|\^/| 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, 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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre add $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp2[1] := (array_tmp1[1] - (array_const_2D0[1])); > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (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 diff $eq_no = 2 i = 1 > array_tmp4[1] := array_y2_higher[6,1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * (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 add $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D0[2] + array_y1[2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp2[2] := (array_tmp1[2] - (array_const_2D0[2])); > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (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 diff $eq_no = 2 i = 2 > array_tmp4[2] := array_y2_higher[6,2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre add $eq_no = 1 i = 3 > array_tmp1[3] := array_const_0D0[3] + array_y1[3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp2[3] := (array_tmp1[3] - (array_const_2D0[3])); > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre diff $eq_no = 2 i = 3 > array_tmp4[3] := array_y2_higher[6,3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add $eq_no = 1 i = 4 > array_tmp1[4] := array_const_0D0[4] + array_y1[4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp2[4] := (array_tmp1[4] - (array_const_2D0[4])); > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (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 diff $eq_no = 2 i = 4 > array_tmp4[4] := array_y2_higher[6,4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * (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 add $eq_no = 1 i = 5 > array_tmp1[5] := array_const_0D0[5] + array_y1[5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp2[5] := (array_tmp1[5] - (array_const_2D0[5])); > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (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 diff $eq_no = 2 i = 5 > array_tmp4[5] := array_y2_higher[6,5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * (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 add $eq_no = 1 > array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; > #emit sub $eq_no = 1 > array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_2D0[kkk])); > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (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 diff $eq_no = 2 > array_tmp4[kkk] := array_y2_higher[6,kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp4[kkk] * (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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; array_tmp2[1] := array_tmp1[1] - array_const_2D0[1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*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_tmp4[1] := array_y2_higher[6, 1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*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] := array_const_0D0[2] + array_y1[2]; array_tmp2[2] := array_tmp1[2] - array_const_2D0[2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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_tmp4[2] := array_y2_higher[6, 2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*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] := array_const_0D0[3] + array_y1[3]; array_tmp2[3] := array_tmp1[3] - array_const_2D0[3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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_tmp4[3] := array_y2_higher[6, 3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*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] := array_const_0D0[4] + array_y1[4]; array_tmp2[4] := array_tmp1[4] - array_const_2D0[4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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_tmp4[4] := array_y2_higher[6, 4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*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] := array_const_0D0[5] + array_y1[5]; array_tmp2[5] := array_tmp1[5] - array_const_2D0[5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[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_tmp4[5] := array_y2_higher[6, 5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*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] := array_const_0D0[kkk] + array_y1[kkk]; array_tmp2[kkk] := array_tmp1[kkk] - array_const_2D0[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*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_tmp4[kkk] := array_y2_higher[6, kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*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) > 2.0 + sin(x); > end; exact_soln_y1 := proc(x) 2.0 + sin(x) end proc > exact_soln_y2 := proc(x) > 2.0 - cos(x); > end; exact_soln_y2 := proc(x) 2.0 - cos(x) end proc > exact_soln_y2p := proc(x) > sin(x); > end; exact_soln_y2p := proc(x) sin(x) end proc > exact_soln_y2pp := proc(x) > cos(x); > end; exact_soln_y2pp := proc(x) cos(x) end proc > exact_soln_y2ppp := proc(x) > -sin(x); > end; exact_soln_y2ppp := proc(x) -sin(x) end proc > exact_soln_y2pppp := proc(x) > -cos(x); > end; exact_soln_y2pppp := proc(x) -cos(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 > DEBUGMASSIVE, > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > #Top Generate Globals Decl > glob_normmax, > glob_iter, > glob_max_rel_trunc_err, > glob_log10_abserr, > glob_dump_analytic, > glob_hmin, > years_in_century, > days_in_year, > glob_smallish_float, > glob_log10relerr, > glob_current_iter, > glob_unchanged_h_cnt, > glob_small_float, > glob_disp_incr, > hours_in_day, > sec_in_min, > glob_dump, > glob_max_minutes, > glob_max_iter, > glob_max_hours, > glob_optimal_expect_sec, > glob_log10normmin, > glob_start, > glob_warned, > glob_optimal_start, > glob_hmax, > djd_debug2, > djd_debug, > glob_html_log, > glob_max_sec, > glob_display_flag, > glob_log10abserr, > glob_optimal_clock_start_sec, > glob_abserr, > glob_reached_optimal_h, > glob_clock_start_sec, > centuries_in_millinium, > MAX_UNCHANGED, > glob_max_trunc_err, > glob_relerr, > glob_large_float, > glob_hmin_init, > glob_not_yet_start_msg, > glob_not_yet_finished, > glob_almost_1, > glob_percent_done, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_warned2, > glob_last_good_h, > glob_clock_sec, > glob_subiter_method, > glob_no_eqs, > glob_log10_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > min_in_hour, > glob_max_opt_iter, > glob_look_poles, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_type_pole, > array_pole, > array_x, > array_m1, > array_y2, > array_y1, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y1_init, > array_last_rel_error, > array_1st_rel_error, > array_y2_init, > array_y2_set_initial, > array_real_pole, > array_y2_higher_work, > array_y1_higher, > array_poles, > array_y2_higher, > array_complex_pole, > array_y2_higher_work2, > array_y1_higher_work2, > array_y1_set_initial, > array_y1_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGMASSIVE := 4; > DEBUGL := 3; > INFO := 2; > glob_iolevel := 5; > glob_max_terms := 30; > ALWAYS := 1; > glob_normmax := 0.0; > glob_iter := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_dump_analytic := false; > glob_hmin := 0.00000000001; > years_in_century := 100.0; > days_in_year := 365.0; > glob_smallish_float := 0.1e-100; > glob_log10relerr := 0.0; > glob_current_iter := 0; > glob_unchanged_h_cnt := 0; > glob_small_float := 0.1e-50; > glob_disp_incr := 0.1; > hours_in_day := 24.0; > sec_in_min := 60.0; > glob_dump := false; > glob_max_minutes := 0.0; > glob_max_iter := 1000; > glob_max_hours := 0.0; > glob_optimal_expect_sec := 0.1; > glob_log10normmin := 0.1; > glob_start := 0; > glob_warned := false; > glob_optimal_start := 0.0; > glob_hmax := 1.0; > djd_debug2 := true; > djd_debug := true; > glob_html_log := true; > glob_max_sec := 10000.0; > glob_display_flag := true; > glob_log10abserr := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_reached_optimal_h := false; > glob_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > MAX_UNCHANGED := 10; > glob_max_trunc_err := 0.1e-10; > glob_relerr := 0.1e-10; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_not_yet_start_msg := true; > glob_not_yet_finished := true; > glob_almost_1 := 0.9990; > glob_percent_done := 0.0; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_warned2 := false; > glob_last_good_h := 0.1; > glob_clock_sec := 0.0; > glob_subiter_method := 3; > glob_no_eqs := 0; > glob_log10_relerr := 0.1e-10; > glob_h := 0.1; > glob_optimal_done := false; > glob_initial_pass := true; > min_in_hour := 60.0; > glob_max_opt_iter := 10; > glob_look_poles := false; > #Write Set Defaults > glob_orig_start_sec := elapsed_time_seconds(); > MAX_UNCHANGED := 10; > glob_curr_iter_when_opt := 0; > glob_display_flag := true; > glob_no_eqs := 2; > glob_iter := -1; > opt_iter := -1; > glob_max_iter := 50000; > glob_max_hours := 0.0; > glob_max_minutes := 15.0; > omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################"); > omniout_str(ALWAYS,"##############temp/mtest9_revpostode.ode#################"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.5;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"glob_subiter_method := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > 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,"2.0 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"-sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_norms:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= 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_y1_init:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher_work := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y2_higher_work2 := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_type_pole[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_x[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_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_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_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_y2_init[term] := 0.0; > term := term + 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 <= 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 <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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_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 <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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 > ; > #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_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_const_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_5[1] := 5; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.5; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > glob_subiter_method := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > 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] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := true; > array_y2_set_initial[1,5] := true; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > 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 := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * 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 := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 6; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 5; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (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 := 6; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 6; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (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) = y1 - 2.0;"); > omniout_str(INFO,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T17:32:39-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9_rev") > ; > logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_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,"mtest9_rev diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9_rev 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) = diff(y2,x,5);") > ; > 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 DEBUGMASSIVE, DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, glob_normmax, glob_iter, glob_max_rel_trunc_err, glob_log10_abserr, glob_dump_analytic, glob_hmin, years_in_century, days_in_year, glob_smallish_float, glob_log10relerr, glob_current_iter, glob_unchanged_h_cnt, glob_small_float, glob_disp_incr, hours_in_day, sec_in_min, glob_dump, glob_max_minutes, glob_max_iter, glob_max_hours, glob_optimal_expect_sec, glob_log10normmin, glob_start, glob_warned, glob_optimal_start, glob_hmax, djd_debug2, djd_debug, glob_html_log, glob_max_sec, glob_display_flag, glob_log10abserr, glob_optimal_clock_start_sec, glob_abserr, glob_reached_optimal_h, glob_clock_start_sec, centuries_in_millinium, MAX_UNCHANGED, glob_max_trunc_err, glob_relerr, glob_large_float, glob_hmin_init, glob_not_yet_start_msg, glob_not_yet_finished, glob_almost_1, glob_percent_done, glob_curr_iter_when_opt, glob_orig_start_sec, glob_warned2, glob_last_good_h, glob_clock_sec, glob_subiter_method, glob_no_eqs, glob_log10_relerr, glob_h, glob_optimal_done, glob_initial_pass, min_in_hour, glob_max_opt_iter, glob_look_poles, array_const_5, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_type_pole, array_pole, array_x, array_m1, array_y2, array_y1, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y1_init, array_last_rel_error, array_1st_rel_error, array_y2_init, array_y2_set_initial, array_real_pole, array_y2_higher_work, array_y1_higher, array_poles, array_y2_higher, array_complex_pole, array_y2_higher_work2, array_y1_higher_work2, array_y1_set_initial, array_y1_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGMASSIVE := 4; DEBUGL := 3; INFO := 2; glob_iolevel := 5; glob_max_terms := 30; ALWAYS := 1; glob_normmax := 0.; glob_iter := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_dump_analytic := false; glob_hmin := 0.1*10^(-10); years_in_century := 100.0; days_in_year := 365.0; glob_smallish_float := 0.1*10^(-100); glob_log10relerr := 0.; glob_current_iter := 0; glob_unchanged_h_cnt := 0; glob_small_float := 0.1*10^(-50); glob_disp_incr := 0.1; hours_in_day := 24.0; sec_in_min := 60.0; glob_dump := false; glob_max_minutes := 0.; glob_max_iter := 1000; glob_max_hours := 0.; glob_optimal_expect_sec := 0.1; glob_log10normmin := 0.1; glob_start := 0; glob_warned := false; glob_optimal_start := 0.; glob_hmax := 1.0; djd_debug2 := true; djd_debug := true; glob_html_log := true; glob_max_sec := 10000.0; glob_display_flag := true; glob_log10abserr := 0.; glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_clock_start_sec := 0.; centuries_in_millinium := 10.0; MAX_UNCHANGED := 10; glob_max_trunc_err := 0.1*10^(-10); glob_relerr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_not_yet_start_msg := true; glob_not_yet_finished := true; glob_almost_1 := 0.9990; glob_percent_done := 0.; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_warned2 := false; glob_last_good_h := 0.1; glob_clock_sec := 0.; glob_subiter_method := 3; glob_no_eqs := 0; glob_log10_relerr := 0.1*10^(-10); glob_h := 0.1; glob_optimal_done := false; glob_initial_pass := true; min_in_hour := 60.0; glob_max_opt_iter := 10; glob_look_poles := false; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 2; glob_iter := -1; opt_iter := -1; glob_max_iter := 50000; glob_max_hours := 0.; glob_max_minutes := 15.0; omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"); omniout_str(ALWAYS, "##############temp/mtest9_revpostode.ode#################"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.5;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "glob_subiter_method := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); 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, "2.0 + sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "-sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_norms := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := 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_y1_init := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_y2_higher_work := Array(1 .. 7, 1 .. max_terms + 1, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); array_y2_higher := Array(1 .. 7, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_y2_higher_work2 := Array(1 .. 7, 1 .. max_terms + 1, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_norms[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_m1[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_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_y1_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 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 <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher[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 <= 6 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[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_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_const_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.5; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; glob_h := 0.0001; 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] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := true; array_y2_set_initial[1, 5] := true; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; 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 := 5; 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 := 5; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( 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 := 6; 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 := 6; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*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) = y1 - 2.0;"); omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T17:32:39-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9_rev"); logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_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, "mtest9_rev diffeq.mxt"); logitem_str(html_log_file, "mtest9_rev 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) = diff(y2,x,5);"); 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/mtest9_revpostode.ode################# diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) 2.0 + sin(x); end; exact_soln_y2 := proc(x) 2.0 - cos(x); end; exact_soln_y2p := proc(x) sin(x); end; exact_soln_y2pp := proc(x) cos(x); end; exact_soln_y2ppp := proc(x) -sin(x); end; exact_soln_y2pppp := proc(x) -cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.0001 x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.0001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5001 y2[1] (analytic) = 1.1224653850513206057226212384082 y2[1] (numeric) = 1.1224653850513206057225812850612 absolute error = 3.99533470e-23 relative error = 3.5594279816631744060018373993147e-21 % h = 0.0001 y1[1] (analytic) = 2.4795132944631180827612490419532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 8.77558589150824879611067376e-05 relative error = 0.0035392372814070356873465959087753 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5002 y2[1] (analytic) = 1.122513340768360069735529546726 y2[1] (numeric) = 1.122513340768360069734251000617 absolute error = 1.2785461090e-21 relative error = 1.1390030412688329777726287466527e-19 % h = 0.0001 y1[1] (analytic) = 2.4796010455269002246139734402722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0001755069226972243406855050566 relative error = 0.0070780306781137923396978378563839 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.42 NO POLE NO POLE x[1] = 0.5003 y2[1] (analytic) = 1.1225613052602661187524483331957 y2[1] (numeric) = 1.1225613052602661187427390775074 absolute error = 9.7092556883e-21 relative error = 8.6491986164166834930999012427343e-19 % h = 0.0001 y1[1] (analytic) = 2.4796887917946719151943709705102 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0002632531904689149210830352946 relative error = 0.010616380222390154323420137410111 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5004 y2[1] (analytic) = 1.122609278526559107854716811747 y2[1] (numeric) = 1.122609278526559107813800840139 absolute error = 4.09159716080e-20 relative error = 3.6447205978648959407660893371546e-18 % h = 0.0001 y1[1] (analytic) = 2.479776533265555691825455945761 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0003509946613526915521680105454 relative error = 0.014154285946503230345708760152732 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5005 y2[1] (analytic) = 1.1226572605667593043798048685764 y2[1] (numeric) = 1.122657260566759304254935423881 absolute error = 1.248694446954e-19 relative error = 1.1122668429753996493912495105327e-17 % h = 0.0001 y1[1] (analytic) = 2.4798642699386741397991217786374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0004387313344711395258338434218 relative error = 0.017691747882717353010916621593082 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5006 y2[1] (analytic) = 1.1227052513803868879261103887678 y2[1] (numeric) = 1.1227052513803868876153857750655 absolute error = 3.107246137023e-19 relative error = 2.7676419373674286810216521185989e-17 % h = 0.0001 y1[1] (analytic) = 2.4799520018131498923849151283452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0005264632089468921116271931296 relative error = 0.021228766063294078377159362912004 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=0.95 NO POLE NO POLE x[1] = 0.5007 y2[1] (analytic) = 1.1227532509669619503577574603049 y2[1] (numeric) = 1.1227532509669619496861386509872 absolute error = 6.716188093177e-19 relative error = 5.9818914684885023123308063921464e-17 % h = 0.0001 y1[1] (analytic) = 2.4800397288881056308388095679803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0006141902839026305655216327647 relative error = 0.024765340520492185513196598099757 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5008 y2[1] (analytic) = 1.1228012593260044958093954554259 y2[1] (numeric) = 1.1228012593260044944999246199035 absolute error = 1.3094708355224e-18 relative error = 1.1662534439162007869017965741049e-16 % h = 0.0001 y1[1] (analytic) = 2.4801274511626640844119787719614 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007019125584610841386908367458 relative error = 0.02830147128656767605558922409793 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5009 y2[1] (analytic) = 1.122849276457034440690998989273 y2[1] (numeric) = 1.1228492764570344383312180610346 absolute error = 2.3597809282384e-18 relative error = 2.1016007915900335475301034839687e-16 % h = 0.0001 y1[1] (analytic) = 2.4802151686359480303595692235113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0007896300317450300862812882957 relative error = 0.031837158393773773766132685611939 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228973023595716096962371645635 absolute error = 3.9964315912251e-18 relative error = 3.5590357041799818917528935659069e-16 % h = 0.0001 y1[1] (analytic) = 2.4803028813070802939494724420977 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008773427028772936761845068821 relative error = 0.035372401874360924089566086208289 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=3.9MB, time=1.48 x[1] = 0.5011 y2[1] (analytic) = 1.1229453370331357557894332408103 y2[1] (numeric) = 1.1229453370331357493529439316358 absolute error = 6.4364893091745e-18 relative error = 5.7317921869464717621046234700062e-16 % h = 0.0001 y1[1] (analytic) = 2.4803905891751837484710967307476 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.000965050570980748197808795532 relative error = 0.038907201760576793711557037472634 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5012 y2[1] (analytic) = 1.1229933804772465202460513123167 y2[1] (numeric) = 1.1229933804772465103010441743599 absolute error = 9.9450071379568e-18 relative error = 8.8558021007482691157362098073858e-16 % h = 0.0001 y1[1] (analytic) = 2.4804782922393813152441384431453 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0010527536351783149708505079297 relative error = 0.04244155808466627011696213787216 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5013 y2[1] (analytic) = 1.1230414326914234726218156877758 y2[1] (numeric) = 1.1230414326914234577819875158068 absolute error = 1.48398281719690e-17 relative error = 1.3213963207398883990633889562694e-15 % h = 0.0001 y1[1] (analytic) = 2.4805659904987959636273527704284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0011404518945929633540648352128 relative error = 0.045975470878871461148362973176003 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5014 y2[1] (analytic) = 1.123089493675186090775357278548 y2[1] (numeric) = 1.1230894936751860692789673900104 absolute error = 2.14963898885376e-17 relative error = 1.9140406895084596337380334996386e-15 % h = 0.0001 y1[1] (analytic) = 2.4806536839525507110273240475931 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0012281453483477107540361123775 relative error = 0.049508940175431694564877530195195 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5015 y2[1] (analytic) = 1.1231375634280537648694504112957 y2[1] (numeric) = 1.1231375634280537345169210419673 absolute error = 3.03525293693284e-17 relative error = 2.7024765583198954362990474455866e-15 % h = 0.0001 y1[1] (analytic) = 2.4807413725997686229072355794206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.001315833995565622633947644205 relative error = 0.05304196600658351760124691565663 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=2.02 NO POLE NO POLE x[1] = 0.5016 y2[1] (analytic) = 1.1231856419495457973758189263517 y2[1] (numeric) = 1.1231856419495457554625295276368 absolute error = 4.19132893987149e-17 relative error = 3.7316439805947654034543240004214e-15 % h = 0.0001 y1[1] (analytic) = 2.4808290564395728127956389858385 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0014035178353698125223510506229 relative error = 0.056574548404560696527197272142876 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5017 y2[1] (analytic) = 1.123233729239181403079943152998 y2[1] (numeric) = 1.1232337292391813463242177139408 absolute error = 5.67557254390572e-17 relative error = 5.0528864974078458410914509585353e-15 % h = 0.0001 y1[1] (analytic) = 2.4809167354710864422952230666275 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0014911968668834420219351314119 relative error = 0.060106687401594216207076782917388 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5018 y2[1] (analytic) = 1.1232818252964797090858677616068 y2[1] (numeric) = 1.1232818252964796335521542787641 absolute error = 7.55337134828427e-17 relative error = 6.7243777814090675165908313209214e-15 % h = 0.0001 y1[1] (analytic) = 2.4810044096934327210915821853874 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0015788710892297208182942501718 relative error = 0.063638383029912279659767657636522 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5019 y2[1] (analytic) = 1.1233299301209597548210104925963 y2[1] (numeric) = 1.1233299301209596558382517109542 absolute error = 9.89827587816421e-17 relative error = 8.8115482484281063216010204630400e-15 % h = 0.0001 y1[1] (analytic) = 2.4810920791057349069619841726739 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0016665405015319066886962374583 relative error = 0.067169635321740307618872990881736 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=3.9MB, time=2.54 NO POLE NO POLE x[1] = 0.502 y2[1] (analytic) = 1.1233780437121404920409717621522 y2[1] (numeric) = 1.1233780437121403641161663103213 absolute error = 1.279248054518309e-16 relative error = 1.1387511636698049527321551304247e-14 % h = 0.0001 y1[1] (analytic) = 2.4811797437071163057841377482187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0017542051029133055108498130031 relative error = 0.070700444309300938093178385518425 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5021 y2[1] (analytic) = 1.1234261660695407848343451446679 y2[1] (numeric) = 1.1234261660695406215612981876383 absolute error = 1.632730469570296e-16 relative error = 1.4533491553633876808755916091875e-14 % h = 0.0001 y1[1] (analytic) = 2.4812674034967002715449594621449 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0018418648924972712716715269293 relative error = 0.074230810024814025927388232900411 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5022 y2[1] (analytic) = 1.1234742971926794096275287318546 y2[1] (numeric) = 1.1234742971926792035907912646409 absolute error = 2.060367374672137e-16 relative error = 1.8339247990101347662833473303597e-14 % h = 0.0001 y1[1] (analytic) = 2.4813550584736102063493401550904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0019295198694072060760522198748 relative error = 0.077760732500496642363136542000036 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5023 y2[1] (analytic) = 1.1235224370810750551895373684732 y2[1] (numeric) = 1.1235224370810747978635332740275 absolute error = 2.573260040944457e-16 relative error = 2.2903503802112024190229846458462e-14 % h = 0.0001 y1[1] (analytic) = 2.4814427086369695604289109371521 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0020171700327665601556230019365 relative error = 0.081290211768563074600272209580537 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=3.9MB, time=3.08 NO POLE NO POLE x[1] = 0.5024 y2[1] (analytic) = 1.12357058573424632263681576464 y2[1] (numeric) = 1.1235705857342460042801557594592 absolute error = 3.183566600051808e-16 relative error = 2.8334371159880153120626016900052e-14 % h = 0.0001 y1[1] (analytic) = 2.4815303539859018321508086855622 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0021048153816988318775207503466 relative error = 0.084819247861224825358418623499678 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5025 y2[1] (analytic) = 1.1236187431517117254380524846586 y2[1] (numeric) = 1.1236187431517113349830340755598 absolute error = 3.904550184090988e-16 relative error = 3.4749777964177241591693042711944e-14 % h = 0.0001 y1[1] (analytic) = 2.4816179945195305680264410610091 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0021924559153275677531531257935 relative error = 0.088347840810690612438807491314677 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5026 y2[1] (analytic) = 1.1236669093329896894189948123286 y2[1] (numeric) = 1.1236669093329892143562873879159 absolute error = 4.750627074244127e-16 relative error = 4.2277894229920022616853460099026e-14 % h = 0.0001 y1[1] (analytic) = 2.4817056302369793627202510425165 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0022800916327763624469631073009 relative error = 0.091875990649166368286386786435399 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5027 y2[1] (analytic) = 1.1237150842775985527672644926845 y2[1] (numeric) = 1.1237150842775979790257786730768 absolute error = 5.737414858196077e-16 relative error = 5.1057558436927830426879629990958e-14 % h = 0.0001 y1[1] (analytic) = 2.4817932611373718590584809807915 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0023677225331688587851930455759 relative error = 0.095403697408855239552202703992763 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=3.9MB, time=3.60 NO POLE NO POLE x[1] = 0.5028 y2[1] (analytic) = 1.1237632679850565660371743501153 y2[1] (numeric) = 1.1237632679850558778591147185545 absolute error = 6.881780596315608e-16 relative error = 6.1238703847785133805350909704015e-14 % h = 0.0001 y1[1] (analytic) = 2.4818808872198317480379361699548 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0024553486156287477646482347392 relative error = 0.098930961121957586656055518714595 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5029 y2[1] (analytic) = 1.123811460454881892154545782817 y2[1] (numeric) = 1.1238114604548810719656461228238 absolute error = 8.201888996599932e-16 relative error = 7.2982784792745193004855153482851e-14 % h = 0.0001 y1[1] (analytic) = 2.4819685084834827688347479375655 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0025429698792797685614600023499 relative error = 0.10245778182067098334942923710964 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.503 y2[1] (analytic) = 1.1238596616865926064215271335312 y2[1] (numeric) = 1.1238596616865916346964672953222 absolute error = 9.717250598382090e-16 relative error = 8.6463202921610960949418515093497e-14 % h = 0.0001 y1[1] (analytic) = 2.4820561249274487088131362528522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0026305863232457085398483176366 relative error = 0.10598415953719021627869493626097 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5031 y2[1] (analytic) = 1.1239078716797066965214129365188 y2[1] (numeric) = 1.1239078716797055516444164564499 absolute error = 1.1448769964800689e-15 relative error = 1.0186573342252896175921696720981e-13 % h = 0.0001 y1[1] (analytic) = 2.4821437365508534035341718530639 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0027181979466504032608839178483 relative error = 0.10951009430370728454858768163501 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=3.9MB, time=4.13 x[1] = 0.5032 y2[1] (analytic) = 1.1239560904337420625234640407234 y2[1] (numeric) = 1.1239560904337407206440756375698 absolute error = 1.3418793884031536e-15 relative error = 1.1938895120763245302642408999210e-13 % h = 0.0001 y1[1] (analytic) = 2.4822313433528207367645378878518 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0028058047486177364912499526362 relative error = 0.11303558615241139928595691624867 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5033 y2[1] (analytic) = 1.1240043179482165168877286090746 y2[1] (numeric) = 1.1240043179482149517717706810076 absolute error = 1.5651159579280670e-15 relative error = 1.3924465706546980840657569167657e-13 % h = 0.0001 y1[1] (analytic) = 2.4823189453324746404852910815948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0028934067282716402120031463792 relative error = 0.11656063511548898320379021363783 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5034 y2[1] (analytic) = 1.1240525542226477844698639938838 y2[1] (numeric) = 1.1240525542226459673455712400517 absolute error = 1.8171242927538321e-15 relative error = 1.6165830378015434572126989312331e-13 % h = 0.0001 y1[1] (analytic) = 2.4824065424889390949006224135825 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0029810038847360946273344783669 relative error = 0.12008524122512367016551028714358 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5035 y2[1] (analytic) = 1.1241007992565535025259594882828 y2[1] (numeric) = 1.1241007992565514019252907789532 absolute error = 2.1006006687093296e-15 relative error = 1.8686942221717160723696120595262e-13 % h = 0.0001 y1[1] (analytic) = 2.4824941348213381284466173159652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0030685962171351281733293807496 relative error = 0.12360940451349630474954514789207 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5036 y2[1] (analytic) = 1.1241490530494512207173599536599 y2[1] (numeric) = 1.124149053049448802312486572926 absolute error = 2.4184048733807339e-15 relative error = 2.1513204737578055642577029106497e-13 % h = 0.0001 y1[1] (analytic) = 2.4825817223287958178000153893858 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0031561837245928175267274541702 relative error = 0.12713312501278494181417130409372 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=3.9MB, time=4.65 NO POLE NO POLE x[1] = 0.5037 y2[1] (analytic) = 1.1241973156008584011154903230418 y2[1] (numeric) = 1.1241973156008556275504597081467 absolute error = 2.7735650306148951e-15 relative error = 2.4671514440794465231405135742305e-13 % h = 0.0001 y1[1] (analytic) = 2.4826693050104362878869696362058 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0032437664062332876136817009902 relative error = 0.13065640275516484606262989421157 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5038 y2[1] (analytic) = 1.1242455869102924182066809803753 y2[1] (numeric) = 1.1242455869102892489242550817546 absolute error = 3.1692824258986207e-15 relative error = 2.8190303460372925576313503835395e-13 % h = 0.0001 y1[1] (analytic) = 2.4827568828653837118918052112356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.00333134426118071161851727602 relative error = 0.13417923777280849160851564650062 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5039 y2[1] (analytic) = 1.1242938669772705588969940156605 y2[1] (numeric) = 1.1242938669772669499606614018517 absolute error = 3.6089363326138088e-15 relative error = 3.2099582134310169248261945844324e-13 % h = 0.0001 y1[1] (analytic) = 2.4828444558927623112657776898846 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.003418917288559310992489754669 relative error = 0.1377016300978855615414385576659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.504 y2[1] (analytic) = 1.1243421558013100225170503558855 y2[1] (numeric) = 1.1243421558013059264282111875028 absolute error = 4.0960888391683827e-15 relative error = 3.6430981601407016810339461234989e-13 % h = 0.0001 y1[1] (analytic) = 2.4829320240916963557358308536409 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035064854874933554625429184253 relative error = 0.14122357976256294749295818319025 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.0MB, time=5.17 NO POLE NO POLE x[1] = 0.5041 y2[1] (analytic) = 1.1243904533819279208268577717167 y2[1] (numeric) = 1.1243904533819232863371807687354 absolute error = 4.6344896770029813e-15 relative error = 4.1217796389709817043255671342151e-13 % h = 0.0001 y1[1] (analytic) = 2.4830195874613101633133539927949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035940488571071630400660575793 relative error = 0.14474508679900474920279043209641 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5042 y2[1] (analytic) = 1.1244387597186412780206397598942 y2[1] (numeric) = 1.1244387597186360499395902865397 absolute error = 5.2280810494733545e-15 relative error = 4.6495027001573057100556050862084e-13 % h = 0.0001 y1[1] (analytic) = 2.4831071460007281003029387263179 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0036816073965251000296507911023 relative error = 0.14826615123937227408528675881179 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5043 y2[1] (analytic) = 1.1244870748109670307316653012861 y2[1] (numeric) = 1.1244870748109611497292036928686 absolute error = 5.8810024616084175e-15 relative error = 5.2299422495336809562984666182024e-13 % h = 0.0001 y1[1] (analytic) = 2.483194699709074581311135338809 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0037691611048715810378474035934 relative error = 0.1517867731158240367961856449255 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5044 y2[1] (analytic) = 1.1245353986584220280370794945515 y2[1] (numeric) = 1.1245353986584154304415287506379 absolute error = 6.5975955507439136e-15 relative error = 5.8669523063612649070641305265234e-13 % h = 0.0001 y1[1] (analytic) = 2.4832822485854740692552086344221 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0038567099812710689819206992065 relative error = 0.15530695246051575879963626359932 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.0MB, time=5.72 NO POLE NO POLE x[1] = 0.5045 y2[1] (analytic) = 1.1245837312605230314627350653647 y2[1] (numeric) = 1.124583731260515649053817033726 absolute error = 7.3824089180316387e-15 relative error = 6.5645702608171707184351871962644e-13 % h = 0.0001 y1[1] (analytic) = 2.4833697926290510753718933076862 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0039442540248480750986053724706 relative error = 0.15882668930560036793549421948315 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5046 y2[1] (analytic) = 1.1246320726167867149880247511533 y2[1] (numeric) = 1.124632072616778474785063926974 absolute error = 8.2402029608241793e-15 relative error = 7.3270211311428525629620837216456e-13 % h = 0.0001 y1[1] (analytic) = 2.4834573318389301592261488311309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0040317932347271589528608959153 relative error = 0.1623459836832279979868892569658 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5047 y2[1] (analytic) = 1.1246804227267296650507145612998 y2[1] (numeric) = 1.1246804227267204890960086261857 absolute error = 9.1759547059351141e-15 relative error = 8.1587218204514356916416315044141e-13 % h = 0.0001 y1[1] (analytic) = 2.4835448662142359287199138596289 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0041193276100329284466259244133 relative error = 0.16586483562554598824806482962048 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5048 y2[1] (analytic) = 1.12472878158986838055177791276 y2[1] (numeric) = 1.1247287815898581856891341381278 absolute error = 1.01948626437746322e-14 relative error = 9.0642853731933591073057686542243e-13 % h = 0.0001 y1[1] (analytic) = 2.4836323957540930401008601513698 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0042068571498900398275722161542 relative error = 0.16938324516469888309248942383736 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.0MB, time=6.27 NO POLE NO POLE x[1] = 0.5049 y2[1] (analytic) = 1.1247771492057192728602306410493 y2[1] (numeric) = 1.1247771492057079705086672805296 absolute error = 1.13023515633605197e-14 relative error = 1.0048525231279698051639080362516e-12 % h = 0.0001 y1[1] (analytic) = 2.4837199204576261979711460053762 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0042943818534231976978580701606 relative error = 0.17290121233282843154123952953543 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.505 y2[1] (analytic) = 1.1248255255737986658179668865485 y2[1] (numeric) = 1.1248255255737861617405786820832 absolute error = 1.25040773882044653e-14 relative error = 1.1116459489862532836901440217852e-12 % h = 0.0001 y1[1] (analytic) = 2.4838074403239601552961692154743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0043819017197571550228812802587 relative error = 0.17641873716207358683165415092659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5051 y2[1] (analytic) = 1.1248739106936227957445958560807 y2[1] (numeric) = 1.1248739106936089898125827824433 absolute error = 1.38059320130736374e-14 relative error = 1.2273315152771732638620767021862e-12 % h = 0.0001 y1[1] (analytic) = 2.4838949553522197134133195406332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0044694167480167131400316054176 relative error = 0.17993581968457050598626075041799 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5052 y2[1] (analytic) = 1.1249223045647078114422794597113 y2[1] (numeric) = 1.1249223045646925973941378322274 absolute error = 1.52140481416274839e-14 relative error = 1.3524532387607522105467943310908e-12 % h = 0.0001 y1[1] (analytic) = 2.4839824655415297220407306915832 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0045569269373267217674427563676 relative error = 0.1834524599324525493819725186141 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=49.5MB, alloc=4.0MB, time=6.82 x[1] = 0.5053 y2[1] (analytic) = 1.1249707071865697742005708227225 y2[1] (numeric) = 1.1249707071865530393964458930158 absolute error = 1.67348041249297067e-14 relative error = 1.4875768780488199749688607474205e-12 % h = 0.0001 y1[1] (analytic) = 2.4840699708910150792860318336276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.004644432286812079012743898412 relative error = 0.18696865793785028031955686358144 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5054 y2[1] (analytic) = 1.1250191185587246578012536727134 y2[1] (numeric) = 1.1250191185587062829724528373515 absolute error = 1.83748288008353619e-14 relative error = 1.6332903590452376588433787333975e-12 % h = 0.0001 y1[1] (analytic) = 2.4841574713998007316550986055588 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0047319327955977313818106703432 relative error = 0.1904844137328914645933750124228 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5055 y2[1] (analytic) = 1.1250675386806883485231826017783 y2[1] (numeric) = 1.1250675386806682075168483487401 absolute error = 2.01410063342530382e-14 relative error = 1.7902042003515105235784214681932e-12 % h = 0.0001 y1[1] (analytic) = 2.4842449670670116740608036545925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0048194284628086737875157193769 relative error = 0.1939997273497010700613926183604 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5056 y2[1] (analytic) = 1.1251159675519766451471242037142 y2[1] (numeric) = 1.1251159675519546046660659216501 absolute error = 2.20404810582820641e-14 relative error = 1.9589519386377268352341251832706e-12 % h = 0.0001 y1[1] (analytic) = 2.4843324578917729498317666872315 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0049069192875699495584787520159 relative error = 0.19751459882040126621546126646809 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5057 y2[1] (analytic) = 1.1251644051721052589605990862088 y2[1] (numeric) = 1.1251644051720811782982828615126 absolute error = 2.40806623162246962e-14 relative error = 2.1401905539787597266574190464716e-12 % h = 0.0001 y1[1] (analytic) = 2.4844199438732096507211040359722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0049944052690066504478161007566 relative error = 0.20102902817711142375187077128874 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.0MB, time=7.38 NO POLE NO POLE x[1] = 0.5058 y2[1] (analytic) = 1.1252128515405898137627247579617 y2[1] (numeric) = 1.1252128515405635445334202847215 absolute error = 2.62692293044732402e-14 relative error = 2.3346008951556691355967337004784e-12 % h = 0.0001 y1[1] (analytic) = 2.4845074250104469169151777417664 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0050818864062439166418898065508 relative error = 0.20454301545194811414217215958604 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5059 y2[1] (analytic) = 1.125261306656945845869059390689 y2[1] (numeric) = 1.1252613066569172317331431186334 absolute error = 2.86141359162720556e-14 relative error = 2.5428881049222408639024943325617e-12 % h = 0.0001 y1[1] (analytic) = 2.4845949013026099370423441521499 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0051693626984069367690562169343 relative error = 0.20805656067702510920427123146752 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.506 y2[1] (analytic) = 1.1253097705206888041164464559634 y2[1] (numeric) = 1.1253097705206576805008601015676 absolute error = 3.11236155863543958e-14 relative error = 2.7657820452365999047702352938993e-12 % h = 0.0001 y1[1] (analytic) = 2.4846823727488239481817020349524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0052568341446209479084140997368 relative error = 0.2115696638844533806737925932691 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5061 y2[1] (analytic) = 1.125358243131334049867860236842 y2[1] (numeric) = 1.1253582431313002436817237828062 absolute error = 3.38061861364540358e-14 relative error = 3.0040377224578352690431124989298e-12 % h = 0.0001 y1[1] (analytic) = 2.4847698393482142358718402074983 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0053443007440112355985522722827 relative error = 0.21508232510634109977571405542669 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.0MB, time=7.92 NO POLE NO POLE x[1] = 0.5062 y2[1] (analytic) = 1.1254067244883968570172522142328 y2[1] (numeric) = 1.1254067244883601863626305225941 absolute error = 3.66706546216916387e-14 relative error = 3.2584357125075734923532679076673e-12 % h = 0.0001 y1[1] (analytic) = 2.4848573010999061341195846812144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0054317624957031338462967459988 relative error = 0.21859454437479363679627128885001 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5063 y2[1] (analytic) = 1.1254552145913924119943983279504 y2[1] (numeric) = 1.1254552145913526858722204921387 absolute error = 3.97261221778358117e-14 relative error = 3.5297825859964380001101863411506e-12 % h = 0.0001 y1[1] (analytic) = 2.4849447580030250254087453215537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0055192193988220251354573863381 relative error = 0.22210632172191356065513263307314 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5064 y2[1] (analytic) = 1.1255037134398358137697471124149 y2[1] (numeric) = 1.1255037134397928317808776736103 absolute error = 4.29819888694388046e-14 relative error = 3.8189113333153317513726772595572e-12 % h = 0.0001 y1[1] (analytic) = 2.4850322100566963407088620231503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0056066714524933404355740879347 relative error = 0.22561765717980063847784394972158 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5065 y2[1] (analytic) = 1.1255522210332420738592687069431 y2[1] (numeric) = 1.1255522210331956259007298601418 absolute error = 4.64479585388468013e-14 relative error = 4.1266817896914804001380728790430e-12 % h = 0.0001 y1[1] (analytic) = 2.4851196572600455594839504001169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0056941186558425592106624649013 relative error = 0.22912855078055183516854341472728 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.0MB, time=8.45 NO POLE NO POLE x[1] = 0.5066 y2[1] (analytic) = 1.1256007373711261163293047405846 y2[1] (numeric) = 1.125600737371075982285648655829 absolute error = 5.01340436560847556e-14 relative error = 4.4539810602091733233471490516041e-12 % h = 0.0001 y1[1] (analytic) = 2.4852070996121982097012469913967 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0057815610079952094279590561811 relative error = 0.23263900255626131298294614276802 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5067 y2[1] (analytic) = 1.1256492624530027778014190914547 y2[1] (numeric) = 1.1256492624529487272312494757303 absolute error = 5.40505701696157244e-14 relative error = 4.8017239447951400644832596296155e-12 % h = 0.0001 y1[1] (analytic) = 2.4852945371122798678399539810846 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.005868998508076867566666045869 relative error = 0.23614901253902043110159853756371 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5068 y2[1] (analytic) = 1.1256977962783868074572495205144 y2[1] (numeric) = 1.1256977962783285992748915458669 absolute error = 5.82081823579746475e-14 relative error = 5.1708533631684994348145102154945e-12 % h = 0.0001 y1[1] (analytic) = 2.4853819697594161588999834336272 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0059564311552131586266954984116 relative error = 0.23965858076091774520340226147838 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5069 y2[1] (analytic) = 1.1257463388467928670433601797501 y2[1] (numeric) = 1.1257463388467302491956779032226 absolute error = 6.26178476822765275e-14 relative error = 5.5623407797552189360431910220380e-12 % h = 0.0001 y1[1] (analytic) = 2.4854693975527327564107010438169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0060438589485297561374131086013 relative error = 0.2431677072540390070394077181413 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.0MB, time=8.99 NO POLE NO POLE x[1] = 0.507 y2[1] (analytic) = 1.1257948901577355308760949947039 y2[1] (numeric) = 1.1257948901576682400144553957441 absolute error = 6.72908616395989598e-14 relative error = 5.9771866285670218968550162568950e-12 % h = 0.0001 y1[1] (analytic) = 2.4855568204913553824396694014904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0061312818871523821663814662748 relative error = 0.24667639205046716400687694163286 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5071 y2[1] (analytic) = 1.1258434502107292858464319213063 y2[1] (numeric) = 1.1258434502106570469938146823407 absolute error = 7.22388526172389656e-14 relative error = 6.4164207380446800131773284727611e-12 % h = 0.0001 y1[1] (analytic) = 2.4856442385744098076013907708465 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0062186999702068073281028356309 relative error = 0.25018463518228235872361578599722 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5072 y2[1] (analytic) = 1.125892019005288531424838076962 y2[1] (numeric) = 1.1258920190052110576380902328845 absolute error = 7.74737867478440775e-14 relative error = 6.8811027558656287285024841520392e-12 % h = 0.0001 y1[1] (analytic) = 2.4857316518010218510660493842931 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0063061131968188507927614490775 relative error = 0.25369243668156192860257530867599 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5073 y2[1] (analytic) = 1.1259405965409275796661257458414 y2[1] (numeric) = 1.1259405965408445716933603282104 absolute error = 8.30079727654176310e-14 relative error = 7.3723225737158432590008025600716e-12 % h = 0.0001 y1[1] (analytic) = 2.4858190601703173805682532507384 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0063935215661143802949653155228 relative error = 0.25719979658038040542672224169378 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=68.6MB, alloc=4.0MB, time=9.54 x[1] = 0.5074 y2[1] (analytic) = 1.1259891828171606552143092583286 y2[1] (numeric) = 1.1259891828170718011474470601158 absolute error = 8.88540668621982128e-14 relative error = 7.8912007520259128946470242922356e-12 % h = 0.0001 y1[1] (analytic) = 2.4859064636814223124157754782377 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0064809250772193121424875430221 relative error = 0.2607067149108095149241784443146 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5075 y2[1] (analytic) = 1.1260377778335018953074627445769 y2[1] (numeric) = 1.126037777833406870229916331361 absolute error = 9.50250775464132159e-14 relative error = 8.4388889446712511673818542269546e-12 % h = 0.0001 y1[1] (analytic) = 2.485993862333462611498295110908 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0065683237292596112250071756924 relative error = 0.26421319170491817634362923095228 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5076 y2[1] (analytic) = 1.126086381589465349782578762124 y2[1] (numeric) = 1.126086381589363815412077855669 absolute error = 1.015343705009064550e-13 relative error = 9.0165703236363798278974674618470e-12 % h = 0.0001 y1[1] (analytic) = 2.4860812561255642912961374800242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0066557175213612910228495448086 relative error = 0.2677192269947725020300004682148 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5077 y2[1] (analytic) = 1.1261349940845649810804277975184 y2[1] (numeric) = 1.1261349940844565854069851577255 absolute error = 1.083956734426397929e-13 relative error = 9.6254600036432243636516425070035e-12 % h = 0.0001 y1[1] (analytic) = 2.4861686450568534138890140692085 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0067431064526504136157261339929 relative error = 0.27122482081243579700040433490639 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5078 y2[1] (analytic) = 1.1261836153183146642504186419074 y2[1] (numeric) = 1.126183615318199041169435573179 absolute error = 1.156230809830687284e-13 relative error = 1.0266805466743358812700560453097e-11 % h = 0.0001 y1[1] (analytic) = 2.486256029126456089964761893626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0068304905222530896914739584104 relative error = 0.2747299731899685585203536388995 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.0MB, time=10.11 NO POLE NO POLE x[1] = 0.5079 y2[1] (analytic) = 1.1262322452902281869554596405387 y2[1] (numeric) = 1.1262322452901049558959702486407 absolute error = 1.232310594893918980e-13 relative error = 1.0941886986874137827520629868585e-11 % h = 0.0001 y1[1] (analytic) = 2.486343408333498478828082393099 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0069178697292954785547944578834 relative error = 0.2782346841594284756802445848015 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.508 y2[1] (analytic) = 1.1262808839998192494768208161278 y2[1] (numeric) = 1.1262808839996880150248741416844 absolute error = 1.312344519466744434e-13 relative error = 1.1652018054378653956058284869067e-11 % h = 0.0001 y1[1] (analytic) = 2.4864307826771067884092798390526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.007005244072903788135991903837 relative error = 0.28173895375287042897210788637658 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5081 y2[1] (analytic) = 1.1263295314466014647189968660408 y2[1] (numeric) = 1.1263295314464618162361760208468 absolute error = 1.396484828208451940e-13 relative error = 1.2398545800489457898370455326369e-11 % h = 0.0001 y1[1] (analytic) = 2.4865181521564072752729992552048 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0070926135522042749997113199892 relative error = 0.28524278200234648986662811774034 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5082 y2[1] (analytic) = 1.1263781876300883582145710332457 y2[1] (numeric) = 1.1263781876299398694516484656273 absolute error = 1.484887629225676184e-13 relative error = 1.3182851421775979963172483994906e-11 % h = 0.0001 y1[1] (analytic) = 2.4866055167705262446269638519124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0071799781663232443536759166968 relative error = 0.28874616893990592039043119730001 % h = 0.0001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.0MB, time=10.68 NO POLE NO POLE x[1] = 0.5083 y2[1] (analytic) = 1.1264268525497933681290798509824 y2[1] (numeric) = 1.1264268525496355968348078664879 absolute error = 1.577712942719844945e-13 relative error = 1.4006350604555590597661469857467e-11 % h = 0.0001 y1[1] (analytic) = 2.4866928765185900503307119740863 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0072673379143870500574240388707 relative error = 0.2922491145975951727036398985382 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5084 y2[1] (analytic) = 1.1264755262052298452658787611032 y2[1] (numeric) = 1.1264755262050623327909144248535 absolute error = 1.675124749643362497e-13 relative error = 1.4870493949268238072457237858129e-11 % h = 0.0001 y1[1] (analytic) = 2.4867802313997250949043335625894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0073546927955220946310456273738 relative error = 0.29575161900745788867769728175415 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5085 y2[1] (analytic) = 1.1265242085959110530710086060352 y2[1] (numeric) = 1.1265242085957333239669721531116 absolute error = 1.777291040364529236e-13 relative error = 1.5776767394814601523147807762084e-11 % h = 0.0001 y1[1] (analytic) = 2.4868675814130578295372061290281 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0074420428088548292639181938125 relative error = 0.29925368220153489947345794082024 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5086 y2[1] (analytic) = 1.126572899721350167638062994316 y2[1] (numeric) = 1.1265728997211617292517288746125 absolute error = 1.884383863341197035e-13 relative error = 1.6726692642857697403250106967312e-11 % h = 0.0001 y1[1] (analytic) = 2.4869549265577147540967302438511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0075293879535117538234423086355 relative error = 0.30275530421186422511954695915242 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.0MB, time=11.25 NO POLE NO POLE x[1] = 0.5087 y2[1] (analytic) = 1.1266215995810602777130565396536 y2[1] (numeric) = 1.1266215995808606197756762236692 absolute error = 1.996579373803159844e-13 relative error = 1.7721827582087877567460973709140e-11 % h = 0.0001 y1[1] (analytic) = 2.4870422668328224171370645376684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0076167282286194168637766024528 relative error = 0.3062564850704810740909864690931 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5088 y2[1] (analytic) = 1.1266703081745543846992939734623 y2[1] (numeric) = 1.1266703081743429789110496455574 absolute error = 2.114057882443279049e-13 relative error = 1.8763766712451157217206964985886e-11 % h = 0.0001 y1[1] (analytic) = 2.4871296022375074159078602157024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0077040636333044156345722804868 relative error = 0.30975722480941784288808970889725 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5089 y2[1] (analytic) = 1.1267190255013454026622401308252 y2[1] (numeric) = 1.1267190255011217022718283965156 absolute error = 2.237003904117343096e-13 relative error = 1.9854141569340810909273242252550e-11 % h = 0.0001 y1[1] (analytic) = 2.4872169327708963963629950852839 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0077913941666933960897071500683 relative error = 0.31325752346070411561562247158066 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.509 y2[1] (analytic) = 1.126767751560946158334390809836 y2[1] (numeric) = 1.1267677515607095977137355437449 absolute error = 2.365606206552660911e-13 relative error = 2.0994621147752175089968880977799e-11 % h = 0.0001 y1[1] (analytic) = 2.4873042584321160531693070963062 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0078787198279130528960191610906 relative error = 0.31675738105636666356223183993781 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.0MB, time=11.80 NO POLE NO POLE x[1] = 0.5091 y2[1] (analytic) = 1.1268164863528693911201445042698 y2[1] (numeric) = 1.1268164863526193853342379654093 absolute error = 2.500057859065388605e-13 relative error = 2.2186912326400595284285708557927e-11 % h = 0.0001 y1[1] (analytic) = 2.4873915792202931297153273945494 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0079660406160901294420394593338 relative error = 0.32025679762842944478014210202461 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5092 y2[1] (analytic) = 1.1268652298766277531006750095348 y2[1] (numeric) = 1.1268652298763636974725463506354 absolute error = 2.640556281286588994e-13 relative error = 2.3432760291802456473213705750257e-11 % h = 0.0001 y1[1] (analytic) = 2.487478895134554418120012887788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0080533565303514178467249525724 relative error = 0.32375577320891360366511774147363 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5093 y2[1] (analytic) = 1.1269139821317338090388049018571 y2[1] (numeric) = 1.1269139821314550787096151995126 absolute error = 2.787303291897023445e-13 relative error = 2.4733948962319235063517289138662e-11 % h = 0.0001 y1[1] (analytic) = 2.4875662061740267592414783245936 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008140667569823758968190389378 relative error = 0.32725430782983747053669339698971 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5094 y2[1] (analytic) = 1.1269627431177000363838798906477 y2[1] (numeric) = 1.1269627431174059858681428230931 absolute error = 2.940505157370675546e-13 relative error = 2.6092301412164510778728624243945e-11 % h = 0.0001 y1[1] (analytic) = 2.4876535123378370426857278857469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0082279737336340424124399505313 relative error = 0.3307524015232165612186706855019 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=87.7MB, alloc=4.0MB, time=12.37 x[1] = 0.5095 y2[1] (analytic) = 1.1270115128340388252766440440054 y2[1] (numeric) = 1.1270115128337287880125713433916 absolute error = 3.100372640727006138e-13 relative error = 2.7509680295373877194885591658868e-11 % h = 0.0001 y1[1] (analytic) = 2.4877408136251122068153862881703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0083152750209092065420983529547 relative error = 0.33425005432106357661988178336379 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5096 y2[1] (analytic) = 1.1270602912802624785541158873053 y2[1] (numeric) = 1.1270602912799357664490866933857 absolute error = 3.267121050291939196e-13 relative error = 2.8987988269737689231769481234105e-11 % h = 0.0001 y1[1] (analytic) = 2.4878281100349792387584294012944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0084025714307762384851414660788 relative error = 0.3377472662553884023152196601067 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5097 y2[1] (analytic) = 1.1271090784558832117544653748244 y2[1] (numeric) = 1.1271090784555391147256186170157 absolute error = 3.440970288467578087e-13 relative error = 3.0529168420696586314053129185082e-11 % h = 0.0001 y1[1] (analytic) = 2.4879154015665651744169143757705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0084898629623621741436264405549 relative error = 0.34124403735819810812693485923398 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5098 y2[1] (analytic) = 1.1271578743604131531218917343559 y2[1] (numeric) = 1.1271578743600509386318406691846 absolute error = 3.622144900510651713e-13 relative error = 3.2135204685199729779104375153932e-11 % h = 0.0001 y1[1] (analytic) = 2.4880026882189970984757092844435 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0085771496147940982024213492279 relative error = 0.34474036766149694770619872066933 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5099 y2[1] (analytic) = 1.1272066789933643436115021847631 y2[1] (numeric) = 1.1272066789929832561991702157581 absolute error = 3.810874123319690050e-13 relative error = 3.3808122275525693174641584394278e-11 % h = 0.0001 y1[1] (analytic) = 2.4880899699914021444112222754956 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.00866443138719914413793434028 relative error = 0.34823625719728635811493293934347 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.0MB, time=12.92 NO POLE NO POLE x[1] = 0.51 y2[1] (analytic) = 1.1272554923542487368941915264245 y2[1] (numeric) = 1.1272554923538479977007684335648 absolute error = 4.007391934230928597e-13 relative error = 3.5549988103065944155883831730206e-11 % h = 0.0001 y1[1] (analytic) = 2.4881772468829074945001302376746 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008751708278704494226842302459 relative error = 0.35173170599756495940790535457244 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5101 y2[1] (analytic) = 1.1273043144425781993615226045203 y2[1] (numeric) = 1.1273043144421570056515403103958 absolute error = 4.211937099822941245e-13 relative error = 3.7362911202070856696183119727494e-11 % h = 0.0001 y1[1] (analytic) = 2.4882645188926403798281069775205 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0088389802884373795548190423049 relative error = 0.35522671409432855421509186490828 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5102 y2[1] (analytic) = 1.1273531452578645101306076451132 y2[1] (numeric) = 1.127353145257422034808134645005 absolute error = 4.424753224730001082e-13 relative error = 3.9249043153358192418192269076777e-11 % h = 0.0001 y1[1] (analytic) = 2.488351786019728080298550908501 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0089262474155250800252629732854 relative error = 0.35872128151957012732430436305127 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5103 y2[1] (analytic) = 1.1274019847996193610489904639729 y2[1] (numeric) = 1.1274019847991547521689440471091 absolute error = 4.646088800464168638e-13 relative error = 4.1210578507983989786012815219048e-11 % h = 0.0001 y1[1] (analytic) = 2.4884390482632979246413122519706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.009013509659094924368024316755 relative error = 0.36221540830527984526408458560895 % h = 0.0001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.0MB, time=13.48 NO POLE NO POLE x[1] = 0.5104 y2[1] (analytic) = 1.1274508330673543566995295480967 y2[1] (numeric) = 1.1274508330668667369741049373875 absolute error = 4.876197254246107092e-13 relative error = 4.3249755210875800098290702642497e-11 % h = 0.0001 y1[1] (analytic) = 2.4885263056224772904214197498644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0091007670182742901481318146488 relative error = 0.36570909448344505588686377237523 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5105 y2[1] (analytic) = 1.127499690060581014405282009877 y2[1] (numeric) = 1.1274996900600694807054975474824 absolute error = 5.115336997844623946e-13 relative error = 4.5368855024428209111271652386633e-11 % h = 0.0001 y1[1] (analytic) = 2.488613558096393604047806889041 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0091880194921906037745189538254 relative error = 0.36920234008605028795238802996703 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5106 y2[1] (analytic) = 1.1275485557788107642343884138662 y2[1] (numeric) = 1.1275485557782743870867459199985 absolute error = 5.363771476424938677e-13 relative error = 4.7570203952060583213917535605611e-11 % h = 0.0001 y1[1] (analytic) = 2.4887008056841743407820376371855 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0092752670799713405087497019699 relative error = 0.37269514514507725071140929455188 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5107 y2[1] (analytic) = 1.1275974302215549490049584760917 y2[1] (numeric) = 1.1275974302209927720832179085034 absolute error = 5.621769217405675883e-13 relative error = 4.9856172661736979161389591576417e-11 % h = 0.0001 y1[1] (analytic) = 2.488788048384947024747031690187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0093625097807440244737437549714 relative error = 0.37618750969250483348964178856813 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.0MB, time=14.05 NO POLE NO POLE x[1] = 0.5108 y2[1] (analytic) = 1.1276463133883248242899576358707 y2[1] (numeric) = 1.1276463133877358639020251775275 absolute error = 5.889603879324583432e-13 relative error = 5.2229176909448156350979380258698e-11 % h = 0.0001 y1[1] (analytic) = 2.4888752861978392289357892309016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.009449747593636228662501295686 relative error = 0.37967943376030910527198386623536 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5109 y2[1] (analytic) = 1.127695205278631558422094500076 y2[1] (numeric) = 1.1276952052780148029920232025637 absolute error = 6.167554300712975123e-13 relative error = 5.4691677962655630664445309353362e-11 % h = 0.0001 y1[1] (analytic) = 2.4889625191219785752201151992156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.009536980517775574946827264 relative error = 0.38317091738046331428700514283263 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.511 y2[1] (analytic) = 1.1277441058919862324987091598053 y2[1] (numeric) = 1.1277441058913406420438112700678 absolute error = 6.455904548978897375e-13 relative error = 5.7246183023697709002664498966166e-11 % h = 0.0001 y1[1] (analytic) = 2.4890497471564927343593430733201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0096242085522897340860551381045 relative error = 0.38666196058493788759169880261458 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5111 y2[1] (analytic) = 1.1277930152278998403866623794037 y2[1] (numeric) = 1.1277930152272243459897324774583 absolute error = 6.754943969299019454e-13 relative error = 5.9895245653157443625172199620154e-11 % h = 0.0001 y1[1] (analytic) = 2.4891369703005094260090581621101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0097114316963064257357702268945 relative error = 0.39015256340570043065649898034276 % h = 0.0001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.0MB, time=14.62 NO POLE NO POLE x[1] = 0.5112 y2[1] (analytic) = 1.1278419332858832887272256577907 y2[1] (numeric) = 1.1278419332851767920038737331164 absolute error = 7.064967233519246743e-13 relative error = 6.2641466193192445402714796058388e-11 % h = 0.0001 y1[1] (analytic) = 2.4892241885531564187298204086218 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0097986499489534184565324734062 relative error = 0.39364272587471572695056311146647 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5113 y2[1] (analytic) = 1.1278908600654473969409721620439 y2[1] (numeric) = 1.1278908600647087695020657563861 absolute error = 7.386274389064056578e-13 relative error = 6.5487492190826495290438086963307e-11 % h = 0.0001 y1[1] (analytic) = 2.4893114019135615299958867044192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0098858633093585297225987692036 relative error = 0.39713244802394573752731914591469 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5114 y2[1] (analytic) = 1.1279397955661028972326685331886 y2[1] (numeric) = 1.127939795565330980141883077574 absolute error = 7.719170907854556146e-13 relative error = 6.8436018821202893129812490619710e-11 % h = 0.0001 y1[1] (analytic) = 2.489398610380852626203932714845 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0099730717766496259306447796294 relative error = 0.4006217298853496006102775206491 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5115 y2[1] (analytic) = 1.1279887397873604345961675641465 y2[1] (numeric) = 1.1279887397865540378226440379495 absolute error = 8.063967735235261970e-13 relative error = 7.1489789310799483184433159911327e-11 % h = 0.0001 y1[1] (analytic) = 2.4894858139541576226817742150457 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0100602753499546224084862798301 relative error = 0.4041105714908836311791077859561 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=106.8MB, alloc=4.0MB, time=15.18 x[1] = 0.5116 y2[1] (analytic) = 1.128037692728730566819301749793 y2[1] (numeric) = 1.1280376927278884686854107897448 absolute error = 8.420981338909600482e-13 relative error = 7.4651595360605295641930505723275e-11 % h = 0.0001 y1[1] (analytic) = 2.489573012632604483697087936687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0101474740284014834238000014714 relative error = 0.40759897287250132055597978073576 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5117 y2[1] (analytic) = 1.1280866543897237644887777090747 y2[1] (numeric) = 1.1280866543888447111129892961547 absolute error = 8.790533757884129200e-13 relative error = 7.7924277569258743487129368987892e-11 % h = 0.0001 y1[1] (analytic) = 2.4896602064153212224661319252692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0102346678111182221928439900536 relative error = 0.41108693406215333599216925182157 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5118 y2[1] (analytic) = 1.1281356247698504109950714791383 y2[1] (numeric) = 1.1281356247689331157299293313368 absolute error = 9.172952651421478015e-13 relative error = 8.1310725856147314102845319748577e-11 % h = 0.0001 y1[1] (analytic) = 2.4897473953014359011624654079576 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.010321856697232900889177472742 relative error = 0.41457445509178752025492781260892 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5119 y2[1] (analytic) = 1.1281846038686208025373246814218 y2[1] (numeric) = 1.1281846038676639454025244804114 absolute error = 9.568571348002010104e-13 relative error = 8.4813879884468695083271353370709e-11 % h = 0.0001 y1[1] (analytic) = 2.4898345792900766309256681718396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.010409040685873630652380236624 relative error = 0.41806153599334889121461713617032 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.512 y2[1] (analytic) = 1.1282335916855451481282415596589 y2[1] (numeric) = 1.1282335916845473752388121394615 absolute error = 9.977728894294201974e-13 relative error = 8.8436729484253273687310699562707e-11 % h = 0.0001 y1[1] (analytic) = 2.4899217583803715718700594525215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0104962197761685715967715173059 relative error = 0.42154817679877964143210727811901 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.0MB, time=15.76 NO POLE NO POLE x[1] = 0.5121 y2[1] (analytic) = 1.128282588220133569598986889748 y2[1] (numeric) = 1.1282825882190934925885735155329 absolute error = 1.0400770104133742151e-12 relative error = 9.2182315075347949478916494426680e-11 % h = 0.0001 y1[1] (analytic) = 2.4900089325714489330934163329783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0105833939672459328201283977627 relative error = 0.42503437754001913774643902452705 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5122 y2[1] (analytic) = 1.1283315934718961016040847614365 y2[1] (numeric) = 1.1283315934708122970433336266342 absolute error = 1.0838045607511348023e-12 relative error = 9.6053728090361199697099840722712e-11 % h = 0.0001 y1[1] (analytic) = 2.4900961018624369726856916525687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0106705632582339724124037173531 relative error = 0.42852013824900392086275016019154 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5123 y2[1] (analytic) = 1.1283806074403426916263182317713 y2[1] (numeric) = 1.1283806074392137004363613017365 absolute error = 1.1289911899569300348e-12 relative error = 1.0005411139756933695592557553922e-10 % h = 0.0001 y1[1] (analytic) = 2.4901832662524639977377314261276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.010757727648260997464443490912 relative error = 0.4320054589576677049404655525788 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5124 y2[1] (analytic) = 1.1284296301249831999816298502668 y2[1] (numeric) = 1.1284296301238075268426691807738 absolute error = 1.1756731389606694930e-12 relative error = 1.0418665972378389884385107536865e-10 % h = 0.0001 y1[1] (analytic) = 2.4902704257406583643499917730516 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.010844887136455364076703837836 relative error = 0.43549033969794137718175094693619 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.0MB, time=16.33 NO POLE NO POLE x[1] = 0.5125 y2[1] (analytic) = 1.128478661525327399824023055742 y2[1] (numeric) = 1.1284786615241035125790137146427 absolute error = 1.2238872450093410993e-12 relative error = 1.0845462007718010927098309260524e-10 % h = 0.0001 y1[1] (analytic) = 2.4903575803261484776412553562859 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0109320417219454773679674210703 relative error = 0.43897478050175299742023036780928 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5126 y2[1] (analytic) = 1.1285277016408849771504644447756 y2[1] (numeric) = 1.1285277016396113062038951652027 absolute error = 1.2736709465692795729e-12 relative error = 1.1286129217008635097420822389264e-10 % h = 0.0001 y1[1] (analytic) = 2.4904447300080627917573473311301 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0110191914038597914840593959145 relative error = 0.4424587814010277977099670225979 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5127 y2[1] (analytic) = 1.1285767504711655308057869117326 y2[1] (numeric) = 1.128576750469840468517557605276 absolute error = 1.3250622882293064566e-12 relative error = 1.1741002884173458925045316730977e-10 % h = 0.0001 y1[1] (analytic) = 2.4905318747855298098798508037723 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0111063361813268096065628685567 relative error = 0.44594234242768818191470760249257 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5128 y2[1] (analytic) = 1.1286258080156785724875936603122 y2[1] (numeric) = 1.1286258080143004725619889186473 absolute error = 1.3780999256047416649e-12 relative error = 1.2210423648097168655857177348628e-10 % h = 0.0001 y1[1] (analytic) = 2.4906190146576780842348217994662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0111934760534750839615338642506 relative error = 0.44942546361365372529738987637684 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.0MB, time=16.88 NO POLE NO POLE x[1] = 0.5129 y2[1] (analytic) = 1.1286748742739335267511630865669 y2[1] (numeric) = 1.1286748742725007036209208000643 absolute error = 1.4328231302422865026e-12 relative error = 1.2694737544893154766150146959208e-10 % h = 0.0001 y1[1] (analytic) = 2.490706149623636216101503740263 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0112806110194332158282158050474 relative error = 0.45290814499084117410991347319669 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.513 y2[1] (analytic) = 1.1287239492454397310143545333464 y2[1] (numeric) = 1.1287239492439504592198287552373 absolute error = 1.4892717945257781091e-12 relative error = 1.3194296050166803555191774590095e-10 % h = 0.0001 y1[1] (analytic) = 2.4907932796825328558210414322121 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0113677410783298555477534969965 relative error = 0.45639038659116444518317374841848 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5131 y2[1] (analytic) = 1.1287730329297064355625149161146 y2[1] (numeric) = 1.1287730329281589491259321008394 absolute error = 1.5474864365828152752e-12 relative error = 1.3709456121274859770027575311568e-10 % h = 0.0001 y1[1] (analytic) = 2.4908804048334967028051945619418 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0114548662292937025319066267262 relative error = 0.45987218844653462551735863011633 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5132 y2[1] (analytic) = 1.128822125326242803553386220092 y2[1] (numeric) = 1.1288221253246352953481939645064 absolute error = 1.6075082051922555856e-12 relative error = 1.4240580239580854277118451841826e-10 % h = 0.0001 y1[1] (analytic) = 2.4909675250756565055450507025352 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0115419864714535052717627673196 relative error = 0.4633535505888599718725083404221 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.0MB, time=17.46 NO POLE NO POLE x[1] = 0.5133 y2[1] (analytic) = 1.1288712264345579110220138686741 y2[1] (numeric) = 1.1288712264328885321373212848367 absolute error = 1.6693788846925838374e-12 relative error = 1.4788036452706590773706576630405e-10 % h = 0.0001 y1[1] (analytic) = 2.4910546404081410616197378286114 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0116291018039380613464498933958 relative error = 0.46683447305004591035933788789886 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5134 y2[1] (analytic) = 1.1289203362541607468856559630772 y2[1] (numeric) = 1.1289203362524276059857648113916 absolute error = 1.7331408998911516856e-12 relative error = 1.5352198416779685542004879014628e-10 % h = 0.0001 y1[1] (analytic) = 2.4911417508300792177051363405274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0117162122258762174318484053118 relative error = 0.47031495586199503603032222664255 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5135 y2[1] (analytic) = 1.1289694547845602129486933931615 y2[1] (numeric) = 1.1289694547827613756277191046951 absolute error = 1.7988373209742884664e-12 relative error = 1.5933445438677154251531294701344e-10 % h = 0.0001 y1[1] (analytic) = 2.4912288563405998695825905976116 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.011803317736396869309302662396 relative error = 0.47379499905660711247104397776858 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5136 y2[1] (analytic) = 1.1290185820252651239075408193829 y2[1] (numeric) = 1.1290185820233986120391225362338 absolute error = 1.8665118684182831491e-12 relative error = 1.6532162518265039818907455062930e-10 % h = 0.0001 y1[1] (analytic) = 2.4913159569388319621476199603439 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0118904183346289618743320251283 relative error = 0.47727460266577907139180360913565 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=125.8MB, alloc=4.0MB, time=18.03 x[1] = 0.5137 y2[1] (analytic) = 1.1290677179757842073555585258256 y2[1] (numeric) = 1.1290677179738479984376572884572 absolute error = 1.9362089179012373684e-12 relative error = 1.7148740390634075347297240726084e-10 % h = 0.0001 y1[1] (analytic) = 2.491403052623904489418629341392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0119775140197014891453414061764 relative error = 0.48075376672140501221949196897542 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5138 y2[1] (analytic) = 1.1291168626356261037879651442635 y2[1] (numeric) = 1.1291168626336181302827493547774 absolute error = 2.0079735052157894861e-12 relative error = 1.7783575568331376146858640641684e-10 % h = 0.0001 y1[1] (analytic) = 2.4914901433949464945456192654214 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0120646047907434942723313302058 relative error = 0.48423249125537620168972506944398 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5139 y2[1] (analytic) = 1.1291660160042993666067512492044 y2[1] (numeric) = 1.1291660160022175152755685395693 absolute error = 2.0818513311827096351e-12 relative error = 1.8437070383588154876126274280301e-10 % h = 0.0001 y1[1] (analytic) = 2.4915772292510870698188954375873 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0121516906468840695456075023717 relative error = 0.48771077629958107343924101577121 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.514 y2[1] (analytic) = 1.1292151780813124621255938238659 y2[1] (numeric) = 1.1292151780791545733590284581706 absolute error = 2.1578887665653656953e-12 relative error = 1.9109633030543453819011577868654e-10 % h = 0.0001 y1[1] (analytic) = 2.4916643101914553566777778206244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0122387715872523564044898854088 relative error = 0.4911886218859052275985589770279 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5141 y2[1] (analytic) = 1.1292643488661737695747715970346 y2[1] (numeric) = 1.1292643488639376367177865368815 absolute error = 2.2361328569850601531e-12 relative error = 1.9801677607463888334707844196747e-10 % h = 0.0001 y1[1] (analytic) = 2.4917513862151805457193092204469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0123258476109775454460212852313 relative error = 0.49466602804623143038490009441421 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.0MB, time=18.59 NO POLE NO POLE x[1] = 0.5142 y2[1] (analytic) = 1.1293135283583915811060812507591 y2[1] (numeric) = 1.1293135283560749497782440129651 absolute error = 2.3166313278372377940e-12 relative error = 2.0513624158959395502304330868460e-10 % h = 0.0001 y1[1] (analytic) = 2.49183845732139187670696338017 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0124129187171888764336754449544 relative error = 0.49814299481243961369537022296511 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5143 y2[1] (analytic) = 1.129362716557474101797754498828 y2[1] (numeric) = 1.1293627165550746692085459346472 absolute error = 2.3994325892085641808e-12 relative error = 2.1245898718194982012482328817907e-10 % h = 0.0001 y1[1] (analytic) = 2.491925523509218638579352582469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0124999849050156383060646472534 relative error = 0.50161952221640687470040440279173 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5144 y2[1] (analytic) = 1.1294119134629294496593760359833 y2[1] (numeric) = 1.1294119134604448639185811611164 absolute error = 2.4845857407948748669e-12 relative error = 2.1998933349098465336099702826160e-10 % h = 0.0001 y1[1] (analytic) = 2.4920125847777901694589347601848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0125870461735871691856468249692 relative error = 0.50509561029000747543747295571818 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5145 y2[1] (analytic) = 1.129461119074265655636802357821 y2[1] (numeric) = 1.1294611190716935150599823625239 absolute error = 2.5721405768199952971e-12 relative error = 2.2773166188564202229152095396718e-10 % h = 0.0001 y1[1] (analytic) = 2.4920996411262358566607201150927 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0126741025220328563874321798771 relative error = 0.50857125906511284240504910352823 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.0MB, time=19.15 NO POLE NO POLE x[1] = 0.5146 y2[1] (analytic) = 1.1295103333909906636170814513276 y2[1] (numeric) = 1.1295103333883285160261260199836 absolute error = 2.6621475909554313440e-12 relative error = 2.3569041488652798599526505589345e-10 % h = 0.0001 y1[1] (analytic) = 2.4921866925536851367009772447452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0127611539494821364276893095296 relative error = 0.51204646857359156615683800382069 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5147 y2[1] (analytic) = 1.1295595564126123304333733560064 y2[1] (numeric) = 1.1295595564098576724521324255723 absolute error = 2.7546579812409304341e-12 relative error = 2.4387009658786794818091730081460e-10 % h = 0.0001 y1[1] (analytic) = 2.4922737390592674953059387773014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0128482004550644950326508420858 relative error = 0.51552123884730940089626709958006 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5148 y2[1] (analytic) = 1.1296087881386384258698715955411 y2[1] (numeric) = 1.1296087881357887022148656823294 absolute error = 2.8497236550059132117e-12 relative error = 2.5227527307942320507546969670948e-10 % h = 0.0001 y1[1] (analytic) = 2.492360780642112467420506514258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0129352420379094671472185790424 relative error = 0.51899556991812926407123767869622 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5149 y2[1] (analytic) = 1.1296580285685766326667254799502 y2[1] (numeric) = 1.1296580285656292354329337042571 absolute error = 2.9473972337917756931e-12 relative error = 2.6091057286836712885411151313207e-10 % h = 0.0001 y1[1] (analytic) = 2.4924478173013496372169560809929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0130222786971466369436681457773 relative error = 0.52246946181791123596913753953951 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.0MB, time=19.71 NO POLE NO POLE x[1] = 0.515 y2[1] (analytic) = 1.1297072777019345465249632781811 y2[1] (numeric) = 1.1297072776988868144666882163203 absolute error = 3.0477320582750618608e-12 relative error = 2.6978068730112092716748496495880e-10 % h = 0.0001 y1[1] (analytic) = 2.4925348490361086381036410850348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0131093104319056378303531498192 relative error = 0.5259429145785125593121146588246 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5151 y2[1] (analytic) = 1.129756535538219676111416261096 y2[1] (numeric) = 1.1297565355350688939182247544465 absolute error = 3.1507821931915066495e-12 relative error = 2.7889037098514891954821082342150e-10 % h = 0.0001 y1[1] (analytic) = 2.4926218758455191527336967819731 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0131963372413161524604088467575 relative error = 0.52941592823178763885261175806471 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5152 y2[1] (analytic) = 1.1298058020769394430636436147992 y2[1] (numeric) = 1.1298058020736828406313826655262 absolute error = 3.2566024322609492730e-12 relative error = 2.8824444221071327127962218946630e-10 % h = 0.0001 y1[1] (analytic) = 2.4927088977287109130137432489187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0132833591245079127404553137031 relative error = 0.53288850280958804096916166480127 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5153 y2[1] (analytic) = 1.1298550773176011819948582242577 y2[1] (numeric) = 1.1298550773142359336917451074124 absolute error = 3.3652483031131168453e-12 relative error = 2.9784778337258812572147032214393e-10 % h = 0.0001 y1[1] (analytic) = 2.4927959146848137001125880654308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0133703760806106998393001302152 relative error = 0.536360638343762493262443365006 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.0MB, time=20.26 NO POLE NO POLE x[1] = 0.5154 y2[1] (analytic) = 1.1299043612597121404988533271647 y2[1] (numeric) = 1.1299043612562353644266390489209 absolute error = 3.4767760722142782438e-12 relative error = 3.0770534139173307564942002314715e-10 % h = 0.0001 y1[1] (analytic) = 2.4928829267129573444699285018216 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.013457388108754344196640566606 relative error = 0.53983233486615688415159864295587 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5155 y2[1] (analytic) = 1.1299536539027794791549300379977 y2[1] (numeric) = 1.1299536538991882364051352698303 absolute error = 3.5912427497947681674e-12 relative error = 3.1782212813692591463893837045005e-10 % h = 0.0001 y1[1] (analytic) = 2.4929699338122717258050532147519 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0135443952080687255317652795363 relative error = 0.5433035924086142624708092049574 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5156 y2[1] (analytic) = 1.1300029552463102715328257422214 y2[1] (numeric) = 1.1300029552426015654380483608818 absolute error = 3.7087060947773813396e-12 relative error = 3.2820322084635460932523527964410e-10 % h = 0.0001 y1[1] (analytic) = 2.4930569359818867731255434500313 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0136313973776837728522555148157 relative error = 0.54677441100297483706613418335622 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5157 y2[1] (analytic) = 1.130052265289811504197643360586 y2[1] (numeric) = 1.1300522652859822795779367237794 absolute error = 3.8292246197066368066e-12 relative error = 3.3885376254916843340214394950040e-10 % h = 0.0001 y1[1] (analytic) = 2.4931439332209324647359737525347 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0137183946167294644626858173191 relative error = 0.55024479068107597639260791721974 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=144.9MB, alloc=4.0MB, time=20.80 x[1] = 0.5158 y2[1] (analytic) = 1.1301015840327900767147814834725 y2[1] (numeric) = 1.1301015840288372191191025711898 absolute error = 3.9528575956789122827e-12 relative error = 3.4977896248698820446643580854455e-10 % h = 0.0001 y1[1] (analytic) = 2.4932309255285388282466121831497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0138053869243358279733242479341 relative error = 0.5537147314747522081115979062281 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5159 y2[1] (analytic) = 1.1301509114747528016548653752341 y2[1] (numeric) = 1.1301509114706731365975919267425 absolute error = 4.0796650572734484916e-12 relative error = 3.6098409653537556452669184223913e-10 % h = 0.0001 y1[1] (analytic) = 2.4933179129038359405821200426662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0138923742996329403088321074506 relative error = 0.55718423341583521868842283420883 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.516 y2[1] (analytic) = 1.1302002476152064045986788484863 y2[1] (numeric) = 1.1302002476109966967911946250296 absolute error = 4.2097078074842234567e-12 relative error = 3.7247450762526124543414636178212e-10 % h = 0.0001 y1[1] (analytic) = 2.4934048953459539279902511025232 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0139793567417509277169631673076 relative error = 0.5606532965361538529902305589296 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5161 y2[1] (analytic) = 1.1302495924536575241420970082945 y2[1] (numeric) = 1.1302495924493144767194443116061 absolute error = 4.3430474226526966884e-12 relative error = 3.8425560616433226008169027299386e-10 % h = 0.0001 y1[1] (analytic) = 2.4934918728540229660505503423234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0140663342498199657772624071078 relative error = 0.56412192086753411388413596461986 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5162 y2[1] (analytic) = 1.1302989459896127119010198662115 y2[1] (numeric) = 1.1302989459851329656436184429896 absolute error = 4.4797462574014232219e-12 relative error = 3.9633287045837796074397732335305e-10 % h = 0.0001 y1[1] (analytic) = 2.4935788454271732796830521940309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0141533068229702794097642588153 relative error = 0.56759010644179916183561857391115 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.0MB, time=21.34 NO POLE NO POLE x[1] = 0.5163 y2[1] (analytic) = 1.1303483082225784325163068241143 y2[1] (numeric) = 1.1303483082179585650667382866604 absolute error = 4.6198674495685374539e-12 relative error = 4.0871184713259490552038108068470e-10 % h = 0.0001 y1[1] (analytic) = 2.4936658130645351431569782927631 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0142402744603321428836903575475 relative error = 0.57105785329076931450717981575012 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5164 y2[1] (analytic) = 1.1303976791520610636587120277912 y2[1] (numeric) = 1.1303976791472975887335689210617 absolute error = 4.7634749251431067295e-12 relative error = 4.2139815155285047413925062146690e-10 % h = 0.0001 y1[1] (analytic) = 2.4937527757652388800994347340921 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0143272371610358798261467988765 relative error = 0.57452516144626204635725984603724 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5165 y2[1] (analytic) = 1.1304470587775668960338205902303 y2[1] (numeric) = 1.1304470587726562626306192355992 absolute error = 4.9106334032013546311e-12 relative error = 4.3439746824690517446620998956442e-10 % h = 0.0001 y1[1] (analytic) = 2.4938397335284148635041088377656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.01441419492421186323082090255 relative error = 0.57799203094009198823941381756471 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5166 y2[1] (analytic) = 1.1304964470986021333869856845598 y2[1] (numeric) = 1.1304964470935407249861419306415 absolute error = 5.0614084008437539183e-12 relative error = 4.4771555132559358085162207176678e-10 % h = 0.0001 y1[1] (analytic) = 2.4939266863531935157399654177629 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0145011477489905154666774825473 relative error = 0.5814584618040709270017474960819 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.0MB, time=21.89 NO POLE NO POLE x[1] = 0.5167 y2[1] (analytic) = 1.1305458441146728925082665065897 y2[1] (numeric) = 1.1305458441094570262701335175199 absolute error = 5.2158662381329890698e-12 relative error = 4.6135822490396384566938721177174e-10 % h = 0.0001 y1[1] (analytic) = 2.4940136342387053085599425585986 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.014588095634502308286654623383 relative error = 0.58492445407000780508661211922851 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5168 y2[1] (analytic) = 1.1305952498252852032373671069077 y2[1] (numeric) = 1.1305952498199111291943343185284 absolute error = 5.3740740430327883793e-12 relative error = 4.7533138352237572552778103792155e-10 % h = 0.0001 y1[1] (analytic) = 2.4941005771840807631096468977851 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0146750385798777628363589625695 relative error = 0.5883900077697087201305583950478 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5169 y2[1] (analytic) = 1.1306446642299450084685760924777 y2[1] (numeric) = 1.1306446642244089087122284669237 absolute error = 5.5360997563476255540e-12 relative error = 4.8964099256755706337237981915437e-10 % h = 0.0001 y1[1] (analytic) = 2.4941875151884504499360484143699 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0147619765842474496627604791543 relative error = 0.59185512293497692456454953701874 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.517 y2[1] (analytic) = 1.1306940873281581641557071976931 y2[1] (numeric) = 1.1306940873224561520190439069253 absolute error = 5.7020121366632907678e-12 relative error = 5.0429308869361866805083139673289e-10 % h = 0.0001 y1[1] (analytic) = 2.4942744482509449889961747234587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0148489096467419887228867882431 relative error = 0.59531979959761282521443323237872 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.0MB, time=22.46 NO POLE NO POLE x[1] = 0.5171 y2[1] (analytic) = 1.1307435191194304393170407248341 y2[1] (numeric) = 1.1307435191135585585517523937153 absolute error = 5.8718807652883311188e-12 relative error = 5.1929378024302753272819635642510e-10 % h = 0.0001 y1[1] (analytic) = 2.4943613763706950496658048766372 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0149358377664920493925169414216 relative error = 0.59878403778941398290167244061523 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5172 y2[1] (analytic) = 1.1307929596032675160402658538812 y2[1] (numeric) = 1.1307929595972217399890694934387 absolute error = 6.0457760511963604425e-12 relative error = 5.3464924766753833374090477254649e-10 % h = 0.0001 y1[1] (analytic) = 2.4944482995468313507481626682069 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0150227609426283504748747329913 relative error = 0.60224783754217511204433491913276 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5173 y2[1] (analytic) = 1.130842408779174989487423821634 y2[1] (numeric) = 1.1308424087729512202514545832031 absolute error = 6.2237692359692384309e-12 relative error = 5.5036574394908315141134585459133e-10 % h = 0.0001 y1[1] (analytic) = 2.4945352177784846604826094471451 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0151096791742816602093215119295 relative error = 0.60571119888768808025834137292889 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5174 y2[1] (analytic) = 1.1308918666466583678998519700868 y2[1] (numeric) = 1.1308918666402524355011108510789 absolute error = 6.4059323987411190079e-12 relative error = 5.6644959502061935440292058208069e-10 % h = 0.0001 y1[1] (analytic) = 2.4946221310647857965533364347042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0151965924605827962800484994886 relative error = 0.60917412185774190795897212534089 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=160.2MB, alloc=4.0MB, time=23.02 x[1] = 0.5175 y2[1] (analytic) = 1.1309413332052230726031286640106 y2[1] (numeric) = 1.1309413331986307341419852960992 absolute error = 6.5923384611433679114e-12 relative error = 5.8290720018693558923551170909416e-10 % h = 0.0001 y1[1] (analytic) = 2.4947090394048656260980565475626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.015283500800662625824768612347 relative error = 0.61263660648412276796263220684376 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5176 y2[1] (analytic) = 1.1309908084543744380120190776941 y2[1] (numeric) = 1.1309908084475913768197687282599 absolute error = 6.7830611922503494342e-12 relative error = 5.9974503254541581677176336223168e-10 % h = 0.0001 y1[1] (analytic) = 2.4947959427978550657166957264401 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0153704041936520654434077912245 relative error = 0.61609865279861398508887475893639 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5177 y2[1] (analytic) = 1.1310402923936177116354218507911 y2[1] (numeric) = 1.1310402923866395364218957685195 absolute error = 6.9781752135260822716e-12 relative error = 6.1696963940676133715330029497539e-10 % h = 0.0001 y1[1] (analytic) = 2.4948828412428850814800837700916 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.015457302638682081206795834876 relative error = 0.61956026083299603576268265021967 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5178 y2[1] (analytic) = 1.1310897850224580540813166132278 y2[1] (numeric) = 1.1310897850152802980775448487992 absolute error = 7.1777560037717644286e-12 relative error = 6.3458764271567074514827860624467e-10 % h = 0.0001 y1[1] (analytic) = 2.4949697347390866889386446745917 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0155441961348836886653567393761 relative error = 0.62302143061904654761700820175434 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5179 memory used=164.0MB, alloc=4.0MB, time=23.60 y2[1] (analytic) = 1.1311392863404005390617123791188 y2[1] (numeric) = 1.1311392863330186591576382119831 absolute error = 7.3818799040741671357e-12 relative error = 6.5260573947147775756693286965221e-10 % h = 0.0001 y1[1] (analytic) = 2.4950566232855909531310864778228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0156310846813879528577985426072 relative error = 0.62648216218854029909557091881769 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.518 y2[1] (analytic) = 1.1311887963469501533975968096429 y2[1] (numeric) = 1.131188796339359529274841911918 absolute error = 7.5906241227548977249e-12 relative error = 6.7103070214874685467181305397810e-10 % h = 0.0001 y1[1] (analytic) = 2.4951435068815289885930906090811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0157179682773259883198026738655 relative error = 0.62994245557324921905591312628167 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5181 y2[1] (analytic) = 1.1312383150416117970238863448289 y2[1] (numeric) = 1.1312383150338077302835658134133 absolute error = 7.8040667403205314156e-12 relative error = 6.8986937911782667738155111846888e-10 % h = 0.0001 y1[1] (analytic) = 2.4952303855260319593660007437126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.015804846921828959092712808497 relative error = 0.63340231080494238637271340477458 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5182 y2[1] (analytic) = 1.1312878424238902829943772042027 y2[1] (numeric) = 1.1312878424158679962799635922412 absolute error = 8.0222867144136119615e-12 relative error = 7.0912869506536112223091553055575e-10 % h = 0.0001 y1[1] (analytic) = 2.495317259218231079005511162692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0158917206140280787322232274764 relative error = 0.63686172791538602954135772485226 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5183 y2[1] (analytic) = 1.131337378493290337486697256245 y2[1] (numeric) = 1.1313373784850449736019327351366 absolute error = 8.2453638847645211084e-12 relative error = 7.2881565141475807598396778513617e-10 % h = 0.0001 y1[1] (analytic) = 2.495404127957257610590354617059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0159785893530546103170666818434 relative error = 0.64032070693634352628176817649953 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.0MB, time=24.18 NO POLE NO POLE x[1] = 0.5184 y2[1] (analytic) = 1.1313869232493165998072587566106 y2[1] (numeric) = 1.1313869232408432208291145397972 absolute error = 8.4733789781442168134e-12 relative error = 7.4893732674661573189033210683174e-10 % h = 0.0001 y1[1] (analytic) = 2.4954909917422428667309896971234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0160654531380398664577017619078 relative error = 0.64377924789957540314248919119098 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5185 y2[1] (analytic) = 1.1314364766914736223962119550608 y2[1] (numeric) = 1.1314364766827672087828941148834 absolute error = 8.7064136133178401774e-12 relative error = 7.6950087721910642973847498835742e-10 % h = 0.0001 y1[1] (analytic) = 2.4955778505723182095782877063537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0161523119681152093049997711381 relative error = 0.64723735083683933510503115390292 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5186 y2[1] (analytic) = 1.1314860388192658708323995710571 y2[1] (numeric) = 1.1314860388103213205264003800183 absolute error = 8.9445503059991910388e-12 relative error = 7.9051353698831796154648209304116e-10 % h = 0.0001 y1[1] (analytic) = 2.4956647044466150508322190398604 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0162391658424120505589311046448 relative error = 0.65069501577989014518847130236044 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5187 y2[1] (analytic) = 1.1315356096321977238383121379692 y2[1] (numeric) = 1.1315356096230098513645060657877 absolute error = 9.1878724738060721815e-12 relative error = 8.1198261862855228523060733608290e-10 % h = 0.0001 y1[1] (analytic) = 2.4957515533642648517505390673899 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0163260147600618514772511321743 relative error = 0.65415224276047980405431181102231 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.1MB, time=24.74 NO POLE NO POLE x[1] = 0.5188 y2[1] (analytic) = 1.1315851891297734732850442158455 y2[1] (numeric) = 1.1315851891203370088438277137403 absolute error = 9.4364644412165021052e-12 relative error = 8.3391551355258158818125015733470e-10 % h = 0.0001 y1[1] (analytic) = 2.4958383973243991231574735207391 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0164128587201961228841855855235 relative error = 0.65760903181035742961159495710669 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5189 y2[1] (analytic) = 1.1316347773114973241972514726985 y2[1] (numeric) = 1.1316347773018069127527256763873 absolute error = 9.6904114445257963112e-12 relative error = 8.5631969243186164317576617334693e-10 % h = 0.0001 y1[1] (analytic) = 2.4959252363261494254524033855063 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0164996977219464251791154502907 relative error = 0.66106538296126928662227526621125 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.519 y2[1] (analytic) = 1.1316843741768733947581086342535 y2[1] (numeric) = 1.1316843741669235951213041172027 absolute error = 9.9497996368045170508e-12 relative error = 8.7920270561670239855857532702130e-10 % h = 0.0001 y1[1] (analytic) = 2.4960120703686473686185492970897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0165865317644443683452613618741 relative error = 0.6645212962449587863068485349416 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5191 y2[1] (analytic) = 1.1317339797254057163142683021134 y2[1] (numeric) = 1.1317339797151910002214110106233 absolute error = 1.02147160928572914901e-11 relative error = 9.0257218355639574525131359546780e-10 % h = 0.0001 y1[1] (analytic) = 2.4960988994510246122316554408486 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.016673360846821611958367505633 relative error = 0.66797677169316648595023762814443 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.1MB, time=25.30 NO POLE NO POLE x[1] = 0.5192 y2[1] (analytic) = 1.1317835939565982333808206402875 y2[1] (numeric) = 1.1317835939461129845666381420486 absolute error = 1.04852488141824982389e-11 relative error = 9.2643583721930040265686702935542e-10 % h = 0.0001 y1[1] (analytic) = 2.4961857235724128654686729563381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0167601849682098651953850211225 relative error = 0.67143180933763008850793494820227 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5193 y2[1] (analytic) = 1.1318332168699548036462539300367 y2[1] (numeric) = 1.1318332168591933169123211078408 absolute error = 1.07614867339328221959e-11 relative error = 9.5080145851288386595896852012798e-10 % h = 0.0001 y1[1] (analytic) = 2.4962725427319438871164428455326 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.016847004127740886843154910317 relative error = 0.67488640921008444221240147405713 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5194 y2[1] (analytic) = 1.1318828484649791979774159929847 y2[1] (numeric) = 1.1318828484539356782555393153248 absolute error = 1.10435197218766776599e-11 relative error = 9.7567692070372135713828640167203e-10 % h = 0.0001 y1[1] (analytic) = 2.4963593569287494855803783849504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0169338183245464853070904497348 relative error = 0.67834057134226154017972226754233 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5195 y2[1] (analytic) = 1.1319324887411751004244764824447 y2[1] (numeric) = 1.1319324887298436618351159827883 absolute error = 1.13314385893604996564e-11 relative error = 1.0010701788374517220396302363034e-09 % h = 0.0001 y1[1] (analytic) = 2.4964461661619615188931470415919 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0170206275577585186198591063763 relative error = 0.68179429576589052001651834464144 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=179.2MB, alloc=4.1MB, time=25.87 x[1] = 0.5196 y2[1] (analytic) = 1.1319821376980461082258900429144 y2[1] (numeric) = 1.1319821376864207731316181394817 absolute error = 1.16253350942719034327e-11 relative error = 1.0269892701586902161919707942359e-09 % h = 0.0001 y1[1] (analytic) = 2.4965329704307118947233518926059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0171074318265088944500639573903 relative error = 0.68524758251269766342711480940376 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5197 y2[1] (analytic) = 1.1320317953350957318133603376867 y2[1] (numeric) = 1.1320317953231704298673566256181 absolute error = 1.19253019460037120686e-11 relative error = 1.0534423145308981215930499329994e-09 % h = 0.0001 y1[1] (analytic) = 2.4966197697341325703842125485964 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0171942311299295701109246133808 relative error = 0.68870043161440639582096514819414 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5198 y2[1] (analytic) = 1.1320814616518273948168049445289 y2[1] (numeric) = 1.1320814616395959620063860923734 absolute error = 1.22314328104188521555e-11 relative error = 1.0804375148562091372141409963268e-09 % h = 0.0001 y1[1] (analytic) = 2.4967065640713555528422455804831 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0172810254671525525689576452675 relative error = 0.69215284310273728592033158201769 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5199 y2[1] (analytic) = 1.1321311366477444340693211193792 y2[1] (numeric) = 1.1321311366352006117545050018862 absolute error = 1.25438223148161174930e-11 relative error = 1.1079831574952124856938163902010e-09 % h = 0.0001 y1[1] (analytic) = 2.4967933534415128987259444498288 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0173678148373098984526565146132 relative error = 0.69560481700940804536822137469172 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.52 y2[1] (analytic) = 1.1321808203223500996121524280115 y2[1] (numeric) = 1.1321808203094875335592556272578 absolute error = 1.28625660528968007537e-11 relative error = 1.1360876126866926788711295855051e-09 % h = 0.0001 y1[1] (analytic) = 2.4968801378437367143344589425478 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0174545992395337140611710073322 relative error = 0.69905635336613352833657899470403 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.1MB, time=26.44 NO POLE NO POLE x[1] = 0.5201 y2[1] (analytic) = 1.1322305126751475546996562456192 y2[1] (numeric) = 1.1322305126619597941099240525522 absolute error = 1.31877605897321930670e-11 relative error = 1.1647593349673258848576341100798e-09 % h = 0.0001 y1[1] (analytic) = 2.4969669172771591556462741059063 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0175413786729561553729861706907 relative error = 0.70250745220462573113473402850511 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5202 y2[1] (analytic) = 1.132280213705639875804272124267 y2[1] (numeric) = 1.1322802136921203723375401727962 absolute error = 1.35195034667319514708e-11 relative error = 1.1940068635913328392200415566914e-09 % h = 0.0001 y1[1] (analytic) = 2.4970536917409124283278886887314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0176281531367094280546007535158 relative error = 0.70595811355659379181810474323556 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5203 y2[1] (analytic) = 1.1323299234133300526214910281627 y2[1] (numeric) = 1.1323299233994721594148776939793 absolute error = 1.38578932066133341834e-11 relative error = 1.2238388229500882431858301996482e-09 % h = 0.0001 y1[1] (analytic) = 2.4971404612341287877424930847378 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0177149226299257874692051495222 relative error = 0.70940833745374398979715719662335 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5204 y2[1] (analytic) = 1.1323796417977209880748254366982 y2[1] (numeric) = 1.1323796417835179587564541330537 absolute error = 1.42030293183713036445e-11 relative error = 1.2542639229916865915240037511858e-09 % h = 0.0001 y1[1] (analytic) = 2.4972272257559405389586467788894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0178016871517375386853588436738 relative error = 0.71285812392777974544661979213889 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.1MB, time=27.02 NO POLE NO POLE x[1] = 0.5205 y2[1] (analytic) = 1.1324293688583154983207803152098 y2[1] (numeric) = 1.1324293688437604860185308179343 absolute error = 1.45550123022494972755e-11 relative error = 1.2852909596404643729082455954518e-09 % h = 0.0001 y1[1] (analytic) = 2.4973139853054800367589552967061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0178884467012770364856673614905 relative error = 0.7163074730104016197149531772528 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5206 y2[1] (analytic) = 1.1324791045946163127538249534095 y2[1] (numeric) = 1.1324791045797023690991128874989 absolute error = 1.49139436547120659106e-11 relative error = 1.3169288152164785857247165762762e-09 % h = 0.0001 y1[1] (analytic) = 2.4974007398818796856487466564309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0179752012776766853754587212153 relative error = 0.71975638473330731373407538286368 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5207 y2[1] (analytic) = 1.1325288490061260740113656714358 y2[1] (numeric) = 1.1325288489908461481379492915879 absolute error = 1.52799258734163798479e-11 relative error = 1.3491864588549415121238313488949e-09 % h = 0.0001 y1[1] (analytic) = 2.4974874894842719398647473239689 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0180619508800689395914593887533 relative error = 0.72320485912819166842934210185494 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5208 y2[1] (analytic) = 1.1325786020923473379787193934759 y2[1] (numeric) = 1.1325786020766942755165327910043 absolute error = 1.56530624621866024716e-11 relative error = 1.3820729469256116933233529575999e-09 % h = 0.0001 y1[1] (analytic) = 2.4975742341117893033837576705131 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0181486955075863031104697352975 relative error = 0.72665289622674666412978200490268 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.1MB, time=27.59 NO POLE NO POLE x[1] = 0.5209 y2[1] (analytic) = 1.1326283638527825737940880889078 y2[1] (numeric) = 1.1326283638367491158580999575141 absolute error = 1.60334579359881313937e-11 relative error = 1.4155974234521410489719508827512e-09 % h = 0.0001 y1[1] (analytic) = 2.4976609737635643299313269327691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0182354351593613296580389975535 relative error = 0.73010049606066142017858699157637 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.521 y2[1] (analytic) = 1.1326781342869341638535340809147 y2[1] (numeric) = 1.1326781342705129460276311738459 absolute error = 1.64212178259029070688e-11 relative error = 1.4497691205313780838817318958093e-09 % h = 0.0001 y1[1] (analytic) = 2.4977477084387296229904276756926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.018322169834526622717139740477 relative error = 0.73354765866162219454385727487693 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5211 y2[1] (analytic) = 1.13272791339430440381595622252 y2[1] (numeric) = 1.132727913377487955131850633691 absolute error = 1.68164486841055888290e-11 relative error = 1.4845973587526271248957048381886e-09 % h = 0.0001 y1[1] (analytic) = 2.4978344381364178358101297576518 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0184088995322148355368418224362 relative error = 0.73699438406131238342960119731663 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5212 y2[1] (analytic) = 1.132777701174395502608066939994 y2[1] (numeric) = 1.1327777011571762445192263417034 absolute error = 1.72192580888405982906e-11 relative error = 1.5200915476168635311113727202123e-09 % h = 0.0001 y1[1] (analytic) = 2.4979211628557616714142737979304 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0184956242515586711409858627148 relative error = 0.74044067229141252088698967681956 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.1MB, time=28.16 NO POLE NO POLE x[1] = 0.5213 y2[1] (analytic) = 1.1328274976267095824293701435829 y2[1] (numeric) = 1.1328274976090798277799701134999 absolute error = 1.76297546494000300830e-11 relative error = 1.5562611859559048206070677066017e-09 % h = 0.0001 y1[1] (analytic) = 2.4980078825958938826101441464811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0185823439916908823368562112655 relative error = 0.74388652338360027842586518052222 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5214 y2[1] (analytic) = 1.1328773027507486787571400055095 y2[1] (numeric) = 1.13287730273270063074603757566 absolute error = 1.80480480111024298495e-11 relative error = 1.5931158623515376567960767388515e-09 % h = 0.0001 y1[1] (analytic) = 2.4980945973559472719971413558462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0186690587517442717238534206306 relative error = 0.74733193736955046462650512485119 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5215 y2[1] (analytic) = 1.1329271165460147403514006051963 y2[1] (numeric) = 1.132927116527540491491128165726 absolute error = 1.84742488602724394703e-11 relative error = 1.6306652555546006376268113079287e-09 % h = 0.0001 y1[1] (analytic) = 2.4981813071350546919754541551558 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0187557685308516917021662199402 relative error = 0.75077691428093502475163960004393 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5216 y2[1] (analytic) = 1.132976939012009629259906441661 y2[1] (numeric) = 1.1329769389931011603306851322028 absolute error = 1.89084689292213094582e-11 relative error = 1.6689191349040228309051565800850e-09 % h = 0.0001 y1[1] (analytic) = 2.4982680119323490447547309261191 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0188424733281460444814429909035 relative error = 0.75422145414942304035872331750834 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=198.3MB, alloc=4.1MB, time=28.71 x[1] = 0.5217 y2[1] (analytic) = 1.1330267701482351208231238130352 y2[1] (numeric) = 1.1330267701288842998218955345581 absolute error = 1.93508210012282784771e-11 relative error = 1.7078873607458179990200563600147e-09 % h = 0.0001 y1[1] (analytic) = 2.4983547117469632823627506809207 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0189291731427602820894627457051 relative error = 0.75766555700668072891246167830532 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5218 y2[1] (analytic) = 1.133076609954192903679213063155 y2[1] (numeric) = 1.1330766099343914847636902432224 absolute error = 1.98014189155228199326e-11 relative error = 1.7475798848520344563230255774936e-09 % h = 0.0001 y1[1] (analytic) = 2.4984414065780304066540935419351 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0190158679738274063808056067195 relative error = 0.76110922288437144339759086112111 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5219 y2[1] (analytic) = 1.1331264584293845797690116951758 y2[1] (numeric) = 1.1331264584091242021967439395888 absolute error = 2.02603775722677555870e-11 relative error = 1.7880067508396605027173025167230e-09 % h = 0.0001 y1[1] (analytic) = 2.4985280964246834693188107231742 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0191025578204804690455227879586 relative error = 0.76455245181415567193191182819121 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.522 y2[1] (analytic) = 1.1331763155733116643410183521593 y2[1] (numeric) = 1.1331763155525838514034751160132 absolute error = 2.07278129375432361461e-11 relative error = 1.8291780945894853766201153279518e-09 % h = 0.0001 y1[1] (analytic) = 2.4986147812860555718910940133795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0191892426818525716178060781639 relative error = 0.76799524382769103737957814754559 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5221 y2[1] (analytic) = 1.1332261813854755859563776645847 y2[1] (numeric) = 1.1332261813642717439080460758142 absolute error = 2.12038420483315887705e-11 relative error = 1.8711041446649156709695580097862e-09 % h = 0.0001 y1[1] (analytic) = 2.4987014611612798657579447606726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.019275922557076865484656825457 relative error = 0.7714375989566322969646375300518 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.1MB, time=29.29 NO POLE NO POLE x[1] = 0.5222 y2[1] (analytic) = 1.133276055865377686493865964733 y2[1] (numeric) = 1.1332760558436891034763629332731 absolute error = 2.16885830175030314599e-11 relative error = 1.9137952227307471556171308158855e-09 % h = 0.0001 y1[1] (analytic) = 2.4987881360494895521678423586783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0193625974452865518945544234627 relative error = 0.77487951723263134188482697979127 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5223 y2[1] (analytic) = 1.133325939012519221154877867895 y2[1] (numeric) = 1.133325938990337066116075613634 absolute error = 2.21821550388022542610e-11 relative error = 1.9572617439718919496725945324676e-09 % h = 0.0001 y1[1] (analytic) = 2.4988748059498178822394122340325 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0194492673456148819661242988169 relative error = 0.77832099868733719692562145625225 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5224 y2[1] (analytic) = 1.1333758308264013584684137203534 y2[1] (numeric) = 1.1333758308037166800765778531036 absolute error = 2.26846783918358672498e-11 relative error = 2.0015142175120609874256703512440e-09 % h = 0.0001 y1[1] (analytic) = 2.4989614708613981569700933351886 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.019535932257195156696805399973 relative error = 0.78176204335239602007453594691337 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5225 y2[1] (analytic) = 1.1334257313065251802960679140882 y2[1] (numeric) = 1.1334257312833289058490071988515 absolute error = 2.31962744470607152367e-11 relative error = 2.0465632468324017212976012108972e-09 % h = 0.0001 y1[1] (analytic) = 2.4990481307833637272448051224361 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0196225921791607269715171872205 relative error = 0.78520265125945110213568084882303 % h = 0.0001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.1MB, time=29.86 NO POLE NO POLE x[1] = 0.5226 y2[1] (analytic) = 1.1334756404523916818370180681572 y2[1] (numeric) = 1.13347564042867461616624500901 absolute error = 2.37170656707730591472e-11 relative error = 2.0924195301900910057040851159822e-09 % h = 0.0001 y1[1] (analytic) = 2.499134785714847993844614059044 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0197092471106449935713261238284 relative error = 0.78864282244014286634457055776735 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5227 y2[1] (analytic) = 1.1335255582635017716330150766997 y2[1] (numeric) = 1.133525558239254596002916452674 absolute error = 2.42471756300986240257e-11 relative error = 2.1390938610368831052836964271834e-09 % h = 0.0001 y1[1] (analytic) = 2.499221435654984407455399603443 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0197958970507814071821116682274 relative error = 0.79208255692610886798318516370612 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5228 y2[1] (analytic) = 1.1335754847393562715733740235147 y2[1] (numeric) = 1.1335754847145695425753905099013 absolute error = 2.47867289979835136134e-11 relative error = 2.1865971284376127712950085042024e-09 % h = 0.0001 y1[1] (analytic) = 2.4993080806029064686765197023594 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0198825419987034684032317671438 relative error = 0.79552185474898379399528515114386 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5229 y2[1] (analytic) = 1.133625419879455916899965963164 y2[1] (numeric) = 1.1336254198541200653417799717122 absolute error = 2.53358515581859914518e-11 relative error = 2.2349403174886533300699702734472e-09 % h = 0.0001 y1[1] (analytic) = 2.4993947205577477280294757848146 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.019969181953544727756187849599 relative error = 0.7989607159403994626019790031736 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.1MB, time=30.42 NO POLE NO POLE x[1] = 0.523 y2[1] (analytic) = 1.133675363683301356212210568549 y2[1] (numeric) = 1.13367536365740668600194144009 absolute error = 2.58946702102691284590e-11 relative error = 2.2841345097363297270720111892165e-09 % h = 0.0001 y1[1] (analytic) = 2.4994813555186417859665772569024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0200558169144387856932893216868 relative error = 0.80239914053198482291754360789496 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5231 y2[1] (analytic) = 1.1337253161503931514720696449126 y2[1] (numeric) = 1.1337253161239298384974753279805 absolute error = 2.64633129745943169321e-11 relative error = 2.3341908835952864706857529477174e-09 % h = 0.0001 y1[1] (analytic) = 2.499567985484722292879605497259 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0201424468805192926063175620434 relative error = 0.80583712855536595456549736604645 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5232 y2[1] (analytic) = 1.1337752772802317780090415102151 y2[1] (numeric) = 1.1337752772531898690117258592923 absolute error = 2.70419089973156509228e-11 relative error = 2.3851207147668104193585275783778e-09 % h = 0.0001 y1[1] (analytic) = 2.4996546104551229491084773531379 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0202290718509199488351894179223 relative error = 0.80927468004216606729492589861545 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5233 y2[1] (analytic) = 1.1338252470723176245251562418353 y2[1] (numeric) = 1.1338252470446870359697810688968 absolute error = 2.76305885553751729385e-11 relative error = 2.4369353766571083562128873965420e-09 % h = 0.0001 y1[1] (analytic) = 2.4997412304289775049499081370034 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0203156918247745046766202017878 relative error = 0.81271179502400550059706025328056 % h = 0.0001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.1MB, time=31.00 NO POLE NO POLE x[1] = 0.5234 y2[1] (analytic) = 1.1338752255261509930999717895459 y2[1] (numeric) = 1.1338752254979215100384728026281 absolute error = 2.82294830614989869178e-11 relative error = 2.4896463407955392949896371445500e-09 % h = 0.0001 y1[1] (analytic) = 2.4998278454054197606660741235564 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0204023068012167603927861883408 relative error = 0.8161484735325017233221075085717 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5235 y2[1] (analytic) = 1.133925212641232099195570954714 y2[1] (numeric) = 1.133925212612393374126376717283 absolute error = 2.88387250691942374310e-11 relative error = 2.5432651772528014613711492874792e-09 % h = 0.0001 y1[1] (analytic) = 2.4999144553835835664932745471055 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0204889167793805662199866118899 relative error = 0.81958471559926933329633367463685 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5236 y2[1] (analytic) = 1.1339752084170610716615592356757 y2[1] (numeric) = 1.133975208387602623383812280621 absolute error = 2.94584482777469550547e-11 relative error = 2.5978035550590738936427032003761e-09 % h = 0.0001 y1[1] (analytic) = 2.5000010603626028226505930991964 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0205755217583998223773051639808 relative error = 0.82302052125592005693939878953541 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5237 y2[1] (analytic) = 1.1340252128531379527400635392363 y2[1] (numeric) = 1.1340252128230491652028427713644 absolute error = 3.00887875372207678719e-11 relative error = 2.6532732426221126068927125000694e-09 % h = 0.0001 y1[1] (analytic) = 2.5000876603416114793485589264142 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0206621217374084790752709911986 relative error = 0.82645589053406274888194411007268 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=217.4MB, alloc=4.1MB, time=31.57 x[1] = 0.5238 y2[1] (analytic) = 1.1340752259489626980707317582446 y2[1] (numeric) = 1.1340752259182328192172752791981 absolute error = 3.07298788534564790465e-11 relative error = 2.7096861081453012647724971445687e-09 % h = 0.0001 y1[1] (analytic) = 2.5001742553197435367978071282706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.020748716715540536524519193055 relative error = 0.82989082346530339158343129611794 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5239 y2[1] (analytic) = 1.1341252477040351766957332151922 y2[1] (numeric) = 1.1341252476726533173026607047699 absolute error = 3.13818593930725104223e-11 relative error = 2.7670541200456563029823810783608e-09 % h = 0.0001 y1[1] (analytic) = 2.5002608452961330452177387550909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0208353066919300449444508198753 relative error = 0.83332532008124509495023348749472 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.524 y2[1] (analytic) = 1.134175278117855171064759971788 y2[1] (numeric) = 1.1341752780858103035762937596902 absolute error = 3.20448674884662120978e-11 relative error = 2.8253893473717864487969800141206e-09 % h = 0.0001 y1[1] (analytic) = 2.5003474302699141048451803058119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0209218916657111045718923705963 relative error = 0.83675938041348809595397817241225 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5241 y2[1] (analytic) = 1.1342253171899223770400290044568 y2[1] (numeric) = 1.1342253171572033343972129665322 absolute error = 3.27190426428160379246e-11 relative error = 2.8847039602218065806742076268465e-09 % h = 0.0001 y1[1] (analytic) = 2.5004340102402208659430427256072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0210084716360178656697547903916 relative error = 0.84019300449362975825014174665207 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5242 y2[1] (analytic) = 1.1342753649197364039012852457129 y2[1] (numeric) = 1.1342753648863318783662006588319 absolute error = 3.34045255350845868810e-11 relative error = 2.9450102301612058723678989574599e-09 % h = 0.0001 y1[1] (analytic) = 2.5005205852061875288089799032504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0210950466019845285356919680348 relative error = 0.84362619235326457179689566251732 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.1MB, time=32.13 NO POLE NO POLE x[1] = 0.5243 y2[1] (analytic) = 1.1343254213067967743508054913587 y2[1] (numeric) = 1.1343254212726953163257829810878 absolute error = 3.41014580250225102709e-11 relative error = 3.0063205306406701658719508579005e-09 % h = 0.0001 y1[1] (analytic) = 2.5006071551669483437840466681318 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0211816165627453435107587329162 relative error = 0.8470589440239841524742040667851 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5244 y2[1] (analytic) = 1.1343754863506029245184031734578 y2[1] (numeric) = 1.1343754863157929413602298887613 absolute error = 3.48099831581732846965e-11 relative error = 3.0686473374138585174231190039406e-09 % h = 0.0001 y1[1] (analytic) = 2.50069372012163761126135628684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0212681815174346109880683516244 relative error = 0.850491259537377241703172826767 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5245 y2[1] (analytic) = 1.1344255600506542039664339990323 y2[1] (numeric) = 1.1344255600151239587955551482765 absolute error = 3.55302451708788507558e-11 relative error = 3.1320032289551338610503246823608e-09 % h = 0.0001 y1[1] (analytic) = 2.5007802800693896816947374592242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0213547414651866814214495240086 relative error = 0.85392313892502970606564984378838 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5246 y2[1] (analytic) = 1.1344756424064498756948024544357 y2[1] (numeric) = 1.1344756423701874861995163370202 absolute error = 3.62623894952861174155e-11 relative error = 3.1964008868772477341633275336047e-09 % h = 0.0001 y1[1] (analytic) = 2.5008668350093389556073908138482 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0214412964051359553341028786326 relative error = 0.85735458221852453692407655323762 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.1MB, time=32.71 NO POLE NO POLE x[1] = 0.5247 y2[1] (analytic) = 1.134525733417489116145969175349 y2[1] (numeric) = 1.134525733380482553381614843342 absolute error = 3.70065627643543320070e-11 relative error = 3.2618530963489790094582825291060e-09 % h = 0.0001 y1[1] (analytic) = 2.5009533849406198836005449027514 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0215278463364168833272569675358 relative error = 0.86078558944944185004159051053822 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5248 y2[1] (analytic) = 1.1345758330832710152099591823525 y2[1] (numeric) = 1.1345758330455081023930958665541 absolute error = 3.77629128168633157984e-11 relative error = 3.3283727465127265779163878303913e-09 % h = 0.0001 y1[1] (analytic) = 2.5010399298623669663621116954295 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0216143912581639660888237602139 relative error = 0.86421616064935888520237896232426 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5249 y2[1] (analytic) = 1.134625941403294576229370982021 y2[1] (numeric) = 1.1346259413647629875269484169315 absolute error = 3.85315887024225650895e-11 relative error = 3.3959728309020559271920419050019e-09 % h = 0.0001 y1[1] (analytic) = 2.5011264697737147546753415719478 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0217009311695117544020536367322 relative error = 0.86764629584985000583228330213903 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.525 y2[1] (analytic) = 1.1346760583770587160043865334936 y2[1] (numeric) = 1.134676058337745975317905315712 absolute error = 3.93127406864812177816e-11 relative error = 3.4646664478591995601503485584643e-09 % h = 0.0001 y1[1] (analytic) = 2.5012130046737978494274778151016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.021787466069594849154189879886 relative error = 0.87107599508248669861965431007077 % h = 0.0001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.1MB, time=33.27 NO POLE NO POLE x[1] = 0.5251 y2[1] (analytic) = 1.1347261840040622647977820804682 y2[1] (numeric) = 1.134726183963955744542443195096 absolute error = 4.01065202553388853722e-11 relative error = 3.5344668009525111982042367061834e-09 % h = 0.0001 y1[1] (analytic) = 2.5012995345617509016184106015367 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0218739959575479013451226663211 relative error = 0.87450525837883757313645807571117 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5252 y2[1] (analytic) = 1.1347763182838039663399398485691 y2[1] (numeric) = 1.1347763182428908862187824982467 absolute error = 4.09130801211573503224e-11 relative error = 3.6053871993938737139390769919874e-09 % h = 0.0001 y1[1] (analytic) = 2.5013860594367086123693304917431 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0219605208325056120960425565275 relative error = 0.8779340857704683614596325038571 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5253 y2[1] (analytic) = 1.134826461215782477833860608039 y2[1] (numeric) = 1.1348264611740499036068874792901 absolute error = 4.17325742269731287489e-11 relative error = 3.6774410584560607379143375308365e-09 % h = 0.0001 y1[1] (analytic) = 2.501472579297805732931381418836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0220470406936027326580934836204 relative error = 0.88136247728894191779269430244675 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5254 y2[1] (analytic) = 1.1348766127994963699601771017051 y2[1] (numeric) = 1.1348766127569312122084662033147 absolute error = 4.25651577517108983904e-11 relative error = 3.7506418998900518843870240496601e-09 % h = 0.0001 y1[1] (analytic) = 2.5015590941441770646943131760372 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0221335555399740644210252408216 relative error = 0.88479043296581821808759635221257 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.1MB, time=33.85 NO POLE NO POLE x[1] = 0.5255 y2[1] (analytic) = 1.1349267730344441268821683381684 y2[1] (numeric) = 1.134926772991033139766970546372 absolute error = 4.34109871151977917964e-11 relative error = 3.8250033523423015405833610727428e-09 % h = 0.0001 y1[1] (analytic) = 2.5016456039749574591951334027701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0222200653707544589218454675545 relative error = 0.88821795283265435966683535756852 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5256 y2[1] (analytic) = 1.1349769419201241462507747501666 y2[1] (numeric) = 1.134976941875853926267596195476 absolute error = 4.42702199831785546906e-11 relative error = 3.9005391517719611645555917205348e-09 % h = 0.0001 y1[1] (analytic) = 2.501732108789281818126759069283 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0223065701850788178534711340674 relative error = 0.89164503692100456084580967833923 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5257 y2[1] (analytic) = 1.1350271194560347392096142180609 y2[1] (numeric) = 1.1350271194108917239372826486036 absolute error = 4.51430152723315694573e-11 relative error = 3.9772631418680550363662197621447e-09 % h = 0.0001 y1[1] (analytic) = 2.5018186085862850933466674597118 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0223930699820820930733795244962 relative error = 0.89507168526242016055542724182736 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5258 y2[1] (analytic) = 1.1350773056416741303999989583955 y2[1] (numeric) = 1.1350773055956445972447132146943 absolute error = 4.60295331552857437012e-11 relative error = 4.0551892744666094075585765574546e-09 % h = 0.0001 y1[1] (analytic) = 2.5019051033651022868855466534991 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0224795647608992866122587182835 relative error = 0.89849789788844961796496343497968 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=236.5MB, alloc=4.1MB, time=34.41 x[1] = 0.5259 y2[1] (analytic) = 1.1351275004765404579659532774799 y2[1] (numeric) = 1.1351275004296105229003150136505 absolute error = 4.69299350656382638294e-11 relative error = 4.1343316099677349937719407220563e-09 % h = 0.0001 y1[1] (analytic) = 2.5019915931248684509559455050793 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0225660545206654506826575698637 relative error = 0.90192367483063851210516887615064 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.526 y2[1] (analytic) = 1.135177703960131773559232189945 y2[1] (numeric) = 1.1351777039122873898562589763371 absolute error = 4.78443837029732136079e-11 relative error = 4.2147043177526627557081097877267e-09 % h = 0.0001 y1[1] (analytic) = 2.5020780778647186879609231217462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0226525392605156876876351865306 relative error = 0.90534901612052954149162696626603 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5261 y2[1] (analytic) = 1.1352279160919460423443409022212 y2[1] (numeric) = 1.1352279160431729993064598445819 absolute error = 4.87730430378810576393e-11 relative error = 4.2963216766007329132032719603934e-09 % h = 0.0001 y1[1] (analytic) = 2.5021645575837881505026978396152 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0227390189795851502294099043996 relative error = 0.90877392178966252374836111904622 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5262 y2[1] (analytic) = 1.135278136871481143003555160889 y2[1] (numeric) = 1.1352781368217650646865761711753 absolute error = 4.97160783169789897137e-11 relative error = 4.3791980751063371376662896562657e-09 % h = 0.0001 y1[1] (analytic) = 2.5022510322812120413912956975938 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0228254936770090411180077623782 relative error = 0.91219839186957439523169157004268 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5263 y2[1] (analytic) = 1.1353283662982348677419424658523 y2[1] (numeric) = 1.1353283662475612116740103198706 absolute error = 5.06736560679321459817e-11 relative error = 4.4633480120958138679117113945123e-09 % h = 0.0001 y1[1] (analytic) = 2.5023375019561256136531984092745 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0229119633519226133799104740589 relative error = 0.91562242639179921065434166428816 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.1MB, time=34.97 NO POLE NO POLE x[1] = 0.5264 y2[1] (analytic) = 1.1353786043717049222923841482833 y2[1] (numeric) = 1.1353786043200589781879084653837 absolute error = 5.16459441044756828996e-11 relative error = 4.5487860970442966945618717312871e-09 % h = 0.0001 y1[1] (analytic) = 2.5024239666076641705399908326621 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0229984280034611702667028974465 relative error = 0.91904602538786814270979352230869 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5265 y2[1] (analytic) = 1.1354288510913889259205983132897 y2[1] (numeric) = 1.1354288510387558143891605933932 absolute error = 5.26331115314377198965e-11 relative error = 4.6355270504925157581975252101645e-09 % h = 0.0001 y1[1] (analytic) = 2.5025104262349630655370079376515 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0230848876307600652637200024359 relative error = 0.92246918888930948169689298443883 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5266 y2[1] (analytic) = 1.1354791064567844114301636472533 y2[1] (numeric) = 1.1354791064031490826804005005405 absolute error = 5.36353287497631467128e-11 relative error = 4.7235857044635521064591755027306e-09 % h = 0.0001 y1[1] (analytic) = 2.5025968808371577023719812711662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0231713422329547020986933359506 relative error = 0.92589191692764863514470373317878 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5267 y2[1] (analytic) = 1.13552937046738882516754408979 y2[1] (numeric) = 1.1355293704127360577060057944298 absolute error = 5.46527674615382953602e-11 relative error = 4.8129770028795449553944360026864e-09 % h = 0.0001 y1[1] (analytic) = 2.5026833304133835350236849198747 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0232577918091805347503969846591 relative error = 0.92931420953440812743761049363999 % h = 0.0001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.1MB, time=35.53 NO POLE NO POLE x[1] = 0.5268 y2[1] (analytic) = 1.1355796431226995270271143702807 y2[1] (numeric) = 1.1355796430670139263520978936279 absolute error = 5.56856006750164766528e-11 relative error = 4.9037160019783518003430464792413e-09 % h = 0.0001 y1[1] (analytic) = 2.5027697749627760677305809703949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0233442363585730674572930351793 relative error = 0.93273606674110759944067121187578 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5269 y2[1] (analytic) = 1.1356299244222137904561864089239 y2[1] (numeric) = 1.1356299243654797877465420276643 absolute error = 5.67340027096443812596e-11 relative error = 4.9958178707301613217531456197741e-09 % h = 0.0001 y1[1] (analytic) = 2.5028562144844708549994644669024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0234306758802678547261765316868 relative error = 0.93615748857926380812521811115384 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.527 y2[1] (analytic) = 1.1356802143654288024600365822581 y2[1] (numeric) = 1.1356802143076306532589472370314 absolute error = 5.77981492010893452267e-11 relative error = 5.0892978912540590311866080662477e-09 % h = 0.0001 y1[1] (analytic) = 2.5029426489776035016141078660558 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0235171103734005013408199308402 relative error = 0.9395784750803906261947075261474 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5271 y2[1] (analytic) = 1.1357305129518416636069338531047 y2[1] (numeric) = 1.1357305128929634465006663731841 absolute error = 5.88782171062674799206e-11 relative error = 5.1841714592345456030845847762185e-09 % h = 0.0001 y1[1] (analytic) = 2.5030290784413096626439049891511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0236035398371066623706170539355 relative error = 0.94299902627599904171081841501345 % h = 0.0001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.1MB, time=36.10 NO POLE NO POLE x[1] = 0.5272 y2[1] (analytic) = 1.1357808201809493880331687648814 y2[1] (numeric) = 1.1357808201209750033247960985403 absolute error = 5.99743847083726663411e-11 relative error = 5.2804540843380078376493370936196e-09 % h = 0.0001 y1[1] (analytic) = 2.5031155028747250434525144714209 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0236899642705220431792265362053 relative error = 0.94641914219759715771979944949928 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5273 y2[1] (analytic) = 1.135831136052248903448083300235 y2[1] (numeric) = 1.1358311359911620718261768864804 absolute error = 6.10868316219064137546e-11 relative error = 5.3781613906291422004413238193590e-09 % h = 0.0001 y1[1] (analytic) = 2.5032019222769853997065027083907 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0237763836727823994332147731751 relative error = 0.94983882287669019187906458311515 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5274 y2[1] (analytic) = 1.1358814605652370511391016039436 y2[1] (numeric) = 1.1358814605030213123413930213476 absolute error = 6.22157387977085825960e-11 relative error = 5.4773091169873308841019067282260e-09 % h = 0.0001 y1[1] (analytic) = 2.5032883366472265373839862992059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0238627980430235371106983639903 relative error = 0.95325806834478047608403699749314 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5275 y2[1] (analytic) = 1.1359317937194105859767615700385 y2[1] (numeric) = 1.1359317936560492974487725984479 absolute error = 6.33612885279889715906e-11 relative error = 5.5779131175229703379341324449038e-09 % h = 0.0001 y1[1] (analytic) = 2.5033747459845843127832739868435 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0239492073803813125099860516279 relative error = 0.95667687863336745609524132709868 % h = 0.0001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.1MB, time=36.67 NO POLE NO POLE x[1] = 0.5276 y2[1] (analytic) = 1.1359821355142661764197472930943 y2[1] (numeric) = 1.1359821354497425119683875240499 absolute error = 6.45236644513597690444e-11 relative error = 5.6799893619937522108502464742839e-09 % h = 0.0001 y1[1] (analytic) = 2.5034611502881946325315080951216 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.024035611683991632258220159906 relative error = 0.96009525377394769116564406245673 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5277 y2[1] (analytic) = 1.1360324859493004045199223836383 y2[1] (numeric) = 1.1360324858835973529620535153851 absolute error = 6.57030515578688682532e-11 relative error = 5.7835539362208966534110276126954e-09 % h = 0.0001 y1[1] (analytic) = 2.5035475495571934535933054624211 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0241220109529904533200175272055 relative error = 0.96351319379801485366824203213651 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5278 y2[1] (analytic) = 1.1360828450240097659273641476272 y2[1] (numeric) = 1.1360828449571101297333301006475 absolute error = 6.68996361940340469797e-11 relative error = 5.8886230425053379246167245282834e-09 % h = 0.0001 y1[1] (analytic) = 2.503633943790716783279397872032 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0242084051865137830061099368164 relative error = 0.96693069873705972872389886369065 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5279 y2[1] (analytic) = 1.1361332127378906698953986299423 y2[1] (numeric) = 1.1361332126697770638275206189941 absolute error = 6.81136060678780109482e-11 relative error = 5.9952130000438622491849414830358e-09 % h = 0.0001 y1[1] (analytic) = 2.5037203329879006792552719790393 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0242947943836976789819840438237 relative error = 0.97034776862257021382942932387789 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=255.5MB, alloc=4.1MB, time=37.23 x[1] = 0.528 y2[1] (analytic) = 1.1361835890904394392856365218521 y2[1] (numeric) = 1.1361835890210942890316722205444 absolute error = 6.93451502539643013077e-11 relative error = 6.1033402453451978711967833781347e-09 % h = 0.0001 y1[1] (analytic) = 2.5038067171478812495498087336605 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0243811785436782492765207984449 relative error = 0.97376440348603131848593143841097 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5281 y2[1] (analytic) = 1.136233974081152310573009932392 y2[1] (numeric) = 1.1362339740105578513745758663807 absolute error = 7.05944591984340660113e-11 relative error = 6.2130213326460572497776510844048e-09 % h = 0.0001 y1[1] (analytic) = 2.5038930962697946525639223009498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0244675576655916522906343657342 relative error = 0.97718060335892516382736629162441 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5282 y2[1] (analytic) = 1.1362843677095254338508100236108 y2[1] (numeric) = 1.136284367637663709126766328548 absolute error = 7.18617247240436950628e-11 relative error = 6.3242729343271313427834977560574e-09 % h = 0.0001 y1[1] (analytic) = 2.5039794703527770970791984767818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0245539317485740968059105415662 relative error = 0.98059636827273098224938540639678 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5283 y2[1] (analytic) = 1.1363347699750548728357255096334 y2[1] (numeric) = 1.1363347699019077328005221900541 absolute error = 7.31471400352033195793e-11 relative error = 6.4371118413290359243188606444620e-09 % h = 0.0001 y1[1] (analytic) = 2.5040658393959648422665326000284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0246403007917618419932446648128 relative error = 0.98401169825892511703840560472849 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5284 y2[1] (analytic) = 1.1363851808772366048728820194899 y2[1] (numeric) = 1.1363851808027857051498658448696 absolute error = 7.44508997230161746203e-11 relative error = 6.5515549635682098821029550150120e-09 % h = 0.0001 y1[1] (analytic) = 2.5041522033984941976947669608425 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0247266647942911974214790256269 relative error = 0.98742659334898102200093124940272 % h = 0.0001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.1MB, time=37.79 NO POLE NO POLE x[1] = 0.5285 y2[1] (analytic) = 1.1364356004155665209408823236602 y2[1] (numeric) = 1.1364356003397933211705634979276 absolute error = 7.57731997703188257326e-11 relative error = 6.6676193303527654406348461141442e-09 % h = 0.0001 y1[1] (analytic) = 2.5042385623595015233393277049626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.024813023755298523066039769747 relative error = 0.99084105357436926109312376720782 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5286 y2[1] (analytic) = 1.1364860285895404256568474242835 y2[1] (numeric) = 1.1364860285124261881001251651241 absolute error = 7.71142375567222591594e-11 relative error = 6.7853220907982902560698845959666e-09 % h = 0.0001 y1[1] (analytic) = 2.5043249162781232295908612339513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0248993776739202293175732987357 relative error = 0.99425507896655750805061835418653 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5287 y2[1] (analytic) = 1.1365364653986540372814585089831 y2[1] (numeric) = 1.1365364653201798254178046733178 absolute error = 7.84742118636538356653e-11 relative error = 6.9046805142436013290503364942293e-09 % h = 0.0001 y1[1] (analytic) = 2.5044112651534957772638701012815 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0249857265492927769905821660659 relative error = 0.99766866955701054601858776344 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5288 y2[1] (analytic) = 1.1365869108424029877239997682555 y2[1] (numeric) = 1.1365869107625496648445996603301 absolute error = 7.98533228794001079254e-11 relative error = 7.0257119906664506814654868514832e-09 % h = 0.0001 y1[1] (analytic) = 2.5044976089847556776053484041843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0250720703805526773320604689687 relative error = 1.0010818253771902671820530760528 % h = 0.0001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.1MB, time=38.36 NO POLE NO POLE x[1] = 0.5289 y2[1] (analytic) = 1.1366373649202828225474020763729 y2[1] (numeric) = 1.1366373648390310503432515749451 absolute error = 8.12517722041505014278e-11 relative error = 7.1484340310991827432536704043335e-09 % h = 0.0001 y1[1] (analytic) = 2.5045839477710394923034166711719 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0251584091668364920301287359563 relative error = 1.0044945464585556723964413557087 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.529 y2[1] (analytic) = 1.1366878276317890009732875357502 y2[1] (numeric) = 1.1366878275491192381182456769097 absolute error = 8.26697628550418588405e-11 relative error = 7.2728642680443433955486040312625e-09 % h = 0.0001 y1[1] (analytic) = 2.504670281511483833495956245149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0252447429072808332226683099334 relative error = 1.0079068328325628708183900876048 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5291 y2[1] (analytic) = 1.1367382989764168958870148847243 y2[1] (numeric) = 1.1367382988923093966158110369335 absolute error = 8.41074992712038477908e-11 relative error = 7.3990204558902406162575913492418e-09 % h = 0.0001 y1[1] (analytic) = 2.5047566102052253637792431620271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0253310716010223635059552268115 relative error = 1.0113186845306650795367983023388 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5292 y2[1] (analytic) = 1.1367887789536617938427257686964 y2[1] (numeric) = 1.1367887788680966065239205366888 absolute error = 8.55651873188052320076e-11 relative error = 7.5269204713264566744018970245656e-09 % h = 0.0001 y1[1] (analytic) = 2.5048429338514007962165815247542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0254173952471977959432935895386 relative error = 1.0147301015843126232041242853993 % h = 0.0001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.1MB, time=38.92 NO POLE NO POLE x[1] = 0.5293 y2[1] (analytic) = 1.1368392675630188950683918745862 y2[1] (numeric) = 1.1368392674759758607722908688106 absolute error = 8.70430342961010057756e-11 relative error = 7.6565823137593118194667715907475e-09 % h = 0.0001 y1[1] (analytic) = 2.5049292524491468943469363726748 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0255037138449438940736484374592 relative error = 1.0181410840249529336679297730138 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5294 y2[1] (analytic) = 1.1368897648039833134708629285482 y2[1] (numeric) = 1.1368897647154420645323825368968 absolute error = 8.85412489384803916514e-11 relative error = 7.7880241057272794121369429320737e-09 % h = 0.0001 y1[1] (analytic) = 2.505015565997600472193566046133 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0255900273933974719202781109174 relative error = 1.0215516318840305496026705350589 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5295 y2[1] (analytic) = 1.136940270676050076640915556899 y2[1] (numeric) = 1.1369402705859900352173998555078 absolute error = 9.00600414235157013912e-11 relative error = 7.9212640933163524428073494584596e-09 % h = 0.0001 y1[1] (analytic) = 2.5051018744958983942726540462327 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0256763358916953939993661110171 relative error = 1.0249617451929871161417332458121 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5296 y2[1] (analytic) = 1.1369907851787141258583030102051 y2[1] (numeric) = 1.1369907850871145024822909501669 absolute error = 9.15996233760120600382e-11 relative error = 8.0563206465753613841585231330949e-09 % h = 0.0001 y1[1] (analytic) = 2.5051881779431775756019403896687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0257626393389745753286524544531 relative error = 1.0283714239832613845097185433509 % h = 0.0001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.1MB, time=39.49 NO POLE NO POLE x[1] = 0.5297 y2[1] (analytic) = 1.1370413083114703160968057504814 y2[1] (numeric) = 1.1370413082183101082237477573601 absolute error = 9.31602078730579931213e-11 relative error = 8.1932122599312433244342530445600e-09 % h = 0.0001 y1[1] (analytic) = 2.5052744763385749817093524585418 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0258489377343719814360645233262 relative error = 1.0317806682862892116549701784048 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5298 y2[1] (analytic) = 1.1370918400738134160292829014489 y2[1] (numeric) = 1.137091839979071406580206024536 absolute error = 9.47420094490768769129e-11 relative error = 8.3319575526042623277652716332378e-09 % h = 0.0001 y1[1] (analytic) = 2.5053607696812276286416353450725 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0259352310770246283683474098569 relative error = 1.0351894781335035598823501535575 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5299 y2[1] (analytic) = 1.1371423804652381080327245618024 y2[1] (numeric) = 1.1371423803688928639318453101061 absolute error = 9.63452441008792516963e-11 relative error = 8.4725752690231809681605595995945e-09 % h = 0.0001 y1[1] (analytic) = 2.5054470579702725829729816911268 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0260215193660695826996937559112 relative error = 1.0385978535563344964862597536838 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.53 y2[1] (analytic) = 1.1371929294852389881933049814358 y2[1] (numeric) = 1.1371929293872688589005889834445 absolute error = 9.79701292927159979913e-11 relative error = 8.6150842792403829836611202193022e-09 % h = 0.0001 y1[1] (analytic) = 2.5055333412048469618136610224661 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0261078026006439615403730872505 relative error = 1.042005794586209193383906368475 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=274.6MB, alloc=4.1MB, time=40.05 x[1] = 0.5301 y2[1] (analytic) = 1.1372434871333105663114366005765 y2[1] (numeric) = 1.1372434870336936823501042248881 absolute error = 9.96168839613323756884e-11 relative error = 8.7595035793469469973497439497069e-09 % h = 0.0001 y1[1] (analytic) = 2.5056196193840879328186485776383 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0261940807798849325453606424227 relative error = 1.0454133012545519267488160081421 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5302 y2[1] (analytic) = 1.1372940534089472659068249517769 y2[1] (numeric) = 1.1372940533076615373858020257365 absolute error = 1.012857285210229260404e-10 relative error = 8.9058522918876712518099363342314e-09 % h = 0.0001 y1[1] (analytic) = 2.5057058925071327141962536314202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0262803539029297139229656962046 relative error = 1.0488203735927840766445914131371 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5303 y2[1] (analytic) = 1.1373446283116434242235244247134 y2[1] (numeric) = 1.1373446282086665393548371882521 absolute error = 1.029768848686872364613e-10 relative error = 9.0541496662760493037642861846433e-09 % h = 0.0001 y1[1] (analytic) = 2.5057921605731185747167473127276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.026366621968915574443459377512 relative error = 1.0522270116323241266589156590132 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5304 y2[1] (analytic) = 1.1373952118408932922349948937413 y2[1] (numeric) = 1.1373952117362027158461083256599 absolute error = 1.046905763888865680814e-10 relative error = 9.2044150792091966255749843748510e-09 % h = 0.0001 y1[1] (analytic) = 2.5058784235811828337209899169052 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0264528849769798334477019816896 relative error = 1.0556332154045876635378011574073 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5305 y2[1] (analytic) = 1.1374458039961910346491592081562 y2[1] (numeric) = 1.1374458038897640066902578621477 absolute error = 1.064270279589013460085e-10 relative error = 9.3566680350827280604175051365653e-09 % h = 0.0001 y1[1] (analytic) = 2.5059646815304628611290577123109 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0265391429262598608557697770953 relative error = 1.0590389849409873768200839542529 % h = 0.0001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.1MB, time=40.61 NO POLE NO POLE x[1] = 0.5306 y2[1] (analytic) = 1.1374964047770307299134615451103 y2[1] (numeric) = 1.137496404668844263959672032866 absolute error = 1.081864659537895122443e-10 relative error = 9.5109281664055860779084862952170e-09 % h = 0.0001 y1[1] (analytic) = 2.5060509344200960774488692411078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0266253958158930771755813058922 relative error = 1.0624443202729330584721632263169 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5307 y2[1] (analytic) = 1.1375470141829063702199266251343 y2[1] (numeric) = 1.1375470140729372519684808839281 absolute error = 1.099691182514457412062e-10 relative error = 9.6672152342148197771059240752027e-09 % h = 0.0001 y1[1] (analytic) = 2.5061371822492199537848111141777 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0267116436450169535115231789621 relative error = 1.0658492214318316025229858771985 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5308 y2[1] (analytic) = 1.1375976322133118615102197902122 y2[1] (numeric) = 1.1375976321015366472725582724099 absolute error = 1.117752142376615178023e-10 relative error = 9.8255491284903145836291730788629e-09 % h = 0.0001 y1[1] (analytic) = 2.5062234250169720118463633000704 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0267978864127690115730753648548 relative error = 1.0692536884490870046992761339816 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5309 y2[1] (analytic) = 1.1376482588677410234807079443612 y2[1] (numeric) = 1.1376482587541360386695218663502 absolute error = 1.136049848111860780110e-10 relative error = 9.9859498685694725880031056805800e-09 % h = 0.0001 y1[1] (analytic) = 2.5063096627224898239567239079014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0268841241182868236834359726858 relative error = 1.0726577213561003620610100456964 % h = 0.0001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.1MB, time=41.18 NO POLE NO POLE x[1] = 0.531 y2[1] (analytic) = 1.1376988941456875895875213566629 y2[1] (numeric) = 1.1376988940302289271987331447504 absolute error = 1.154586623887882119125e-10 relative error = 1.0148437603561843472010717611996e-08 % h = 0.0001 y1[1] (analytic) = 2.5063958953649110130614334641129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0269703567607080127881455288973 relative error = 1.0760613201842698726371347848636 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5311 y2[1] (analytic) = 1.1377495380466452070516163266988 y2[1] (numeric) = 1.1377495379293087261412973975746 absolute error = 1.173364809103189291242e-10 relative error = 1.0313032612763705970292000445825e-08 % h = 0.0001 y1[1] (analytic) = 2.5064821229433732527369986830109 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0270565843391702524637107477953 relative error = 1.0794644849649908350615326533462 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5312 y2[1] (analytic) = 1.1378001905701074368638387123358 y2[1] (numeric) = 1.1378001904508687610200637257498 absolute error = 1.192386758437749865860e-10 relative error = 1.0479755306072599813939859300805e-08 % h = 0.0001 y1[1] (analytic) = 2.5065683454570142671995157309935 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0271428068528112669262277957779 relative error = 1.082867215729655648209229693853 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5313 y2[1] (analytic) = 1.1378508517155677537899883198135 y2[1] (numeric) = 1.1378508515944022695996250411655 absolute error = 1.211654841903632786480e-10 relative error = 1.0648626224401808103455585557176e-08 % h = 0.0001 y1[1] (analytic) = 2.5066545629049718313132929843823 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0272290243007688310400050491667 relative error = 1.086269512509653810832848808342 % h = 0.0001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.1MB, time=41.75 NO POLE NO POLE x[1] = 0.5314 y2[1] (analytic) = 1.1379015214825195463758841560826 y2[1] (numeric) = 1.1379015213594024018863180666741 absolute error = 1.231171444895660894085e-10 relative error = 1.0819666040094790058062417394064e-08 % h = 0.0001 y1[1] (analytic) = 2.5067407752863837705994732807722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0273152366821807703261853455566 relative error = 1.0896713753363719211993072847384 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5315 y2[1] (analytic) = 1.137952199870456116952430543342 y2[1] (numeric) = 1.1379521997453622201282233360907 absolute error = 1.250938968242072072513e-10 relative error = 1.0992895557339564088512806030266e-08 % h = 0.0001 y1[1] (analytic) = 2.5068269826003879612446556638129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0274014439961849609713677285973 relative error = 1.0930728042411936767267586333313 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5316 y2[1] (analytic) = 1.1380028868788706816406840957254 y2[1] (numeric) = 1.1380028867517746988151651941931 absolute error = 1.270959828255189015323e-10 relative error = 1.1168335712583041140653264825630e-08 % h = 0.0001 y1[1] (analytic) = 2.5069131848461223301095166213358 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0274876462419193298362286861202 relative error = 1.0964737992554998736217786342611 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5317 y2[1] (analytic) = 1.138053582507256370356921558087 y2[1] (numeric) = 1.1380535823781327246787117967218 absolute error = 1.291236456782097613652e-10 relative error = 1.1346007574945308257033459504800e-08 % h = 0.0001 y1[1] (analytic) = 2.5069993820227248547374308167398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0275738434185218544641428815242 relative error = 1.099874360410668406516795497531 % h = 0.0001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.1MB, time=42.31 NO POLE NO POLE x[1] = 0.5318 y2[1] (analytic) = 1.1381042867551062268177085068342 y2[1] (numeric) = 1.1381042866239290966921751103801 absolute error = 1.311771301255333964541e-10 relative error = 1.1525932346633862303710828396795e-08 % h = 0.0001 y1[1] (analytic) = 2.5070855741293335633630913135505 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0276600355251305630898033783349 relative error = 1.1032744877380742681077640370474 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5319 y2[1] (analytic) = 1.1381549996219132085449689127576 y2[1] (numeric) = 1.138154999488656526070610912834 absolute error = 1.332566824743579999236e-10 relative error = 1.1708131363357793809688458066072e-08 % h = 0.0001 y1[1] (analytic) = 2.5071717611650865349211292930662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0277462225608835346478413578506 relative error = 1.1066741812690895487920837601789 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.532 y2[1] (analytic) = 1.138205721107170186871055565808 y2[1] (numeric) = 1.1382057209718076362708187927122 absolute error = 1.353625506002367730958e-10 relative error = 1.1892626094741920866358847415121e-08 % h = 0.0001 y1[1] (analytic) = 2.5072579431291218990547332650042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0278324045249188987814453297886 relative error = 1.1100734410350834363067607743614 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5321 y2[1] (analytic) = 1.1382564512103699469438213617681 y2[1] (numeric) = 1.1382564510728749629913421496061 absolute error = 1.374949839524792121620e-10 relative error = 1.2079438144740873034226002024771e-08 % h = 0.0001 y1[1] (analytic) = 2.5073441200205778361242677710618 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0279185814163748358509798358462 relative error = 1.1134722670674222153668134123376 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=293.7MB, alloc=4.1MB, time=42.88 x[1] = 0.5322 y2[1] (analytic) = 1.1383071899310051877316914507701 y2[1] (numeric) = 1.13830718979135095417246819407 absolute error = 1.396542335592232567001e-10 relative error = 1.2268589252053125204499844519837e-08 % h = 0.0001 y1[1] (analytic) = 2.5074302918385925772158915813056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.02800475323438957694260364609 relative error = 1.1168706593974692673039214776249 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5323 y2[1] (analytic) = 1.1383579372685685220287362476072 y2[1] (numeric) = 1.1383579371267279699962279476207 absolute error = 1.418405520325082999865e-10 relative error = 1.2460101290534981363003990642132e-08 % h = 0.0001 y1[1] (analytic) = 2.5075164585823044041501753833025 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0280909199781014038768874480869 relative error = 1.120268618056585069705319011821 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5324 y2[1] (analytic) = 1.1384086932225524764597453037885 y2[1] (numeric) = 1.1384086930784982828863962427378 absolute error = 1.440541935733490610507e-10 relative error = 1.2653996269614508203825629320457e-08 % h = 0.0001 y1[1] (analytic) = 2.5076026202508516494907189639071 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0281770816466486492174310286915 relative error = 1.1236661430761271960529304854445 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5325 y2[1] (analytic) = 1.1384594577924494914853020412869 y2[1] (numeric) = 1.1384594576461540775084917228637 absolute error = 1.462954139768103184232e-10 relative error = 1.2850296334705418540387468888454e-08 % h = 0.0001 y1[1] (analytic) = 2.5076887768433726965527678836183 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0282632382391696962794799484027 relative error = 1.1270632344874503153627503139588 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5326 y2[1] (analytic) = 1.1385102309777519214068593479292 y2[1] (numeric) = 1.1385102308291874507697768424036 absolute error = 1.485644706370825055256e-10 relative error = 1.3049023767620904461512731213484e-08 % h = 0.0001 y1[1] (analytic) = 2.5077749283590059794118296434197 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0283493897548029791385417082041 relative error = 1.1304598923219061918244656007314 % h = 0.0001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.1MB, time=43.45 NO POLE NO POLE x[1] = 0.5327 y2[1] (analytic) = 1.1385610127779520343718160343771 y2[1] (numeric) = 1.1385610126270904118192578667252 absolute error = 1.508616225525581676519e-10 relative error = 1.3250200986987420180103349395908e-08 % h = 0.0001 y1[1] (analytic) = 2.5078610747968899829122893440173 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0284355361926869826390014088017 relative error = 1.1338561166108436844413220086679 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5328 y2[1] (analytic) = 1.1386118031925420123785941526494 y2[1] (numeric) = 1.138611803039354882047684872159 absolute error = 1.531871303309092804904e-10 relative error = 1.3453850548658414522127042994335e-08 % h = 0.0001 y1[1] (analytic) = 2.5079472161561632426760248373888 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0285216775519602424027369021732 relative error = 1.1372519073856087466702326623193 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5329 y2[1] (analytic) = 1.138662602221013951281717176133 y2[1] (numeric) = 1.1386626020654726950875517459984 absolute error = 1.555412561941654301346e-10 relative error = 1.3659995146128013003561497697933e-08 % h = 0.0001 y1[1] (analytic) = 2.508033352435964345111021370557 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0286078138317613448377334353414 relative error = 1.1406472646775444260621299822239 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.533 y2[1] (analytic) = 1.1387134098628598607968890410339 y2[1] (numeric) = 1.1387134097049355968130961864993 absolute error = 1.579242639837928545346e-10 relative error = 1.3868657610944649443256520086899e-08 % h = 0.0001 y1[1] (analytic) = 2.5081194836354319274199857215036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.028693945031228927146697786288 relative error = 1.1440421885179908639025603534242 % h = 0.0001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.1MB, time=44.02 NO POLE NO POLE x[1] = 0.5331 y2[1] (analytic) = 1.1387642261175716645060740492155 y2[1] (numeric) = 1.1387642259572352453402997028805 absolute error = 1.603364191657743463350e-10 relative error = 1.4079860913124647059232367895914e-08 % h = 0.0001 y1[1] (analytic) = 2.5082056097537046776089598271341 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0287800711495016773356718919185 relative error = 1.1474366789382852948525215299069 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5332 y2[1] (analytic) = 1.138815050984641199862577632375 y2[1] (numeric) = 1.1388150508218632110268876153234 absolute error = 1.627779888356900170516e-10 relative error = 1.4293628161565748996526144656303e-08 % h = 0.0001 y1[1] (analytic) = 2.5082917307899213344959339032108 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0288661921857183342226459679952 relative error = 1.1508307359697620465895426769959 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5333 y2[1] (analytic) = 1.1388658844635602181961279775064 y2[1] (numeric) = 1.1388658842983109764723290549722 absolute error = 1.652492417237989225342e-10 relative error = 1.4509982604460598234299398653540e-08 % h = 0.0001 y1[1] (analytic) = 2.5083778467432206877194590561657 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0289523081390176874461711209501 relative error = 1.1542243596437525394490069535521 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5334 y2[1] (analytic) = 1.1389167265538203847179585135981 y2[1] (numeric) = 1.1389167263860699365178369639339 absolute error = 1.677504482001215496642e-10 relative error = 1.4728947629710166820083430977645e-08 % h = 0.0001 y1[1] (analytic) = 2.5084639576127415777472593867073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0290384190085385774739714514917 relative error = 1.1576175499915852860657165359493 % h = 0.0001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.1MB, time=44.58 NO POLE NO POLE x[1] = 0.5335 y2[1] (analytic) = 1.1389675772549132785258912595174 y2[1] (numeric) = 1.138967577084631398246368095278 absolute error = 1.702818802795231642394e-10 relative error = 1.4950546765337134379404070104906e-08 % h = 0.0001 y1[1] (analytic) = 2.5085500633976228958848435851368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0291245247934198956115556499212 relative error = 1.1610103070445858910156999858894 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5336 y2[1] (analytic) = 1.1390184365663303926094210330271 y2[1] (numeric) = 1.139018436393486580982623013037 absolute error = 1.728438116267980199901e-10 relative error = 1.5174803679899215848339253776161e-08 % h = 0.0001 y1[1] (analytic) = 2.5086361640970035842841160182853 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0292106254928005840108280830697 relative error = 1.164402630834077050458261863991 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5337 y2[1] (analytic) = 1.139069304487563133854800520887 y2[1] (numeric) = 1.139069304312126616293046092206 absolute error = 1.754365175617544286810e-10 relative error = 1.5401742182902438377516326145162e-08 % h = 0.0001 y1[1] (analytic) = 2.5087222597100226359519873079882 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0292967211058196356786993727726 relative error = 1.167794521391378551778274491302 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5338 y2[1] (analytic) = 1.1391201810181028230501262099866 y2[1] (numeric) = 1.1391201808400425479858255187427 absolute error = 1.780602750643006912439e-10 relative error = 1.5631386225214367355262196010909e-08 % h = 0.0001 y1[1] (analytic) = 2.5088083502358190947589844010083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0293828116316160944856964657927 relative error = 1.1711859787478072732287117607295 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=308.9MB, alloc=4.1MB, time=45.16 x[1] = 0.5339 y2[1] (analytic) = 1.1391710661574406948904251794606 y2[1] (numeric) = 1.1391710659767253321108932895678 absolute error = 1.807153627795318898928e-10 relative error = 1.5863759899477281498239383222073e-08 % h = 0.0001 y1[1] (analytic) = 2.5088944356735320554478601303237 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0294688970693290551745721951081 relative error = 1.1745770029346771835734249005924 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.534 y2[1] (analytic) = 1.1392219599050678979827427537335 y2[1] (numeric) = 1.1392219597216658369599252125645 absolute error = 1.834020610228175411690e-10 relative error = 1.6098887440521296957590168961567e-08 % h = 0.0001 y1[1] (analytic) = 2.508980516022300663642202267693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0295549774180976633689143324774 relative error = 1.1779675939832993417301600923899 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5341 y2[1] (analytic) = 1.1392728622604754948512310164456 y2[1] (numeric) = 1.1392728620743548430663409065788 absolute error = 1.861206517848901098668e-10 relative error = 1.6336793225777440388914822213681e-08 % h = 0.0001 y1[1] (analytic) = 2.5090665912812641158550420674123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0296410526770611155817541321967 relative error = 1.1813577519249818964138178449903 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5342 y2[1] (analytic) = 1.1393237732231544619422381852069 y2[1] (numeric) = 1.1393237730342830432053038014195 absolute error = 1.888714187369343837874e-10 relative error = 1.6577501775690670934186897052101e-08 % h = 0.0001 y1[1] (analytic) = 2.5091526614495616594974623011776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.029727122845358659224174365962 relative error = 1.1847474767910300857799540274361 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5343 memory used=312.8MB, alloc=4.1MB, time=45.73 y2[1] (analytic) = 1.1393746927925956896293988471295 y2[1] (numeric) = 1.1393746926009410423937211378581 absolute error = 1.916546472356777092714e-10 relative error = 1.6821037754132851063994774550799e-08 % h = 0.0001 y1[1] (analytic) = 2.509238726526332592887204783967 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0298131879221295926139168487514 relative error = 1.1881367686127462370685224626272 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5344 y2[1] (analytic) = 1.1394256209682899822187250550871 y2[1] (numeric) = 1.1394256207738193578902439676287 absolute error = 1.944706243284810874584e-10 relative error = 1.7067425968815666228372214678820e-08 % h = 0.0001 y1[1] (analytic) = 2.5093247865107162652572773908559 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0298992479065132649839894556403 relative error = 1.1915256274214297662478589841224 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5345 y2[1] (analytic) = 1.1394765577497280579536982846503 y2[1] (numeric) = 1.1394765575524084191952671534283 absolute error = 1.973196387584311312220e-10 relative error = 1.7316691371703493264503533228616e-08 % h = 0.0001 y1[1] (analytic) = 2.5094108414018520767645605646798 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0299853027976490764912726294642 relative error = 1.1949140532483771776589068583893 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5346 y2[1] (analytic) = 1.139527503136400549020362251648 y2[1] (numeric) = 1.1395275029361985680509293689165 absolute error = 2.002019809694328827315e-10 relative error = 1.7568859059426217509892693460792e-08 % h = 0.0001 y1[1] (analytic) = 2.5094968911988794784984133144586 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.030071352594676478225125379243 relative error = 1.1983020461248820636596834748325 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5347 y2[1] (analytic) = 1.1395784571277980015524165903022 y2[1] (numeric) = 1.1395784569246800584411130987158 absolute error = 2.031179431113034915864e-10 relative error = 1.7823954273691998569169606237642e-08 % h = 0.0001 y1[1] (analytic) = 2.5095829359009379724892787044953 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0301573972967349722159907692797 relative error = 1.2016896060822351042699882059217 % h = 0.0001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.1MB, time=46.30 NO POLE NO POLE x[1] = 0.5348 y2[1] (analytic) = 1.1396294197234108756363113918874 y2[1] (numeric) = 1.1396294195173430565914446384112 absolute error = 2.060678190448667534762e-10 relative error = 1.8082002401699984683308994567491e-08 % h = 0.0001 y1[1] (analytic) = 2.5096689755071671117172888340648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0302434369029641114440008988492 relative error = 1.2050767331517240668163513398824 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5349 y2[1] (analytic) = 1.139680390922729545316342603861 y2[1] (numeric) = 1.1396803907136776409692940945506 absolute error = 2.090519043470485093104e-10 relative error = 1.8343028976552975649410599722158e-08 % h = 0.0001 y1[1] (analytic) = 2.5097550100167065001208693076055 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0303294714125034998475813723899 relative error = 1.2084634273646338055772239883227 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.535 y2[1] (analytic) = 1.1397313707252442985997482894172 y2[1] (numeric) = 1.1397313705131738022837753846445 absolute error = 2.120704963159729047727e-10 relative error = 1.8607059677670034240028452958339e-08 % h = 0.0001 y1[1] (analytic) = 2.5098410394286957926053431953273 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0304155008244927923320552601117 relative error = 1.211849688752246261428408871237 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5351 y2[1] (analytic) = 1.1397823591304453374618057474091 y2[1] (numeric) = 1.1397823589153214434857462371663 absolute error = 2.151238939760595102428e-10 relative error = 1.8874120331199046070147161818867e-08 % h = 0.0001 y1[1] (analytic) = 2.509927063742274695051534484152 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0305015251380716947782465489364 relative error = 1.2152355173458404614887318819512 % h = 0.0001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.1MB, time=46.86 NO POLE NO POLE x[1] = 0.5352 y2[1] (analytic) = 1.1398333561378227778509294925929 y2[1] (numeric) = 1.139833355919610379767808191552 absolute error = 2.182123980831213010409e-10 relative error = 1.9144236910429227860970185324148e-08 % h = 0.0001 y1[1] (analytic) = 2.5100130829565829643243710188971 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0305875443523799640510830836815 relative error = 1.2186209131766925187659543344069 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5353 y2[1] (analytic) = 1.1398843617468666496937700961386 y2[1] (numeric) = 1.1398843615255303385643065982003 absolute error = 2.213363111294634979383e-10 relative error = 1.9417435536203584048698844181301e-08 % h = 0.0001 y1[1] (analytic) = 2.51009909707076040828148693362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0306735584665574080081989984044 relative error = 1.2220058762760756318029257954497 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5354 y2[1] (analytic) = 1.1399353759570668969003138863597 y2[1] (numeric) = 1.1399353757325709595513306184727 absolute error = 2.244959373489832678870e-10 relative error = 1.9693742477331311687354751433204e-08 % h = 0.0001 y1[1] (analytic) = 2.5101851060839468857818245730341 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0307595674797438855085366378185 relative error = 1.2253904066752600843239774045999 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5355 y2[1] (analytic) = 1.1399863987679133773689835096089 y2[1] (numeric) = 1.1399863985402217946467132246934 absolute error = 2.276915827222702849155e-10 relative error = 1.9973184151000153594238602959040e-08 % h = 0.0001 y1[1] (analytic) = 2.5102711099952823066942359039123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0308455713910793064209479686967 relative error = 1.2287745044055132448815555839711 % h = 0.0001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.1MB, time=47.43 NO POLE NO POLE x[1] = 0.5356 y2[1] (analytic) = 1.1400374301788958629917393512899 y2[1] (numeric) = 1.1400374299479723080100312001494 absolute error = 2.309235549817081511405e-10 relative error = 2.0255787123188699686877996803525e-08 % h = 0.0001 y1[1] (analytic) = 2.5103571088039066319060834163915 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0309315701997036316327954811759 relative error = 1.2321581694980995665030960409583 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5357 y2[1] (analytic) = 1.140088470189504039659181816933 y2[1] (numeric) = 1.1400884699553118760426051390903 absolute error = 2.341921636165766778427e-10 relative error = 2.0541578109078636460225741114250e-08 % h = 0.0001 y1[1] (analytic) = 2.5104431025089598733318405150914 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0310175639047568730585525798758 relative error = 1.2355414019842805863381379663349 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5358 y2[1] (analytic) = 1.1401395187992275072656544732855 y2[1] (numeric) = 1.1401395185617297873874994467286 absolute error = 2.374977198781550265569e-10 relative error = 2.0830583973466944553085933772738e-08 % h = 0.0001 y1[1] (analytic) = 2.5105290911095820939216913999629 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0311035525053790936484034647473 relative error = 1.2389242018953149253056783305078 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5359 y2[1] (analytic) = 1.1401905760075557797143480493636 y2[1] (numeric) = 1.1401905757667152429295223392393 absolute error = 2.408405367848257101243e-10 relative error = 2.1122831731178044352583718989638e-08 % h = 0.0001 y1[1] (analytic) = 2.5106150746049134076701304367793 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0311895360007104073968425015637 relative error = 1.242306569262458287741766180626 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=328.0MB, alloc=4.1MB, time=47.99 x[1] = 0.536 y2[1] (analytic) = 1.1402416418139782849224052974161 y2[1] (numeric) = 1.1402416415697573557952258437603 absolute error = 2.442209291271794536558e-10 relative error = 2.1418348547475889585613971364893e-08 % h = 0.0001 y1[1] (analytic) = 2.5107010529940939796245610171836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.031275514389890979351273081968 relative error = 1.2456885041169634610473368412739 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5361 y2[1] (analytic) = 1.1402927162179843648260267137493 y2[1] (numeric) = 1.1402927159703451513529057983922 absolute error = 2.476392134731209153571e-10 relative error = 2.1717161738476008846419937264213e-08 % h = 0.0001 y1[1] (analytic) = 2.5107870262762640258938939082078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0313614876720610256206059729922 relative error = 1.2490700064900803153362859216102 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5362 y2[1] (analytic) = 1.1403437992190632753855771193601 y2[1] (numeric) = 1.1403437989679675672126018521983 absolute error = 2.510957081729752671618e-10 relative error = 2.2019298771557495009089798629971e-08 % h = 0.0001 y1[1] (analytic) = 2.5108729944505638136571450911764 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0314474558463608133838571559608 relative error = 1.2524510764130558030837830317025 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5363 y2[1] (analytic) = 1.1403948908167041865906931003287 y2[1] (numeric) = 1.1403948905621134532260974652047 absolute error = 2.545907333645956351240e-10 relative error = 2.2324787265774942474264342015036e-08 % h = 0.0001 y1[1] (analytic) = 2.5109589575161336611720330899091 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0315334189119306608987451546935 relative error = 1.2558317139171339587748251109423 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5364 y2[1] (analytic) = 1.1404459910103961824653913079173 y2[1] (numeric) = 1.1404459907522715714869199084001 absolute error = 2.581246109784713995172e-10 relative error = 2.2633654992270332198977095385710e-08 % h = 0.0001 y1[1] (analytic) = 2.5110449154721139377835757881367 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0316193768679109375102878529211 relative error = 1.2592119190335558985530292714205 % h = 0.0001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.1MB, time=48.55 NO POLE NO POLE x[1] = 0.5365 y2[1] (analytic) = 1.1404970997996282610731776183262 y2[1] (numeric) = 1.140497099537930596330340263736 absolute error = 2.616976647428373545902e-10 relative error = 2.2945929874684864458930697737071e-08 % h = 0.0001 y1[1] (analytic) = 2.5111308683176450639326867360432 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0317053297134420636593988008276 relative error = 1.2625916917935598198696650591326 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5366 y2[1] (analytic) = 1.1405482171838893345221571520545 y2[1] (numeric) = 1.1405482169185791143333734241266 absolute error = 2.653102201887837279279e-10 relative error = 2.3261639989570739292308093728385e-08 % h = 0.0001 y1[1] (analytic) = 2.51121681605186751116477094585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0317912774476645108914830106344 relative error = 1.2659710322283810011329260360259 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5367 y2[1] (analytic) = 1.1405993431626682289701451528144 y2[1] (numeric) = 1.1405993428937056243147780934489 absolute error = 2.689626046553670593655e-10 relative error = 2.3580813566802884574310159987313e-08 % h = 0.0001 y1[1] (analytic) = 2.5113027586739218021383201763547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0318772200697188018650322411391 relative error = 1.2693499403692518013574405857996 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5368 y2[1] (analytic) = 1.1406504777354536846297787259488 y2[1] (numeric) = 1.1406504774627985373350567865425 absolute error = 2.726551472947219394063e-10 relative error = 2.3903478989990631671800798508259e-08 % h = 0.0001 y1[1] (analytic) = 2.5113886961829485106335077063386 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.031963157578745510360219771123 relative error = 1.27272841624740165981402184646 % h = 0.0001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.1MB, time=49.11 NO POLE NO POLE x[1] = 0.5369 y2[1] (analytic) = 1.1407016209017343557736294363014 y2[1] (numeric) = 1.1407016206253461766964558292099 absolute error = 2.763881790771736070915e-10 relative error = 2.4229664796889338627323071837072e-08 % h = 0.0001 y1[1] (analytic) = 2.511474628578088261560782596758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0320490899738852612874946615424 relative error = 1.2761064598940570956796566727031 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.537 y2[1] (analytic) = 1.1407527726609988107393167654858 y2[1] (numeric) = 1.1407527723808367779429653582162 absolute error = 2.801620327963514072696e-10 relative error = 2.4559399679811960821720218392355e-08 % h = 0.0001 y1[1] (analytic) = 2.511560555858481730969463441633 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0321350172542787306961755064174 relative error = 1.2794840713404417076877335311725 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5371 y2[1] (analytic) = 1.1408039330127355319346224285054 y2[1] (numeric) = 1.1408039327287584888603193212893 absolute error = 2.839770430743031072161e-10 relative error = 2.4892712486040569064907541714818e-08 % h = 0.0001 y1[1] (analytic) = 2.5116464780232696460563316075464 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0322209394190666457830436723308 relative error = 1.2828612506177761737785092316255 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5372 y2[1] (analytic) = 1.1408551019564329158426055496716 y2[1] (numeric) = 1.1408551016685993694759954771198 absolute error = 2.878335463666100725518e-10 relative error = 2.5229632218237815064171117951361e-08 % h = 0.0001 y1[1] (analytic) = 2.5117323950715927851742239616691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0323068564673897849009360264535 relative error = 1.2862379977572782507498143972222 % h = 0.0001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.1MB, time=49.69 NO POLE NO POLE x[1] = 0.5373 y2[1] (analytic) = 1.1409062794915792730267186977685 y2[1] (numeric) = 1.140906279199847392059215395361 absolute error = 2.917318809675033024075e-10 relative error = 2.5570188034858344219365834837932e-08 % h = 0.0001 y1[1] (analytic) = 2.5118183070025919778406250882247 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0323927683983889775673371530091 relative error = 1.2896143127901627739079975770352 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5374 y2[1] (analytic) = 1.1409574656176628281359247804144 y2[1] (numeric) = 1.1409574653219904411209444566289 absolute error = 2.956723870149803237855e-10 relative error = 2.5914409250560155694653562972717e-08 % h = 0.0001 y1[1] (analytic) = 2.5119042138154081047462589933073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0324786752112051044729710580917 relative error = 1.2929901957476416567191079039599 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5375 y2[1] (analytic) = 1.1410086603341717199098147975678 y2[1] (numeric) = 1.1410086600345163134138918525024 absolute error = 2.996554064959229450654e-10 relative error = 2.6262325336615909716208425269614e-08 % h = 0.0001 y1[1] (analytic) = 2.511990115509182097763680297967 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0325645769049790974903923627514 relative error = 1.296365646660923890460316201253 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5376 y2[1] (analytic) = 1.1410598636405940011837264541273 y2[1] (numeric) = 1.1410598633369127179325105855229 absolute error = 3.036812832512158686044e-10 relative error = 2.6613965921324182045593169213394e-08 % h = 0.0001 y1[1] (analytic) = 2.5120760120830549399558649194776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.032650473478851939682576984262 relative error = 1.2997406655612155438715744409606 % h = 0.0001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.1MB, time=50.24 NO POLE NO POLE x[1] = 0.5377 y2[1] (analytic) = 1.1411110755364176388938636315738 y2[1] (numeric) = 1.1411110752286672759129974691947 absolute error = 3.077503629808661623791e-10 relative error = 2.6969360790420665578270548961911e-08 % h = 0.0001 y1[1] (analytic) = 2.5121619035361676655848002406993 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0327363649319646653115123054837 relative error = 1.3031152524797197628075134574565 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5378 y2[1] (analytic) = 1.1411622960211305140824167186042 y2[1] (numeric) = 1.1411622957092675208332931279847 absolute error = 3.118629932491235906195e-10 relative error = 2.7328539887489319017078285889922e-08 % h = 0.0001 y1[1] (analytic) = 2.5122477898676613601200747674517 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0328222512634583598467868322361 relative error = 1.3064894074476367698895788194419 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5379 y2[1] (analytic) = 1.1412135250942204219026838007055 y2[1] (numeric) = 1.1412135247782008984130819973226 absolute error = 3.160195234896018033829e-10 relative error = 2.7691533314373462570273611562586e-08 % h = 0.0001 y1[1] (analytic) = 2.5123336710766771602474672738109 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0329081324724741599741793385953 relative error = 1.3098631304961638641584047637287 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.538 y2[1] (analytic) = 1.1412647627551750716241927086173 y2[1] (numeric) = 1.1412647624349547666137923236009 absolute error = 3.202203050104003850164e-10 relative error = 2.8058371331586820623881426203049e-08 % h = 0.0001 y1[1] (analytic) = 2.5124195471623562538775354352446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.032994008558153253604247500029 relative error = 1.3132364216564954207264260941613 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=347.1MB, alloc=4.1MB, time=50.79 x[1] = 0.5381 y2[1] (analytic) = 1.1413160090034820866378239256324 y2[1] (numeric) = 1.1413160086790163956385961641747 absolute error = 3.244656909992277614577e-10 relative error = 2.8429084358724511338208098519186e-08 % h = 0.0001 y1[1] (analytic) = 2.5125054181238398801542039494992 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0330798795196368798809160142836 relative error = 1.3166092809598228904307279490677 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5382 y2[1] (analytic) = 1.1413672638386290044609343536835 y2[1] (numeric) = 1.1413672635098729679324093873619 absolute error = 3.287560365285249663216e-10 relative error = 2.8803702974873983118221762330008e-08 % h = 0.0001 y1[1] (analytic) = 2.5125912839602693294633521451535 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0331657453560663291900642099379 relative error = 1.3199817084373347994861333406812 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5383 y2[1] (analytic) = 1.1414185272601032767424819381656 y2[1] (numeric) = 1.141418526927011578181891672443 absolute error = 3.330916985605902657226e-10 relative error = 2.9182257919025897907803210036359e-08 % h = 0.0001 y1[1] (analytic) = 2.5126771446707859434414010777526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.033251606066582943168113142537 relative error = 1.3233537041202167491385283699696 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5384 y2[1] (analytic) = 1.141469799267392269268151151442 y2[1] (numeric) = 1.1414697989299192333154465096615 absolute error = 3.374730359527046417805e-10 relative error = 2.9564780090484961257605179158629e-08 % h = 0.0001 y1[1] (analytic) = 2.5127630002545311149839001134369 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0333374616503281147106121782213 relative error = 1.3267252680396514153184250203833 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5385 y2[1] (analytic) = 1.1415210798599832619654793349833 y2[1] (numeric) = 1.1415210795180828525032212002233 absolute error = 3.419004094622581347600e-10 relative error = 2.9951300549280699116657425677807e-08 % h = 0.0001 y1[1] (analytic) = 2.5128488507106462882541129999789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0334233121064432879808250647633 relative error = 1.3300964002268185482947614339844 % h = 0.0001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.1MB, time=51.35 NO POLE NO POLE x[1] = 0.5386 y2[1] (analytic) = 1.1415723690373634489089839000877 y2[1] (numeric) = 1.1415723686909892671571068562973 absolute error = 3.463741817518770437904e-10 relative error = 3.0341850516578181297466042966848e-08 % h = 0.0001 y1[1] (analytic) = 2.5129346960382729586916034251438 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0335091574340699584183154899282 relative error = 1.3334671007128949723289395735718 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5387 y2[1] (analytic) = 1.1416236667990199383252903871314 y2[1] (numeric) = 1.141623666448125220930738401015 absolute error = 3.508947173945519861164e-10 relative error = 3.0736461375088691564825149220076e-08 % h = 0.0001 y1[1] (analytic) = 2.5130205362365526730208200622869 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0335949976323496727475321270713 relative error = 1.3368373695290545853291001743356 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5388 y2[1] (analytic) = 1.1416749731444397525982613832985 y2[1] (numeric) = 1.1416749727889773697194945684707 absolute error = 3.554623828787668148278e-10 relative error = 3.1135164669480344298319071952089e-08 % h = 0.0001 y1[1] (analytic) = 2.5131063713046270292596811031014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0336808327004240289863931678858 relative error = 1.3402072067064683585046348886218 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5389 y2[1] (analytic) = 1.1417262880731098282741262987375 y2[1] (numeric) = 1.1417262877130322816604979037213 absolute error = 3.600775466136283950162e-10 relative error = 3.1537992106788647678559829472913e-08 % h = 0.0001 y1[1] (analytic) = 2.5131922012416376767281582774322 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0337666626374346764548703422166 relative error = 1.343576612276304336020935527502 % h = 0.0001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.1MB, time=51.92 NO POLE NO POLE x[1] = 0.539 y2[1] (analytic) = 1.1417776115845170160666120010952 y2[1] (numeric) = 1.1417776112197764371326147627865 absolute error = 3.647405789339972383087e-10 relative error = 3.1944975556827013347411501295589e-08 % h = 0.0001 y1[1] (analytic) = 2.5132780260467263160568603600697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0338524874425233157835724248541 relative error = 1.346945586269727634654380302806 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5391 y2[1] (analytic) = 1.1418289436781480808620743083752 y2[1] (numeric) = 1.1418289433086962287564553126488 absolute error = 3.694518521056189957264e-10 relative error = 3.2356147052597212492300730060352e-08 % h = 0.0001 y1[1] (analytic) = 2.5133638457190346991956161644354 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0339383071148316989223282292198 relative error = 1.3503141287179004434475569732209 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5392 y2[1] (analytic) = 1.1418802843534897017246303400693 y2[1] (numeric) = 1.1418802839792779613943735312533 absolute error = 3.742117403302568088160e-10 relative error = 3.2771538790699778304796777179290e-08 % h = 0.0001 y1[1] (analytic) = 2.5134496602577046294220570230776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.034024121653501629148769087862 relative error = 1.3536822396519820233647227983446 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5393 y2[1] (analytic) = 1.1419316336100284719012917265133 y2[1] (numeric) = 1.1419316332310078521504672075079 absolute error = 3.790206197508245190054e-10 relative error = 3.3191183131744354763912614154424e-08 % h = 0.0001 y1[1] (analytic) = 2.5135354696618779613501987548872 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0341099310576749610769108196716 relative error = 1.3570499191031287069475012042869 % h = 0.0001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.1MB, time=52.50 NO POLE NO POLE x[1] = 0.5394 y2[1] (analytic) = 1.1419829914472508988270986764115 y2[1] (numeric) = 1.1419829910633720303705779412833 absolute error = 3.838788684565207351282e-10 relative error = 3.3615112600759991694093422003369e-08 % h = 0.0001 y1[1] (analytic) = 2.5136212739306966009390231189507 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0341957353264936006657351837351 relative error = 1.3604171671024938979708150647169 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5395 y2[1] (analytic) = 1.1420343578646434041302549024824 y2[1] (numeric) = 1.1420343574758565376422911434127 absolute error = 3.887868664879637590697e-10 relative error = 3.4043359887605386048573586894194e-08 % h = 0.0001 y1[1] (analytic) = 2.5137070730633025055010587549529 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0342815344590995052277708197373 relative error = 1.3637839836812280710990565011093 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5396 y2[1] (analytic) = 1.1420857328616923236372634051728 y2[1] (numeric) = 1.1420857324679473277949360356923 absolute error = 3.937449958423273694805e-10 relative error = 3.4475957847379069368254382465288e-08 % h = 0.0001 y1[1] (analytic) = 2.5137928670588376837109616100452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0343673284546346834376736748296 relative error = 1.3671503688704787715424931061019 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5397 y2[1] (analytic) = 1.1421371164378839073780631143877 y2[1] (numeric) = 1.1421371160391302668995856508809 absolute error = 3.987536404784774635068e-10 relative error = 3.4912939500829541366557634963752e-08 % h = 0.0001 y1[1] (analytic) = 2.5138786559164441956140948520909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0344531173122411953408069168753 relative error = 1.3705163227013906147139104937308 % h = 0.0001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.1MB, time=53.08 NO POLE NO POLE x[1] = 0.5398 y2[1] (analytic) = 1.1421885085927043195911663891873 y2[1] (numeric) = 1.1421885081888911332690568327 absolute error = 4.038131863221095564873e-10 relative error = 3.5354338034765349590821052795828e-08 % h = 0.0001 y1[1] (analytic) = 2.5139644396352641526351082692053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0345389010310611523618203339897 relative error = 1.3738818452051052858854910805922 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5399 y2[1] (analytic) = 1.1422399093256396387287973753972 y2[1] (numeric) = 1.1422399089167156174579102358338 absolute error = 4.089240212708871395634e-10 relative error = 3.5800186802465115110561068854584e-08 % h = 0.0001 y1[1] (analytic) = 2.5140502182144397175865171555015 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0346246796102367173132292202859 relative error = 1.3772469364127615398459290017368 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.54 y2[1] (analytic) = 1.1422913186361758574620312210822 y2[1] (numeric) = 1.1422913182220893222624503259294 absolute error = 4.140865351995808951528e-10 relative error = 3.6250519324087504183267109078253e-08 % h = 0.0001 y1[1] (analytic) = 2.5141359916531131046772806829582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0347104530489101044039927477426 relative error = 1.3806115963554952005577810653469 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5401 y2[1] (analytic) = 1.1423427365237988826859341498308 y2[1] (numeric) = 1.1423427361044977627207253795964 absolute error = 4.193011199652087702344e-10 relative error = 3.6705369287081145848238923353432e-08 % h = 0.0001 y1[1] (analytic) = 2.5142217599504265795213797593233 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0347962213462235792480918241077 relative error = 1.3839758250644391608150536501747 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=366.2MB, alloc=4.1MB, time=53.63 x[1] = 0.5402 y2[1] (analytic) = 1.1423941629879945355247043918009 y2[1] (numeric) = 1.1423941625634263661125274844073 absolute error = 4.245681694121769073936e-10 relative error = 3.7164770546594495399124034878000e-08 % h = 0.0001 y1[1] (analytic) = 2.5143075231055224591463943719664 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0348819845013194588731064367508 relative error = 1.3873396225707233819010254497268 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5403 y2[1] (analytic) = 1.1424455980282485513368139724727 y2[1] (numeric) = 1.1424455975983604719593925388973 absolute error = 4.298880793774214335754e-10 relative error = 3.7628757125885643685703898880441e-08 % h = 0.0001 y1[1] (analytic) = 2.5143932811175431120020804175962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0349677425133401117287924823806 relative error = 1.3907029889054748932463059673205 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5404 y2[1] (analytic) = 1.1424970416440465797201513590606 y2[1] (numeric) = 1.1424970412087853320246002525643 absolute error = 4.352612476955511064963e-10 relative error = 3.8097363216732072195832851566692e-08 % h = 0.0001 y1[1] (analytic) = 2.514479033985630957968946017756 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0350534953814279576956580825404 relative error = 1.3940659240998177920871296660574 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5405 y2[1] (analytic) = 1.1425484938348741845171649645292 y2[1] (numeric) = 1.1425484933941861103131741458689 absolute error = 4.406880742039908186603e-10 relative error = 3.8570623179840353867975321328905e-08 % h = 0.0001 y1[1] (analytic) = 2.5145647817089284683668273200107 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0351392431047254680935393847951 relative error = 1.3974284281848732431238856778016 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5406 y2[1] (analytic) = 1.1425999546002168438200075091654 y2[1] (numeric) = 1.1425999541540478830718815502345 absolute error = 4.461689607481259589309e-10 relative error = 3.9048571545255799585404858554821e-08 % h = 0.0001 y1[1] (analytic) = 2.5146505242865781659634637847422 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0352249856823751656901758495266 relative error = 1.4007905011917594781798829754097 % h = 0.0001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.1MB, time=54.20 NO POLE NO POLE x[1] = 0.5407 y2[1] (analytic) = 1.1426514239395599499756812396516 y2[1] (numeric) = 1.1426514234878556387892336080472 absolute error = 4.517043111864476316044e-10 relative error = 3.9531243012772050302591181283990e-08 % h = 0.0001 y1[1] (analytic) = 2.5147362617177226249830729574643 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0353107231135196247097850222487 relative error = 1.4041521431515917958603509122702 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5408 y2[1] (analytic) = 1.1427029018523888095911840055921 y2[1] (numeric) = 1.1427029013950942781954852726558 absolute error = 4.572945313956987329363e-10 relative error = 4.0018672452340614754910712393370e-08 % h = 0.0001 y1[1] (analytic) = 2.5148219940015044711149247265736 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.035396455397301470841636791358 relative error = 1.4075133540954825612116750334447 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5409 y2[1] (analytic) = 1.1427543883381886435386561934388 y2[1] (numeric) = 1.1427543878752486142626353083718 absolute error = 4.629400292760208850670e-10 relative error = 4.0510894904480352702366285254097e-08 % h = 0.0001 y1[1] (analytic) = 2.5149077211370663815219150664494 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0354821825328633812486271312338 relative error = 1.4108741340545412053808680626005 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.541 y2[1] (analytic) = 1.1428058833964445869605285177651 y2[1] (numeric) = 1.1428058829278033722044262904695 absolute error = 4.686412147561022272956e-10 relative error = 4.1007945580686903658269625567168e-08 % h = 0.0001 y1[1] (analytic) = 2.514993443123551084849139265818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0355679045193480845758513306024 relative error = 1.414234483059874225275275969045 % h = 0.0001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.1MB, time=54.77 NO POLE NO POLE x[1] = 0.5411 y2[1] (analytic) = 1.1428573870266416892746706698375 y2[1] (numeric) = 1.1428573865522431894763446051859 absolute error = 4.743984997983260646516e-10 relative error = 4.1509859863842061053968054240366e-08 % h = 0.0001 y1[1] (analytic) = 2.5150791599601013612324646412942 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0356536213558983609591767060786 relative error = 1.4175944011425851832225190191031 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5412 y2[1] (analytic) = 1.1429088992282649141795408234329 y2[1] (numeric) = 1.1429088987480526157756204497207 absolute error = 4.802122984039203737122e-10 relative error = 4.2016673308623091790553418702774e-08 % h = 0.0001 y1[1] (analytic) = 2.5151648716458600423071027360159 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0357393330416570420338148008003 relative error = 1.4209538883337747066306677162267 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5413 y2[1] (analytic) = 1.1429604200007991396593359978492 y2[1] (numeric) = 1.1429604195147161130412278322364 absolute error = 4.860830266181081656128e-10 relative error = 4.2528421641912001128522879878123e-08 % h = 0.0001 y1[1] (analytic) = 2.5152505781799700112161810032844 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0358250395757670109428930680688 relative error = 1.4243129446645404876486535341289 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5414 y2[1] (analytic) = 1.1430119493437291579891432780595 y2[1] (numeric) = 1.1430119488517180554538845718582 absolute error = 4.920111025352587062013e-10 relative error = 4.3045140763204742866664017242912e-08 % h = 0.0001 y1[1] (analytic) = 2.5153362795615742026193139751262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0359107409573712023460260399106 relative error = 1.4276715701659772828269143473886 % h = 0.0001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.1MB, time=55.33 NO POLE NO POLE x[1] = 0.5415 y2[1] (analytic) = 1.1430634872565396757400918919566 y2[1] (numeric) = 1.143063486758542729436052298674 absolute error = 4.979969463040395932826e-10 relative error = 4.3566866745020374761109555373685e-08 % h = 0.0001 y1[1] (analytic) = 2.5154219757898156027011739156898 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0359964371856126024278859804742 relative error = 1.4310297648691769127782744639128 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5416 y2[1] (analytic) = 1.1431150337387153137845061446377 y2[1] (numeric) = 1.1431150332346743336519364537344 absolute error = 5.040409801325696909033e-10 relative error = 4.4093635833310159135862350011823e-08 % h = 0.0001 y1[1] (analytic) = 2.5155076668638372491800609593918 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0360821282596342489067730241762 relative error = 1.4343875288052282618390591637019 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5417 y2[1] (analytic) = 1.1431665887897406073010592096766 y2[1] (numeric) = 1.1431665882795969790074862890529 absolute error = 5.101436282935729206237e-10 relative error = 4.4625484447866608635877880959866e-08 % h = 0.0001 y1[1] (analytic) = 2.5155933527827822313164727337265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0361678141785792310431847985109 relative error = 1.4377448620052172777304436483931 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5418 y2[1] (analytic) = 1.1432181524091000057799277773328 y2[1] (numeric) = 1.1432181518927946886503948676055 absolute error = 5.163053171295329097273e-10 relative error = 4.5162449182732477074103044075290e-08 % h = 0.0001 y1[1] (analytic) = 2.5156790335457936899216734666541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0362534949415906896483855314385 relative error = 1.441101764500226971220036306119 % h = 0.0001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.1MB, time=55.89 NO POLE NO POLE x[1] = 0.5419 y2[1] (analytic) = 1.1432697245962778730279475596455 y2[1] (numeric) = 1.143269724073751397970099063331 absolute error = 5.225264750578484963145e-10 relative error = 4.5704566806609695323604176388007e-08 % h = 0.0001 y1[1] (analytic) = 2.5157647091520148173662625784809 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0363391705478118170929746432653 relative error = 1.4444582363213374157836961961817 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.542 y2[1] (analytic) = 1.1433213053507584871737696523608 y2[1] (numeric) = 1.143321304821950954597779561131 absolute error = 5.288075325759900912298e-10 relative error = 4.6251874263268252206185046179351e-08 % h = 0.0001 y1[1] (analytic) = 2.5158503796005888575887427581458 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0364248409963858573154548229302 relative error = 1.4478142774996257472675846581109 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5421 y2[1] (analytic) = 1.1433728946720260406730177536412 y2[1] (numeric) = 1.1433728941368771184063608568698 absolute error = 5.351489222666568967714e-10 relative error = 4.6804408671955020328900862193560e-08 % h = 0.0001 y1[1] (analytic) = 2.5159360448906591061040875238285 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0365105062864561058307995886129 relative error = 1.4511698880661661635504509497426 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5422 y2[1] (analytic) = 1.1434244925595646403134462395044 y2[1] (numeric) = 1.1434244920180135615105112573744 absolute error = 5.415510788029349821300e-10 relative error = 4.7362207327802526819731014916462e-08 % h = 0.0001 y1[1] (analytic) = 2.5160217050213689100123082677928 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0365961664171659097390203325772 relative error = 1.4545250680520299242061518189102 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=385.2MB, alloc=4.1MB, time=56.45 x[1] = 0.5423 y2[1] (analytic) = 1.1434760990128583072200990959422 y2[1] (numeric) = 1.1434760984648438682666428804345 absolute error = 5.480144389534562155077e-10 relative error = 4.7925307702237668914072200968780e-08 % h = 0.0001 y1[1] (analytic) = 2.5161073599918616680070207853786 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.036681821387658667733732850163 relative error = 1.4578798174882853501664049133754 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5424 y2[1] (analytic) = 1.1435277140313909768604697076654 y2[1] (numeric) = 1.1435277134768515352729116548026 absolute error = 5.545394415875580528628e-10 relative error = 4.8493747443390374343307844582894e-08 % h = 0.0001 y1[1] (analytic) = 2.5161930098012808303840112880594 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0367674711970778301107233528438 relative error = 1.4612341364059978233837759337814 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5425 y2[1] (analytic) = 1.1435793376146464990496615034246 y2[1] (numeric) = 1.1435793370535199713692173201939 absolute error = 5.611265276804441832307e-10 relative error = 4.9067564376502206477134897643515e-08 % h = 0.0001 y1[1] (analytic) = 2.516278654448769899049801900477 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0368531158445668987765139652614 relative error = 1.4645880248362297864948994342425 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5426 y2[1] (analytic) = 1.1436309697621086379555494578549 y2[1] (numeric) = 1.1436309691943324976372034272864 absolute error = 5.677761403183460305685e-10 relative error = 4.9646796504334914171142023774252e-08 % h = 0.0001 y1[1] (analytic) = 2.5163642939334724275302156413688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0369387553292694272569277061532 relative error = 1.4679414828100407424839331753563 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5427 y2[1] (analytic) = 1.1436826104732610721039424497927 y2[1] (numeric) = 1.1436826098987723474002573377207 absolute error = 5.744887247036851120720e-10 relative error = 5.0231482007578926271269702991868e-08 % h = 0.0001 y1[1] (analytic) = 2.5164499282545320209789408883031 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0370243896503290207056529530875 relative error = 1.4712945103584872543462459344556 % h = 0.0001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.1MB, time=57.03 NO POLE NO POLE x[1] = 0.5428 y2[1] (analytic) = 1.1437342597475873943837464770136 y2[1] (numeric) = 1.1437342591663226662235102241002 absolute error = 5.812647281602362529134e-10 relative error = 5.0821659245261790726788134385535e-08 % h = 0.0001 y1[1] (analytic) = 2.5165355574110923361860953261344 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0371100188068893359128073909188 relative error = 1.4746471075126229447523386778154 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5429 y2[1] (analytic) = 1.1437859175845711120521287273387 y2[1] (numeric) = 1.1437859169964665119138370699909 absolute error = 5.881046001382916573478e-10 relative error = 5.1417366755156558263451653522840e-08 % h = 0.0001 y1[1] (analytic) = 2.5166211814022970815867893790958 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0371956427980940813135014438802 relative error = 1.4779992743034984957119989997551 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.543 y2[1] (analytic) = 1.1438375839836956467396825060591 y2[1] (numeric) = 1.1438375833886868545198566699218 absolute error = 5.950087922198258361373e-10 relative error = 5.2018643254190110568589908427030e-08 % h = 0.0001 y1[1] (analytic) = 2.51670680022729001726968912644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0372812616230870169964011912244 relative error = 1.4813510107621616482386887333922 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5431 y2[1] (analytic) = 1.143889258944444334455593019625 y2[1] (numeric) = 1.1438892583424665763319316293844 absolute error = 6.019777581236613902406e-10 relative error = 5.2625527638851432939857664828099e-08 % h = 0.0001 y1[1] (analytic) = 2.5167924138852149549855787015462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0373668752810119547122907663306 relative error = 1.4847023169196572020141646380555 % h = 0.0001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.1MB, time=57.60 NO POLE NO POLE x[1] = 0.5432 y2[1] (analytic) = 1.14394094246630042559280401555 y2[1] (numeric) = 1.143940941857288471882168364833 absolute error = 6.090119537106356507170e-10 relative error = 5.3238058985599831349492860982898e-08 % h = 0.0001 y1[1] (analytic) = 2.5168780223752157581559221744044 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0374524837710127578826342391888 relative error = 1.4880531928070270150533320681714 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5433 y2[1] (analytic) = 1.1439926345487470849331852784775 y2[1] (numeric) = 1.1439926339326352479444171036846 absolute error = 6.161118369887681747929e-10 relative error = 5.3856276551273093875902900976790e-08 % h = 0.0001 y1[1] (analytic) = 2.5169636256964363418814249173945 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0375380870922333416081369821789 relative error = 1.4914036384553100033693315286968 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5434 y2[1] (analytic) = 1.1440443351912673916527009823571 y2[1] (numeric) = 1.144044334567989523534271884319 absolute error = 6.232778681184290980381e-10 relative error = 5.4480219773495596454369570695870e-08 % h = 0.0001 y1[1] (analytic) = 2.5170492238480206729505944542712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0376236852438176726773065190556 relative error = 1.4947536538955421406388580219499 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5435 y2[1] (analytic) = 1.1440960443933443393265788986813 y2[1] (numeric) = 1.1440960437628338299090705560786 absolute error = 6.305105094175083426027e-10 relative error = 5.5109928271086352899009225160682e-08 % h = 0.0001 y1[1] (analytic) = 2.5171348168291127698483007922726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.037709278224909769575012857057 relative error = 1.4981032391587564578677130909925 % h = 0.0001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.1MB, time=58.17 NO POLE NO POLE x[1] = 0.5436 y2[1] (analytic) = 1.1441477621544608359344804607284 y2[1] (numeric) = 1.1441477615166506105678947792687 absolute error = 6.378102253665856814597e-10 relative error = 5.5745441844467009147666942216833e-08 % h = 0.0001 y1[1] (analytic) = 2.5172204046388567027643362372638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0377948660346537024910483020482 relative error = 1.5014523942759830430565894644851 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5437 y2[1] (analytic) = 1.1441994884740997038656716837619 y2[1] (numeric) = 1.1441994878289222212515700251572 absolute error = 6.451774826141016586047e-10 relative error = 5.6386800476069781682014352891597e-08 % h = 0.0001 y1[1] (analytic) = 2.5173059872763965936019746918321 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0378804486721935933286867566165 relative error = 1.5048011192782490408670882081776 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5438 y2[1] (analytic) = 1.1442512233517436799241949411334 y2[1] (numeric) = 1.1442512226991309299426655759748 absolute error = 6.526127499815293651586e-10 relative error = 5.7034044330745340074680406111458e-08 % h = 0.0001 y1[1] (analytic) = 2.5173915647408766159865304362469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0379660261366736157132425010313 relative error = 1.5081494141965786522879682880866 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5439 y2[1] (analytic) = 1.144302966786875415334041596238 y2[1] (numeric) = 1.1443029661267589168654945249149 absolute error = 6.601164984685470713231e-10 relative error = 5.7687213756170633615625527354665e-08 % h = 0.0001 y1[1] (analytic) = 2.5174771370314409952739163921999 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0380515984272379950006284569843 relative error = 1.5114972790619931343016284505402 % h = 0.0001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.1MB, time=58.74 NO POLE NO POLE x[1] = 0.544 y2[1] (analytic) = 1.1443547187789774757443254902696 y2[1] (numeric) = 1.1443547181112882744861137761336 absolute error = 6.676892012582117141360e-10 relative error = 5.8346349283256661969765209327483e-08 % h = 0.0001 y1[1] (analytic) = 2.5175627041472340085592018692383 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0381371655430310082859139340227 relative error = 1.5148447139055107995508213241878 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5441 y2[1] (analytic) = 1.1444064793275323412344572857263 y2[1] (numeric) = 1.1444064786522010075123240447498 absolute error = 6.753313337221332409765e-10 relative error = 5.9011491626556189818169038194856e-08 % h = 0.0001 y1[1] (analytic) = 2.5176482660873999846851697938073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0382227274831969844118818585917 relative error = 1.5181917187581470160055996492403 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5442 y2[1] (analytic) = 1.1444582484320224063193196656111 y2[1] (numeric) = 1.144458247748979032893669856845 absolute error = 6.830433734256498087661e-10 relative error = 5.9682681684671405434799463428161e-08 % h = 0.0001 y1[1] (analytic) = 2.517733822851083304250873420815 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0383082842468803039775854855994 relative error = 1.521538293650914206630494539113 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5443 y2[1] (analytic) = 1.1445100260919299799544433882795 y2[1] (numeric) = 1.1445100254011041798214395494635 absolute error = 6.908258001330038388160e-10 relative error = 6.0359960540661523151258084545387e-08 % h = 0.0001 y1[1] (analytic) = 2.5178193744374283996201925276348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0383938358332253993469045924192 relative error = 1.5248844386148218490519256797503 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=404.3MB, alloc=4.1MB, time=59.30 x[1] = 0.5444 y2[1] (analytic) = 1.1445618123067372855411841978792 y2[1] (numeric) = 1.1445618116080581897286652706124 absolute error = 6.986790958125189272668e-10 relative error = 6.1043369462450329661601858068864e-08 % h = 0.0001 y1[1] (analytic) = 2.5179049208455797549303890904596 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.038479382241376754657101155244 relative error = 1.5282301536808764752258433719086 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5445 y2[1] (analytic) = 1.1446136070759264609319005903327 y2[1] (numeric) = 1.1446136063693227162901229792615 absolute error = 7.066037446417776110712e-10 relative error = 6.1732949903233674119760094826036e-08 % h = 0.0001 y1[1] (analytic) = 2.5179904620746819061006624429217 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0385649234704789058273745077061 relative error = 1.5315754388800816711056023216897 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5446 y2[1] (analytic) = 1.1446654103989795584351324348094 y2[1] (numeric) = 1.1446654096843793254223324453432 absolute error = 7.146002330127999894662e-10 relative error = 6.2428743501886901981756416068571e-08 % h = 0.0001 y1[1] (analytic) = 2.5180759981238794408407039168939 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0386504595196764405674159816783 relative error = 1.5349202942434380763100670847074 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5447 y2[1] (analytic) = 1.1447172222753785448207804506355 y2[1] (numeric) = 1.1447172215527094952835572497528 absolute error = 7.226690495372232008827e-10 relative error = 6.3130792083372232545102486469391e-08 % h = 0.0001 y1[1] (analytic) = 2.5181615289923169986592509653857 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0387359903881139983859630301701 relative error = 1.5382647198019433837919490692383 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5448 y2[1] (analytic) = 1.144769042704605301325286539591 y2[1] (numeric) = 1.1447690419737946162738047843482 absolute error = 7.308106850514817552428e-10 relative error = 6.3839137659146080137980293689486e-08 % h = 0.0001 y1[1] (analytic) = 2.5182470546791392708726407674483 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0388215160749362705993528322327 relative error = 1.5416087155865923395063750037273 % h = 0.0001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.1MB, time=59.86 NO POLE NO POLE x[1] = 0.5449 y2[1] (analytic) = 1.1448208716861416236568149735411 y2[1] (numeric) = 1.1448208709471159910348262519501 absolute error = 7.390256326219887215910e-10 relative error = 6.4553822427566318910511833980066e-08 % h = 0.0001 y1[1] (analytic) = 2.5183325751834910006133633150044 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0389070365792880003400753797888 relative error = 1.544952281628376742079686774141 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.545 y2[1] (analytic) = 1.1448727092194692220004344373497 y2[1] (numeric) = 1.144872708472154834450116666342 absolute error = 7.473143875503177710077e-10 relative error = 6.5274888774299491180647576451144e-08 % h = 0.0001 y1[1] (analytic) = 2.5184180905045169828386139815162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0389925519003139825653260463006 relative error = 1.548295417958285442478472536587 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5451 y2[1] (analytic) = 1.1449245553040697210233009270249 y2[1] (numeric) = 1.1449245545483922736449148522699 absolute error = 7.556774473783860747550e-10 relative error = 6.6002379272727959287385106250675e-08 % h = 0.0001 y1[1] (analytic) = 2.5185036006413620643388455724061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0390780620371590640655576371905 relative error = 1.551638124607304343678829010692 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5452 y2[1] (analytic) = 1.1449764099394246598798415030428 y2[1] (numeric) = 1.1449764091753093479862034454427 absolute error = 7.641153118936380576001e-10 relative error = 6.6736336684357000903659085796834e-08 % h = 0.0001 y1[1] (analytic) = 2.5185891055931711437463198571452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0391635669889681434730319219296 relative error = 1.5549804016064164003358548592818 % h = 0.0001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.1MB, time=60.43 NO POLE NO POLE x[1] = 0.5453 y2[1] (analytic) = 1.1450282731250154922169388987993 y2[1] (numeric) = 1.145028272352387009082708892532 absolute error = 7.726284831342300062673e-10 relative error = 6.7476803959221847761781851843847e-08 % h = 0.0001 y1[1] (analytic) = 2.5186746053590891715436585829237 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0392490667548861712703706477081 relative error = 1.5583222489866016184533750598997 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5454 y2[1] (analytic) = 1.1450801448603235861791169841364 y2[1] (numeric) = 1.1450801440791061207849014511722 absolute error = 7.812174653942155329642e-10 relative error = 6.8223824236294667743882575305967e-08 % h = 0.0001 y1[1] (analytic) = 2.5187600999382611500723939698173 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0393345613340581497991060346017 relative error = 1.561663666778837055053896173728 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5455 y2[1] (analytic) = 1.1451320251448302244137270838932 y2[1] (numeric) = 1.1451320243549474591849951899603 absolute error = 7.898827652287318939329e-10 relative error = 6.8977440843891490290287367497914e-08 % h = 0.0001 y1[1] (analytic) = 2.5188455893298321335415186873648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0394200507256291332682307521492 relative error = 1.565004655014096817848792417548 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5456 y2[1] (analytic) = 1.1451839139780166040761351514276 y2[1] (numeric) = 1.145183913179391712616947988456 absolute error = 7.986248914591871629716e-10 relative error = 6.9737697300079075078351370376136e-08 % h = 0.0001 y1[1] (analytic) = 2.5189310735329472280360353124711 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0395055349287442277627473772555 relative error = 1.5683452137233520649087224443675 % h = 0.0001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.1MB, time=60.99 NO POLE NO POLE x[1] = 0.5457 y2[1] (analytic) = 1.1452358113593638368349097970586 y2[1] (numeric) = 1.1452358105519194816564615371819 absolute error = 8.074443551784482598767e-10 relative error = 7.0504637313081723924704626860616e-08 % h = 0.0001 y1[1] (analytic) = 2.5190165525467515915255052685502 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0395910139425485912522173333346 relative error = 1.571685342937571004334276738388 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5458 y2[1] (analytic) = 1.1452877172883529488770111713762 y2[1] (numeric) = 1.1452877164720112791209813376232 absolute error = 8.163416697560298337530e-10 relative error = 7.1278304781688035863695453281523e-08 % h = 0.0001 y1[1] (analytic) = 2.519102026370390433872597245822 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0396764877661874335993093106064 relative error = 1.5750250426877188939268555299817 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5459 y2[1] (analytic) = 1.1453396317644648809129807033675 y2[1] (numeric) = 1.1453396309391475300696967022279 absolute error = 8.253173508432840011396e-10 relative error = 7.2058743795657605354855324662188e-08 % h = 0.0001 y1[1] (analytic) = 2.5191874950030090168416351026793 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0397619563988060165683471674637 relative error = 1.5783643130047580408597771364802 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.546 y2[1] (analytic) = 1.1453915547871804881821316933069 y2[1] (numeric) = 1.1453915539528085718035407544067 absolute error = 8.343719163785909389002e-10 relative error = 7.2845998636127663572345607043468e-08 % h = 0.0001 y1[1] (analytic) = 2.5192729584437526541071452480364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0398474198395496538338573128208 relative error = 1.5817031539196478013496166344112 % h = 0.0001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.1MB, time=61.57 NO POLE NO POLE x[1] = 0.5461 y2[1] (analytic) = 1.1454434863559805404577407603588 y2[1] (numeric) = 1.1454434855124746538651904285329 absolute error = 8.435058865925503318259e-10 relative error = 7.3640113776019662729334339012732e-08 % h = 0.0001 y1[1] (analytic) = 2.5193584166917667112624035045775 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0399328780875637109891155693619 relative error = 1.5850415654633445803277747691134 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5462 y2[1] (analytic) = 1.1454954264703457220522401448402 y2[1] (numeric) = 1.1454954256176259380390664699428 absolute error = 8.527197840131736748974e-10 relative error = 7.4441133880445803390186772606624e-08 % h = 0.0001 y1[1] (analytic) = 2.5194438697461966058279814528167 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0400183311419936055546935176011 relative error = 1.5883795476668018311122770074401 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5463 y2[1] (analytic) = 1.1455473751297566318224108650923 y2[1] (numeric) = 1.1455473742677424983513334349352 absolute error = 8.620141334710774301571e-10 relative error = 7.5249103807115504723707945923892e-08 % h = 0.0001 y1[1] (analytic) = 2.5195293176061878072602922558848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0401037790019848069870043206692 relative error = 1.5917171005609700550798026394241 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5464 y2[1] (analytic) = 1.1455993323336937831745767289085 y2[1] (numeric) = 1.1455993314623043210698996907717 absolute error = 8.713894621046770381368e-10 relative error = 7.6064068606741817650296750765860e-08 % h = 0.0001 y1[1] (analytic) = 2.5196147602708858369601359649584 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0401892216666828366868480297428 relative error = 1.5950542241767968013379438348172 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=423.4MB, alloc=4.1MB, time=62.13 x[1] = 0.5465 y2[1] (analytic) = 1.1456512980816376040697991994664 y2[1] (numeric) = 1.1456512972007913047044174156767 absolute error = 8.808462993653817837897e-10 relative error = 7.6886073523447780836173153771756e-08 % h = 0.0001 y1[1] (analytic) = 2.5197001977394362682812443052446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.040274659135233268007956370029 relative error = 1.5983909185452266663976945603617 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5466 y2[1] (analytic) = 1.1457032723730684370290731157131 y2[1] (numeric) = 1.1457032714826832600062825988372 absolute error = 8.903851770227905168759e-10 relative error = 7.7715163995172719487924108887512e-08 % h = 0.0001 y1[1] (analytic) = 2.5197856300109847265388249424368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0403600914067817262655370072212 relative error = 1.601727183697201293846169263766 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5467 y2[1] (analytic) = 1.145755255207466539138523267151 y2[1] (numeric) = 1.145755254307459909968635040403 absolute error = 9.000066291698882267480e-10 relative error = 7.8551385654078486900426994339529e-08 % h = 0.0001 y1[1] (analytic) = 2.5198710570846768890181052295551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0404455184804738887448172943395 relative error = 1.6050630196636593740195512303076 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5468 y2[1] (analytic) = 1.1458072465843120820546018229721 y2[1] (numeric) = 1.1458072456746008898263583514866 absolute error = 9.097111922282434714855e-10 relative error = 7.9394784326955648711432984096379e-08 % h = 0.0001 y1[1] (analytic) = 2.5199564789596584849828754340872 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0405309403554554847095874988716 relative error = 1.6083984264755366436762705181117 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5469 y2[1] (analytic) = 1.1458592465030851520092866154893 y2[1] (numeric) = 1.1458592455835857470560799541633 absolute error = 9.194994049532066613260e-10 relative error = 8.0245406035629609816071905309167e-08 % h = 0.0001 y1[1] (analytic) = 2.5200418956350752956840314453434 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0406163570308722954107435101278 relative error = 1.6117334041637658856704113780888 % h = 0.0001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.1MB, time=62.68 NO POLE NO POLE x[1] = 0.547 y2[1] (analytic) = 1.1459112549632657498152802778119 y2[1] (numeric) = 1.1459112540338939413761710814711 absolute error = 9.293718084391091963408e-10 relative error = 8.1103296997366683894545477343920e-08 % h = 0.0001 y1[1] (analytic) = 2.5201273071100731543681169619403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0407017685058701540948290267247 relative error = 1.6150679527592769286253490645899 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5471 y2[1] (analytic) = 1.1459632719643337908712102357147 y2[1] (numeric) = 1.1459632710250048447467467774106 absolute error = 9.393289461244634583041e-10 relative error = 8.1968503625280105506455709679371e-08 % h = 0.0001 y1[1] (analytic) = 2.5202127133837979462858651593285 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0407871747795949460125772241129 relative error = 1.6184020722929966466076159428863 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5472 y2[1] (analytic) = 1.1460152975057691051668295536472 y2[1] (numeric) = 1.1460152965563977413696658969453 absolute error = 9.493713637971636567019e-10 relative error = 8.2841072528735984704984941471372e-08 % h = 0.0001 y1[1] (analytic) = 2.5202981144553956087007398372781 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0408725758511926084274519020625 relative error = 1.62173576279584895880099679956 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5473 y2[1] (analytic) = 1.1460673315870514372882186348317 y2[1] (numeric) = 1.1460673306275518276885311060014 absolute error = 9.594996095996875288303e-10 relative error = 8.3721050513759204124498427100690e-08 % h = 0.0001 y1[1] (analytic) = 2.5203835103240121308974760472366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.040957971719809130624188112021 relative error = 1.6250690242987548291808532619447 % h = 0.0001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.1MB, time=63.25 NO POLE NO POLE x[1] = 0.5474 y2[1] (analytic) = 1.1461193742076604464229877753981 y2[1] (numeric) = 1.1461193732379462123886888814677 absolute error = 9.697142340342988939304e-10 relative error = 8.4608484583439258494962431978986e-08 % h = 0.0001 y1[1] (analytic) = 2.5204689009887935541906201994749 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0410433623845905539173322642593 relative error = 1.6284018568326322661886772328337 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5475 y2[1] (analytic) = 1.1461714253670757063654805725036 y2[1] (numeric) = 1.1461714243870599163972295111959 absolute error = 9.800157899682510613077e-10 relative error = 8.5503421938336036536672139878221e-08 % h = 0.0001 y1[1] (analytic) = 2.5205542864488859719330696499346 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041128747844682971659781714719 relative error = 1.6317342604283963224068732466012 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5476 y2[1] (analytic) = 1.1462234850647767055219781863851 y2[1] (numeric) = 1.1462234840743718728829870940003 absolute error = 9.904048326389910923848e-10 relative error = 8.6405909976885545188902431219899e-08 % h = 0.0001 y1[1] (analytic) = 2.5206396667034355295246117666916 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041214128099232529251323831476 relative error = 1.6350662351169590942337696529821 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5477 y2[1] (analytic) = 1.1462755533002428469159044562916 y2[1] (numeric) = 1.146275552299360927256539539658 absolute error = 1.0008819196593649166336e-09 relative error = 8.7315996295805576125907978645008e-08 % h = 0.0001 y1[1] (analytic) = 2.5207250417515884244204624759516 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041299503147385424147174540736 relative error = 1.6383977809292297215588585348117 % h = 0.0001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.1MB, time=63.82 NO POLE NO POLE x[1] = 0.5478 y2[1] (analytic) = 1.1463276300729534481930318702458 y2[1] (numeric) = 1.1463276290615058371702085689088 absolute error = 1.0114476110228233013370e-09 relative error = 8.8233728690501314514070887909923e-08 % h = 0.0001 y1[1] (analytic) = 2.5208104115924909061398042874904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0413848729882879058665163522748 relative error = 1.6417288978961143874382642659453 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5479 y2[1] (analytic) = 1.1463797153823877416266883885823 y2[1] (numeric) = 1.1463797143602852725180597134552 absolute error = 1.0221024691086286751271e-09 relative error = 8.9159155155470889963772584133480e-08 % h = 0.0001 y1[1] (analytic) = 2.5208957762252892762743237994552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0414702376210862760010358642396 relative error = 1.645059586048516317770440615741 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.548 y2[1] (analytic) = 1.1464318092280248741229651212096 y2[1] (numeric) = 1.1464318081951778154359023159625 absolute error = 1.0328470586870628052471e-09 relative error = 9.0092323884710869629624346806428e-08 % h = 0.0001 y1[1] (analytic) = 2.5209811356491298884967486824406 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041555597044926888223460747225 relative error = 1.6483898454173357809720963064167 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5481 y2[1] (analytic) = 1.1464839116093439072259248585452 y2[1] (numeric) = 1.1464839105656619603012895300586 absolute error = 1.0436819469246353284866e-09 relative error = 9.1033283272121693412949204055719e-08 % h = 0.0001 y1[1] (analytic) = 2.5210664898631591485693841427541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0416409512589561482960962075385 relative error = 1.6517196760334700876543489296678 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=438.7MB, alloc=4.1MB, time=64.39 x[1] = 0.5482 y2[1] (analytic) = 1.1465360225258238171228114560702 y2[1] (numeric) = 1.1465360214712161137335183203343 absolute error = 1.0546077033892931357359e-09 relative error = 9.1982081911913051220090465001862e-08 % h = 0.0001 y1[1] (analytic) = 2.521151838866523514352648864786 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0417263002623205140793609295704 relative error = 1.6550490779278135902991071289617 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5483 y2[1] (analytic) = 1.1465881419769434946492600724531 y2[1] (numeric) = 1.1465881409113185945936294623431 absolute error = 1.0656249000556306101100e-09 relative error = 9.2938768599009202230607261618611e-08 % h = 0.0001 y1[1] (analytic) = 2.5212371826583694958136104323982 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0418116440541664955403224971826 relative error = 1.6583780511312576829356809539429 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5484 y2[1] (analytic) = 1.1466402699621817452945082611885 y2[1] (numeric) = 1.1466402688854476339844075426011 absolute error = 1.0767341113101007185874e-09 relative error = 9.3903392329454236128969218496143e-08 % h = 0.0001 y1[1] (analytic) = 2.5213225212378436550345202292461 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0418969826336406547612322940305 relative error = 1.6617065956746908008176202933961 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5485 y2[1] (analytic) = 1.1466924064810172892066079157008 y2[1] (numeric) = 1.1466924053930813752503809585872 absolute error = 1.0879359139562269571136e-09 relative error = 9.4876002300817276253821269491015e-08 % h = 0.0001 y1[1] (analytic) = 2.5214078546040926062213478179493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0419823159998896059480598827337 relative error = 1.6650347115889984200997812933052 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=442.5MB, alloc=4.1MB, time=64.95 x[1] = 0.5486 y2[1] (analytic) = 1.1467445515329287611976380678591 y2[1] (numeric) = 1.146744550433697873977821918743 absolute error = 1.0992308872198161491161e-09 relative error = 9.5856647912597624618659460223185e-08 % h = 0.0001 y1[1] (analytic) = 2.5214931827562630157123147980249 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0420676441520600154390268628093 relative error = 1.6683623989050630575156206665007 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5487 y2[1] (analytic) = 1.1467967051173947107489185398523 y2[1] (numeric) = 1.1467967040067750979947464424729 absolute error = 1.1106196127541720973794e-09 relative error = 9.6845378766629848757947060521393e-08 % h = 0.0001 y1[1] (analytic) = 2.5215785056935016019864281424975 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0421529670892986017131402072819 relative error = 1.6716896576537642700547178004275 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5488 y2[1] (analytic) = 1.1468488672338936020162244493712 y2[1] (numeric) = 1.146848866111790927370914360144 absolute error = 1.1221026746453100892272e-09 relative error = 9.7842244667488810352627146386636e-08 % h = 0.0001 y1[1] (analytic) = 2.5216638234149551356720130131029 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0422382848107521353987250778873 relative error = 1.6750164878659786546405245697093 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5489 y2[1] (analytic) = 1.1469010378819038138350015680469 y2[1] (numeric) = 1.1469010367482231544178293130861 absolute error = 1.1336806594171722549608e-09 relative error = 9.8847295622894635589184983825540e-08 % h = 0.0001 y1[1] (analytic) = 2.5217491359197704395552450539971 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0423235973155674392819571187815 relative error = 1.6783428895725798478083427600035 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.549 y2[1] (analytic) = 1.1469532170609036397255825330915 y2[1] (numeric) = 1.1469532159155494836887387535918 absolute error = 1.1453541560368437794997e-09 relative error = 9.9860581844117627206192152673174e-08 % h = 0.0001 y1[1] (analytic) = 2.5218344432070943885886821638876 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.042408904602891388315394228672 relative error = 1.6816688628044385253835290098796 % h = 0.0001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.1MB, time=65.52 NO POLE NO POLE x[1] = 0.5491 y2[1] (analytic) = 1.1470054047703712878984039120907 y2[1] (numeric) = 1.1470054036132475319786339449163 absolute error = 1.1571237559197699671744e-09 relative error = 1.0088215374638311818265334351003e-07 % h = 0.0001 y1[1] (analytic) = 2.5219197452760739098997957465008 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0424942066718709096265078112852 relative error = 1.6849944075924224021599271773604 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5492 y2[1] (analytic) = 1.147057601009784881259224120895 y2[1] (numeric) = 1.1470575998407948283242499612776 absolute error = 1.1689900529349741596174e-09 relative error = 1.0191206194927626702216817359608e-07 % h = 0.0001 y1[1] (analytic) = 2.5220050421258559827995014393003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0425795035216529825262135040847 relative error = 1.6883195239673962315785280378321 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5493 y2[1] (analytic) = 1.1471098057786224574143421945579 y2[1] (numeric) = 1.1471098045976688140040656878565 absolute error = 1.1809536434102765067014e-09 relative error = 1.0295035727714679458722214991798e-07 % h = 0.0001 y1[1] (analytic) = 2.5220903337555876387906893203702 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0426647951513846385174013851546 relative error = 1.6916442119602218054063562200307 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5494 y2[1] (analytic) = 1.1471620190763619686758174112684 y2[1] (numeric) = 1.1471620178833468425383038207964 absolute error = 1.1930151261375135904720e-09 relative error = 1.0399709075951366243781287301914e-07 % h = 0.0001 y1[1] (analytic) = 2.5221756201644159615767535933795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0427500815602129613034656581639 relative error = 1.6949684716017579534155842869215 % h = 0.0001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.1MB, time=66.08 NO POLE NO POLE x[1] = 0.5495 y2[1] (analytic) = 1.1472142409024812820666897692261 y2[1] (numeric) = 1.1472142396973061796889308672035 absolute error = 1.2051751023777589020226e-09 relative error = 1.0505231363146969262869265090325e-07 % h = 0.0001 y1[1] (analytic) = 2.522260901351488087070121750541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0428353627472850867968338153254 relative error = 1.6982923029228605430628738682096 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5496 y2[1] (analytic) = 1.1472664712564581793262013164064 y2[1] (numeric) = 1.1472664700390240034596571451467 absolute error = 1.2174341758665441712597e-09 relative error = 1.0611607733408612891959246722365e-07 % h = 0.0001 y1[1] (analytic) = 2.5223461773159512034007832134795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0429206387117482031274952782639 relative error = 1.7016157059543824791689437513061 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5497 y2[1] (analytic) = 1.1473187101377703569150183331638 y2[1] (numeric) = 1.1473187089079774040959367836577 absolute error = 1.2297929528190815495061e-09 relative error = 1.0718843351481713935277141054145e-07 % h = 0.0001 y1[1] (analytic) = 2.5224314480569525509248174519256 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.04300590945274955065152951671 relative error = 1.7049386807271737035983648376587 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5498 y2[1] (analytic) = 1.1473709575458954260204543676211 y2[1] (numeric) = 1.1473709563036433840849677227308 absolute error = 1.2422520419354866448903e-09 relative error = 1.0826943402790426015234558984151e-07 % h = 0.0001 y1[1] (analytic) = 2.5225167135736394222329215801468 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0430911749694364219596336449312 relative error = 1.7082612272720811949395818712096 % h = 0.0001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.1MB, time=66.65 NO POLE NO POLE x[1] = 0.5499 y2[1] (analytic) = 1.1474232134803109125616941237914 y2[1] (numeric) = 1.1474232122254988581556917133231 absolute error = 1.2548120544060024104683e-09 relative error = 1.0935913093478078089970770826386e-07 % h = 0.0001 y1[1] (analytic) = 2.5226019738651591621589374310344 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0431764352609561618856494958188 relative error = 1.7115833456199489681851618460334 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.55 y2[1] (analytic) = 1.1474754779404942571950182023822 y2[1] (numeric) = 1.1474754766730206532787943173545 absolute error = 1.2674736039162238850277e-09 relative error = 1.1045757650447607093971114336754e-07 % h = 0.0001 y1[1] (analytic) = 2.5226872289306591677883781077573 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0432616903264561675150901725417 relative error = 1.7149050358016180744122689999509 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5501 y2[1] (analytic) = 1.1475277509259228153190286942285 y2[1] (numeric) = 1.1475277496456855086667049077075 absolute error = 1.2802373066523237865210e-09 relative error = 1.1156482321401984697207105967934e-07 % h = 0.0001 y1[1] (analytic) = 2.5227724787692868884669540129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0433469401650838881936660776844 relative error = 1.7182262978479266004633663011868 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5502 y2[1] (analytic) = 1.1475800324360738570798756263018 y2[1] (numeric) = 1.1475800311429700757735966682274 absolute error = 1.2931037813062789580744e-09 relative error = 1.1268092374884638178242299674219e-07 % h = 0.0001 y1[1] (analytic) = 2.5228577233801898258090983549984 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0434321847759868255358104197828 relative error = 1.721547131789709668627143335019 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=457.7MB, alloc=4.1MB, time=67.22 x[1] = 0.5503 y2[1] (analytic) = 1.1476323224704245673764842602447 y2[1] (numeric) = 1.1476323211643509182953865937222 absolute error = 1.3060736490810976665225e-09 relative error = 1.1380593100319865406787685071834e-07 % h = 0.0001 y1[1] (analytic) = 2.5229429627625155337064921323883 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0435174241583125334332041971727 relative error = 1.7248675376577994363196704974539 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5504 y2[1] (analytic) = 1.1476846210284520458657832433774 y2[1] (numeric) = 1.1476846197093045121697354899626 absolute error = 1.3191475336960477534148e-09 relative error = 1.1493989808053243931155215824672e-07 % h = 0.0001 y1[1] (analytic) = 2.5230281969154116183365885942817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0436026583112086180633006590661 relative error = 1.7281875154830250957657794029936 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5505 y2[1] (analytic) = 1.1477369281096333069679336121236 y2[1] (numeric) = 1.1477369267773072455760479736822 absolute error = 1.3323260613918856384414e-09 relative error = 1.1608287829392034166075150764021e-07 % h = 0.0001 y1[1] (analytic) = 2.5231134258380257381711371789847 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0436878872338227378978492437691 relative error = 1.7315070652962128736806694135408 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5506 y2[1] (analytic) = 1.1477892437134452798715586478048 y2[1] (numeric) = 1.1477892423678354189354724725771 absolute error = 1.3456098609360861752277e-09 relative error = 1.1723492516645576676367817396121e-07 % h = 0.0001 y1[1] (analytic) = 2.5231986495295056039847069291735 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0437731109253026037114189939579 relative error = 1.7348261871281860309517401956242 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5507 y2[1] (analytic) = 1.1478415678393648085389745847497 y2[1] (numeric) = 1.1478415664803652449109012253062 absolute error = 1.3589995636280733594435e-09 relative error = 1.1839609243165683551926084096774e-07 % h = 0.0001 y1[1] (analytic) = 2.5232838679889989788632093841411 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0438583293847959785899214489255 relative error = 1.7381448810097648623206502129989 % h = 0.0001 memory used=461.5MB, alloc=4.1MB, time=67.78 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5508 y2[1] (analytic) = 1.1478939004868686517114221706666 y2[1] (numeric) = 1.1478938991143728484069702814912 absolute error = 1.3724958033044518891754e-09 relative error = 1.1956643403387023869499341057417e-07 % h = 0.0001 y1[1] (analytic) = 2.5233690812156536782124209489314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0439435426114506779391330137158 relative error = 1.7414631469717666960656010618713 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5509 y2[1] (analytic) = 1.1479462416554334829142990792269 y2[1] (numeric) = 1.1479462402693342665700595017165 absolute error = 1.3860992163442395775104e-09 relative error = 1.2074600412867503236765090560860e-07 % h = 0.0001 y1[1] (analytic) = 2.5234542892086175697665047402741 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0440287506044145694932168050585 relative error = 1.7447809850450058936838475558936 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.551 y2[1] (analytic) = 1.1479985913445358904623931748063 y2[1] (numeric) = 1.1479985899447254487882925575292 absolute error = 1.3998104416741006172771e-09 relative error = 1.2193485708328637414165195545431e-07 % h = 0.0001 y1[1] (analytic) = 2.5235394919670385735965319092362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0441139533628355733232439740206 relative error = 1.7480983952602938495744334681979 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5511 y2[1] (analytic) = 1.1480509495536523774651166293329 y2[1] (numeric) = 1.1480509481400222566915369314392 absolute error = 1.4136301207735796978937e-09 relative error = 1.2313304747695920010012243640467e-07 % h = 0.0001 y1[1] (analytic) = 2.523624689490064662119002440504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0441991508858616618457145052884 relative error = 1.7514153776484389907211528376945 % h = 0.0001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.1MB, time=68.34 NO POLE NO POLE x[1] = 0.5512 y2[1] (analytic) = 1.1481033162822593618317408911886 y2[1] (numeric) = 1.148103314854700464151403916919 absolute error = 1.4275588976803369742696e-09 relative error = 1.2434063010139184244354589674383e-07 % h = 0.0001 y1[1] (analytic) = 2.5237098817768438601043654282112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0442843431726408598310774929956 relative error = 1.7547319322402467763757367469544 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5513 y2[1] (analytic) = 1.1481556915298331762766325061121 y2[1] (numeric) = 1.1481556900882357572812486184039 absolute error = 1.4415974189953838877082e-09 relative error = 1.2555765996112958777099624534031e-07 % h = 0.0001 y1[1] (analytic) = 2.523795068826524244685538828227 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0443695302223212444122508930114 relative error = 1.7580480590665196977412654789585 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5514 y2[1] (analytic) = 1.1482080752958500683244897900508 y2[1] (numeric) = 1.1482080738401037344361699512919 absolute error = 1.4557463338883198387589e-09 relative error = 1.2678419227396817595902316274857e-07 % h = 0.0001 y1[1] (analytic) = 2.5238802506382539453664286868201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0444547120340509450931407516045 relative error = 1.7613637581580572776558059601028 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5515 y2[1] (analytic) = 1.1482604675797862003155803539094 y2[1] (numeric) = 1.1482604661097799062130106419438 absolute error = 1.4700062941025697119656e-09 relative error = 1.2802028247135723959323985954474e-07 % h = 0.0001 y1[1] (analytic) = 2.5239654272111811440304478456125 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0445398886069781437571599103969 relative error = 1.7646790295456560702762743968011 % h = 0.0001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.1MB, time=68.92 NO POLE NO POLE x[1] = 0.5516 y2[1] (analytic) = 1.1483128683811176494109794801431 y2[1] (numeric) = 1.1483128668967396954503572276831 absolute error = 1.4843779539606222524600e-09 relative error = 1.2926598619880368390779003755652e-07 % h = 0.0001 y1[1] (analytic) = 2.5240505985444540749490341227382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0446250599402510746757461875226 relative error = 1.7679938732601096607625240131003 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5517 y2[1] (analytic) = 1.1483652776993204075978093511421 y2[1] (numeric) = 1.148365276200458437228540056796 absolute error = 1.4988619703692692943461e-09 relative error = 1.3052135931627500718774556880519e-07 % h = 0.0001 y1[1] (analytic) = 2.5241357646372210247901679701215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0447102260330180245168800349059 relative error = 1.7713082893322086649616577967398 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5518 y2[1] (analytic) = 1.1484176955338703816944791293563 y2[1] (numeric) = 1.1484176940204113788696332885314 absolute error = 1.5134590028248458408249e-09 relative error = 1.3178645789860256158975297444727e-07 % h = 0.0001 y1[1] (analytic) = 2.5242209254886303326268896067908 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0447953868844273323536016715752 relative error = 1.7746222777927407290925661611596 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5519 y2[1] (analytic) = 1.1484701218842433933559258891068 y2[1] (numeric) = 1.148470120356073679937454893101 absolute error = 1.5281697134184709960058e-09 relative error = 1.3306133823588475433606918830025e-07 % h = 0.0001 y1[1] (analytic) = 2.5243060810978303899458156281403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0448805424936273896725276929247 relative error = 1.777935838672490529430689430855 % h = 0.0001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.1MB, time=69.50 NO POLE NO POLE x[1] = 0.552 y2[1] (analytic) = 1.1485225567499151790788564000321 y2[1] (numeric) = 1.1485225552069204122375666516791 absolute error = 1.5429947668412897483530e-09 relative error = 1.3434605683389018923732397213043e-07 % h = 0.0001 y1[1] (analytic) = 2.5243912314639696406556550910571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0449656928597666403823671558415 relative error = 1.7812489720022397719930050577058 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5521 y2[1] (analytic) = 1.1485750001303613902069897621166 y2[1] (numeric) = 1.148574998572426559817274156403 absolute error = 1.5579348303897156057136e-09 relative error = 1.3564067041446074849924714591800e-07 % h = 0.0001 y1[1] (analytic) = 2.5244763765861965810957250748271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0450508379819935808224371396115 relative error = 1.7845616778127671922232394757722 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5522 y2[1] (analytic) = 1.1486274520250575929363008922494 y2[1] (numeric) = 1.1486274504520670189656268103724 absolute error = 1.5729905739706740818770e-09 relative error = 1.3694523591591461476889141832813e-07 % h = 0.0001 y1[1] (analytic) = 2.5245615164636597600444657177347 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0451359778594567597711777825191 relative error = 1.7878739561348485546773045021468 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5523 y2[1] (analytic) = 1.1486799124334792683202648622596 y2[1] (numeric) = 1.14867991084531659821341782765 absolute error = 1.5881626701068470346096e-09 relative error = 1.3825981049344923337543413778923e-07 % h = 0.0001 y1[1] (analytic) = 2.524646651095507778727954729271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0452211124913047784546667940554 relative error = 1.7911858069992566527089581914645 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=476.8MB, alloc=4.1MB, time=70.06 x[1] = 0.5524 y2[1] (analytic) = 1.1487323813551018122751020883775 y2[1] (numeric) = 1.148732379751650018333184233261 absolute error = 1.6034517939419178551165e-09 relative error = 1.3958445151954421472135181485780e-07 % h = 0.0001 y1[1] (analytic) = 2.5247317804808892908284213778662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0453062418766862905551334426506 relative error = 1.7944972304367613081556900517433 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5525 y2[1] (analytic) = 1.1487848587894005355850243720683 y2[1] (numeric) = 1.1487848571705419123392068631935 absolute error = 1.6188586232458175088748e-09 relative error = 1.4091921658436417677918320022029e-07 % h = 0.0001 y1[1] (analytic) = 2.5248169046189530024927599540604 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0453913660147500022194720188448 relative error = 1.7978082264781293710248305291967 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5526 y2[1] (analytic) = 1.1488373447358506639074817921849 y2[1] (numeric) = 1.1488373431014668254875103643983 absolute error = 1.6343838384199714277866e-09 relative error = 1.4226416349616152764944155912718e-07 % h = 0.0001 y1[1] (analytic) = 2.5249020235088476723410427090272 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0454764849046446720677547738116 relative error = 1.8011187951541247191798846696985 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5527 y2[1] (analytic) = 1.1488898391939273377784104483898 y2[1] (numeric) = 1.1488898375438992152758631947888 absolute error = 1.6500281225025472536010e-09 relative error = 1.4361935028167918813538131770906e-07 % h = 0.0001 y1[1] (analytic) = 2.5249871371497221114750322683658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0455615985455191112017443331502 relative error = 1.804428936495508258027089864657 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5528 y2[1] (analytic) = 1.1489423421631056126174810557909 y2[1] (numeric) = 1.1489423404973134514437776232413 absolute error = 1.6657921611737034325496e-09 relative error = 1.4498483518655325428994652560536e-07 % h = 0.0001 y1[1] (analytic) = 2.5250722455407251834866935210768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0456467069365221832134055858612 relative error = 1.8077386505330379202021975890667 % h = 0.0001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.1MB, time=70.62 NO POLE NO POLE x[1] = 0.5529 y2[1] (analytic) = 1.1489948536428604587333483907405 y2[1] (numeric) = 1.1489948519611838159725097295947 absolute error = 1.6816766427608386611458e-09 relative error = 1.4636067667571559989077356229780e-07 % h = 0.0001 y1[1] (analytic) = 2.5251573486810058044667049836351 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0457318100768028041934170484195 relative error = 1.8110479372974686652574790394657 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.553 y2[1] (analytic) = 1.1490473736326667613289015877443 y2[1] (numeric) = 1.1490473719349845030850594046507 absolute error = 1.6976822582438421830936e-09 relative error = 1.4774693343379641879876018897131e-07 % h = 0.0001 y1[1] (analytic) = 2.525242446569712943012969639076 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0458169079655099427396817038604 relative error = 1.8143567968195524793489545796575 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5531 y2[1] (analytic) = 1.1490999021319993205065152874284 y2[1] (numeric) = 1.1490999004181896192461703501737 absolute error = 1.7138097012603449372547e-09 relative error = 1.4914366436552670715602297317865e-07 % h = 0.0001 y1[1] (analytic) = 2.5253275392059956202391252510091 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0459020006017926199658373157935 relative error = 1.8176652291300383749238469020305 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5532 y2[1] (analytic) = 1.1491524391403328512733016355109 y2[1] (numeric) = 1.1491524374102731831623300788909 absolute error = 1.7300596681109715566200e-09 relative error = 1.5055092859614068537887020488731e-07 % h = 0.0001 y1[1] (analytic) = 2.5254126265890029097830541524749 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0459870879847999095097662172593 relative error = 1.8209732342596723904082578123453 % h = 0.0001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.1MB, time=71.18 NO POLE NO POLE x[1] = 0.5533 y2[1] (analytic) = 1.1492049846571419835463631327267 y2[1] (numeric) = 1.1492049829107091257817699144921 absolute error = 1.7464328577645932182346e-09 relative error = 1.5196878547177815990171860215241e-07 % h = 0.0001 y1[1] (analytic) = 2.5254977087178839378153925095592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0460721701136809375421045743436 relative error = 1.8242808122391975898950685458998 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5534 y2[1] (analytic) = 1.1492575386819012621580463356516 y2[1] (numeric) = 1.1492575369189712902944649916299 absolute error = 1.7629299718635813440217e-09 relative error = 1.5339729455988682462760018843157e-07 % h = 0.0001 y1[1] (analytic) = 2.5255827855917878830480390596788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0461572469875848827747511244632 relative error = 1.8275879630993540628320635229471 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5535 y2[1] (analytic) = 1.1493101012140851468611964083752 y2[1] (numeric) = 1.1493100994345334321321342559196 absolute error = 1.7795517147290621524556e-09 relative error = 1.5483651564962450204136351053658e-07 % h = 0.0001 y1[1] (analytic) = 2.5256678572098639767426633244563 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0462423186056609764693753892407 relative error = 1.8308946868708789237102774514363 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5536 y2[1] (analytic) = 1.1493626722531680123344125249671 y2[1] (numeric) = 1.1493626704568692189682404639393 absolute error = 1.7962987933661720610278e-09 relative error = 1.5628650875226132394117392573820e-07 % h = 0.0001 y1[1] (analytic) = 2.5257529235712615027192132970958 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0463273849670585024459253618802 relative error = 1.8342009835845063117525656849451 % h = 0.0001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.1MB, time=71.73 NO POLE NO POLE x[1] = 0.5537 y2[1] (analytic) = 1.1494152517986241481873041226876 y2[1] (numeric) = 1.1494152499854522307179901832298 absolute error = 1.8131719174693139394578e-09 relative error = 1.5774733410158185174461907516310e-07 % h = 0.0001 y1[1] (analytic) = 2.5258379846751297973644226041766 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.046412446070926797091134668961 relative error = 1.8375068532709673906023977439036 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5538 y2[1] (analytic) = 1.1494678398499277589657480058863 y2[1] (numeric) = 1.1494678380197559595383337922945 absolute error = 1.8301717994274142135918e-09 relative error = 1.5921905215428713632503482510911e-07 % h = 0.0001 y1[1] (analytic) = 2.5259230405206182496403171417787 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0464975019164152493670292065631 relative error = 1.8408122959609903480128739081143 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5539 y2[1] (analytic) = 1.1495204364065529641571463005395 y2[1] (numeric) = 1.1495204345592538098279654805997 absolute error = 1.8472991543291808199398e-09 relative error = 1.6070172359039671733434220675247e-07 % h = 0.0001 y1[1] (analytic) = 2.5260080911068763010927211858551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0465825525026733008194332506395 relative error = 1.844117311685300395535964788644 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.554 y2[1] (analytic) = 1.1495730414679737981956852593716 y2[1] (numeric) = 1.1495730396034190982273232485744 absolute error = 1.8645546999683620107972e-09 relative error = 1.6219540931365056196834309941896e-07 % h = 0.0001 y1[1] (analytic) = 2.5260931364330534458597629767672 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0466675978288504455864750415516 relative error = 1.8474219004746197682119737872459 % h = 0.0001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.1MB, time=72.29 NO POLE NO POLE x[1] = 0.5541 y2[1] (analytic) = 1.1496256550336642104675949175089 y2[1] (numeric) = 1.1496256531517250536185889076103 absolute error = 1.8819391568490060098986e-09 relative error = 1.6370017045191094313060168043179e-07 % h = 0.0001 y1[1] (analytic) = 2.5261781764982992306803797778957 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0467526378940962304070918426801 relative error = 1.850726062359667724259222351346 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5542 y2[1] (analytic) = 1.149678277103098065316409598613 y2[1] (numeric) = 1.1496782752036448171256880800618 absolute error = 1.8994532481907215185512e-09 relative error = 1.6521606835756425695105261793317e-07 % h = 0.0001 y1[1] (analytic) = 2.5262632113017632549028224082446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.046837672697560254629534473029 relative error = 1.85402979737116054476395793286 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5543 y2[1] (analytic) = 1.1497309076757491420482292714408 y2[1] (numeric) = 1.149730905758651442114290199246 absolute error = 1.9170976999339390721948e-09 relative error = 1.6674316460792277961548224599116e-07 % h = 0.0001 y1[1] (analytic) = 2.5263482408425951704931592489515 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0469227022383921702198713137359 relative error = 1.8573331055398115333704845589621 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5544 y2[1] (analytic) = 1.1497835467510911349369817567794 y2[1] (numeric) = 1.1497835448162178941918085094428 absolute error = 1.9348732407451732473366e-09 relative error = 1.6828152100562636346217339163552e-07 % h = 0.0001 y1[1] (analytic) = 2.5264332651199446820437797236197 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0470077265157416817704917884041 relative error = 1.8606359868963310159715159230495 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=495.9MB, alloc=4.1MB, time=72.87 x[1] = 0.5545 y2[1] (analytic) = 1.1498361943285976532296857847023 y2[1] (numeric) = 1.1498361923758170512074000658948 absolute error = 1.9527806020222857188075e-09 relative error = 1.6983119957904407230191409117861e-07 % h = 0.0001 y1[1] (analytic) = 2.5265182841329615467818972523873 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0470927455287585465086093171717 relative error = 1.8639384414714263403987509041593 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5546 y2[1] (analytic) = 1.149888850407742221151714902095 y2[1] (numeric) = 1.1498888484369217032519657348073 absolute error = 1.9708205178997491672877e-09 relative error = 1.7139226258267575591770615987944e-07 % h = 0.0001 y1[1] (analytic) = 2.5266032978807955745780516796481 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0471777592765925743047637444325 relative error = 1.8672404692958018761136714231102 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5547 y2[1] (analytic) = 1.1499415149879982779120622303964 y2[1] (numeric) = 1.1499415129990045526581501933485 absolute error = 1.9889937252539120370479e-09 relative error = 1.7296477249755356370041916424338e-07 % h = 0.0001 y1[1] (analytic) = 2.5266883063625966279546111753388 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0472627677583936276813232401232 relative error = 1.8705420704001590138985625436584 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5548 y2[1] (analytic) = 1.1499941880688391777086060735051 y2[1] (numeric) = 1.1499941860615382140003419296491 absolute error = 2.0073009637082641438560e-09 relative error = 1.7454879203164339737698846214559e-07 % h = 0.0001 y1[1] (analytic) = 2.5267733095775146220942736097088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0473477709733116218209856744932 relative error = 1.8738432448151961655477547270548 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5549 y2[1] (analytic) = 1.1500468696497381897333763757958 y2[1] (numeric) = 1.1500468676239952140946732428026 absolute error = 2.0257429756387031329932e-09 relative error = 1.7614438412024630278727421060451e-07 % h = 0.0001 y1[1] (analytic) = 2.5268583075246995248485674014853 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0474327689204965245752794662697 relative error = 1.8771439925716087635590881482798 % h = 0.0001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.1MB, time=73.43 NO POLE NO POLE x[1] = 0.555 y2[1] (analytic) = 1.150099559730168498177822030195 y2[1] (numeric) = 1.1500995576858479919990202428652 absolute error = 2.0443205061788017873298e-09 relative error = 1.7775161192639980066629485464989e-07 % h = 0.0001 y1[1] (analytic) = 2.5269433002033013567463518393519 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0475177615990983564730639041363 relative error = 1.8804443137000892608255989824759 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5551 y2[1] (analytic) = 1.1501522583096032022380790362615 y2[1] (numeric) = 1.150152256246568899013002850856 absolute error = 2.0630343032250761854055e-09 relative error = 1.7937053884127915638811034563508e-07 % h = 0.0001 y1[1] (analytic) = 2.527028287612470191002316876652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0476027490082671907290289414364 relative error = 1.8837442082313271303274275698563 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5552 y2[1] (analytic) = 1.1502049653875153161202395082212 y2[1] (numeric) = 1.1502049633056301986779847987566 absolute error = 2.0818851174422547094646e-09 relative error = 1.8100122848459858862815731115731e-07 % h = 0.0001 y1[1] (analytic) = 2.5271132697513561535254823992356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.04768773114715315325219446402 relative error = 1.8870436761960088648239483676828 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5553 y2[1] (analytic) = 1.1502576809633777690456215329018 y2[1] (numeric) = 1.1502576788625040667770736295115 absolute error = 2.1008737022685479033903e-09 relative error = 1.8264374470501241690033931099759e-07 % h = 0.0001 y1[1] (analytic) = 2.5271982466191094229276969663615 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0477727080149064226544090311459 relative error = 1.8903427176248179765461215976767 % h = 0.0001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.1MB, time=74.00 NO POLE NO POLE x[1] = 0.5554 y2[1] (analytic) = 1.1503104050366634052560398775146 y2[1] (numeric) = 1.1503104029166625913351206970279 absolute error = 2.1200008139209191804867e-09 relative error = 1.8429815158051614792559793476155e-07 % h = 0.0001 y1[1] (analytic) = 2.5272832182148802305321360245719 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0478576796106772302588480893563 relative error = 1.8936413325484349968890664974499 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5555 y2[1] (analytic) = 1.1503631376068449840190775472328 y2[1] (numeric) = 1.1503631354675777726187211661756 absolute error = 2.1392672114003563810572e-09 relative error = 1.8596451341884750078873916167312e-07 % h = 0.0001 y1[1] (analytic) = 2.5273681845378188603817995944535 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0479426459336158601085116592379 relative error = 1.8969395209975374761048560844605 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5556 y2[1] (analytic) = 1.1504158786733951796333581925108 y2[1] (numeric) = 1.1504158765147215231362140127872 absolute error = 2.1586736564971441797236e-09 relative error = 1.8764289475788737083994689752539e-07 % h = 0.0001 y1[1] (analytic) = 2.5274531455870756492480094302008 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0480276069828726489747214949852 relative error = 1.9002372830027999829955333410867 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5557 y2[1] (analytic) = 1.1504686282357865814338193660934 y2[1] (numeric) = 1.1504686260575656676376820236581 absolute error = 2.1782209137961373424353e-09 relative error = 1.8933336036606073229789900287380e-07 % h = 0.0001 y1[1] (analytic) = 2.5275381013618009866389056518951 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0481125627575979863656177166795 relative error = 1.9035346185948941046063487293557 % h = 0.0001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.1MB, time=74.57 NO POLE NO POLE x[1] = 0.5558 y2[1] (analytic) = 1.1505213862934916937969866296625 y2[1] (numeric) = 1.1505213840955819431149517965464 absolute error = 2.1979097506820348331161e-09 relative error = 1.9103597524273747951127591915157e-07 % h = 0.0001 y1[1] (analytic) = 2.5276230518611453148079428504166 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.048197513256942314534654915201 relative error = 1.9068315278044884459192189440477 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5559 y2[1] (analytic) = 1.1505741528459829361462485100672 y2[1] (numeric) = 1.1505741506282419988015937401729 absolute error = 2.2177409373446547698943e-09 relative error = 1.9275080461863320683533554766022e-07 % h = 0.0001 y1[1] (analytic) = 2.5277079970842591287623856649027 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0482824584800561284890977296871 relative error = 1.9101280106622486295464068127515 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.556 y2[1] (analytic) = 1.1506269278927326429571323050854 y2[1] (numeric) = 1.1506269256550173961729220742211 absolute error = 2.2377152467842102308643e-09 relative error = 1.9447791395620992708048535476148e-07 % h = 0.0001 y1[1] (analytic) = 2.5277929370302929762718038326678 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0483673984260899759985158974522 relative error = 1.9134240671988372954244222515677 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5561 y2[1] (analytic) = 1.1506797114332130637625807386644 y2[1] (numeric) = 1.1506797091753796089459948293372 absolute error = 2.2578334548165859093272e-09 relative error = 1.9621736895007672848976180497998e-07 % h = 0.0001 y1[1] (analytic) = 2.5278778716983974578765667115013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0484523330941944576032787762857 relative error = 1.9167196974449141005081441852349 % h = 0.0001 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.1MB, time=75.13 NO POLE NO POLE x[1] = 0.5562 y2[1] (analytic) = 1.150732503466896363158229465587 y2[1] (numeric) = 1.1507325011888000230796138471303 absolute error = 2.2780963400786156184567e-09 relative error = 1.9796923552739037020206292281228e-07 % h = 0.0001 y1[1] (analytic) = 2.5279628010877232268963372742561 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0485372624835202266230493390405 relative error = 1.9200149014311357184651633403139 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5563 y2[1] (analytic) = 1.1507853039932546208076854255104 y2[1] (numeric) = 1.1507853016947499367743247801721 absolute error = 2.2985046840333606453383e-09 relative error = 1.9973357984825581615816752417334e-07 % h = 0.0001 y1[1] (analytic) = 2.5280477251974209894385655756453 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0486221865932179891652776404297 relative error = 1.9233096791881558393703458203021 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5564 y2[1] (analytic) = 1.1508381130117598314478060463265 y2[1] (numeric) = 1.150838110692700560472417091997 absolute error = 2.3190592709753889543295e-09 relative error = 2.0151046830612670740658854730747e-07 % h = 0.0001 y1[1] (analytic) = 2.5281326440266415044069816911606 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.048707105422438504133693755945 relative error = 1.926604030746625169400617371417 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5565 y2[1] (analytic) = 1.1508909305218839048939792967879 y2[1] (numeric) = 1.1508909281821230168579240571022 absolute error = 2.3397608880360552396857e-09 relative error = 2.0329996752820577276608720792128e-07 % h = 0.0001 y1[1] (analytic) = 2.5282175575745355835100881280276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.048792018970332583236800192812 relative error = 1.9298979561371914305299682478819 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=514.9MB, alloc=4.1MB, time=75.69 x[1] = 0.5566 y2[1] (analytic) = 1.1509437565230986660454045883505 y2[1] (numeric) = 1.1509437541624883408566227609476 absolute error = 2.3606103251887818274029e-09 relative error = 2.0510214437584517780227082307044e-07 % h = 0.0001 y1[1] (analytic) = 2.5283024658402540912696517081144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0488769272360510909963637728988 relative error = 1.9331914553904993602246785856217 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5567 y2[1] (analytic) = 1.1509965910148758548903745261767 y2[1] (numeric) = 1.1509965886332674796360340999558 absolute error = 2.3816083752543404262209e-09 relative error = 2.0691706594494681207509407352988e-07 % h = 0.0001 y1[1] (analytic) = 2.5283873688229479450291949227059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0489618302187449447559069874903 relative error = 1.9364845285371907111387641931509 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5568 y2[1] (analytic) = 1.1510494339966871265115575092481 y2[1] (numeric) = 1.1510494315939312926054227815122 absolute error = 2.4027558339061347277359e-09 relative error = 2.0874479956636251461457531450780e-07 % h = 0.0001 y1[1] (analytic) = 2.5284722665217681149624867590622 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0490467279175651146891988238466 relative error = 1.9397771756079042508096426686963 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5569 y2[1] (analytic) = 1.1511022854680040510912811795346 y2[1] (numeric) = 1.1511022830439505514157973239648 absolute error = 2.4240534996754838555698e-09 relative error = 2.1058541280629423758194045600383e-07 % h = 0.0001 y1[1] (analytic) = 2.5285571589358656240820329986738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0491316203316626238087450634582 relative error = 1.9430693966332757613540197524059 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.557 y2[1] (analytic) = 1.1511551454282981139168167201663 y2[1] (numeric) = 1.1511551429827959399599100566245 absolute error = 2.4455021739569066635418e-09 relative error = 2.1243897346669414807329921210823e-07 % h = 0.0001 y1[1] (analytic) = 2.5286420460643915482475659871291 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0492165074601885479742780519135 relative error = 1.946361191643938039163995822631 % h = 0.0001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.1MB, time=76.25 NO POLE NO POLE x[1] = 0.5571 y2[1] (analytic) = 1.1512080138770407153856640025569 y2[1] (numeric) = 1.1512080114099380543722571197648 absolute error = 2.4671026610134068827921e-09 relative error = 2.1430554958566466802336335873227e-07 % h = 0.0001 y1[1] (analytic) = 2.5287269279064970161745338755102 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0493013893022940159012459402946 relative error = 1.9496525606705208946033924453181 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5572 y2[1] (analytic) = 1.151260890813703171010837582424 y2[1] (numeric) = 1.151260888324847403029078464622 absolute error = 2.4888557679817591178020e-09 relative error = 2.1618520943785845216627877022472e-07 % h = 0.0001 y1[1] (analytic) = 2.5288118044613332094425893332314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0493862658571302091693013980158 relative error = 1.9529435037436511517042988855122 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5573 y2[1] (analytic) = 1.1513137762377567114261535446545 y2[1] (numeric) = 1.1513137737269944065483578533951 absolute error = 2.5107623048777956912594e-09 relative error = 2.1807802153487830401109127418687e-07 % h = 0.0001 y1[1] (analytic) = 2.5288966757280513625040777322355 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0494711371238483622307897970199 relative error = 1.9562340208939526478638384900305 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5574 y2[1] (analytic) = 1.1513666701486724823915171969622 y2[1] (numeric) = 1.1513666676158493977898228592459 absolute error = 2.5328230846016943377163e-09 relative error = 2.1998405462567702978919780143317e-07 % h = 0.0001 y1[1] (analytic) = 2.5289815417058027626925248024635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0495560031015997624192368672479 relative error = 1.9595241121520462335411548504119 % h = 0.0001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.1MB, time=76.83 NO POLE NO POLE x[1] = 0.5575 y2[1] (analytic) = 1.1514195725459215447982116122843 y2[1] (numeric) = 1.1514195699908826218549448662988 absolute error = 2.5550389229432667459855e-09 relative error = 2.2190337769695723033122637577746e-07 % h = 0.0001 y1[1] (analytic) = 2.5290664023937387502311237585118 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0496408637895357499578358232962 relative error = 1.9628137775485497719546176552197 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5576 y2[1] (analytic) = 1.1514724834289748746741870198642 y2[1] (numeric) = 1.1514724808515642360869390696409 absolute error = 2.5774106385872479502233e-09 relative error = 2.2383605997357103083079368515625e-07 % h = 0.0001 y1[1] (analytic) = 2.5291512577910107182412218973938 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0497257191868077179679339621782 relative error = 1.9661030171140781387792481409095 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5577 y2[1] (analytic) = 1.1515254027973033631893510449673 y2[1] (numeric) = 1.1515254001973643100707644753222 absolute error = 2.5999390531185865696451e-09 relative error = 2.2578217091891974845263760341530e-07 % h = 0.0001 y1[1] (analytic) = 2.5292361078967701127508066673188 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0498105692925671124775187321032 relative error = 1.9693918308792432218443640503524 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5578 y2[1] (analytic) = 1.151578330650377816660859797178 y2[1] (numeric) = 1.1515783280277528256331239003553 absolute error = 2.6226249910277358968227e-09 relative error = 2.2774178023535349774282695946073e-07 % h = 0.0001 y1[1] (analytic) = 2.5293209527101684327029912074054 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0498954141059654324297032721898 relative error = 1.9726802188746539208314440082925 % h = 0.0001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.1MB, time=77.39 NO POLE NO POLE x[1] = 0.5579 y2[1] (analytic) = 1.1516312669876689565584098072233 y2[1] (numeric) = 1.1516312643421996768424639727156 absolute error = 2.6454692797159458345077e-09 relative error = 2.2971495786457073379840865541741e-07 % h = 0.0001 y1[1] (analytic) = 2.5294057922303572299644993582431 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0499802536261542296912114230275 relative error = 1.9759681811309161469722112229166 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.558 y2[1] (analytic) = 1.1516842118086474195095308122717 y2[1] (numeric) = 1.1516842091401746700089751313412 absolute error = 2.6684727495005556809305e-09 relative error = 2.3170177398801773315433507323963e-07 % h = 0.0001 y1[1] (analytic) = 2.5294906264564881093341501432183 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0500650878522851090608622080027 relative error = 1.9792557176786328227469364228357 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5581 y2[1] (analytic) = 1.1517371651127837573048793896533 y2[1] (numeric) = 1.151737162421147523684591626133 absolute error = 2.6916362336202877635203e-09 relative error = 2.3370229902728801234519856634012e-07 % h = 0.0001 y1[1] (analytic) = 2.5295754553877127285513417205185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0501499167835097282780537853029 relative error = 1.9825428285484038815829599387152 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5582 y2[1] (analytic) = 1.1517901268995484369035334389488 y2[1] (numeric) = 1.1517901241845878686629915179544 absolute error = 2.7149605682405419209944e-09 relative error = 2.3571660364452168409959158270459e-07 % h = 0.0001 y1[1] (analytic) = 2.5296602790231827983045348057319 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0502347404189797980312468705163 relative error = 1.9858295137708262675534328389489 % h = 0.0001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.1MB, time=77.93 NO POLE NO POLE x[1] = 0.5583 y2[1] (analytic) = 1.1518430971684118404382875123948 y2[1] (numeric) = 1.1518430944299652479795966786318 absolute error = 2.7384465924586908337630e-09 relative error = 2.3774475874280475112476852062781e-07 % h = 0.0001 y1[1] (analytic) = 2.5297450973620500822397355649552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0503195587578470819664476297396 relative error = 1.9891157733764939350762770286343 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5584 y2[1] (analytic) = 1.1518960759188442652209489935506 y2[1] (numeric) = 1.1518960731567491169115727909542 absolute error = 2.7620951483093762025964e-09 relative error = 2.3978683546656833743938612166051e-07 % h = 0.0001 y1[1] (analytic) = 2.5298299104034663969689779783267 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0504043717992633966956900431111 relative error = 1.9924016073959978486133642212953 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5585 y2[1] (analytic) = 1.1519490631503159237476351241765 y2[1] (numeric) = 1.1519490603644088429778293486733 absolute error = 2.7859070807698057755032e-09 relative error = 2.4184290520198785721228668888326e-07 % h = 0.0001 y1[1] (analytic) = 2.5299147181465836120788056738989 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0504891795423806118055177386833 relative error = 1.9956870158599259823699136927213 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5586 y2[1] (analytic) = 1.1520020588622969437040708792677 y2[1] (numeric) = 1.1520020560524137059390196565036 absolute error = 2.8098832377650512227641e-09 relative error = 2.4391303957738212106498104608656e-07 % h = 0.0001 y1[1] (analytic) = 2.5299995205905536501387532317659 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0505739819863506498654652965503 relative error = 1.998971998798863319994108726358 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=534.0MB, alloc=4.1MB, time=78.48 x[1] = 0.5587 y2[1] (analytic) = 1.1520550630542573679708876901929 y2[1] (numeric) = 1.1520550602202328977975408301223 absolute error = 2.8340244701733468600706e-09 relative error = 2.4599731046361237979593609269524e-07 % h = 0.0001 y1[1] (analytic) = 2.5300843177345284867098269583611 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0506587791303254864365390231455 relative error = 2.0022565562433918542769316597232 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5588 y2[1] (analytic) = 1.1521080757256671546289230158834 y2[1] (numeric) = 1.1521080728673355227975337961693 absolute error = 2.8583316318313892197141e-09 relative error = 2.4809578997448130548448179739053e-07 % h = 0.0001 y1[1] (analytic) = 2.5301691095776601503529851308399 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0507435709734571500796971956243 relative error = 2.0055406882240905868522174413196 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5589 y2[1] (analytic) = 1.1521610968759961769645207620205 y2[1] (numeric) = 1.1521610939931905974248832922473 absolute error = 2.8828055795396374697732e-09 relative error = 2.5020855046713190993239203370138e-07 % h = 0.0001 y1[1] (analytic) = 2.5302538961191007226376177114634 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0508283575148977223643297762478 relative error = 2.0088243947715355278969256075924 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.559 y2[1] (analytic) = 1.1522141265047142234748325481675 y2[1] (numeric) = 1.1522141235972670504072178669216 absolute error = 2.9074471730676146812459e-09 relative error = 2.5233566454244640040113805019794e-07 % h = 0.0001 y1[1] (analytic) = 2.530338677358002338150025531897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0509131387537993378767375966814 relative error = 2.0121076759162996958316305894297 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5591 y2[1] (analytic) = 1.1522671646112909978731198227937 y2[1] (numeric) = 1.1522671616790337227139098797204 absolute error = 2.9322572751592099430733e-09 relative error = 2.5447720504544497260284457799116e-07 % h = 0.0001 y1[1] (analytic) = 2.5304234532935171845018989473405 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0509979146893141842286110121249 relative error = 2.0153905316889531170212302578351 % h = 0.0001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.1MB, time=79.02 NO POLE NO POLE x[1] = 0.5592 y2[1] (analytic) = 1.1523202111951961190940568261377 y2[1] (numeric) = 1.1523202082379593675560755011345 absolute error = 2.9572367515379813250032e-09 relative error = 2.5663324506568454090317467236119e-07 % h = 0.0001 y1[1] (analytic) = 2.5305082239247975023387959604043 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0510826853205945020655080251887 relative error = 2.0186729621200628254758726183532 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5593 y2[1] (analytic) = 1.1523732662558991212990344008557 y2[1] (numeric) = 1.1523732632735126503865747126175 absolute error = 2.9823864709124596882382e-09 relative error = 2.5880385793765740569407945679140e-07 % h = 0.0001 y1[1] (analytic) = 2.5305929892509955853486198146464 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0511674506467925850753318794308 relative error = 2.0219549672401928625521005638605 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5594 y2[1] (analytic) = 1.1524263297928694538814646504037 y2[1] (numeric) = 1.1524263267851621489000113065857 absolute error = 3.0077073049814533438180e-09 relative error = 2.6098911724118985789483142511021e-07 % h = 0.0001 y1[1] (analytic) = 2.5306777492712637802700960576868 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0512522106670607799968081224712 relative error = 2.0252365470799042766542145954384 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5595 y2[1] (analytic) = 1.1524794018055764814720864450986 y2[1] (numeric) = 1.1524793987723763530327328864181 absolute error = 3.0332001284393535586805e-09 relative error = 2.6318909680184072053935720880404e-07 % h = 0.0001 y1[1] (analytic) = 2.5307625039847544869012490738126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.051336965380551486627961138597 relative error = 2.0285177016697551229358534209423 % h = 0.0001 TOP MAIN SOLVE Loop memory used=541.7MB, alloc=4.1MB, time=79.57 NO POLE NO POLE x[1] = 0.5596 y2[1] (analytic) = 1.1525324822934894839442717758068 y2[1] (numeric) = 1.1525324792346236649628308664564 absolute error = 3.0588658189814409093504e-09 relative error = 2.6540387069129982740828138913336e-07 % h = 0.0001 y1[1] (analytic) = 2.5308472533906201581078780859913 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0514217147864171578345901507757 relative error = 2.0317984310403004630017923410742 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5597 y2[1] (analytic) = 1.1525855712560776564193329552053 y2[1] (numeric) = 1.1525855681713723991101404720051 absolute error = 3.0847052573091924832002e-09 relative error = 2.6763351322778643866380303897159e-07 % h = 0.0001 y1[1] (analytic) = 2.530931997488013299832032627205 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0515064588838102995587446919894 relative error = 2.0350787352220923646099593326087 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5598 y2[1] (analytic) = 1.1526386686928101092718306665652 y2[1] (numeric) = 1.1526386655820907821362407393315 absolute error = 3.1107193271355899272337e-09 relative error = 2.6987809897644759344601773399447e-07 % h = 0.0001 y1[1] (analytic) = 2.5310167362760864711004874810238 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0515911976718834708271995458082 relative error = 2.0383586142456799013736687386667 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5599 y2[1] (analytic) = 1.1526917746031558681348828600005 y2[1] (numeric) = 1.1526917714662469529444545156655 absolute error = 3.1369089151904283443350e-09 relative error = 2.7213770274975639938872156857891e-07 % h = 0.0001 y1[1] (analytic) = 2.53110146975399228403321709133 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0516759311497892837599291561144 relative error = 2.0416380681416091524640724756997 % h = 0.0001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.1MB, time=80.12 NO POLE NO POLE x[1] = 0.56 y2[1] (analytic) = 1.1527448889865838739054744961337 y2[1] (numeric) = 1.1527448858233089626798484591997 absolute error = 3.1632749112256260369340e-09 relative error = 2.7441239960791025901346767538929e-07 % h = 0.0001 y1[1] (analytic) = 2.531186197920883403851869441112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0517606593166804035785815058964 relative error = 2.0449170969404232023128286671607 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5601 y2[1] (analytic) = 1.1527980118425629827497681371204 y2[1] (numeric) = 1.1527980086527447747292330390896 absolute error = 3.1898182080205350980308e-09 relative error = 2.7670226485922903295993944433323e-07 % h = 0.0001 y1[1] (analytic) = 2.5312709207759125488882394002406 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.051845382171709548614951465025 relative error = 2.048195700672662140314987613623 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5602 y2[1] (analytic) = 1.1528511431705619661084153849842 y2[1] (numeric) = 1.1528511399540222647211625354532 absolute error = 3.2165397013872528495310e-09 relative error = 2.7900737406055314001157733294622e-07 % h = 0.0001 y1[1] (analytic) = 2.5313556383182324905927415421435 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0519300997140294903194536069279 relative error = 2.0514738793688630605320950092607 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5603 y2[1] (analytic) = 1.152904282970049510701869167205 y2[1] (numeric) = 1.1529042797266092205259350393714 absolute error = 3.2434402901759341278336e-09 relative error = 2.8132780301764159387454243117364e-07 % h = 0.0001 y1[1] (analytic) = 2.531440350546996053542882429295 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0520148119427930532695944940794 relative error = 2.0547516330595600613955123146737 % h = 0.0001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.1MB, time=80.65 NO POLE NO POLE x[1] = 0.5604 y2[1] (analytic) = 1.1529574312404942185356968695106 y2[1] (numeric) = 1.1529574279699733422555924528878 absolute error = 3.2705208762801044166228e-09 relative error = 2.8366362778556997666897257664491e-07 % h = 0.0001 y1[1] (analytic) = 2.5315250574613561154517323674331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0520995188571531151784444322175 relative error = 2.0580289617752842454099541958902 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5605 y2[1] (analytic) = 1.1530105879813646069058943158163 y2[1] (numeric) = 1.1530105846835822422639204890088 absolute error = 3.2977823646419738268075e-09 relative error = 2.8601492466912834909087602578502e-07 % h = 0.0001 y1[1] (analytic) = 2.5316097590604656071763966284221 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0521842204562626069031086932065 relative error = 2.061305865546563718857242939628 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5606 y2[1] (analytic) = 1.1530637531921291084042005952604 y2[1] (numeric) = 1.1530637498669034451464486717033 absolute error = 3.3252256632577519235571e-09 relative error = 2.8838177022321909720346388408175e-07 % h = 0.0001 y1[1] (analytic) = 2.5316944553434775127264861416742 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0522689167392745124531982064586 relative error = 2.0645823444039235915002797547537 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5607 y2[1] (analytic) = 1.1531169268722560709234137362829 y2[1] (numeric) = 1.1531169235194043877404503359031 absolute error = 3.3528516831829634003798e-09 relative error = 2.9076424125325471581655412495416e-07 % h = 0.0001 y1[1] (analytic) = 2.5317791463095448692725876540469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0523536077053418689992997188313 relative error = 2.0678583983778859762872328700302 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=553.1MB, alloc=4.1MB, time=81.20 x[1] = 0.5608 y2[1] (analytic) = 1.1531701090212137576627072276925 y2[1] (numeric) = 1.1531701056405524191249426275027 absolute error = 3.3806613385377646001898e-09 relative error = 2.9316241481555552841273720008831e-07 % h = 0.0001 y1[1] (analytic) = 2.5318638319578207671547333581294 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0524382933536177668814454229138 relative error = 2.0711340274989699890559423381334 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5609 y2[1] (analytic) = 1.1532232996384703471329473866708 y2[1] (numeric) = 1.1532232962298148006206865033594 absolute error = 3.4086555465122608833114e-09 relative error = 2.9557636821774734357917180467101e-07 % h = 0.0001 y1[1] (analytic) = 2.5319485122874583498908699888357 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0525229736832553496175820536201 relative error = 2.0744092317976917482385414561219 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.561 y2[1] (analytic) = 1.153276498723493933162011573659 y2[1] (numeric) = 1.153276495286658705790186731293 absolute error = 3.4368352273718248423660e-09 relative error = 2.9800617901915904790374570527022e-07 % h = 0.0001 y1[1] (analytic) = 2.5320331872976108141853273882178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0526076486934078139120394530022 relative error = 2.0776840113045643745662947124054 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5611 y2[1] (analytic) = 1.1533297062757525249001072540749 y2[1] (numeric) = 1.1533297028105512204376918900863 absolute error = 3.4652013044624153639886e-09 relative error = 3.0045192503122013529442838409953e-07 % h = 0.0001 y1[1] (analytic) = 2.5321178569874314099372865384156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0526923183832284096639986032 relative error = 2.080958366050097990774652170408 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5612 y2[1] (analytic) = 1.1533829222947140468250919068062 y2[1] (numeric) = 1.1533829188009593426091943694847 absolute error = 3.4937547042158975373215e-09 relative error = 3.0291368431785817268077742396429e-07 % h = 0.0001 y1[1] (analytic) = 2.5322025213560734402492470626576 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.052776982751870439975959127442 relative error = 2.0842322960647997213085201990573 % h = 0.0001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.1MB, time=81.74 NO POLE NO POLE x[1] = 0.5613 y2[1] (analytic) = 1.1534361467798463387477937794275 y2[1] (numeric) = 1.1534361432573499825924303701963 absolute error = 3.5224963561553634092312e-09 relative error = 3.0539153519589620205645293162927e-07 % h = 0.0001 y1[1] (analytic) = 2.5322871804026902614354941942294 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0528616417984872611622062590138 relative error = 2.087505801379173692027748460367 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5614 y2[1] (analytic) = 1.1534893797306171558173334900879 y2[1] (numeric) = 1.1534893761791899629168799038919 absolute error = 3.5514271929004535861960e-09 relative error = 3.0788555623545007882176414650901e-07 % h = 0.0001 y1[1] (analytic) = 2.5323718341264352830305652133234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0529462955222322827572772781078 relative error = 2.090778882023721029912833064273 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5615 y2[1] (analytic) = 1.1535426211464941685264464760148 y2[1] (numeric) = 1.1535426175659460183537667932052 absolute error = 3.5805481501726796828096e-09 relative error = 3.1039582626032574638512142107481e-07 % h = 0.0001 y1[1] (analytic) = 2.5324564825264619677977153516866 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.053030943922258967524427416471 relative error = 2.0940515380289398627708358010443 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5616 y2[1] (analytic) = 1.1535958710269449627168062885827 y2[1] (numeric) = 1.1535958674170847959160586717325 absolute error = 3.6098601668007476168502e-09 relative error = 3.1292242434841644698267066046424e-07 % h = 0.0001 y1[1] (analytic) = 2.5325411256019238317373831649808 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0531155869977208314640952297652 relative error = 2.09732376942532531894151936152 % h = 0.0001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.1MB, time=82.32 NO POLE NO POLE x[1] = 0.5617 y2[1] (analytic) = 1.1536491293714370395843487348915 y2[1] (numeric) = 1.1536491257320728548584669840328 absolute error = 3.6393641847258817508587e-09 relative error = 3.1546542983209986867491557114738e-07 % h = 0.0001 y1[1] (analytic) = 2.5326257633519744440956553727713 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0532002247477714438223674375557 relative error = 2.1005955762433695270036984555183 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5618 y2[1] (analytic) = 1.1537023961794378156845968658031 y2[1] (numeric) = 1.1537023925103766666774469856279 absolute error = 3.6690611490071498801752e-09 relative error = 3.1802492229863522847965832955301e-07 % h = 0.0001 y1[1] (analytic) = 2.5327103957757674273727311660588 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0532848571715644270994432308432 relative error = 2.1038669585135616154818067387418 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5619 y2[1] (analytic) = 1.1537556714504146229379868103815 y2[1] (numeric) = 1.1537556677514626151111977430023 absolute error = 3.6989520078267890673792e-09 relative error = 3.2060098159056029160029960568951e-07 % h = 0.0001 y1[1] (analytic) = 2.5327950228724564573313859822706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.053369484268253457058098047055 relative error = 2.1071379162663877125526794585813 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.562 y2[1] (analytic) = 1.1538089551838347086351944566842 y2[1] (numeric) = 1.1538089514547969961396621336033 absolute error = 3.7290377124955323230809e-09 relative error = 3.2319368780608832670875201597611e-07 % h = 0.0001 y1[1] (analytic) = 2.5328796446411952630054347476258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0534541060369922627321468124102 relative error = 2.1104084495323309457525517291988 % h = 0.0001 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.1MB, time=82.88 NO POLE NO POLE x[1] = 0.5621 y2[1] (analytic) = 1.1538622473791652354424629788508 y2[1] (numeric) = 1.1538622436198460179845268458408 absolute error = 3.7593192174579361330100e-09 relative error = 3.2580312129950499724217414556586e-07 % h = 0.0001 y1[1] (analytic) = 2.5329642610811376267081945867896 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.053538722476934626434906651574 relative error = 2.1136785583418714416842723463099 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5622 y2[1] (analytic) = 1.1539155480358732814069312104362 y2[1] (numeric) = 1.1539155442460758011092223790875 absolute error = 3.7897974802977088313487e-09 relative error = 3.2842936268156518867279803770191e-07 % h = 0.0001 y1[1] (analytic) = 2.5330488721914373840409469997339 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0536233335872343837676590645183 relative error = 2.1169482427254863257247330521991 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5623 y2[1] (analytic) = 1.1539688571534258399619628639348 y2[1] (numeric) = 1.1539688533329523782189230436789 absolute error = 3.8204734617430398202559e-09 relative error = 3.3107249281988977171018878937111e-07 % h = 0.0001 y1[1] (analytic) = 2.5331334779712484239013995057166 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.053707939367045423628111570501 relative error = 2.1202175027136497217325131613407 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5624 y2[1] (analytic) = 1.1540221747312898199324765964423 y2[1] (numeric) = 1.154022170879941694260546960913 absolute error = 3.8513481256719296355293e-09 relative error = 3.3373259283936230139528862661568e-07 % h = 0.0001 y1[1] (analytic) = 2.5332180784197246884921467542982 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0537925398155216882188588190826 relative error = 2.1234863383368327517557394572691 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=568.4MB, alloc=4.1MB, time=83.46 x[1] = 0.5625 y2[1] (analytic) = 1.1540755007689320455402769214025 y2[1] (numeric) = 1.1540754968865096064227560630508 absolute error = 3.8824224391175208583517e-09 relative error = 3.3640974412252565204560290806216e-07 % h = 0.0001 y1[1] (analytic) = 2.5333026735360201733291311033082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0538771349318171730558431680926 relative error = 2.1267547496255035357401612711322 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5626 y2[1] (analytic) = 1.1541288352658192564093859663841 y2[1] (numeric) = 1.1541288313521218841359560933158 absolute error = 3.9136973722734298730683e-09 relative error = 3.3910402830997858801096857096077e-07 % h = 0.0001 y1[1] (analytic) = 2.5333872633192889272501026636789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0539617247150859269768147284633 relative error = 2.1300227366101271912374406525875 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5627 y2[1] (analytic) = 1.1541821782214181075713760768367 y2[1] (numeric) = 1.1541821742762442090722966058944 absolute error = 3.9451738984990794709423e-09 relative error = 3.4181552730077227019942857695327e-07 % h = 0.0001 y1[1] (analytic) = 2.5334718477686850524230788110611 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0540463091644820521497908758455 relative error = 2.1332902993211658331136575436109 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5628 y2[1] (analytic) = 1.1542355296351951694707032657701 y2[1] (numeric) = 1.1542355256583421751456709659357 absolute error = 3.9768529943250322998344e-09 relative error = 3.4454432325280669833262833254081e-07 % h = 0.0001 y1[1] (analytic) = 2.5335564268833627043548031641364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0541308882791597040815152289208 relative error = 2.1365574377890785732580298658214 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=572.2MB, alloc=4.1MB, time=84.03 x[1] = 0.5629 y2[1] (analytic) = 1.1542888895066169279700415093059 y2[1] (numeric) = 1.1542888854978812885117163495514 absolute error = 4.0087356394583251597545e-09 relative error = 3.4729049858322708889042372049542e-07 % h = 0.0001 y1[1] (analytic) = 2.5336410006624760918992040295428 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0542154620582730916259160943272 relative error = 2.1398241520443215202918484320307 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.563 y2[1] (analytic) = 1.1543422578351497843556178880455 y2[1] (numeric) = 1.1543422537943269675678137438161 absolute error = 4.0408228167878041442294e-09 relative error = 3.5005413596882018870404020575863e-07 % h = 0.0001 y1[1] (analytic) = 2.5337255691051794772658523133289 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0543000305009764769925643781133 relative error = 2.143090442117347779277626592704 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5631 y2[1] (analytic) = 1.1543956346202600553425485742043 y2[1] (numeric) = 1.154395630547144542953087946767 absolute error = 4.0731155123894606274373e-09 relative error = 3.5283531834641052415776865629140e-07 % h = 0.0001 y1[1] (analytic) = 2.5338101322106271760284188988503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0543845936064241757551309636347 relative error = 2.146356308038607451428464527976 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5632 y2[1] (analytic) = 1.1544490198614139730801756644553 y2[1] (numeric) = 1.1544490157557992575484075674041 absolute error = 4.1056147155317680970512e-09 relative error = 3.5563412891325658595846948294951e-07 % h = 0.0001 y1[1] (analytic) = 2.5338946899779735571331314910267 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0544691513737705568598435558111 relative error = 2.149621749838547633817628096087 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5633 y2[1] (analytic) = 1.1545024135580776851574048584317 y2[1] (numeric) = 1.1545024094197562664763850256901 absolute error = 4.1383214186810198327416e-09 relative error = 3.5845065112744694943291547066234e-07 % h = 0.0001 y1[1] (analytic) = 2.5339792424063730429072309268718 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0545537038021700426339429916562 relative error = 2.152886767547612419088342148884 % h = 0.0001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.1MB, time=84.60 NO POLE NO POLE x[1] = 0.5634 y2[1] (analytic) = 1.1545558157097172546080439828334 y2[1] (numeric) = 1.1545558115384806371013765525504 absolute error = 4.1712366175066674302830e-09 relative error = 3.6128496870829633031253222705485e-07 % h = 0.0001 y1[1] (analytic) = 2.5340637894949801090674269522144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0546382508907771087941390169988 relative error = 2.1561513611962428951637982253031 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5635 y2[1] (analytic) = 1.154609226315798659916142361084 y2[1] (numeric) = 1.1546092221114373490294821898732 absolute error = 4.2043613108866601712108e-09 relative error = 3.6413716563674157596531681143498e-07 % h = 0.0001 y1[1] (analytic) = 2.5341483312429492847283534645241 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0547227926387462844550655293085 relative error = 2.1594155308148771449573765335832 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5636 y2[1] (analytic) = 1.1546626453757877950213310284866 y2[1] (numeric) = 1.1546626411380912941085457905094 absolute error = 4.2376965009127852379772e-09 relative error = 3.6700732615573759203492800268217e-07 % h = 0.0001 y1[1] (analytic) = 2.5342328676494351524110232217577 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0548073290452321521377352865421 relative error = 2.1626792764339502460830821330975 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5637 y2[1] (analytic) = 1.1547160728891504693241637928222 y2[1] (numeric) = 1.1547160686179072764281550182726 absolute error = 4.2712431928960087745496e-09 relative error = 3.6989553477065320444653961335939e-07 % h = 0.0001 y1[1] (analytic) = 2.5343173987135923480512820171425 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0548918601093893477779940819269 relative error = 2.165942598083894270566195226715 % h = 0.0001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.1MB, time=85.18 NO POLE NO POLE x[1] = 0.5638 y2[1] (analytic) = 1.1547695088553524076914591403404 y2[1] (numeric) = 1.1547695045503500123196413479391 absolute error = 4.3050023953718177924013e-09 relative error = 3.7280187624966695673963359511871e-07 % h = 0.0001 y1[1] (analytic) = 2.5344019244345755610082623198101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0549763858303725607349743845945 relative error = 2.1692054957951382845541354745386 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5639 y2[1] (analytic) = 1.1548229532738592504616429870865 y2[1] (numeric) = 1.154822948934884130356080065248 absolute error = 4.3389751201055629218385e-09 relative error = 3.7572643562416284268744700639393e-07 % h = 0.0001 y1[1] (analytic) = 2.5344864448115395340728363811988 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0550609062073365337995484459832 relative error = 2.1724679695981083480275402400631 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.564 y2[1] (analytic) = 1.1548764061441365534500922755128 y2[1] (numeric) = 1.1548764017709741713522902669011 absolute error = 4.3731623820978020086117e-09 relative error = 3.7866929818912597416318167808562e-07 % h = 0.0001 y1[1] (analytic) = 2.5345709598436390634760688071373 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0551454212394360632027808719217 relative error = 2.1757300195232275145115566796189 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5641 y2[1] (analytic) = 1.1549298674656497879544794163201 y2[1] (numeric) = 1.154929863058084588364834860563 absolute error = 4.4075651995896445557571e-09 relative error = 3.8163054950353818421290856151600e-07 % h = 0.0001 y1[1] (analytic) = 2.5346554695300289988976685955271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0552299309258259986243806603115 relative error = 2.1789916456009158307873475861755 % h = 0.0001 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.1MB, time=85.76 NO POLE NO POLE x[1] = 0.5642 y2[1] (analytic) = 1.1549833372378643407601175754771 y2[1] (numeric) = 1.1549833327956797466920205648609 absolute error = 4.4421845940680970106162e-09 relative error = 3.8461027539077356529536354148108e-07 % h = 0.0001 y1[1] (analytic) = 2.5347399738698642434744406395387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0553144352656612432011527043231 relative error = 2.1822528478615903366038108985191 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5643 y2[1] (analytic) = 1.1550368154602455141453068063625 y2[1] (numeric) = 1.1550368109832239238738979093848 absolute error = 4.4770215902714088969777e-09 relative error = 3.8760856193899394264851612887225e-07 % h = 0.0001 y1[1] (analytic) = 2.534824472862299753808736696236 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0553989342580967535354487610204 relative error = 2.1855136263356650643895127868186 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5644 y2[1] (analytic) = 1.1550903021322585258866810269772 y2[1] (numeric) = 1.1550902976201813096922612346874 absolute error = 4.5120772161944197922898e-09 relative error = 3.9062549550154428274317846573645e-07 % h = 0.0001 y1[1] (analytic) = 2.5349089665064905399769058205462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0554834279022875397036178853306 relative error = 2.188773981053551038964834225735 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5645 y2[1] (analytic) = 1.1551437972533685092645558421743 y2[1] (numeric) = 1.1551437927060160061706486922841 absolute error = 4.5473525030939071498902e-09 relative error = 3.9366116269734803678389241200009e-07 % h = 0.0001 y1[1] (analytic) = 2.5349934548015916655377442644889 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0555679161973886652644563292733 relative error = 2.1920339120456562772543309661187 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=587.4MB, alloc=4.1MB, time=86.34 x[1] = 0.5646 y2[1] (analytic) = 1.1551973008230405130682772108507 y2[1] (numeric) = 1.1551972962401920275743422446531 absolute error = 4.5828484854939349661976e-09 relative error = 3.9671565041130241921706911691928e-07 % h = 0.0001 y1[1] (analytic) = 2.5350779377467582475409448415813 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0556523991425552472676569063657 relative error = 2.1952934193423857879993068164891 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5647 y2[1] (analytic) = 1.1552508128407395016015709580497 y2[1] (numeric) = 1.1552508082221733004103676652354 absolute error = 4.6185662011912032928143e-09 relative error = 3.9978904579467362120689725336646e-07 % h = 0.0001 y1[1] (analytic) = 2.5351624153411454565355457563342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0557368767369424562622578211186 relative error = 2.1985525029741415714706001454374 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5648 y2[1] (analytic) = 1.155304333305930354687893131919 y2[1] (numeric) = 1.1553043286514236634274945384345 absolute error = 4.6545066912603985934845e-09 relative error = 4.0288143626549195903914283510465e-07 % h = 0.0001 y1[1] (analytic) = 2.5352468875839085165783788987547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0558213489797055163050909635391 relative error = 2.2018111629713226191815835161624 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5649 y2[1] (analytic) = 1.1553578622180778676757812054718 y2[1] (numeric) = 1.1553578575274068676162362596168 absolute error = 4.6906710000595449458550e-09 relative error = 4.0599290950894695741318498277569e-07 % h = 0.0001 y1[1] (analytic) = 2.5353313544742027052425176037705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0559058158699997049692296685549 relative error = 2.2050693993643249136013763643456 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.565 y2[1] (analytic) = 1.1554113995766467514442061230971 y2[1] (numeric) = 1.1554113948495865762088500351114 absolute error = 4.7270601752353560879857e-09 relative error = 4.0912355347778236758273220003973e-07 % h = 0.0001 memory used=591.2MB, alloc=4.1MB, time=86.93 y1[1] (analytic) = 2.5354158160111833536257238754924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0559902774069803533524359402768 relative error = 2.2083272121835414278682706306582 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5651 y2[1] (analytic) = 1.155464945381101632407925191765 y2[1] (numeric) = 1.1554649406174263646793368822102 absolute error = 4.7636752677285883095548e-09 relative error = 4.1227345639269112030548694181377e-07 % h = 0.0001 y1[1] (analytic) = 2.5355002721940058463588950762297 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0560747335898028460856071410141 relative error = 2.2115846014593621255033692591543 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5652 y2[1] (analytic) = 1.1555184996309070525228358168756 y2[1] (numeric) = 1.1555184948303897207434416291676 absolute error = 4.8005173317793941877080e-09 relative error = 4.1544270674271021356244669668953e-07 % h = 0.0001 y1[1] (analytic) = 2.5355847230218256216145100801739 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0561591844176226213412221449583 relative error = 2.2148415672221739601244374728527 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5653 y2[1] (analytic) = 1.1555720623255274692913300826944 y2[1] (numeric) = 1.1555720574879400443586529152009 absolute error = 4.8375874249326771674935e-09 relative error = 4.1863139328561553500692028876495e-07 % h = 0.0001 y1[1] (analytic) = 2.5356691684937981711150748916672 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0562436298895951708417869564516 relative error = 2.2180981095023608751599667378871 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5654 y2[1] (analytic) = 1.1556256334644272557676501773249 y2[1] (numeric) = 1.1556256285895406477242031904902 absolute error = 4.8748866080434469868347e-09 relative error = 4.2183960504831661910425183741189e-07 % h = 0.0001 y1[1] (analytic) = 2.5357536086090790401415677279701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0563280700048760398682797927545 relative error = 2.2213542283303038035634513275415 % h = 0.0001 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.1MB, time=87.50 NO POLE NO POLE x[1] = 0.5655 y2[1] (analytic) = 1.1556792130470707005632446621613 y2[1] (numeric) = 1.1556792081346547552810687161781 absolute error = 4.9124159452821759459832e-09 relative error = 4.2506743132725133892247951045157e-07 % h = 0.0001 y1[1] (analytic) = 2.5358380433668238275418835664447 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0564125047626208272685956312291 relative error = 2.2246099237363806675278773976087 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5656 y2[1] (analytic) = 1.1557328010729220078521255857696 y2[1] (numeric) = 1.1557327961227455037119695643702 absolute error = 4.9501765041401560213994e-09 relative error = 4.2831496168878053253460258636556e-07 % h = 0.0001 y1[1] (analytic) = 2.535922472766188185739278156069 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0564969341619851854659902208534 relative error = 2.2278651957509663782004244844854 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5657 y2[1] (analytic) = 1.1557863975414452973762264421427 y2[1] (numeric) = 1.1557863925532759419413696181346 absolute error = 4.9881693554348568240081e-09 relative error = 4.3158228596958256399317854900359e-07 % h = 0.0001 y1[1] (analytic) = 2.5360068968063278207408114931966 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.056581358202124820467523557981 relative error = 2.2311200444044328353973793374107 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5658 y2[1] (analytic) = 1.1558400024521046044507609732774 y2[1] (numeric) = 1.1558399974257090311354765715022 absolute error = 5.0263955733152844017752e-09 relative error = 4.3486949427704781883789901319426e-07 % h = 0.0001 y1[1] (analytic) = 2.53609131548639849214579076148 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0566657768821954918725028262644 relative error = 2.2343744697271489273192619964315 % h = 0.0001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.1MB, time=88.09 NO POLE NO POLE x[1] = 0.5659 y2[1] (analytic) = 1.1558936158043638799695828160169 y2[1] (numeric) = 1.1558936107395076447022419294666 absolute error = 5.0648562352673408865503e-09 relative error = 4.3817667698967313409672039630334e-07 % h = 0.0001 y1[1] (analytic) = 2.5361757288055560131542127358697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0567501902013530128809248006541 relative error = 2.2376284717494805302661640274712 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.566 y2[1] (analytic) = 1.1559472375976869904105459931083 y2[1] (numeric) = 1.1559472324941345682913610079843 absolute error = 5.1035524221191849851240e-09 relative error = 4.4150392475745616274151090754613e-07 % h = 0.0001 y1[1] (analytic) = 2.5362601367629562505752056506075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0568345981587532503019177153919 relative error = 2.2408820505017905083532988261491 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5661 y2[1] (analytic) = 1.1560008678315377178408662484196 y2[1] (numeric) = 1.1560008626890524997942729339743 absolute error = 5.1424852180465933144453e-09 relative error = 4.4485132850228967255892079595255e-07 % h = 0.0001 y1[1] (analytic) = 2.5363445393577551248354705311282 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0569190007535521245621825959126 relative error = 2.2441352060144387132267639018607 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5662 y2[1] (analytic) = 1.1560545065053797599224832262628 y2[1] (numeric) = 1.1560545013237240493441606453184 absolute error = 5.1816557105783225809444e-09 relative error = 4.4821897941835577939721373814351e-07 % h = 0.0001 y1[1] (analytic) = 2.5364289365891086099877219897857 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0570033979849056097144340545701 relative error = 2.2473879383177819837795150537286 % h = 0.0001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.1MB, time=88.67 NO POLE NO POLE x[1] = 0.5663 y2[1] (analytic) = 1.1561081536186767299174234947703 y2[1] (numeric) = 1.1561081483976117393159508908613 absolute error = 5.2210649906014726039090e-09 relative error = 4.5160696897252011475007902723641e-07 % h = 0.0001 y1[1] (analytic) = 2.5365133284561727337191284853185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0570877898519697334458405501029 relative error = 2.2506402474421741458675523500217 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5664 y2[1] (analytic) = 1.15616180917089215669316441327 y2[1] (numeric) = 1.1561618039101780043263142304101 absolute error = 5.2607141523668501828599e-09 relative error = 4.5501538890472592763828478316207e-07 % h = 0.0001 y1[1] (analytic) = 2.5365977149581035773597520459711 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0571721763539005770864641107555 relative error = 2.2538921334179660120263178227274 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5665 y2[1] (analytic) = 1.1562154731614894847279988436062 y2[1] (numeric) = 1.156215467860885191233665034735 absolute error = 5.3006042934943338088712e-09 relative error = 4.5844433122838812075002872171065e-07 % h = 0.0001 y1[1] (analytic) = 2.5366820960940572758909874561865 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0572565574898542756176995209709 relative error = 2.2571435962755053811873047889382 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5666 y2[1] (analytic) = 1.1562691455899320741164007053519 y2[1] (numeric) = 1.1562691402491955591381614855686 absolute error = 5.3407365149782392197833e-09 relative error = 4.6189388823078722080113339856725e-07 % h = 0.0001 y1[1] (analytic) = 2.5367664718631900179540009067851 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0573409332589870176807129715695 relative error = 2.2603946360451370383948787107457 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=606.5MB, alloc=4.1MB, time=89.23 x[1] = 0.5667 y2[1] (analytic) = 1.1563228264556832005743913748602 y2[1] (numeric) = 1.1563228210745712793817055756064 absolute error = 5.3811119211926857992538e-09 relative error = 4.6536415247346328307600422715822e-07 % h = 0.0001 y1[1] (analytic) = 2.5368508422646580458581681085459 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0574253036604550455848801733303 relative error = 2.2636452527572027545233095053886 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5668 y2[1] (analytic) = 1.1563765157582060554449069280987 y2[1] (numeric) = 1.1563765103364744355479431085066 absolute error = 5.4217316198969638195921e-09 relative error = 4.6885521679260973011036867101383e-07 % h = 0.0001 y1[1] (analytic) = 2.5369352072976176555895118691059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0575096686934146553162239338903 relative error = 2.2668954464420412859940152174251 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5669 y2[1] (analytic) = 1.1564302134969637457031662272166 y2[1] (numeric) = 1.1564302080343670234622636988902 absolute error = 5.4625967222409025283264e-09 relative error = 4.7236717429946712447710532317470e-07 % h = 0.0001 y1[1] (analytic) = 2.5370195669612251968191391330927 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0575940283570221965458511978771 relative error = 2.2701452171299883744930169646968 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.567 y2[1] (analytic) = 1.1564839196714192939620398507875 y2[1] (numeric) = 1.1564839141677109511918007723408 absolute error = 5.5037083427702390784467e-09 relative error = 4.7590011838071687563607003484025e-07 % h = 0.0001 y1[1] (analytic) = 2.5371039212546370729116774854067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0576783826504340726383895501911 relative error = 2.2733945648513767466886050699314 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5671 y2[1] (analytic) = 1.1565376342810356384774198676763 y2[1] (numeric) = 1.1565376287359680390454315654047 absolute error = 5.5450675994319883022716e-09 relative error = 4.7945414269887488080922900830173e-07 % h = 0.0001 y1[1] (analytic) = 2.5371882701770097409337111175672 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0577627315728067406604231823516 relative error = 2.2766434896365361139492162897784 % h = 0.0001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.1MB, time=89.76 NO POLE NO POLE x[1] = 0.5672 y2[1] (analytic) = 1.1565913573252756331535904544757 y2[1] (numeric) = 1.1565913517386000195737771255911 absolute error = 5.5866756135798133288846e-09 relative error = 4.8302934119268509984226666077382e-07 % h = 0.0001 y1[1] (analytic) = 2.5372726137274997116622162570402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0578470751232967113889283218246 relative error = 2.2798919915157931720615220532363 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5673 y2[1] (analytic) = 1.1566450888036020475485993564594 y2[1] (numeric) = 1.1566450831750685375692023113719 absolute error = 5.6285335099793970450875e-09 relative error = 4.8662580807751306401403985553537e-07 % h = 0.0001 y1[1] (analytic) = 2.5373569519052635495929960594612 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0579314133010605493197081242456 relative error = 2.2831400705194716009487276212815 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5674 y2[1] (analytic) = 1.1566988287154775668796301919964 y2[1] (numeric) = 1.1566988230448351500658157921816 absolute error = 5.6706424168138143998148e-09 relative error = 4.9024363784573931875496967605074e-07 % h = 0.0001 y1[1] (analytic) = 2.53744128470945787294911496367 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0580157461052548726758270284544 relative error = 2.2863877266778920643890820796827 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5675 y2[1] (analytic) = 1.1567525770603647920283756003752 y2[1] (numeric) = 1.1567525713473613263394700484174 absolute error = 5.7130034656889055519578e-09 relative error = 4.9388292526715280023591644201889e-07 % h = 0.0001 y1[1] (analytic) = 2.5375256121392393536893325094736 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.058100073535036353416044574258 relative error = 2.2896349600213722097345990769745 % h = 0.0001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.1MB, time=90.34 NO POLE NO POLE x[1] = 0.5676 y2[1] (analytic) = 1.1568063338377262395464112329824 y2[1] (numeric) = 1.1568063280821084479077613714395 absolute error = 5.7556177916386498615429e-09 relative error = 4.9754376538934414578876000652273e-07 % h = 0.0001 y1[1] (analytic) = 2.537609934193764717516536618051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0581843955895617172432486828354 relative error = 2.2928817705802266676299882195072 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5677 y2[1] (analytic) = 1.156860099047024341660570587782 y2[1] (numeric) = 1.1568600932485378085300298635705 absolute error = 5.7984865331305407242115e-09 relative error = 5.0122625353809893812019759022795e-07 % h = 0.0001 y1[1] (analytic) = 2.5376942508721907438861763349178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0582687122679877436128883997022 relative error = 2.2961281583847670517317970356709 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5678 y2[1] (analytic) = 1.1569138726877214462783206870432 y2[1] (numeric) = 1.156913866846110614207359438096 absolute error = 5.8416108320709612489472e-09 relative error = 5.0493048531779088328016390544433e-07 % h = 0.0001 y1[1] (analytic) = 2.5377785621736742660146940353642 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0583530235694712657414061001486 relative error = 2.2993741234653019584277634212579 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5679 y2[1] (analytic) = 1.1569676547592798169931385982608 y2[1] (numeric) = 1.1569676488742879831825778192641 absolute error = 5.8849918338105607789967e-09 relative error = 5.0865655661177492234637831447779e-07 % h = 0.0001 y1[1] (analytic) = 2.5378628680973721708879570922837 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0584373294931691706146691570681 relative error = 2.3026196658521369665563784780959 % h = 0.0001 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.1MB, time=90.90 NO POLE NO POLE x[1] = 0.568 y2[1] (analytic) = 1.157021445261161633089888798216 y2[1] (numeric) = 1.1570214393325309459402565422858 absolute error = 5.9286306871496322559302e-09 relative error = 5.1240456358278027678651136998882e-07 % h = 0.0001 y1[1] (analytic) = 2.5379471686424413992696890063077 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0585216300382383989964010710921 relative error = 2.3058647855755746371266596580326 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5681 y2[1] (analytic) = 1.1570752441928289895502013801237 y2[1] (numeric) = 1.1570752382203004452067109533348 absolute error = 5.9725285443434904267889e-09 relative error = 5.1617460267330342745965812402868e-07 % h = 0.0001 y1[1] (analytic) = 2.5380314638080389457098999981608 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0586059252038359454366120629452 relative error = 2.3091094826659145130381341243628 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5682 y2[1] (analytic) = 1.157129051553743897057851103811 y2[1] (numeric) = 1.1571290455370573359500002095475 absolute error = 6.0166865611078508942635e-09 relative error = 5.1996677060600102721852524639226e-07 % h = 0.0001 y1[1] (analytic) = 2.5381157535933218585533170631541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0586902149891188582800291279385 relative error = 2.3123537571534531188010322429158 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5683 y2[1] (analytic) = 1.1571828673433682820041372888757 y2[1] (numeric) = 1.157182861282262385379927279023 absolute error = 6.0611058966242100098527e-09 relative error = 5.2378116438408274707421924265889e-07 % h = 0.0001 y1[1] (analytic) = 2.5382000379974472399478134877304 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0587744993932442396745255525148 relative error = 2.315597609068483960256691114915 % h = 0.0001 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.1MB, time=91.47 NO POLE NO POLE x[1] = 0.5684 y2[1] (analytic) = 1.1572366915611639864932645507682 y2[1] (numeric) = 1.1572366854553762729480389408231 absolute error = 6.1057877135452256099451e-09 relative error = 5.2761788129170405588507850558166e-07 % h = 0.0001 y1[1] (analytic) = 2.5382843170195722458528378279791 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0588587784153692455795498927635 relative error = 2.3188410384412975242981680639023 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5685 y2[1] (analytic) = 1.1572905242065927683477243797455 y2[1] (numeric) = 1.1572905180558595903476257849724 absolute error = 6.1507331780000985947731e-09 relative error = 5.3147701889435893353148078795828e-07 % h = 0.0001 y1[1] (analytic) = 2.5383685906588540860478423500338 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0589430520546510857745544148182 relative error = 2.3220840453021812785910639888608 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5686 y2[1] (analytic) = 1.1573443652791163011136775626413 y2[1] (numeric) = 1.1573443590831728415137222124582 absolute error = 6.1959434595999553501831e-09 relative error = 5.3535867503927251753822550115102e-07 % h = 0.0001 y1[1] (analytic) = 2.5384528589144500241407109322718 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0590273203102470238674229970562 relative error = 2.3253266296814196712945564959362 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5687 y2[1] (analytic) = 1.1573982147781961740663374474004 y2[1] (numeric) = 1.1573982085367764426231064352306 absolute error = 6.2414197314432310121698e-09 relative error = 5.3926294785579368310643213471801e-07 % h = 0.0001 y1[1] (analytic) = 2.5385371217855173775761864292274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0591115831813143773028984940118 relative error = 2.3285687916092941307826427209052 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=625.6MB, alloc=4.1MB, time=92.05 x[1] = 0.5688 y2[1] (analytic) = 1.1574520727032938922153540503216 y2[1] (numeric) = 1.1574520664161307220943004762023 absolute error = 6.2871631701210535741193e-09 relative error = 5.4318993575578755651666763364115e-07 % h = 0.0001 y1[1] (analytic) = 2.5386213792712135176442974971379 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0591958406670105173710095619223 relative error = 2.331810531116083065365591754835 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5689 y2[1] (analytic) = 1.1575059390538708763101990059571 y2[1] (numeric) = 1.1575059327206959205875701692488 absolute error = 6.3331749557226288367083e-09 relative error = 5.4713973743402796186527965522098e-07 % h = 0.0001 y1[1] (analytic) = 2.538705631370695869488784881036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0592800927664928692154969458204 relative error = 2.3350518482320618630116065852056 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.569 y2[1] (analytic) = 1.1575598138293884628455513596132 y2[1] (numeric) = 1.1575598074499321910049251592084 absolute error = 6.3794562718406262004048e-09 relative error = 5.5111245186858980109578786472870e-07 % h = 0.0001 y1[1] (analytic) = 2.5387898780831219121155271633056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.05936433947891891184223922809 relative error = 2.3382927429875028910686954649239 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5691 y2[1] (analytic) = 1.1576136970293079040666842023987 y2[1] (numeric) = 1.157613690603299598490118901882 absolute error = 6.4260083055765653005167e-09 relative error = 5.5510817832124136728731124432296e-07 % h = 0.0001 y1[1] (analytic) = 2.538874119407649178400965973616 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0594485808034461781276780384004 relative error = 2.3415332154126754959867526216049 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5692 y2[1] (analytic) = 1.1576675886530903679748521487683 y2[1] (numeric) = 1.1576675821802581204286486640332 absolute error = 6.4728322475462034847351e-09 relative error = 5.5912701633783659116208333491028e-07 % h = 0.0001 y1[1] (analytic) = 2.5389583553434352551005306601502 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0595328167392322548272427249346 relative error = 2.3447732655378460030398482195539 % h = 0.0001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.1MB, time=92.65 NO POLE NO POLE x[1] = 0.5693 y2[1] (analytic) = 1.1577214887001969383326796565049 y2[1] (numeric) = 1.1577214821802676464477555233885 absolute error = 6.5199292918849241331164e-09 relative error = 5.6316906574870722077391348825699e-07 % h = 0.0001 y1[1] (analytic) = 2.5390425858896377828570624220441 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0596170472854347825837744868285 relative error = 2.3480128933932777160487274869523 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5694 y2[1] (analytic) = 1.1577753971700886146695501890894 y2[1] (numeric) = 1.157775390602787978416424368637 absolute error = 6.5673006362531258204524e-09 relative error = 5.6723442666905493433993216207027e-07 % h = 0.0001 y1[1] (analytic) = 2.5391268110454144562092379029502 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0597012724412114559359499677346 relative error = 2.3512520990092309171035189206536 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5695 y2[1] (analytic) = 1.1578293140622263122869962204019 y2[1] (numeric) = 1.1578293074472788304453838994306 absolute error = 6.6149474818416123209713e-09 relative error = 5.7132319949934338617745345474329e-07 % h = 0.0001 y1[1] (analytic) = 2.5392110308099230235999922456449 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0597854922057200233267043104293 relative error = 2.354490882415962866286651481236 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5696 y2[1] (analytic) = 1.1578832393760708622640900817024 y2[1] (numeric) = 1.1578832327131998288871066263839 absolute error = 6.6628710333769834553185e-09 relative error = 5.7543548492569018570834574598004e-07 % h = 0.0001 y1[1] (analytic) = 2.5392952451823212873849416075912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0598697065781182871116536723756 relative error = 2.3577292436437278013959806907049 % h = 0.0001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.1MB, time=93.24 NO POLE NO POLE x[1] = 0.5697 y2[1] (analytic) = 1.1579371731110830114628356508352 y2[1] (numeric) = 1.1579371664000105123358088710742 absolute error = 6.7110724991270267797610e-09 relative error = 5.7957138392025880949290015483428e-07 % h = 0.0001 y1[1] (analytic) = 2.5393794541617671038408051373761 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0599539155575641035675172021605 relative error = 2.360967182722776937668123545556 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5698 y2[1] (analytic) = 1.1579911152667234225335608836043 y2[1] (numeric) = 1.1579911085071703316274507660415 absolute error = 6.7595530909061101175628e-09 relative error = 5.8373099774165044625553685194263e-07 % h = 0.0001 y1[1] (analytic) = 2.539463657747418383173826411936 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0600381191432153829005384767204 relative error = 2.3642046996833584675020021577029 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5699 y2[1] (analytic) = 1.1580450658424526739203111872661 y2[1] (numeric) = 1.1580450590341386498397362547886 absolute error = 6.8083140240805749324775e-09 relative error = 5.8791442793529577486462496020022e-07 % h = 0.0001 y1[1] (analytic) = 2.5395478559384330895281943344876 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.060122317334230089254906399272 relative error = 2.3674417945557175601825960359675 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.57 y2[1] (analytic) = 1.158099024837731259866243636084 y2[1] (numeric) = 1.1580990179803747422921130917811 absolute error = 6.8573565175741305443029e-09 relative error = 5.9212177633384667522861024353287e-07 % h = 0.0001 y1[1] (analytic) = 2.5396320487339692409944634930788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0602065101297662407211755578632 relative error = 2.3706784673700963616049029207394 % h = 0.0001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.1MB, time=93.82 NO POLE NO POLE x[1] = 0.5701 y2[1] (analytic) = 1.1581529922520195904190220288925 y2[1] (numeric) = 1.1581529853453377965457728424471 absolute error = 6.9066817938732491864454e-09 relative error = 5.9635314505756787207094320894788e-07 % h = 0.0001 y1[1] (analytic) = 2.5397162361331849096179739796762 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0602906975289819093446860444606 relative error = 2.373914718156733993998108084521 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5702 y2[1] (analytic) = 1.158206968084777991436212788616 y2[1] (numeric) = 1.1582069611284869124036508831776 absolute error = 6.9562910790325619054384e-09 relative error = 6.0060863651472851154602871175246e-07 % h = 0.0001 y1[1] (analytic) = 2.5398004181352382214072706697044 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0603748795310352211339827344888 relative error = 2.3771505469458665556499620110495 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5703 y2[1] (analytic) = 1.158260952335466704590681703689 y2[1] (numeric) = 1.1582609453292811019104264013264 absolute error = 7.0061856026802553023626e-09 relative error = 6.0488835340199367065877699824773e-07 % h = 0.0001 y1[1] (analytic) = 2.5398845947392873563425219619542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0604590561350843560692340267386 relative error = 2.3803859537677271206313663657847 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5704 y2[1] (analytic) = 1.1583149450035458873759915113221 y2[1] (numeric) = 1.1583149379471792893525223952098 absolute error = 7.0563665980234691161123e-09 relative error = 6.0919239870481579945004733245877e-07 % h = 0.0001 y1[1] (analytic) = 2.5399687659444905483839379787732 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0605432273402875481106500435576 relative error = 2.3836209386525457385211681704445 % h = 0.0001 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.1MB, time=94.40 NO POLE NO POLE x[1] = 0.5705 y2[1] (analytic) = 1.1583689460884756131118003225629 y2[1] (numeric) = 1.158368938981640311258105674107 absolute error = 7.1068353018536946484559e-09 relative error = 6.1352087569782609591066869086701e-07 % h = 0.0001 y1[1] (analytic) = 2.5400529317500060854801882264569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0606273931458030852069002912413 relative error = 2.3868555016305494341311620944727 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5706 y2[1] (analytic) = 1.1584229555897158709492608890942 y2[1] (numeric) = 1.1584229484321229163970868582598 absolute error = 7.1575929545521740308344e-09 relative error = 6.1787388794522581358638143593717e-07 % h = 0.0001 y1[1] (analytic) = 2.5401370921549923095768187157553 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0607115535507893093035307805397 relative error = 2.3900896427319622072313007762298 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5707 y2[1] (analytic) = 1.1584769735067265658764207117182 y2[1] (numeric) = 1.1584769662980857657811203788729 absolute error = 7.2086408000953003328453e-09 relative error = 6.2225153930117750183639402135711e-07 % h = 0.0001 y1[1] (analytic) = 2.5402212471586076166246685424101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0607957085544046163513806071945 relative error = 2.3933233619870050322751130867351 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5708 y2[1] (analytic) = 1.1585309998389675187236229904716 y2[1] (numeric) = 1.1585309925789874326636044781136 absolute error = 7.2599800860600185123580e-09 relative error = 6.2665393391019617870817583829643e-07 % h = 0.0001 y1[1] (analytic) = 2.5403053967600104565882859276393 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0608798581558074563149979924237 relative error = 2.3965566594258958581253302488742 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=644.7MB, alloc=4.1MB, time=94.98 x[1] = 0.5709 y2[1] (analytic) = 1.1585850345858984661689084163176 y2[1] (numeric) = 1.1585850272742864025396812091119 absolute error = 7.3116120636292272072057e-09 relative error = 6.3108117620754043639105167195216e-07 % h = 0.0001 y1[1] (analytic) = 2.5403895409583593334543437184849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0609640023541563331810557832693 relative error = 2.3997895350788496077797197249765 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.571 y2[1] (analytic) = 1.158639077746979060743417804361 y2[1] (numeric) = 1.1586390703834410731462364359607 absolute error = 7.3635379875971813684003e-09 relative error = 6.3553337091960347921133203270926e-07 % h = 0.0001 y1[1] (analytic) = 2.540473679752812805240054347939 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0610481411486098049667664127234 relative error = 2.4030219889760781780971267856779 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5711 y2[1] (analytic) = 1.1586931293216688708367955685321 y2[1] (numeric) = 1.1586931219059097544618998337155 absolute error = 7.4157591163748957348166e-09 relative error = 6.4001062306430409413173564396842e-07 % h = 0.0001 y1[1] (analytic) = 2.5405578131425294840015842547646 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.061132274538326483728296319549 relative error = 2.4062540211477904395237236730486 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5712 y2[1] (analytic) = 1.1587471893094273807025940376861 y2[1] (numeric) = 1.1587471818411506687070448883945 absolute error = 7.4682767119955491492916e-09 relative error = 6.4451303795147755371785649764248e-07 % h = 0.0001 y1[1] (analytic) = 2.5406419411266680358424677629273 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0612164025224650355691798277117 relative error = 2.4094856316241922358194662709918 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5713 y2[1] (analytic) = 1.1588012577097139904636786130629 y2[1] (numeric) = 1.1588012501886219503437888969787 absolute error = 7.5210920401198897160842e-09 relative error = 6.4904072118326645153442402939054e-07 % h = 0.0001 y1[1] (analytic) = 2.5407260637043871809220204205524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0613005251001841806487324853368 relative error = 2.4127168204354863837847581958802 % h = 0.0001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.1MB, time=95.56 NO POLE NO POLE x[1] = 0.5714 y2[1] (analytic) = 1.1588553345219880161176337670538 y2[1] (numeric) = 1.1588553269477816460759929674117 absolute error = 7.5742063700416407996421e-09 relative error = 6.5359377865451146993427370292771e-07 % h = 0.0001 y1[1] (analytic) = 2.5408101808748456934637517983252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0613846422706426931904638631096 relative error = 2.4159475876118726729873222205518 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5715 y2[1] (analytic) = 1.1589094197457086895421698832215 y2[1] (numeric) = 1.1589094121180877148492620186001 absolute error = 7.6276209746929078646214e-09 relative error = 6.5817231655314208020287236317297e-07 % h = 0.0001 y1[1] (analytic) = 2.5408942926372024017637777472486 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.061468754032999401490489812033 relative error = 2.4191779331835478654892789446714 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5716 y2[1] (analytic) = 1.1589635133803351585005309375181 y2[1] (numeric) = 1.1589635056989980278509447804129 absolute error = 7.6813371306495861571052e-09 relative error = 6.6277644136056717502135102587956e-07 % h = 0.0001 y1[1] (analytic) = 2.540978398990616188199232115675 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0615528603864131879259441804594 relative error = 2.4224078571807056955744326246044 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5717 y2[1] (analytic) = 1.1590176154253264866469030206484 y2[1] (numeric) = 1.1590176076899703685101337936821 absolute error = 7.7353561181367692269663e-09 relative error = 6.6740625985206563321093348429142e-07 % h = 0.0001 y1[1] (analytic) = 2.5410624999342459892366779255283 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0616369613300429889633899903127 relative error = 2.4256373596335368694757640759298 % h = 0.0001 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.1MB, time=96.14 NO POLE NO POLE x[1] = 0.5718 y2[1] (analytic) = 1.1590717258801416535318237015234 y2[1] (numeric) = 1.1590717180904624324976654102023 absolute error = 7.7896792210341582913211e-09 relative error = 6.7206187909717681672186094670104e-07 % h = 0.0001 y1[1] (analytic) = 2.5411465954672507954405180076305 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0617210568630477951672300724149 relative error = 2.4288664405722290651031305616971 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5719 y2[1] (analytic) = 1.1591258447442395546075922317506 y2[1] (numeric) = 1.1591258368999318277261197927308 absolute error = 7.8443077268814724390198e-09 relative error = 6.7674340646009099982977958589428e-07 % h = 0.0001 y1[1] (analytic) = 2.5412306855887896514814050960515 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0618051469845866512081171608359 relative error = 2.4320951000269669317711725797176 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.572 y2[1] (analytic) = 1.1591799720170790012336805911064 y2[1] (numeric) = 1.1591799641178360743498209149877 absolute error = 7.8992429268838596761187e-09 relative error = 6.8145094960003973050265753826374e-07 % h = 0.0001 y1[1] (analytic) = 2.5413147702980216561446513813949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0618892316938186558713634461793 relative error = 2.4353233380279320899274274619847 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5721 y2[1] (analytic) = 1.1592341076981187206821453739366 y2[1] (numeric) = 1.1592340997436326047648365616559 absolute error = 7.9544861159173088122807e-09 relative error = 6.8618461647168612390136301014442e-07 % h = 0.0001 y1[1] (analytic) = 2.5413988495941059623386375229383 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0619733109899029620653495877227 relative error = 2.4385511546053031308806496995634 % h = 0.0001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.1MB, time=96.72 NO POLE NO POLE x[1] = 0.5722 y2[1] (analytic) = 1.1592882517868173561430405164318 y2[1] (numeric) = 1.1592882437767787636089783283808 absolute error = 8.0100385925340621880510e-09 relative error = 6.9094451532551508797715200759145e-07 % h = 0.0001 y1[1] (analytic) = 2.5414829234762017771032211195423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0620573848719987768299331843267 relative error = 2.4417785497892556165293379061544 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5723 y2[1] (analytic) = 1.159342404282633466729830864722 y2[1] (numeric) = 1.1593423962167318077618016217707 absolute error = 8.0659016589680292429513e-09 relative error = 6.9573075470822348112903424905997e-07 % h = 0.0001 y1[1] (analytic) = 2.5415669919434683616181446392451 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0621414533392653613448567040295 relative error = 2.4450055236099620790904683336652 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5724 y2[1] (analytic) = 1.1593965651850255274848065837377 y2[1] (numeric) = 1.1593965570629489063446056593966 absolute error = 8.1220766211402009243411e-09 relative error = 7.0054344346311020188448225758893e-07 % h = 0.0001 y1[1] (analytic) = 2.5416510549950650312114428074576 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.062225516390862030938154872242 relative error = 2.4482320760975920208284348530761 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5725 y2[1] (analytic) = 1.1594507344934519293844984067822 y2[1] (numeric) = 1.1594507263148871407204334697922 absolute error = 8.1785647886640649369900e-09 relative error = 7.0538269073046621056658239052785e-07 % h = 0.0001 y1[1] (analytic) = 2.5417351126301511553678494536766 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.062309574025948155094561518461 relative error = 2.4514582072823119137841953140154 % h = 0.0001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.1MB, time=97.29 NO POLE NO POLE x[1] = 0.5726 y2[1] (analytic) = 1.1595049122073709793450937257621 y2[1] (numeric) = 1.1595049039720035044940718924539 absolute error = 8.2353674748510218333082e-09 relative error = 7.1024860594796448291105044018786e-07 % h = 0.0001 y1[1] (analytic) = 2.5418191648478861577372038166302 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0623936262436831574639158814146 relative error = 2.4546839171942851995046241963552 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5727 y2[1] (analytic) = 1.1595590983262409002278535220204 y2[1] (numeric) = 1.1595590900337549035120515778409 absolute error = 8.2924859967158019441795e-09 relative error = 7.1514129885104989559632350228888e-07 % h = 0.0001 y1[1] (analytic) = 2.5419032116474295161428563077725 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0624776730432265158695683725569 relative error = 2.457909205863672288772071467279 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5728 y2[1] (analytic) = 1.1596132928495198308445301377202 y2[1] (numeric) = 1.1596132844995981558626469873752 absolute error = 8.3499216749818831503450e-09 relative error = 7.2006087947332904365031537392517e-07 % h = 0.0001 y1[1] (analytic) = 2.5419872530279407625900737330428 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0625617144237377623167857978272 relative error = 2.4611340733206305613341275572292 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5729 y2[1] (analytic) = 1.1596674957766658259627858877217 y2[1] (numeric) = 1.1596674873689899918758763934413 absolute error = 8.4076758340869094942804e-09 relative error = 7.2500745814695998969700482909811e-07 % h = 0.0001 y1[1] (analytic) = 2.5420712889885794832744439728064 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0626457503843764830011560375908 relative error = 2.4643585195953143656335943682404 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=663.7MB, alloc=4.1MB, time=97.85 x[1] = 0.573 y2[1] (analytic) = 1.1597217071071368563116125119018 y2[1] (numeric) = 1.1597216986413870541235018793866 absolute error = 8.4657498021881106325152e-09 relative error = 7.2998114550304194500653102734820e-07 % h = 0.0001 y1[1] (analytic) = 2.5421553195285053185902801198912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0627297809243023183169921846756 relative error = 2.467582544717875018538662228083 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5731 y2[1] (analytic) = 1.1597759268403908085867514678594 y2[1] (numeric) = 1.1597759183162458974190293395212 absolute error = 8.5241449111677221283382e-09 relative error = 7.3498205247200488231217313734400e-07 % h = 0.0001 y1[1] (analytic) = 2.5422393446468779631390240756382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0628138060426749628657361404226 relative error = 2.4708061487184608050732927038171 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5732 y2[1] (analytic) = 1.1598301549758854854561150639533 y2[1] (numeric) = 1.1598301463930229888177084791179 absolute error = 8.5828624966384065848354e-09 relative error = 7.4001029028399908035777704814399e-07 % h = 0.0001 y1[1] (analytic) = 2.5423233643428571657376496038794 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0628978257386541654643616686638 relative error = 2.4740293316272169781478071882093 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5733 y2[1] (analytic) = 1.1598843915130786055652084326189 y2[1] (numeric) = 1.1598843828711747076165328144123 absolute error = 8.6419038979486756182066e-09 relative error = 7.4506597046928460013924844053354e-07 % h = 0.0001 y1[1] (analytic) = 2.5424073786156027294270648427614 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0629818400113997291537769075458 relative error = 2.4772520934742857582896811726728 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5734 y2[1] (analytic) = 1.1599386364514278035425523439084 y2[1] (numeric) = 1.1599386277501573453542396726026 absolute error = 8.7012704581883126713058e-09 relative error = 7.5014920485862069280366718094235e-07 % h = 0.0001 y1[1] (analytic) = 2.5424913874642745114805142743294 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0630658488600715112072263391138 relative error = 2.4804744342898063333745441202875 % h = 0.0001 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.1MB, time=98.42 NO POLE NO POLE x[1] = 0.5735 y2[1] (analytic) = 1.1599928897903906300051068592012 y2[1] (numeric) = 1.1599928810294271058113101918498 absolute error = 8.7609635241937966673514e-09 relative error = 7.5526010558365513916969476338697e-07 % h = 0.0001 y1[1] (analytic) = 2.5425753908880324234119801517877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0631498522838294231386922165721 relative error = 2.483696354103914858357384852529 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5736 y2[1] (analytic) = 1.1600471515294245515636958250294 y2[1] (numeric) = 1.1600471427084401050099693212776 absolute error = 8.8209844465537265037518e-09 relative error = 7.6039878507731352083295118444826e-07 % h = 0.0001 y1[1] (analytic) = 2.5426593888860364309845833843526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.063233850281833430711295449137 relative error = 2.4869178529467444550039623633635 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5737 y2[1] (analytic) = 1.1601014216679869508284322069658 y2[1] (numeric) = 1.1601014127866523712141858209725 absolute error = 8.8813345796142463859933e-09 relative error = 7.6556535607418842282018884295973e-07 % h = 0.0001 y1[1] (analytic) = 2.5427433814574465542189838796146 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.063317842853243553945695944399 relative error = 2.4901389308484252116224219744258 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5738 y2[1] (analytic) = 1.1601557002055351264141442635175 y2[1] (numeric) = 1.1601556912635198449296722619837 absolute error = 8.9420152814844720015338e-09 relative error = 7.7075993161092856775583709119690e-07 % h = 0.0001 y1[1] (analytic) = 2.5428273686014228674017803433245 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0634018299972198671284924081089 relative error = 2.4933595878390841827951167449389 % h = 0.0001 TOP MAIN SOLVE Loop memory used=671.4MB, alloc=4.1MB, time=98.99 NO POLE NO POLE x[1] = 0.5739 y2[1] (analytic) = 1.1602099871415262929458025599734 y2[1] (numeric) = 1.1602099781384983789038850263231 absolute error = 9.0030279140419175336503e-09 relative error = 7.7598262502662788150491812774038e-07 % h = 0.0001 y1[1] (analytic) = 2.5429113503171254990939095365206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.063485811712922498820621601305 relative error = 2.4965798239488453891106340501609 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.574 y2[1] (analytic) = 1.1602642824754175810639478221502 y2[1] (numeric) = 1.1602642734110437381260243069654 absolute error = 9.0643738429379235151848e-09 relative error = 7.8123354996321449025608093652192e-07 % h = 0.0001 y1[1] (analytic) = 2.5429953266037146321390449899122 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0635697879995116318657570546966 relative error = 2.4997996392078298168960272420956 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5741 y2[1] (analytic) = 1.1603185862066660374301196299818 y2[1] (numeric) = 1.1603185770806115998270341078479 absolute error = 9.1260544376030855221339e-09 relative error = 7.8651282036583964900859945915770e-07 % h = 0.0001 y1[1] (analytic) = 2.5430792974603505036719951754361 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0636537588561475033987072402205 relative error = 2.5030190336461554179492523062862 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5742 y2[1] (analytic) = 1.1603728983347286247322859509002 y2[1] (numeric) = 1.1603728891466575534796022438707 absolute error = 9.1880710712526837070295e-09 relative error = 7.9182055048326660142740128934491e-07 % h = 0.0001 y1[1] (analytic) = 2.543163262886193405127101134901 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0637377242819904048538131996854 relative error = 2.5062380072939371092718094284737 % h = 0.0001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.1MB, time=99.57 NO POLE NO POLE x[1] = 0.5743 y2[1] (analytic) = 1.1604272188590622216902735129509 y2[1] (numeric) = 1.1604272096086371007981603408966 absolute error = 9.2504251208921131720543e-09 relative error = 7.9715685486825937102991338120800e-07 % h = 0.0001 y1[1] (analytic) = 2.5432472228804036822466335656377 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0638216842762006819733456304221 relative error = 2.5094565601812867728015893850398 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5744 y2[1] (analytic) = 1.1604815477791236230611990175898 y2[1] (numeric) = 1.1604815384660056557388838357512 absolute error = 9.3131179673223151818386e-09 relative error = 8.0252184837797148366879170680876e-07 % h = 0.0001 y1[1] (analytic) = 2.5433311774421417350891893630691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0639056388379387348159014278535 relative error = 2.512674692338313255145924671035 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5745 y2[1] (analytic) = 1.160535885094369539644901192108 y2[1] (numeric) = 1.1605358757182185444996919762228 absolute error = 9.3761509951452092158852e-09 relative error = 8.0791564617433462127466671555618e-07 % h = 0.0001 y1[1] (analytic) = 2.5434151265705680180380876201172 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0639895879663650177647996849016 relative error = 2.5158924037951223673148452797407 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5746 y2[1] (analytic) = 1.1605902308042565982893736816288 y2[1] (numeric) = 1.1605902213647310055202478210624 absolute error = 9.4395255927691258605664e-09 relative error = 8.1333836372444720682283424296031e-07 % h = 0.0001 y1[1] (analytic) = 2.543499070264843039809765083363 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0640735316606400395364771481474 relative error = 2.5191096945818168844545390476931 % h = 0.0001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.1MB, time=100.13 NO POLE NO POLE x[1] = 0.5747 y2[1] (analytic) = 1.1606445849082413418961987806231 y2[1] (numeric) = 1.1606445754049981894819582399837 absolute error = 9.5032431524142405406394e-09 relative error = 8.1879011680096292048805881710071e-07 % h = 0.0001 y1[1] (analytic) = 2.5435830085241273634621710658752 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0641574699199243631888831306596 relative error = 2.5223265647284965455810164791226 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5748 y2[1] (analytic) = 1.1606989474057802294259820038889 y2[1] (numeric) = 1.1606989378384751593079739136632 absolute error = 9.5673050701180080902257e-09 relative error = 8.2427102148247914695163505716835e-07 % h = 0.0001 y1[1] (analytic) = 2.5436669413475816064031618166234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0642414027433786061298738814078 relative error = 2.5255430142652580533139799637837 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5749 y2[1] (analytic) = 1.1607533182963296359037874969412 y2[1] (numeric) = 1.1607533086646168901631893337401 absolute error = 9.6317127457405981632011e-09 relative error = 8.2978119415392535382497807997697e-07 % h = 0.0001 y1[1] (analytic) = 2.5437508687343664403988943463929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0643253301301634401256064111773 relative error = 2.5287590432221950736108973022297 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.575 y2[1] (analytic) = 1.1608076975793458524245742857562 y2[1] (numeric) = 1.1608076878828782694542428028163 absolute error = 9.6964675829703314829399e-09 relative error = 8.3532075150695140115379442140929e-07 % h = 0.0001 y1[1] (analytic) = 2.5438347906836425915822197101162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0644092520794395913089317749006 relative error = 2.5319746516293982355012794525378 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=682.8MB, alloc=4.1MB, time=100.71 x[1] = 0.5751 y2[1] (analytic) = 1.1608620852542850861586333658177 y2[1] (numeric) = 1.1608620754927140968295164344565 absolute error = 9.7615709893291169313612e-09 relative error = 8.4088981054031578196729451628827e-07 % h = 0.0001 y1[1] (analytic) = 2.543918707194570840461075745537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0644931685903678401877878103214 relative error = 2.5351898395169551308211624125459 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5752 y2[1] (analytic) = 1.1609164813206034603570256304096 y2[1] (numeric) = 1.1609164714935790841791361531881 absolute error = 9.8270243761778894772215e-09 relative error = 8.4648848856027379383662804325882e-07 % h = 0.0001 y1[1] (analytic) = 2.5440026182663120219268792681242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0645770796621090216535913329086 relative error = 2.5384046069149503139477931517512 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5753 y2[1] (analytic) = 1.1609708857777570143570206381004 y2[1] (numeric) = 1.1609708758849278556349716945011 absolute error = 9.8928291587220489435993e-09 relative error = 8.5211690318096564140689173320051e-07 % h = 0.0001 y1[1] (analytic) = 2.5440865238980270252629177221507 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0646609852938240249896297869351 relative error = 2.5416189538534653015345195069492 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5754 y2[1] (analytic) = 1.1610252986252017035875362193663 y2[1] (numeric) = 1.1610252886662149475706366048484 absolute error = 9.9589867560168996145179e-09 relative error = 8.5777517232480446986714133982898e-07 % h = 0.0001 y1[1] (analytic) = 2.5441704240888767941527402878537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0647448854846737938794523526381 relative error = 2.5448328803625785722458839557871 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5755 y2[1] (analytic) = 1.1610797198623933995745789222973 y2[1] (numeric) = 1.1610797098368948086014882416456 absolute error = 1.00254985909730906806517e-08 relative error = 8.6346341422286432932280096913150e-07 % h = 0.0001 y1[1] (analytic) = 2.5442543188380223266885484445916 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.064828780233819326415260509376 relative error = 2.5480463864723655664929211823755 % h = 0.0001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.1MB, time=101.30 NO POLE NO POLE x[1] = 0.5756 y2[1] (analytic) = 1.1611341494887878899466852973327 y2[1] (numeric) = 1.161134139396421799584627773271 absolute error = 1.00923660903620575240617e-08 relative error = 8.6918174741526807003493644789060e-07 % h = 0.0001 y1[1] (analytic) = 2.5443382081446246753795859899157 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0649126695404216751062980547001 relative error = 2.5512594722128986861686593492461 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5757 y2[1] (analytic) = 1.1611885875038408784403640209714 y2[1] (numeric) = 1.1611885773442501936189001790656 absolute error = 1.01595906848214638419058e-08 relative error = 8.7493029075157516849088981471320e-07 % h = 0.0001 y1[1] (analytic) = 2.5444220920078449471605285144705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0649965534036419468872405792549 relative error = 2.5544721376142472943838249898017 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5758 y2[1] (analytic) = 1.1612430339070079849055388584019 y2[1] (numeric) = 1.1612430236798341760448942493331 absolute error = 1.02271738088606446090688e-08 relative error = 8.8070916339116948427075074840766e-07 % h = 0.0001 y1[1] (analytic) = 2.5445059704268443033998723326397 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0650804318226413031265843974241 relative error = 2.5576843827064777152027514355607 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5759 y2[1] (analytic) = 1.1612974886977447453109924649986 y2[1] (numeric) = 1.16129747840262784444494258534 absolute error = 1.02951169008660498796586e-08 relative error = 8.8651848480364694767431755313419e-07 % h = 0.0001 y1[1] (analytic) = 2.5445898434007839599083228688548 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0651643047965809596350349336392 relative error = 2.5608962075196532333794906925145 % h = 0.0001 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.1MB, time=101.89 NO POLE NO POLE x[1] = 0.576 y2[1] (analytic) = 1.1613519518755066117498110266296 y2[1] (numeric) = 1.1613519415120852086431215993156 absolute error = 1.03634214031066894273140e-08 relative error = 8.9235837476920317807314457190552e-07 % h = 0.0001 y1[1] (analytic) = 2.5446737109288251869471824994803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0652481723246221866738945642647 relative error = 2.5641076120838340940941286808358 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5761 y2[1] (analytic) = 1.1614064234397489524448297387213 y2[1] (numeric) = 1.1614064130076601907052515144517 absolute error = 1.04320887617395782242696e-08 relative error = 8.9822895337902103295232050850279e-07 % h = 0.0001 y1[1] (analytic) = 2.5447575730101293092367378501947 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0653320344059263089634499149791 relative error = 2.5673185964290775026893037523998 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5762 y2[1] (analytic) = 1.1614609033899270517540791240254 y2[1] (numeric) = 1.1614608928888066249388963649031 absolute error = 1.05011204268151827591223e-08 relative error = 9.0413034103565808760657502776253e-07 % h = 0.0001 y1[1] (analytic) = 2.5448414296438577059646465487795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0654158910396547056913586135639 relative error = 2.5705291605854376244069284003404 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5763 y2[1] (analytic) = 1.161515391725496110176232189034 y2[1] (numeric) = 1.1615153811549782578933639957871 absolute error = 1.05705178522828681932469e-08 relative error = 9.1006265845343404545560830146851e-07 % h = 0.0001 y1[1] (analytic) = 2.5449252808291718107943234332365 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0654997422249688105210354980209 relative error = 2.5737393045829655841251140752004 % h = 0.0001 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.1MB, time=102.48 NO POLE NO POLE x[1] = 0.5764 y2[1] (analytic) = 1.1615698884459112443560524189885 y2[1] (numeric) = 1.1615698778056287483597060631839 absolute error = 1.06402824959963463558046e-08 relative error = 9.1602602665881807894325854304552e-07 % h = 0.0001 y1[1] (analytic) = 2.5450091265652331118733262151464 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0655835879610301116000382799308 relative error = 2.5769490284517094660952990219839 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5765 y2[1] (analytic) = 1.1616243935506274870898426114274 y2[1] (numeric) = 1.1616243828402116673707180341363 absolute error = 1.07104158197191245772911e-08 relative error = 9.2202056699081610098541124790846e-07 % h = 0.0001 y1[1] (analytic) = 2.5450929668512031518417405981861 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0656674282470001515684526629705 relative error = 2.5801583322217143136795790526125 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5766 y2[1] (analytic) = 1.1616789070390997873308945482187 y2[1] (numeric) = 1.1616788962581804982009391866499 absolute error = 1.07809192891299553615688e-08 relative error = 9.2804640110135796693140339808529e-07 % h = 0.0001 y1[1] (analytic) = 2.5451768016862435278405648517209 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0657512630820405275672769165053 relative error = 2.5833672159230221290882411682694 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5767 y2[1] (analytic) = 1.1617334289107830101949395060221 y2[1] (numeric) = 1.161733418058988636366652609693 absolute error = 1.08517943738282868963291e-08 relative error = 9.3410365095568460700384399434844e-07 % h = 0.0001 y1[1] (analytic) = 2.5452606310695158915200938393876 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.065835092465312891246805904172 relative error = 2.5865756795856718731174999461359 % h = 0.0001 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.1MB, time=103.07 NO POLE NO POLE x[1] = 0.5768 y2[1] (analytic) = 1.1617879591651319369655996051278 y2[1] (numeric) = 1.1617879482420893896258852031966 absolute error = 1.09230425473397144019312e-08 relative error = 9.4019243883273508918184564079067e-07 % h = 0.0001 y1[1] (analytic) = 2.5453444550001819490483025025849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0659189163959789487750145673693 relative error = 2.5897837232396994648874366050649 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5769 y2[1] (analytic) = 1.1618424978016012650998399966154 y2[1] (numeric) = 1.1618424868069359779784076780545 absolute error = 1.09946652871214323185609e-08 relative error = 9.4631288732553361249245121557844e-07 % h = 0.0001 y1[1] (analytic) = 2.5454282734774034611192287987857 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0660027348732004608459408635701 relative error = 2.5929913469151377815801406646972 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.577 y2[1] (analytic) = 1.1618970448196456082334218877795 y2[1] (numeric) = 1.1618970337529815336657345561232 absolute error = 1.10666640745676873316563e-08 relative error = 9.5246511934157643067537128582262e-07 % h = 0.0001 y1[1] (analytic) = 2.5455120865003422429613560945909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0660865478961392426880681593753 relative error = 2.5961985506420166581780541127425 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5771 y2[1] (analytic) = 1.1619516002187194961863564057677 y2[1] (numeric) = 1.1619515890796791011711241702219 absolute error = 1.11390403950152322355458e-08 relative error = 9.5864925810321870618605771399878e-07 % h = 0.0001 y1[1] (analytic) = 2.5455958940681601643459950134367 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0661703554639571640727070782211 relative error = 2.5994053344503628872025179948841 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=701.9MB, alloc=4.1MB, time=103.65 x[1] = 0.5772 y2[1] (analytic) = 1.1620061639982773749683592993764 y2[1] (numeric) = 1.1620061527864816372195786641326 absolute error = 1.12117957377487806352438e-08 relative error = 9.6486542714806129450217782769859e-07 % h = 0.0001 y1[1] (analytic) = 2.5456796961800191495956647378751 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0662541575758161493223768026595 relative error = 2.6026116983702002184525213420896 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5773 y2[1] (analytic) = 1.1620607361577736067843064789481 y2[1] (numeric) = 1.1620607248728420107778439925999 absolute error = 1.12849315960064624863482e-08 relative error = 9.7111375032933745869848057182045e-07 % h = 0.0001 y1[1] (analytic) = 2.5457634928350811775924737663412 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0663379542308781773191858311256 relative error = 2.6058176424315493587436523499006 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5774 y2[1] (analytic) = 1.1621153166966624700396903943192 y2[1] (numeric) = 1.1621153053382130030544099213312 absolute error = 1.13584494669852804729880e-08 relative error = 9.7739435181629951425544642500009e-07 % h = 0.0001 y1[1] (analytic) = 2.5458472840325082817865001243255 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0664217454283052815132121891099 relative error = 2.6090231666644279716472517244808 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5775 y2[1] (analytic) = 1.1621699056143981593460772507597 y2[1] (numeric) = 1.1621698941820473074995100269967 absolute error = 1.14323508518465672237630e-08 relative error = 9.8370735609460540406660958283953e-07 % h = 0.0001 y1[1] (analytic) = 2.5459310697714625502041710298662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0665055311672595499308830946506 relative error = 2.612228271098850677229768110104 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5776 y2[1] (analytic) = 1.1622245029104347855265650628534 y2[1] (numeric) = 1.1622244914037975298051216972293 absolute error = 1.15066372557214433656241e-08 relative error = 9.9005288796670520361003918984022e-07 % h = 0.0001 y1[1] (analytic) = 2.5460148500511061254566420132775 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0665893114469031251833540780619 relative error = 2.6154329557648290517923155128308 % h = 0.0001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.1MB, time=104.24 NO POLE NO POLE x[1] = 0.5777 y2[1] (analytic) = 1.1622791085842263756212425462622 y2[1] (numeric) = 1.1622790970029161879049661306245 absolute error = 1.15813101877162764156377e-08 relative error = 9.9643107255222755624907500268892e-07 % h = 0.0001 y1[1] (analytic) = 2.5460986248706012047481754910316 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.066673086266398204474887555816 relative error = 2.6186372206923716276104326352135 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5778 y2[1] (analytic) = 1.1623337226352268728926488473208 y2[1] (numeric) = 1.1623337109788557119745083367407 absolute error = 1.16563711609181405105801e-08 relative error = 1.0028420352883660386276582935159e-06 % h = 0.0001 y1[1] (analytic) = 2.5461823942291100398845187937086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.066756855624907039611230858493 relative error = 2.6218410659114838926740440367627 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5779 y2[1] (analytic) = 1.1623883450628901368312341104067 y2[1] (numeric) = 1.1623883333310684444309571360989 absolute error = 1.17318216924002769743078e-08 relative error = 1.0092859019302654561256376620940e-06 % h = 0.0001 y1[1] (analytic) = 2.5462661581257949372812816479326 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.066840619521591937007993712717 relative error = 2.6250444914521682904276230350936 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.578 y2[1] (analytic) = 1.162442975866669943160820883031 y2[1] (numeric) = 1.1624429640590066399332651601828 absolute error = 1.18076633032275557228482e-08 relative error = 1.0157627985514080683393478433895e-06 % h = 0.0001 y1[1] (analytic) = 2.546349916559818257972313112208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0669243779556152576990251769924 relative error = 2.628247497344424219510556262531 % h = 0.0001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.1MB, time=104.84 NO POLE NO POLE x[1] = 0.5781 y2[1] (analytic) = 1.1624976150460199838440663585958 y2[1] (numeric) = 1.162497603162122465382128851439 absolute error = 1.18838975184619375071568e-08 relative error = 1.0222728515439997445529361234084e-06 % h = 0.0001 y1[1] (analytic) = 2.5464336695303424176180779665744 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0670081309261394173447900313588 relative error = 2.6314500836182480334977097931486 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5782 y2[1] (analytic) = 1.1625522626003938670879254567633 y2[1] (numeric) = 1.1625522506398679999199884632768 absolute error = 1.19605258671679369934865e-08 relative error = 1.0288161876193560491659068006437e-06 % h = 0.0001 y1[1] (analytic) = 2.546517417036529886514032555995 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0670918784323268862407446207794 relative error = 2.6346522503036330406401967551114 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5783 y2[1] (analytic) = 1.162606918529245117349114741381 y2[1] (numeric) = 1.162606906491695234931028060068 absolute error = 1.20375498824180866813130e-08 relative error = 1.0353929338082882570422553511055e-06 % h = 0.0001 y1[1] (analytic) = 2.5466011590775431895990000873949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0671756204733401893257121521793 relative error = 2.6378539974305695036063463432745 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5784 y2[1] (analytic) = 1.1626615828320271753395771759107 y2[1] (numeric) = 1.1626615707170560740411755171474 absolute error = 1.21149711012984016587633e-08 relative error = 1.0420032174614892987468608708148e-06 % h = 0.0001 y1[1] (analytic) = 2.546684895652544906463545380266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0672593570483419061902574450504 relative error = 2.6410553250290446392228741470288 % h = 0.0001 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.1MB, time=105.44 NO POLE NO POLE x[1] = 0.5785 y2[1] (analytic) = 1.1627162555081933980319477163042 y2[1] (numeric) = 1.1627162433154023331181025208124 absolute error = 1.21927910649138451954918e-08 relative error = 1.0486471662499196356346291391354e-06 % h = 0.0001 y1[1] (analytic) = 2.5467686267606976713583490707543 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0673430881564946710850611355387 relative error = 2.6442562331290426182162537083787 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5786 y2[1] (analytic) = 1.1627709365571970586650197412722 y2[1] (numeric) = 1.1627709242861857402712245683232 absolute error = 1.22710113183937951729490e-08 relative error = 1.0553249081651930647579605042078e-06 % h = 0.0001 y1[1] (analytic) = 2.5468523524011641732025812691462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0674268137969611729292933339306 relative error = 2.6474567217605445649542892252933 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5787 y2[1] (analytic) = 1.1628256259784913467492123198923 y2[1] (numeric) = 1.1628256136288579358517009679026 absolute error = 1.23496334108975113519897e-08 relative error = 1.0620365715199624535583190208672e-06 % h = 0.0001 y1[1] (analytic) = 2.5469360725731071555922746706695 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0675105339689041553189867354539 relative error = 2.6506567909535285571878893153659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5788 y2[1] (analytic) = 1.1628803237715293680720383164999 y2[1] (numeric) = 1.1628803113428704724524348387362 absolute error = 1.24286588956196034777637e-08 relative error = 1.0687822849483054043073826628255e-06 % h = 0.0001 y1[1] (analytic) = 2.5470197872756894168086971195267 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0675942486714864165354091843111 relative error = 2.6538564407379696257930417549156 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=717.1MB, alloc=4.1MB, time=106.02 x[1] = 0.5789 y2[1] (analytic) = 1.1629350299357641447035733328085 y2[1] (numeric) = 1.1629350174276748149080731109723 absolute error = 1.25080893297955002218362e-08 relative error = 1.0755621774061098482636544708201e-06 % h = 0.0001 y1[1] (analytic) = 2.5471034965080738098267236260749 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0676779579038708095534356908593 relative error = 2.6570556711438397545129891085659 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.579 y2[1] (analytic) = 1.1629897444706486150019254872046 y2[1] (numeric) = 1.1629897318827223402950065257221 absolute error = 1.25879262747069189614825e-08 relative error = 1.0823763781714595695102296785300e-06 % h = 0.0001 y1[1] (analytic) = 2.5471872002694232423232078370701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0677616616652202420499199018545 relative error = 2.6602544822011078797006051644972 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5791 y2[1] (analytic) = 1.1630444673756356336187060311618 y2[1] (numeric) = 1.1630444547074643379313696350593 absolute error = 1.26681712956873363961025e-08 relative error = 1.0892250168450196584395300601093e-06 % h = 0.0001 y1[1] (analytic) = 2.5472708985589006766853529588917 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0678453599546976764120650236761 relative error = 2.6634528739397398900609720905183 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5792 y2[1] (analytic) = 1.1630991986501779715045008027205 y2[1] (numeric) = 1.1630991859013520093770408020204 absolute error = 1.27488259621274600007001e-08 relative error = 1.0961082233504218948508211350887e-06 % h = 0.0001 y1[1] (analytic) = 2.5473545913756691300190821336638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0679290527714661297457941984482 relative error = 2.6666508463896986263941582261622 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5793 y2[1] (analytic) = 1.1631539382937283159143425169771 y2[1] (numeric) = 1.1631539254638364684336422006047 memory used=720.9MB, alloc=4.1MB, time=106.60 absolute error = 1.28298918474807003163724e-08 relative error = 1.1030261279346500606263494604360e-06 % h = 0.0001 y1[1] (analytic) = 2.5474382787188916741574082681885 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0680127401146886738841203329729 relative error = 2.6698483995809438813381964259826 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5794 y2[1] (analytic) = 1.1632086863057392704131838935292 y2[1] (numeric) = 1.1632086733943687411445398157741 absolute error = 1.29113705292686440777551e-08 relative error = 1.1099788611684251819521049812963e-06 % h = 0.0001 y1[1] (analytic) = 2.5475219605877314356688033156093 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0680964219835284353955153803937 relative error = 2.6730455335434323991122628693673 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5795 y2[1] (analytic) = 1.1632634426856633548813716208217 y2[1] (numeric) = 1.1632634296923997657948434434533 absolute error = 1.29932635890865281773684e-08 relative error = 1.1169665539465907010490716177754e-06 % h = 0.0001 y1[1] (analytic) = 2.5476056369813515958655670097189 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0681800983771485955922790745033 relative error = 2.6762422483071178752600562520658 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5796 y2[1] (analytic) = 1.1633182074329530055201211573387 y2[1] (numeric) = 1.1633181943573803929114066905298 absolute error = 1.30755726126087144668089e-08 relative error = 1.1239893374884975773809712116771e-06 % h = 0.0001 y1[1] (analytic) = 2.5476893078989153908121950518296 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.068263769294712390538907116614 relative error = 2.6794385439019509563933772748037 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5797 y2[1] (analytic) = 1.1633729805470605748569923695864 y2[1] (numeric) = 1.1633729673887613852628269748538 absolute error = 1.31582991895941653947326e-08 relative error = 1.1310473433383893183045103217120e-06 % h = 0.0001 y1[1] (analytic) = 2.5477729733395861113337467501213 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0683474347353831110604588149057 relative error = 2.6826344203578792399359083442615 % h = 0.0001 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.1MB, time=107.19 NO POLE NO POLE x[1] = 0.5798 y2[1] (analytic) = 1.1634277620274383317513660068138 y2[1] (numeric) = 1.1634277487859934178594455252381 absolute error = 1.32414449138919204815757e-08 relative error = 1.1381407033657869391283156335825e-06 % h = 0.0001 y1[1] (analytic) = 2.5478566333025271030242121113838 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0684310946983241027509241761682 relative error = 2.6858298777048472738671934017893 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5799 y2[1] (analytic) = 1.1634825518735384613999210124132 y2[1] (numeric) = 1.1634825385485270779533473814583 absolute error = 1.33250113834465736309549e-08 relative error = 1.1452695497658738525463527013377e-06 % h = 0.0001 y1[1] (analytic) = 2.5479402877869017662548783850701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0685147491826987659815904498545 relative error = 2.689024915972796556466817795252 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.58 y2[1] (analytic) = 1.16353735008481306534211267195 y2[1] (numeric) = 1.1635373366758128650383613942528 absolute error = 1.34090002003037512776972e-08 relative error = 1.1524340150598806874123749273954e-06 % h = 0.0001 y1[1] (analytic) = 2.5480239367918735561826960595765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0685983981876705559094081243609 relative error = 2.6922195351916655360587881093964 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5801 y2[1] (analytic) = 1.1635921566607141614656515977625 y2[1] (numeric) = 1.1635921431673011908500602253227 absolute error = 1.34934129706155913724398e-08 relative error = 1.1596342320954700368211804185845e-06 % h = 0.0001 y1[1] (analytic) = 2.5481075803166059827586443106658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0686820417124029824853563754502 relative error = 2.6954137353913896107561118701734 % h = 0.0001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.1MB, time=107.78 NO POLE NO POLE x[1] = 0.5802 y2[1] (analytic) = 1.1636469716006936840119835500812 y2[1] (numeric) = 1.1636469580224423793657603473317 absolute error = 1.35782513046462232027495e-08 relative error = 1.1668703340471211354632494690333e-06 % h = 0.0001 y1[1] (analytic) = 2.5481912183602626107360959019513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0687656797560596104628079667357 relative error = 2.6986075166019011282055770385341 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5803 y2[1] (analytic) = 1.1637017949042034835817700946091 y2[1] (numeric) = 1.1637017812406866668045220439064 absolute error = 1.36635168167772480507027e-08 relative error = 1.1741424544165144662186607578047e-06 % h = 0.0001 y1[1] (analytic) = 2.5482748509220070596791815373552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0688493123178040594058936021396 relative error = 2.7018008788531293853327312090828 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5804 y2[1] (analytic) = 1.1637566265706953271403700965106 y2[1] (numeric) = 1.1637566128214842016271494096361 absolute error = 1.37492111255132206868745e-08 relative error = 1.1814507270329162959568590607871e-06 % h = 0.0001 y1[1] (analytic) = 2.548358478001003003971153665461 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0689329393968000036978657302454 relative error = 2.7049938221750006280870604292315 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5805 y2[1] (analytic) = 1.1638114665996208980233220507538 y2[1] (numeric) = 1.1638114527642850445361903500727 absolute error = 1.38353358534871317006811e-08 relative error = 1.1887952860535631405085163936608e-06 % h = 0.0001 y1[1] (analytic) = 2.5484420995964141728227497356738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0690165609922111725494618004582 relative error = 2.7081863465974380511873675543065 % h = 0.0001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.1MB, time=108.38 NO POLE NO POLE x[1] = 0.5806 y2[1] (analytic) = 1.16386631499043179594182724875 y2[1] (numeric) = 1.1638663010685391684759365817309 absolute error = 1.39218926274658906670191e-08 relative error = 1.1961762659640461587757156754585e-06 % h = 0.0001 y1[1] (analytic) = 2.5485257157074043502805549061057 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0691001771032013500072669708901 relative error = 2.7113784521503617978673500542115 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5807 y2[1] (analytic) = 1.1639211717425795369882337812375 y2[1] (numeric) = 1.1639211577336964586324236320882 absolute error = 1.40088830783558101491493e-08 relative error = 1.2035938015786954759470684053549e-06 % h = 0.0001 y1[1] (analytic) = 2.5486093263331373752353642031035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0691837877289343749620762678879 relative error = 2.7145701388636889596213771872791 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5808 y2[1] (analytic) = 1.1639760368555155536415213773533 y2[1] (numeric) = 1.1639760227592067124334308395848 absolute error = 1.40963088412080905377685e-08 relative error = 1.2110480280409644357840642048038e-06 % h = 0.0001 y1[1] (analytic) = 2.5486929314727771414305441323332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0692673928685741411572561971176 relative error = 2.7177614067673335759504664568646 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5809 y2[1] (analytic) = 1.1640309103286911947727870798387 y2[1] (numeric) = 1.1640308961445196395484813536236 absolute error = 1.41841715552243057262151e-08 relative error = 1.2185390808238137819451863923782e-06 % h = 0.0001 y1[1] (analytic) = 2.5487765311254875974703937413397 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0693509925212845971971058061241 relative error = 2.7209522558912066341084592664157 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=736.2MB, alloc=4.1MB, time=108.97 x[1] = 0.581 y2[1] (analytic) = 1.1640857921615577256507317563242 y2[1] (numeric) = 1.1640857778890848618888421345702 absolute error = 1.42724728637618896217540e-08 relative error = 1.2260670957300957683143406315737e-06 % h = 0.0001 y1[1] (analytic) = 2.548860125290432746828505133497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0694345866862297465552171982814 relative error = 2.724142686265216068848395688654 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5811 y2[1] (analytic) = 1.1641406823535663279471474466374 y2[1] (numeric) = 1.1641406679923519136075239537529 absolute error = 1.43612144143396234928845e-08 relative error = 1.2336322088929381983000277179957e-06 % h = 0.0001 y1[1] (analytic) = 2.548943713966776647856123433265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0695181753625736475828354980494 relative error = 2.7273326979192667621690882645682 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5812 y2[1] (analytic) = 1.1641955809041680997424055460806 y2[1] (numeric) = 1.1641955664537702410992813934629 absolute error = 1.44503978586431241526177e-08 relative error = 1.2412345567761283930719707794447e-06 % h = 0.0001 y1[1] (analytic) = 2.5490272971536834137905062026699 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0696017585494804135172182674543 relative error = 2.7305222908832605430618947479762 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5813 y2[1] (analytic) = 1.1642504878128140555309458246228 y2[1] (numeric) = 1.1642504732727892030006128469539 absolute error = 1.45400248525303329776689e-08 relative error = 1.2488742761744970887018598698966e-06 % h = 0.0001 y1[1] (analytic) = 2.5491108748503172127632823089255 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0696853362461142124899943737099 relative error = 2.7337114651870961872576897114523 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5814 y2[1] (analytic) = 1.1643054030789551262267662819506 y2[1] (numeric) = 1.1643053884488580701897605184425 absolute error = 1.46300970560370057635081e-08 relative error = 1.2565515042143022621747094316265e-06 % h = 0.0001 y1[1] (analytic) = 2.5491944470558422678088102431088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0697689084516392675355223078932 relative error = 2.7369002208606694169740349292938 % h = 0.0001 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.1MB, time=109.56 NO POLE NO POLE x[1] = 0.5815 y2[1] (analytic) = 1.1643603267020421591689138383233 y2[1] (numeric) = 1.164360311981426025786710423108 absolute error = 1.47206161333822034152153e-08 relative error = 1.2642663783536128862376719775530e-06 % h = 0.0001 y1[1] (analytic) = 2.5492780137694228568725358898106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.069852475165219856599247954595 relative error = 2.7400885579338729006625484535078 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5816 y2[1] (analytic) = 1.1644152586815259181269758611785 y2[1] (numeric) = 1.1644152438699421651531923870923 absolute error = 1.48115837529737834740862e-08 relative error = 1.2720190363826926130530954490439e-06 % h = 0.0001 y1[1] (analytic) = 2.5493615749902233128193497476731 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0699360363860203125460618124575 relative error = 2.7432764764365962527564722984927 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5817 y2[1] (analytic) = 1.164470199016857083306572527431 y2[1] (numeric) = 1.1644701841138554958926800475002 absolute error = 1.49030015874138924799308e-08 relative error = 1.2798096164243833866223840884142e-06 % h = 0.0001 y1[1] (analytic) = 2.5494451307174080234419436007346 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.070019592113205023168655665519 relative error = 2.7464639763987260334184386504247 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5818 y2[1] (analytic) = 1.1645251477074862513548500214126 y2[1] (numeric) = 1.1645251327126149378503908523992 absolute error = 1.49948713135044591690134e-08 relative error = 1.2876382569344889839477765894059e-06 % h = 0.0001 y1[1] (analytic) = 2.5495286809501414314691666404955 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0701031423459384311958787052799 relative error = 2.7496510578501457482884345171619 % h = 0.0001 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.1MB, time=110.15 NO POLE NO POLE x[1] = 0.5819 y2[1] (analytic) = 1.1645801047528639353659745683955 y2[1] (numeric) = 1.1645800896656693231132860608194 absolute error = 1.50871946122526885075761e-08 relative error = 1.2955050967021584848986442253747e-06 % h = 0.0001 y1[1] (analytic) = 2.5496122256875880345743810386228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0701866870833850343010931034072 relative error = 2.7528377208207358482319647346199 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.582 y2[1] (analytic) = 1.1646350701524405648866273036464 y2[1] (numeric) = 1.1646350549724673960100707427537 absolute error = 1.51799731688765565608927e-08 relative error = 1.3034102748502696707493624919807e-06 % h = 0.0001 y1[1] (analytic) = 2.5496957649289123853838169702094 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0702702263247093851105290349938 relative error = 2.7560239653403737290884132455654 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5821 y2[1] (analytic) = 1.1646900439056664859214999769552 y2[1] (numeric) = 1.1646900286324578131111937791578 absolute error = 1.52732086728103061977974e-08 relative error = 1.3113539308358123513556336795977e-06 % h = 0.0001 y1[1] (analytic) = 2.5497792986732790914849270875053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0703537600690760912116391522897 relative error = 2.7592097914389337314196025668305 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5822 y2[1] (analytic) = 1.1647450260119919609387914925832 y2[1] (numeric) = 1.1647450106450891432288478619501 absolute error = 1.53669028177099436306331e-08 relative error = 1.3193362044502716209362107343635e-06 % h = 0.0001 y1[1] (analytic) = 2.5498628269198528154347404440354 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0704372883156498151614525088198 relative error = 2.7623951991462871402585513608867 % h = 0.0001 TOP MAIN SOLVE Loop memory used=747.7MB, alloc=4.1MB, time=110.74 NO POLE NO POLE x[1] = 0.5823 y2[1] (analytic) = 1.1648000164708671688757052845766 y2[1] (numeric) = 1.1648000010098098674169694940116 absolute error = 1.54610573014587357905650e-08 relative error = 1.3273572358200110424270886143215e-06 % h = 0.0001 y1[1] (analytic) = 2.5499463496677982747682158690227 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0705208110635952744949279338071 relative error = 2.7655801884923021848584300279019 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5824 y2[1] (analytic) = 1.1648550152817422051439475273903 y2[1] (numeric) = 1.1648549997260683789712389891862 absolute error = 1.55556738261727085382041e-08 relative error = 1.3354171654066557603751734591632e-06 % h = 0.0001 y1[1] (analytic) = 2.5500298669162802420065947920319 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0706043283120772417333068568163 relative error = 2.7687647595068440384417142342819 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5825 y2[1] (analytic) = 1.1649100224440670816352261817655 y2[1] (numeric) = 1.1649100067933129834290804722804 absolute error = 1.56507540982061457094851e-08 relative error = 1.3435161340074755423384698803707e-06 % h = 0.0001 y1[1] (analytic) = 2.5501133786644635446657535177497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0706878400602605443924655825341 relative error = 2.7719489122197748179495362937783 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5826 y2[1] (analytic) = 1.1649650379572917267267508758087 y2[1] (numeric) = 1.1649650222109918985696618790636 absolute error = 1.57462998281570889967451e-08 relative error = 1.3516542827557677487600283419931e-06 % h = 0.0001 y1[1] (analytic) = 2.550196884911513065264554950819 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0707713463073100649912670156034 relative error = 2.7751326466609535837912343173038 % h = 0.0001 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.1MB, time=111.32 NO POLE NO POLE x[1] = 0.5827 y2[1] (analytic) = 1.1650200618208659852867336212147 y2[1] (numeric) = 1.1650200459785532544138949562677 absolute error = 1.58423127308728386649470e-08 relative error = 1.3598317531212402312827185130431e-06 % h = 0.0001 y1[1] (analytic) = 2.5502803856565937413331997706438 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0708548470523907410599118354282 relative error = 2.7783159628602363395940990476076 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5828 y2[1] (analytic) = 1.16507509403423961867989036458 y2[1] (numeric) = 1.1650750780954450932244352615874 absolute error = 1.59387945254554551029926e-08 relative error = 1.3680486869103941594720274599257e-06 % h = 0.0001 y1[1] (analytic) = 2.5503638808988705654215770560795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0709383422946675651482891208639 relative error = 2.7814988608474760319533182949092 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5829 y2[1] (analytic) = 1.1651301345968623047729433737509 y2[1] (numeric) = 1.1651301185611153695056821636803 absolute error = 1.60357469352672612100706e-08 relative error = 1.3763052262669067759141372425210e-06 % h = 0.0001 y1[1] (analytic) = 2.550447370637508585107614359928 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0710218320333055848343264247124 relative error = 2.7846813406525225501821188897989 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.583 y2[1] (analytic) = 1.165185183508183637940124459152 y2[1] (numeric) = 1.1651851673750119500037788421665 absolute error = 1.61331716879363456169855e-08 relative error = 1.3846015136720140796566436518983e-06 % h = 0.0001 y1[1] (analytic) = 2.5505308548716729030056272331506 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.071105316267469902732339297935 relative error = 2.7878634023052227260621060694901 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=755.3MB, alloc=4.1MB, time=111.91 x[1] = 0.5831 y2[1] (analytic) = 1.165240240767653129068679030039 y2[1] (numeric) = 1.165240224536582613706612287629 absolute error = 1.62310705153620667424100e-08 relative error = 1.3929376919448934379590245245836e-06 % h = 0.0001 y1[1] (analytic) = 2.5506143336005286767746681987182 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0711887949963256765013802635026 relative error = 2.7910450458354203335938002137875 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5832 y2[1] (analytic) = 1.1652953063747202055643709856217 y2[1] (numeric) = 1.1652952900452750518438133016134 absolute error = 1.63294451537205576840083e-08 relative error = 1.4013139042430461263204165660800e-06 % h = 0.0001 y1[1] (analytic) = 2.5506978068232411191268751750141 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0712722682190381188535872397985 relative error = 2.7942262712729560887473708470015 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5833 y2[1] (analytic) = 1.1653503803288342113569884410021 y2[1] (numeric) = 1.1653503639005368678867564966281 absolute error = 1.64282973434702319443740e-08 relative error = 1.4097302940626797967519805370283e-06 % h = 0.0001 y1[1] (analytic) = 2.5507812745389754978358193487052 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0713557359347724975625314134896 relative error = 2.797407078647667649213567822082 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5834 y2[1] (analytic) = 1.1654054626294444069058502878713 y2[1] (numeric) = 1.1654054461018155775485602961442 absolute error = 1.65276288293572899917271e-08 relative error = 1.4181870052390908742612418352639e-06 % h = 0.0001 y1[1] (analytic) = 2.5508647367468971357448524969996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.071439198142694135471564561784 relative error = 2.8005874679893896141548496033587 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5835 y2[1] (analytic) = 1.1654605532759999692053135899123 y2[1] (numeric) = 1.1654605366485586087840869345955 absolute error = 1.66274413604212266553168e-08 relative error = 1.4266841819470468815160207743156e-06 % h = 0.0001 y1[1] (analytic) = 2.5509481934461714107754537592061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0715226548419684105021658239905 relative error = 2.8037674393279535239567085642046 % h = 0.0001 TOP MAIN SOLVE Loop memory used=759.1MB, alloc=4.1MB, time=112.49 NO POLE NO POLE x[1] = 0.5836 y2[1] (analytic) = 1.1655156522679499917902818128517 y2[1] (numeric) = 1.1655156355402133017899424573786 absolute error = 1.67277366900003393554731e-08 relative error = 1.4352219687011686916552878245789e-06 % h = 0.0001 y1[1] (analytic) = 2.5510316446359637559355758575124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0716061060317607556622879222968 relative error = 2.8069469926931878599791932160158 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5837 y2[1] (analytic) = 1.1655707596047434847417138891059 y2[1] (numeric) = 1.1655707427762269090044767208528 absolute error = 1.68285165757372371682531e-08 relative error = 1.4438005103563127092145664227380e-06 % h = 0.0001 y1[1] (analytic) = 2.5511150903154396593279907668987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0716895517112366590547028316831 relative error = 2.810126128114918044308627284925 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5838 y2[1] (analytic) = 1.165625875285829374692134116967 y2[1] (numeric) = 1.1656258583560465951077833923401 absolute error = 1.69297827795843507246269e-08 relative error = 1.4524199521079529791334585966834e-06 % h = 0.0001 y1[1] (analytic) = 2.5511985304837646641586348341029 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0717729918795616638853468988873 relative error = 2.8133048456229664395095255526708 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5839 y2[1] (analytic) = 1.1656809993106565048311428942731 y2[1] (numeric) = 1.1656809822791194370216999501253 absolute error = 1.70315370678094429441478e-08 relative error = 1.4610804394925632238128899531334e-06 % h = 0.0001 y1[1] (analytic) = 2.5512819651401043687449533455543 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0718564265359013684716654103387 relative error = 2.8164831452471523483767063781019 % h = 0.0001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.1MB, time=113.08 NO POLE NO POLE x[1] = 0.584 y2[1] (analytic) = 1.1657361316786736349109282865074 y2[1] (numeric) = 1.1657361145448924239098076834559 absolute error = 1.71337812110011206030515e-08 relative error = 1.4697821183879988081897090313450e-06 % h = 0.0001 y1[1] (analytic) = 2.5513653942836244265242445441924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0719398556794214262509566089768 relative error = 2.8196610270172920136876008158076 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5841 y2[1] (analytic) = 1.1657912723893294412517784292721 y2[1] (numeric) = 1.165791255152812457177431692542 absolute error = 1.72365169840743467367301e-08 relative error = 1.4785251350138786327964088313387e-06 % h = 0.0001 y1[1] (analytic) = 2.5514488179134905460620030950867 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0720232793092875457887151598711 relative error = 2.8228384909631986179547582483676 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5842 y2[1] (analytic) = 1.1658464214420725167475947650807 y2[1] (numeric) = 1.1658464041023263504716408885566 absolute error = 1.73397461662759538765241e-08 relative error = 1.4873096359319669547735537162983e-06 % h = 0.0001 y1[1] (analytic) = 2.5515322360288684910602629997749 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0721066974246654907869750645593 relative error = 2.8260155371146822831785484487969 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5843 y2[1] (analytic) = 1.1659015788363513708714061144144 y2[1] (numeric) = 1.1659015613928808296812479936354 absolute error = 1.74434705411901581207790e-08 relative error = 1.4961357680465551368028249905024e-06 % h = 0.0001 y1[1] (analytic) = 2.5516156486289240803659399592356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.07219011002472108009265202402 relative error = 2.8291921655015500706000599897405 % h = 0.0001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.1MB, time=113.68 NO POLE NO POLE x[1] = 0.5844 y2[1] (analytic) = 1.1659567445716144296808835809872 y2[1] (numeric) = 1.1659567270239225329368095408768 absolute error = 1.75476918967440740401104e-08 relative error = 1.5050036786048433239284052485148e-06 % h = 0.0001 y1[1] (analytic) = 2.5516990557128231879791731854124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0722735171086201877058852501968 relative error = 2.8323683761536059804541949160265 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5845 y2[1] (analytic) = 1.1660119186473100358238562911647 y2[1] (numeric) = 1.1660119009948980106106258743419 absolute error = 1.76524120252132304168228e-08 relative error = 1.5139135151973220482345715262890e-06 % h = 0.0001 y1[1] (analytic) = 2.5517824572797317430616666612052 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0723569186755287427883787259896 relative error = 2.8355441691006509517229595971753 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5846 y2[1] (analytic) = 1.1660671010628864485438279674812 y2[1] (numeric) = 1.1660670833052537253167411490545 absolute error = 1.77576327232270868184267e-08 relative error = 1.5228654257581537613473542237202e-06 % h = 0.0001 y1[1] (analytic) = 2.5518658533288157299450298488463 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0724403147246127296717419136307 relative error = 2.838719544372482861888951676553 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5847 y2[1] (analytic) = 1.1661222918177918436854943362 y2[1] (numeric) = 1.1661222739544360519109433310012 absolute error = 1.78633557917745510051988e-08 relative error = 1.5318595585655542947281743246834e-06 % h = 0.0001 y1[1] (analytic) = 2.5519492438592411881391178465777 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0725237052550381878658299113621 relative error = 2.8418945019988965266890430338428 % h = 0.0001 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.1MB, time=114.27 NO POLE NO POLE x[1] = 0.5848 y2[1] (analytic) = 1.1661774909114743137002613688618 y2[1] (numeric) = 1.1661774729418912774907641971313 absolute error = 1.79695830362094971717305e-08 relative error = 1.5408960622421742477274441321165e-06 % h = 0.0001 y1[1] (analytic) = 2.552032628870174212340370993545 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0726070902659712120670830583294 relative error = 2.8450690420096836998682586774925 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5849 y2[1] (analytic) = 1.1662326983433818676517643577661 y2[1] (numeric) = 1.1662326802670656013954793353569 absolute error = 1.80763162662562850224092e-08 relative error = 1.5499750857554803033660950840769e-06 % h = 0.0001 y1[1] (analytic) = 2.5521160083607809524401539228266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.072690469756577952166865987611 relative error = 2.8482431644346330729338514839512 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.585 y2[1] (analytic) = 1.1662879141129624312213878253303 y2[1] (numeric) = 1.1662878959294051352061081445527 absolute error = 1.81835572960152796807776e-08 relative error = 1.5590967784181364718130946218489e-06 % h = 0.0001 y1[1] (analytic) = 2.5521993823302276135330940625129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0727738437260246132598061272973 relative error = 2.8514168693035302749095727003818 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5851 y2[1] (analytic) = 1.1663431382196638467137862672711 y2[1] (numeric) = 1.1663431199283559027454138345562 absolute error = 1.82913079439683724327149e-08 relative error = 1.5682612898883852615269409768741e-06 % h = 0.0001 y1[1] (analytic) = 2.5522827507776804559254195847529 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0728572121734774556521316495373 relative error = 2.8545901566461578720901381276655 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=774.4MB, alloc=4.1MB, time=114.84 x[1] = 0.5852 y2[1] (analytic) = 1.1663983706629338730624057295537 y2[1] (numeric) = 1.1663983522633638400779034261677 absolute error = 1.83995700329845023033860e-08 relative error = 1.5774687701704287780293517476878e-06 % h = 0.0001 y1[1] (analytic) = 2.5523661137023057951432968026853 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0729405750981027948700088674697 relative error = 2.857763026492295367795889900528 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5853 y2[1] (analytic) = 1.1664536114422201858350062190522 y2[1] (numeric) = 1.16645359293387479550982775115 absolute error = 1.85083453903251784679022e-08 relative error = 1.5867193696148097502791775505702e-06 % h = 0.0001 y1[1] (analytic) = 2.5524494711032700019411670151696 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.073023932499067001667879079954 relative error = 2.8609354788717192021276537815867 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5854 y2[1] (analytic) = 1.1665088605569703772391849478679 y2[1] (numeric) = 1.1665088419393345295891814522289 absolute error = 1.86176358476500034956390e-08 relative error = 1.5960132389187924846147904389788e-06 % h = 0.0001 y1[1] (analytic) = 2.5525328229797395023100827992348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0731072843755365020367948640192 relative error = 2.8641075138142027517217918862193 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5855 y2[1] (analytic) = 1.1665641180066319561279004112484 y2[1] (numeric) = 1.1665640992791887151057029830928 absolute error = 1.87274432410221974281556e-08 relative error = 1.6053505291267437462331493760025e-06 % h = 0.0001 y1[1] (analytic) = 2.5526161693308807774860437501623 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0731906307266777772127558149467 relative error = 2.8672791313495163295054507551487 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5856 y2[1] (analytic) = 1.1666193837906523480049972990536 y2[1] (numeric) = 1.1666193649528829370908746083928 absolute error = 1.88377694109141226906608e-08 relative error = 1.6147313916305135681737919514940e-06 % h = 0.0001 y1[1] (analytic) = 2.5526995101558603639583316691182 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0732739715516573636850437339026 relative error = 2.8704503315074271844520046916062 % h = 0.0001 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.1MB, time=115.40 NO POLE NO POLE x[1] = 0.5857 y2[1] (analytic) = 1.1666746579084788950307322407126 y2[1] (numeric) = 1.1666746389598626928179224037427 absolute error = 1.89486162022128098369699e-08 relative error = 1.6241559781698159877760312887263e-06 % h = 0.0001 y1[1] (analytic) = 2.5527828454538448534778451982544 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0733573068496418532045572630388 relative error = 2.8736211143176995013366942801273 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5858 y2[1] (analytic) = 1.1667299403595588560273003836163 y2[1] (numeric) = 1.1667299212995733918018162557192 absolute error = 1.90599854642254841278971e-08 relative error = 1.6336244408326097105776668344094e-06 % h = 0.0001 y1[1] (analytic) = 2.5528661752240008930654339031921 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0734406366197978927921459679765 relative error = 2.8767914798100944004924600038354 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5859 y2[1] (analytic) = 1.1667852311433394064843628048914 y2[1] (numeric) = 1.1667852119714603557992698618616 absolute error = 1.91718790506850929430298e-08 relative error = 1.6431369320554787016237188818450e-06 % h = 0.0001 y1[1] (analytic) = 2.5529494994654951850202318028063 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0735239608612921847469438675907 relative error = 2.8799614280143699375659708772888 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.586 y2[1] (analytic) = 1.1668405302592676385645747564984 y2[1] (numeric) = 1.1668405109749688188087407306719 absolute error = 1.92842988197558340258265e-08 relative error = 1.6526936046240127041533321256120e-06 % h = 0.0001 y1[1] (analytic) = 2.553032818177494486927990346228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0736072795732914866547024110124 relative error = 2.8831309589602811032738480119188 % h = 0.0001 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.1MB, time=115.97 NO POLE NO POLE x[1] = 0.5861 y2[1] (analytic) = 1.1668958377067905611091147436013 y2[1] (numeric) = 1.1668958183095439270704301816149 absolute error = 1.93972466340386845619864e-08 relative error = 1.6622946116731876856335804004331e-06 % h = 0.0001 y1[1] (analytic) = 2.5531161313591656116694108369795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0736905927549626113961229017639 relative error = 2.8863000726775798231590830310643 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5862 y2[1] (analytic) = 1.1669511534853550996432144361505 y2[1] (numeric) = 1.1669511339746307390662833451181 absolute error = 1.95107243605769310910324e-08 relative error = 1.6719401066877462111083944938868e-06 % h = 0.0001 y1[1] (analytic) = 2.55319943900967542742847630416 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0737739004054724271551883689444 relative error = 2.889468769196014957347651251704 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5863 y2[1] (analytic) = 1.1670064775944080963816894136262 y2[1] (numeric) = 1.1670064579696742255199891625717 absolute error = 1.96247338708617002510545e-08 relative error = 1.6816302435025777438313274508233e-06 % h = 0.0001 y1[1] (analytic) = 2.5532827411281908577007828205998 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0738572025239878574274948853842 relative error = 2.8926370485453323003053195500541 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5864 y2[1] (analytic) = 1.1670618100333963102344707428856 y2[1] (numeric) = 1.1670617902941192693969803863288 absolute error = 1.97392770408374903565568e-08 relative error = 1.6913651763030988731505843779542e-06 % h = 0.0001 y1[1] (analytic) = 2.5533660377138788813018702678965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0739404991096758810285823326809 relative error = 2.895804910755274580594648828041 % h = 0.0001 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.1MB, time=116.55 NO POLE NO POLE x[1] = 0.5865 y2[1] (analytic) = 1.1671171508017664168121373890589 y2[1] (numeric) = 1.1671171309474106659044335797049 absolute error = 1.98543557509077038093540e-08 relative error = 1.7011450596256334696150134064968e-06 % h = 0.0001 y1[1] (analytic) = 2.553449328765906532375552548253 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0740237901617035321022646130374 relative error = 2.8989723558555814606321909979281 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5866 y2[1] (analytic) = 1.1671724998989650084314494594392 y2[1] (numeric) = 1.1671724799289931224912691169786 absolute error = 1.99699718859401803424606e-08 relative error = 1.7109700483577927672695613569529e-06 % h = 0.0001 y1[1] (analytic) = 2.5535326142834409004022472430324 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0741070756792379001289593078168 relative error = 2.9021393838759895364458804022228 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5867 y2[1] (analytic) = 1.1672278573244385941208822803097 y2[1] (numeric) = 1.1672278372383112588481511833909 absolute error = 2.00861273352727310969188e-08 relative error = 1.7208402977388553731089758289925e-06 % h = 0.0001 y1[1] (analytic) = 2.5536158942656491302073047179472 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0741903556614461299340167827316 relative error = 2.9053059948462323374326195861041 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5868 y2[1] (analytic) = 1.1672832230776335996261613066551 y2[1] (numeric) = 1.1672832028748096069074877751457 absolute error = 2.02028239927186735315094e-08 relative error = 1.7307559633601472036584279973769e-06 % h = 0.0001 y1[1] (analytic) = 2.5536991687116984219693366747982 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0742736301074954216960487395826 relative error = 2.9084721887960403261160593395628 % h = 0.0001 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.1MB, time=117.12 NO POLE NO POLE x[1] = 0.5869 y2[1] (analytic) = 1.1673385971579963674157978646988 y2[1] (numeric) = 1.1673385768379326108434306994097 absolute error = 2.03200637565723671652891e-08 relative error = 1.7407172011654213486496915389837e-06 % h = 0.0001 y1[1] (analytic) = 2.5537824376207560312285441496819 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0743568990165530309552562144663 relative error = 2.9116379657551408979045729265997 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.587 y2[1] (analytic) = 1.1673939795649731566866257272142 y2[1] (numeric) = 1.1673939591271246270718755743121 absolute error = 2.04378485296147501529021e-08 relative error = 1.7507241674512378617619368538014e-06 % h = 0.0001 y1[1] (analytic) = 2.5538657009919892688950449575815 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0744401623877862686217570223659 relative error = 2.9148033257532583808494244187152 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5871 y2[1] (analytic) = 1.1674493702980101433693385215508 y2[1] (numeric) = 1.1674493497418299242504618289451 absolute error = 2.05561802191188766926057e-08 relative error = 1.7607770188673434783955354663853e-06 % h = 0.0001 y1[1] (analytic) = 2.5539489588245655012572005832587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0745234202203625009839126480431 relative error = 2.9179682688201140354031310500293 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5872 y2[1] (analytic) = 1.1675047693565534201340279703235 y2[1] (numeric) = 1.1675047486814926832785727033634 absolute error = 2.06750607368554552669601e-08 relative error = 1.7708759124170512604482072163046e-06 % h = 0.0001 y1[1] (analytic) = 2.5540322111176521499899425183632 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0746066725134491497166545831476 relative error = 2.9211327949854260541780195113852 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=793.4MB, alloc=4.1MB, time=117.69 x[1] = 0.5873 y2[1] (analytic) = 1.1675601767400489963957229647063 y2[1] (numeric) = 1.1675601559455569972973352485845 absolute error = 2.07944919990983877161218e-08 relative error = 1.7810210054576201680619558589608e-06 % h = 0.0001 y1[1] (analytic) = 2.5541154578704166921630980446764 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0746899192662136918898101094608 relative error = 2.9242969042789095617049761008014 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5874 y2[1] (analytic) = 1.167615592447942798319929470278 y2[1] (numeric) = 1.1676155715334668716896203265887 absolute error = 2.09144759266303091436893e-08 relative error = 1.7912124557006345583100735549851e-06 % h = 0.0001 y1[1] (analytic) = 2.5541986990820266602497154634062 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0747731604778236599764275281906 relative error = 2.9274605967302766141923906476807 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5875 y2[1] (analytic) = 1.1676710164796806688281712653621 y2[1] (numeric) = 1.167670995444666224080042610319 absolute error = 2.10350144447481286550431e-08 relative error = 1.8014504212123836107929589860437e-06 % h = 0.0001 y1[1] (analytic) = 2.5542819347516496421343887704497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0748563961474466418611008352341 relative error = 2.9306238723692361992852941282031 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5876 y2[1] (analytic) = 1.1677264488347083676035315118072 y2[1] (numeric) = 1.167726427678598884334960583681 absolute error = 2.11561094832685709281262e-08 relative error = 1.8117350604142406801118917693238e-06 % h = 0.0001 y1[1] (analytic) = 2.55436516487845328112158177754 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0749396262742502808482938423244 relative error = 2.9337867312254942358246898893378 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5877 y2[1] (analytic) = 1.1677818895124715710961951581514 y2[1] (numeric) = 1.1677818682347085945624765415432 absolute error = 2.12777629765337186166082e-08 relative error = 1.8220665320830425751896784989586e-06 % h = 0.0001 y1[1] (analytic) = 2.554448389461605275943951679195 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0750228508574022756706637439794 relative error = 2.9369491733287535736070783989967 % h = 0.0001 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.1MB, time=118.26 NO POLE NO POLE x[1] = 0.5878 y2[1] (analytic) = 1.1678373385124158725289921751159 y2[1] (numeric) = 1.1678373171124390091124365897368 absolute error = 2.13999768634165555853791e-08 relative error = 1.8324449953514687654073808369893e-06 % h = 0.0001 y1[1] (analytic) = 2.5545316085002733807706720653838 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0751060698960703804973841301682 relative error = 2.9401111987087139931441754397934 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5879 y2[1] (analytic) = 1.1678927958339867819029416233722 y2[1] (numeric) = 1.1678927743112336945764306450556 absolute error = 2.15227530873265109783166e-08 relative error = 1.8428706097084205135261772441493e-06 % h = 0.0001 y1[1] (analytic) = 2.5546148219936254052157553798277 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0751892833894224049424674446121 relative error = 2.9432728073950722054228236639501 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.588 y2[1] (analytic) = 1.1679482614766297260027965535271 y2[1] (numeric) = 1.1679482398305361297877924352562 absolute error = 2.16460935962150041182709e-08 relative error = 1.8533435349993999353634652350782e-06 % h = 0.0001 y1[1] (analytic) = 2.5546980299408292143463748238537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0752724913366262140730868886381 relative error = 2.9464339994175218516650974269552 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5881 y2[1] (analytic) = 1.1680037354397900484025897382705 y2[1] (numeric) = 1.168003713669789705821599499058 absolute error = 2.17700003425809902392125e-08 relative error = 1.8638639314268889861924776224682e-06 % h = 0.0001 y1[1] (analytic) = 2.5547812323410527286911857057154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0753556937368497284178977704998 relative error = 2.9495947748057535030886008174877 % h = 0.0001 TOP MAIN SOLVE Loop memory used=801.1MB, alloc=4.1MB, time=118.83 NO POLE NO POLE x[1] = 0.5882 y2[1] (analytic) = 1.1680592177229130094711802366307 y2[1] (numeric) = 1.1680591958284377259946731861431 absolute error = 2.18944752834765070504876e-08 relative error = 1.8744319595507283738346472624772e-06 % h = 0.0001 y1[1] (analytic) = 2.5548644291934639242486462352996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.075438890589260923975358300084 relative error = 2.95275513358945466066695880128 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5883 y2[1] (analytic) = 1.168114708325443786377800790281 y2[1] (numeric) = 1.1681146863059234058655786571563 absolute error = 2.20195203805122221331247e-08 relative error = 1.8850477802884963984139073255658e-06 % h = 0.0001 y1[1] (analytic) = 2.5549476204972308324953377641349 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0755220818930278322220498289193 relative error = 2.9559150757983097548905013965388 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5884 y2[1] (analytic) = 1.1681702072468274730976060518428 y2[1] (numeric) = 1.1681701851016898732346248837051 absolute error = 2.21451375998629811681377e-08 relative error = 1.8957115549158877187422977878796e-06 % h = 0.0001 y1[1] (analytic) = 2.5550308062515215403942844706189 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0756052676473185401209965354033 relative error = 2.9590746014620001455271407985863 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5885 y2[1] (analytic) = 1.1682257144865090804172216451294 y2[1] (numeric) = 1.1682256922151801681438646483597 absolute error = 2.22713289122733569967697e-08 relative error = 1.9064234450670920453061927591662e-06 % h = 0.0001 y1[1] (analytic) = 2.555113986455504190403272490381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0756884478513011901299845551654 relative error = 2.96223371061020412138344137142 % h = 0.0001 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.1MB, time=119.40 NO POLE NO POLE x[1] = 0.5886 y2[1] (analytic) = 1.1682812300439335359402940572751 y2[1] (numeric) = 1.1682812076458372428770945446532 absolute error = 2.23980962930631995126219e-08 relative error = 1.9171836127351727598225184907449e-06 % h = 0.0001 y1[1] (analytic) = 2.5551971611083469804831684916976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.075771622504143980209880556482 relative error = 2.965392403272596900065882423912 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5887 y2[1] (analytic) = 1.1683367539185456840930413626944 y2[1] (numeric) = 1.1683367313931039619598549770812 absolute error = 2.25254417221331863856132e-08 relative error = 1.9279922202724454613344727108208e-06 % h = 0.0001 y1[1] (analytic) = 2.5552803302092181641062376958765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0758547916050151638329497606609 relative error = 2.968550679478850627742313688394 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5888 y2[1] (analytic) = 1.1683922861097902861298047788146 y2[1] (numeric) = 1.1683922634564231021594301611022 absolute error = 2.26533671839703746177124e-08 relative error = 1.9388494303908564388159773063845e-06 % h = 0.0001 y1[1] (analytic) = 2.5553634937572860502644613425274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0759379551530830499911734073118 relative error = 2.9717085392586343789036034194034 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5889 y2[1] (analytic) = 1.1684478266171120201386010535284 y2[1] (numeric) = 1.1684478038352373524848481231374 absolute error = 2.27818746676537529303910e-08 relative error = 1.9497554061623610702546565896465e-06 % h = 0.0001 y1[1] (analytic) = 2.555446651751719003477853599635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0760211131475160032045656644194 relative error = 2.9748659826416141561254790303778 % h = 0.0001 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.1MB, time=119.97 NO POLE NO POLE x[1] = 0.589 y2[1] (analytic) = 1.1685033754399554810466756843086 y2[1] (numeric) = 1.1685033525289893141868807005707 absolute error = 2.29109661668597949837379e-08 relative error = 1.9607103110193021481825979557947e-06 % h = 0.0001 y1[1] (analytic) = 2.5555298041916854438027779183523 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0761042655874824435294899831367 relative error = 2.9780230096574528898305601861543 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5891 y2[1] (analytic) = 1.1685589325777651806260569689315 y2[1] (numeric) = 1.1685589095371215007580435417487 absolute error = 2.30406436798680134271828e-08 relative error = 1.9717143087547881316246605657130e-06 % h = 0.0001 y1[1] (analytic) = 2.5556129510763538468402628324293 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0761874124721508465669748972137 relative error = 2.9811796203358104380505842690629 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5892 y2[1] (analytic) = 1.1686144980299855474991108877513 y2[1] (numeric) = 1.1686144748590763379325961059807 absolute error = 2.31709092095665147817706e-08 relative error = 1.9827675635230713244337505903357e-06 % h = 0.0001 y1[1] (analytic) = 2.5556960924048927437443172021966 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.076270553800689743471029266981 relative error = 2.9843358147063435861888241365946 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5893 y2[1] (analytic) = 1.1686700717960609271440968174727 y2[1] (numeric) = 1.1686700484942961636865416635388 absolute error = 2.33017647634575551539339e-08 relative error = 1.9938702398399259799829303892124e-06 % h = 0.0001 y1[1] (analytic) = 2.5557792281764707212302449030178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0763536895722677209569569678022 relative error = 2.9874915927987060467826980884386 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=812.5MB, alloc=4.1MB, time=120.54 x[1] = 0.5894 y2[1] (analytic) = 1.1687256538754355819007240763629 y2[1] (numeric) = 1.1687256304422232282376272956579 absolute error = 2.34332123536630967807050e-08 relative error = 2.0050225025830263321837792332778e-06 % h = 0.0001 y1[1] (analytic) = 2.5558623583902564215829589581301 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0764368197860534213096710229145 relative error = 2.9906469546425484592665719609163 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5895 y2[1] (analytic) = 1.1687812442675536909757093008502 y2[1] (numeric) = 1.1687812207022996940453438945355 absolute error = 2.35652539969303654063147e-08 relative error = 2.0162245169923245528009661065274e-06 % h = 0.0001 y1[1] (analytic) = 2.5559454830454185426652951157875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0765199444412155423920071805719 relative error = 2.9938019002675183897347532666786 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5896 y2[1] (analytic) = 1.1688368429718593504483346534523 y2[1] (numeric) = 1.1688368192739676358109261633319 absolute error = 2.36978917146374084901204e-08 relative error = 2.0274764486704286350326223816433e-06 % h = 0.0001 y1[1] (analytic) = 2.5560286021411258379263248706262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0766030635369228376530369354106 relative error = 2.9969564297032603307046772977555 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5897 y2[1] (analytic) = 1.1688924499877965732760068619787 y2[1] (numeric) = 1.16889242615666904047735261617 absolute error = 2.38311275327986542458087e-08 relative error = 2.0387784635829802033263712254711e-06 % h = 0.0001 y1[1] (analytic) = 2.5561117156765471164096679291665 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0766861770723441161363799939509 relative error = 3.000110542979415700880285109871 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5898 y2[1] (analytic) = 1.1689480653148092892998170899519 y2[1] (numeric) = 1.1689480413498458072293455781356 absolute error = 2.39649634820704715118163e-08 relative error = 2.0501307280590322494007888011949e-06 % h = 0.0001 y1[1] (analytic) = 2.5561948236508512427618041193698 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0767692850466482424885161841542 relative error = 3.0032642401256228449155933061286 % h = 0.0001 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.1MB, time=121.12 NO POLE NO POLE x[1] = 0.5899 y2[1] (analytic) = 1.1690036889523413452501016381922 y2[1] (numeric) = 1.1690036648529397474933711852772 absolute error = 2.40994015977567304529150e-08 relative error = 2.0615334087914267944422814339189e-06 % h = 0.0001 y1[1] (analytic) = 2.5562779260632071372403847441673 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0768523874590041369670968089517 relative error = 3.0064175211715170331784555381202 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.59 y2[1] (analytic) = 1.1690593208998365047520034775093 y2[1] (numeric) = 1.1690592966653925849376393846059 absolute error = 2.42344439198143640929034e-08 relative error = 2.0729866728371724774471271225527e-06 % h = 0.0001 y1[1] (analytic) = 2.5563610229127837757225433788758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0769354843085807754492554436602 relative error = 3.0095703861467304615145156424937 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5901 y2[1] (analytic) = 1.1691149611567384483310346124465 y2[1] (numeric) = 1.1691149367866459554721039340956 absolute error = 2.43700924928589306783509e-08 relative error = 2.0844906876178220696787244216392e-06 % h = 0.0001 y1[1] (analytic) = 2.5564441141987501897132061124199 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0770185755945471894399181772043 relative error = 3.0127228350808922510113523311882 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5902 y2[1] (analytic) = 1.1691706097224907734186392760209 y2[1] (numeric) = 1.169170585216141407248462402683 absolute error = 2.45063493661701768733379e-08 relative error = 2.0960456209198499152099842448805e-06 % h = 0.0001 y1[1] (analytic) = 2.5565271999202754663534012322758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0771016613160724660801132970602 relative error = 3.0158748680036284477628153534157 % h = 0.0001 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.1MB, time=121.69 NO POLE NO POLE x[1] = 0.5903 y2[1] (analytic) = 1.1692262665965369943577579554042 y2[1] (numeric) = 1.1692262419533204006601561702675 absolute error = 2.46432165936976017851367e-08 relative error = 2.1076516408950292975208894354107e-06 % h = 0.0001 y1[1] (analytic) = 2.5566102800765287484285683530542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0771847414723257481552804178386 relative error = 3.0190264849445620226335530475845 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5904 y2[1] (analytic) = 1.1692819317783205424083922484887 y2[1] (numeric) = 1.1692819069976243083423704277111 absolute error = 2.47806962340660218207776e-08 relative error = 2.1193089160608097321212848972557e-06 % h = 0.0001 y1[1] (analytic) = 2.5566933546666792343768669886384 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0772678160624762341035790534228 relative error = 3.0221776859333128710237312013272 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5905 y2[1] (analytic) = 1.1693376052672847657531705512829 y2[1] (numeric) = 1.1693375803484944151720341768387 absolute error = 2.49187903505811363744442e-08 relative error = 2.1310176153006941851689562641498e-06 % h = 0.0001 y1[1] (analytic) = 2.5567764236898961782974845677966 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.077350885085693178024196632581 relative error = 3.0253284709994978126339431379395 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5906 y2[1] (analytic) = 1.1693932870628729295029145760801 y2[1] (numeric) = 1.1693932620053719182678202304378 absolute error = 2.50575010112350943456423e-08 relative error = 2.1427779078646162180531272365193e-06 % h = 0.0001 y1[1] (analytic) = 2.5568594871453488899589438931825 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0774339485411458896856559579669 relative error = 3.0284788401727305912303109473697 % h = 0.0001 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.1MB, time=122.24 NO POLE NO POLE x[1] = 0.5907 y2[1] (analytic) = 1.169448977164528215702206700346 y2[1] (numeric) = 1.1694489519676979269901452122587 absolute error = 2.51968302887120614880873e-08 relative error = 2.1545899633693170579135864000300e-06 % h = 0.0001 y1[1] (analytic) = 2.5569425450322067348074100436434 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0775170064280037345341221084278 relative error = 3.0316287934826218744097777801229 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5908 y2[1] (analytic) = 1.169504675571693723334958146268 y2[1] (numeric) = 1.1695046502349134629411695570144 absolute error = 2.53367802603937885892536e-08 relative error = 2.1664539517987225940655725329913e-06 % h = 0.0001 y1[1] (analytic) = 2.5570255973496391339749967197514 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0776000587454361337017087845358 relative error = 3.0347783309587792533655911223314 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5909 y2[1] (analytic) = 1.1695603822838124683299779909115 y2[1] (numeric) = 1.1695603568064594599647975103807 absolute error = 2.54773530083651804805308e-08 relative error = 2.1783700435043203003006965026384e-06 % h = 0.0001 y1[1] (analytic) = 2.5571086440968155642880720324759 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0776831054926125640147840972603 relative error = 3.037927452630807242652976970369 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.591 y2[1] (analytic) = 1.1696160973003273835665430069271 y2[1] (numeric) = 1.169616071681776764146677128996 absolute error = 2.56185506194198658779311e-08 relative error = 2.1903384092055360830341815401084e-06 % h = 0.0001 y1[1] (analytic) = 2.5571916852729055582755637349123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0777661466687025580022757996967 relative error = 3.0410761585283072799550048232859 % h = 0.0001 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.1MB, time=122.81 NO POLE NO POLE x[1] = 0.5911 y2[1] (analytic) = 1.1696718206206813188799683337533 y2[1] (numeric) = 1.1696717948603061338142002804616 absolute error = 2.57603751850657680532917e-08 relative error = 2.2023592199901110552686902810983e-06 % h = 0.0001 y1[1] (analytic) = 2.5572747208770787041772638969861 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0778491822728757039039759617705 relative error = 3.0442244486808777258486434115325 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5912 y2[1] (analytic) = 1.1697275522443170410671789792586 y2[1] (numeric) = 1.1697275263414882395365026433413 absolute error = 2.59028288015306763359173e-08 relative error = 2.2144326473144782363451560008683e-06 % h = 0.0001 y1[1] (analytic) = 2.5573577509085046459521330230484 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0779322123043016456788450878328 relative error = 3.0473723231181138635710070803439 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5913 y2[1] (analytic) = 1.1697832921706772338922821517677 y2[1] (numeric) = 1.1697832661247636641244637071618 absolute error = 2.60459135697678184446059e-08 relative error = 2.2265588630041391774509109028435e-06 % h = 0.0001 y1[1] (analytic) = 2.5574407753663530832866036122786 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.078015236762150083013315677063 relative error = 3.0505197818696078987857927461751 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5914 y2[1] (analytic) = 1.1698390403992044980921404224158 y2[1] (numeric) = 1.1698390142095729026307067724125 absolute error = 2.61896315954614336500033e-08 relative error = 2.2387380392540405128556302873758e-06 % h = 0.0001 y1[1] (analytic) = 2.5575237942497937716028831618139 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0780982556455907713295952265983 relative error = 3.0536668249649489593499073447488 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=831.6MB, alloc=4.1MB, time=123.37 x[1] = 0.5915 y2[1] (analytic) = 1.1698947969293413513819457177752 y2[1] (numeric) = 1.1698947705953563623495989505455 absolute error = 2.63339849890323467672297e-08 relative error = 2.2509703486289504368454782987275e-06 % h = 0.0001 y1[1] (analytic) = 2.55760680755799652206725661252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0781812689537935217939686773044 relative error = 3.0568134524337230950802856891043 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5916 y2[1] (analytic) = 1.1699505617605302284607941426988 y2[1] (numeric) = 1.1699505352815543628172511639756 absolute error = 2.64789758656435429787232e-08 relative error = 2.2632559640638351063259984952157e-06 % h = 0.0001 y1[1] (analytic) = 2.5576898152901312015983882373213 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0782642766859282013251003021057 relative error = 3.0599596643055132775208986562131 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5917 y2[1] (analytic) = 1.1700063348922134810172616333246 y2[1] (numeric) = 1.1700063082676071358115181460804 absolute error = 2.66246063452057434872442e-08 relative error = 2.2755950588642349690642619412929e-06 % h = 0.0001 y1[1] (analytic) = 2.5577728174453677328756229720073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0783472788411647326023350367917 relative error = 3.0631054606098993997099516206884 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5918 y2[1] (analytic) = 1.1700621163238333777349804401852 y2[1] (numeric) = 1.1700620895529548253519984412002 absolute error = 2.67708785523829819989850e-08 relative error = 2.2879878067066410175408490070722e-06 % h = 0.0001 y1[1] (analytic) = 2.5578558140228760943472871884324 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0784302754186730940739992532168 relative error = 3.0662508413764582759472730541653 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5919 y2[1] (analytic) = 1.1701179060548321042982164413665 y2[1] (numeric) = 1.170117879137037487700034404638 absolute error = 2.69177946165981820367285e-08 relative error = 2.3004343816388709683822447049448e-06 % h = 0.0001 y1[1] (analytic) = 2.5579388050218263202389889100258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0785132664176233199657009748102 relative error = 3.0693958066347636415618932089306 % h = 0.0001 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.1MB, time=123.94 NO POLE NO POLE x[1] = 0.592 y2[1] (analytic) = 1.1701737040846517633974472856612 y2[1] (numeric) = 1.1701736770192950913587122026596 absolute error = 2.70653566720387350830016e-08 relative error = 2.3129349580804453673444105037154e-06 % h = 0.0001 y1[1] (analytic) = 2.5580217904413885005619174695279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0785962518371855002886295343123 relative error = 3.0725403564143861526798128044012 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5921 y2[1] (analytic) = 1.1702295104127343747349413656586 y2[1] (numeric) = 1.1702294831991675170728618124934 absolute error = 2.72135668576620795531652e-08 relative error = 2.3254897108229636198180171525946e-06 % h = 0.0001 y1[1] (analytic) = 2.5581047702807327811211426088724 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0786792316765297808478546736568 relative error = 3.0756844907448933859919616351776 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5922 y2[1] (analytic) = 1.1702853250385218750303376207177 y2[1] (numeric) = 1.1702852976760945578290570223307 absolute error = 2.73624273172012805983870e-08 relative error = 2.3380988150304799468262283603765e-06 % h = 0.0001 y1[1] (analytic) = 2.5581877445390293635239130211279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0787622059348263632506250859123 relative error = 3.0788282096558498385223470192237 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5923 y2[1] (analytic) = 1.1703411479614561180262261697658 y2[1] (numeric) = 1.1703411204495159188556154313253 absolute error = 2.75119401991706107384405e-08 relative error = 2.3507624462398792664857236611043e-06 % h = 0.0001 y1[1] (analytic) = 2.558270713215448505187954334419 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0788451746112455049146663992034 relative error = 3.0819715131768169273963920049834 % h = 0.0001 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.1MB, time=124.50 NO POLE NO POLE x[1] = 0.5924 y2[1] (analytic) = 1.1703969791809788744937297738683 y2[1] (numeric) = 1.170396951518871217622598449594 absolute error = 2.76621076568711313242743e-08 relative error = 2.3634807803612530009017464214062e-06 % h = 0.0001 y1[1] (analytic) = 2.5583536763091605193497665377419 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0789281377049575190764786025263 relative error = 3.0851144013373529896094632560814 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5925 y2[1] (analytic) = 1.1704528186965318322380861285129 y2[1] (numeric) = 1.1704527908835999838418112982161 absolute error = 2.78129318483962748302968e-08 relative error = 2.3762539936782748084680861653836e-06 % h = 0.0001 y1[1] (analytic) = 2.5584366338193357750729208485925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0790110952151327747996329133769 relative error = 3.0882568741670132817955885323969 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5926 y2[1] (analytic) = 1.170508666507556596104230985552 y2[1] (numeric) = 1.1705086385431416594668030092338 absolute error = 2.79644149366374279763182e-08 relative error = 2.3890822628485762415426687499421e-06 % h = 0.0001 y1[1] (analytic) = 2.5585195857451446972563560223238 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0790940471409416969830680871082 relative error = 3.0913989316953499799963636862765 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5927 y2[1] (analytic) = 1.1705645226134946879823821047492 y2[1] (numeric) = 1.1705644944969355986928664256519 absolute error = 2.81165590892895156790973e-08 relative error = 2.4019657649041223294699441632403e-06 % h = 0.0001 y1[1] (analytic) = 2.5586025320857577666426741031497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0791769934815547663693861679341 relative error = 3.0945405739519121794300490926931 % h = 0.0001 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.1MB, time=125.06 NO POLE NO POLE x[1] = 0.5928 y2[1] (analytic) = 1.1706203870137875468136240348724 y2[1] (numeric) = 1.170620358744421067957038201438 absolute error = 2.82693664788565858334344e-08 relative error = 2.4149046772515870869207697320997e-06 % h = 0.0001 y1[1] (analytic) = 2.5586854728403455198264356167117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0792599342361425195531476814961 relative error = 3.097681800966245894260855432159 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5929 y2[1] (analytic) = 1.1706762597078765285954937242781 y2[1] (numeric) = 1.1706762312850372459380988015224 absolute error = 2.84228392826573949227557e-08 relative error = 2.4278991776727289475208745895134e-06 % h = 0.0001 y1[1] (analytic) = 2.5587684080080785492624542041271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0793428694038755489891662689115 relative error = 3.1008226127678940573684187453073 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.593 y2[1] (analytic) = 1.1707321406952029063875669609314 y2[1] (numeric) = 1.1707321121182232235565725017982 absolute error = 2.85769796828309944591332e-08 relative error = 2.4409494443247661227389093680963e-06 % h = 0.0001 y1[1] (analytic) = 2.5588513375881275032740906974331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0794257989839245030008027622175 relative error = 3.103963009386396520117464677924 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5931 y2[1] (analytic) = 1.170788029975207870317045641806 y2[1] (numeric) = 1.1707880012434180039747273891211 absolute error = 2.87317898663423182526849e-08 relative error = 2.4540556557407518860051911503175e-06 % h = 0.0001 y1[1] (analytic) = 2.5589342615796630860615466363469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0795087229754600857882587011313 relative error = 3.1071029908512900521276618354528 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=846.8MB, alloc=4.1MB, time=125.63 x[1] = 0.5932 y2[1] (analytic) = 1.1708439275473325275843458716069 y2[1] (numeric) = 1.1708438986600605025965753613096 absolute error = 2.88872720249877705102973e-08 relative error = 2.4672179908299497820320522627791e-06 % h = 0.0001 y1[1] (analytic) = 2.5590171799818560577101572262565 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0795916413776530574368692910409 relative error = 3.1102425571921083410436641658182 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5933 y2[1] (analytic) = 1.170899833411017902468686890762 y2[1] (numeric) = 1.1708998043675895470678721271449 absolute error = 2.90434283554008147636171e-08 relative error = 2.4804366288782087613071577661489e-06 % h = 0.0001 y1[1] (analytic) = 2.5591000927938772341986837373605 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0796745541896742339253958021449 relative error = 3.1133817084383819923053422895742 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5934 y2[1] (analytic) = 1.1709557475657049363336808326251 y2[1] (numeric) = 1.170955718365443877276117206371 absolute error = 2.92002610590575636262541e-08 relative error = 2.4937117495483382397307756449915e-06 % h = 0.0001 y1[1] (analytic) = 2.5591830000148974874076053448736 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.079757461410694487134317409658 relative error = 3.1165204446196385289182036963499 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5935 y2[1] (analytic) = 1.1710116700108344876329233098352 y2[1] (numeric) = 1.1710116406530621453505539296945 absolute error = 2.93577723422823693801407e-08 relative error = 2.5070435328804830833683118143032e-06 % h = 0.0001 y1[1] (analytic) = 2.5592659016440877451274104102148 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0798403630398847448541224749992 relative error = 3.1196587657654023912240017266039 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5936 memory used=850.7MB, alloc=4.1MB, time=126.20 y2[1] (analytic) = 1.1710676007458473319155848297757 y2[1] (numeric) = 1.1710675712298829156621694387848 absolute error = 2.95159644162534153909909e-08 relative error = 2.5204321592924985182892462247999e-06 % h = 0.0001 y1[1] (analytic) = 2.5593487976806189910668872030958 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0799232590764159907935992678802 relative error = 3.1227966719051949366715332577405 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5937 y2[1] (analytic) = 1.1711235397701841618320030390784 y2[1] (numeric) = 1.1711235100953446648236946862741 absolute error = 2.96748394970083083528043e-08 relative error = 2.5338778095803249654638660765085e-06 % h = 0.0001 y1[1] (analytic) = 2.559431688123662264861414064426 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0800061495194592645881261292104 relative error = 3.1259341630685344395876250136283 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5938 y2[1] (analytic) = 1.171179487083285587139275797115 y2[1] (numeric) = 1.1711794572488857816896044357573 absolute error = 2.98343998054496713613577e-08 relative error = 2.5473806649183628006889821614540e-06 % h = 0.0001 y1[1] (analytic) = 2.5595145729723886620812490099519 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0800890343681856618079610747363 relative error = 3.1290712392849360909483084166385 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5939 y2[1] (analytic) = 1.1712354426845921347068550784218 y2[1] (numeric) = 1.1712354126899445673561172617919 absolute error = 2.99946475673507378166299e-08 relative error = 2.5609409068598470395141082067370e-06 % h = 0.0001 y1[1] (analytic) = 2.5595974522259693342398187745477 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0801719136217663339665308393321 relative error = 3.1322079005839119981501829013099 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.594 y2[1] (analytic) = 1.1712914065735442485221417040005 y2[1] (numeric) = 1.1712913764179592351611955498983 absolute error = 3.01555850133609461541022e-08 relative error = 2.5745587173372219471393560281950e-06 % h = 0.0001 y1[1] (analytic) = 2.559680325883575488802007297074 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0802547872793724885287193618584 relative error = 3.1353441469949711847819676087763 % h = 0.0001 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.1MB, time=126.77 NO POLE NO POLE x[1] = 0.5941 y2[1] (analytic) = 1.1713473787495822896960809014392 y2[1] (numeric) = 1.1713473484323679106845454965595 absolute error = 3.03172143790115354048797e-08 relative error = 2.5882342786625155732565589678325e-06 % h = 0.0001 y1[1] (analytic) = 2.5597631939443783891924436457219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0803376553401753889191557105063 relative error = 3.1384799785476195903962413811338 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5942 y2[1] (analytic) = 1.1714033592121465364687586937988 y2[1] (numeric) = 1.1714033287326086317476171092212 absolute error = 3.04795379047211415845776e-08 relative error = 2.6019677735277142118050968600152e-06 % h = 0.0001 y1[1] (analytic) = 2.5598460564075493548037893837604 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0804205178033463545305014485448 relative error = 3.1416153952713600702813709749732 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5943 y2[1] (analytic) = 1.1714593479606771842149991172071 y2[1] (numeric) = 1.171459317318119348413604206292 absolute error = 3.06425578358013949109151e-08 relative error = 2.6157593850051367856137968129247e-06 % h = 0.0001 y1[1] (analytic) = 2.5599289132722597610050253756021 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0805033746680567607317374403865 relative error = 3.1447503971956923952336274132208 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5944 y2[1] (analytic) = 1.1715153449946143454499622671058 y2[1] (numeric) = 1.1715153141883379229874444171431 absolute error = 3.08062764224625178499627e-08 relative error = 2.6296092965478091559005949089317e-06 % h = 0.0001 y1[1] (analytic) = 2.560011764537681039149738033107 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0805862259334780388764500978914 relative error = 3.1478849843501132513294903946363 % h = 0.0001 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.1MB, time=127.34 NO POLE NO POLE x[1] = 0.5945 y2[1] (analytic) = 1.1715713503133980498347431730947 y2[1] (numeric) = 1.1715713193427021300158191821085 absolute error = 3.09706959198189239909862e-08 relative error = 2.6435176919898383566014680922952e-06 % h = 0.0001 y1[1] (analytic) = 2.5600946102029846765844050020396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.080669071598781676311117066824 relative error = 3.1510191567641162396981406801692 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5946 y2[1] (analytic) = 1.1716273639164682441819715023157 y2[1] (numeric) = 1.1716273327806496562871537524849 absolute error = 3.11358185878948177498308e-08 relative error = 2.6574847555467867535001916738516e-06 % h = 0.0001 y1[1] (analytic) = 2.5601774502673422166566802885973 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0807519116631392163833923533817 relative error = 3.1541529144671918762941403755087 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5947 y2[1] (analytic) = 1.1716833858032647924614120913219 y2[1] (numeric) = 1.1716833545016181008316171905317 absolute error = 3.13016466916297949007902e-08 relative error = 2.6715106718160461281306435172786e-06 % h = 0.0001 y1[1] (analytic) = 2.5602602847299252587236788259266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.080834746125722258450390890711 relative error = 3.1572862574888275916703010291273 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5948 y2[1] (analytic) = 1.1717394159732274758055663063754 y2[1] (numeric) = 1.171739384505044974921122369471 absolute error = 3.14681825008844439369044e-08 relative error = 2.6855956257772116864233111158136e-06 % h = 0.0001 y1[1] (analytic) = 2.5603431135899054581602604805455 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0809175749857024578869725453299 relative error = 3.1604191858585077307507394652203 % h = 0.0001 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.1MB, time=127.91 NO POLE NO POLE x[1] = 0.5949 y2[1] (analytic) = 1.1717954544257959925152742321176 y2[1] (numeric) = 1.1717954227903677020693259734877 absolute error = 3.16354282904459482586299e-08 relative error = 2.6997398027924559920676953547389e-06 % h = 0.0001 y1[1] (analytic) = 2.5604259368464545263673134985878 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0810003982422515260940255633722 relative error = 3.1635516996057135526041212708654 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.595 y2[1] (analytic) = 1.1718515011604099580653176885558 y2[1] (numeric) = 1.1718514693570236180316284977294 absolute error = 3.18033863400336891908264e-08 relative error = 2.7139433886069028245623764664929e-06 % h = 0.0001 y1[1] (analytic) = 2.5605087544987442307800373917875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0810832158945412305067494565719 relative error = 3.1666837987599232302170918568458 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5951 y2[1] (analytic) = 1.1719075561765089051100240763114 y2[1] (numeric) = 1.1719075242044499708051742483064 absolute error = 3.19720589343048498280050e-08 relative error = 2.7282065693490009619246220386921e-06 % h = 0.0001 y1[1] (analytic) = 2.5605915665459463948762252631193 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0811660279417433946029373279037 relative error = 3.1698154833506118502678950115249 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5952 y2[1] (analytic) = 1.1719636194735322834888710500712 y2[1] (numeric) = 1.1719635873320839206288513422918 absolute error = 3.21414483628600197077794e-08 relative error = 2.7425295315308978880311558085234e-06 % h = 0.0001 y1[1] (analytic) = 2.5606743729872328981845455720145 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0812488343830298979112576367989 relative error = 3.1729467534072514129001788673108 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=865.9MB, alloc=4.1MB, time=128.48 x[1] = 0.5953 y2[1] (analytic) = 1.1720196910509194602320920201885 y2[1] (numeric) = 1.1720196587393625399832917077214 absolute error = 3.23115569202488003124671e-08 relative error = 2.7569124620488134245622128749548e-06 % h = 0.0001 y1[1] (analytic) = 2.5607571738217756762928233390671 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0813316352175726760195354038515 relative error = 3.1760776089593108314969891991046 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5954 y2[1] (analytic) = 1.1720757709081097195662824823759 y2[1] (numeric) = 1.1720757384257228135908710835937 absolute error = 3.24823869059754113987822e-08 relative error = 2.7713555481834132875205836732187e-06 % h = 0.0001 y1[1] (analytic) = 2.5608399690487467208563207901487 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0814144304445437205830328549331 relative error = 3.1792080500362559324549499742942 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5955 y2[1] (analytic) = 1.1721318590445422629200071754344 y2[1] (numeric) = 1.17213182639060163841570901987 absolute error = 3.26539406245042981555644e-08 relative error = 2.7858589776001825682976426013641e-06 % h = 0.0001 y1[1] (analytic) = 2.5609227586673180796060174398487 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0814972200631150793327295046331 relative error = 3.1823380766675494549586310738055 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5956 y2[1] (analytic) = 1.1721879554596562089294080669637 y2[1] (numeric) = 1.1721879226334358236636688774742 absolute error = 3.28262203852657391894895e-08 relative error = 2.8004229383497991392584544005780e-06 % h = 0.0001 y1[1] (analytic) = 2.561005542676661856356889614158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0815800040724588560836016789424 relative error = 3.1854676888826510507551031038095 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5957 y2[1] (analytic) = 1.1722440601528905934438131669956 y2[1] (numeric) = 1.172244027153662090782357828293 absolute error = 3.29992285026614553387026e-08 relative error = 2.8150476188685069838177390971348e-06 % h = 0.0001 y1[1] (analytic) = 2.5610883210759502110161894123123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0816627824717472107429014770967 relative error = 3.1885968867110172839286792176326 % h = 0.0001 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.1MB, time=129.05 NO POLE NO POLE x[1] = 0.5958 y2[1] (analytic) = 1.172300173123684369531346169496 y2[1] (numeric) = 1.1723001399507170734611268551759 absolute error = 3.31729672960702193143201e-08 relative error = 2.8297332079784894509789318831121e-06 % h = 0.0001 y1[1] (analytic) = 2.5611710938643553595917231077124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0817455552601523593184351724968 relative error = 3.1917256701821016306758438674902 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5959 y2[1] (analytic) = 1.1723562943714764074845369216795 y2[1] (numeric) = 1.172356261024037317631070751935 absolute error = 3.33474390898534661697445e-08 relative error = 2.8444798948882424343084326051392e-06 % h = 0.0001 y1[1] (analytic) = 2.5612538610410495742001289878394 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0818283224368465739268410526238 relative error = 3.1948540393253544790803684057111 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.596 y2[1] (analytic) = 1.172412423895705494825932721079 y2[1] (numeric) = 1.1724123903730592814650281233452 absolute error = 3.35226462133609045977338e-08 relative error = 2.8592878691929474753169893613064e-06 % h = 0.0001 y1[1] (analytic) = 2.5613366226052051830751546330814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0819110840010021828018666978658 relative error = 3.1979819941702231288886134550952 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5961 y2[1] (analytic) = 1.1724685616958103363137104403155 y2[1] (numeric) = 1.1724685279972193353775813851441 absolute error = 3.36985910009361290551714e-08 relative error = 2.8741573208748447912205479368971e-06 % h = 0.0001 y1[1] (analytic) = 2.5614193785559945705759336343894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0819938399517915703026456991738 relative error = 3.2011095347461517912850179681138 % h = 0.0001 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.1MB, time=129.62 NO POLE NO POLE x[1] = 0.5962 y2[1] (analytic) = 1.1725247077712295539472894795121 y2[1] (numeric) = 1.1725246738959537620250567640321 absolute error = 3.38752757919222327154800e-08 relative error = 2.8890884403036062270527315211128e-06 % h = 0.0001 y1[1] (analytic) = 2.5615021288925901771952617496785 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0820765902883871769219738144629 relative error = 3.204236661082581588667774894629 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5963 y2[1] (analytic) = 1.1725808621214016869729455462945 y2[1] (numeric) = 1.1725808280686987563055242976722 absolute error = 3.40527029306674212486223e-08 relative error = 2.9040814182367081321010929169702e-06 % h = 0.0001 y1[1] (analytic) = 2.5615848736141644995678724988935 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0821593350099614992945845636779 relative error = 3.207363373208950554424693377947 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5964 y2[1] (analytic) = 1.1726370247457651918894252633243 y2[1] (numeric) = 1.1726369905148904253587978346902 absolute error = 3.42308747665306274286341e-08 relative error = 2.9191364458198041606395577158198e-06 % h = 0.0001 y1[1] (analytic) = 2.5616676127198900904787121976545 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0822420741156870902054242624389 relative error = 3.2104896711546936327092473989131 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5965 y2[1] (analytic) = 1.172693195643758442453561603306 y2[1] (numeric) = 1.1726931612339647885664350346747 absolute error = 3.44097936538871265686313e-08 relative error = 2.9342537145870979969291646660411e-06 % h = 0.0001 y1[1] (analytic) = 2.5617503462089395588712144294006 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.082324807604736558597926494185 relative error = 3.2136155549492426782168107878771 % h = 0.0001 TOP MAIN SOLVE Loop memory used=877.4MB, alloc=4.1MB, time=130.17 NO POLE NO POLE x[1] = 0.5966 y2[1] (analytic) = 1.1727493748148197296858901514149 y2[1] (numeric) = 1.1727493402253577775517373681769 absolute error = 3.45894619521341527832380e-08 relative error = 2.9494334164617160044597330083640e-06 % h = 0.0001 y1[1] (analytic) = 2.5618330740804855698555739559487 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0824075354762825695822860207331 relative error = 3.216741024622026455961078524342 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5967 y2[1] (analytic) = 1.1728055622583872618762661950862 y2[1] (numeric) = 1.1728055274885052361797501167108 absolute error = 3.47698820256965160783754e-08 relative error = 2.9646757437560797994044843683040e-06 % h = 0.0001 y1[1] (analytic) = 2.5619157963337008447170200663844 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0824902577294978444437321311688 relative error = 3.2198660802024706410506742441353 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5968 y2[1] (analytic) = 1.1728617579738991645894826411126 y2[1] (numeric) = 1.1728617230228429205572623727531 absolute error = 3.49510562440322202683595e-08 relative error = 2.9799808891722787482603920131739e-06 % h = 0.0001 y1[1] (analytic) = 2.5619985129677581609240893642032 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0825729743635551606508014289876 relative error = 3.2229907217199978184659438740105 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5969 y2[1] (analytic) = 1.1729179619607934806708887599909 y2[1] (numeric) = 1.1729179268278064990328070397433 absolute error = 3.51329869816380817202476e-08 relative error = 2.9953490458024423896463854873766e-06 % h = 0.0001 y1[1] (analytic) = 2.562081223981830352136897992618 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0826556853776273518636100574024 relative error = 3.2261149492040274828359353135342 % h = 0.0001 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.1MB, time=130.74 NO POLE NO POLE x[1] = 0.597 y2[1] (analytic) = 1.1729741742185081702520097574644 y2[1] (numeric) = 1.1729741389028315521966608320835 absolute error = 3.53156766180553489253809e-08 relative error = 3.0107804071291127802321985074572e-06 % h = 0.0001 y1[1] (analytic) = 2.5621639293750903082154132979511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0827383907708873079421253627355 relative error = 3.2292387626839760382155640842174 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5971 y2[1] (analytic) = 1.1730303947464811107561671732026 y2[1] (numeric) = 1.1730303592473535728808442751387 absolute error = 3.54991275378753228980639e-08 relative error = 3.0262751670256167647701226236230e-06 % h = 0.0001 y1[1] (analytic) = 2.5622466291467109752277249310275 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0828210905425079749544369958119 relative error = 3.2323621621892567978629648658266 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5972 y2[1] (analytic) = 1.1730866235441500969041001065637 y2[1] (numeric) = 1.1730865878608079661591217052364 absolute error = 3.56833421307449784013273e-08 relative error = 3.0418335197564381702024781026809e-06 % h = 0.0001 y1[1] (analytic) = 2.5623293232958653554583153864875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0829037846916623551850274512719 relative error = 3.2354851477492799840170288398792 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5973 y2[1] (analytic) = 1.173142860610952840719587269382 y2[1] (numeric) = 1.173142824742630049347001269667 absolute error = 3.58683227913725859997150e-08 relative error = 3.0574556599775899238171307883754e-06 % h = 0.0001 y1[1] (analytic) = 2.5624120118217265074163299799346 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.082986473217523507143042044719 relative error = 3.2386077193934527276751267602791 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=885.0MB, alloc=4.1MB, time=131.31 x[1] = 0.5974 y2[1] (analytic) = 1.1731991059463269715350698657258 y2[1] (numeric) = 1.1731990698922550520017349266836 absolute error = 3.60540719195333349390422e-08 relative error = 3.0731417827369860954239666740991e-06 % h = 0.0001 y1[1] (analytic) = 2.5624946947234675458438462628371 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0830691561192645455705583276215 relative error = 3.2417298771511790683710176711643 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5975 y2[1] (analytic) = 1.1732553595497100359972752985684 y2[1] (numeric) = 1.173255323309118115922318445502 absolute error = 3.62405919200749568530664e-08 relative error = 3.0888920834748138635248299553434e-06 % h = 0.0001 y1[1] (analytic) = 2.5625773720002616417241428751009 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0831518333960586414508549398853 relative error = 3.2448516210518599539529431920292 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5976 y2[1] (analytic) = 1.1733116214205394980728417033156 y2[1] (numeric) = 1.1733115849926542951494914063008 absolute error = 3.64278852029233502970148e-08 relative error = 3.1047067580239054054496126227687e-06 % h = 0.0001 y1[1] (analytic) = 2.5626600436512820222899678352294 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0832345050470790220166799000138 relative error = 3.2479729511248932403619072901515 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5977 y2[1] (analytic) = 1.1733678915582527390539433081352 y2[1] (numeric) = 1.1733678549422985559657372002212 absolute error = 3.66159541830882061079140e-08 relative error = 3.1205860026101097114314255359164e-06 % h = 0.0001 y1[1] (analytic) = 2.5627427096757019710318062679893 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0833171710714989707585183327737 relative error = 3.2510938673996736914101414604873 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5978 y2[1] (analytic) = 1.1734241699622870575639166210304 y2[1] (numeric) = 1.1734241331574857768952830293672 absolute error = 3.68048012806686335916632e-08 relative error = 3.1365300138526643225934176324524e-06 % h = 0.0001 y1[1] (analytic) = 2.5628253700726948277061475694989 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0833998314684918274328596342833 relative error = 3.254214369905592978559755233141 % h = 0.0001 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.1MB, time=131.87 NO POLE NO POLE x[1] = 0.5979 y2[1] (analytic) = 1.1734804566320796695628874436015 y2[1] (numeric) = 1.1734804196376507487040999068056 absolute error = 3.69944289208587875367959e-08 relative error = 3.1525389887645669928201711473669e-06 % h = 0.0001 y1[1] (analytic) = 2.562908024841433988343752009656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0834824862372309880704640744404 relative error = 3.2573344586720396807015719285612 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.598 y2[1] (analytic) = 1.1735367515670677083533987114403 y2[1] (numeric) = 1.1735367143822281743999026565658 absolute error = 3.71848395339534960548745e-08 relative error = 3.1686131247529472744865868520819e-06 % h = 0.0001 y1[1] (analytic) = 2.5629906739810929052579167718239 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0835651353768899049846288366083 relative error = 3.2604541337283992839341495806934 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5981 y2[1] (analytic) = 1.1735930547666882245860391610998 y2[1] (numeric) = 1.17359301739065266923214991364 absolute error = 3.73760355553538892474598e-08 relative error = 3.1847526196194380280170060966545e-06 % h = 0.0001 y1[1] (analytic) = 2.5630733174908450870527414296912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0836477788866420867794534944756 relative error = 3.2635733951040541813429869482372 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5982 y2[1] (analytic) = 1.1736493662303781862650728235835 y2[1] (numeric) = 1.1736493286623587606920441239831 absolute error = 3.75680194255730286996004e-08 relative error = 3.2009576715605468552476093938845e-06 % h = 0.0001 y1[1] (analytic) = 2.563155955369864098631392861224 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0837304167656610983581049260084 relative error = 3.2666922428283836727799145342959 % h = 0.0001 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.1MB, time=132.43 NO POLE NO POLE x[1] = 0.5983 y2[1] (analytic) = 1.1737056859575744787540693442984 y2[1] (numeric) = 1.1737056481967808885125315445127 absolute error = 3.77607935902415377997857e-08 relative error = 3.2172284791680274565650577591312e-06 % h = 0.0001 y1[1] (analytic) = 2.5632385876173235612043695996275 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0838130490131205609310816644119 relative error = 3.2698106769307639646426705346662 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5984 y2[1] (analytic) = 1.1737620139477139047815351294143 y2[1] (numeric) = 1.1737619759933534046683022431092 absolute error = 3.79543605001132328863051e-08 relative error = 3.2335652414292509117942865724330e-06 % h = 0.0001 y1[1] (analytic) = 2.5633212142323971522977656212337 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0838956756281941520244776860181 relative error = 3.2729286974405681696546616350335 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5985 y2[1] (analytic) = 1.1738183502002331844465453185742 y2[1] (numeric) = 1.1738183120515105733757900986157 absolute error = 3.81487226110707552199585e-08 relative error = 3.2499681577275768848086120049167e-06 % h = 0.0001 y1[1] (analytic) = 2.5634038352142586057615335702342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0839782966100556054882456350186 relative error = 3.2760463043871663066449085774512 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5986 y2[1] (analytic) = 1.1738746947145689552243765838989 y2[1] (numeric) = 1.173874656370686571093172800838 absolute error = 3.83438823841312037830609e-08 relative error = 3.2664374278427247518351513233572e-06 % h = 0.0001 y1[1] (analytic) = 2.5634864505620817117777474201731 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0840609119578787115044594849575 relative error = 3.2791634977999253003281764163527 % h = 0.0001 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.1MB, time=133.00 NO POLE NO POLE x[1] = 0.5987 y2[1] (analytic) = 1.1739310474901577719721407552294 y2[1] (numeric) = 1.1739310089503154865203718505447 absolute error = 3.85398422854517689046847e-08 relative error = 3.2829732519511446534286638039884e-06 % h = 0.0001 y1[1] (analytic) = 2.56356906027504031686886457212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0841435216708373165955766369044 relative error = 3.2822802777082089810852893845658 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5988 y2[1] (analytic) = 1.1739874085264361069344192715511 y2[1] (numeric) = 1.1739873697898313205990525594671 absolute error = 3.87366047863353667120840e-08 relative error = 3.2995758306263884700870158471773e-06 % h = 0.0001 y1[1] (analytic) = 2.5636516643523083239059873894381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0842261257481053236326994542225 relative error = 3.28539664414137808474363028963 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5989 y2[1] (analytic) = 1.1740437778228403497488984585433 y2[1] (numeric) = 1.1740437388886679865126240502991 absolute error = 3.89341723632362744082442e-08 relative error = 3.3162453648394807214814259113251e-06 % h = 0.0001 y1[1] (analytic) = 2.5637342627930596921171241690665 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0843087241888566918438362338509 relative error = 3.2885125971287902523578243609006 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.599 y2[1] (analytic) = 1.1741001553788068074520056321979 y2[1] (numeric) = 1.1741001162462593096862392566975 absolute error = 3.91325474977657663755004e-08 relative error = 3.3329820559592893892746991445136e-06 % h = 0.0001 y1[1] (analytic) = 2.5638168555964684370954495492333 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0843913169922654368221616140177 relative error = 3.2916281366998000299906074678557 % h = 0.0001 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.1MB, time=133.56 NO POLE NO POLE x[1] = 0.5991 y2[1] (analytic) = 1.1741565411937717044845460284501 y2[1] (numeric) = 1.1741565018620390277867949232818 absolute error = 3.93317326766977511051683e-08 relative error = 3.3497861057528966635007158358773e-06 % h = 0.0001 y1[1] (analytic) = 2.5638994427617086308075643535166 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.084473904157505630534276418301 relative error = 3.2947432628837588684938786300634 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5992 y2[1] (analytic) = 1.1742129352671711826973405587655 y2[1] (numeric) = 1.1742128957354407907229316056342 absolute error = 3.95317303919744089531313e-08 relative error = 3.3666577163859696124784750027483e-06 % h = 0.0001 y1[1] (analytic) = 2.5639820242879544016017548711722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0845564856837514013284669359566 relative error = 3.2978579757100151232899367393593 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5993 y2[1] (analytic) = 1.1742693375984413013568643916278 y2[1] (numeric) = 1.1742692978658981606450336702996 absolute error = 3.97325431407118307213282e-08 relative error = 3.3835970904231307762340912258615e-06 % h = 0.0001 y1[1] (analytic) = 2.5640646001743799342162515736432 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0846390615701769339429636384276 relative error = 3.300972275207914054152901414673 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5994 y2[1] (analytic) = 1.1743257481870180371508863598688 y2[1] (numeric) = 1.1743257082528446119452292947856 absolute error = 3.99341734252056570650832e-08 relative error = 3.4006044308283286834039500781836e-06 % h = 0.0001 y1[1] (analytic) = 2.5641471704201594697874872671714 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0847216318159564695141993319558 relative error = 3.3040861614067978249903179101442 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=904.1MB, alloc=4.1MB, time=134.12 x[1] = 0.5995 y2[1] (analytic) = 1.1743821670323372841941091937863 y2[1] (numeric) = 1.1743821268957135312573904675627 absolute error = 4.01366237529367187262236e-08 relative error = 3.4176799409652082915925797836091e-06 % h = 0.0001 y1[1] (analytic) = 2.5642297350244673058583546814255 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0848041964202643055850667462099 relative error = 3.3071996343360055036249459970131 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5996 y2[1] (analytic) = 1.1744385941338348540338105799923 y2[1] (numeric) = 1.1744385537939382174571329880639 absolute error = 4.03398966365766775919284e-08 relative error = 3.4348238245974813511586465191717e-06 % h = 0.0001 y1[1] (analytic) = 2.5643122939864777963864634940661 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0848867553822747961131755588505 relative error = 3.3103126940248730615767327399782 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5997 y2[1] (analytic) = 1.1744950294909464756554850459353 y2[1] (numeric) = 1.1744949889469518816618164666851 absolute error = 4.05439945939936685792502e-08 relative error = 3.4520362858892966924024498235738e-06 % h = 0.0001 y1[1] (analytic) = 2.5643948473053653517523967911618 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0849693087011623514791088559462 relative error = 3.3134253405027333738449690885329 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5998 y2[1] (analytic) = 1.1745514731031077954884866700411 y2[1] (numeric) = 1.1745514323541876472305443247848 absolute error = 4.07489201482579423452563e-08 relative error = 3.4693175294056104361286297412419e-06 % h = 0.0001 y1[1] (analytic) = 2.5644773949803044387679669633772 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0850518563761014384946790281616 relative error = 3.3165375737989162186906302040542 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.5999 y2[1] (analytic) = 1.1746079249697543774116726174142 y2[1] (numeric) = 1.1746078840150785497641637946843 absolute error = 4.09546758276475088227299e-08 relative error = 3.4866677601125561275574087135000e-06 % h = 0.0001 y1[1] (analytic) = 2.5645599370104695806844710378474 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0851343984062665804111831026318 relative error = 3.3196493939427482774188994432179 % h = 0.0001 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.1MB, time=134.68 NO POLE NO POLE x[1] = 0.6 y2[1] (analytic) = 1.1746643850903217027590475010446 y2[1] (numeric) = 1.1746643439290575371052659196677 absolute error = 4.11612641656537815813769e-08 relative error = 3.5040871833778147935581200402358e-06 % h = 0.0001 y1[1] (analytic) = 2.5646424733950353572009454456587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0852169347908323569276575104431 relative error = 3.3227608009635531341618759185234 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); Iterations = 1000 Total Elapsed Time = 2 Minutes 14 Seconds Elapsed Time(since restart) = 2 Minutes 14 Seconds Expected Time Remaining = 3 Hours 30 Minutes 50 Seconds Optimized Time Remaining = 3 Hours 30 Minutes 47 Seconds Time to Timeout = 12 Minutes 45 Seconds Percent Done = 1.054 % > quit memory used=908.8MB, alloc=4.1MB, time=134.82