19 relative error = 1.8162068384513492683874777404101e-17 % h = 0.001 y1[1] (analytic) = 1.9921976672293290531490969077882 y1[1] (numeric) = 1.9921976672293290519443012060226 absolute error = 1.2047957017656e-18 relative error = 6.0475710898767538051266636756011e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.126 y2[1] (analytic) = 0.87433313145027074842610976010826 y2[1] (numeric) = 0.87433313145027074859269892521102 absolute error = 1.6658916510276e-19 relative error = 1.9053282909048157806304700361267e-17 % h = 0.001 y1[1] (analytic) = 1.9920724964179306735546179218037 y1[1] (numeric) = 1.992072496417930672301796354694 absolute error = 1.2528215671097e-18 relative error = 6.2890360133101395637902749953587e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.3MB, time=3.27 NO POLE NO POLE x[1] = 0.127 y2[1] (analytic) = 0.87334112195262726430021706667654 y2[1] (numeric) = 0.87334112195262726447451442765712 absolute error = 1.7429736098058e-19 relative error = 1.9957535102765312172764540173423e-17 % h = 0.001 y1[1] (analytic) = 1.9919463335341185487347444518721 y1[1] (numeric) = 1.9919463335341185474339110867888 absolute error = 1.3008333650833e-18 relative error = 6.5304639145340659593987397168872e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.128 y2[1] (analytic) = 0.87234923911385127264090795551028 y2[1] (numeric) = 0.87234923911385127282300969608233 absolute error = 1.8210174057205e-19 relative error = 2.0874866671177745892751492126015e-17 % h = 0.001 y1[1] (analytic) = 1.9918191787040555519880280173089 y1[1] (numeric) = 1.9918191787040555506391970659988 absolute error = 1.3488309513101e-18 relative error = 6.7718544219847040236435512405753e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=3.51 NO POLE NO POLE x[1] = 0.129 y2[1] (analytic) = 0.87135748392582552956727360981603 y2[1] (numeric) = 0.87135748392582552975727589292971 absolute error = 1.9000228311368e-19 relative error = 2.1805319472054248201598095017397e-17 % h = 0.001 y1[1] (analytic) = 1.9916910320548965027812298794554 y1[1] (numeric) = 1.9916910320548965013844156980143 absolute error = 1.3968141814411e-18 relative error = 7.0132071639643750996304573244244e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.13 y2[1] (analytic) = 0.87036585738030514045879418929169 y2[1] (numeric) = 0.87036585738030514065679315694119 absolute error = 1.9799896764950e-19 relative error = 2.2748935516088911657831443142384e-17 % h = 0.001 y1[1] (analytic) = 1.9915618937147880395945121711518 y1[1] (numeric) = 1.9915618937147880381497292599974 absolute error = 1.4447829111544e-18 relative error = 7.2545217686380759680459885615648e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.4MB, time=3.75 NO POLE NO POLE x[1] = 0.131 y2[1] (analytic) = 0.86937436046891656820031609690237 y2[1] (numeric) = 0.86937436046891656840640786993343 absolute error = 2.0609177303106e-19 relative error = 2.3705756967562256835110681765088e-17 % h = 0.001 y1[1] (analytic) = 1.9914317638128684917748100954616 y1[1] (numeric) = 1.9914317638128684902820730993056 absolute error = 1.4927369961560e-18 relative error = 7.4957978640350239786815166052499e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.132 y2[1] (analytic) = 0.86838299418315664155567172956986 y2[1] (numeric) = 0.86838299418315664176995240748733 absolute error = 2.1428067791747e-19 relative error = 2.4675826145010226392881536589220e-17 % h = 0.001 y1[1] (analytic) = 1.991300642479267750397513340263 y1[1] (numeric) = 1.9913006424792677488568370480836 absolute error = 1.5406762921794e-18 relative error = 7.7370350780441764169325861697022e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=3.98 NO POLE NO POLE x[1] = 0.133 y2[1] (analytic) = 0.86739175951439156367093333907315 y2[1] (numeric) = 0.86739175951439156389349899984859 absolute error = 2.2256566077544e-19 relative error = 2.5659185521896492259467143037881e-17 % h = 0.001 y1[1] (analytic) = 1.9911685298451071381365858470171 y1[1] (numeric) = 1.9911685298451071365479851920305 absolute error = 1.5886006549866e-18 relative error = 7.9782330384167789895381769263193e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.134 y2[1] (analytic) = 0.86640065745385592070829249982374 y2[1] (numeric) = 0.86640065745385592093923919970303 absolute error = 2.3094669987929e-19 relative error = 2.6655877727284632093481394865675e-17 % h = 0.001 y1[1] (analytic) = 1.9910354260424992781432540635797 y1[1] (numeric) = 1.9910354260424992765067441232122 absolute error = 1.6365099403675e-18 relative error = 8.2193913727608791426299677279037e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=4.22 NO POLE NO POLE x[1] = 0.135 y2[1] (analytic) = 0.86540968899265169061155654955344 y2[1] (numeric) = 0.86540968899265169085098032286447 absolute error = 2.3942377331103e-19 relative error = 2.7665945546521721375596559598765e-17 % h = 0.001 y1[1] (analytic) = 1.9909013312045479619333948023605 y1[1] (numeric) = 1.9909013312045479602489907982195 absolute error = 1.6844040041410e-18 relative error = 8.4605097085443758650034012416460e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.136 y2[1] (analytic) = 0.86441885512174725200425323733583 y2[1] (numeric) = 0.86441885512174725225225009629617 absolute error = 2.4799685896034e-19 relative error = 2.8689431921913758466020385872745e-17 % h = 0.001 y1[1] (analytic) = 1.990766245465348016283754816428 y1[1] (numeric) = 1.9907662454653480145514721142736 absolute error = 1.7322827021544e-18 relative error = 8.7015876730895311306670325250387e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=4.45 NO POLE NO POLE x[1] = 0.137 y2[1] (analytic) = 0.86342815683197639322133468075391 y2[1] (numeric) = 0.86342815683197639347800061527859 absolute error = 2.5666593452468e-19 relative error = 2.9726379953419487078699189776473e-17 % h = 0.001 y1[1] (analytic) = 1.9906301689599851691371351973316 y1[1] (numeric) = 1.9906301689599851673569893070473 absolute error = 1.7801458902843e-18 relative error = 8.9426248935750142459467811629611e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.138 y2[1] (analytic) = 0.86243759511403732147547160042766 y2[1] (numeric) = 0.86243759511403732174090257793691 absolute error = 2.6543097750925e-19 relative error = 3.0776832899330289993517966990118e-17 % h = 0.001 y1[1] (analytic) = 1.9904931018245359145166746894438 y1[1] (numeric) = 1.9904931018245359126886812650074 absolute error = 1.8279934244364e-18 relative error = 9.1836209970324205924677240428908e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=4.69 NO POLE NO POLE x[1] = 0.139 y2[1] (analytic) = 0.86144717095849167215892866552446 y2[1] (numeric) = 0.86144717095849167243322063075152 absolute error = 2.7429196522706e-19 relative error = 3.1840834176966215591357142476185e-17 % h = 0.001 y1[1] (analytic) = 1.9903550441960673764493670065295 y1[1] (numeric) = 1.9903550441960673745735418459833 absolute error = 1.8758251605462e-18 relative error = 9.4245756103473105705509047047901e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.14 y2[1] (analytic) = 0.86045688535576351828201164829463 y2[1] (numeric) = 0.8604568853557635185652605230936 absolute error = 2.8324887479897e-19 relative error = 3.2918427363371988667271733213064e-17 % h = 0.001 y1[1] (analytic) = 1.9902159962126371718989482270114 y1[1] (numeric) = 1.9902159962126371699753072724328 absolute error = 1.9236409545786e-18 relative error = 9.6654883602547217644075419741395e-17 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=4.93 NO POLE NO POLE x[1] = 0.141 y2[1] (analytic) = 0.85946673929613838004907694910232 y2[1] (numeric) = 0.85946673929613838034137863225605 absolute error = 2.9230168315373e-19 relative error = 3.4009656196016487739946879667769e-17 % h = 0.001 y1[1] (analytic) = 1.9900759580132932727082913350357 y1[1] (numeric) = 1.9900759580132932707368506725068 absolute error = 1.9714406625289e-18 relative error = 9.9063588733417139598198527132018e-17 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.142 y2[1] (analytic) = 0.85847673376976223457309391585971 y2[1] (numeric) = 0.85847673376976223487454428288771 absolute error = 3.0145036702800e-19 relative error = 3.5114564573493378891430638418004e-17 % h = 0.001 y1[1] (analytic) = 1.9899349297380738665514459649294 y1[1] (numeric) = 1.989934929738073864532221824507 absolute error = 2.0192241404224e-18 relative error = 1.0147186776042879652164912790633e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=5.17 NO POLE NO POLE x[1] = 0.143 y2[1] (analytic) = 0.85748686976664052572975024321969 y2[1] (numeric) = 0.85748686976664052604044514618609 absolute error = 3.1069490296640e-19 relative error = 3.6233196556228738172389930962193e-17 % h = 0.001 y1[1] (analytic) = 1.9897929115280072168954623969991 y1[1] (numeric) = 1.9897929115280072148284711526842 absolute error = 2.0669912443149e-18 relative error = 1.0387971694640375556310389904528e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.144 y2[1] (analytic) = 0.85649714827663717415209059733904 y2[1] (numeric) = 0.85649714827663717447212586466058 absolute error = 3.2003526732154e-19 relative error = 3.7365596367189873013416001867101e-17 % h = 0.001 y1[1] (analytic) = 1.9896499035251115219721398428361 y1[1] (numeric) = 1.989649903525111519857398012543 absolute error = 2.1147418302931e-18 relative error = 1.0628713255263451343943875826455e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=5.41 NO POLE NO POLE x[1] = 0.145 y2[1] (analytic) = 0.85550757028947358736667847149108 y2[1] (numeric) = 0.85550757028947358769614990774515 absolute error = 3.2947143625407e-19 relative error = 3.8511808392600019504930759481043e-17 % h = 0.001 y1[1] (analytic) = 1.989505905872394772759840048366 y1[1] (numeric) = 1.9895059058723947705973642938916 absolute error = 2.1624757544744e-18 relative error = 1.0869411083884962174787257897387e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.146 y2[1] (analytic) = 0.85451813679472767007227113628341 y2[1] (numeric) = 0.85451813679472767041127452201611 absolute error = 3.3900338573270e-19 relative error = 3.9671877182653103431893460771225e-17 % h = 0.001 y1[1] (analytic) = 1.9893609187138546099755082328197 y1[1] (numeric) = 1.9893609187138546077653153598121 absolute error = 2.2101928730076e-18 relative error = 1.1110064806322403595585313578381e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=5.65 NO POLE NO POLE x[1] = 0.147 y2[1] (analytic) = 0.85352884878183283456199740572324 y2[1] (numeric) = 0.8535288487818328349106284972575 absolute error = 3.4863109153426e-19 relative error = 4.0845847452236758266348362888519e-17 % h = 0.001 y1[1] (analytic) = 1.9892149421944781800770443715908 y1[1] (numeric) = 1.9892149421944781778191513295179 absolute error = 2.2578930420729e-18 relative error = 1.1350674048235427727071354491635e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.148 y2[1] (analytic) = 0.85253970724007701129002779687021 y2[1] (numeric) = 0.85253970724007701164838232611395 absolute error = 3.5835452924374e-19 relative error = 4.2033764081656620770164032449428e-17 % h = 0.001 y1[1] (analytic) = 1.9890679764602419902761688205978 y1[1] (numeric) = 1.9890679764602419879705927027155 absolute error = 2.3055761178823e-18 relative error = 1.1591238435125369165790780167764e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=5.89 NO POLE NO POLE x[1] = 0.149 y2[1] (analytic) = 0.85155071315860165958372651632402 y2[1] (numeric) = 0.85155071315860165995190019057829 absolute error = 3.6817367425427e-19 relative error = 4.3235672117357208588197489720510e-17 % h = 0.001 y1[1] (analytic) = 1.9889200216581117625619272692718 y1[1] (numeric) = 1.9889200216581117602086853125923 absolute error = 2.3532419566795e-18 relative error = 1.1831757592332256560207231033339e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.15 y2[1] (analytic) = 0.85056186752640077850227456131236 y2[1] (numeric) = 0.85056186752640077888036306307962 absolute error = 3.7808850176726e-19 relative error = 4.4451616772665208520551120342119e-17 % h = 0.001 y1[1] (analytic) = 1.9887710779360422867349809986543 y1[1] (numeric) = 1.9887710779360422843340905839138 absolute error = 2.4008904147405e-18 relative error = 1.2072231145035342422675357534337e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=6.13 NO POLE NO POLE x[1] = 0.151 y2[1] (analytic) = 0.8495731713323199178427530766738 y2[1] (numeric) = 0.84957317133231991823085206346617 absolute error = 3.8809898679237e-19 relative error = 4.5681643428516506212639633455878e-17 % h = 0.001 y1[1] (analytic) = 1.9886211454429772724528294103012 y1[1] (numeric) = 1.9886211454429772700043080619274 absolute error = 2.4485213483738e-18 relative error = 1.2312658718251621539680624332369e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.152 y2[1] (analytic) = 0.84858462556505518929467596156972 y2[1] (numeric) = 0.84858462556505518969288106571727 absolute error = 3.9820510414755e-19 relative error = 4.6925797634195098143577879949598e-17 % h = 0.001 y1[1] (analytic) = 1.9884702243288492002861127807586 y1[1] (numeric) = 1.9884702243288491977899781668383 absolute error = 2.4961346139203e-18 relative error = 1.2553039936832839824114401688326e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.4MB, time=6.37 NO POLE NO POLE x[1] = 0.153 y2[1] (analytic) = 0.84759623121315227774396057131025 y2[1] (numeric) = 0.84759623121315227815236739976938 absolute error = 4.0840682845913e-19 relative error = 4.8184125108081614372011575817492e-17 % h = 0.001 y1[1] (analytic) = 1.9883183147445791717861441852958 y1[1] (numeric) = 1.9883183147445791692424141175417 absolute error = 2.5437300677541e-18 relative error = 1.2793374425467028045457977939837e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.154 y2[1] (analytic) = 0.84660798926500545272732521024132 y2[1] (numeric) = 0.84660798926500545314602934440311 absolute error = 4.1870413416179e-19 relative error = 4.9456671738391441420216584022269e-17 % h = 0.001 y1[1] (analytic) = 1.9881654168420767585638205233501 y1[1] (numeric) = 1.988165416842076755972512957068 absolute error = 2.5913075662821e-18 relative error = 1.3033661808674000348839553240284e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=6.61 NO POLE NO POLE x[1] = 0.155 y2[1] (analytic) = 0.84561990070885658003810196121268 y2[1] (numeric) = 0.84561990070885658046719895671133 absolute error = 4.2909699549865e-19 relative error = 5.0743483583930732670169294312041e-17 % h = 0.001 y1[1] (analytic) = 1.9880115307742398503800635667605 y1[1] (numeric) = 1.9880115307742398477411966008156 absolute error = 2.6388669659449e-18 relative error = 1.3273901710807389696308661144234e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.156 y2[1] (analytic) = 0.84463196653279413348445324573189 y2[1] (numeric) = 0.84463196653279413392403863225322 absolute error = 4.3958538652133e-19 relative error = 5.2044606874852684391030786293726e-17 % h = 0.001 y1[1] (analytic) = 1.9878566566949545022479429403361 y1[1] (numeric) = 1.9878566566949544995615348171197 absolute error = 2.6864081232164e-18 relative error = 1.3514093756050144342214652277108e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=6.85 NO POLE NO POLE x[1] = 0.157 y2[1] (analytic) = 0.84364418772475220680098035650535 y2[1] (numeric) = 0.84364418772475220725114963759527 absolute error = 4.5016928108992e-19 relative error = 5.3360088013406958326127560998952e-17 % h = 0.001 y1[1] (analytic) = 1.9877007947590947805466339326243 y1[1] (numeric) = 1.9877007947590947778127030380198 absolute error = 2.7339308946045e-18 relative error = 1.3754237568415556034344133572480e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.158 y2[1] (analytic) = 0.84265656527250952571471205067536 y2[1] (numeric) = 0.84265656527250952617556070354846 absolute error = 4.6084865287310e-19 relative error = 5.4689973574710666663832923499555e-17 % h = 0.001 y1[1] (analytic) = 1.9875439451225226081473640229073 y1[1] (numeric) = 1.987543945122522605365928886256 absolute error = 2.7814351366513e-18 relative error = 1.3994332771745772820899101189866e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=7.08 NO POLE NO POLE x[1] = 0.159 y2[1] (analytic) = 0.84166910016368846016646113768246 y2[1] (numeric) = 0.84166910016368846063808461303057 absolute error = 4.7162347534811e-19 relative error = 5.6034310307505443682410073553811e-17 % h = 0.001 y1[1] (analytic) = 1.9873861079420876085515029984672 y1[1] (numeric) = 1.9873861079420876057225822925343 absolute error = 2.8289207059329e-18 relative error = 1.4234378989708298256897269325264e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.16 y2[1] (analytic) = 0.84068179338575403668853684031401 y2[1] (numeric) = 0.84068179338575403717103056211487 absolute error = 4.8249372180086e-19 relative error = 5.7393145134934976028376736348088e-17 % h = 0.001 y1[1] (analytic) = 1.9872272833756269490409525240183 y1[1] (numeric) = 1.9872272833756269461645650649581 absolute error = 2.8763874590602e-18 relative error = 1.4474375845797520867556960036101e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=7.32 NO POLE NO POLE x[1] = 0.161 y2[1] (analytic) = 0.83969464592601295093980055114447 y2[1] (numeric) = 0.83969464592601295143325991647038 absolute error = 4.9345936532591e-19 relative error = 5.8766525155310995968602900553057e-17 % h = 0.001 y1[1] (analytic) = 1.9870674715819651828409920129024 y1[1] (numeric) = 1.9870674715819651799171567602234 absolute error = 2.9238352526790e-18 relative error = 1.4714322963332721350890991162043e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.162 y2[1] (analytic) = 0.83870765877161258039905244922922 y2[1] (numeric) = 0.83870765877161258090357282805578 absolute error = 5.0452037882656e-19 relative error = 6.0154497642896248422183963731122e-17 % h = 0.001 y1[1] (analytic) = 1.9869066727209140902957386371875 y1[1] (numeric) = 1.9869066727209140873244746937177 absolute error = 2.9712639434698e-18 relative error = 1.4954219965454568727484723810267e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=7.56 NO POLE NO POLE x[1] = 0.163 y2[1] (analytic) = 0.83772083290953999721773628358307 y2[1] (numeric) = 0.83772083290953999773341301859796 absolute error = 5.1567673501489e-19 relative error = 6.1557110048685462674022099590585e-17 % h = 0.001 y1[1] (analytic) = 1.9867448869532725190563803011996 y1[1] (numeric) = 1.9867448869532725160377069130508 absolute error = 3.0186733881488e-18 relative error = 1.5194066475127654601419703267946e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.164 y2[1] (analytic) = 0.8367341693266209812329494706565 y2[1] (numeric) = 0.83673416932662098175987787706826 absolute error = 5.2692840641176e-19 relative error = 6.2974410001185497676080592940843e-17 % h = 0.001 y1[1] (analytic) = 1.9865821144408262232823413902376 y1[1] (numeric) = 1.9865821144408262202162779467703 absolute error = 3.0660634434673e-18 relative error = 1.5433862115134974407166458567322e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=7.79 NO POLE NO POLE x[1] = 0.165 y2[1] (analytic) = 0.83574766900951903314174549271711 y2[1] (numeric) = 0.83574766900951903368002085806402 absolute error = 5.3827536534691e-19 relative error = 6.4406445307211395779051387652001e-17 % h = 0.001 y1[1] (analytic) = 1.9864183553463477018555420932949 y1[1] (numeric) = 1.9864183553463476987421081270823 absolute error = 3.1134339662126e-18 relative error = 1.5673606508079957006910781815180e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=129.7MB, alloc=4.4MB, time=8.03 x[1] = 0.166 y2[1] (analytic) = 0.83476133294473438783771542275181 y2[1] (numeric) = 0.83476133294473438838743300671078 absolute error = 5.4971758395897e-19 relative error = 6.5853263952675705626184210199799e-17 % h = 0.001 y1[1] (analytic) = 1.9862536098335960356079130855139 y1[1] (numeric) = 1.9862536098335960324471282723057 absolute error = 3.1607848132082e-18 relative error = 1.5913299276384970842745598408669e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.167 y2[1] (analytic) = 0.83377516211860302791083523922592 y2[1] (numeric) = 0.83377516211860302847209027342142 absolute error = 5.6125503419550e-19 relative error = 6.7314914103385400875950661405856e-17 % h = 0.001 y1[1] (analytic) = 1.9860878780673167235623283428443 y1[1] (numeric) = 1.986087878067316720354212501531 absolute error = 3.2081158413133e-18 relative error = 1.6152940042286304614590950410868e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=8.27 NO POLE NO POLE x[1] = 0.168 y2[1] (analytic) = 0.83278915751729569731156543076966 y2[1] (numeric) = 0.83278915751729569788445311858272 absolute error = 5.7288768781306e-19 relative error = 6.8791444105846447700803318871182e-17 % h = 0.001 y1[1] (analytic) = 1.985921160213241518187119847961 y1[1] (numeric) = 1.9859211602132415149316929405369 absolute error = 3.2554269074241e-18 relative error = 1.6392528427838209020907083452833e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.169 y2[1] (analytic) = 0.83180332012681691518018922661023 y2[1] (numeric) = 0.83180332012681691576480474298747 absolute error = 5.8461551637724e-19 relative error = 7.0282902488067658970816819214910e-17 % h = 0.001 y1[1] (analytic) = 1.9857534564380882596643389329105 y1[1] (numeric) = 1.9857534564380882563616210644373 absolute error = 3.3027178684732e-18 relative error = 1.6632064054907372148398175187619e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=8.50 NO POLE NO POLE x[1] = 0.17 y2[1] (analytic) = 0.83081765093300398984237562332915 y2[1] (numeric) = 0.83081765093300399043881411459185 absolute error = 5.9643849126270e-19 relative error = 7.1789337960369837177667361406203e-17 % h = 0.001 y1[1] (analytic) = 1.9855847669095607091719299902125 y1[1] (numeric) = 1.9855847669095607058219414087824 absolute error = 3.3499885814301e-18 relative error = 1.6871546545172931770743290855110e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.171 y2[1] (analytic) = 0.8298321509215260329719532122995 y2[1] (numeric) = 0.82983215092152603358030979595274 absolute error = 6.0835658365324e-19 relative error = 7.3310799416202649945515112301930e-17 % h = 0.001 y1[1] (analytic) = 1.9854150917963483811799832702289 y1[1] (numeric) = 1.985415091796348377782744366927 absolute error = 3.3972389033019e-18 relative error = 1.7110975520127494761817616959939e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=8.75 NO POLE NO POLE x[1] = 0.172 y2[1] (analytic) = 0.82884682107788297392188064494727 y2[1] (numeric) = 0.82884682107788297454225040948909 absolute error = 6.2036976454182e-19 relative error = 7.4847335932959640183515965021763e-17 % h = 0.001 y1[1] (analytic) = 1.9852444312681263747612344685321 y1[1] (numeric) = 1.9852444312681263713167657773994 absolute error = 3.4444686911327e-18 relative error = 1.7350350601071608492777212168808e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.173 y2[1] (analytic) = 0.82786166238740457422439940478408 y2[1] (numeric) = 0.82786166238740457485687740951468 absolute error = 6.3247800473060e-19 relative error = 7.6398996772799800438230982028523e-17 % h = 0.001 y1[1] (analytic) = 1.9850727854955552039159797927608 y1[1] (numeric) = 1.9850727854955552004243019907562 absolute error = 3.4916778020046e-18 relative error = 1.7589671409116289304243470161310e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=8.99 NO POLE NO POLE x[1] = 0.174 y2[1] (analytic) = 0.82687667583524944226135438597639 y2[1] (numeric) = 0.82687667583524944290603566080741 absolute error = 6.4468127483102e-19 relative error = 7.7965831383478174446639282437007e-17 % h = 0.001 y1[1] (analytic) = 1.9849001546502806269115761840325 y1[1] (numeric) = 1.9849001546502806233727100909952 absolute error = 3.5388660930373e-18 relative error = 1.7828937565178498798659660504237e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.175 y2[1] (analytic) = 0.82589186240640404810566760804859 y2[1] (numeric) = 0.82589186240640404876264715331241 absolute error = 6.5697954526382e-19 relative error = 7.9547889399173442551627890837358e-17 % h = 0.001 y1[1] (analytic) = 1.9847265389049334746366973533995 y1[1] (numeric) = 1.9847265389049334710506639320107 absolute error = 3.5860334213888e-18 relative error = 1.8068148689982159862530115786579e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=9.22 NO POLE NO POLE x[1] = 0.176 y2[1] (analytic) = 0.82490722308568173853495022516409 y2[1] (numeric) = 0.82490722308568173920432301142319 absolute error = 6.6937278625910e-19 relative error = 8.1145220641324577687264573156214e-17 % h = 0.001 y1[1] (analytic) = 1.9845519384331294779705172790773 y1[1] (numeric) = 1.9845519384331294743373376348217 absolute error = 3.6331796442556e-18 relative error = 1.8307304404056653517739070493416e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.177 y2[1] (analytic) = 0.82392275885772175221823781629032 y2[1] (numeric) = 0.82392275885772175290009878414667 absolute error = 6.8186096785635e-19 relative error = 8.2757875119468141141783680072576e-17 % h = 0.001 y1[1] (analytic) = 1.9843763534094690941669937952475 y1[1] (numeric) = 1.9843763534094690904866891763748 absolute error = 3.6803046188727e-18 relative error = 1.8546404327734306870097952556231e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=9.46 NO POLE NO POLE x[1] = 0.178 y2[1] (analytic) = 0.82293847070698823507683376943031 y2[1] (numeric) = 0.82293847070698823577127782933482 absolute error = 6.9444405990451e-19 relative error = 8.4385903032083503581965791942178e-17 % h = 0.001 y1[1] (analytic) = 1.9841997840095373322544258881378 y1[1] (numeric) = 1.9841997840095373285270176856238 absolute error = 3.7274082025140e-18 relative error = 1.8785448081149895407962510993609e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.179 y2[1] (analytic) = 0.82195435961776925582024539899536 y2[1] (numeric) = 0.82195435961776925652736743105741 absolute error = 7.0712203206205e-19 relative error = 8.6029354767444830262916978494107e-17 % h = 0.001 y1[1] (analytic) = 1.9840222304099035774504592998064 y1[1] (numeric) = 1.9840222304099035736759690473141 absolute error = 3.7744902524923e-18 relative error = 1.9024435284238128681661014219710e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=9.70 NO POLE NO POLE x[1] = 0.18 y2[1] (analytic) = 0.82097042657417582165819726030079 y2[1] (numeric) = 0.82097042657417582237809211409772 absolute error = 7.1989485379693e-19 relative error = 8.7688280904462823197830088065322e-17 % h = 0.001 y1[1] (analytic) = 1.9838436927881214145927160246115 y1[1] (numeric) = 1.9838436927881214107711653984514 absolute error = 3.8215506261601e-18 relative error = 1.9263365556735166959720976615507e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.181 y2[1] (analytic) = 0.81998667256014089418970594908918 y2[1] (numeric) = 0.81998667256014089492246844347593 absolute error = 7.3276249438675e-19 relative error = 8.9362732213553928679787933851097e-17 % h = 0.001 y1[1] (analytic) = 1.9836641713227284505852242677207 y1[1] (numeric) = 1.9836641713227284467166350868114 absolute error = 3.8685891809093e-18 relative error = 1.9502238518174593163071267401234e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.4MB, time=9.93 NO POLE NO POLE x[1] = 0.182 y2[1] (analytic) = 0.81900309855941840547020049692454 y2[1] (numeric) = 0.81900309855941840621592541984327 absolute error = 7.4572492291873e-19 relative error = 9.1052759657493274071527032835930e-17 % h = 0.001 y1[1] (analytic) = 1.983483666193246135860826419216 y1[1] (numeric) = 1.9834836661932461319452206450445 absolute error = 3.9156057741715e-18 relative error = 1.9741053787886407347742797755531e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.183 y2[1] (analytic) = 0.81801970555558227425767229525488 y2[1] (numeric) = 0.81801970555558227501645440354468 absolute error = 7.5878210828980e-19 relative error = 9.2758414392285414659294139773678e-17 % h = 0.001 y1[1] (analytic) = 1.9833021775801795848597435813723 y1[1] (numeric) = 1.9833021775801795808971433179537 absolute error = 3.9626002634186e-18 relative error = 1.9979810984997533009387699979419e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=10.17 NO POLE NO POLE x[1] = 0.184 y2[1] (analytic) = 0.81703649453202542243883830191132 y2[1] (numeric) = 0.81703649453202542321077232111792 absolute error = 7.7193401920660e-19 relative error = 9.4479747768028550609392632807486e-17 % h = 0.001 y1[1] (analytic) = 1.9831197056650173955244761705281 y1[1] (numeric) = 1.9831197056650173915149036643656 absolute error = 4.0095725061625e-18 relative error = 2.0218509728427785108924965447354e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.185 y2[1] (analytic) = 0.81605346647195879163630110379855 y2[1] (numeric) = 0.81605346647195879242148172798414 absolute error = 7.8518062418559e-19 relative error = 9.6216811329796655737371998159273e-17 % h = 0.001 y1[1] (analytic) = 1.9829362506302314678112210986348 y1[1] (numeric) = 1.9829362506302314637546987386789 absolute error = 4.0565223599559e-18 relative error = 2.0457149636891382946430151247998e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.4MB, time=10.41 NO POLE NO POLE x[1] = 0.186 y2[1] (analytic) = 0.81507062235841035999768922853466 y2[1] (numeric) = 0.81507062235841036079621112008771 absolute error = 7.9852189155305e-19 relative error = 9.7969656818512666293629223820296e-17 % h = 0.001 y1[1] (analytic) = 1.9827518126592768212179870230509 y1[1] (numeric) = 1.9827518126592768171145373406587 absolute error = 4.1034496823922e-18 relative error = 2.0695730328893924468637493993042e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.187 y2[1] (analytic) = 0.81408796317422415916776091581804 y2[1] (numeric) = 0.8140879631742241599797187052632 absolute error = 8.1195778944516e-19 relative error = 9.9738336171835981615748815584320e-17 % h = 0.001 y1[1] (analytic) = 1.9825663919365914113295901364508 y1[1] (numeric) = 1.9825663919365914071792358053452 absolute error = 4.1503543311056e-18 relative error = 2.0934251422730367426498195346717e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=10.64 NO POLE NO POLE x[1] = 0.188 y2[1] (analytic) = 0.81310548990205929144445437633573 y2[1] (numeric) = 0.81310548990205929226994266214377 absolute error = 8.2548828580804e-19 relative error = 1.0152290152504962782870675726051e-16 % h = 0.001 y1[1] (analytic) = 1.9823799886475959453797139518383 y1[1] (numeric) = 1.9823799886475959411824777880664 absolute error = 4.1972361637719e-18 relative error = 2.1172712536486540242798838041599e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.189 y2[1] (analytic) = 0.81212320352438894711986738208099 y2[1] (numeric) = 0.8121232035243889479589807304788 absolute error = 8.3911334839781e-19 relative error = 1.0332340521195445800858836422442e-16 % h = 0.001 y1[1] (analytic) = 1.9821926029786936968302175205875 y1[1] (numeric) = 1.9821926029786936925861224824794 absolute error = 4.2440950381081e-18 relative error = 2.1411113288034599567576644495174e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=10.88 NO POLE NO POLE x[1] = 0.19 y2[1] (analytic) = 0.81114110502349942200714884701869 y2[1] (numeric) = 0.81114110502349942285998179179929 absolute error = 8.5283294478060e-19 relative error = 1.0513989976576180678898652669291e-16 % h = 0.001 y1[1] (analytic) = 1.9820042351172703189678775041899 y1[1] (numeric) = 1.9820042351172703146769466923169 absolute error = 4.2909308118730e-18 relative error = 2.1649453295033530393345123830090e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.191 y2[1] (analytic) = 0.81015919538148913515428487112495 y2[1] (numeric) = 0.81015919538148913602093191345761 absolute error = 8.6664704233266e-19 relative error = 1.0697243792000308923550832931275e-16 % h = 0.001 y1[1] (analytic) = 1.9818148852516936575187505029481 y1[1] (numeric) = 1.9818148852516936531810071600807 absolute error = 4.3377433428674e-18 relative error = 2.1887732174927627831446845534532e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=11.12 NO POLE NO POLE x[1] = 0.192 y2[1] (analytic) = 0.80917747558026764674576153393323 y2[1] (numeric) = 0.80917747558026764762631714217362 absolute error = 8.8055560824039e-19 relative error = 1.0882107260943423107591316887348e-16 % h = 0.001 y1[1] (analytic) = 1.9816245535713135622803430272392 y1[1] (numeric) = 1.9816245535713135578958105383049 absolute error = 4.3845324889343e-18 relative error = 2.2125949544944977751616680735961e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.193 y2[1] (analytic) = 0.80819594660155467619308653584224 y2[1] (numeric) = 0.80819594660155467708764514534261 absolute error = 8.9455860950037e-19 relative error = 1.1068585697094477278000232273769e-16 % h = 0.001 y1[1] (analytic) = 1.9814332402664616977717774791618 y1[1] (numeric) = 1.9814332402664616933404793712028 absolute error = 4.4312981079590e-18 relative error = 2.2364105022095431591056843381025e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=11.35 NO POLE NO POLE x[1] = 0.194 y2[1] (analytic) = 0.8072146094268791204151515965821 y2[1] (numeric) = 0.80721460942687912132380760950154 absolute error = 9.0865601291944e-19 relative error = 1.1256684434447786920357880339488e-16 % h = 0.001 y1[1] (analytic) = 1.9812409455284513529021434943852 y1[1] (numeric) = 1.9812409455284513484241034365156 absolute error = 4.4780400578696e-18 relative error = 2.2602198223170598652453688983105e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.195 y2[1] (analytic) = 0.80623346503757807230941733039465 y2[1] (numeric) = 0.80623346503757807323226511550938 absolute error = 9.2284778511473e-19 relative error = 1.1446408827394886196395980824365e-16 % h = 0.001 y1[1] (analytic) = 1.9810476695495772496572249758333 y1[1] (numeric) = 1.9810476695495772451324667791963 absolute error = 4.5247581966370e-18 relative error = 2.2840228764741314205060469720885e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=11.58 NO POLE NO POLE x[1] = 0.196 y2[1] (analytic) = 0.80525251441479583941490212666118 y2[1] (numeric) = 0.80525251441479584035203601917492 absolute error = 9.3713389251374e-19 relative error = 1.1637764250817481842309930430228e-16 % h = 0.001 y1[1] (analytic) = 1.9808534125231153508047941324606 y1[1] (numeric) = 1.9808534125231153462333417501851 absolute error = 4.5714523822755e-18 relative error = 2.3078196263158134826110062128478e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.197 y2[1] (analytic) = 0.80427175853948296276795637290694 y2[1] (numeric) = 0.8042717585394829637194706742613 absolute error = 9.5151430135436e-19 relative error = 1.1830756100180144143877476001380e-16 % h = 0.001 y1[1] (analytic) = 1.980658174643322666618664817809 y1[1] (numeric) = 1.9806581746433226620005423449666 absolute error = 4.6181224728424e-18 relative error = 2.3316100334546784930306212166935e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.4MB, time=11.82 NO POLE NO POLE x[1] = 0.198 y2[1] (analytic) = 0.80329119839239523595180316432647 y2[1] (numeric) = 0.80329119839239523691779214201141 absolute error = 9.6598897768494e-19 relative error = 1.2025389791624100847303515281928e-16 % h = 0.001 y1[1] (analytic) = 1.9804619561054370606216984442784 y1[1] (numeric) = 1.9804619561054370559569301178394 absolute error = 4.6647683264390e-18 relative error = 2.3553940594810669383858168664117e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.199 y2[1] (analytic) = 0.8023108349540927243408264502072 y2[1] (numeric) = 0.80231083495409272532138433757156 absolute error = 9.8055788736436e-19 relative error = 1.2221670762061518973116722048311e-16 % h = 0.001 y1[1] (analytic) = 1.9802647571056770543479567300861 y1[1] (numeric) = 1.9802647571056770496365669288759 absolute error = 4.7113898012102e-18 relative error = 2.3791716659626317565944280493370e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=12.06 NO POLE NO POLE x[1] = 0.2 y2[1] (analytic) = 0.80133066920493878454058737288161 y2[1] (numeric) = 0.80133066920493878553580836894367 absolute error = 9.9522099606206e-19 relative error = 1.2419604469269778261279807478469e-16 % h = 0.001 y1[1] (analytic) = 1.9800665778412416311241965167482 y1[1] (numeric) = 1.9800665778412416263662097614032 absolute error = 4.7579867553450e-18 relative error = 2.4029428144443369730585975536981e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.201 y2[1] (analytic) = 0.80035070212509908402454935910971 y2[1] (numeric) = 0.8003507021250990850345276283678 absolute error = 1.00997826925809e-18 relative error = 1.2619196391986484557661564539433e-16 % h = 0.001 y1[1] (analytic) = 1.979867418510310038870902875571 y1[1] (numeric) = 1.9798674185103100340663438284942 absolute error = 4.8045590470768e-18 relative error = 2.4267074664483552900553008525720e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=12.30 NO POLE NO POLE x[1] = 0.202 y2[1] (analytic) = 0.79937093469454062096849232708521 y2[1] (numeric) = 0.79937093469454062199332199932839 absolute error = 1.02482967224318e-18 relative error = 1.2820452030005228193577777480669e-16 % h = 0.001 y1[1] (analytic) = 1.9796672793120415919230577021024 y1[1] (numeric) = 1.9796672793120415870719511674188 absolute error = 4.8511065346836e-18 relative error = 2.4504655834739150721600299296162e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.203 y2[1] (analytic) = 0.79839136789303074428359617456935 y2[1] (numeric) = 0.79839136789303074532337134468817 absolute error = 1.03977517011882e-18 relative error = 1.3023376904271967196875023932723e-16 % h = 0.001 y1[1] (analytic) = 1.9794661604465754718708419777594 y1[1] (numeric) = 1.9794661604465754669732129012711 absolute error = 4.8976290764883e-18 relative error = 2.4742171269971977288059864950144e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.4MB, time=12.53 NO POLE NO POLE x[1] = 0.204 y2[1] (analytic) = 0.79741200270013617384917351498742 y2[1] (numeric) = 0.79741200270013617490398824278466 absolute error = 1.05481472779724e-18 relative error = 1.3227976556980659924440160328093e-16 % h = 0.001 y1[1] (analytic) = 1.979264062115030527420470857911 y1[1] (numeric) = 1.9792640621150305224763443270525 absolute error = 4.9441265308585e-18 relative error = 2.4979620584709823862490551461080e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.205 y2[1] (analytic) = 0.79643284009522202094603142867336 y2[1] (numeric) = 0.79643284009522202201597973867489 absolute error = 1.06994831000153e-18 relative error = 1.3434256551671152763166332442320e-16 % h = 0.001 y1[1] (analytic) = 1.9790609845195050732753617255673 y1[1] (numeric) = 1.97906098451950506828476296936 absolute error = 4.9905987562073e-18 relative error = 2.5217003393247956023777423591898e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.4MB, time=12.77 NO POLE NO POLE x[1] = 0.206 y2[1] (analytic) = 0.79545388105745080889144179581925 y2[1] (numeric) = 0.79545388105745080997661767708494 absolute error = 1.08517588126569e-18 relative error = 1.3642222473326700990513333455636e-16 % h = 0.001 y1[1] (analytic) = 1.9788569278630766880378363294873 y1[1] (numeric) = 1.978856927863076683000790718494 absolute error = 5.0370456109933e-18 relative error = 2.5454319309646568700099203798314e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.207 y2[1] (analytic) = 0.79447512656578149387669957607767 y2[1] (numeric) = 0.79447512656578149497719698201232 absolute error = 1.10049740593465e-18 relative error = 1.3851879928471621754799476723036e-16 % h = 0.001 y1[1] (analytic) = 1.9786518923498020111315591049884 y1[1] (numeric) = 1.9786518923498020060480921512674 absolute error = 5.0834669537210e-18 relative error = 2.5691567947730260913808507434941e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=13.01 NO POLE NO POLE x[1] = 0.208 y2[1] (analytic) = 0.79349657759896848600824819717701 y2[1] (numeric) = 0.79349657759896848712416104534138 absolute error = 1.11591284816437e-18 relative error = 1.4063234545270465226015026214262e-16 % h = 0.001 y1[1] (analytic) = 1.9784458781847165387449147550011 y1[1] (numeric) = 1.9784458781847165336150521120605 absolute error = 5.1298626429406e-18 relative error = 2.5928748921084477219806632745494e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.209 y2[1] (analytic) = 0.79251823513556067055335101134286 y2[1] (numeric) = 0.79251823513556067168477318326471 absolute error = 1.13142217192185e-18 relative error = 1.4276291973626570607602182373506e-16 % h = 0.001 y1[1] (analytic) = 1.9782388855738344187955291479752 y1[1] (numeric) = 1.9782388855738344136192966107266 absolute error = 5.1762325372486e-18 relative error = 2.6165861843055990620165093207649e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=13.25 NO POLE NO POLE x[1] = 0.21 y2[1] (analytic) = 0.79154010015390042939128757377236 y2[1] (numeric) = 0.79154010015390043053831291475758 absolute error = 1.14702534098522e-18 relative error = 1.4491057885282148016406337155763e-16 % h = 0.001 y1[1] (analytic) = 1.9780309147241482449161385680994 y1[1] (numeric) = 1.9780309147241482396935620728111 absolute error = 5.2225764952883e-18 relative error = 2.6402906326752879921267343239923e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.211 y2[1] (analytic) = 0.79056217363212266267105329188374 y2[1] (numeric) = 0.79056217363212266383377561082754 absolute error = 1.16272231894380e-18 relative error = 1.4707537973918506640452433130100e-16 % h = 0.001 y1[1] (analytic) = 1.9778219658436288494620133319462 y1[1] (numeric) = 1.9778219658436288441931189561972 absolute error = 5.2688943757490e-18 relative error = 2.6639881985037933892679077396241e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.4MB, time=13.48 NO POLE NO POLE x[1] = 0.212 y2[1] (analytic) = 0.78958445654815381067654078755991 y2[1] (numeric) = 0.78958445654815381185505385675804 absolute error = 1.17851306919813e-18 relative error = 1.4925737955256429038246807108533e-16 % h = 0.001 y1[1] (analytic) = 1.977612039141225095540142764105 y1[1] (numeric) = 1.9776120391412250902249567267374 absolute error = 5.3151860373676e-18 relative error = 2.6876788430534186784491761367902e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.213 y2[1] (analytic) = 0.7886069498797108759001811071231 y2[1] (numeric) = 0.78860694987971087709457866208316 absolute error = 1.19439755496006e-18 relative error = 1.5145663567157832687632228238533e-16 % h = 0.001 y1[1] (analytic) = 1.9774011348268636680603895025966 y1[1] (numeric) = 1.9774011348268636626989381636686 absolute error = 5.3614513389280e-18 relative error = 2.7113625275619331343109521231793e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=13.72 NO POLE NO POLE x[1] = 0.214 y2[1] (analytic) = 0.78762965460430044532602270531804 y2[1] (numeric) = 0.78762965460430044653639844457079 absolute error = 1.21037573925275e-18 relative error = 1.5367320569726824094724004951558e-16 % h = 0.001 y1[1] (analytic) = 1.9771892531114488638088220829006 y1[1] (numeric) = 1.9771892531114488584011319436393 absolute error = 5.4076901392613e-18 relative error = 2.7350392132424174102121512608641e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=225.0MB, alloc=4.4MB, time=13.95 x[1] = 0.215 y2[1] (analytic) = 0.78665257169921771292322592014294 y2[1] (numeric) = 0.78665257169921771414967350505377 absolute error = 1.22644758491083e-18 relative error = 1.5590714745413316767604750113890e-16 % h = 0.001 y1[1] (analytic) = 1.9769763942068623805434357272442 y1[1] (numeric) = 1.976976394206862375089533429998 absolute error = 5.4539022972462e-18 relative error = 2.7587088612832101007518071296869e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.216 y2[1] (analytic) = 0.78567570214154550235095044495269 y2[1] (numeric) = 0.78567570214154550359356349953305 absolute error = 1.24261305458036e-18 relative error = 1.5815851899114651884489082726087e-16 % h = 0.001 y1[1] (analytic) = 1.9767625583259631051124722434151 y1[1] (numeric) = 1.9767625583259630996123845716054 absolute error = 5.5000876718097e-18 relative error = 2.7823714328480060012208231099635e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=228.8MB, alloc=4.4MB, time=14.19 x[1] = 0.217 y2[1] (analytic) = 0.78469904690815328987561309286506 y2[1] (numeric) = 0.78469904690815329113448520358398 absolute error = 1.25887211071892e-18 relative error = 1.6042737858279408224731686784318e-16 % h = 0.001 y1[1] (analytic) = 1.9765477456825869005955509147589 y1[1] (numeric) = 1.9765477456825868950493047928324 absolute error = 5.5462461219265e-18 relative error = 2.8060268890752966874566025152617e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.218 y2[1] (analytic) = 0.78372260697569622750149293613085 y2[1] (numeric) = 0.78372260697569622877671765172653 absolute error = 1.27522471559568e-18 relative error = 1.6271378473011505052380321191698e-16 % h = 0.001 y1[1] (analytic) = 1.976331956491546392467823240215 y1[1] (numeric) = 1.9763319564915463868754457335952 absolute error = 5.5923775066198e-18 relative error = 2.8296751910785190825349663776982e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.4MB, time=14.42 NO POLE NO POLE x[1] = 0.219 y2[1] (analytic) = 0.78274638332061416631566068978145 y2[1] (numeric) = 0.78274638332061416760733152107292 absolute error = 1.29167083129147e-18 relative error = 1.6501779616174854538593678516780e-16 % h = 0.001 y1[1] (analytic) = 1.9761151909686307537873653602166 y1[1] (numeric) = 1.9761151909686307481488836752551 absolute error = 5.6384816849615e-18 relative error = 2.8533162999459004622041421379456e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.22 y2[1] (analytic) = 0.78177037691913068004820899454299 y2[1] (numeric) = 0.7817703769191306813564194142418 absolute error = 1.30821041969881e-18 relative error = 1.6733947183498055374434680314065e-16 % h = 0.001 y1[1] (analytic) = 1.9758974493306054894060229810447 y1[1] (numeric) = 1.9758974493306054837214644649725 absolute error = 5.6845585160722e-18 relative error = 2.8769501767402021069272918370995e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=14.66 NO POLE NO POLE x[1] = 0.221 y2[1] (analytic) = 0.78079458874725208884876003870549 y2[1] (numeric) = 0.78079458874725209017360348122748 absolute error = 1.32484344252199e-18 relative error = 1.6967887093680279102930328366377e-16 % h = 0.001 y1[1] (analytic) = 1.9756787317952122192039245867742 y1[1] (numeric) = 1.9756787317952122134733167276527 absolute error = 5.7306078591215e-18 relative error = 2.9005767824986145988013358831282e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.222 y2[1] (analytic) = 0.77981901978076648328022674235797 y2[1] (numeric) = 0.77981901978076648462179660363508 absolute error = 1.34156986127711e-18 relative error = 1.7203605288497203989274500394242e-16 % h = 0.001 y1[1] (analytic) = 1.9754590385811684603478797042797 y1[1] (numeric) = 1.9754590385811684545712501309514 absolute error = 5.7766295733283e-18 relative error = 2.9241960782326530161432894555125e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.4MB, time=14.90 NO POLE NO POLE x[1] = 0.223 y2[1] (analytic) = 0.778843670995242748530803510147 y2[1] (numeric) = 0.77884367099524274988919314743916 absolute error = 1.35838963729216e-18 relative error = 1.7441107732908022482199500277238e-16 % h = 0.001 y1[1] (analytic) = 1.975238369908167408573879962885 y1[1] (numeric) = 1.9752383699081674027512564449239 absolute error = 5.8226235179611e-18 relative error = 2.9478080249280520254149658256522e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.224 y2[1] (analytic) = 0.77786854336602958884516234048672 y2[1] (numeric) = 0.77786854336602959022046507219379 absolute error = 1.37530273170707e-18 relative error = 1.7680400415162630256177083765571e-16 % h = 0.001 y1[1] (analytic) = 1.9750167259968777184939216661375 y1[1] (numeric) = 1.9750167259968777126253321137993 absolute error = 5.8685895523382e-18 relative error = 2.9714125835446102376737693403695e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.4MB, time=15.14 NO POLE NO POLE x[1] = 0.225 y2[1] (analytic) = 0.7768936378682545521758298599428 y2[1] (numeric) = 0.77689363786825455356813896541659 absolute error = 1.39230910547379e-18 relative error = 1.7921489346909769184755149191978e-16 % h = 0.001 y1[1] (analytic) = 1.9747941070689432829273695688655 y1[1] (numeric) = 1.9747941070689432770128420330377 absolute error = 5.9145275358278e-18 relative error = 2.9950097150159837892646863802632e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.226 y2[1] (analytic) = 0.77591895547682305505572063133211 y2[1] (numeric) = 0.77591895547682305646512935068843 absolute error = 1.40940871935632e-18 relative error = 1.8164380563305100036652810667189e-16 % h = 0.001 y1[1] (analytic) = 1.9745705133469830112570825281373 y1[1] (numeric) = 1.9745705133469830052966452002889 absolute error = 5.9604373278484e-18 relative error = 3.0185993802496316814299655792683e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.4MB, time=15.37 NO POLE NO POLE x[1] = 0.227 y2[1] (analytic) = 0.77494449716641740769280186292349 y2[1] (numeric) = 0.77494449716641740911940339685429 absolute error = 1.42660153393080e-18 relative error = 1.8409080123120622157151959630438e-16 % h = 0.001 y1[1] (analytic) = 1.9743459450545906068105226719777 y1[1] (numeric) = 1.9743459450545906008042038841088 absolute error = 6.0063187878689e-18 relative error = 3.0421815401266091002591331490020e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.228 y2[1] (analytic) = 0.7739702639114958392878644239937 y2[1] (numeric) = 0.77397026391149584073175193357924 absolute error = 1.44388750958554e-18 relative error = 1.8655594108853899972558086852086e-16 % h = 0.001 y1[1] (analytic) = 1.9741204024163343432660707047136 y1[1] (numeric) = 1.9741204024163343372138989293046 absolute error = 6.0521717754090e-18 relative error = 3.0657561555015125285075515090914e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.4MB, time=15.61 NO POLE NO POLE x[1] = 0.229 y2[1] (analytic) = 0.77299625668629152357637484888623 y2[1] (numeric) = 0.77299625668629152503764145540736 absolute error = 1.46126660652113e-18 relative error = 1.8903928626838904147431835415459e-16 % h = 0.001 y1[1] (analytic) = 1.9738938856577568400847709426156 y1[1] (numeric) = 1.9738938856577568339867747925764 absolute error = 6.0979961500392e-18 relative error = 3.0893231872022221409259054900933e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.23 y2[1] (analytic) = 0.77202247646481160459538278763993 y2[1] (numeric) = 0.77202247646481160607412157239038 absolute error = 1.47873878475045e-18 relative error = 1.9154089807356148504255104394481e-16 % h = 0.001 y1[1] (analytic) = 1.9736663950053748369677306480716 y1[1] (numeric) = 1.9736663950053748308239388766902 absolute error = 6.1437917713814e-18 relative error = 3.1128825960299479910568436700938e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=15.85 NO POLE NO POLE x[1] = 0.231 y2[1] (analytic) = 0.77104892422083622267645813619863 y2[1] (numeric) = 0.77104892422083622417276214029738 absolute error = 1.49630400409875e-18 relative error = 1.9406083804744319642702044017992e-16 % h = 0.001 y1[1] (analytic) = 1.9734379306866789673393992048733 y1[1] (numeric) = 1.9734379306866789611498407057647 absolute error = 6.1895584991086e-18 relative error = 3.1364343427588201390182797057775e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.232 y2[1] (analytic) = 0.77007560092791754066563185318355 y2[1] (numeric) = 0.7700756009279175421795940773873 absolute error = 1.51396222420375e-18 relative error = 1.9659916797512761546478051422253e-16 % h = 0.001 y1[1] (analytic) = 1.9732084929301335308569536513194 y1[1] (numeric) = 1.9732084929301335246216574583737 absolute error = 6.2352961929457e-18 relative error = 3.1599783881360359280327705807626e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=16.09 NO POLE NO POLE x[1] = 0.233 y2[1] (analytic) = 0.76910250755937877037131424320659 y2[1] (numeric) = 0.76910250755937877190302764772223 absolute error = 1.53171340451564e-18 relative error = 1.9915594988453260839710026673788e-16 % h = 0.001 y1[1] (analytic) = 1.9729780819651762649460180617296 y1[1] (numeric) = 1.9729780819651762586650133490602 absolute error = 6.2810047126694e-18 relative error = 3.1835146928815511657596639321508e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.234 y2[1] (analytic) = 0.7681296450883131992411642587249 y2[1] (numeric) = 0.76812964508831320079072176302211 absolute error = 1.54955750429721e-18 relative error = 2.0173124604754119114180935551744e-16 % h = 0.001 y1[1] (analytic) = 1.972746698022218115362945240631 y1[1] (numeric) = 1.9727466980222181090362613225226 absolute error = 6.3266839181084e-18 relative error = 3.2070432176879231272779748520401e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=16.32 NO POLE NO POLE x[1] = 0.235 y2[1] (analytic) = 0.7671570144875832172688831434866 y2[1] (numeric) = 0.76715701448758321883637762611043 absolute error = 1.56749448262383e-18 relative error = 2.0432511898112881115929401080682e-16 % h = 0.001 y1[1] (analytic) = 1.9725143413326430057838901673172 y1[1] (numeric) = 1.9725143413326429994115564981733 absolute error = 6.3723336691439e-18 relative error = 3.2305639232203055025611096463546e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.236 y2[1] (analytic) = 0.76618461672981934413190551069257 y2[1] (numeric) = 0.76618461672981934571742980907619 absolute error = 1.58552429838362e-18 relative error = 2.0693763144852142729531143209963e-16 % h = 0.001 y1[1] (analytic) = 1.9722810121288076064209056016861 y1[1] (numeric) = 1.9722810121288076000029517759763 absolute error = 6.4179538257098e-18 relative error = 3.2540767701162911972157895765561e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=16.56 NO POLE NO POLE x[1] = 0.237 y2[1] (analytic) = 0.76521245278741925656096071810253 y2[1] (numeric) = 0.76521245278741925816460762837995 absolute error = 1.60364691027742e-18 relative error = 2.0956884646033367831534703111036e-16 % h = 0.001 y1[1] (analytic) = 1.9720467106440411016652912352422 y1[1] (numeric) = 1.9720467106440410952017469874498 absolute error = 6.4635442477924e-18 relative error = 3.2775817189855014432728921806352e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.238 y2[1] (analytic) = 0.76424052363254681594247717044265 y2[1] (numeric) = 0.76424052363254681756433944726156 absolute error = 1.62186227681891e-18 relative error = 2.1221882727573274274503332891172e-16 % h = 0.001 y1[1] (analytic) = 1.9718114371126449567584287438953 y1[1] (numeric) = 1.9718114371126449502493239484639 absolute error = 6.5091047954314e-18 relative error = 3.3010787304098338735606062956116e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.4MB, time=16.80 NO POLE NO POLE x[1] = 0.239 y2[1] (analytic) = 0.76326883023713109615480194662958 y2[1] (numeric) = 0.76326883023713109779497230296423 absolute error = 1.64017035633465e-18 relative error = 2.1488763740359796821831332333630e-16 % h = 0.001 y1[1] (analytic) = 1.9715751917698926834903360717 y1[1] (numeric) = 1.9715751917698926769357007429804 absolute error = 6.5546353287196e-18 relative error = 3.3245677649430513664860400159532e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.24 y2[1] (analytic) = 0.76229737357286541163920791551018 y2[1] (numeric) = 0.76229737357286541329777902247432 absolute error = 1.65857110696414e-18 relative error = 2.1757534060368933337846704344359e-16 % h = 0.001 y1[1] (analytic) = 1.9713379748520296049261752469634 y1[1] (numeric) = 1.9713379748520295983260395391598 absolute error = 6.6001357078036e-18 relative error = 3.3480487831108778296442824806928e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.4MB, time=17.03 NO POLE NO POLE x[1] = 0.241 y2[1] (analytic) = 0.76132615461120634570666026902879 y2[1] (numeric) = 0.7613261546112063473837247556887 absolute error = 1.67706448665991e-18 relative error = 2.2028200088782611717868358679043e-16 % h = 0.001 y1[1] (analytic) = 1.9710997865962726191609490041922 y1[1] (numeric) = 1.9710997865962726125153432113088 absolute error = 6.6456057928834e-18 relative error = 3.3715217454105359525953321927945e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.242 y2[1] (analytic) = 0.76035517432337277908131416597463 y2[1] (numeric) = 0.7603551743233727807769646191622 absolute error = 1.69565045318757e-18 relative error = 2.2300768252106664292479618205777e-16 % h = 0.001 y1[1] (analytic) = 1.9708606272408099621026224571645 y1[1] (numeric) = 1.9708606272408099554115770129514 absolute error = 6.6910454442131e-18 relative error = 3.3949866123108427202602568223868e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=17.27 NO POLE NO POLE x[1] = 0.243 y2[1] (analytic) = 0.75938443368034491868171494273065 y2[1] (numeric) = 0.75938443368034492039604390685656 absolute error = 1.71432896412591e-18 relative error = 2.2575245002290094053978525913195e-16 % h = 0.001 y1[1] (analytic) = 1.9706204970248009692839070399837 y1[1] (numeric) = 1.9706204970248009625474525178825 absolute error = 6.7364545221012e-18 relative error = 3.4184433442521019772080586247246e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.244 y2[1] (analytic) = 0.7584139336528633266406721097428 y2[1] (numeric) = 0.75841393365286332837377208660968 absolute error = 1.73309997686688e-18 relative error = 2.2851636816843400961848044076444e-16 % h = 0.001 y1[1] (analytic) = 1.9703793961883758367029449043108 y1[1] (numeric) = 1.9703793961883758299211120174004 absolute error = 6.7818328869104e-18 relative error = 3.4418919016457431192030151489812e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=17.52 NO POLE NO POLE x[1] = 0.245 y2[1] (analytic) = 0.7574436752114279495647781137546 y2[1] (numeric) = 0.75744367521142795131674156237034 absolute error = 1.75196344861574e-18 relative error = 2.3129950198959786753646732489505e-16 % h = 0.001 y1[1] (analytic) = 1.9701373249726353806931329320715 y1[1] (numeric) = 1.9701373249726353738659525330131 absolute error = 6.8271803990584e-18 relative error = 3.4653322448744670616566288542110e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.246 y2[1] (analytic) = 0.75647365932629714803454260620757 y2[1] (numeric) = 0.75647365932629714980546194259869 absolute error = 1.77091933639112e-18 relative error = 2.3410191677635825282113948392558e-16 % h = 0.001 y1[1] (analytic) = 1.9698942836196507968223264937931 y1[1] (numeric) = 1.9698942836196507899498295747756 absolute error = 6.8724969190175e-18 relative error = 3.4887643342917831090181315874954e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.4MB, time=17.76 NO POLE NO POLE x[1] = 0.247 y2[1] (analytic) = 0.75550388696748672634611271759229 y2[1] (numeric) = 0.75550388696748672813608031461731 absolute error = 1.78996759702502e-18 relative error = 2.3692367807791988816125429754715e-16 % h = 0.001 y1[1] (analytic) = 1.9696502723724634178216640533481 y1[1] (numeric) = 1.9696502723724634109038817460329 absolute error = 6.9177823073152e-18 relative error = 3.5121881302220531488266229530077e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.248 y2[1] (analytic) = 0.75453435910476896249554959594889 y2[1] (numeric) = 0.75453435910476896430465778311186 absolute error = 1.80910818716297e-18 relative error = 2.3976485170395942863097220995814e-16 % h = 0.001 y1[1] (analytic) = 1.9694052914750844705442546902599 y1[1] (numeric) = 1.9694052914750844635812182657252 absolute error = 6.9630364245347e-18 relative error = 3.5356035929604850640080886144295e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.4MB, time=18.00 NO POLE NO POLE x[1] = 0.249 y2[1] (analytic) = 0.75356507670767163840663122515975 y2[1] (numeric) = 0.75356507670767164023497228842376 absolute error = 1.82834106326401e-18 relative error = 2.4262550372584120692331519930157e-16 % h = 0.001 y1[1] (analytic) = 1.9691593411724948319539715808613 y1[1] (numeric) = 1.9691593411724948249457124495469 absolute error = 7.0082591313144e-18 relative error = 3.5590106827726182725162958523162e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.25 y2[1] (analytic) = 0.75259604074547707040315129515061 y2[1] (numeric) = 0.75259604074547707225081747675145 absolute error = 1.84766618160084e-18 relative error = 2.4550570047786210732717888769545e-16 % h = 0.001 y1[1] (analytic) = 1.9689124217106447841445954494942 y1[1] (numeric) = 1.9689124217106447770911451611452 absolute error = 7.0534502883490e-18 relative error = 3.5824093598946214752535752159240e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=18.23 NO POLE NO POLE x[1] = 0.251 y2[1] (analytic) = 0.75162725218722113992668365162059 y2[1] (numeric) = 0.7516272521872211417937671498804 absolute error = 1.86708349825981e-18 relative error = 2.4840550855848190762994506935332e-16 % h = 0.001 y1[1] (analytic) = 1.9686645333364537683895529705847 y1[1] (numeric) = 1.9686645333364537612909432141959 absolute error = 7.0986097563888e-18 relative error = 3.6057995845326762646190754593926e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.252 y2[1] (analytic) = 0.75065871200169232450078160745575 y2[1] (numeric) = 0.75065871200169232638737457659678 absolute error = 1.88659296914103e-18 relative error = 2.5132499483157623907465915438176e-16 % h = 0.001 y1[1] (analytic) = 1.9684156762978101382224960718362 y1[1] (numeric) = 1.9684156762978101310787586755953 absolute error = 7.1437373962409e-18 relative error = 3.6291813168633254729223324508754e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.4MB, time=18.48 NO POLE NO POLE x[1] = 0.253 y2[1] (analytic) = 0.74969042115743072894258115154618 y2[1] (numeric) = 0.74969042115743073084877570150465 absolute error = 1.90619454995847e-18 relative error = 2.5426422642769500917694994531628e-16 % h = 0.001 y1[1] (analytic) = 1.9681658508435709115489690579392 y1[1] (numeric) = 1.9681658508435709043601359891706 absolute error = 7.1888330687686e-18 relative error = 3.6525545170329071894953598818371e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.254 y2[1] (analytic) = 0.7487223806227271168227768433228 y2[1] (numeric) = 0.74872238062272711874866503956276 absolute error = 1.92588819623996e-18 relative error = 2.5722327074531429690808214740404e-16 % h = 0.001 y1[1] (analytic) = 1.9679150572235615217894114431114 y1[1] (numeric) = 1.9679150572235615145555148082193 absolute error = 7.2338966348921e-18 relative error = 3.6759191451576489065573136617991e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.4MB, time=18.72 NO POLE NO POLE x[1] = 0.255 y2[1] (analytic) = 0.74775459136562194217493893295701 y2[1] (numeric) = 0.7477545913656219441206127962843 absolute error = 1.94567386332729e-18 relative error = 2.6020219545210838824608041579983e-16 % h = 0.001 y1[1] (analytic) = 1.9676632956885755680537453494437 y1[1] (numeric) = 1.9676632956885755607748173938549 absolute error = 7.2789279555888e-18 relative error = 3.6992751613235584111480416160473e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.256 y2[1] (analytic) = 0.7467870543539043814551399978256 y2[1] (numeric) = 0.74678705435390438342069150420192 absolute error = 1.96555150637632e-18 relative error = 2.6320106848623006346203854871372e-16 % h = 0.001 y1[1] (analytic) = 1.9674105664903745643477972964435 y1[1] (numeric) = 1.9674105664903745570238704045504 absolute error = 7.3239268918931e-18 relative error = 3.7226225255860604139829747818570e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.4MB, time=18.96 NO POLE NO POLE x[1] = 0.257 y2[1] (analytic) = 0.74581977055511136575285913553355 y2[1] (numeric) = 0.74581977055511136773838021589052 absolute error = 1.98552108035697e-18 relative error = 2.6621995805758176066047017331768e-16 % h = 0.001 y1[1] (analytic) = 1.967156869881687687811805175334 y1[1] (numeric) = 1.9671568698816876804429118704371 absolute error = 7.3688933048969e-18 relative error = 3.7459611979699887028832070626424e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.258 y2[1] (analytic) = 0.74485274093652661325413150250981 y2[1] (numeric) = 0.74485274093652661525971404256315 absolute error = 2.00558254005334e-18 relative error = 2.6925893264911107626147110524122e-16 % h = 0.001 y1[1] (analytic) = 1.9669022061162115259912621695806 y1[1] (numeric) = 1.9669022061162115185774351138304 absolute error = 7.4138270557502e-18 relative error = 3.7692911384696290919168873642229e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.4MB, time=19.20 NO POLE NO POLE x[1] = 0.259 y2[1] (analytic) = 0.74388596646517966195791073494597 y2[1] (numeric) = 0.74388596646517966398364657500977 absolute error = 2.02573584006380e-18 relative error = 2.7231806101810929503482824046963e-16 % h = 0.001 y1[1] (analytic) = 1.9666465754486098231403503507787 y1[1] (numeric) = 1.9666465754486098156816223451182 absolute error = 7.4587280056605e-18 relative error = 3.7926123070481521895692988589464e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.26 y2[1] (analytic) = 0.74291944810784490264661153563478 y2[1] (numeric) = 0.74291944810784490469259247043579 absolute error = 2.04598093480101e-18 relative error = 2.7539741219750757270851664064408e-16 % h = 0.001 y1[1] (analytic) = 1.9663899781345132255582176464501 y1[1] (numeric) = 1.9663899781345132180546216305564 absolute error = 7.5035960158937e-18 relative error = 3.8159246636378085044364082196157e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.4MB, time=19.44 NO POLE NO POLE x[1] = 0.261 y2[1] (analytic) = 0.74195318683104061211179945608533 y2[1] (numeric) = 0.74195318683104061417811723457736 absolute error = 2.06631777849203e-18 relative error = 2.7849705549719229391957827977227e-16 % h = 0.001 y1[1] (analytic) = 1.9661324144305190259583528434479 y1[1] (numeric) = 1.9661324144305190184099218956739 absolute error = 7.5484309477740e-18 relative error = 3.8392281681396150506781999642700e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.262 y2[1] (analytic) = 0.74098718360102798663599464814456 y2[1] (numeric) = 0.7409871836010279887227409733229 absolute error = 2.08674632517834e-18 relative error = 2.8161706050531546794938713359115e-16 % h = 0.001 y1[1] (analytic) = 1.9658738845941909068713142575752 y1[1] (numeric) = 1.9658738845941908992780815948906 absolute error = 7.5932326626846e-18 relative error = 3.8625227804234486113601989522027e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.4MB, time=19.67 NO POLE NO POLE x[1] = 0.263 y2[1] (analytic) = 0.74002143938381017573155610324072 y2[1] (numeric) = 0.74002143938381017783882263195673 absolute error = 2.10726652871601e-18 relative error = 2.8475749708963252752620598602009e-16 % h = 0.001 y1[1] (analytic) = 1.9656143888840586830810686666656 y1[1] (numeric) = 1.9656143888840586754430676445985 absolute error = 7.6380010220671e-18 relative error = 3.8858084603274776648906046957916e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=320.4MB, alloc=4.4MB, time=19.90 x[1] = 0.264 y2[1] (analytic) = 0.73905595514513131613761264028424 y2[1] (numeric) = 0.7390559551451313182654909830599 absolute error = 2.12787834277566e-18 relative error = 2.8791843539881904954041969719680e-16 % h = 0.001 y1[1] (analytic) = 1.9653539275596180430951980707674 y1[1] (numeric) = 1.965353927559618035412462183345 absolute error = 7.6827358874224e-18 relative error = 3.9090851676583570426715136752864e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.265 y2[1] (analytic) = 0.73809073185047556607600664521424 y2[1] (numeric) = 0.73809073185047556822458836605682 absolute error = 2.14858172084258e-18 relative error = 2.9109994586381631278983766584230e-16 % h = 0.001 y1[1] (analytic) = 1.9650925008813302896492328092017 y1[1] (numeric) = 1.9650925008813302819217956888907 absolute error = 7.7274371203110e-18 relative error = 3.9323528621911173713003906220324e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.4MB, time=20.14 NO POLE NO POLE x[1] = 0.266 y2[1] (analytic) = 0.73712577046506613976721630616662 y2[1] (numeric) = 0.73712577046506614193659292238347 absolute error = 2.16937661621685e-18 relative error = 2.9430209919918422985001193056822e-16 % h = 0.001 y1[1] (analytic) = 1.9648301091106220792453705301393 y1[1] (numeric) = 1.9648301091106220714732659477868 absolute error = 7.7721045823525e-18 relative error = 3.9556115036686472269329763334560e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.267 y2[1] (analytic) = 0.73616107195386434220722182826113 y2[1] (numeric) = 0.73616107195386434439748481027445 absolute error = 2.19026298201332e-18 relative error = 2.9752496640444268158048323118387e-16 % h = 0.001 y1[1] (analytic) = 1.9645667525098851607258414739579 y1[1] (numeric) = 1.9645667525098851529091033387309 absolute error = 7.8167381352270e-18 relative error = 3.9788610518021419681931348208480e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.4MB, time=20.38 NO POLE NO POLE x[1] = 0.268 y2[1] (analytic) = 0.73519663728156860420628085106048 y2[1] (numeric) = 0.73519663728156860641752162222223 absolute error = 2.21124077116175e-18 relative error = 3.0076861876544193145590178381852e-16 % h = 0.001 y1[1] (analytic) = 1.9643024313424761128811814969892 y1[1] (numeric) = 1.9643024313424761050198438563153 absolute error = 7.8613376406739e-18 relative error = 4.0021014662702292641390591340761e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.269 y2[1] (analytic) = 0.73423246741261351769057802984597 y2[1] (numeric) = 0.73423246741261351992288796625283 absolute error = 2.23230993640686e-18 relative error = 3.0403312785572831611242093500320e-16 % h = 0.001 y1[1] (analytic) = 1.9640371458727160810936752273647 y1[1] (numeric) = 1.9640371458727160731877722668715 absolute error = 7.9059029604932e-18 relative error = 4.0253327067193667638570440145746e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.4MB, time=20.61 NO POLE NO POLE x[1] = 0.27 y2[1] (analytic) = 0.73326856331116887126771347897946 y2[1] (numeric) = 0.73326856331116887352118390928787 absolute error = 2.25347043030841e-18 relative error = 3.0731856553792151163304696754523e-16 % h = 0.001 y1[1] (analytic) = 1.9637708963658905130162327094922 y1[1] (numeric) = 1.9637708963658905050657987529466 absolute error = 7.9504339565456e-18 relative error = 4.0485547327636289767351857490409e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.271 y2[1] (analytic) = 0.73230492594113868605699451178298 y2[1] (numeric) = 0.73230492594113868833171671702424 absolute error = 2.27472220524126e-18 relative error = 3.1062500396509663226946103796082e-16 % h = 0.001 y1[1] (analytic) = 1.9635036830882488932869638582654 y1[1] (numeric) = 1.9635036830882488852920333675131 absolute error = 7.9949304907523e-18 relative error = 4.0717675039843411508648332345393e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.4MB, time=20.85 NO POLE NO POLE x[1] = 0.272 y2[1] (analytic) = 0.73134155626616025178549484656383 y2[1] (numeric) = 0.73134155626616025408156005995929 absolute error = 2.29606521339546e-18 relative error = 3.1395251558217802053074911536040e-16 % h = 0.001 y1[1] (analytic) = 1.9632355063070044772797160084106 y1[1] (numeric) = 1.9632355063070044692403235833151 absolute error = 8.0393924250955e-18 relative error = 4.0949709799300693652139778593101e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.273 y2[1] (analytic) = 0.73037845524960316315084518264563 y2[1] (numeric) = 0.73037845524960316546834458942197 absolute error = 2.31749940677634e-18 relative error = 3.1730117312734070656005564190675e-16 % h = 0.001 y1[1] (analytic) = 1.9629663662903340238908408084099 y1[1] (numeric) = 1.9629663662903340158070211867911 absolute error = 8.0838196216188e-18 relative error = 4.1181651201165596281182799794742e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.4MB, time=21.09 NO POLE NO POLE x[1] = 0.274 y2[1] (analytic) = 0.72941562385456835645171878353456 y2[1] (numeric) = 0.72941562385456835879074352073908 absolute error = 2.33902473720452e-18 relative error = 3.2067104963340861723375845329153e-16 % h = 0.001 y1[1] (analytic) = 1.9626962633073775273624576722117 y1[1] (numeric) = 1.9626962633073775192342457297848 absolute error = 8.1282119424269e-18 relative error = 4.1413498840263202318560632249207e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.275 y2[1] (analytic) = 0.72845306304388714648697543665472 y2[1] (numeric) = 0.72845306304388714884761659297079 absolute error = 2.36064115631607e-18 relative error = 3.2406221842928105574991577914248e-16 % h = 0.001 y1[1] (analytic) = 1.9624251976282379481424819654439 y1[1] (numeric) = 1.9624251976282379399699127157575 absolute error = 8.1725692496864e-18 relative error = 4.1645252311087642510639015414287e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.4MB, time=21.32 NO POLE NO POLE x[1] = 0.276 y2[1] (analytic) = 0.72749077378012026372442689042862 y2[1] (numeric) = 0.72749077378012026610677550599113 absolute error = 2.38234861556251e-18 relative error = 3.2747475314134507822311896771062e-16 % h = 0.001 y1[1] (analytic) = 1.9621531695239809427816870660775 y1[1] (numeric) = 1.9621531695239809345647956604517 absolute error = 8.2168914056258e-18 relative error = 4.1876911207799444011983882855127e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.277 y2[1] (analytic) = 0.72652875702555689174018659985692 y2[1] (numeric) = 0.72652875702555689414433366606787 absolute error = 2.40414706621095e-18 relative error = 3.3090872769491490544044380130697e-16 % h = 0.001 y1[1] (analytic) = 1.9618801792666345928680704024572 y1[1] (numeric) = 1.9618801792666345846068921299216 absolute error = 8.2611782725356e-18 relative error = 4.2108475124223386059785166519666e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.4MB, time=21.56 NO POLE NO POLE x[1] = 0.278 y2[1] (analytic) = 0.72556701374221370492956634116763 y2[1] (numeric) = 0.72556701374221370735560280051174 absolute error = 2.42603645934411e-18 relative error = 3.3436421631566276320293655099001e-16 % h = 0.001 y1[1] (analytic) = 1.9616062271291891329987945343101 y1[1] (numeric) = 1.9616062271291891246933648215413 absolute error = 8.3054297127688e-18 relative error = 4.2339943653848392574531480317961e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.279 y2[1] (analytic) = 0.72460554489183390649048198455785 y2[1] (numeric) = 0.72460554489183390893849873041828 absolute error = 2.44801674586043e-18 relative error = 3.3784129353107002920804069279264e-16 % h = 0.001 y1[1] (analytic) = 1.9613313133855966777899753047686 y1[1] (numeric) = 1.9613313133855966694403297160277 absolute error = 8.3496455887409e-18 relative error = 4.2571316389824874952647841077356e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.4MB, time=21.80 NO POLE NO POLE x[1] = 0.28 y2[1] (analytic) = 0.72364435143588626668033044154215 y2[1] (numeric) = 0.7236443514358862691504183180163 absolute error = 2.47008787647415e-18 relative error = 3.4134003417188226877526170242677e-16 % h = 0.001 y1[1] (analytic) = 1.9610554383107709479245900535965 y1[1] (numeric) = 1.9610554383107709395307642906663 absolute error = 8.3938257629302e-18 relative error = 4.2802592924963601984146819302869e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.281 y2[1] (analytic) = 0.72268343433556416134729952995054 y2[1] (numeric) = 0.72268343433556416383954933166589 absolute error = 2.49224980171535e-18 relative error = 3.4486051337356678781708435712607e-16 % h = 0.001 y1[1] (analytic) = 1.9607786021805869952387798436879 y1[1] (numeric) = 1.9607786021805869868008097458098 absolute error = 8.4379700978781e-18 relative error = 4.3033772851734568381890713943774e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.4MB, time=22.04 NO POLE NO POLE x[1] = 0.282 y2[1] (analytic) = 0.72172279455178461073707222518593 y2[1] (numeric) = 0.721722794551784613251574697116 absolute error = 2.51450247193007e-18 relative error = 3.4840280657778932917112639847680e-16 % h = 0.001 y1[1] (analytic) = 1.9605008052718809268468206145129 y1[1] (numeric) = 1.9605008052718809183647421583235 absolute error = 8.4820784561894e-18 relative error = 4.3264855762265861918613774739034e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.283 y2[1] (analytic) = 0.72076243304518731857588649095688 y2[1] (numeric) = 0.72076243304518732111273232823724 absolute error = 2.53684583728036e-18 relative error = 3.5196698953388925517950300819035e-16 % h = 0.001 y1[1] (analytic) = 1.9602220478624496283050391375165 y1[1] (numeric) = 1.9602220478624496197788884369842 absolute error = 8.5261507005323e-18 relative error = 4.3495841248340998728983949709189e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.4MB, time=22.28 NO POLE NO POLE x[1] = 0.284 y2[1] (analytic) = 0.71980235077613371143091160634557 y2[1] (numeric) = 0.71980235077613371399019145408994 absolute error = 2.55927984774437e-18 relative error = 3.5555313830036845970289874815943e-16 % h = 0.001 y1[1] (analytic) = 1.9599423302310504858149506095312 y1[1] (numeric) = 1.9599423302310504772447639158926 absolute error = 8.5701866936386e-18 relative error = 4.3726728901397276339367351565447e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.285 y2[1] (analytic) = 0.71884254870470597834890162875478 y2[1] (numeric) = 0.71884254870470598093070608187118 absolute error = 2.58180445311640e-18 relative error = 3.5916132924638298411954282852729e-16 % h = 0.001 y1[1] (analytic) = 1.959661652657401107465895681044 y1[1] (numeric) = 1.9596616526574010988517093827395 absolute error = 8.6141862983045e-18 relative error = 4.3957518312527186596134013461262e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.4MB, time=22.52 NO POLE NO POLE x[1] = 0.286 y2[1] (analytic) = 0.71788302779070611077408635400021 y2[1] (numeric) = 0.71788302779070611337850595700724 absolute error = 2.60441960300703e-18 relative error = 3.6279163905325405341119082823644e-16 % h = 0.001 y1[1] (analytic) = 1.9593800154221790435174556766546 y1[1] (numeric) = 1.9593800154221790348593062992648 absolute error = 8.6581493773898e-18 relative error = 4.4188209072471663522113935526624e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.287 y2[1] (analytic) = 0.71692378899365494274625985557732 y2[1] (numeric) = 0.71692378899365494537338510242049 absolute error = 2.62712524684317e-18 relative error = 3.6644414471597637148363716675441e-16 % h = 0.001 y1[1] (analytic) = 1.9590974188070215057219257252902 y1[1] (numeric) = 1.9590974188070214970198499314708 absolute error = 8.7020757938194e-18 relative error = 4.4418800771625065006808611790486e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.4MB, time=22.75 NO POLE NO POLE x[1] = 0.288 y2[1] (analytic) = 0.71596483327279119138002640493412 y2[1] (numeric) = 0.71596483327279119402994773880223 absolute error = 2.64992133386811e-18 relative error = 3.7011892354473479829970767388220e-16 % h = 0.001 y1[1] (analytic) = 1.9588138630945250856871264776764 y1[1] (numeric) = 1.9588138630945250769411610670941 absolute error = 8.7459654105823e-18 relative error = 4.4649293000027395534775625592403e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.289 y2[1] (analytic) = 0.71500616158707049762616329342395 y2[1] (numeric) = 0.71500616158707050029897110656559 absolute error = 2.67280781314164e-18 relative error = 3.7381605316643925204852912252615e-16 % h = 0.001 y1[1] (analytic) = 1.9585293485682454722798360482323 y1[1] (numeric) = 1.9585293485682454634900179574995 absolute error = 8.7898180907328e-18 relative error = 4.4879685347367754636278533067768e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.4MB, time=22.99 NO POLE NO POLE x[1] = 0.29 y2[1] (analytic) = 0.71404777489516446731605979449563 y2[1] (numeric) = 0.71404777489516447001184442803576 absolute error = 2.69578463354013e-18 relative error = 3.7753561152626257667634753561139e-16 % h = 0.001 y1[1] (analytic) = 1.9582438755126971680701247779319 y1[1] (numeric) = 1.9582438755126971592364910805418 absolute error = 8.8336336973901e-18 relative error = 4.5109977402979617303174267964475e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.291 y2[1] (analytic) = 0.71308967415545971249019122160201 y2[1] (numeric) = 0.7130896741554597152090429653586 absolute error = 2.71885174375659e-18 relative error = 3.8127767688918418130379405978563e-16 % h = 0.001 y1[1] (analytic) = 1.9579574442133532048168763737751 y1[1] (numeric) = 1.9579574442133531959394642800363 absolute error = 8.8774120937388e-18 relative error = 4.5340168755840706458686126031958e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.4MB, time=23.23 NO POLE NO POLE x[1] = 0.292 y2[1] (analytic) = 0.71213186032605689301158675327299 y2[1] (numeric) = 0.71213186032605689575359584557372 absolute error = 2.74200909230073e-18 relative error = 3.8504232784154228811787459524114e-16 % h = 0.001 y1[1] (analytic) = 1.9576700549566448579947799393226 y1[1] (numeric) = 1.9576700549566448490736267962935 absolute error = 8.9211531430291e-18 relative error = 4.5570258994571332425026185969552e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.293 y2[1] (analytic) = 0.71117433436476975846524941180534 y2[1] (numeric) = 0.71117433436476976123050603930443 absolute error = 2.76525662749909e-18 relative error = 3.8882964329260468633845200400651e-16 % h = 0.001 y1[1] (analytic) = 1.9573817080299613603630783692788 y1[1] (numeric) = 1.9573817080299613513982216607017 absolute error = 8.9648567085771e-18 relative error = 4.5800247707433241362302205967788e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.4MB, time=23.47 NO POLE NO POLE x[1] = 0.294 y2[1] (analytic) = 0.71021709722912419034448629606947 y2[1] (numeric) = 0.71021709722912419313308059356457 absolute error = 2.78859429749510e-18 relative error = 3.9263970247613842795600116561385e-16 % h = 0.001 y1[1] (analytic) = 1.9570924037216496145763595393507 y1[1] (numeric) = 1.9570924037216496055678368855859 absolute error = 9.0085226537648e-18 relative error = 4.6030134482326929349350079975121e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.295 y2[1] (analytic) = 0.70926014987635724452510688202316 y2[1] (numeric) = 0.70926014987635724733712893227229 absolute error = 2.81202205024913e-18 relative error = 3.9647258495198688784886237242808e-16 % h = 0.001 y1[1] (analytic) = 1.956802142321013904837677680568 y1[1] (numeric) = 1.9568021423210138957855268385275 absolute error = 9.0521508420405e-18 relative error = 4.6259918906790997775929820153881e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.4MB, time=23.71 NO POLE NO POLE x[1] = 0.296 y2[1] (analytic) = 0.70830349326341619402844691665405 y2[1] (numeric) = 0.70830349326341619686398675019265 absolute error = 2.83553983353860e-18 relative error = 4.0032837060766411362723513233472e-16 % h = 0.001 y1[1] (analytic) = 1.9565109241183156075942932849186 y1[1] (numeric) = 1.9565109241183155984985521479994 absolute error = 9.0957411369192e-18 relative error = 4.6489600568001507699213285559729e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.297 y2[1] (analytic) = 0.70734712834695757207417514224732 y2[1] (numeric) = 0.7073471283469575749333227372054 absolute error = 2.85914759495808e-18 relative error = 4.0420713965995670545584570998394e-16 % h = 0.001 y1[1] (analytic) = 1.9562187494047729012763208465347 y1[1] (numeric) = 1.9562187494047728921370274445523 absolute error = 9.1392934019824e-18 relative error = 4.6719179052768266024610662687811e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.4MB, time=23.94 NO POLE NO POLE x[1] = 0.298 y2[1] (analytic) = 0.70639105608334621542383979809208 y2[1] (numeric) = 0.70639105608334621830668508001141 absolute error = 2.88284528191933e-18 relative error = 4.0810897265652619141962525404130e-16 % h = 0.001 y1[1] (analytic) = 1.9559256184725604750785746997598 y1[1] (numeric) = 1.9559256184725604658957671988811 absolute error = 9.1828075008787e-18 relative error = 4.6948653947535198031366633161519e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.299 y2[1] (analytic) = 0.70543527742865430801611155600021 y2[1] (numeric) = 0.7054352774286543109227443976516 absolute error = 2.90663284165139e-18 relative error = 4.1203395047752746858860403338470e-16 % h = 0.001 y1[1] (analytic) = 1.9556315316148092367859041722236 y1[1] (numeric) = 1.9556315316148092275596208748998 absolute error = 9.2262832973238e-18 relative error = 4.7178024838377651702963162092357e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.4MB, time=24.18 NO POLE NO POLE x[1] = 0.3 y2[1] (analytic) = 0.70447979333866042489467925431497 y2[1] (numeric) = 0.70447979333866042782518947551568 absolute error = 2.93051022120071e-18 relative error = 4.1598215433724201492255658862444e-16 % h = 0.001 y1[1] (analytic) = 1.955336489125606019642310227568 y1[1] (numeric) = 1.9553364891256060103725895724673 absolute error = 9.2697206551007e-18 relative error = 4.7407291311000722002279230382028e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.301 y2[1] (analytic) = 0.70352460476884857642975450243418 y2[1] (numeric) = 0.70352460476884857938423186986533 absolute error = 2.95447736743115e-18 relative error = 4.1995366578570182016577526223915e-16 % h = 0.001 y1[1] (analytic) = 1.9550404912999932882641367286816 y1[1] (numeric) = 1.955040491299993278951017290621 absolute error = 9.3131194380606e-18 relative error = 4.7636452950741153646043498969355e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.4MB, time=24.42 NO POLE NO POLE x[1] = 0.302 y2[1] (analytic) = 0.70256971267440725283414093426342 y2[1] (numeric) = 0.70256971267440725581267516128754 absolute error = 2.97853422702412e-18 relative error = 4.2394856671034234931822179476714e-16 % h = 0.001 y1[1] (analytic) = 1.9547435384339688435976304082261 y1[1] (numeric) = 1.9547435384339688342411508981043 absolute error = 9.3564795101218e-18 relative error = 4.7865509342559013622583000098217e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.303 y2[1] (analytic) = 0.7016151180102284689748235944506 y2[1] (numeric) = 0.70161511801022847197750434092928 absolute error = 3.00268074647868e-18 relative error = 4.2796693933765913156782140812806e-16 % h = 0.001 y1[1] (analytic) = 1.9544456308244855269211645888734 y1[1] (numeric) = 1.954445630824485517521363853602 absolute error = 9.3998007352714e-18 relative error = 4.8094460071043681960258285093144e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.4MB, time=24.66 NO POLE NO POLE x[1] = 0.304 y2[1] (analytic) = 0.70066082173090680948103364573289 y2[1] (numeric) = 0.70066082173090681250795051784443 absolute error = 3.02691687211154e-18 relative error = 4.3200886623485941696854241414197e-16 % h = 0.001 y1[1] (analytic) = 1.9541467687694509228924226510006 y1[1] (numeric) = 1.9541467687694509134493396734362 absolute error = 9.4430829775644e-18 relative error = 4.8323304720406542455603018446877e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.305 y2[1] (analytic) = 0.69970682479073847414974328925156 y2[1] (numeric) = 0.69970682479073847720098583930878 absolute error = 3.05124255005722e-18 relative error = 4.3607443031154598309266963100980e-16 % h = 0.001 y1[1] (analytic) = 1.9538469525677270616408382006383 y1[1] (numeric) = 1.9538469525677270521545120995138 absolute error = 9.4863261011245e-18 relative error = 4.8552042874482367011011479719788e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.4MB, time=24.90 NO POLE NO POLE x[1] = 0.306 y2[1] (analytic) = 0.69875312814372032364954549226047 y2[1] (numeric) = 0.69875312814372032672520321852859 absolute error = 3.07565772626812e-18 relative error = 4.4016371482139759157841293271186e-16 % h = 0.001 y1[1] (analytic) = 1.9535461825191301199055898452054 y1[1] (numeric) = 1.9535461825191301103760598750611 absolute error = 9.5295299701443e-18 relative error = 4.8780674116727629424789141086064e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.307 y2[1] (analytic) = 0.69779973274354892552387281926885 y2[1] (numeric) = 0.69779973274354892862403516578343 absolute error = 3.10016234651458e-18 relative error = 4.4427680336385749747410741680531e-16 % h = 0.001 y1[1] (analytic) = 1.9532444589244301212194494390108 y1[1] (numeric) = 1.9532444589244301116467549901254 absolute error = 9.5726944488854e-18 relative error = 4.9009198030218305180547600187498e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.4MB, time=25.13 NO POLE NO POLE x[1] = 0.308 y2[1] (analytic) = 0.69684663954361960049450936332003 y2[1] (numeric) = 0.69684663954361960361926571970501 absolute error = 3.12475635638498e-18 relative error = 4.4841377988583723386836670164968e-16 % h = 0.001 y1[1] (analytic) = 1.9529417820853506351387836146492 y1[1] (numeric) = 1.9529417820853506255229642129709 absolute error = 9.6158194016783e-18 relative error = 4.9237614197646644622564826308167e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.309 y2[1] (analytic) = 0.6958938494970254690663494738148 y2[1] (numeric) = 0.6958938494970254722157891751006 absolute error = 3.14943970128580e-18 relative error = 4.5257472868342429218474841489921e-16 % h = 0.001 y1[1] (analytic) = 1.9526381523045684755200093702652 y1[1] (numeric) = 1.9526381523045684658611046773417 absolute error = 9.6589046929235e-18 relative error = 4.9465922201324088173890876854389e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.4MB, time=25.37 NO POLE NO POLE x[1] = 0.31 y2[1] (analytic) = 0.69494136355655649843435667604104 y2[1] (numeric) = 0.69494136355655650160856900248281 absolute error = 3.17421232644177e-18 relative error = 4.5675973440361241182087864518534e-16 % h = 0.001 y1[1] (analytic) = 1.9523335698857133978428054362022 y1[1] (numeric) = 1.9523335698857133881408552491114 absolute error = 9.7019501870908e-18 relative error = 4.9694121623174964054682026937206e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.311 y2[1] (analytic) = 0.69398918267469854969367587537158 y2[1] (numeric) = 0.69398918267469855289275005226744 absolute error = 3.19907417689586e-18 relative error = 4.6096888204601864216038468181066e-16 % h = 0.001 y1[1] (analytic) = 1.9520280351333677955803820978034 y1[1] (numeric) = 1.9520280351333677858354263490832 absolute error = 9.7449557487202e-18 relative error = 4.9922212044738376223729206459706e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.4MB, time=25.61 NO POLE NO POLE x[1] = 0.312 y2[1] (analytic) = 0.69303730780363242535385163593833 y2[1] (numeric) = 0.69303730780363242857787683344778 absolute error = 3.22402519750945e-18 relative error = 4.6520225696463607832214981965804e-16 % h = 0.001 y1[1] (analytic) = 1.9517215483530663956171131040662 y1[1] (numeric) = 1.9517215483530663858291918616445 absolute error = 9.7879212424217e-18 relative error = 5.0150193047164457550650170256565e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=415.8MB, alloc=4.4MB, time=25.84 x[1] = 0.313 y2[1] (analytic) = 0.69208573989523291715810501948532 y2[1] (numeric) = 0.69208573989523292040717035244769 absolute error = 3.24906533296237e-18 relative error = 4.6945994486957779094697501911818e-16 % h = 0.001 y1[1] (analytic) = 1.9514141098512959527138342444951 y1[1] (numeric) = 1.9514141098512959428829877116193 absolute error = 9.8308465328758e-18 relative error = 5.0378064211214206113662820670529e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.314 y2[1] (analytic) = 0.69113447990106785420862116504429 y2[1] (numeric) = 0.69113447990106785748281569279729 absolute error = 3.27419452775300e-18 relative error = 4.7374203182883932481619896099335e-16 % h = 0.001 y1[1] (analytic) = 1.9511057199354949430211141288279 y1[1] (numeric) = 1.9511057199354949331473826439943 absolute error = 9.8737314848336e-18 relative error = 5.0605825117257270729877320036316e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=419.6MB, alloc=4.4MB, time=26.08 x[1] = 0.315 y2[1] (analytic) = 0.69018352877239715139879948406602 y2[1] (numeric) = 0.69018352877239715469821221026435 absolute error = 3.29941272619833e-18 relative error = 4.7804860427006542502073375241288e-16 % h = 0.001 y1[1] (analytic) = 1.9507963789140532566408036563392 y1[1] (numeric) = 1.9507963789140532467242276932222 absolute error = 9.9165759631170e-18 relative error = 5.0833475345270246505596972210474e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.316 y2[1] (analytic) = 0.68923288746017185815341803867781 y2[1] (numeric) = 0.68923288746017186147813791111191 absolute error = 3.32471987243410e-18 relative error = 4.8237974898233841034810918640709e-16 % h = 0.001 y1[1] (analytic) = 1.9504860870963118892361716131461 y1[1] (numeric) = 1.9504860870963118792767917805272 absolute error = 9.9593798326189e-18 relative error = 5.1061014474834968268919079495781e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.4MB, time=26.31 NO POLE NO POLE x[1] = 0.317 y2[1] (analytic) = 0.6882825569150332074776633628236 y2[1] (numeric) = 0.68828255691503321082777927323844 absolute error = 3.35011591041484e-18 relative error = 4.8673555311796221904693519545266e-16 % h = 0.001 y1[1] (analytic) = 1.9501748447925626326909347873552 y1[1] (numeric) = 1.9501748447925626226887918290515 absolute error = 1.00021429583037e-17 relative error = 5.1288442085138340198170569870479e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.318 y2[1] (analytic) = 0.68733253808731166531597667717754 y2[1] (numeric) = 0.6873325380873116686915774610915 absolute error = 3.37560078391396e-18 relative error = 4.9111610419426387621315274151446e-16 % h = 0.001 y1[1] (analytic) = 1.9498626523140477648174919429938 y1[1] (numeric) = 1.9498626523140477547726267377866 absolute error = 1.00448652052072e-17 relative error = 5.1515757754969087650473435106516e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.4MB, time=26.55 NO POLE NO POLE x[1] = 0.319 y2[1] (analytic) = 0.6863828319270259802216671389056 y2[1] (numeric) = 0.68638283192702598362284157542948 absolute error = 3.40117443652388e-18 relative error = 4.9552149009541106211527665042084e-16 % h = 0.001 y1[1] (analytic) = 1.9495495099729597381146719444671 y1[1] (numeric) = 1.9495495099729597280271255060301 absolute error = 1.00875464384370e-17 relative error = 5.1742961062717070067052671080376e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.32 y2[1] (analytic) = 0.68543343938388223333824245658285 y2[1] (numeric) = 0.68543343938388223676507926823891 absolute error = 3.42683681165606e-18 relative error = 4.9995179907422547969667126995341e-16 % h = 0.001 y1[1] (analytic) = 1.9492354180824408675753072737661 y1[1] (numeric) = 1.9492354180824408574451207505935 absolute error = 1.01301865231726e-17 relative error = 5.1970051586371053647295309025610e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.4MB, time=26.79 NO POLE NO POLE x[1] = 0.321 y2[1] (analytic) = 0.68448436140727288869340688885654 y2[1] (numeric) = 0.68448436140727289214599474139765 absolute error = 3.45258785254111e-18 relative error = 5.0440711975401824448734157176343e-16 % h = 0.001 y1[1] (analytic) = 1.9489203769565830175439451328269 y1[1] (numeric) = 1.9489203769565830073711598081611 absolute error = 1.01727853246658e-17 relative error = 5.2197028903518020679077866054824e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.322 y2[1] (analytic) = 0.68353559894627584380667633277783 y2[1] (numeric) = 0.68353559894627584728510383500674 absolute error = 3.47842750222891e-18 relative error = 5.0888754113043723673641178139962e-16 % h = 0.001 y1[1] (analytic) = 1.9486043869104272876250092733052 y1[1] (numeric) = 1.9486043869104272774096665650644 absolute error = 1.02153427082408e-17 relative error = 5.2423892591340938129922002030225e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.4MB, time=27.02 NO POLE NO POLE x[1] = 0.323 y2[1] (analytic) = 0.68258715294965348061155989410811 y2[1] (numeric) = 0.68258715294965348411591559769676 absolute error = 3.50435570358865e-18 relative error = 5.1339315257331331331095929397211e-16 % h = 0.001 y1[1] (analytic) = 1.948287448259963697641726645576 y1[1] (numeric) = 1.9482874482599636873838681062816 absolute error = 1.02578585392944e-17 relative error = 5.2650642226617036832419711446167e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.324 y2[1] (analytic) = 0.68163902436585171669325701733906 y2[1] (numeric) = 0.681639024365851720223629416648 absolute error = 3.53037239930894e-18 relative error = 5.1792404382852734007878572551696e-16 % h = 0.001 y1[1] (analytic) = 1.9479695613221308716461339080079 y1[1] (numeric) = 1.9479695613221308613458012247115 absolute error = 1.03003326832964e-17 relative error = 5.2877277385717115189288391987567e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.4MB, time=27.26 NO POLE NO POLE x[1] = 0.325 y2[1] (analytic) = 0.68069121414299905684281893765035 y2[1] (numeric) = 0.68069121414299906039929646954825 absolute error = 3.55647753189790e-18 relative error = 5.2248030501988499173313567895340e-16 % h = 0.001 y1[1] (analytic) = 1.9476507264148157209804797864775 y1[1] (numeric) = 1.9476507264148157106377147806877 absolute error = 1.03427650057898e-17 relative error = 5.3103797644603814808041800955810e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.326 y2[1] (analytic) = 0.67974372322890564492872290056454 y2[1] (numeric) = 0.67974372322890564851139394424778 absolute error = 3.58267104368324e-18 relative error = 5.2706202665100083148838862798130e-16 % h = 0.001 y1[1] (analytic) = 1.9473309438568531263903402226954 y1[1] (numeric) = 1.9473309438568531160051848503048 absolute error = 1.03851553723906e-17 relative error = 5.3330202578827839839497266627005e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.4MB, time=27.50 NO POLE NO POLE x[1] = 0.327 y2[1] (analytic) = 0.67879655257106231608680727764583 y2[1] (numeric) = 0.67879655257106231969576015445819 absolute error = 3.60895287681236e-18 relative error = 5.3166929960719614612017639421299e-16 % h = 0.001 y1[1] (analytic) = 1.9470102139680256191897641982033 y1[1] (numeric) = 1.9470102139680256087622605494145 absolute error = 1.04275036487888e-17 relative error = 5.3556491763530335369112437604327e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.328 y2[1] (analytic) = 0.67784970311663964922951538822866 y2[1] (numeric) = 0.6778497031166396528648383614811 absolute error = 3.63532297325244e-18 relative error = 5.3630221515740621006516550585231e-16 % h = 0.001 y1[1] (analytic) = 1.9466885370690630614787690688678 y1[1] (numeric) = 1.94668853706906305100895936812 absolute error = 1.04698097007478e-17 relative error = 5.3782664773437048556607435142599e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.4MB, time=27.73 NO POLE NO POLE x[1] = 0.329 y2[1] (analytic) = 0.67690317581248701987539551785335 y2[1] (numeric) = 0.67690317581248702353717679264386 absolute error = 3.66178127479051e-18 relative error = 5.4096086495609555822013338540766e-16 % h = 0.001 y1[1] (analytic) = 1.9463659134816423254135051923513 y1[1] (numeric) = 1.946365913481642314901431798246 absolute error = 1.05120733941053e-17 relative error = 5.4008721182860190141892184498378e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.33 y2[1] (analytic) = 0.67595697160513165329980430382978 y2[1] (numeric) = 0.67595697160513165698813202686335 absolute error = 3.68832772303357e-18 relative error = 5.4564534104519166599139577162048e-16 % h = 0.001 y1[1] (analytic) = 1.9460423435283869715294105783662 y1[1] (numeric) = 1.9460423435283869609751159835931 absolute error = 1.05542945947731e-17 relative error = 5.4234660565694644780792961972964e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.4MB, time=27.97 NO POLE NO POLE x[1] = 0.331 y2[1] (analytic) = 0.67501109144077767800776033714693 y2[1] (numeric) = 0.67501109144077768172272259655558 absolute error = 3.71496225940865e-18 relative error = 5.5035573585602088524961855155529e-16 % h = 0.001 y1[1] (analytic) = 1.9457178275328669261176772385331 y1[1] (numeric) = 1.9457178275328669155212040697955 absolute error = 1.05964731687376e-17 relative error = 5.4460482495417774726376684478285e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.332 y2[1] (analytic) = 0.67406553626530517952989450779567 y2[1] (numeric) = 0.67406553626530518327157933295861 absolute error = 3.74168482516294e-18 relative error = 5.5509214221126590806002335797695e-16 % h = 0.001 y1[1] (analytic) = 1.9453923658195981576553518593481 y1[1] (numeric) = 1.9453923658195981470167428772884 absolute error = 1.06386089820597e-17 relative error = 5.4686186545086138578759411025869e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.4MB, time=28.22 NO POLE NO POLE x[1] = 0.333 y2[1] (analytic) = 0.67312030702426925454244329747574 y2[1] (numeric) = 0.67312030702426925831093865883956 absolute error = 3.76849536136382e-18 relative error = 5.5985465332691967783945884883714e-16 % h = 0.001 y1[1] (analytic) = 1.9450659587140423522893943681328 y1[1] (numeric) = 1.9450659587140423416086924672574 absolute error = 1.06807019008754e-17 relative error = 5.4911772287335805065573598555067e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.334 y2[1] (analytic) = 0.67217540466289906531223089961467 y2[1] (numeric) = 0.67217540466289906910762470851368 absolute error = 3.79539380889901e-18 relative error = 5.6464336281426840568487477723821e-16 % h = 0.001 y1[1] (analytic) = 1.9447386065426065883750189078808 y1[1] (numeric) = 1.9447386065426065776522671164849 absolute error = 1.07227517913959e-17 relative error = 5.5137239294380095570571185289463e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.4MB, time=28.45 NO POLE NO POLE x[1] = 0.335 y2[1] (analytic) = 0.67123083012609689446758572163781 y2[1] (numeric) = 0.67123083012609689828996583011446 absolute error = 3.82238010847665e-18 relative error = 5.6945836468187563536827648976332e-16 % h = 0.001 y1[1] (analytic) = 1.9444103096326430100686426826321 y1[1] (numeric) = 1.9444103096326429993038841627245 absolute error = 1.07647585199076e-17 relative error = 5.5362587138006809563682399761710e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.336 y2[1] (analytic) = 0.67028658435843720009613649849422 y2[1] (numeric) = 0.67028658435843720394559069911958 absolute error = 3.84945420062536e-18 relative error = 5.7429975333757478934977142604261e-16 % h = 0.001 y1[1] (analytic) = 1.9440810683124484999757690804005 y1[1] (numeric) = 1.944081068312448489169047127628 absolute error = 1.08067219527725e-17 relative error = 5.5587815389577504215784347661499e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.4MB, time=28.69 NO POLE NO POLE x[1] = 0.337 y2[1] (analytic) = 0.66934266830416567117043291956346 y2[1] (numeric) = 0.66934266830416567504704894525781 absolute error = 3.87661602569435e-18 relative error = 5.7916762359048069986540403802217e-16 % h = 0.001 y1[1] (analytic) = 1.943750882911264350854132425743 y1[1] (numeric) = 1.9437508829112643400054904693144 absolute error = 1.08486419564286e-17 relative error = 5.5812923620026772745729371770329e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.338 y2[1] (analytic) = 0.66839908290719828330233534324402 y2[1] (numeric) = 0.66839908290719828720620086709755 absolute error = 3.90386552385353e-18 relative error = 5.8406207065301279417612889201977e-16 % h = 0.001 y1[1] (analytic) = 1.9434197537592759363724326587988 y1[1] (numeric) = 1.943419753759275925481914261409 absolute error = 1.08905183973898e-17 relative error = 5.6037911399858948716529114186224e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.4MB, time=28.93 NO POLE NO POLE x[1] = 0.339 y2[1] (analytic) = 0.66745582911112035482711784475499 y2[1] (numeric) = 0.66745582911112035875832047984857 absolute error = 3.93120263509358e-18 relative error = 5.8898319014292401800885383487425e-16 % h = 0.001 y1[1] (analytic) = 1.9430876811876123809249891820363 y1[1] (numeric) = 1.94308768118761236999263803979 absolute error = 1.09323511422463e-17 relative error = 5.6262778299147379652314386143570e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.34 y2[1] (analytic) = 0.66651290785918560321822851296921 y2[1] (numeric) = 0.66651290785918560717685581219527 absolute error = 3.95862729922606e-18 relative error = 5.9393107808534751811668654033371e-16 % h = 0.001 y1[1] (analytic) = 1.9427546655283462285026440600266 y1[1] (numeric) = 1.9427546655283462175285040023616 absolute error = 1.09741400576650e-17 relative error = 5.6487523887533699370408437736053e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.4MB, time=29.17 NO POLE NO POLE x[1] = 0.341 y2[1] (analytic) = 0.66557032009431520183365058143904 y2[1] (numeric) = 0.66557032009431520581979003732251 absolute error = 3.98613945588347e-18 relative error = 5.9890583091484769885459425418601e-16 % h = 0.001 y1[1] (analytic) = 1.9424207071144931106202457013121 y1[1] (numeric) = 1.942420707114493099604360690923 absolute error = 1.10158850103891e-17 relative error = 5.6712147734222980457525513647451e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.342 y2[1] (analytic) = 0.66462806675909683699480764717492 y2[1] (numeric) = 0.66462806675909684100854669169431 absolute error = 4.01373904451939e-18 relative error = 6.0390754547749521668670463185095e-16 % h = 0.001 y1[1] (analytic) = 1.9420858062800114133010450948604 y1[1] (numeric) = 1.9420858062800114022434592276212 absolute error = 1.10575858672392e-17 relative error = 5.6936649407986604856862621170352e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.4MB, time=29.41 NO POLE NO POLE x[1] = 0.343 y2[1] (analytic) = 0.66368614879578376539895589819304 y2[1] (numeric) = 0.66368614879578376944038190260158 absolute error = 4.04142600440854e-18 relative error = 6.0893631903294200311046045462435e-16 % h = 0.001 y1[1] (analytic) = 1.9417499633598019431183376166772 y1[1] (numeric) = 1.9417499633598019320190951215645 absolute error = 1.10992424951127e-17 relative error = 5.7161028477156381891624891357724e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.344 y2[1] (analytic) = 0.66274456714629387186600593736127 y2[1] (numeric) = 0.66274456714629387593520621200814 absolute error = 4.06920027464687e-18 relative error = 6.1399224925651287392680644391004e-16 % h = 0.001 y1[1] (analytic) = 1.9414131786897075922946843649114 y1[1] (numeric) = 1.9414131786897075811538296039265 absolute error = 1.11408547609849e-17 relative error = 5.7385284509627416152070349173036e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.4MB, time=29.65 NO POLE NO POLE x[1] = 0.345 y2[1] (analytic) = 0.66180332275220872742071645564298 y2[1] (numeric) = 0.66180332275220873151777824979467 absolute error = 4.09706179415169e-18 relative error = 6.1907543424131536080731963925067e-16 % h = 0.001 y1[1] (analytic) = 1.9410754526065130028590479241997 y1[1] (numeric) = 1.9410754526065129916766253922916 absolute error = 1.11824225319081e-17 relative error = 5.7609417072850674255080958444391e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.346 y2[1] (analytic) = 0.66086241655477264771120167246664 y2[1] (numeric) = 0.66086241655477265183621217412839 absolute error = 4.12501050166175e-18 relative error = 6.2418597250035428761890301815468e-16 % h = 0.001 y1[1] (analytic) = 1.9407367854479442298621784020909 y1[1] (numeric) = 1.940736785447944218638232727078 absolute error = 1.12239456750129e-17 relative error = 5.7833425733836879198105656223338e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.4MB, time=29.89 NO POLE NO POLE x[1] = 0.347 y2[1] (analytic) = 0.65992184949489175176469412463536 y2[1] (numeric) = 0.65992184949489175591774046037265 absolute error = 4.15304633573729e-18 relative error = 6.2932396296865412852688146599853e-16 % h = 0.001 y1[1] (analytic) = 1.9403971775526684036505865221322 y1[1] (numeric) = 1.9403971775526683923851624646244 absolute error = 1.12654240575078e-17 relative error = 5.8057310059151647142064214724139e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.348 y2[1] (analytic) = 0.65898162251313302108150404793491 y2[1] (numeric) = 0.65898162251313302526267328269511 absolute error = 4.18116923476020e-18 relative error = 6.3448950500541042926393729088962e-16 % h = 0.001 y1[1] (analytic) = 1.9400566292602933911994414996184 y1[1] (numeric) = 1.9400566292602933798925839529389 absolute error = 1.13068575466795e-17 relative error = 5.8281069614914226685288807535412e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.4MB, time=30.12 NO POLE NO POLE x[1] = 0.349 y2[1] (analytic) = 0.65804173654972335906811625740272 y2[1] (numeric) = 0.6580417365497233632774953943368 absolute error = 4.20937913693408e-18 relative error = 6.3968269839613862774794875561621e-16 % h = 0.001 y1[1] (analytic) = 1.9397151409113674565047323670778 y1[1] (numeric) = 1.9397151409113674451564863571842 absolute error = 1.13482460098936e-17 relative error = 5.8504703966798298410052472238039e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.35 y2[1] (analytic) = 0.65710219254454865081036509308237 y2[1] (numeric) = 0.65710219254454865504804107336671 absolute error = 4.23767598028434e-18 relative error = 6.4490364335484151163573075236127e-16 % h = 0.001 y1[1] (analytic) = 1.9393727128473789200350323573037 y1[1] (numeric) = 1.9393727128473789086454430427095 absolute error = 1.13895893145942e-17 relative error = 5.8728212680027102786012047559451e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.4MB, time=30.36 NO POLE NO POLE x[1] = 0.351 y2[1] (analytic) = 0.65616299143715282318762765801042 y2[1] (numeric) = 0.65616299143715282745368736066873 absolute error = 4.26605970265831e-18 relative error = 6.5015244052619088527906547124615e-16 % h = 0.001 y1[1] (analytic) = 1.9390293454107558172432068921403 y1[1] (numeric) = 1.9390293454107558058123195638362 absolute error = 1.14308873283041e-17 relative error = 5.8951595319371656691869552363350e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.352 y2[1] (analytic) = 0.65522413416673690532897523416392 y2[1] (numeric) = 0.65522413416673690962350547588922 absolute error = 4.29453024172530e-18 relative error = 6.5542919098771438878720336971990e-16 % h = 0.001 y1[1] (analytic) = 1.9386850389448655561384066652863 y1[1] (numeric) = 1.9386850389448655446662667466606 absolute error = 1.14721399186257e-17 relative error = 5.9174851449152578169372992108104e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.4MB, time=30.60 NO POLE NO POLE x[1] = 0.353 y2[1] (analytic) = 0.65428562167215808941222242013895 y2[1] (numeric) = 0.6542856216721580937353099551157 absolute error = 4.32308753497675e-18 relative error = 6.6073399625200887529445979520915e-16 % h = 0.001 y1[1] (analytic) = 1.9383397937940145739186882470937 y1[1] (numeric) = 1.938339793794014562405341293853 absolute error = 1.15133469532407e-17 relative error = 5.9397980633235721697775020666328e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.354 y2[1] (analytic) = 0.65334745489192879180681319143277 y2[1] (numeric) = 0.65334745489192879615854471115905 absolute error = 4.35173151972628e-18 relative error = 6.6606695826895148909348170075874e-16 % h = 0.001 y1[1] (analytic) = 1.9379936103034479926646055787134 y1[1] (numeric) = 1.937993610303447981110097278803 absolute error = 1.15545082999104e-17 relative error = 5.9620982435030904234714253839741e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.4MB, time=30.84 NO POLE NO POLE x[1] = 0.355 y2[1] (analytic) = 0.65240963476421571456148274036527 y2[1] (numeric) = 0.65240963476421571894194487347507 absolute error = 4.38046213310980e-18 relative error = 6.7142817942793290217073466986823e-16 % h = 0.001 y1[1] (analytic) = 1.937646488819349274094116661967 y1[1] (numeric) = 1.9376464888193492624984928354911 absolute error = 1.15956238264759e-17 relative error = 5.9843856417490113235421574388410e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.356 y2[1] (analytic) = 0.65147216222683890723763360789966 y2[1] (numeric) = 0.65147216222683891164691291998528 absolute error = 4.40927931208562e-18 relative error = 6.7681776256010367844673294415722e-16 % h = 0.001 y1[1] (analytic) = 1.9372984296888398733791506900099 y1[1] (numeric) = 1.9372984296888398617424572891514 absolute error = 1.16366934008585e-17 relative error = 6.0066602143106744544532188134754e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.4MB, time=31.08 NO POLE NO POLE x[1] = 0.357 y2[1] (analytic) = 0.65053503821727082908936427390812 y2[1] (numeric) = 0.65053503821727083352754726734266 absolute error = 4.43818299343454e-18 relative error = 6.8223581094063077924862576415278e-16 % h = 0.001 y1[1] (analytic) = 1.9369494332599788920241818021889 y1[1] (numeric) = 1.9369494332599788803464649111291 absolute error = 1.16777168910598e-17 relative error = 6.0289219173913290073052188745779e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.358 y2[1] (analytic) = 0.64959826367263541159108802577568 y2[1] (numeric) = 0.64959826367263541605826113953562 absolute error = 4.46717311375994e-18 relative error = 6.8768242829096734638674103486087e-16 % h = 0.001 y1[1] (analytic) = 1.9365994998817627298071565844923 y1[1] (numeric) = 1.9365994998817627180884624193304 absolute error = 1.17186941651619e-17 relative error = 6.0511707071479538778586238298577e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.4MB, time=31.31 NO POLE NO POLE x[1] = 0.359 y2[1] (analytic) = 0.64866183952970712131367957764527 y2[1] (numeric) = 0.64866183952970712580992918713315 absolute error = 4.49624960948788e-18 relative error = 6.9315771878113739348259496073742e-16 % h = 0.001 y1[1] (analytic) = 1.9362486299041247357831233746356 y1[1] (numeric) = 1.936248629904124724023498283308 absolute error = 1.17596250913276e-17 relative error = 6.0734065396910775124418750136154e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.36 y2[1] (analytic) = 0.64772576672491002315008656407927 y2[1] (numeric) = 0.64772576672491002767549898094649 absolute error = 4.52541241686722e-18 relative error = 6.9866178703203705468855035462608e-16 % h = 0.001 y1[1] (analytic) = 1.9358968236779348583509123681247 y1[1] (numeric) = 1.9358968236779348465504028303239 absolute error = 1.18005095378008e-17 relative error = 6.0956293710847008119471624915530e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.4MB, time=31.55 NO POLE NO POLE x[1] = 0.361 y2[1] (analytic) = 0.64679004619431684389134268244803 y2[1] (numeric) = 0.64679004619431684844600415441772 absolute error = 4.55466147196969e-18 relative error = 7.0419473811774168986526092223788e-16 % h = 0.001 y1[1] (analytic) = 1.935544081554999294383216458587 y1[1] (numeric) = 1.9355440815549992825418690856804 absolute error = 1.18413473729066e-17 relative error = 6.1178391573460648993211549652718e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.362 y2[1] (analytic) = 0.64585467887364803615391890795416 y2[1] (numeric) = 0.64585467887364804073791561864414 absolute error = 4.58399671068998e-18 relative error = 7.0975667756782969758985837243364e-16 % h = 0.001 y1[1] (analytic) = 1.9351904038880601374204236822605 y1[1] (numeric) = 1.9351904038880601255382852172092 absolute error = 1.18821384650513e-17 relative error = 6.1400358544453669013647536817706e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.4MB, time=31.78 NO POLE NO POLE x[1] = 0.363 y2[1] (analytic) = 0.64491966569827084265934885386328 y2[1] (numeric) = 0.64491966569827084727276692260917 absolute error = 4.61341806874589e-18 relative error = 7.1534771136972936123357691692338e-16 % h = 0.001 y1[1] (analytic) = 1.9348357910307950249285530727796 y1[1] (numeric) = 1.9348357910307950130056703900566 absolute error = 1.19228826827230e-17 relative error = 6.1622194183057854646632694636084e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=514.9MB, alloc=4.4MB, time=32.02 x[1] = 0.364 y2[1] (analytic) = 0.64398500760319836086706399723811 y2[1] (numeric) = 0.64398500760319836550998947891648 absolute error = 4.64292548167837e-18 relative error = 7.2096794597106251691440563805787e-16 % h = 0.001 y1[1] (analytic) = 1.9344802433378167846216466682912 y1[1] (numeric) = 1.9344802433378167726580667737994 absolute error = 1.19635798944918e-17 relative error = 6.1843898048032994676050854367370e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.365 y2[1] (analytic) = 0.64305070552308860796137413726246 y2[1] (numeric) = 0.64305070552308861263389302211413 absolute error = 4.67251888485167e-18 relative error = 7.2661748828201917535284951674293e-16 % h = 0.001 y1[1] (analytic) = 1.9341237611646730798489713484808 y1[1] (numeric) = 1.9341237611646730678447413794712 absolute error = 1.20042299690096e-17 relative error = 6.2065469697662996630034591533694e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=518.8MB, alloc=4.4MB, time=32.26 x[1] = 0.366 y2[1] (analytic) = 0.64211676039224358619352809909695 y2[1] (numeric) = 0.64211676039224359089572631255036 absolute error = 4.70219821345341e-18 relative error = 7.3229644567773377538158568619754e-16 % h = 0.001 y1[1] (analytic) = 1.9337663448678460540473851142766 y1[1] (numeric) = 1.9337663448678460420025523392657 absolute error = 1.20448327750109e-17 relative error = 6.2286908689757169584281718097723e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.367 y2[1] (analytic) = 0.64118317314460834857978934112779 y2[1] (numeric) = 0.64118317314460835331175274362247 absolute error = 4.73196340249468e-18 relative error = 7.3800492600068019315798856841819e-16 % h = 0.001 y1[1] (analytic) = 1.9334079948047519742592233578357 y1[1] (numeric) = 1.9334079948047519621738351765232 absolute error = 1.20853881813125e-17 relative error = 6.2508214581645818367295606735711e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.4MB, time=32.50 NO POLE NO POLE x[1] = 0.368 y2[1] (analytic) = 0.64024994471377006495646076745515 y2[1] (numeric) = 0.64024994471377006971827515426529 absolute error = 4.76181438681014e-18 relative error = 7.4374303756308096415496798494201e-16 % h = 0.001 y1[1] (analytic) = 1.9330487113337408737160616048967 y1[1] (numeric) = 1.9330487113337408615901655480826 absolute error = 1.21258960568141e-17 relative error = 6.2729386930180488140967839460128e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.369 y2[1] (analytic) = 0.63931707603295708839279269051843 y2[1] (numeric) = 0.63931707603295709318454379157658 absolute error = 4.79175110105815e-18 relative error = 7.4951088914933550652563002376004e-16 % h = 0.001 y1[1] (analytic) = 1.9326884948140961934887121457059 y1[1] (numeric) = 1.9326884948140961813223558752076 absolute error = 1.21663562704983e-17 relative error = 6.2950425291731104180468182727006e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.4MB, time=32.74 NO POLE NO POLE x[1] = 0.37 y2[1] (analytic) = 0.63838456803503802196270753087285 y2[1] (numeric) = 0.63838456803503802678448101059368 absolute error = 4.82177347972083e-18 relative error = 7.5530859001845182610102164434819e-16 % h = 0.001 y1[1] (analytic) = 1.9323273456060344232038129044909 y1[1] (numeric) = 1.9323273456060344109970442130599 absolute error = 1.22067686914310e-17 relative error = 6.3171329222185177911362028992045e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.371 y2[1] (analytic) = 0.63745242165252078587627448231464 y2[1] (numeric) = 0.63745242165252079072815593941884 absolute error = 4.85188145710420e-18 relative error = 7.6113624990650521986500819010829e-16 % h = 0.001 y1[1] (analytic) = 1.9319652640707047408273678308622 y1[1] (numeric) = 1.9319652640707047285802346421009 absolute error = 1.22471331887613e-17 relative error = 6.3392098276944423427700723765133e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.4MB, time=32.97 NO POLE NO POLE x[1] = 0.372 y2[1] (analytic) = 0.63652063781755168497186701080265 y2[1] (numeric) = 0.63652063781755168985394197814087 absolute error = 4.88207496733822e-18 relative error = 7.6699397902909592557560045825426e-16 % h = 0.001 y1[1] (analytic) = 1.9316022505701886515155990295735 y1[1] (numeric) = 1.9316022505701886392281493978513 absolute error = 1.22874496317222e-17 relative error = 6.3612732010925511251328891641520e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.373 y2[1] (analytic) = 0.63558921746191447656993569494098 y2[1] (numeric) = 0.63558921746191448148228963931796 absolute error = 4.91235394437698e-18 relative error = 7.7288188808384498948377710068202e-16 % h = 0.001 y1[1] (analytic) = 1.9312383054674996255334717777569 y1[1] (numeric) = 1.9312383054674996132057538881265 absolute error = 1.23277178896304e-17 relative error = 6.3833229978556162124400804844629e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.4MB, time=33.21 NO POLE NO POLE x[1] = 0.374 y2[1] (analytic) = 0.6346581615170294386893285541723 y2[1] (numeric) = 0.63465816151702944363204687617103 absolute error = 4.94271832199873e-18 relative error = 7.7880008825287984836834705303974e-16 % h = 0.001 y1[1] (analytic) = 1.9308734291265827352412545110794 y1[1] (numeric) = 1.9308734291265827228733166791926 absolute error = 1.23679378318868e-17 relative error = 6.4053591733774861094902025425174e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.375 y2[1] (analytic) = 0.63372747091395243862709064828374 y2[1] (numeric) = 0.63372747091395244360025868208973 absolute error = 4.97316803380599e-18 relative error = 7.8474869120534733954874178781430e-16 % h = 0.001 y1[1] (analytic) = 1.9305076219123142911494767922296 y1[1] (numeric) = 1.930507621912314278741367464253 absolute error = 1.24081093279766e-17 relative error = 6.4273816830028498685342013859878e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.4MB, time=33.45 NO POLE NO POLE x[1] = 0.376 y2[1] (analytic) = 0.63279714658337400190267436834815 y2[1] (numeric) = 0.63279714658337400690637738157386 absolute error = 5.00370301322571e-18 relative error = 7.9072780909994962839106807661302e-16 % h = 0.001 y1[1] (analytic) = 1.9301408841905014770426492067458 y1[1] (numeric) = 1.9301408841905014645944169592766 absolute error = 1.24482322474692e-17 relative error = 6.4493904820268972589407482497491e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.377 y2[1] (analytic) = 0.63186718945561838156749147481296 y2[1] (numeric) = 0.63186718945561838660181466832226 absolute error = 5.03432319350930e-18 relative error = 7.9673755458747474992694051988224e-16 % h = 0.001 y1[1] (analytic) = 1.929773216327881984172110062437 y1[1] (numeric) = 1.9297732163278819716838036024179 absolute error = 1.24883064600191e-17 relative error = 6.4713855256954966844623710438894e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.4MB, time=33.68 NO POLE NO POLE x[1] = 0.378 y2[1] (analytic) = 0.6309376004606426278807375731069 y2[1] (numeric) = 0.63093760046064263294576608083968 absolute error = 5.06502850773278e-18 relative error = 8.0277804081336127958578353875574e-16 % h = 0.001 y1[1] (analytic) = 1.9294046186921236445183646995176 y1[1] (numeric) = 1.9294046186921236319900328641519 absolute error = 1.25283318353657e-17 relative error = 6.4933667692048031194789710866481e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.379 y2[1] (analytic) = 0.63000838052803565835241935086267 y2[1] (numeric) = 0.63000838052803566344823823965953 absolute error = 5.09581888879686e-18 relative error = 8.0884938142026727386356673789606e-16 % h = 0.001 y1[1] (analytic) = 1.929035091651824063123284149087 y1[1] (numeric) = 1.9290350916518240505549759057533 absolute error = 1.25683082433337e-17 relative error = 6.5153341677011765724292147092913e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.4MB, time=33.92 NO POLE NO POLE x[1] = 0.38 y2[1] (analytic) = 0.6290795305870173281545145336508 y2[1] (numeric) = 0.62907953058701733328120880307785 absolute error = 5.12669426942705e-18 relative error = 8.1495169055065936740613259041145e-16 % h = 0.001 y1[1] (analytic) = 1.9286646355765102494925308077246 y1[1] (numeric) = 1.9286646355765102368842952538917 absolute error = 1.26082355538329e-17 relative error = 6.5372876762807892989352787027319e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.381 y2[1] (analytic) = 0.62815105156643750090119414798726 y2[1] (numeric) = 0.62815105156643750605884873016105 absolute error = 5.15765458217379e-18 relative error = 8.2108508284942058887604130351920e-16 % h = 0.001 y1[1] (analytic) = 1.9282932508366382480685797257438 y1[1] (numeric) = 1.9282932508366382354204660888849 absolute error = 1.26481136368589e-17 relative error = 6.5592272499896992352615091132370e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.4MB, time=34.16 NO POLE NO POLE x[1] = 0.382 y2[1] (analytic) = 0.6272229443947751197990363113152 y2[1] (numeric) = 0.62722294439477512498773607072767 absolute error = 5.18869975941247e-18 relative error = 8.2724967346645630848218148200794e-16 % h = 0.001 y1[1] (analytic) = 1.9279209378035927677747050360532 y1[1] (numeric) = 1.9279209378035927550867626735601 absolute error = 1.26879423624931e-17 relative error = 6.5811528438235603699361941269200e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.383 y2[1] (analytic) = 0.62629521000013727916816039866944 y2[1] (numeric) = 0.6262952100001372843879901320131 absolute error = 5.21982973334366e-18 relative error = 8.3344557805934933668794473121815e-16 % h = 0.001 y1[1] (analytic) = 1.927547696849686810630301979607 y1[1] (numeric) = 1.9275476968496867979025803787039 absolute error = 1.27277216009031e-17 relative error = 6.6030644127275402365779323192534e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.4MB, time=34.40 NO POLE NO POLE x[1] = 0.384 y2[1] (analytic) = 0.62536784931025829633521006481245 y2[1] (numeric) = 0.62536784931025830158625450080556 absolute error = 5.25104443599311e-18 relative error = 8.3967291279599427024124390278590e-16 % h = 0.001 y1[1] (analytic) = 1.9271735283481612994379159120923 y1[1] (numeric) = 1.9271735283481612866704646897496 absolute error = 1.27674512223427e-17 relative error = 6.6249619115960296919001820686757e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.385 y2[1] (analytic) = 0.6244408632524987838991132287812 y2[1] (numeric) = 0.6244408632524987891814570279931 absolute error = 5.28234379921190e-18 relative error = 8.4593179435727166795487913110480e-16 % h = 0.001 y1[1] (analytic) = 1.9267984326731847045423506047928 y1[1] (numeric) = 1.9267984326731846917352195076407 absolute error = 1.28071310971521e-17 relative error = 6.6468452952724560935096808712176e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.4MB, time=34.63 NO POLE NO POLE x[1] = 0.386 y2[1] (analytic) = 0.62351425275384472237054675500772 y2[1] (numeric) = 0.62351425275384472768427450968426 absolute error = 5.31372775467654e-18 relative error = 8.5222233993973033795249360879322e-16 % h = 0.001 y1[1] (analytic) = 1.9264224101998526696622290804899 y1[1] (numeric) = 1.9264224101998526568154679847316 absolute error = 1.28467610957583e-17 relative error = 6.6687145185492000169644391154723e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.387 y2[1] (analytic) = 0.62258801874090653318603319147135 y2[1] (numeric) = 0.62258801874090653853122942536044 absolute error = 5.34519623388909e-18 relative error = 8.5854466725828900709153170977510e-16 % h = 0.001 y1[1] (analytic) = 1.9260454613041876367943811528091 y1[1] (numeric) = 1.9260454613041876239080400641338 absolute error = 1.28863410886753e-17 relative error = 6.6905695361674079737543418904410e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.4MB, time=34.87 NO POLE NO POLE x[1] = 0.388 y2[1] (analytic) = 0.62166216213991815209759655070879 y2[1] (numeric) = 0.62166216213991815747434571888599 absolute error = 5.37674916817720e-18 relative error = 8.6489889454894143118760072222664e-16 % h = 0.001 y1[1] (analytic) = 1.9256675863631384701914327645926 y1[1] (numeric) = 1.9256675863631384572655618180883 absolute error = 1.29258709465043e-17 relative error = 6.7124103028168048477178311584059e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.389 y2[1] (analytic) = 0.62073668387673610293890374394874 y2[1] (numeric) = 0.62073668387673610834729023264307 absolute error = 5.40838648869433e-18 relative error = 8.7128514057150680960603416916164e-16 % h = 0.001 y1[1] (analytic) = 1.9252887857545800794129731476774 y1[1] (numeric) = 1.9252887857545800664476226077436 absolute error = 1.29653505399338e-17 relative error = 6.7342367731354541084815413827461e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.4MB, time=35.11 NO POLE NO POLE x[1] = 0.39 y2[1] (analytic) = 0.61981158487683857176881790215284 y2[1] (numeric) = 0.61981158487683857720892602857257 absolute error = 5.44010812641973e-18 relative error = 8.7770352461235815664013527453989e-16 % h = 0.001 y1[1] (analytic) = 1.9249090598573130414506767528811 y1[1] (numeric) = 1.9249090598573130284458970131413 absolute error = 1.30047797397398e-17 relative error = 6.7560489017095696300558916847651e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.391 y2[1] (analytic) = 0.61888686606532448139328944033205 y2[1] (numeric) = 0.6188868660653244868652034524907 absolute error = 5.47191401215865e-18 relative error = 8.8415416648720428266853426776179e-16 % h = 0.001 y1[1] (analytic) = 1.9245284090510632219277578250411 y1[1] (numeric) = 1.9245284090510632088835994082548 absolute error = 1.30441584167863e-17 relative error = 6.7778466430734831063085805312541e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=568.4MB, alloc=4.4MB, time=35.35 NO POLE NO POLE x[1] = 0.392 y2[1] (analytic) = 0.61796252836691256626651034317064 y2[1] (numeric) = 0.61796252836691257177031441971301 absolute error = 5.50380407654237e-18 relative error = 8.9063718654385954009303263510267e-16 % h = 0.001 y1[1] (analytic) = 1.9241468337164813953731364236214 y1[1] (numeric) = 1.9241468337164813822896499815961 absolute error = 1.30834864420253e-17 relative error = 6.7996299517093515098586613912231e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.393 y2[1] (analytic) = 0.6170385727059404477722567707261 y2[1] (numeric) = 0.61703857270594045330803502075448 absolute error = 5.53577825002838e-18 relative error = 8.9715270566505462683250157192664e-16 % h = 0.001 y1[1] (analytic) = 1.9237643342351428645706956146894 y1[1] (numeric) = 1.9237643342351428514479319281922 absolute error = 1.31227636864972e-17 relative error = 6.8213987820470720661621317492345e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.4MB, time=35.59 NO POLE NO POLE x[1] = 0.394 y2[1] (analytic) = 0.61611500000636370988634470278558 y2[1] (numeric) = 0.61611500000636371545418116568601 absolute error = 5.56783646290043e-18 relative error = 9.0370084527124337176768837636622e-16 % h = 0.001 y1[1] (analytic) = 1.9233809109895470789840104849733 y1[1] (numeric) = 1.9233809109895470658220204636429 absolute error = 1.31619900213304e-17 relative error = 6.8431530884637811291733448084754e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.395 y2[1] (analytic) = 0.61519181119175497522112295934603 y2[1] (numeric) = 0.61519181119175498082110160461465 absolute error = 5.59997864526862e-18 relative error = 9.1028172732343303238939585393087e-16 % h = 0.001 y1[1] (analytic) = 1.9229965643631172522569305532408 y1[1] (numeric) = 1.9229965643631172390557652354983 absolute error = 1.32011653177425e-17 relative error = 6.8648928252841844288622920907056e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.4MB, time=35.82 NO POLE NO POLE x[1] = 0.396 y2[1] (analytic) = 0.61426900718530298145292755264793 y2[1] (numeric) = 0.61426900718530298708513227971755 absolute error = 5.63220472706962e-18 relative error = 9.1689547432605294202428513646077e-16 % h = 0.001 y1[1] (analytic) = 1.9226112947401999787903980783825 y1[1] (numeric) = 1.9226112947401999655501086313427 absolute error = 1.32402894470398e-17 relative error = 6.8866179467800034372709071858822e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.397 y2[1] (analytic) = 0.61334658890981165813342094323165 y2[1] (numeric) = 0.61334658890981166379793558129827 absolute error = 5.66451463806662e-18 relative error = 9.2354220932979663232993281843130e-16 % h = 0.001 y1[1] (analytic) = 1.9222251025060648493958856873514 y1[1] (numeric) = 1.9222251025060648361165234067336 absolute error = 1.32793622806178e-17 relative error = 6.9083284071699412366992514858904e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.4MB, time=36.06 NO POLE NO POLE x[1] = 0.398 y2[1] (analytic) = 0.61242455728769920388573938859978 y2[1] (numeric) = 0.61242455728769920958264769644936 absolute error = 5.69690830784958e-18 relative error = 9.3022205593453016135451919396720e-16 % h = 0.001 y1[1] (analytic) = 1.9218379880469040660258376694886 y1[1] (numeric) = 1.9218379880469040527074539795274 absolute error = 1.33183836899612e-17 relative error = 6.9300241606193881152533748048446e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.399 y2[1] (analytic) = 0.6115029132409971639863711882616 y2[1] (numeric) = 0.61150291324099716971575685409684 absolute error = 5.72938566583524e-18 relative error = 9.3693513829217897582183124621908e-16 % h = 0.001 y1[1] (analytic) = 1.9214499517498320555815002067615 y1[1] (numeric) = 1.921449951749832042224146660117 absolute error = 1.33573535466445e-17 relative error = 6.9517051612404390069645677082220e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.4MB, time=36.30 NO POLE NO POLE x[1] = 0.4 y2[1] (analytic) = 0.61058165769134950833368824320429 y2[1] (numeric) = 0.61058165769134951409563488447158 absolute error = 5.76194664126729e-18 relative error = 9.4368158110965852823888555418774e-16 % h = 0.001 y1[1] (analytic) = 1.9210609940028850827985267320518 y1[1] (numeric) = 1.9210609940028850694022550097201 absolute error = 1.33962717223317e-17 relative error = 6.9733713630914423981233601421143e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.401 y2[1] (analytic) = 0.60966079156001170980405296118265 y2[1] (numeric) = 0.60966079156001171559864412439908 absolute error = 5.79459116321643e-18 relative error = 9.5046150965180476052125095543580e-16 % h = 0.001 y1[1] (analytic) = 1.9206711151950208622107455298569 y1[1] (numeric) = 1.9206711151950208487756074410797 absolute error = 1.34351380887772e-17 relative error = 6.9950227201771734032285340432446e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.4MB, time=36.53 NO POLE NO POLE x[1] = 0.402 y2[1] (analytic) = 0.60874031576784982299642215164349 y2[1] (numeric) = 0.60874031576784982882374131222404 absolute error = 5.82731916058055e-18 relative error = 9.5727504974434217075784713535131e-16 % h = 0.001 y1[1] (analytic) = 1.9202803157161181691924776156028 y1[1] (numeric) = 1.9202803157161181557185250977776 absolute error = 1.34739525178252e-17 relative error = 7.0166591864482258516268324398928e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.403 y2[1] (analytic) = 0.60782023123533956336636916560423 y2[1] (numeric) = 0.60782023123533956922649972768897 absolute error = 5.86013056208474e-18 relative error = 9.6412232777684208466109863577055e-16 % h = 0.001 y1[1] (analytic) = 1.9198885959569764500797938512206 y1[1] (numeric) = 1.9198885959569764365670789698099 absolute error = 1.35127148814107e-17 relative error = 7.0382807158012369493384390016275e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.4MB, time=36.77 NO POLE NO POLE x[1] = 0.404 y2[1] (analytic) = 0.60690053888256538675044514638653 y2[1] (numeric) = 0.60690053888256539264347044266803 absolute error = 5.89302529628150e-18 relative error = 9.7100347070573192726444933137584e-16 % h = 0.001 y1[1] (analytic) = 1.9194959563093154313711011756945 y1[1] (numeric) = 1.9194959563093154178196761241354 absolute error = 1.35514250515591e-17 relative error = 7.0598872620783827929559246268013e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.405 y2[1] (analytic) = 0.60598123962921956928179986676729 y2[1] (numeric) = 0.60598123962921957520780315831807 absolute error = 5.92600329155078e-18 relative error = 9.7791860605729491223402507535718e-16 % h = 0.001 y1[1] (analytic) = 1.9191023971657747280074487499645 y1[1] (numeric) = 1.9191023971657747144173658495778 absolute error = 1.35900829003867e-17 relative error = 7.0814787790673421692931120305397e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.4MB, time=37.01 NO POLE NO POLE x[1] = 0.406 y2[1] (analytic) = 0.60506233439460128769798223684934 y2[1] (numeric) = 0.60506233439460129365704671294945 absolute error = 5.95906447610011e-18 relative error = 9.8486786193070295046623417424610e-16 % h = 0.001 y1[1] (analytic) = 1.9187079189199134507329457358444 y1[1] (numeric) = 1.9187079189199134371042574357433 absolute error = 1.36286883001011e-17 relative error = 7.1030552205012081267504671170171e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.407 y2[1] (analytic) = 0.60414382409761570004184017477465 y2[1] (numeric) = 0.6041438240976157060340489527394 absolute error = 5.99220877796475e-18 relative error = 9.9185136700107147743139764751563e-16 % h = 0.001 y1[1] (analytic) = 1.9183125219662098125356833485036 y1[1] (numeric) = 1.9183125219662097988684422255026 absolute error = 1.36672411230010e-17 relative error = 7.1246165400580865981022532428049e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.4MB, time=37.25 NO POLE NO POLE x[1] = 0.408 y2[1] (analytic) = 0.60322570965677302675643913930379 y2[1] (numeric) = 0.60322570965677303278187526431149 absolute error = 6.02543612500770e-18 relative error = 9.9886925052250984050879591206546e-16 % h = 0.001 y1[1] (analytic) = 1.9179162067000607341695547415594 y1[1] (numeric) = 1.9179162067000607204638135000828 absolute error = 1.37057412414766e-17 relative error = 7.1461626913610073013746315887511e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.409 y2[1] (analytic) = 0.60230799199018763217491822926617 y2[1] (numeric) = 0.60230799199018763823366467418613 absolute error = 6.05874644491996e-18 relative error = 1.0059216423312318810436179512840e-15 % h = 0.001 y1[1] (analytic) = 1.9175189735177814487573672029263 y1[1] (numeric) = 1.9175189735177814350131786749163 absolute error = 1.37441885280100e-17 relative error = 7.1676936279778344644607005328614e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.4MB, time=37.49 NO POLE NO POLE x[1] = 0.41 y2[1] (analytic) = 0.60139067201557710640620235994886 y2[1] (numeric) = 0.60139067201557711249834202516936 absolute error = 6.09213966522050e-18 relative error = 1.0130086728486374928552781714221e-15 % h = 0.001 y1[1] (analytic) = 1.917120822816605105475642058277 y1[1] (numeric) = 1.9171208228166050916930592031017 absolute error = 1.37825828551753e-17 relative error = 7.1892093034210208888406773912749e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.411 y2[1] (analytic) = 0.6004737506502613476174886306349 y2[1] (numeric) = 0.60047375065026135374310434389136 absolute error = 6.12561571325646e-18 relative error = 1.0201304730844513749792367031134e-15 % h = 0.001 y1[1] (analytic) = 1.9167217549946823723214985972821 y1[1] (numeric) = 1.9167217549946823585005745016435 absolute error = 1.38209240956386e-17 relative error = 7.2107096711473094691978026201699e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.4MB, time=37.73 NO POLE NO POLE x[1] = 0.412 y2[1] (analytic) = 0.59955722881116164471442460072855 y2[1] (numeric) = 0.59955722881116165087359911693175 absolute error = 6.15917451620320e-18 relative error = 1.0272871746398561403467893071538e-15 % h = 0.001 y1[1] (analytic) = 1.9163217704510810379620192557123 y1[1] (numeric) = 1.9163217704510810241028071335539 absolute error = 1.38592121221584e-17 relative error = 7.2321946845576430073882320704142e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.413 y2[1] (analytic) = 0.59864110741479976041989579421255 y2[1] (numeric) = 0.59864110741479976661271179527702 absolute error = 6.19281600106447e-18 relative error = 1.0344789097106647507461949961965e-15 % h = 0.001 y1[1] (analytic) = 1.915920869585785612666494204004 y1[1] (numeric) = 1.9159208695857855987690473964181 absolute error = 1.38974468075859e-17 relative error = 7.2536642969970216529368179751885e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.4MB, time=37.98 NO POLE NO POLE x[1] = 0.414 y2[1] (analytic) = 0.59772538737729701475233935357361 y2[1] (numeric) = 0.59772538737729702097887944824612 absolute error = 6.22654009467251e-18 relative error = 1.0417058110905008410248261253577e-15 % h = 0.001 y1[1] (analytic) = 1.9155190527996969283219444100102 y1[1] (numeric) = 1.9155190527996969143863163851451 absolute error = 1.39356280248651e-17 relative error = 7.2751184617542556882680655865602e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.415 y2[1] (analytic) = 0.5968100696143733689045003648061 y2[1] (numeric) = 0.59681006961437337516484708849422 absolute error = 6.26034672368812e-18 relative error = 1.0489680121739936470267671897879e-15 % h = 0.001 y1[1] (analytic) = 1.9151163204946317375323231603814 y1[1] (numeric) = 1.9151163204946317235585675133485 absolute error = 1.39737556470329e-17 relative error = 7.2965571320617179366757460002928e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.4MB, time=38.21 NO POLE NO POLE x[1] = 0.416 y2[1] (analytic) = 0.59589515504134650952354697466115 y2[1] (numeric) = 0.59589515504134651581778278926197 absolute error = 6.29423581460082e-18 relative error = 1.0562656469600077590303155471146e-15 % h = 0.001 y1[1] (analytic) = 1.9147126730733223118017969413405 y1[1] (numeric) = 1.9147126730733222977899673941208 absolute error = 1.40118295472197e-17 relative error = 7.3179802610953569269745836421943e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.417 y2[1] (analytic) = 0.59498064457313093339346001994986 y2[1] (numeric) = 0.59498064457313093972166731367879 absolute error = 6.32820729372893e-18 relative error = 1.0635988500548794295093677477709e-15 % h = 0.001 y1[1] (analytic) = 1.9143081109394160388025074955377 y1[1] (numeric) = 1.9143081109394160247526578968885 absolute error = 1.40498495986492e-17 relative error = 7.3393878019742921027659796161144e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.4MB, time=38.45 NO POLE NO POLE x[1] = 0.418 y2[1] (analytic) = 0.59406653912423703252061248643465 y2[1] (numeric) = 0.59406653912423703888287357365437 absolute error = 6.36226108721972e-18 relative error = 1.0709677566756846811487484938988e-15 % h = 0.001 y1[1] (analytic) = 1.9139026344974750187272177871901 y1[1] (numeric) = 1.9139026344974750046394021125511 absolute error = 1.40878156746390e-17 relative error = 7.3607797077608264460096658151132e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=621.8MB, alloc=4.4MB, time=38.69 x[1] = 0.419 y2[1] (analytic) = 0.59315283960877017962345371165307 y2[1] (numeric) = 0.59315283960877018601985083270257 absolute error = 6.39639712104950e-18 relative error = 1.0783725026535175664203889898041e-15 % h = 0.001 y1[1] (analytic) = 1.9134962441529756597272455228257 y1[1] (numeric) = 1.9134962441529756456015178742255 absolute error = 1.41257276486002e-17 relative error = 7.3821559314599364461441386242395e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.42 y2[1] (analytic) = 0.59223954694042981402721284191366 y2[1] (numeric) = 0.59223954694042982045782816293737 absolute error = 6.43061532102371e-18 relative error = 1.0858132244367887437132110110191e-15 % h = 0.001 y1[1] (analytic) = 1.9130889403123082724360887896657 y1[1] (numeric) = 1.9130889403123082582725033956273 absolute error = 1.41635853940384e-17 relative error = 7.4035164260194931528053503553466e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=625.6MB, alloc=4.4MB, time=38.92 x[1] = 0.421 y2[1] (analytic) = 0.59132666203250852796453564868418 y2[1] (numeric) = 0.59132666203250853442945126146128 absolute error = 6.46491561277710e-18 relative error = 1.0932900590945597334499618300710e-15 % h = 0.001 y1[1] (analytic) = 1.912680723382776663579149287984 y1[1] (numeric) = 1.9126807233827766493777605034307 absolute error = 1.42013887845533e-17 relative error = 7.4248611443297514865135143149840e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.422 y2[1] (analytic) = 0.59041418579789115328296840365935 y2[1] (numeric) = 0.59041418579789115978226632543313 absolute error = 6.49929792177378e-18 relative error = 1.1008031443198759014251940909983e-15 % h = 0.001 y1[1] (analytic) = 1.9122715937725977286699595476886 y1[1] (numeric) = 1.9122715937725977144308218538494 absolute error = 1.42391376938392e-17 relative error = 7.4461900392233094728878264029751e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.4MB, time=39.16 NO POLE NO POLE x[1] = 0.423 y2[1] (analytic) = 0.58950211914905384856020210494802 y2[1] (numeric) = 0.5895021191490538550939642782554 absolute error = 6.53376217330738e-18 relative error = 1.1083526184331387902284426949235e-15 % h = 0.001 y1[1] (analytic) = 1.9118615518909010437933214328626 y1[1] (numeric) = 1.9118615518909010295164894371772 absolute error = 1.42768319956854e-17 relative error = 7.4675030634750150515581364164922e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.424 y2[1] (analytic) = 0.58859046299806318662798993905953 y2[1] (numeric) = 0.58859046299806319319629823156064 absolute error = 6.56830829250111e-18 relative error = 1.1159386203854824688899267157043e-15 % h = 0.001 y1[1] (analytic) = 1.911450598147728456475764151092 y1[1] (numeric) = 1.9114505981477284421612925871164 absolute error = 1.43144715639756e-17 relative error = 7.4888001698013495350926177329231e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.4MB, time=39.40 NO POLE NO POLE x[1] = 0.425 y2[1] (analytic) = 0.58767921825657524250565045469569 y2[1] (numeric) = 0.58767921825657524910858665900365 absolute error = 6.60293620430796e-18 relative error = 1.1235612897621947039980295752501e-15 % h = 0.001 y1[1] (analytic) = 1.9110387329540336756437308970901 y1[1] (numeric) = 1.9110387329540336612916746244008 absolute error = 1.43520562726893e-17 relative error = 7.5100813108608567555794196411745e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.426 y2[1] (analytic) = 0.58676838583583468174406851476933 y2[1] (numeric) = 0.58676838583583468838171434828005 absolute error = 6.63764583351072e-18 relative error = 1.1312207667861288239158196354063e-15 % h = 0.001 y1[1] (analytic) = 1.9106259567216818606699041723951 y1[1] (numeric) = 1.9106259567216818462803181764939 absolute error = 1.43895859959012e-17 relative error = 7.5313464392535259205752452358457e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.4MB, time=39.63 NO POLE NO POLE x[1] = 0.427 y2[1] (analytic) = 0.58585796664667384918110568257234 y2[1] (numeric) = 0.58585796664667385585354278729451 absolute error = 6.67243710472217e-18 relative error = 1.1389171923211658358557406203318e-15 % h = 0.001 y1[1] (analytic) = 1.910212269863449209508080734783 y1[1] (numeric) = 1.9102122698634491950810201270015 absolute error = 1.44270606077815e-17 relative error = 7.5525955075206447536941338016675e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.428 y2[1] (analytic) = 0.58494796159951185810933128660698 y2[1] (numeric) = 0.58494796159951186481664122899215 absolute error = 6.70730994238517e-18 relative error = 1.1466507078756811044240401940480e-15 % h = 0.001 y1[1] (analytic) = 1.9097976727930225459170080424865 y1[1] (numeric) = 1.9097976727930225314525280598902 absolute error = 1.44644799825963e-17 relative error = 7.5738284681447047370016760620952e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.4MB, time=39.87 NO POLE NO POLE x[1] = 0.429 y2[1] (analytic) = 0.58403837160435367985698499627348 y2[1] (numeric) = 0.58403837160435368659924926704624 absolute error = 6.74226427077276e-18 relative error = 1.1544214556060343939262101540921e-15 % h = 0.001 y1[1] (analytic) = 1.9093821659249989057735949693482 y1[1] (numeric) = 1.9093821659249988912717509746403 absolute error = 1.45018439947079e-17 relative error = 7.5950452735492537884190543733060e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.43 y2[1] (analytic) = 0.58312919757078923378308132737543 y2[1] (numeric) = 0.58312919757078924056038134136374 absolute error = 6.77730001398831e-18 relative error = 1.1622295783200903066951764112145e-15 % h = 0.001 y1[1] (analytic) = 1.9089657496748851224759104776634 y1[1] (numeric) = 1.9089657496748851079367579590889 absolute error = 1.45391525185745e-17 relative error = 7.6162458760984343722254285568094e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.4MB, time=40.11 NO POLE NO POLE x[1] = 0.431 y2[1] (analytic) = 0.58222044040799247768756608226273 y2[1] (numeric) = 0.58222044040799248449998317822831 absolute error = 6.81241709596558e-18 relative error = 1.1700752194807453206610678735467e-15 % h = 0.001 y1[1] (analytic) = 1.90854842445909741143638484568 y1[1] (numeric) = 1.9085484244590973968599794169288 absolute error = 1.45764054287512e-17 relative error = 7.6374302280972020819182402135203e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.432 y2[1] (analytic) = 0.58131210102472049863743431437966 y2[1] (numeric) = 0.58131210102472050548504975484859 absolute error = 6.84761544046893e-18 relative error = 1.1779585232095027003954375814794e-15 % h = 0.001 y1[1] (analytic) = 1.9081301906949609536656289565175 y1[1] (numeric) = 1.9081301906949609390520263566281 absolute error = 1.46136025998894e-17 relative error = 7.6585982817907059236585862529938e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.4MB, time=40.34 NO POLE NO POLE x[1] = 0.433 y2[1] (analytic) = 0.58040418032931260420971899102467 y2[1] (numeric) = 0.580404180329312611092613962118 absolute error = 6.88289497109333e-18 relative error = 1.1858796342900354186847504520741e-15 % h = 0.001 y1[1] (analytic) = 1.9077110488007094784472880646543 y1[1] (numeric) = 1.9077110488007094637965441579166 absolute error = 1.46507439067377e-17 relative error = 7.6797499893644539984917160145004e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.434 y2[1] (analytic) = 0.57949667922968941415225911125708 y2[1] (numeric) = 0.57949667922968942107051472252165 absolute error = 6.91825561126457e-18 relative error = 1.1938386981718058971389242646487e-15 % h = 0.001 y1[1] (analytic) = 1.9072909991954848451043473650912 y1[1] (numeric) = 1.9072909991954848304165181409496 absolute error = 1.46878292241416e-17 relative error = 7.7008853029438501688161515388214e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.4MB, time=40.58 NO POLE NO POLE x[1] = 0.435 y2[1] (analytic) = 0.57858959863335195246315561810729 y2[1] (numeric) = 0.5785895986333519594168529023466 absolute error = 6.95369728423931e-18 relative error = 1.2018358609736808834093169452639e-15 % h = 0.001 y1[1] (analytic) = 1.9068700422993366238573075988539 y1[1] (numeric) = 1.9068700422993366091324491718098 absolute error = 1.47248584270441e-17 relative error = 7.7220041745942020211175651341832e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.436 y2[1] (analytic) = 0.5776829394473807398898230255586 y2[1] (numeric) = 0.57768293944738074687904293866383 absolute error = 6.98921991310523e-18 relative error = 1.2098712694875863319986401085532e-15 % h = 0.001 y1[1] (analytic) = 1.9064481785332216757746498366219 y1[1] (numeric) = 1.9064481785332216610128184461362 absolute error = 1.47618313904857e-17 relative error = 7.7431065563204140481688722596593e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.4MB, time=40.82 NO POLE NO POLE x[1] = 0.437 y2[1] (analytic) = 0.57677670257843488684854426117356 y2[1] (numeric) = 0.57677670257843489387336768195474 absolute error = 7.02482342078118e-18 relative error = 1.2179450711821853035995036743098e-15 % h = 0.001 y1[1] (analytic) = 1.9060254083190037318160094899842 y1[1] (numeric) = 1.9060254083190037170172615003797 absolute error = 1.47987479896045e-17 relative error = 7.7641924000667328196714221875824e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.438 y2[1] (analytic) = 0.57587088893275118676543580473445 y2[1] (numeric) = 0.57587088893275119382594353475168 absolute error = 7.06050773001723e-18 relative error = 1.2260574142065616830699524745563e-15 % h = 0.001 y1[1] (analytic) = 1.9056017320794529709684805071144 y1[1] (numeric) = 1.9056017320794529561328724074775 absolute error = 1.48356080996369e-17 relative error = 7.7852616577168066047535488585780e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.4MB, time=41.06 NO POLE NO POLE x[1] = 0.439 y2[1] (analytic) = 0.57496549941614320983972978185704 y2[1] (numeric) = 0.57496549941614321693600254525184 absolute error = 7.09627276339480e-18 relative error = 1.2342084473939409973017809124751e-15 % h = 0.001 y1[1] (analytic) = 1.9051771502382455974764716165229 y1[1] (numeric) = 1.9051771502382455826040600206058 absolute error = 1.48724115959171e-17 relative error = 7.8063142810931151415561843085888e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.44 y2[1] (analytic) = 0.57406053493400039723027924922008 y2[1] (numeric) = 0.57406053493400040436239769254694 absolute error = 7.13211844332686e-18 relative error = 1.2423983202654469107849188732446e-15 % h = 0.001 y1[1] (analytic) = 1.9047516632199634171655373889984 y1[1] (numeric) = 1.9047516632199634022563790351204 absolute error = 1.49091583538780e-17 relative error = 7.8273502219571335782195777781508e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.4MB, time=41.30 NO POLE NO POLE x[1] = 0.441 y2[1] (analytic) = 0.57315599639128715566619248482993 y2[1] (numeric) = 0.57315599639128716283423717688787 absolute error = 7.16804469205794e-18 relative error = 1.2506271830338483395223222682044e-15 % h = 0.001 y1[1] (analytic) = 1.9043252714500934128606077938682 y1[1] (numeric) = 1.9043252714500933979147595448174 absolute error = 1.49458482490508e-17 relative error = 7.8483694320088139065378621614635e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.442 y2[1] (analytic) = 0.57225188469254195248250167261022 y2[1] (numeric) = 0.57225188469254195968655310427456 absolute error = 7.20405143166434e-18 relative error = 1.2588951866073651397469441190409e-15 % h = 0.001 y1[1] (analytic) = 1.9038979753550273188990408313166 y1[1] (numeric) = 1.9038979753550273039165596742508 absolute error = 1.49824811570658e-17 relative error = 7.8693718628866959145223031134515e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.4MB, time=41.54 NO POLE NO POLE x[1] = 0.443 y2[1] (analytic) = 0.57134820074187641108177094557285 y2[1] (numeric) = 0.57134820074187641832190952962702 absolute error = 7.24013858405417e-18 relative error = 1.2672024825934681689723491165740e-15 % h = 0.001 y1[1] (analytic) = 1.9034697753620611947389237276696 y1[1] (numeric) = 1.9034697753620611797198667740174 absolute error = 1.50190569536522e-17 relative error = 7.8903574661674928612313849738591e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.444 y2[1] (analytic) = 0.57044494544297440682254832588658 y2[1] (numeric) = 0.57044494544297441409885439685412 absolute error = 7.27630607096754e-18 relative error = 1.2755492233027296603259602770692e-15 % h = 0.001 y1[1] (analytic) = 1.9030406718993949976630490853117 y1[1] (numeric) = 1.9030406718993949826074735706733 absolute error = 1.50555755146384e-17 relative error = 7.9113261933659392594274313561170e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=671.4MB, alloc=4.4MB, time=41.78 NO POLE NO POLE x[1] = 0.445 y2[1] (analytic) = 0.56954211969909116333556567331613 y2[1] (numeric) = 0.56954211969909117064811948729276 absolute error = 7.31255381397663e-18 relative error = 1.2839355617526769683673176040326e-15 % h = 0.001 y1[1] (analytic) = 1.9026106653961321545789932832218 y1[1] (numeric) = 1.9026106653961321394869565672695 absolute error = 1.50920367159523e-17 relative error = 7.9322779959346383810746024461077e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.446 y2[1] (analytic) = 0.56863972441305234926859032575643 y2[1] (numeric) = 0.56863972441305235661747206024229 absolute error = 7.34888173448586e-18 relative error = 1.2923616516716883178431859370089e-15 % h = 0.001 y1[1] (analytic) = 1.9021797562822791329157253280146 y1[1] (numeric) = 1.9021797562822791177872848943931 absolute error = 1.51284404336215e-17 relative error = 7.9532128252638569137365440326101e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.4MB, time=42.02 NO POLE NO POLE x[1] = 0.447 y2[1] (analytic) = 0.56773776048725317546083168693519 y2[1] (numeric) = 0.56773776048725318284612144066715 absolute error = 7.38528975373196e-18 relative error = 1.3008276475028956996395142881567e-15 % h = 0.001 y1[1] (analytic) = 1.9017479449887450106171752588427 y1[1] (numeric) = 1.9017479449887449954523887150693 absolute error = 1.51647865437734e-17 relative error = 7.9741306326812666836393427481480e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.448 y2[1] (analytic) = 0.56683622882365749254780558680187 y2[1] (numeric) = 0.56683622882365749996958337958598 absolute error = 7.42177779278411e-18 relative error = 1.3093337044081248880917932295407e-15 % h = 0.001 y1[1] (analytic) = 1.9013152319473410452331921125551 y1[1] (numeric) = 1.9013152319473410300321171899195 absolute error = 1.52010749226356e-17 relative error = 7.9950313694518437409979024242296e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.4MB, time=42.25 NO POLE NO POLE x[1] = 0.449 y2[1] (analytic) = 0.56593513032379688899755880966357 y2[1] (numeric) = 0.56593513032379689645590458220765 absolute error = 7.45834577254408e-18 relative error = 1.3178799782718605274837792112788e-15 % h = 0.001 y1[1] (analytic) = 1.9008816175907802421083223581184 y1[1] (numeric) = 1.9008816175907802268710169115825 absolute error = 1.52373054465359e-17 relative error = 8.0159149867775568074168110466298e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.45 y2[1] (analytic) = 0.5650344658887697895791557537681 y2[1] (numeric) = 0.56503446588876979707414936751444 absolute error = 7.49499361374634e-18 relative error = 1.3264666257052311599933801335073e-15 % h = 0.001 y1[1] (analytic) = 1.9004471023526769216688406114864 y1[1] (numeric) = 1.9004471023526769063953626195838 absolute error = 1.52734779919026e-17 relative error = 8.0367814357972130829126092138061e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.4MB, time=42.49 NO POLE NO POLE x[1] = 0.451 y2[1] (analytic) = 0.56413423641924055426432875377253 y2[1] (numeric) = 0.56413423641924056179604999073069 absolute error = 7.53172123695816e-18 relative error = 1.3350938040500178641794031899840e-15 % h = 0.001 y1[1] (analytic) = 1.9000116866675462858084653438511 y1[1] (numeric) = 1.9000116866675462704988729085862 absolute error = 1.53095924352649e-17 relative error = 8.0576306675863564006712865658399e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.452 y2[1] (analytic) = 0.56323444281543857756319316437161 y2[1] (numeric) = 0.56323444281543858513172172695137 absolute error = 7.56852856257976e-18 relative error = 1.3437616713826973210984037907868e-15 % h = 0.001 y1[1] (analytic) = 1.8995753709708039833731931975225 y1[1] (numeric) = 1.89957537097080396802754454427 absolute error = 1.53456486532525e-17 relative error = 8.0784626331567440233760968050777e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.4MB, time=42.72 NO POLE NO POLE x[1] = 0.453 y2[1] (analytic) = 0.56233508597715738829492786929617 y2[1] (numeric) = 0.56233508597715739590034338014059 absolute error = 7.60541551084442e-18 relative error = 1.3524703865185035882357356569151e-15 % h = 0.001 y1[1] (analytic) = 1.899138155698765674745686424569 y1[1] (numeric) = 1.8991381556987656593640399019723 absolute error = 1.53816465225967e-17 relative error = 8.0992772834566124780285034149819e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.454 y2[1] (analytic) = 0.56143616680375374979432144492579 y2[1] (numeric) = 0.56143616680375375743670344674441 absolute error = 7.64238200181862e-18 relative error = 1.3612201090155211573658043374483e-15 % h = 0.001 y1[1] (analytic) = 1.898700041288646595529648863792 y1[1] (numeric) = 1.8987000412886465801120629436619 absolute error = 1.54175859201301e-17 relative error = 8.1200745693702063390351032157674e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.4MB, time=42.96 NO POLE NO POLE x[1] = 0.455 y2[1] (analytic) = 0.56053768619414676055508377189468 y2[1] (numeric) = 0.56053768619414676823451172729682 absolute error = 7.67942795540214e-18 relative error = 1.3700109991787970569825398282462e-15 % h = 0.001 y1[1] (analytic) = 1.8982610281785611193346267716233 y1[1] (numeric) = 1.8982610281785611038811600488368 absolute error = 1.54534667227865e-17 relative error = 8.1408544417174116470069946852640e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.456 y2[1] (analytic) = 0.55963964504681695531082245130418 y2[1] (numeric) = 0.55963964504681696302737574263236 absolute error = 7.71655329132818e-18 relative error = 1.3788432180644828310532655190955e-15 % h = 0.001 y1[1] (analytic) = 1.8978211168075223196616717221096 y1[1] (numeric) = 1.8978211168075223041723829145078 absolute error = 1.54892888076018e-17 relative error = 8.1616168512539156657194918083206e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.4MB, time=43.20 NO POLE NO POLE x[1] = 0.457 y2[1] (analytic) = 0.55874204425980540655458294449053 y2[1] (numeric) = 0.55874204425980541430834087365405 absolute error = 7.75375792916352e-18 relative error = 1.3877169274840102053826112829966e-15 % h = 0.001 y1[1] (analytic) = 1.8973803076154415308903036902821 y1[1] (numeric) = 1.8973803076154415153652516385681 absolute error = 1.55250520517140e-17 relative error = 8.1823617486708924501869638219697e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.458 y2[1] (analytic) = 0.55784488473071282649785091673299 y2[1] (numeric) = 0.55784488473071283428889270504159 absolute error = 7.79104178830860e-18 relative error = 1.3966322900082792043493654649584e-15 % h = 0.001 y1[1] (analytic) = 1.8969386010431279083672133319129 y1[1] (numeric) = 1.8969386010431278928064569995501 absolute error = 1.55607563323628e-17 relative error = 8.2030890845944770384434395840762e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.4MB, time=43.43 NO POLE NO POLE x[1] = 0.459 y2[1] (analytic) = 0.55694816735669866946991482582499 y2[1] (numeric) = 0.55694816735669867729831961382267 absolute error = 7.82840478799768e-18 relative error = 1.4055894689718874801446354466973e-15 % h = 0.001 y1[1] (analytic) = 1.8964959975322879875971433709198 y1[1] (numeric) = 1.8964959975322879720007418440292 absolute error = 1.55964015268906e-17 relative error = 8.2237988095859770387069775796189e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.46 y2[1] (analytic) = 0.5560518930344802347584863560711 y2[1] (numeric) = 0.55605189303448024262433320337004 absolute error = 7.86584684729894e-18 relative error = 1.4145886284773760351237844566596e-15 % h = 0.001 y1[1] (analytic) = 1.8960524975255252425363899035004 y1[1] (numeric) = 1.8960524975255252269044023907577 absolute error = 1.56319875127427e-17 relative error = 8.2444908741416625099793582364982e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.4MB, time=43.67 NO POLE NO POLE x[1] = 0.461 y2[1] (analytic) = 0.55515606266033176989247585701442 y2[1] (numeric) = 0.55515606266033177779584374212901 absolute error = 7.90336788511459e-18 relative error = 1.4236299333995040234405257734478e-15 % h = 0.001 y1[1] (analytic) = 1.895608101466339642989365325457 y1[1] (numeric) = 1.8956081014663396273218511579904 absolute error = 1.56675141674666e-17 relative error = 8.2651652286920806939533220925531e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.462 y2[1] (analytic) = 0.55426067713008357436781950404435 y2[1] (numeric) = 0.55426067713008358230878732422542 absolute error = 7.94096782018107e-18 relative error = 1.4327135493895672855936694603402e-15 % h = 0.001 y1[1] (analytic) = 1.8951628097991272111086654861145 y1[1] (numeric) = 1.8951628097991271954056841174012 absolute error = 1.57029813687133e-17 relative error = 8.2858218236024250275171357368082e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.4MB, time=43.91 NO POLE NO POLE x[1] = 0.463 y2[1] (analytic) = 0.55336573733912110381725445498295 y2[1] (numeric) = 0.55336573733912111179590102605202 absolute error = 7.97864657106907e-18 relative error = 1.4418396428797122088156246433982e-15 % h = 0.001 y1[1] (analytic) = 1.8947166229691795769990845687246 y1[1] (numeric) = 1.8947166229691795612606955744877 absolute error = 1.57383889942369e-17 relative error = 8.3064606091720073696820693068476e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.464 y2[1] (analytic) = 0.55247124418238407462493783279988 y2[1] (numeric) = 0.5524712441823840826413418889836 absolute error = 8.01640405618372e-18 relative error = 1.4510083810873081009486208947458e-15 % h = 0.001 y1[1] (analytic) = 1.8942695414226835334260220933066 y1[1] (numeric) = 1.8942695414226835176522851714117 absolute error = 1.57737369218949e-17 relative error = 8.3270815356340989454739867748894e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.4MB, time=44.15 NO POLE NO POLE x[1] = 0.465 y2[1] (analytic) = 0.55157719855436556898680491976248 y2[1] (numeric) = 0.55157719855436557704104511352722 absolute error = 8.05424019376474e-18 relative error = 1.4602199320193405575482557782916e-15 % h = 0.001 y1[1] (analytic) = 1.8938215656067205896287273334791 y1[1] (numeric) = 1.8938215656067205738197023038306 absolute error = 1.58090250296485e-17 relative error = 8.3476845531557709904283993968079e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.466 y2[1] (analytic) = 0.55068360134911114041756150258825 y2[1] (numeric) = 0.55068360134911114850971640447472 absolute error = 8.09215490188647e-18 relative error = 1.4694744644768114202333308561976e-15 % h = 0.001 y1[1] (analytic) = 1.8933726959692665242388273340021 y1[1] (numeric) = 1.8933726959692665083945741384394 absolute error = 1.58442531955627e-17 relative error = 8.3682696118376294633533521597815e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.4MB, time=44.39 NO POLE NO POLE x[1] = 0.467 y2[1] (analytic) = 0.54979045346021791970520486153262 y2[1] (numeric) = 0.54979045346021792783535295999072 absolute error = 8.13014809845810e-18 relative error = 1.4787721480592034913021601204941e-15 % h = 0.001 y1[1] (analytic) = 1.8929229329591909373045856104637 y1[1] (numeric) = 1.8929229329591909214251643126569 absolute error = 1.58794212978068e-17 relative error = 8.3888366617137606210561281257736e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.468 y2[1] (analytic) = 0.54889775578083372131396744881682 y2[1] (numeric) = 0.54889775578083372948218715004056 absolute error = 8.16821970122374e-18 relative error = 1.4881131531689450412760945096682e-15 % h = 0.001 y1[1] (analytic) = 1.892472277026256801421339506815 y1[1] (numeric) = 1.8924722770262567855068102921609 absolute error = 1.59145292146541e-17 relative error = 8.4093856527512537140538776966096e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.4MB, time=44.62 NO POLE NO POLE x[1] = 0.469 y2[1] (analytic) = 0.54800550920365615023657685337748 y2[1] (numeric) = 0.54800550920365615844294648114002 absolute error = 8.20636962776254e-18 relative error = 1.4974976510159123115782079257690e-15 % h = 0.001 y1[1] (analytic) = 1.8920207286211200119685650802794 y1[1] (numeric) = 1.8920207286211199960189882557969 absolute error = 1.59495768244825e-17 relative error = 8.4299165348501986078557591637604e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.47 y2[1] (analytic) = 0.54711371462093170929672519960359 y2[1] (numeric) = 0.54711371462093171754132299509245 absolute error = 8.24459779548886e-18 relative error = 1.5069258136219703291231183080077e-15 % h = 0.001 y1[1] (analytic) = 1.8915682881953289364540192765334 y1[1] (numeric) = 1.8915682881953289204694552707587 absolute error = 1.59845640057747e-17 relative error = 8.4504292578434718612101765203420e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.4MB, time=44.86 NO POLE NO POLE x[1] = 0.471 y2[1] (analytic) = 0.54622237292445490690264067751721 y2[1] (numeric) = 0.54622237292445491518554479916954 absolute error = 8.28290412165233e-18 relative error = 1.5163978138255230604003129859714e-15 % h = 0.001 y1[1] (analytic) = 1.8911149562013239629654100509787 y1[1] (numeric) = 1.8911149562013239469459194138606 absolute error = 1.60194906371181e-17 relative error = 8.4709237714963637865409882696857e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.472 y2[1] (analytic) = 0.54533148500556736525265345075175 y2[1] (numeric) = 0.54533148500556737357394197408983 absolute error = 8.32128852333808e-18 relative error = 1.5259138252861242376103747676068e-15 % h = 0.001 y1[1] (analytic) = 1.890660733092437047730045984399 y1[1] (numeric) = 1.8906607330924370316756893871935 absolute error = 1.60543565972055e-17 relative error = 8.4914000255066280315810261952939e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.4MB, time=45.10 NO POLE NO POLE x[1] = 0.473 y2[1] (analytic) = 0.54444105175515692899364773668793 y2[1] (numeric) = 0.5444410517551569373533986541547 absolute error = 8.35975091746677e-18 relative error = 1.5354740224890814719767008070282e-15 % h = 0.001 y1[1] (analytic) = 1.8902056193228912617829178333128 y1[1] (numeric) = 1.8902056193228912456937560684782 absolute error = 1.60891617648346e-17 relative error = 8.5118579695038963060610296378409e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.474 y2[1] (analytic) = 0.54355107406365677433329140022077 y2[1] (numeric) = 0.5435510740636567827315826210155 absolute error = 8.39829122079473e-18 relative error = 1.5450785807501104881599186437278e-15 % h = 0.001 y1[1] (analytic) = 1.8897496153478003367436653469044 y1[1] (numeric) = 1.8897496153478003206197593279953 absolute error = 1.61239060189091e-17 relative error = 8.5322975530499388607374207189748e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.4MB, time=45.33 NO POLE NO POLE x[1] = 0.475 y2[1] (analytic) = 0.54266155282104451860693394885391 y2[1] (numeric) = 0.54266155282104452704384329876808 absolute error = 8.43690934991417e-18 relative error = 1.5547276762200325618665652129659e-15 % h = 0.001 y1[1] (analytic) = 1.8892927216231682097028835735269 y1[1] (numeric) = 1.8892927216231681935442943350887 absolute error = 1.61585892384382e-17 relative error = 8.5527187256380783905279179900711e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.476 y2[1] (analytic) = 0.54177248891684133030006336214914 y2[1] (numeric) = 0.54177248891684133877566858340234 absolute error = 8.47560522125320e-18 relative error = 1.5644214858894675429275374612159e-15 % h = 0.001 y1[1] (analytic) = 1.8888349386058885672182237704341 y1[1] (numeric) = 1.888834938605888551025012467897 absolute error = 1.61932113025371e-17 relative error = 8.5731214366931324393652008375055e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.4MB, time=45.57 NO POLE NO POLE x[1] = 0.477 y2[1] (analytic) = 0.54088388324011103952721173299992 y2[1] (numeric) = 0.54088388324011104804159048407595 absolute error = 8.51437875107603e-18 relative error = 1.5741601875935906949080830866321e-15 % h = 0.001 y1[1] (analytic) = 1.8883762667537443884207449206015 y1[1] (numeric) = 1.8883762667537443721929728301746 absolute error = 1.62277720904269e-17 relative error = 8.5935056355710379121690799475661e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.478 y2[1] (analytic) = 0.53999573667945924896819924174937 y2[1] (numeric) = 0.53999573667945925752142909723245 absolute error = 8.55322985548308e-18 relative error = 1.5839439600169039603660852365315e-15 % h = 0.001 y1[1] (analytic) = 1.8879167065254074872319727502484 y1[1] (numeric) = 1.8879167065254074709697012688129 absolute error = 1.62622714814355e-17 relative error = 8.6138712715590046480951609241567e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=736.2MB, alloc=4.4MB, time=45.81 NO POLE NO POLE x[1] = 0.479 y2[1] (analytic) = 0.53910805012303244526260552683451 y2[1] (numeric) = 0.53910805012303245385476397724561 absolute error = 8.59215845041110e-18 relative error = 1.5937729826980402402545905570452e-15 % h = 0.001 y1[1] (analytic) = 1.8874562583804380536921240299613 y1[1] (numeric) = 1.8874562583804380373954146749642 absolute error = 1.62967093549971e-17 relative error = 8.6342182938749274035495506735897e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=740.0MB, alloc=4.4MB, time=46.05 x[1] = 0.48 y2[1] (analytic) = 0.53822082445851711086335705741136 y2[1] (numeric) = 0.53822082445851711949452150904467 absolute error = 8.63116445163331e-18 relative error = 1.6036474360346027986200395198360e-15 % h = 0.001 y1[1] (analytic) = 1.8869949227792841943999548311587 y1[1] (numeric) = 1.886994922779284178068869240506 absolute error = 1.63310855906527e-17 relative error = 8.6545466516673268422598334373113e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.481 y2[1] (analytic) = 0.53733406057313883635031865429955 y2[1] (numeric) = 0.53733406057313884502056642905906 absolute error = 8.67024777475951e-18 relative error = 1.6135675012880307642122793246988e-15 % h = 0.001 y1[1] (analytic) = 1.8865327001832814720646922980094 y1[1] (numeric) = 1.8865327001832814556992922299589 absolute error = 1.63654000680505e-17 relative error = 8.6748562940152373550075363753746e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=743.8MB, alloc=4.4MB, time=46.28 x[1] = 0.482 y2[1] (analytic) = 0.5364477593536614332047768455809 y2[1] (numeric) = 0.53644775935366144191418518081715 absolute error = 8.70940833523625e-18 relative error = 1.6235333605885076776665229970851e-15 % h = 0.001 y1[1] (analytic) = 1.8860695910546524441705103828338 y1[1] (numeric) = 1.8860695910546524277708577158885 absolute error = 1.63996526669453e-17 relative error = 8.6951471699275644356333628136442e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.483 y2[1] (analytic) = 0.53556192168638604704570228229476 y2[1] (numeric) = 0.53556192168638605579434833064167 absolute error = 8.74864604834691e-18 relative error = 1.6335451969398854434274441071048e-15 % h = 0.001 y1[1] (analytic) = 1.8856055958565062007540108804759 y1[1] (numeric) = 1.885605595856506184320167613276 absolute error = 1.64338432671999e-17 relative error = 8.7154192283435017007111999673243e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.4MB, time=46.52 NO POLE NO POLE x[1] = 0.484 y2[1] (analytic) = 0.53467654845715027132867797789364 y2[1] (numeric) = 0.53467654845715028011663880710552 absolute error = 8.78796082921188e-18 relative error = 1.6436031942246592678374126229456e-15 % h = 0.001 y1[1] (analytic) = 1.8851407150528379012951719841238 y1[1] (numeric) = 1.8851407150528378848272002353392 absolute error = 1.64679717487846e-17 relative error = 8.7356724181319405660514781036478e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.485 y2[1] (analytic) = 0.53379164055132726150837967245725 y2[1] (numeric) = 0.5337916405513272703357322652459 absolute error = 8.82735259278865e-18 relative error = 1.6537075372089584471102208692994e-15 % h = 0.001 y1[1] (analytic) = 1.8846749491085283107222274715935 y1[1] (numeric) = 1.8846749491085282942201894798164 absolute error = 1.65020379917771e-17 relative error = 8.7559066880910912125144506262556e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.4MB, time=46.76 NO POLE NO POLE x[1] = 0.486 y2[1] (analytic) = 0.53290719885382484966549415911054 y2[1] (numeric) = 0.5329071988538248585323154129825 absolute error = 8.86682125387196e-18 relative error = 1.6638584115475812017380905589473e-15 % h = 0.001 y1[1] (analytic) = 1.884208298489343334530940517158 y1[1] (numeric) = 1.8842082984893433179948986407944 absolute error = 1.65360418763636e-17 relative error = 8.7761219869487397845310839621124e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.487 y2[1] (analytic) = 0.53202322424908465959896094565383 y2[1] (numeric) = 0.53202322424908466850532767274776 absolute error = 8.90636672709393e-18 relative error = 1.6740560037890588966969708632087e-15 % h = 0.001 y1[1] (analytic) = 1.8837407636619335530187370096079 y1[1] (numeric) = 1.8837407636619335364487537267697 absolute error = 1.65699832828382e-17 relative error = 8.7963182633616034344155918311280e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.4MB, time=46.99 NO POLE NO POLE x[1] = 0.488 y2[1] (analytic) = 0.53113971762108122238442215908945 y2[1] (numeric) = 0.53113971762108123133041108601364 absolute error = 8.94598892692419e-18 relative error = 1.6843005013807536176771100334716e-15 % h = 0.001 y1[1] (analytic) = 1.8832723450938337546341641423728 y1[1] (numeric) = 1.8832723450938337380303020507693 absolute error = 1.66038620916035e-17 relative error = 8.8164954659153215185762636205010e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.489 y2[1] (analytic) = 0.53025667985332109239976513452147 y2[1] (numeric) = 0.53025667985332110138545290219146 absolute error = 8.98568776766999e-18 relative error = 1.6945920926739855818156145986914e-15 % h = 0.001 y1[1] (analytic) = 1.882803043253462468442140926205 y1[1] (numeric) = 1.8828030432534624518044627430342 absolute error = 1.66376781831708e-17 relative error = 8.8366535431242342538490049451761e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.4MB, time=47.23 NO POLE NO POLE x[1] = 0.49 y2[1] (analytic) = 0.52937411182884196381864166281204 y2[1] (numeric) = 0.52937411182884197284410482628844 absolute error = 9.02546316347640e-18 relative error = 1.7049309669292113705106686712856e-15 % h = 0.001 y1[1] (analytic) = 1.8823328586101214957054681591367 y1[1] (numeric) = 1.8823328586101214790340367209765 absolute error = 1.66714314381602e-17 relative error = 8.8567924434311078403652477143375e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.491 y2[1] (analytic) = 0.52849201443021178757284740340174 y2[1] (numeric) = 0.52849201443021179663816243172807 absolute error = 9.06531502832633e-18 relative error = 1.7153173143212023482936106887569e-15 % h = 0.001 y1[1] (analytic) = 1.8818617916339954405830662721614 y1[1] (numeric) = 1.8818617916339954238779445348606 absolute error = 1.67051217373008e-17 relative error = 8.8769121152069122341313506862962e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.4MB, time=47.47 NO POLE NO POLE x[1] = 0.492 y2[1] (analytic) = 0.52761038853952788878444449984064 y2[1] (numeric) = 0.52761038853952789788968777588142 absolute error = 9.10524327604078e-18 relative error = 1.7257513259443008361433467995123e-15 % h = 0.001 y1[1] (analytic) = 1.8813898427961512399454103523624 y1[1] (numeric) = 1.8813898427961512232066613909315 absolute error = 1.67387489614309e-17 relative error = 8.8970125067505985083025059750714e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.493 y2[1] (analytic) = 0.52672923503841608466850996583417 y2[1] (numeric) = 0.52672923503841609381375778611306 absolute error = 9.14524782027889e-18 relative error = 1.7362331938176731705845467144330e-15 % h = 0.001 y1[1] (analytic) = 1.8809170125685376923076325280146 y1[1] (numeric) = 1.8809170125685376755353195365162 absolute error = 1.67723129914984e-17 relative error = 8.9170935662889821327911010764219e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.4MB, time=47.71 NO POLE NO POLE x[1] = 0.494 y2[1] (analytic) = 0.52584855480802980290739193898176 y2[1] (numeric) = 0.52584855480802981209272051351988 absolute error = 9.18532857453812e-18 relative error = 1.7467631108906222223464509439114e-15 % h = 0.001 y1[1] (analytic) = 1.8804433014239849858807627825173 y1[1] (numeric) = 1.8804433014239849690749490739567 absolute error = 1.68058137085606e-17 relative error = 8.9371552419763069266380876743286e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.495 y2[1] (analytic) = 0.52496834872904920049735542787856 y2[1] (numeric) = 0.52496834872904920972284088003291 absolute error = 9.22548545215435e-18 relative error = 1.7573412710479199240056042349223e-15 % h = 0.001 y1[1] (analytic) = 1.8799687098362042257415801458792 y1[1] (numeric) = 1.8799687098362042089023291520942 absolute error = 1.68392509937850e-17 relative error = 8.9571974818943401971474578986016e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.4MB, time=47.95 NO POLE NO POLE x[1] = 0.496 y2[1] (analytic) = 0.52408861768168028306849870586105 y2[1] (numeric) = 0.52408861768168029233421707216309 absolute error = 9.26571836630204e-18 relative error = 1.7679678691151866069351189956266e-15 % h = 0.001 y1[1] (analytic) = 1.8794932382797869601215470938628 y1[1] (numeric) = 1.8794932382797869432489223654139 absolute error = 1.68726247284489e-17 relative error = 8.9772202340518294753093413993168e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.497 y2[1] (analytic) = 0.52320936254565402467882103140682 y2[1] (numeric) = 0.52320936254565403398484826140115 absolute error = 9.30602722999433e-18 relative error = 1.7786431008642946139526062642241e-15 % h = 0.001 y1[1] (analytic) = 1.8790168872302047058153008658165 y1[1] (numeric) = 1.8790168872302046889093660718768 absolute error = 1.69059347939397e-17 relative error = 8.9972234463843308840739373974704e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.4MB, time=48.18 NO POLE NO POLE x[1] = 0.498 y2[1] (analytic) = 0.52233058420022548808332190104733 y2[1] (numeric) = 0.52233058420022549742973385713056 absolute error = 9.34641195608323e-18 relative error = 1.7893671630188250405499646740480e-15 % h = 0.001 y1[1] (analytic) = 1.8785396571638084727091762926628 y1[1] (numeric) = 1.8785396571638084557699952209071 absolute error = 1.69391810717557e-17 relative error = 9.0172070667543033307880740119959e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.499 y2[1] (analytic) = 0.52145228352417294547901156562125 y2[1] (numeric) = 0.52145228352417295486588402288094 absolute error = 9.38687245725969e-18 relative error = 1.8001402532595378073617796724166e-15 % h = 0.001 y1[1] (analytic) = 1.8780615485578282874302356064793 y1[1] (numeric) = 1.8780615485578282704578721629736 absolute error = 1.69723634435057e-17 relative error = 9.0371710429505638086237900018121e-16 % h = 0.001 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.4MB, time=48.42 NO POLE NO POLE x[1] = 0.5 y2[1] (analytic) = 0.52057446139579699972671206478443 y2[1] (numeric) = 0.52057446139579700915412071083819 absolute error = 9.42740864605376e-18 relative error = 1.8109625702298954079609224409995e-15 % h = 0.001 y1[1] (analytic) = 1.8775825618903727161162815826038 y1[1] (numeric) = 1.8775825618903726991107997916947 absolute error = 1.70054817909091e-17 relative error = 9.0571153226880080880554610745880e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 0.5196971186929197060505275579023 y2[1] (numeric) = 0.51969711869291971551854799273706 absolute error = 9.46802043483476e-18 relative error = 1.8218343135416254184191420848730e-15 % h = 0.001 y1[1] (analytic) = 1.8771026976404283863073312442114 y1[1] (numeric) = 1.8771026976404283692687952484146 absolute error = 1.70385359957968e-17 relative error = 9.0770398536077570901847411802462e-16 % h = 0.001 Finished! diff ( y2 , x , 1 ) = m1 * y1 + 1.0; diff ( y1 , x , 1 ) = y2 - 1.0; Iterations = 401 Total Elapsed Time = 48 Seconds Elapsed Time(since restart) = 48 Seconds Time to Timeout = 14 Minutes 11 Seconds Percent Done = 100.5 % > quit memory used=780.9MB, alloc=4.4MB, time=48.58