|\^/| 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 > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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 ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, 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 > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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 ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, 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 > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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 ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, 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 > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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 - 4 - 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 - 4 - 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 ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; n := glob_max_terms; m := n - 5; 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 - 5; 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 > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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 ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, 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 > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > 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_1D0[1])); > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,5] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (4)) * factorial_3(0,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,3] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,2] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,1] := 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[4,1]; > # emit pre mult $eq_no = 2 i = 1 > array_tmp5[1] := (array_m1[1] * (array_tmp4[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre 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_1D0[2])); > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (4)) * factorial_3(1,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,3] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,2] := 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[4,2]; > # emit pre mult $eq_no = 2 i = 2 > array_tmp5[2] := ats(2,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre 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_1D0[3])); > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,7] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (4)) * factorial_3(2,6); > array_y2[7] := temporary; > array_y2_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,4] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,3] := 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[4,3]; > # emit pre mult $eq_no = 2 i = 3 > array_tmp5[3] := ats(3,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre 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_1D0[4])); > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,8] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (4)) * factorial_3(3,7); > array_y2[8] := temporary; > array_y2_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,5] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,4] := 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[4,4]; > # emit pre mult $eq_no = 2 i = 4 > array_tmp5[4] := ats(4,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre 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_1D0[5])); > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,9] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (4)) * factorial_3(4,8); > array_y2[9] := temporary; > array_y2_higher[1,9] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,8] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y2_higher[3,7] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y2_higher[4,6] := temporary > ; > temporary := temporary / glob_h * (5.0); > array_y2_higher[5,5] := 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[4,5]; > # emit pre mult $eq_no = 2 i = 5 > array_tmp5[5] := ats(5,array_m1,array_tmp4,1); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp5[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit 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_1D0[kkk])); > #emit assign $eq_no = 1 > order_d := 4; > 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[4,kkk]; > #emit mult $eq_no = 2 > array_tmp5[kkk] := ats(kkk,array_m1,array_tmp4,1); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp5[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; array_tmp2[1] := array_tmp1[1] - array_const_1D0[1]; if not array_y2_set_initial[1, 5] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h^4*factorial_3(0, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 3] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 2] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := array_y2_higher[4, 1]; array_tmp5[1] := array_m1[1]*array_tmp4[1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[1]*glob_h*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D0[2] + array_y1[2]; array_tmp2[2] := array_tmp1[2] - array_const_1D0[2]; if not array_y2_set_initial[1, 6] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h^4*factorial_3(1, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 3] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 2] := temporary end if end if; kkk := 3; array_tmp4[2] := array_y2_higher[4, 2]; array_tmp5[2] := ats(2, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[2]*glob_h*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_const_0D0[3] + array_y1[3]; array_tmp2[3] := array_tmp1[3] - array_const_1D0[3]; if not array_y2_set_initial[1, 7] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h^4*factorial_3(2, 6); array_y2[7] := temporary; array_y2_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 4] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 3] := temporary end if end if; kkk := 4; array_tmp4[3] := array_y2_higher[4, 3]; array_tmp5[3] := ats(3, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[3]*glob_h*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_const_0D0[4] + array_y1[4]; array_tmp2[4] := array_tmp1[4] - array_const_1D0[4]; if not array_y2_set_initial[1, 8] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h^4*factorial_3(3, 7); array_y2[8] := temporary; array_y2_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 5] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 4] := temporary end if end if; kkk := 5; array_tmp4[4] := array_y2_higher[4, 4]; array_tmp5[4] := ats(4, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[4]*glob_h*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_const_0D0[5] + array_y1[5]; array_tmp2[5] := array_tmp1[5] - array_const_1D0[5]; if not array_y2_set_initial[1, 9] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h^4*factorial_3(4, 8); array_y2[9] := temporary; array_y2_higher[1, 9] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 8] := temporary; temporary := temporary*3.0/glob_h; array_y2_higher[3, 7] := temporary; temporary := temporary*4.0/glob_h; array_y2_higher[4, 6] := temporary; temporary := temporary*5.0/glob_h; array_y2_higher[5, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := array_y2_higher[4, 5]; array_tmp5[5] := ats(5, array_m1, array_tmp4, 1); if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[5]*glob_h*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; array_tmp2[kkk] := array_tmp1[kkk] - array_const_1D0[kkk]; order_d := 4; 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[4, kkk]; array_tmp5[kkk] := ats(kkk, array_m1, array_tmp4, 1); order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp5[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > # Begin Function number 17 > factorial_1 := proc(nnn) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > 1.0 + sin(x); > end; exact_soln_y1 := proc(x) 1.0 + sin(x) end proc > exact_soln_y2 := proc(x) > 1.0 + sin(x); > end; exact_soln_y2 := proc(x) 1.0 + sin(x) end proc > exact_soln_y2p := proc(x) > cos(x); > end; exact_soln_y2p := proc(x) cos(x) end proc > exact_soln_y2pp := proc(x) > -sin(x); > end; exact_soln_y2pp := proc(x) -sin(x) end proc > exact_soln_y2ppp := proc(x) > -cos(x); > end; exact_soln_y2ppp := 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,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > ALWAYS, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_max_sec, > glob_optimal_clock_start_sec, > glob_max_trunc_err, > glob_max_iter, > glob_max_hours, > glob_dump_analytic, > glob_large_float, > hours_in_day, > glob_log10normmin, > glob_smallish_float, > glob_no_eqs, > glob_max_rel_trunc_err, > glob_abserr, > glob_optimal_done, > glob_not_yet_finished, > min_in_hour, > glob_start, > glob_warned, > glob_small_float, > glob_initial_pass, > glob_clock_start_sec, > djd_debug, > glob_percent_done, > glob_log10abserr, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_clock_sec, > years_in_century, > glob_max_minutes, > centuries_in_millinium, > djd_debug2, > glob_current_iter, > glob_warned2, > glob_relerr, > glob_hmax, > glob_h, > glob_disp_incr, > glob_not_yet_start_msg, > days_in_year, > sec_in_min, > glob_display_flag, > MAX_UNCHANGED, > glob_max_opt_iter, > glob_iter, > glob_log10_relerr, > glob_hmin, > glob_normmax, > glob_curr_iter_when_opt, > glob_log10_abserr, > glob_look_poles, > glob_hmin_init, > glob_dump, > glob_log10relerr, > glob_orig_start_sec, > glob_almost_1, > glob_html_log, > glob_optimal_expect_sec, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_1, > array_const_4, > array_const_0D0, > array_const_1D0, > #END CONST > array_1st_rel_error, > array_y2, > array_y1, > array_norms, > array_m1, > array_fact_1, > array_x, > array_last_rel_error, > array_pole, > array_y1_init, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_y2_init, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_fact_2, > array_poles, > array_y1_higher_work, > array_y2_set_initial, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > INFO := 2; > glob_max_terms := 30; > glob_iolevel := 5; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_max_sec := 10000.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_max_iter := 1000; > glob_max_hours := 0.0; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > hours_in_day := 24.0; > glob_log10normmin := 0.1; > glob_smallish_float := 0.1e-100; > glob_no_eqs := 0; > glob_max_rel_trunc_err := 0.1e-10; > glob_abserr := 0.1e-10; > glob_optimal_done := false; > glob_not_yet_finished := true; > min_in_hour := 60.0; > glob_start := 0; > glob_warned := false; > glob_small_float := 0.1e-50; > glob_initial_pass := true; > glob_clock_start_sec := 0.0; > djd_debug := true; > glob_percent_done := 0.0; > glob_log10abserr := 0.0; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_last_good_h := 0.1; > glob_reached_optimal_h := false; > glob_clock_sec := 0.0; > years_in_century := 100.0; > glob_max_minutes := 0.0; > centuries_in_millinium := 10.0; > djd_debug2 := true; > glob_current_iter := 0; > glob_warned2 := false; > glob_relerr := 0.1e-10; > glob_hmax := 1.0; > glob_h := 0.1; > glob_disp_incr := 0.1; > glob_not_yet_start_msg := true; > days_in_year := 365.0; > sec_in_min := 60.0; > glob_display_flag := true; > MAX_UNCHANGED := 10; > glob_max_opt_iter := 10; > glob_iter := 0; > glob_log10_relerr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_normmax := 0.0; > glob_curr_iter_when_opt := 0; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_hmin_init := 0.001; > glob_dump := false; > glob_log10relerr := 0.0; > glob_orig_start_sec := 0.0; > glob_almost_1 := 0.9990; > glob_html_log := true; > glob_optimal_expect_sec := 0.1; > glob_subiter_method := 3; > #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/mtest8postode.ode#################"); > omniout_str(ALWAYS,"diff ( y2 , x , 4 ) = y1 - 1.0;"); > omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.1;"); > 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,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y1 := proc(x)"); > omniout_str(ALWAYS,"1.0 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"1.0 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"-sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > 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_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_tmp5:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_y2_higher_work2 := Array(0..(5+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(5+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher := Array(0..(5+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > 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[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_norms[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_fact_1[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_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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=5 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 <=5 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 <=5 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 <=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 <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <=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[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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > 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_4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_4[1] := 4; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1D0[1] := 1.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.1; > 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); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y2_set_initial[1,1] := true; > array_y2_set_initial[1,2] := true; > array_y2_set_initial[1,3] := true; > array_y2_set_initial[1,4] := true; > array_y2_set_initial[1,5] := false; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 4; > #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 <= 5 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 5 + 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 := 4; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 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 , 4 ) = y1 - 1.0;"); > omniout_str(INFO,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); > 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,"2012-06-17T23:31:51-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest8") > ; > logitem_str(html_log_file,"diff ( y2 , x , 4 ) = y1 - 1.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 5 > ; > log_revs(html_log_file," 092 ") > ; > logitem_str(html_log_file,"mtest8 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest8 maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;") > ; > 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, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global ALWAYS, INFO, glob_max_terms, glob_iolevel, DEBUGL, DEBUGMASSIVE, glob_max_sec, glob_optimal_clock_start_sec, glob_max_trunc_err, glob_max_iter, glob_max_hours, glob_dump_analytic, glob_large_float, hours_in_day, glob_log10normmin, glob_smallish_float, glob_no_eqs, glob_max_rel_trunc_err, glob_abserr, glob_optimal_done, glob_not_yet_finished, min_in_hour, glob_start, glob_warned, glob_small_float, glob_initial_pass, glob_clock_start_sec, djd_debug, glob_percent_done, glob_log10abserr, glob_unchanged_h_cnt, glob_optimal_start, glob_last_good_h, glob_reached_optimal_h, glob_clock_sec, years_in_century, glob_max_minutes, centuries_in_millinium, djd_debug2, glob_current_iter, glob_warned2, glob_relerr, glob_hmax, glob_h, glob_disp_incr, glob_not_yet_start_msg, days_in_year, sec_in_min, glob_display_flag, MAX_UNCHANGED, glob_max_opt_iter, glob_iter, glob_log10_relerr, glob_hmin, glob_normmax, glob_curr_iter_when_opt, glob_log10_abserr, glob_look_poles, glob_hmin_init, glob_dump, glob_log10relerr, glob_orig_start_sec, glob_almost_1, glob_html_log, glob_optimal_expect_sec, glob_subiter_method, array_const_3, array_const_1, array_const_4, array_const_0D0, array_const_1D0, array_1st_rel_error, array_y2, array_y1, array_norms, array_m1, array_fact_1, array_x, array_last_rel_error, array_pole, array_y1_init, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_y2_init, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_fact_2, array_poles, array_y1_higher_work, array_y2_set_initial, array_y1_set_initial, array_y1_higher, array_real_pole, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; INFO := 2; glob_max_terms := 30; glob_iolevel := 5; DEBUGL := 3; DEBUGMASSIVE := 4; glob_max_sec := 10000.0; glob_optimal_clock_start_sec := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_max_iter := 1000; glob_max_hours := 0.; glob_dump_analytic := false; glob_large_float := 0.90*10^101; hours_in_day := 24.0; glob_log10normmin := 0.1; glob_smallish_float := 0.1*10^(-100); glob_no_eqs := 0; glob_max_rel_trunc_err := 0.1*10^(-10); glob_abserr := 0.1*10^(-10); glob_optimal_done := false; glob_not_yet_finished := true; min_in_hour := 60.0; glob_start := 0; glob_warned := false; glob_small_float := 0.1*10^(-50); glob_initial_pass := true; glob_clock_start_sec := 0.; djd_debug := true; glob_percent_done := 0.; glob_log10abserr := 0.; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_last_good_h := 0.1; glob_reached_optimal_h := false; glob_clock_sec := 0.; years_in_century := 100.0; glob_max_minutes := 0.; centuries_in_millinium := 10.0; djd_debug2 := true; glob_current_iter := 0; glob_warned2 := false; glob_relerr := 0.1*10^(-10); glob_hmax := 1.0; glob_h := 0.1; glob_disp_incr := 0.1; glob_not_yet_start_msg := true; days_in_year := 365.0; sec_in_min := 60.0; glob_display_flag := true; MAX_UNCHANGED := 10; glob_max_opt_iter := 10; glob_iter := 0; glob_log10_relerr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_normmax := 0.; glob_curr_iter_when_opt := 0; glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_hmin_init := 0.001; glob_dump := false; glob_log10relerr := 0.; glob_orig_start_sec := 0.; glob_almost_1 := 0.9990; glob_html_log := true; glob_optimal_expect_sec := 0.1; glob_subiter_method := 3; 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/mtest8postode.ode#################"); omniout_str(ALWAYS, "diff ( y2 , x , 4 ) = y1 - 1.0;"); omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;") ; omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.1;"); 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, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y1 := proc(x)"); omniout_str(ALWAYS, "1.0 +\tsin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "1.0 +\tsin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "-sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); 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_1st_rel_error := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_tmp5 := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_y2_higher_work2 := Array(0 .. 6, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 6, 0 .. max_terms + 1, []); array_y2_higher := Array(0 .. 6, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); 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[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_norms[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_fact_1[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_last_rel_error[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_y1_init[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_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 5 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 <= 5 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 <= 5 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 <= 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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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[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; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_const_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; 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_4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_4[term] := 0.; term := term + 1 end do; array_const_4[1] := 4; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1D0[term] := 0.; term := term + 1 end do; array_const_1D0[1] := 1.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.1; 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); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y2_set_initial[1, 1] := true; array_y2_set_initial[1, 2] := true; array_y2_set_initial[1, 3] := true; array_y2_set_initial[1, 4] := true; array_y2_set_initial[1, 5] := false; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 4; 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 <= 5 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 5 + 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 := 4; 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)/factorial_1(calc_term - 1)!; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( 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)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y2 , x , 4 ) = y1 - 1.0;"); omniout_str(INFO, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); 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, "2012-06-17T23:31:51-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest8") ; logitem_str(html_log_file, "diff ( y2 , x , 4 ) = y1 - 1.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 092 "); logitem_str(html_log_file, "mtest8 diffeq.mxt"); logitem_str(html_log_file, "mtest8 maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ;"); 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/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.1; 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); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) 1.0 + sin(x); end; exact_soln_y2 := proc(x) 1.0 + sin(x); end; exact_soln_y2p := proc(x) cos(x); end; exact_soln_y2pp := proc(x) -sin(x); end; exact_soln_y2ppp := proc(x) -cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.001 y1[1] (analytic) = 1.0998334166468281523068141984106 y1[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.001 x[1] = 0.1 y2[1] (analytic) = 1.0998334166468281523068141984106 y2[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.001 y1[1] (analytic) = 1.0998334166468281523068141984106 y1[1] (numeric) = 1.0998334166468281523068141984106 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.18 NO POLE NO POLE x[1] = 0.101 y2[1] (analytic) = 1.1008283707295679951297521195232 y2[1] (numeric) = 1.100828370729562157183038504093 absolute error = 5.8379467136154302e-15 relative error = 5.3032306114588624519980605911872e-13 % h = 0.001 y1[1] (analytic) = 1.1008283707295679951297521195232 y1[1] (numeric) = 1.1008318740131052080279606730552 absolute error = 3.5032835372128982085535320e-06 relative error = 0.00031824066588065096494565212313096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.102 y2[1] (analytic) = 1.1018232239839455107486422960806 y2[1] (numeric) = 1.1018232241460198403282321650806 absolute error = 1.620743295795898690000e-10 relative error = 1.4709649066350722339491159206787e-08 % h = 0.001 y1[1] (analytic) = 1.1018232239839455107486422960806 y1[1] (numeric) = 1.1018303708975022212301580387922 absolute error = 7.1469135567104815157427116e-06 relative error = 0.0006486443016574696963758910851686 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.3MB, time=0.38 NO POLE NO POLE x[1] = 0.103 y2[1] (analytic) = 1.1028179754151075276904042105046 y2[1] (numeric) = 1.1028179767200672148092450974481 absolute error = 1.3049596871188408869435e-09 relative error = 1.1832956264859991649175185993223e-07 % h = 0.001 y1[1] (analytic) = 1.1028179754151075276904042105046 y1[1] (numeric) = 1.1028289062958569314099413161518 absolute error = 1.09308807494037195371056472e-05 relative error = 0.00099117723804685611958939191897789 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.4MB, time=0.59 NO POLE NO POLE x[1] = 0.104 y2[1] (analytic) = 1.1038126240283026976889707546695 y2[1] (numeric) = 1.1038126284453691860012438248222 absolute error = 4.4170664883122730701527e-09 relative error = 4.0016451997010461041864658800755e-07 % h = 0.001 y1[1] (analytic) = 1.1038126240283026976889707546695 y1[1] (numeric) = 1.103827479203825833552081067892 absolute error = 1.48551755231358631103132225e-05 relative error = 0.0013458059094235330771401629082963 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.4MB, time=0.80 NO POLE NO POLE x[1] = 0.105 y2[1] (analytic) = 1.1048071688288824904365536000268 y2[1] (numeric) = 1.1048071793170062584779772212797 absolute error = 1.04881237680414236212529e-08 relative error = 9.4931713551053826130608505578965e-07 % h = 0.001 y1[1] (analytic) = 1.1048071688288824904365536000268 y1[1] (numeric) = 1.1048260886168851681209179993989 absolute error = 1.89197880026776843643993721e-05 relative error = 0.0017124968534312675455985695202768 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=19.0MB, alloc=4.4MB, time=1.01 x[1] = 0.106 y2[1] (analytic) = 1.1058016088223021882320906180187 y2[1] (numeric) = 1.1058016293300713469103575054042 absolute error = 2.05077691586782668873855e-08 relative error = 1.8545613422030914959876824798573e-06 % h = 0.001 y1[1] (analytic) = 1.1058016088223021882320906180187 y1[1] (numeric) = 1.1058247335303319113742736846095 absolute error = 2.31247080297231421830665908e-05 relative error = 0.002091216710595253666077746768113 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.107 y2[1] (analytic) = 1.1067959430141218805258807024165 y2[1] (numeric) = 1.1067959784796580878318664770489 absolute error = 3.54655362073059857746324e-08 relative error = 3.2043428087315885934308737402330e-06 % h = 0.001 y1[1] (analytic) = 1.1067959430141218805258807024165 y1[1] (numeric) = 1.1068234129392847659989816415693 absolute error = 2.74699251628854731009391528e-05 relative error = 0.002481932223936149501908822580314 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.4MB, time=1.23 NO POLE NO POLE x[1] = 0.108 y2[1] (analytic) = 1.1077901704100074583594114490316 y2[1] (numeric) = 1.1077902267608607472446028616359 absolute error = 5.63508532888851914126043e-08 relative error = 5.0867804024681869466416953571469e-06 % h = 0.001 y1[1] (analytic) = 1.1077901704100074583594114490316 y1[1] (numeric) = 1.1078221258386851520670825210499 absolute error = 3.19554286776937076710720183e-05 relative error = 0.0028846102385857594808113517784073 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.5MB, time=1.44 NO POLE NO POLE x[1] = 0.109 y2[1] (analytic) = 1.1087842900157316086993852530554 y2[1] (numeric) = 1.1087843741687742248574141749635 absolute error = 8.41530426161580289219081e-08 relative error = 7.5896676543788379347381815853930e-06 % h = 0.001 y1[1] (analytic) = 1.1087842900157316086993852530554 y1[1] (numeric) = 1.1088208712232981983117267118642 absolute error = 3.65812075665896123414588088e-05 relative error = 0.0032992177014043545226035826302841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=4.5MB, time=1.65 x[1] = 0.11 y2[1] (analytic) = 1.1097783008371748086649494900834 y2[1] (numeric) = 1.1097784206984940591293700835992 absolute error = 1.198613192504644205935158e-07 relative error = 1.0800474217241909598557986057990e-05 % h = 0.001 y1[1] (analytic) = 1.1097783008371748086649494900834 y1[1] (numeric) = 1.1098196480877137337218272076338 absolute error = 4.13472505389250568777175504e-05 relative error = 0.0037257216605996218969323951415833 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.111 y2[1] (analytic) = 1.1107722018803263196471365536769 y2[1] (numeric) = 1.1107723663451164323200160148287 absolute error = 1.644647901126728794611518e-07 relative error = 1.4806347317142545868410536880203e-05 % h = 0.001 y1[1] (analytic) = 1.1107722018803263196471365536769 y1[1] (numeric) = 1.1108184554263472794545051217804 absolute error = 4.62535460209598073685681035e-05 relative error = 0.0041640892653472368986766969493029 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.5MB, time=1.86 NO POLE NO POLE x[1] = 0.112 y2[1] (analytic) = 1.1117659921512851813195196301052 y2[1] (numeric) = 1.1117662111037381755397472841691 absolute error = 2.189524529942202276540639e-07 relative error = 1.9694113198276886382110100190223e-05 % h = 0.001 y1[1] (analytic) = 1.1117659921512851813195196301052 y1[1] (numeric) = 1.1118172922334410410643697804365 absolute error = 5.13000821558597448501503313e-05 relative error = 0.0046142877654130484715924635264519 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.5MB, time=2.07 NO POLE NO POLE x[1] = 0.113 y2[1] (analytic) = 1.1127596706562612055390901996952 y2[1] (numeric) = 1.112759954969456773800243186958 absolute error = 2.843131955682611529872628e-07 relative error = 2.5550278561100672069072005503101e-05 % h = 0.001 y1[1] (analytic) = 1.1127596706562612055390901996952 y1[1] (numeric) = 1.1128161575030649010486748667958 absolute error = 5.64868468036955095846671006e-05 relative error = 0.005076284510776870953424174701939 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.5MB, time=2.29 NO POLE NO POLE x[1] = 0.114 y2[1] (analytic) = 1.1137532364015759701363633639937 y2[1] (numeric) = 1.1137535979373703710649554929075 absolute error = 3.615357944009285921289138e-07 relative error = 3.2461031993856571652942786759459e-05 % h = 0.001 y1[1] (analytic) = 1.1137532364015759701363633639937 y1[1] (numeric) = 1.1138150502291174117073916351559 absolute error = 6.18138275414415710282711622e-05 relative error = 0.0055500469512578741581078284851093 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.115 y2[1] (analytic) = 1.1147466883936638125937172087197 y2[1] (numeric) = 1.1147471400025777752996462400109 absolute error = 4.516089139627059290312912e-07 relative error = 4.0512245397514370478408939068595e-05 % h = 0.001 y1[1] (analytic) = 1.1147466883936638125937172087197 y1[1] (numeric) = 1.1148139694053267883172397585413 absolute error = 6.72810116629757235225498216e-05 relative error = 0.0060355426361415640528366921295391 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.5MB, time=2.50 NO POLE NO POLE x[1] = 0.116 y2[1] (analytic) = 1.1157400256390728236109725242508 y2[1] (numeric) = 1.1157405811601784635229697272367 absolute error = 5.555211056399119972029859e-07 relative error = 4.9789475404157970480313537554050e-05 % h = 0.001 y1[1] (analytic) = 1.1157400256390728236109725242508 y1[1] (numeric) = 1.115812914025251902618715920337 absolute error = 7.28883861790790077433960862e-05 relative error = 0.0065327392138083463296541539615499 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.5MB, time=2.71 NO POLE NO POLE x[1] = 0.117 y2[1] (analytic) = 1.1167332471444658405572193181459 y2[1] (numeric) = 1.1167339214052725868570936047092 absolute error = 6.742608067462998742865633e-07 relative error = 6.0377964788852958717634110441855e-05 % h = 0.001 y1[1] (analytic) = 1.1167332471444658405572193181459 y1[1] (numeric) = 1.1168118830822832766151598078116 absolute error = 7.86359378174360579404896657e-05 relative error = 0.0070416044313636652128801304593423 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.5MB, time=2.92 NO POLE NO POLE x[1] = 0.118 y2[1] (analytic) = 1.117726351916621440807896667961 y2[1] (numeric) = 1.1177271607329609755783539593111 absolute error = 8.088163395347704572913501e-07 relative error = 7.2362643875028311683543586808018e-05 % h = 0.001 y1[1] (analytic) = 1.117726351916621440807896667961 y1[1] (numeric) = 1.117810875569644076682896713765 absolute error = 8.45236530226358750000458040e-05 relative error = 0.0075621061342697098850701116092063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.119 y2[1] (analytic) = 1.1187193389624349349661325773612 y2[1] (numeric) = 1.1187202991383451441679392928891 absolute error = 9.601759102092018067155279e-07 relative error = 8.5828131933405613567717653590615e-05 % h = 0.001 y1[1] (analytic) = 1.1187193389624349349661325773612 y1[1] (numeric) = 1.1188098904803911079914955017987 absolute error = 9.05515179561730253629244375e-05 relative error = 0.0080942122659786809553507327868246 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.5MB, time=3.14 NO POLE NO POLE x[1] = 0.12 y2[1] (analytic) = 1.119712207288919359967350614271 y2[1] (numeric) = 1.119713336616527296362598289488 absolute error = 1.1293276079363952476752170e-06 relative error = 0.00010085873857450897878034853771706 % h = 0.001 y1[1] (analytic) = 1.119712207288919359967350614271 y1[1] (numeric) = 1.1198089268074158092331802408771 absolute error = 9.67195184964492658296266061e-05 relative error = 0.0086378908675676094348743703266302 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=3.34 NO POLE NO POLE x[1] = 0.121 y2[1] (analytic) = 1.1207049559032064720661502265403 y2[1] (numeric) = 1.1207062731626103302053662672935 absolute error = 1.3172594038581392160407532e-06 relative error = 0.00011753846513478868234111861641701 % h = 0.001 y1[1] (analytic) = 1.1207049559032064720661502265403 y1[1] (numeric) = 1.1208079835434452476604333659313 absolute error = 0.000103027640238775594283139391 relative error = 0.0091931100773747207247892860953305 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.5MB, time=3.56 NO POLE NO POLE x[1] = 0.122 y2[1] (analytic) = 1.1216975838125477397044677483272 y2[1] (numeric) = 1.1216991087716978430963052102215 absolute error = 1.5249591501033918374618943e-06 relative error = 0.00013595100605639131618287552324788 % h = 0.001 y1[1] (analytic) = 1.1216975838125477397044677483272 y1[1] (numeric) = 1.1218070596810431144308277732434 absolute error = 0.0001094758684953747263600249162 relative error = 0.0097598381306373361625328975146975 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.123 y2[1] (analytic) = 1.1226900900243153362600252291201 y2[1] (numeric) = 1.1226918434388941368432522733541 absolute error = 1.7534145788005832270442340e-06 relative error = 0.00015617975026060910501118783964821 % h = 0.001 y1[1] (analytic) = 1.1226900900243153362600252291201 y1[1] (numeric) = 1.122806154212610720258124812251 absolute error = 0.0001160641882953839980995831309 relative error = 0.010338043359131304712425416220328 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.5MB, time=3.77 NO POLE NO POLE x[1] = 0.124 y2[1] (analytic) = 1.1236824735460031326740743370329 y2[1] (numeric) = 1.12368447715930422271257165569 absolute error = 2.0036133010900384973186571e-06 relative error = 0.00017830778251504083208965908493309 % h = 0.001 y1[1] (analytic) = 1.1236824735460031326740743370329 y1[1] (numeric) = 1.1238052661303879913686746892214 absolute error = 0.0001227925843848586946003521885 relative error = 0.010927694190811957426470962010926 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=3.98 NO POLE NO POLE x[1] = 0.125 y2[1] (analytic) = 1.1246747333852276899574427087121 y2[1] (numeric) = 1.124677009928033826479904732951 absolute error = 2.2765428061365224620242389e-06 relative error = 0.00020241788479449664317920457836088 % h = 0.001 y1[1] (analytic) = 1.1246747333852276899574427087121 y1[1] (numeric) = 1.124804394426454465762155352966 absolute error = 0.0001296610412267758047126442539 relative error = 0.011528759149456577340964888651895 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=4.20 NO POLE NO POLE x[1] = 0.126 y2[1] (analytic) = 1.1256668685497292515738902398917 y2[1] (numeric) = 1.1256694417401893934809133424643 absolute error = 2.5731904601419070231025726e-06 relative error = 0.00022859253763567881583987351347591 % h = 0.001 y1[1] (analytic) = 1.1256668685497292515738902398917 y1[1] (numeric) = 1.1258035380927302897756854883983 absolute error = 0.0001366695430010382017952485066 relative error = 0.012141206854308377513961013243601 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.127 y2[1] (analytic) = 1.1266588780473727356997829333235 y2[1] (numeric) = 1.1266617725908780936620111114217 absolute error = 2.8945435053579622281780982e-06 relative error = 0.00025691392148567040139870479251512 % h = 0.001 y1[1] (analytic) = 1.1266588780473727356997829333235 y1[1] (numeric) = 1.126802696120977214950346800285 absolute error = 0.0001438180736044792505638669615 relative error = 0.012765006019721979947872268631678 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.5MB, time=4.41 NO POLE NO POLE x[1] = 0.128 y2[1] (analytic) = 1.1276507608861487273590920444897 y2[1] (numeric) = 1.1276540024752078266310777191073 absolute error = 3.2415890590992719856746176e-06 relative error = 0.00028746391804426346808907338656228 % h = 0.001 y1[1] (analytic) = 1.1276507608861487273590920444897 y1[1] (numeric) = 1.1278018675027995951991503269972 absolute error = 0.0001511066166508678400582825075 relative error = 0.013400125454810388180464535661306 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.5MB, time=4.62 NO POLE NO POLE x[1] = 0.129 y2[1] (analytic) = 1.128642516074174470432726390184 y2[1] (numeric) = 1.1286461313882872267081509829767 absolute error = 3.6153141127562754245927927e-06 relative error = 0.00032032411160015849616859902620314 % h = 0.001 y1[1] (analytic) = 1.128642516074174470432726390184 y1[1] (numeric) = 1.1288010512296453842754810824405 absolute error = 0.0001585351554709138427546922565 relative error = 0.014046534063093446366257583659546 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=4.84 NO POLE NO POLE x[1] = 0.13 y2[1] (analytic) = 1.1296341426196948595412058107083 y2[1] (numeric) = 1.1296381593252256679760916577706 absolute error = 4.0167055308084348858470623e-06 relative error = 0.00035557579036106629921659362056243 % h = 0.001 y1[1] (analytic) = 1.1296341426196948595412058107083 y1[1] (numeric) = 1.1298002462928071335410548836287 absolute error = 0.0001661036731122739998490729204 relative error = 0.014704200842147777708870669684438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.131 y2[1] (analytic) = 1.1306256395310834317996839030976 y2[1] (numeric) = 1.1306300862811332693312158361469 absolute error = 4.4467500498375315319330493e-06 relative error = 0.00039329994777774367029090904846921 % h = 0.001 y1[1] (analytic) = 1.1306256395310834317996839030976 y1[1] (numeric) = 1.1307994516834229900324207815651 absolute error = 0.0001738121523395582327368784675 relative error = 0.015373094883258195143144921637123 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.5MB, time=5.06 NO POLE NO POLE x[1] = 0.132 y2[1] (analytic) = 1.1316170058168433584443282704301 y2[1] (numeric) = 1.1316219122511208995338898386259 absolute error = 4.9064342775410895615681958e-06 relative error = 0.00043357728386199377718066257747378 % h = 0.001 y1[1] (analytic) = 1.1316170058168433584443282704301 y1[1] (numeric) = 1.1317986663924776948250420742127 absolute error = 0.0001816605756343363807138037826 relative error = 0.016053185371070577203941653237097 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.5MB, time=5.28 NO POLE NO POLE x[1] = 0.133 y2[1] (analytic) = 1.1326082404856084363290666609268 y2[1] (numeric) = 1.1326136372303001822590824799564 absolute error = 5.3967446917459300158190296e-06 relative error = 0.00047648820649866215761845968069507 % h = 0.001 y1[1] (analytic) = 1.1326082404856084363290666609268 y1[1] (numeric) = 1.1327978894108035816939884423634 absolute error = 0.0001896489251951453649217814366 relative error = 0.016744441583246202056356710062069 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=5.49 NO POLE NO POLE x[1] = 0.134 y2[1] (analytic) = 1.1335993425461440792917075001763 y2[1] (numeric) = 1.1336052612137835011468695983269 absolute error = 5.9186676394218551620981506e-06 relative error = 0.00052211283275165899300625652117799 % h = 0.001 y1[1] (analytic) = 1.1335993425461440792917075001763 y1[1] (numeric) = 1.1337971197290815760702713121655 absolute error = 0.0001977771829374967785638119892 relative error = 0.017446832890117532699707299947953 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.135 y2[1] (analytic) = 1.1345903110073483093884434504466 y2[1] (numeric) = 1.1345967841966840048528857331733 absolute error = 6.4731893356954644422827267e-06 relative error = 0.00057053099016403816795580967238494 % h = 0.001 y1[1] (analytic) = 1.1345903110073483093884434504466 y1[1] (numeric) = 1.1347963563378421942918541119323 absolute error = 0.0002060453304938849034106614857 relative error = 0.018160328754345446395040978253659 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=5.70 NO POLE NO POLE x[1] = 0.136 y2[1] (analytic) = 1.1355811448782527479957467626642 y2[1] (numeric) = 1.1355882061741156120987178366603 absolute error = 7.0612958628641029710739961e-06 relative error = 0.00062182221805216345274070225998694 % h = 0.001 y1[1] (analytic) = 1.1355811448782527479957467626642 y1[1] (numeric) = 1.135795598227466543148368655637 absolute error = 0.0002144533492137951526218929728 relative error = 0.018884898730577901403087990778604 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.5MB, time=5.92 NO POLE NO POLE x[1] = 0.137 y2[1] (analytic) = 1.1365718431680236067786653192461 y2[1] (numeric) = 1.1365795271411930167222359032483 absolute error = 7.6839731694099435705840022e-06 relative error = 0.00067606576879399197659522034214961 % h = 0.001 y1[1] (analytic) = 1.1365718431680236067786653192461 y1[1] (numeric) = 1.1367948443881873197185684511976 absolute error = 0.0002230012201637129399031319515 relative error = 0.019620512465110034156529465794464 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.5MB, time=6.14 NO POLE NO POLE x[1] = 0.138 y2[1] (analytic) = 1.1375624048859626785245283995723 y2[1] (numeric) = 1.1375707470930316927278554010981 absolute error = 8.3422070690142033270015258e-06 relative error = 0.00073334060911150499166893567707252 % h = 0.001 y1[1] (analytic) = 1.1375624048859626785245283995723 y1[1] (numeric) = 1.1377940938100898114995492982759 absolute error = 0.0002316889241271329750208987036 relative error = 0.020367139695545680027186422225864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.139 y2[1] (analytic) = 1.1385528290415083278410713344755 y2[1] (numeric) = 1.1385618660247478993367263884065 absolute error = 9.0369832395714956550539310e-06 relative error = 0.00079372542134731576034783734879948 % h = 0.001 y1[1] (analytic) = 1.1385528290415083278410713344755 y1[1] (numeric) = 1.1387933454831128968267671078505 absolute error = 0.000240516441604568985695773375 relative error = 0.021124750250460310885249644513102 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=6.35 NO POLE NO POLE x[1] = 0.14 y2[1] (analytic) = 1.1395431146442364817179883517054 y2[1] (numeric) = 1.1395528839314586860368441971182 absolute error = 9.7692872222043188558454128e-06 relative error = 0.00085729860473548423257640129098321 % h = 0.001 y1[1] (analytic) = 1.1395431146442364817179883517054 y1[1] (numeric) = 1.1397925983970500455838824442818 absolute error = 0.0002494837528135638658940925764 relative error = 0.021893314049065382683969577032874 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.5MB, time=6.57 NO POLE NO POLE x[1] = 0.141 y2[1] (analytic) = 1.1405332607038616199509230508977 y2[1] (numeric) = 1.1405438008082818976330765658113 absolute error = 1.05401044202776821535149136e-05 relative error = 0.00092413827666656801475329749214241 % h = 0.001 y1[1] (analytic) = 1.1405332607038616199509230508977 y1[1] (numeric) = 1.1407918515415503202014608599646 absolute error = 0.0002585908376887002505378090669 relative error = 0.022672801100874086339309912600732 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.5MB, time=6.78 NO POLE NO POLE x[1] = 0.142 y2[1] (analytic) = 1.1415232662302377654269060841403 y2[1] (numeric) = 1.1415346166503361792971021029141 absolute error = 1.13504200984138701960187738e-05 relative error = 0.00099432227394693896771976454410403 % h = 0.001 y1[1] (analytic) = 1.1415232662302377654269060841403 y1[1] (numeric) = 1.141791103906119376943557662962 absolute error = 0.0002678376758816115166515788217 relative error = 0.023463181505368495209939881675193 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.143 y2[1] (analytic) = 1.1425131302333594742702497567803 y2[1] (numeric) = 1.1425253314527409816172549607745 absolute error = 1.22012193815073470052039942e-05 relative error = 0.0010679281540523946083073323821438 % h = 0.001 y1[1] (analytic) = 1.1425131302333594742702497567803 y1[1] (numeric) = 1.1427903544801204674812153292346 absolute error = 0.0002772242467609932109655724543 relative error = 0.024264425451668102518599772701916 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=6.99 NO POLE NO POLE x[1] = 0.144 y2[1] (analytic) = 1.143502851723362825847909402661 y2[1] (numeric) = 1.1435159452106165656482706004729 absolute error = 1.30934872537398003611978119e-05 relative error = 0.0011450331963760933268538970569274 % h = 0.001 y1[1] (analytic) = 1.143502851723362825847909402661 y1[1] (numeric) = 1.1437896022527754407519013432208 absolute error = 0.0002867505294126149039919405598 relative error = 0.025076503218199742091323300305421 % h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=7.21 NO POLE NO POLE x[1] = 0.145 y2[1] (analytic) = 1.1444924297105264126333215285089 y2[1] (numeric) = 1.1445064579190840079609275266445 absolute error = 1.40282085575953276059981356e-05 relative error = 0.0012257144034708422720275455263119 % h = 0.001 y1[1] (analytic) = 1.1444924297105264126333215285089 y1[1] (numeric) = 1.1447888462131657451039138235878 absolute error = 0.0002964165026393324705922950789 relative error = 0.02589938517236888582624044924865 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.5MB, time=7.43 NO POLE NO POLE x[1] = 0.146 y2[1] (analytic) = 1.1454818632052723299277288637166 y2[1] (numeric) = 1.1454968695732652056915798709555 absolute error = 1.50063679928757638510072389e-05 relative error = 0.0013100485022857665942094387828968 % h = 0.001 y1[1] (analytic) = 1.1454818632052723299277288637166 y1[1] (numeric) = 1.1457880853502334307247818649614 absolute error = 0.0003062221449611007970530012448 relative error = 0.026733041770232311338716709646639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.147 y2[1] (analytic) = 1.1464711512181671654380025942768 y2[1] (numeric) = 1.1464871801682828815915757022632 absolute error = 1.60289501157161535731079864e-05 relative error = 0.0013981119453973885795739825955878 % h = 0.001 y1[1] (analytic) = 1.1464711512181671654380025942768 y1[1] (numeric) = 1.1467873186527821523526871013531 absolute error = 0.0003161674346149869146845070763 relative error = 0.027577443556172133264410526142036 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=7.64 NO POLE NO POLE x[1] = 0.148 y2[1] (analytic) = 1.1474602927599229887099722031298 y2[1] (numeric) = 1.1474773896992605890765559408792 absolute error = 1.70969393376003665837377494e-05 relative error = 0.0014899809122351450488599850607954 % h = 0.001 y1[1] (analytic) = 1.1474602927599229887099722031298 y1[1] (numeric) = 1.1477865451094781722699325728394 absolute error = 0.0003262523495551835599603697096 relative error = 0.028432561162571191736451642793493 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=7.85 NO POLE NO POLE x[1] = 0.149 y2[1] (analytic) = 1.148449286841398340416273483676 y2[1] (numeric) = 1.1484674981613227172756287537504 absolute error = 1.82113199243768593552700744e-05 relative error = 0.0015857313103013712376441068937277 % h = 0.001 y1[1] (analytic) = 1.148449286841398340416273483676 y1[1] (numeric) = 1.1487857637088513635774845538073 absolute error = 0.0003364768674530231612110701313 relative error = 0.029298365309489791587360161106893 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=8.07 NO POLE NO POLE x[1] = 0.15 y2[1] (analytic) = 1.1494381324735992214977254386876 y2[1] (numeric) = 1.149457505549594496080414306771 absolute error = 1.93730759952745826888680834e-05 relative error = 0.0016854387763857792187012848745368 % h = 0.001 y1[1] (analytic) = 1.1494381324735992214977254386876 y1[1] (numeric) = 1.1497849734392962137496125787665 absolute error = 0.0003468409656969922518871400789 relative error = 0.030174826804343785860540854739751 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=148.7MB, alloc=4.5MB, time=8.28 x[1] = 0.151 y2[1] (analytic) = 1.1504268286676800821572469233262 y2[1] (numeric) = 1.1504474118592020011939547498458 absolute error = 2.05831915219190367078265196e-05 relative error = 0.0017891786777744587717596298157652 % h = 0.001 y1[1] (analytic) = 1.1504268286676800821572469233262 y1[1] (numeric) = 1.15078417328907282846765248034 absolute error = 0.0003573446213927463104055570138 relative error = 0.031061916541583997250200906195591 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.152 y2[1] (analytic) = 1.1514153744349448107053240384303 y2[1] (numeric) = 1.1514372170852721591794843097336 absolute error = 2.18426503273484741602713033e-05 relative error = 0.0018970261134534284516232908393591 % h = 0.001 y1[1] (analytic) = 1.1514153744349448107053240384303 y1[1] (numeric) = 1.1517833622463079357319168335827 absolute error = 0.0003679878113631250265927951524 relative error = 0.031959605502376971122353044911868 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.5MB, time=8.50 NO POLE NO POLE x[1] = 0.153 y2[1] (analytic) = 1.1524037687868477222560394286898 y2[1] (numeric) = 1.1524269212229327525090543651156 absolute error = 2.31524360850302530149364258e-05 relative error = 0.0020090559153067644522397053727818 % h = 0.001 y1[1] (analytic) = 1.1524037687868477222560394286898 y1[1] (numeric) = 1.1527825392989958902507767812434 absolute error = 0.0003787705121481679947373525536 relative error = 0.032867864754287053803181358590398 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=8.71 NO POLE NO POLE x[1] = 0.154 y2[1] (analytic) = 1.1533920107349945472726747897587 y2[1] (numeric) = 1.1534165242673124246120083777532 absolute error = 2.45135323178773393335879945e-05 relative error = 0.0021253426493093347118213327666002 % h = 0.001 y1[1] (analytic) = 1.1533920107349945472726747897587 y1[1] (numeric) = 1.1537817034349996781059387959769 absolute error = 0.0003896927000051308332640062182 relative error = 0.033786665450959789854465099391675 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=160.2MB, alloc=4.5MB, time=8.92 x[1] = 0.155 y2[1] (analytic) = 1.1543800992911434199618980387873 y2[1] (numeric) = 1.1544060262135406849233015530258 absolute error = 2.59269223972649614035142385e-05 relative error = 0.0022459606167141655525902547916984 % h = 0.001 y1[1] (analytic) = 1.1543800992911434199618980387873 y1[1] (numeric) = 1.1547808536420519216929395178349 absolute error = 0.0004007543509085017310414790476 relative error = 0.034715978831806632088977881793719 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.156 y2[1] (analytic) = 1.1553680334672058665155467542681 y2[1] (numeric) = 1.1553954270567479139316601025699 absolute error = 2.73935895420474161133483018e-05 relative error = 0.0023709838552344679980908203775052 % h = 0.001 y1[1] (analytic) = 1.1553680334672058665155467542681 y1[1] (numeric) = 1.1557799889077558849358813886129 absolute error = 0.0004119554405500184203346343448 relative error = 0.035655776221690958111807030330915 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=9.13 NO POLE NO POLE x[1] = 0.157 y2[1] (analytic) = 1.1563558122752477931990196434946 y2[1] (numeric) = 1.1563847267920653682275749811754 absolute error = 2.89145168175750285553376808e-05 relative error = 0.0025004861402203507613047584518693 % h = 0.001 y1[1] (analytic) = 1.1563558122752477931990196434946 y1[1] (numeric) = 1.1567791082195864787754313888104 absolute error = 0.0004232959443386855764117453158 relative error = 0.036606029030615387206371733938394 % h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.5MB, time=9.35 NO POLE NO POLE x[1] = 0.158 y2[1] (analytic) = 1.1573434347274904742852879493246 y2[1] (numeric) = 1.1573739254146251855511249695369 absolute error = 3.04906871347112658370202123e-05 relative error = 0.0026345409858302467479988700955487 % h = 0.001 y1[1] (analytic) = 1.1573434347274904742852879493246 y1[1] (numeric) = 1.1577782105648912669291047680683 absolute error = 0.0004347758374007926438168187437 relative error = 0.037566708753410391416560341671845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=171.6MB, alloc=4.5MB, time=9.56 x[1] = 0.159 y2[1] (analytic) = 1.1583308998363115398335388623175 y2[1] (numeric) = 1.1583630229195603898396239739024 absolute error = 3.21230832488500060851115849e-05 relative error = 0.0027732216461970797718315698602359 % h = 0.001 y1[1] (analytic) = 1.1583308998363115398335388623175 y1[1] (numeric) = 1.1587772949308914719228552459879 absolute error = 0.0004463950945799320893163836704 relative error = 0.03853778696942419470885782674133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.16 y2[1] (analytic) = 1.159318206614245963311463159686 y2[1] (numeric) = 1.1593520193020048962750874131143 absolute error = 3.38126877589329636242534283e-05 relative error = 0.0029166011165891980307352490683621 % h = 0.001 y1[1] (analytic) = 1.159318206614245963311463159686 y1[1] (numeric) = 1.1597763603046829813929927472049 absolute error = 0.0004581536904370180815295875189 relative error = 0.039519235342213954130595376136924 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=9.78 NO POLE NO POLE x[1] = 0.161 y2[1] (analytic) = 1.1603053540739870490601994488555 y2[1] (numeric) = 1.1603409145570935163315125629924 absolute error = 3.55604831064672713131141369e-05 relative error = 0.0030647521345661007479707971862391 % h = 0.001 y1[1] (analytic) = 1.1603053540739870490601994488555 y1[1] (numeric) = 1.160775405673237354657449322493 absolute error = 0.0004700515992503055972498736375 relative error = 0.040511025619238216912526449514057 % h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.6MB, time=9.99 NO POLE NO POLE x[1] = 0.162 y2[1] (analytic) = 1.1612923412283874196009475507708 y2[1] (numeric) = 1.1613297086799619628219677274702 absolute error = 3.73674515745432210201766994e-05 relative error = 0.0032177471811289842360127977772879 % h = 0.001 y1[1] (analytic) = 1.1612923412283874196009475507708 y1[1] (numeric) = 1.1617744300234028295554134965054 absolute error = 0.0004820887950154099544659457346 relative error = 0.041513129631550647495818700602056 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=183.1MB, alloc=4.6MB, time=10.21 x[1] = 0.163 y2[1] (analytic) = 1.1622791670904600027822637164169 y2[1] (numeric) = 1.1623184016657468549454851053627 absolute error = 3.92345752868521632213889458e-05 relative error = 0.0033756584818661334970631130917832 % h = 0.001 y1[1] (analytic) = 1.1622791670904600027822637164169 y1[1] (numeric) = 1.1627734323419053295543528725277 absolute error = 0.0004942652514453267720891561108 relative error = 0.042525519293495018495250067882221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.164 y2[1] (analytic) = 1.1632658306733790187670505293435 y2[1] (numeric) = 1.1633069935095857233337522211137 absolute error = 4.11628362067045667016917702e-05 relative error = 0.0035385580080931853305010248916489 % h = 0.001 y1[1] (analytic) = 1.1632658306733790187670505293435 y1[1] (numeric) = 1.1637724116153494711234444153153 absolute error = 0.0005065809419704523563938859718 relative error = 0.043548166602401459641911308957001 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.6MB, time=10.42 NO POLE NO POLE x[1] = 0.165 y2[1] (analytic) = 1.1642523309904809668582545072829 y2[1] (numeric) = 1.164295484206617015097596787349 absolute error = 4.31532161360482393422800661e-05 relative error = 0.0037065174779882887749540920186007 % h = 0.001 y1[1] (analytic) = 1.1642523309904809668582545072829 y1[1] (numeric) = 1.1647713668302195713724314247193 absolute error = 0.0005190358397386045141769174364 relative error = 0.044581043638283958780047459233602 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.6MB, time=10.63 NO POLE NO POLE x[1] = 0.166 y2[1] (analytic) = 1.1652386670552656121622845772482 y2[1] (numeric) = 1.1652838737519800988732598665427 absolute error = 4.52066967144867109752892945e-05 relative error = 0.0038796083577221885709097372156015 % h = 0.001 y1[1] (analytic) = 1.1652386670552656121622845772482 y1[1] (numeric) = 1.1657702969728806559549258053746 absolute error = 0.0005316299176150437926412281264 relative error = 0.045624122563539109023818313996372 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=194.5MB, alloc=4.6MB, time=10.85 x[1] = 0.167 y2[1] (analytic) = 1.1662248378813969720891647607741 y2[1] (numeric) = 1.1662721621408152698684521985898 absolute error = 4.73242594182977792874378157e-05 relative error = 0.004057901862583257188877650988498 % h = 0.001 y1[1] (analytic) = 1.1662248378813969720891647607741 y1[1] (numeric) = 1.1667692010295794672351738312214 absolute error = 0.0005443631481824951460090704473 relative error = 0.046677375622646096210724230932574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.168 y2[1] (analytic) = 1.1672108424827043026884345692303 y2[1] (numeric) = 1.167260349368263754908188560572 absolute error = 4.95068855594522197539913417e-05 relative error = 0.0042414689580975008280518001989047 % h = 0.001 y1[1] (analytic) = 1.1672108424827043026884345692303 y1[1] (numeric) = 1.1677680779864454727173031980717 absolute error = 0.0005572355037411700288686288414 relative error = 0.047740775141867920819229486282693 % h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.6MB, time=11.06 NO POLE NO POLE x[1] = 0.169 y2[1] (analytic) = 1.1681966798731830848198107733898 y2[1] (numeric) = 1.1682484354294677174803950244985 absolute error = 5.17555562846326605842511087e-05 relative error = 0.0044303803611435646512025958009331 % h = 0.001 y1[1] (analytic) = 1.1681966798731830848198107733898 y1[1] (numeric) = 1.1687669268294918737360687528023 absolute error = 0.0005702469563087889162579794125 relative error = 0.048814293528953848548722241959147 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.6MB, time=11.28 NO POLE NO POLE x[1] = 0.17 y2[1] (analytic) = 1.1691823490669960101576243766708 y2[1] (numeric) = 1.1692364203195702627812839783073 absolute error = 5.40712525742526236596016365e-05 relative error = 0.0046247065410627623831490898815566 % h = 0.001 y1[1] (analytic) = 1.1691823490669960101576243766708 y1[1] (numeric) = 1.1697657465446166144081138840663 absolute error = 0.0005833974776206042504895073955 relative error = 0.049897903272843083790379036657341 % h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.6MB, time=11.50 NO POLE NO POLE x[1] = 0.171 y2[1] (analytic) = 1.1701678490784739670280467877005 y2[1] (numeric) = 1.1702243040337154427604917749193 absolute error = 5.64549552414757324449872188e-05 relative error = 0.0048245177207641552626124563099899 % h = 0.001 y1[1] (analytic) = 1.1701678490784739670280467877005 y1[1] (numeric) = 1.1707645361176033908427641566595 absolute error = 0.000596687039129423814717368959 relative error = 0.050991576943369660247753734327623 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.172 y2[1] (analytic) = 1.1711531789221170260781193550527 y2[1] (numeric) = 1.1712120865670482611659738736489 absolute error = 5.89076449312350878545185962e-05 relative error = 0.0050298838778247052005300230903142 % h = 0.001 y1[1] (analytic) = 1.1711531789221170260781193550527 y1[1] (numeric) = 1.1717632945341226606113693698629 absolute error = 0.0006101156120056345332500148102 relative error = 0.052095287190968542995987177226738 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.6MB, time=11.71 NO POLE NO POLE x[1] = 0.173 y2[1] (analytic) = 1.1721383376125954257756005952159 y2[1] (numeric) = 1.1721997679147146785886523377944 absolute error = 6.14303021192528130517425785e-05 relative error = 0.0052408747455845268620083639252358 % h = 0.001 y1[1] (analytic) = 1.1721383376125954257756005952159 y1[1] (numeric) = 1.1727620207797326524742098192022 absolute error = 0.0006236831671372266986092239863 relative error = 0.053209006746382936298435514145435 % h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.6MB, time=11.93 NO POLE NO POLE x[1] = 0.174 y2[1] (analytic) = 1.1731233241647505577386456140236 y2[1] (numeric) = 1.1731873480718616175068105517515 absolute error = 6.40239071110597681649377279e-05 relative error = 0.0054575598142372632540090597659011 % h = 0.001 y1[1] (analytic) = 1.1731233241647505577386456140236 y1[1] (numeric) = 1.1737607138398803763639821411257 absolute error = 0.0006373896751298186253365271021 relative error = 0.054332708420372791529243421542594 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.6MB, time=12.15 NO POLE NO POLE x[1] = 0.175 y2[1] (analytic) = 1.1741081375935959518943323919514 y2[1] (numeric) = 1.1741748270336369673302300205233 absolute error = 6.66894400410154358976285719e-05 relative error = 0.0056800083319156092665863808913116 % h = 0.001 y1[1] (analytic) = 1.1741081375935959518943323919514 y1[1] (numeric) = 1.1747593726999026336248797211013 absolute error = 0.0006512351063066817305473291499 relative error = 0.055466365103424509579944307032248 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.176 y2[1] (analytic) = 1.1750927769143182614650497748359 y2[1] (numeric) = 1.1751622047951895894440641140312 absolute error = 6.94278808713279790143391953e-05 relative error = 0.0059082893057720074820270291366674 % h = 0.001 y1[1] (analytic) = 1.1750927769143182614650497748359 y1[1] (numeric) = 1.1757579963450270275062822475696 absolute error = 0.0006652194307087660412324727337 relative error = 0.056609949765461832157554178290627 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.6MB, time=12.36 NO POLE NO POLE x[1] = 0.177 y2[1] (analytic) = 1.1760772411422782477817621837097 y2[1] (numeric) = 1.1761494813516693222524436181707 absolute error = 7.22402093910744706814344610e-05 relative error = 0.0061424715030545404335729671739461 % h = 0.001 y1[1] (analytic) = 1.1760772411422782477817621837097 y1[1] (numeric) = 1.1767565837603729739100685970715 absolute error = 0.0006793426180947261283064133618 relative error = 0.057763435455557916410840263837553 % h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.6MB, time=12.57 NO POLE NO POLE x[1] = 0.178 y2[1] (analytic) = 1.1770615292930117649231662305697 y2[1] (numeric) = 1.1771366566982269862218089540976 absolute error = 7.51274052152212986427235279e-05 relative error = 0.0063826234521780433635340334264628 % h = 0.001 y1[1] (analytic) = 1.1770615292930117649231662305697 y1[1] (numeric) = 1.1777551339309527123905668396856 absolute error = 0.0006936046379409474674006091159 relative error = 0.058926795301648587350490765554661 % h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.6MB, time=12.79 NO POLE NO POLE x[1] = 0.179 y2[1] (analytic) = 1.1780456403822307441797546010046 y2[1] (numeric) = 1.17812373083001438892396392678 absolute error = 7.80904477836447442093257754e-05 relative error = 0.0066288134437904613995123207479794 % h = 0.001 y1[1] (analytic) = 1.1780456403822307441797546010046 y1[1] (numeric) = 1.1787536458416723174061547586713 absolute error = 0.0007080054594415732264001576667 relative error = 0.060100002510246762557789379893923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.18 y2[1] (analytic) = 1.1790295734258241783418027396992 y2[1] (numeric) = 1.1791107037421843300788458634035 absolute error = 8.11303163601517370431237043e-05 relative error = 0.0068811095318344749371600437520755 % h = 0.001 y1[1] (analytic) = 1.1790295734258241783418027396992 y1[1] (numeric) = 1.1797521184773327098215238839176 absolute error = 0.0007225450515085314797211442184 relative error = 0.061283030366158043705108511459671 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.6MB, time=13.00 NO POLE NO POLE x[1] = 0.181 y2[1] (analytic) = 1.1800133274398591058102940509108 y2[1] (numeric) = 1.1800975754298906065970070017765 absolute error = 8.42479900315007867129508657e-05 relative error = 0.0071395795346044168883717297249978 % h = 0.001 y1[1] (analytic) = 1.1800133274398591058102940509108 y1[1] (numeric) = 1.1807505508226306686596196454385 absolute error = 0.0007372233827715628493255945277 relative error = 0.062475852232197469440079476568056 % h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.6MB, time=13.22 NO POLE NO POLE x[1] = 0.182 y2[1] (analytic) = 1.1809969014405815945297995030755 y2[1] (numeric) = 1.1810843458882880176218019884455 absolute error = 8.74444477064230920024853700e-05 relative error = 0.0074042910357985053250649730110282 % h = 0.001 y1[1] (analytic) = 1.1809969014405815945297995030755 y1[1] (numeric) = 1.1817489418621598431022698607465 absolute error = 0.000752040421578248572470357671 relative error = 0.063678441548907424213677507772114 % h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.6MB, time=13.44 NO POLE NO POLE x[1] = 0.183 y2[1] (analytic) = 1.1819802944444177257423277047451 y2[1] (numeric) = 1.1820710151125323695712763457993 absolute error = 9.07206681146438289486410542e-05 relative error = 0.0076753113855664149207266607614637 % h = 0.001 y1[1] (analytic) = 1.1819802944444177257423277047451 y1[1] (numeric) = 1.1827472905804117647385133784637 absolute error = 0.0007669961359940389961856737186 relative error = 0.064890771834276697660675066339349 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.184 y2[1] (analytic) = 1.1829635054679745775611616980887 y2[1] (numeric) = 1.1830575830977804811797507670155 absolute error = 9.40776298059036185890689268e-05 relative error = 0.007952707701552210464688511067944 % h = 0.001 y1[1] (analytic) = 1.1829635054679745775611616980887 y1[1] (numeric) = 1.1837455959617768600596403100058 absolute error = 0.0007820904938022824984786119171 relative error = 0.066112816683460689168969884936987 % h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.6MB, time=13.64 NO POLE NO POLE x[1] = 0.185 y2[1] (analytic) = 1.1839465335280412083636988962014 y2[1] (numeric) = 1.1840440498391901885390960972806 absolute error = 9.75163111489801753972010792e-05 relative error = 0.0082365468699326655976420020430563 % h = 0.001 y1[1] (analytic) = 1.1839465335280412083636988962014 y1[1] (numeric) = 1.1847438569905454631999548915916 absolute error = 0.0007973234625042548362559953902 relative error = 0.067344549768502752302185327592867 % h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.6MB, time=13.86 NO POLE NO POLE x[1] = 0.186 y2[1] (analytic) = 1.1849293776415896400023107714653 y2[1] (numeric) = 1.1850304153319203501396938593003 absolute error = 0.000101037690330710137383087835 relative error = 0.008526895546450989791203384077549 % h = 0.001 y1[1] (analytic) = 1.1849293776415896400023107714653 y1[1] (numeric) = 1.185742072650908828922271630196 absolute error = 0.0008126950093191889199608587307 relative error = 0.068585944838056673767671089653092 % h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.6MB, time=14.08 NO POLE NO POLE x[1] = 0.187 y2[1] (analytic) = 1.185912036825775840832239084182 y2[1] (numeric) = 1.1860166795711308519110771807057 absolute error = 0.0001046427453550110788380965237 relative error = 0.0088238201574459864693895666236342 % h = 0.001 y1[1] (analytic) = 1.185912036825775840832239084182 y1[1] (numeric) = 1.1867402419269601458471549993717 absolute error = 0.0008282051011843050149159151897 relative error = 0.069836975717110281649602983753944 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.188 y2[1] (analytic) = 1.1868945100979407085555456236643 y2[1] (numeric) = 1.1870028425519826122622469805545 absolute error = 0.0001083324540419037067013568902 relative error = 0.0091273869008766650456603955278859 % h = 0.001 y1[1] (analytic) = 1.1868945100979407085555456236643 y1[1] (numeric) = 1.1877383638026955499249125641212 absolute error = 0.0008438537047548413693669404569 relative error = 0.071097616306710177654292575797302 % h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.6MB, time=14.29 NO POLE NO POLE x[1] = 0.189 y2[1] (analytic) = 1.187876796475611052880132617919 y2[1] (numeric) = 1.1879889042696375871216582717283 absolute error = 0.0001121077940265342415256538093 relative error = 0.0094376617473423295257173652539472 % h = 0.001 y1[1] (analytic) = 1.187876796475611052880132617919 y1[1] (numeric) = 1.1887364372620151381493510282011 absolute error = 0.0008596407864040852692184102821 relative error = 0.072367840583687588142071750165192 % h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.6MB, time=14.50 NO POLE NO POLE x[1] = 0.19 y2[1] (analytic) = 1.1888588949765005779928511529813 y2[1] (numeric) = 1.1889748647192587749768714356291 absolute error = 0.0001159697427581969840202826478 relative error = 0.0097547104410981662035183508163076 % h = 0.001 y1[1] (analytic) = 1.1888588949765005779928511529813 y1[1] (numeric) = 1.1897344612887239825123043123903 absolute error = 0.000875566312223404519453159409 relative error = 0.07364762260038532874721489019948 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.6MB, time=14.72 NO POLE NO POLE x[1] = 0.191 y2[1] (analytic) = 1.189840804618510864845715128875 y2[1] (numeric) = 1.18996072389601022191386332519 absolute error = 0.000119919277499357068148196315 relative error = 0.010078598501066352855967741247104 % h = 0.001 y1[1] (analytic) = 1.189840804618510864845715128875 y1[1] (numeric) = 1.1907324348665331441979423883484 absolute error = 0.0008916302480222793522272594734 relative error = 0.074936936484385877414303245642172 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.192 y2[1] (analytic) = 1.1908225244197323532542384660668 y2[1] (numeric) = 1.1909464817950570266559930518298 absolute error = 0.000123957375324673401754585763 relative error = 0.010409391221842711720466686651904 % h = 0.001 y1[1] (analytic) = 1.1908225244197323532542384660668 y1[1] (numeric) = 1.1917303569790606880158692097364 absolute error = 0.0009078325593283347616307436696 relative error = 0.076235756438240550706223205143003 % h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.6MB, time=14.94 NO POLE NO POLE x[1] = 0.193 y2[1] (analytic) = 1.1918040533984453238069134641578 y2[1] (numeric) = 1.1919321384115653456026173116006 absolute error = 0.0001280850131200217957038474428 relative error = 0.010747153674698928418954344516622 % h = 0.001 y1[1] (analytic) = 1.1918040533984453238069134641578 y1[1] (numeric) = 1.1927282266098326970720177002627 absolute error = 0.0009241732113873732651042361049 relative error = 0.077544056739199778265623572794771 % h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=15.16 NO POLE NO POLE x[1] = 0.194 y2[1] (analytic) = 1.1927853905731208795848484034179 y2[1] (numeric) = 1.1929176937407023978673501054036 absolute error = 0.0001323031675815182825017019857 relative error = 0.011091950708580358872233370320127 % h = 0.001 y1[1] (analytic) = 1.1927853905731208795848484034179 y1[1] (numeric) = 1.1937260427422842876763493772601 absolute error = 0.0009406521691634080915009738422 relative error = 0.078861811738944470338137530475162 % h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.6MB, time=15.37 NO POLE NO POLE x[1] = 0.195 y2[1] (analytic) = 1.1937665349624219276905826696054 y2[1] (numeric) = 1.1939031477776364703159617077791 absolute error = 0.0001366128152145426253790381737 relative error = 0.011443846951099446129246819110119 % h = 0.001 y1[1] (analytic) = 1.1937665349624219276905826696054 y1[1] (numeric) = 1.1947238043597606244863658092914 absolute error = 0.000957269397338696795783139686 relative error = 0.080188995863318473292003714424235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.196 y2[1] (analytic) = 1.1947474855852041605850978733388 y2[1] (numeric) = 1.1948885005175369226039117384112 absolute error = 0.0001410149323327620188138650724 relative error = 0.011802906809524768917554515022009 % h = 0.001 y1[1] (analytic) = 1.1947474855852041605850978733388 y1[1] (numeric) = 1.195721510445517935885438727121 absolute error = 0.0009740248603137753003408537822 relative error = 0.081525583612062108094898698021008 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.6MB, time=15.58 NO POLE NO POLE x[1] = 0.197 y2[1] (analytic) = 1.1957282414605170372320436270931 y2[1] (numeric) = 1.1958737519555741922135111901301 absolute error = 0.000145510495057154981467563037 relative error = 0.01216919447176574360354024562473 % h = 0.001 y1[1] (analytic) = 1.1957282414605170372320436270931 y1[1] (numeric) = 1.1967191599827245295949652291846 absolute error = 0.0009909185222074923629216020915 relative error = 0.082871549558546786734821102176024 % h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.6MB, time=15.79 NO POLE NO POLE x[1] = 0.198 y2[1] (analytic) = 1.1967088016076047640481968356735 y2[1] (numeric) = 1.1968589020869197994907082668392 absolute error = 0.0001501004793150354425114311657 relative error = 0.012542773907353001133862319141134 % h = 0.001 y1[1] (analytic) = 1.1967088016076047640481968356735 y1[1] (numeric) = 1.1977167519544618085193541454293 absolute error = 0.0010079503468570444711573097558 relative error = 0.084226868349510701597746491117426 % h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.6MB, time=16.01 NO POLE NO POLE x[1] = 0.199 y2[1] (analytic) = 1.1976891650459072756591735497928 y2[1] (numeric) = 1.1978439509067463526814928844467 absolute error = 0.0001547858608390770223193346539 relative error = 0.012923708868414460413334587434918 % h = 0.001 y1[1] (analytic) = 1.1976891650459072756591735497928 y1[1] (numeric) = 1.1987142853437252868228492470949 absolute error = 0.0010251202978180111636756973021 relative error = 0.085591514704795582840503089121336 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.2 y2[1] (analytic) = 1.1986693307950612154594126271184 y2[1] (numeric) = 1.1988288984102275529679146875372 absolute error = 0.0001595676151663375085020604188 relative error = 0.013312062890647119458788522737866 % h = 0.001 y1[1] (analytic) = 1.1986693307950612154594126271184 y1[1] (numeric) = 1.1997117591334256062371946146517 absolute error = 0.0010424283383643907777819875333 relative error = 0.086965463417084518822902102634061 % h = 0.001 TOP MAIN SOLVE Loop memory used=289.9MB, alloc=4.6MB, time=16.22 NO POLE NO POLE x[1] = 0.201 y2[1] (analytic) = 1.1996492978749009159754506408903 y2[1] (numeric) = 1.19981374459253819950370943418 absolute error = 0.0001644467176372835282587932897 relative error = 0.01370789929428458555351490498724 % h = 0.001 y1[1] (analytic) = 1.1996492978749009159754506408903 y1[1] (numeric) = 1.2007091723063895525991471017114 absolute error = 0.0010598744314886366236964608211 relative error = 0.088348689351640834688593972843139 % h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.6MB, time=16.44 NO POLE NO POLE x[1] = 0.202 y2[1] (analytic) = 1.2006290653054593790315076729148 y2[1] (numeric) = 1.2007984894488541944495286009376 absolute error = 0.0001694241433948154180209280228 relative error = 0.014111281185060365512611728520013 % h = 0.001 y1[1] (analytic) = 1.2006290653054593790315076729148 y1[1] (numeric) = 1.2017065238453610726168404592806 absolute error = 0.0010774585399016935853327863658 relative error = 0.089741167446048024209414133873173 % h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.6MB, time=16.65 NO POLE NO POLE x[1] = 0.203 y2[1] (analytic) = 1.2016086321069692557164038254306 y2[1] (numeric) = 1.2017831329743525480077670598094 absolute error = 0.0001745008673832922913632343788 relative error = 0.014522271455166937055968697383715 % h = 0.001 y1[1] (analytic) = 1.2016086321069692557164038254306 y1[1] (numeric) = 1.2027038127330022908640053122333 absolute error = 0.0010951806260330351476014868027 relative error = 0.09114287270995073003312971949548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.204 y2[1] (analytic) = 1.2025879972998638261508264850126 y2[1] (numeric) = 1.202767675164211383456983678524 absolute error = 0.0001796778643475573061571935114 relative error = 0.014940932784210622172693806797411 % h = 0.001 y1[1] (analytic) = 1.2025879972998638261508264850126 y1[1] (numeric) = 1.2037010379518945270010488083407 absolute error = 0.0011130406520307008502223233281 relative error = 0.092553780224796767499503051076296 % h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.6MB, time=16.87 NO POLE NO POLE x[1] = 0.205 y2[1] (analytic) = 1.2035671599047779790539685713266 y2[1] (numeric) = 1.2037521160136099421859096952727 absolute error = 0.0001849561088319631319411239461 relative error = 0.015367327640162283248529691746535 % h = 0.001 y1[1] (analytic) = 1.2035671599047779790539685713266 y1[1] (numeric) = 1.2046981984845393132219973896111 absolute error = 0.0011310385797613341680288182845 relative error = 0.093973865143580187214449548297978 % h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.6MB, time=17.09 NO POLE NO POLE x[1] = 0.206 y2[1] (analytic) = 1.2045461189425491911085582041808 y2[1] (numeric) = 1.2047364555177285887270397186668 absolute error = 0.000190336575179397618481514486 relative error = 0.015801518280303862616212380843914 % h = 0.001 y1[1] (analytic) = 1.2045461189425491911085582041808 y1[1] (numeric) = 1.2056952933133594119263057660652 absolute error = 0.0011491743708102208177475618844 relative error = 0.09540310269058537159678782313227 % h = 0.001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.6MB, time=17.30 NO POLE NO POLE x[1] = 0.207 y2[1] (analytic) = 1.2055248734342185061233004239223 y2[1] (numeric) = 1.2057206936717488157898002033925 absolute error = 0.0001958202375303096664997794702 relative error = 0.016243566752170786077788572816866 % h = 0.001 y1[1] (analytic) = 1.2055248734342185061233004239223 y1[1] (numeric) = 1.2066923214206998336145348033991 absolute error = 0.0011674479864813274912343794768 relative error = 0.09684146816113216063665903270191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=312.8MB, alloc=4.6MB, time=17.51 x[1] = 0.208 y2[1] (analytic) = 1.206503422401031513991751802823 y2[1] (numeric) = 1.2067048304708532492932902517346 absolute error = 0.0002014080698217353015384489116 relative error = 0.016693534894490250837625330146588 % h = 0.001 y1[1] (analytic) = 1.206503422401031513991751802823 y1[1] (numeric) = 1.2076892817888288550069006682703 absolute error = 0.0011858593877973410151488654473 relative error = 0.098288936921322002129131955223487 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.209 y2[1] (analytic) = 1.2074817648644393294466489886571 y2[1] (numeric) = 1.2076888659102256533985895908435 absolute error = 0.0002071010457863239519406021864 relative error = 0.01715148433811541817521396894113 % h = 0.001 y1[1] (analytic) = 1.2074817648644393294466489886571 y1[1] (numeric) = 1.2086861733999390373836972081814 absolute error = 0.0012044085354997079370482195243 relative error = 0.099745484407785121670810591010177 % h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.6MB, time=17.72 NO POLE NO POLE x[1] = 0.21 y2[1] (analytic) = 1.2084598998460995706087124262276 y2[1] (numeric) = 1.2086727999850509355406285753274 absolute error = 0.0002129001389513649319161490998 relative error = 0.017617476506955531077883748840328 % h = 0.001 y1[1] (analytic) = 1.2084598998460995706087124262276 y1[1] (numeric) = 1.2096829952361482451465931771358 absolute error = 0.0012230953900486745378807509082 relative error = 0.10121108612742870773142324204258 % h = 0.001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.6MB, time=17.93 NO POLE NO POLE x[1] = 0.211 y2[1] (analytic) = 1.2094378263678773373289467081163 y2[1] (numeric) = 1.2096566326905151514596150644654 absolute error = 0.0002188063226378141306683563491 relative error = 0.018091572618901976945196599556107 % h = 0.001 y1[1] (analytic) = 1.2094378263678773373289467081163 y1[1] (numeric) = 1.2106797462795006645998055533927 absolute error = 0.0012419199116233272708588452764 relative error = 0.10268571765718610713639685256493 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=324.2MB, alloc=4.6MB, time=18.15 x[1] = 0.212 y2[1] (analytic) = 1.2104155434518461893234592124401 y2[1] (numeric) = 1.2106403640218055102320130230541 absolute error = 0.000224820569959320908553810614 relative error = 0.018573833686750315369087452299528 % h = 0.001 y1[1] (analytic) = 1.2104155434518461893234592124401 y1[1] (numeric) = 1.2116764255119678229501498317632 absolute error = 0.0012608820601216336266906193231 relative error = 0.10416935464376702632030875321455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.213 y2[1] (analytic) = 1.2113930501202891240998188928769 y2[1] (numeric) = 1.2116239939741103793010676946255 absolute error = 0.0002309438538212552012488017486 relative error = 0.019064320519118290886741698765061 % h = 0.001 y1[1] (analytic) = 1.2113930501202891240998188928769 y1[1] (numeric) = 1.2126730319154496075249678099626 absolute error = 0.0012799817951604834251489170857 relative error = 0.10566197280340873373486069334033 % h = 0.001 TOP MAIN SOLVE Loop memory used=328.0MB, alloc=4.6MB, time=18.36 NO POLE NO POLE x[1] = 0.214 y2[1] (analytic) = 1.212370345395699554673977294682 y2[1] (numeric) = 1.212607522542619289506872195501 absolute error = 0.000237177146919734832894900819 relative error = 0.019563093721359850496757826753832 % h = 0.001 y1[1] (analytic) = 1.212370345395699554673977294682 y1[1] (numeric) = 1.2136695644717752852069330265645 absolute error = 0.0012992190760757305329557318825 relative error = 0.1071635479216282588186380137539 % h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.6MB, time=18.57 NO POLE NO POLE x[1] = 0.215 y2[1] (analytic) = 1.2133474283007822870767740798571 y2[1] (numeric) = 1.2135909497225229401159703778807 absolute error = 0.0002435214217406530391962980236 relative error = 0.020070213696475185623325358052669 % h = 0.001 y1[1] (analytic) = 1.2133474283007822870767740798571 y1[1] (numeric) = 1.2146660221627045220847336470936 absolute error = 0.0013185938619222350079595672365 relative error = 0.10867405585297558295940084311108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=335.7MB, alloc=4.6MB, time=18.79 x[1] = 0.216 y2[1] (analytic) = 1.2143242978584544976490495550473 y2[1] (numeric) = 1.2145742755090132038504908099068 absolute error = 0.0002499776505587062014412548595 relative error = 0.020585740646016818107951847644683 % h = 0.001 y1[1] (analytic) = 1.2143242978584544976490495550473 y1[1] (numeric) = 1.2156624039699284033186322347482 absolute error = 0.0013381061114739056695826797009 relative error = 0.11019347252078781790300512904883 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.217 y2[1] (analytic) = 1.2153009530918467101243869071349 y2[1] (numeric) = 1.2155574998972831319168067203823 absolute error = 0.0002565468054364217924198132474 relative error = 0.021109734570991749703693926502539 % h = 0.001 y1[1] (analytic) = 1.2153009530918467101243869071349 y1[1] (numeric) = 1.2166587088750704532199014831535 absolute error = 0.0013577557832237430955145760186 relative error = 0.11172177391694436708626996573493 % h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.6MB, time=19.00 NO POLE NO POLE x[1] = 0.218 y2[1] (analytic) = 1.2162773930243037724985070638692 y2[1] (numeric) = 1.216540622882526959033716755577 absolute error = 0.0002632298582231865352096917078 relative error = 0.021642255272759694442882244892584 % h = 0.001 y1[1] (analytic) = 1.2162773930243037724985070638692 y1[1] (numeric) = 1.2176549358596876555431346304226 absolute error = 0.0013775428353838830446275665534 relative error = 0.11325893610162306539419487494803 % h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.6MB, time=19.22 NO POLE NO POLE x[1] = 0.219 y2[1] (analytic) = 1.2172536166793858336843393102186 y2[1] (numeric) = 1.2175236444599401084601413953069 absolute error = 0.0002700277805542747758020850883 relative error = 0.022183362353927413145974787177523 % h = 0.001 y1[1] (analytic) = 1.2172536166793858336843393102186 y1[1] (numeric) = 1.2186510839052714739904289166376 absolute error = 0.001397467225885640306089606419 relative error = 0.11480493520305729286488725343307 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=347.1MB, alloc=4.6MB, time=19.43 x[1] = 0.22 y2[1] (analytic) = 1.218229623080869319951791005457 y2[1] (numeric) = 1.2185065646247191970223298752321 absolute error = 0.0002769415438498770705388697751 relative error = 0.022733115219239169236423497808865 % h = 0.001 y1[1] (analytic) = 1.218229623080869319951791005457 y1[1] (numeric) = 1.2196471519932488729264400906604 absolute error = 0.0014175289123795529746490852034 relative error = 0.11635974741729405788838692528395 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.221 y2[1] (analytic) = 1.2192054112527479111512399612945 y2[1] (numeric) = 1.2194893833720620401405724620835 absolute error = 0.000283972119314128989332500789 relative error = 0.023291573076463324924291624265682 % h = 0.001 y1[1] (analytic) = 1.2192054112527479111512399612945 y1[1] (numeric) = 1.2206431391049833383033056169462 absolute error = 0.0014377278522354271520656556517 relative error = 0.11792334900795304546827244010823 % h = 0.001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.6MB, time=19.64 NO POLE NO POLE x[1] = 0.222 y2[1] (analytic) = 1.220180980219233516719773257642 y2[1] (numeric) = 1.2204721006971676568554129282994 absolute error = 0.0002911204779341401356396706574 relative error = 0.02385879493727509671980981400928 % h = 0.001 y1[1] (analytic) = 1.220180980219233516719773257642 y1[1] (numeric) = 1.2216390442217758987944338787546 absolute error = 0.0014580640025423820746606211126 relative error = 0.11949571630598662613750323362939 % h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.6MB, time=19.86 NO POLE NO POLE x[1] = 0.223 y2[1] (analytic) = 1.221156329004757251469196489853 y2[1] (numeric) = 1.2214547165952362748533560723261 absolute error = 0.0002983875904790233841595824731 relative error = 0.024434839618135489137103994534689 % h = 0.001 y1[1] (analytic) = 1.221156329004757251469196489853 y1[1] (numeric) = 1.2226348663248661471361563208426 absolute error = 0.0014785373201088956669598309896 relative error = 0.12107682570944082114239381244591 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=358.5MB, alloc=4.6MB, time=20.07 x[1] = 0.224 y2[1] (analytic) = 1.2221314566339704111548376595133 y2[1] (numeric) = 1.2224372310614693354920651306196 absolute error = 0.0003057744274989243372274711063 relative error = 0.025019765741166425347963640307297 % h = 0.001 y1[1] (analytic) = 1.2221314566339704111548376595133 y1[1] (numeric) = 1.2236306043954332616762391223762 absolute error = 0.0014991477614628505214014628629 relative error = 0.12266665368321721953093152711148 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.225 y2[1] (analytic) = 1.2231063621317454478241701400572 y2[1] (numeric) = 1.2234196440910694988250439271689 absolute error = 0.0003132819593240510008737871117 relative error = 0.025613631735022093445741433777031 % h = 0.001 y1[1] (analytic) = 1.2231063621317454478241701400572 y1[1] (numeric) = 1.2246262574145970281282506394151 absolute error = 0.0015198952828515803040804993579 relative error = 0.12426517675883584280383904040769 % h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.6MB, time=20.28 NO POLE NO POLE x[1] = 0.226 y2[1] (analytic) = 1.2240810445231769449442793686679 y2[1] (numeric) = 1.2244019556792406486257986061532 absolute error = 0.0003209111560637036815192374853 relative error = 0.026216495835756526880280834356461 % h = 0.001 y1[1] (analytic) = 1.2240810445231769449442793686679 y1[1] (numeric) = 1.2256218243634188615307805059055 absolute error = 0.0015407798402419165865011372376 relative error = 0.12587237153419895280884705916288 % h = 0.001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.6MB, time=20.50 NO POLE NO POLE x[1] = 0.227 y2[1] (analytic) = 1.2250555028335825923071981370765 y2[1] (numeric) = 1.2253841658211878974114737931408 absolute error = 0.0003286629876053051042756560643 relative error = 0.026828416087687437526152977131203 % h = 0.001 y1[1] (analytic) = 1.2250555028335825923071981370765 y1[1] (numeric) = 1.2266173042229028284105059326678 absolute error = 0.0015618013893202361033077955913 relative error = 0.12748821467335579858058305113763 % h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.6MB, time=20.71 NO POLE NO POLE x[1] = 0.228 y2[1] (analytic) = 1.2260297360885041607121355760063 y2[1] (numeric) = 1.2263662745121175914659580300385 absolute error = 0.0003365384236134307538224540322 relative error = 0.027449450344256319748444956708627 % h = 0.001 y1[1] (analytic) = 1.2260297360885041607121355760063 y1[1] (numeric) = 1.2276126959739966691481003953771 absolute error = 0.0015829598854925084359648193708 relative error = 0.12911268290626829785029828006794 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.229 y2[1] (analytic) = 1.2270037433137084764236251511138 y2[1] (numeric) = 1.2273482817472373158624533288072 absolute error = 0.0003445384335288394388281776934 relative error = 0.028079656268884843732874260810574 % h = 0.001 y1[1] (analytic) = 1.2270037433137084764236251511138 y1[1] (numeric) = 1.2286079985975928205459795550184 absolute error = 0.0016042552838843441223544039046 relative error = 0.13074575302857764897134932567954 % h = 0.001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.6MB, time=20.93 NO POLE NO POLE x[1] = 0.23 y2[1] (analytic) = 1.2279775235351883954046172123601 y2[1] (numeric) = 1.2283301875217558994855036887695 absolute error = 0.0003526639865675040808864764094 relative error = 0.028719091335827556250105276915493 % h = 0.001 y1[1] (analytic) = 1.2279775235351883954046172123601 y1[1] (numeric) = 1.2296032110745294385968789077458 absolute error = 0.0016256875393410431922616953857 relative error = 0.1323874019013718690279220674122 % h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.6MB, time=21.14 NO POLE NO POLE x[1] = 0.231 y2[1] (analytic) = 1.2289510757791637773235418638014 y2[1] (numeric) = 1.2293119918308834200524774221535 absolute error = 0.0003609160517196427289355583521 relative error = 0.029367812831020906927809803741002 % h = 0.001 y1[1] (analytic) = 1.2289510757791637773235418638014 y1[1] (numeric) = 1.2305983323855914214522573154914 absolute error = 0.00164725660642764412871545169 relative error = 0.13403760645095425391593665374679 % h = 0.001 TOP MAIN SOLVE Loop memory used=381.4MB, alloc=4.6MB, time=21.36 NO POLE NO POLE x[1] = 0.232 y2[1] (analytic) = 1.2299243990720824593343681468164 y2[1] (numeric) = 1.2302936946698312091344981323371 absolute error = 0.0003692955977487498001299855207 relative error = 0.030025877852928618008240781145992 % h = 0.001 y1[1] (analytic) = 1.2299243990720824593343681468164 y1[1] (numeric) = 1.2315933615115114325895202240549 absolute error = 0.0016689624394289732551520772385 relative error = 0.13569634366861275620640200040591 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.233 y2[1] (analytic) = 1.2308974924406212296286857567934 y2[1] (numeric) = 1.2312752960338118571768191890848 absolute error = 0.0003778035931906275481334322914 relative error = 0.030693343313383415473873456146574 % h = 0.001 y1[1] (analytic) = 1.2308974924406212296286857567934 y1[1] (numeric) = 1.2325882974329709241770560317579 absolute error = 0.0016908049923496945483702749645 relative error = 0.13736359061039027662269860216443 % h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.6MB, time=21.57 NO POLE NO POLE x[1] = 0.234 y2[1] (analytic) = 1.2318703549116868007588357412751 y2[1] (numeric) = 1.2322567959180392185186365449023 absolute error = 0.0003864410063524177598008036272 relative error = 0.031370265938425139329007402509665 % h = 0.001 y1[1] (analytic) = 1.2318703549116868007588357412751 y1[1] (numeric) = 1.2335831391306011606360787290689 absolute error = 0.0017127842189143598772429877938 relative error = 0.13903932439685586498435964226159 % h = 0.001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.6MB, time=21.78 NO POLE NO POLE x[1] = 0.235 y2[1] (analytic) = 1.2328429855124167827311168565134 y2[1] (numeric) = 1.2332381943177284164123347364691 absolute error = 0.0003952088053116336812178799557 relative error = 0.032056702269135250731112702948465 % h = 0.001 y1[1] (analytic) = 1.2328429855124167827311168565134 y1[1] (numeric) = 1.2345778855849842423982695878982 absolute error = 0.0017349000725674596671527313848 relative error = 0.14072352221287682649089327209774 % h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.6MB, time=22.00 NO POLE NO POLE x[1] = 0.236 y2[1] (analytic) = 1.2338153832701806558680944893074 y2[1] (numeric) = 1.2342194912280958480421609149541 absolute error = 0.0004041079579151921740664256467 relative error = 0.032752708662467753572140709153179 % h = 0.001 y1[1] (analytic) = 1.2338153832701806558680944893074 y1[1] (numeric) = 1.2355725357766541298582103385233 absolute error = 0.0017571525064734739901158492159 relative error = 0.14241616130739172924004424008959 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.237 y2[1] (analytic) = 1.2347875472125807434390392818975 y2[1] (numeric) = 1.235200686644359189542321748866 absolute error = 0.0004131394317784461032824669685 relative error = 0.033458341292076548017000659082057 % h = 0.001 y1[1] (analytic) = 1.2347875472125807434390392818975 y1[1] (numeric) = 1.2365670886860976675195999323393 absolute error = 0.0017795414735169240805606504418 relative error = 0.1441172189931843088956314940251 % h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.6MB, time=22.21 NO POLE NO POLE x[1] = 0.238 y2[1] (analytic) = 1.2357594763674531840575228295574 y2[1] (numeric) = 1.2361817805617374010144980429435 absolute error = 0.0004223041942842169569752133861 relative error = 0.034173656149139233413924622848463 % h = 0.001 y1[1] (analytic) = 1.2357594763674531840575228295574 y1[1] (numeric) = 1.2375615432937556083342466498324 absolute error = 0.001802066926302424276723820275 relative error = 0.14582667264665826644072068414457 % h = 0.001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.6MB, time=22.43 NO POLE NO POLE x[1] = 0.239 y2[1] (analytic) = 1.2367311697628689038451980533704 y2[1] (numeric) = 1.237162772975450731544771916448 absolute error = 0.0004316032125818276995738630776 relative error = 0.034898709043177377899501359538354 % h = 0.001 y1[1] (analytic) = 1.2367311697628689038451980533704 y1[1] (numeric) = 1.2385558985800236382328269753501 absolute error = 0.0018247288171547343876289219797 relative error = 0.14754449970761295497239736691979 % h = 0.001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.6MB, time=22.64 NO POLE NO POLE x[1] = 0.24 y2[1] (analytic) = 1.2377026264271345883607920844898 y2[1] (numeric) = 1.2381436638807207242199613840851 absolute error = 0.0004410374535861358591692995953 relative error = 0.035633555602873271929751313385619 % h = 0.001 y1[1] (analytic) = 1.2377026264271345883607920844898 y1[1] (numeric) = 1.2395501535252534008464023233906 absolute error = 0.0018475270981188124856102389008 relative error = 0.14927067767901995151479886081532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.241 y2[1] (analytic) = 1.2386738453887936542933397309712 y2[1] (numeric) = 1.2391244532727702211433571826508 absolute error = 0.0004506078839765668500174516796 relative error = 0.036378251276883182877736796900762 % h = 0.001 y1[1] (analytic) = 1.2386738453887936542933397309712 y1[1] (numeric) = 1.2405443071097535224176843652531 absolute error = 0.0018704617209598681243446342819 relative error = 0.15100518412680050984734083777346 % h = 0.001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.6MB, time=22.85 NO POLE NO POLE x[1] = 0.242 y2[1] (analytic) = 1.2396448256766272209186858340254 y2[1] (numeric) = 1.2401051411468233684498566863696 absolute error = 0.0004603154701961475311708523442 relative error = 0.037132851334647127747850061966641 % h = 0.001 y1[1] (analytic) = 1.2396448256766272209186858340254 y1[1] (numeric) = 1.2415383583137906369010393699845 absolute error = 0.0018935326371634159823535359591 relative error = 0.15274799667960389036523954685623 % h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.6MB, time=23.07 NO POLE NO POLE x[1] = 0.243 y2[1] (analytic) = 1.2406155663196550813182850572694 y2[1] (numeric) = 1.2410857274981056213204897537731 absolute error = 0.0004701611784505400022046965037 relative error = 0.03789741086719518096709413282255 % h = 0.001 y1[1] (analytic) = 1.2406155663196550813182850572694 y1[1] (numeric) = 1.2425323061175904112502216396261 absolute error = 0.0019167397979353299319365823567 relative error = 0.15449909302858656300948275372761 % h = 0.001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.6MB, time=23.28 NO POLE NO POLE x[1] = 0.244 y2[1] (analytic) = 1.2415860663471366733593278902572 y2[1] (numeric) = 1.2420662123218437489963313488505 absolute error = 0.0004801459747070756370034585933 relative error = 0.038671984787950334124363672704843 % h = 0.001 y1[1] (analytic) = 1.2415860663471366733593278902572 y1[1] (numeric) = 1.2435261495013385708928257858023 absolute error = 0.0019400831542018975334978955451 relative error = 0.156258450927192279323342729853 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.245 y2[1] (analytic) = 1.2425563247885720504352218862454 y2[1] (numeric) = 1.2430465956132658397917957790922 absolute error = 0.0004902708246937893565738928468 relative error = 0.039456627833527924439942508860917 % h = 0.001 y1[1] (analytic) = 1.2425563247885720504352218862454 y1[1] (numeric) = 1.2445198874451819253904472627121 absolute error = 0.0019635626566098749552253764667 relative error = 0.15802604819093300971235362447755 % h = 0.001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.6MB, time=23.50 NO POLE NO POLE x[1] = 0.246 y2[1] (analytic) = 1.2435263406737028519654573937924 y2[1] (numeric) = 1.2440268773676013061073073929412 absolute error = 0.0005005366938984541418499991488 relative error = 0.040251394564531648659157499796758 % h = 0.001 y1[1] (analytic) = 1.2435263406737028519654573937924 y1[1] (numeric) = 1.2455135189292293942835402405712 absolute error = 0.0019871782555265423180828467788 relative error = 0.15980186269717074200439397968448 % h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.6MB, time=23.72 NO POLE NO POLE x[1] = 0.247 y2[1] (analytic) = 1.2444961130325132736538872824077 y2[1] (numeric) = 1.2450070575800808894413425790691 absolute error = 0.0005109445475676157874552966614 relative error = 0.041056339366346178976361967662141 % h = 0.001 y1[1] (analytic) = 1.2444961130325132736538872824077 y1[1] (numeric) = 1.2465070429335530331199615735207 absolute error = 0.002010929901039759466074291113 relative error = 0.16158587238490013742612368053647 % h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.6MB, time=23.94 NO POLE NO POLE x[1] = 0.248 y2[1] (analytic) = 1.2454656408952310375044504040511 y2[1] (numeric) = 1.2459871362459366654018379097955 absolute error = 0.0005214953507056278973875057444 relative error = 0.041871516449926397508162733123409 % h = 0.001 y1[1] (analytic) = 1.2454656408952310375044504040511 y1[1] (numeric) = 1.2475004584381890596661892869592 absolute error = 0.0020348175429580221617388829081 relative error = 0.16337805525453204013152393958223 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.249 y2[1] (analytic) = 1.2464349232923283615933687748402 y2[1] (numeric) = 1.2469671133604020487169592708822 absolute error = 0.000532190068073687123590496042 relative error = 0.0426969798525832657480496973233 % h = 0.001 y1[1] (analytic) = 1.2464349232923283615933687748402 y1[1] (numeric) = 1.2484937644231388803002036811726 absolute error = 0.0020588411308105187068349063324 relative error = 0.16517838936767783643767966409023 % h = 0.001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.6MB, time=24.15 NO POLE NO POLE x[1] = 0.25 y2[1] (analytic) = 1.2474039592545229295968487048494 y2[1] (numeric) = 1.2479469889187117982452268198468 absolute error = 0.0005430296641888686483781149974 relative error = 0.043532783438766345348332754458894 % h = 0.001 y1[1] (analytic) = 1.2474039592545229295968487048494 y1[1] (numeric) = 1.2494869598683701165850188210318 absolute error = 0.0020830006138471869881701161824 relative error = 0.16698685284693465994222640836697 % h = 0.001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.6MB, time=24.37 NO POLE NO POLE x[1] = 0.251 y2[1] (analytic) = 1.2483727478127788600733163483794 y2[1] (numeric) = 1.2489267629161020219849906148632 absolute error = 0.0005540151033231619116742664838 relative error = 0.04437898090084298648953444988782 % h = 0.001 y1[1] (analytic) = 1.2483727478127788600733163483794 y1[1] (numeric) = 1.2504800437538176320218518554001 absolute error = 0.0021072959410387719485355070207 relative error = 0.16880342387567143871605972966926 % h = 0.001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.6MB, time=24.59 NO POLE NO POLE x[1] = 0.252 y2[1] (analytic) = 1.2493412879983076754992183925442 y2[1] (numeric) = 1.2499064353478101820832517562398 absolute error = 0.0005651473495025065840333636956 relative error = 0.045235625759874200012125103391252 % h = 0.001 y1[1] (analytic) = 1.2493412879983076754992183925442 y1[1] (numeric) = 1.2514730150593845589819172847419 absolute error = 0.0021317270610768834826988921977 relative error = 0.17062808069781578078397379811268 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.253 y2[1] (analytic) = 1.2503095788425692710574188484538 y2[1] (numeric) = 1.250886006209075099843823882399 absolute error = 0.0005764273665058287864050339452 relative error = 0.046102771366387229400716999624345 % h = 0.001 y1[1] (analytic) = 1.2503095788425692710574188484538 y1[1] (numeric) = 1.2524658727649433258158329712526 absolute error = 0.0021562939223740547584141227988 relative error = 0.17246080161764169412485920850053 % h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.6MB, time=24.81 NO POLE NO POLE x[1] = 0.254 y2[1] (analytic) = 1.2512776193772728831772231566772 y2[1] (numeric) = 1.2518654754951369607348298622168 absolute error = 0.0005878561178640775576067055396 relative error = 0.046980470901144838626552630232499 % h = 0.001 y1[1] (analytic) = 1.2512776193772728831772231566772 y1[1] (numeric) = 1.2534586158503366841396243626364 absolute error = 0.0021809964730638009624012059592 relative error = 0.17430156499955813744194774902161 % h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.6MB, time=25.02 NO POLE NO POLE x[1] = 0.255 y2[1] (analytic) = 1.252245408634378057825061067043 y2[1] (numeric) = 1.2528448432012373193955285255233 absolute error = 0.0005994345668592615704674584803 relative error = 0.047868777375911331770325800418064 % h = 0.001 y1[1] (analytic) = 1.252245408634378057825061067043 y1[1] (numeric) = 1.2544512432953787362963130784454 absolute error = 0.0022058346610006784712520114024 relative error = 0.17615034926789839797234503968245 % h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.6MB, time=25.24 NO POLE NO POLE x[1] = 0.256 y2[1] (analytic) = 1.2532129456460956185448600021744 y2[1] (numeric) = 1.2538241093226191046424662735105 absolute error = 0.0006111636765234860976062713361 relative error = 0.048767743634215320264060652051711 % h = 0.001 y1[1] (analytic) = 1.2532129456460956185448600021744 y1[1] (numeric) = 1.2554437540798559629920756866576 absolute error = 0.0022308084337603444472156844832 relative error = 0.17800713290671029262374109823586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.257 y2[1] (analytic) = 1.2541802294448886342471408644664 y2[1] (numeric) = 1.2548032738545266244749484107465 absolute error = 0.0006230444096379902278075462801 relative error = 0.049677422352109253507939291629138 % h = 0.001 y1[1] (analytic) = 1.2541802294448886342471408644664 y1[1] (numeric) = 1.2564361471835282511059581779182 absolute error = 0.0022559177386396168588173134518 relative error = 0.17987189445954718874473465538171 % h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.6MB, time=25.45 NO POLE NO POLE x[1] = 0.258 y2[1] (analytic) = 1.2551472590634733867458684974902 y2[1] (numeric) = 1.2557823367922055710798250404521 absolute error = 0.0006350777287321843339565429619 relative error = 0.050597866038925728535610751055836 % h = 0.001 y1[1] (analytic) = 1.2551472590634733867458684974902 y1[1] (numeric) = 1.2574284215861299216721313255955 absolute error = 0.0022811625226565349262628281053 relative error = 0.18174461252925984085365005229483 % h = 0.001 TOP MAIN SOLVE Loop memory used=457.7MB, alloc=4.6MB, time=25.67 NO POLE NO POLE x[1] = 0.259 y2[1] (analytic) = 1.256114033534820338042089265054 y2[1] (numeric) = 1.2567612981309030258355863646577 absolute error = 0.0006472645960826877934970996037 relative error = 0.051529127038030594319629479034512 % h = 0.001 y1[1] (analytic) = 1.256114033534820338042089265054 y1[1] (numeric) = 1.2584205762673707580336718015076 absolute error = 0.0023065427325504199915825364536 relative error = 0.1836252657777890396690664356184 % h = 0.001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.6MB, time=25.88 NO POLE NO POLE x[1] = 0.26 y2[1] (analytic) = 1.2570805518921550973533884643652 y2[1] (numeric) = 1.2577401578658674643157622308251 absolute error = 0.0006596059737123669623737664599 relative error = 0.052471257527572866227257507085139 % h = 0.001 y1[1] (analytic) = 1.2570805518921550973533884643652 y1[1] (numeric) = 1.2594126102069370341668535998683 absolute error = 0.0023320583147819368134651355031 relative error = 0.18551383292595906980351833797101 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.261 y2[1] (analytic) = 1.2580468131689593878882005439147 y2[1] (numeric) = 1.2587189159923487612916207664938 absolute error = 0.0006721028233893734034202225791 relative error = 0.053424309521231466055917924848362 % h = 0.001 y1[1] (analytic) = 1.2580468131689593878882005439147 y1[1] (numeric) = 1.2604045223844925431749340056678 absolute error = 0.0023577092155331552867334617531 relative error = 0.18741029275327197249996521125757 % h = 0.001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.6MB, time=26.09 NO POLE NO POLE x[1] = 0.262 y2[1] (analytic) = 1.2590128163989720133640053518554 y2[1] (numeric) = 1.2596975725055981957341609434857 absolute error = 0.0006847561066261823701555916303 relative error = 0.054388334868958802997105418832662 % h = 0.001 y1[1] (analytic) = 1.2590128163989720133640053518554 y1[1] (numeric) = 1.2613963117796796259504180283601 absolute error = 0.0023834953807076125864126765047 relative error = 0.18931462409770260980866567700072 % h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.6MB, time=26.30 NO POLE NO POLE x[1] = 0.263 y2[1] (analytic) = 1.2599785606161898242684438967593 y2[1] (numeric) = 1.2606761274008684558153939131892 absolute error = 0.0006975667846786315469500164299 relative error = 0.055363385257721210797539485585555 % h = 0.001 y1[1] (analytic) = 1.2599785606161898242684438967593 y1[1] (numeric) = 1.2623879773721202000047849073624 absolute error = 0.0024094167559303757363410106031 relative error = 0.19122680585549452662003078019864 % h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.6MB, time=26.52 NO POLE NO POLE x[1] = 0.264 y2[1] (analytic) = 1.2609440448548686838623873597158 y2[1] (numeric) = 1.2616545806734136439089079544278 absolute error = 0.000710535818544960046520594712 relative error = 0.056349512212236256306784648429796 % h = 0.001 y1[1] (analytic) = 1.2609440448548686838623873597158 y1[1] (numeric) = 1.2633795181414167884646599824933 absolute error = 0.0024354732865481046022726227775 relative error = 0.19314681698095660698686998478837 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=476.8MB, alloc=4.6MB, time=26.74 x[1] = 0.265 y2[1] (analytic) = 1.2619092681495244339239933547858 y2[1] (numeric) = 1.2626329323184892815897118754155 absolute error = 0.0007236641689648476657185206297 relative error = 0.057346767095706934521456732130625 % h = 0.001 y1[1] (analytic) = 1.2619092681495244339239933547858 y1[1] (numeric) = 1.2643709330671535492334149100773 absolute error = 0.0024616649176291153094215552915 relative error = 0.1950746364862605211871846277847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.266 y2[1] (analytic) = 1.2628742295349338602327836938334 y2[1] (numeric) = 1.2636111823313523146333517112973 absolute error = 0.0007369527964184544005680174639 relative error = 0.058355201110552765157482146800328 % h = 0.001 y1[1] (analytic) = 1.2628742295349338602327836938334 y1[1] (numeric) = 1.2653622211288973043171788940334 absolute error = 0.0024879915939634440843952002 relative error = 0.19701024344123895999630665339638 % h = 0.001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.6MB, time=26.95 NO POLE NO POLE x[1] = 0.267 y2[1] (analytic) = 1.2638389280461356577927781717389 y2[1] (numeric) = 1.2645893307072611180142955587787 absolute error = 0.0007504026611254602215173870398 relative error = 0.059374865299137805703675383720439 % h = 0.001 y1[1] (analytic) = 1.2638389280461356577927781717389 y1[1] (numeric) = 1.2663533813061985693142432908338 absolute error = 0.0025144532600629115214651190949 relative error = 0.19895361697318465265472626701099 % h = 0.001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.6MB, time=27.17 NO POLE NO POLE x[1] = 0.268 y2[1] (analytic) = 1.2648033627184313957937191489395 y2[1] (numeric) = 1.2655673774414755009035813893561 absolute error = 0.0007640147230441051098622404166 relative error = 0.060405810544495595832145734475505 % h = 0.001 y1[1] (analytic) = 1.2648033627184313957937191489395 y1[1] (numeric) = 1.2673444125785925830668416377803 absolute error = 0.0025410498601611872731224888408 relative error = 0.20090473626665016503540127192448 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=488.2MB, alloc=4.6MB, time=27.38 x[1] = 0.269 y2[1] (analytic) = 1.265767532587386482309421970154 y2[1] (numeric) = 1.2665453225292567116657226826751 absolute error = 0.0007777899418702293563007125211 relative error = 0.0614480875710510479637348319073 % h = 0.001 y1[1] (analytic) = 1.265767532587386482309421970154 y1[1] (numeric) = 1.2683353139256003374742868455837 absolute error = 0.0025677813382138551648648754297 relative error = 0.2028635805632484745316938610277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.27 y2[1] (analytic) = 1.2667314366888311287322865210205 y2[1] (numeric) = 1.2675231659658674428548667215628 absolute error = 0.0007917292770363141225802005423 relative error = 0.06250174694533929870981921690359 % h = 0.001 y1[1] (analytic) = 1.2667314366888311287322865210205 y1[1] (numeric) = 1.2693260843267296074664469887653 absolute error = 0.0025946476378984787341604677448 relative error = 0.20483012916145431820433811328182 % h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.6MB, time=27.60 NO POLE NO POLE x[1] = 0.271 y2[1] (analytic) = 1.267695074058861313943005488217 y2[1] (numeric) = 1.2685009077465718362102003903057 absolute error = 0.0008058336877105222671949020887 relative error = 0.063566839076721535835384017132654 % h = 0.001 y1[1] (analytic) = 1.267695074058861313943005488217 y1[1] (numeric) = 1.2703167227614759811365408209104 absolute error = 0.0026216487026146671935353326934 relative error = 0.2068043614164063107430039649624 % h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.6MB, time=27.81 NO POLE NO POLE x[1] = 0.272 y2[1] (analytic) = 1.2686584437338397482145051534362 y2[1] (numeric) = 1.2694785478666354876505983177732 absolute error = 0.000820104132795739436093164337 relative error = 0.064643414218097815312282259714872 % h = 0.001 y1[1] (analytic) = 1.2686584437338397482145051534362 y1[1] (numeric) = 1.2713072282093238900322338363088 absolute error = 0.0026487844754841418177286828726 relative error = 0.20878625673970982881509156271141 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=499.7MB, alloc=4.6MB, time=28.02 x[1] = 0.273 y2[1] (analytic) = 1.2696215447503968368491548173544 y2[1] (numeric) = 1.2704560863213254522685082070244 absolute error = 0.00083454157092861541935338967 relative error = 0.0657315224666168829560366246046 % h = 0.001 y1[1] (analytic) = 1.2696215447503968368491548173544 y1[1] (numeric) = 1.2722975996497476396040153950055 absolute error = 0.0026760548993508027548605776511 relative error = 0.2107757945992406583913642266336 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.274 y2[1] (analytic) = 1.2705843761454316435482812164654 y2[1] (numeric) = 1.2714335231059102493230681930738 absolute error = 0.0008491469604786057747869766084 relative error = 0.066831213764383015064413892098177 % h = 0.001 y1[1] (analytic) = 1.2705843761454316435482812164654 y1[1] (numeric) = 1.2732878360622124398098371247628 absolute error = 0.0027034599167807962615559082974 relative error = 0.21277295451894940165490932283341 % h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.6MB, time=28.23 NO POLE NO POLE x[1] = 0.275 y2[1] (analytic) = 1.2715469369561128535130245633453 y2[1] (numeric) = 1.2724108582156598672324510705389 absolute error = 0.0008639212595470137194265071936 relative error = 0.067942537899159892401304278314684 % h = 0.001 y1[1] (analytic) = 1.2715469369561128535130245633453 y1[1] (numeric) = 1.2742779364261754358749925108999 absolute error = 0.0027309994700625823619679475546 relative error = 0.21477771607866664011670472676483 % h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.6MB, time=28.45 NO POLE NO POLE x[1] = 0.276 y2[1] (analytic) = 1.2725092262198797362755731095714 y2[1] (numeric) = 1.2733880916458457685654302329431 absolute error = 0.0008788654259660322898571233717 relative error = 0.069065544505071521795165635548057 % h = 0.001 y1[1] (analytic) = 1.2725092262198797362755731095714 y1[1] (numeric) = 1.2752678997210867392062172834312 absolute error = 0.0027586735012070029306441738598 relative error = 0.21679005891390885057776480948502 % h = 0.001 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.6MB, time=28.67 NO POLE NO POLE x[1] = 0.277 y2[1] (analytic) = 1.2734712429744431082598134001431 y2[1] (numeric) = 1.2743652233917408950321621655026 absolute error = 0.0008939804172977867723487653595 relative error = 0.070200283063300219547443486786977 % h = 0.001 y1[1] (analytic) = 1.2734712429744431082598134001431 y1[1] (numeric) = 1.2762577249263904584589899103681 absolute error = 0.002786481951947350199176510225 relative error = 0.21880996271568507059444455170697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.278 y2[1] (analytic) = 1.2744329862577862950704336588324 y2[1] (numeric) = 1.2753422534486196724741803332893 absolute error = 0.0009092671908333774037466744569 relative error = 0.071346802902781670772949451273144 % h = 0.001 y1[1] (analytic) = 1.2744329862577862950704336588324 y1[1] (numeric) = 1.2772474110215257307570112064812 absolute error = 0.0028144247637394356865775476488 relative error = 0.22083740723030431011999403666828 % h = 0.001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.6MB, time=28.88 NO POLE NO POLE x[1] = 0.279 y2[1] (analytic) = 1.2753944551081660935095180154422 y2[1] (numeric) = 1.2763191818117580158535953067258 absolute error = 0.0009247267035919223440772912836 relative error = 0.072505153200897078721170201019389 % h = 0.001 y1[1] (analytic) = 1.2753944551081660935095180154422 y1[1] (numeric) = 1.2782369569859277530628417682449 absolute error = 0.0028425018777616595533237528027 relative error = 0.22287237225918370601187873802622 % h = 0.001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.6MB, time=29.09 NO POLE NO POLE x[1] = 0.28 y2[1] (analytic) = 1.2763556485641137333196695584578 y2[1] (numeric) = 1.2772960084764333342414959664423 absolute error = 0.0009403599123196009218264079845 relative error = 0.073675382984162418054884088055523 % h = 0.001 y1[1] (analytic) = 1.2763556485641137333196695584578 y1[1] (numeric) = 1.2792263617990288136986756480978 absolute error = 0.00287071323491508037900608964 relative error = 0.2249148376586574161107142469312 % h = 0.001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.6MB, time=29.31 NO POLE NO POLE x[1] = 0.281 y2[1] (analytic) = 1.2773165656644358386527004700495 y2[1] (numeric) = 1.2782727334379245358055466296018 absolute error = 0.0009561677734886971528461595523 relative error = 0.074857541128914805990280434357045 % h = 0.001 y1[1] (analytic) = 1.2773165656644358386527004700495 y1[1] (numeric) = 1.2802156244402593240162283845591 absolute error = 0.0028990587758234853635279145096 relative error = 0.226964783339786249612907912681 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.282 y2[1] (analytic) = 1.2782772054482153892629277748141 y2[1] (numeric) = 1.2792493566915120327967749398812 absolute error = 0.0009721512432966435338471650671 relative error = 0.076051676361996005131004635584516 % h = 0.001 y1[1] (analytic) = 1.2782772054482153892629277748141 y1[1] (numeric) = 1.2812047438890488502147172091363 absolute error = 0.0029275384408334609517894343222 relative error = 0.22902218926816803047525483998272 % h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.6MB, time=29.53 NO POLE NO POLE x[1] = 0.283 y2[1] (analytic) = 1.2792375669548126814241135090431 y2[1] (numeric) = 1.2802258782324777465355453633846 absolute error = 0.0009883112776650651114318543415 relative error = 0.077257837261433071757188166049704 % h = 0.001 y1[1] (analytic) = 1.2792375669548126814241135090431 y1[1] (numeric) = 1.2821937191248271453059109563471 absolute error = 0.002956152170014463881797447304 relative error = 0.23108703546374869060580232468528 % h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.6MB, time=29.75 NO POLE NO POLE x[1] = 0.284 y2[1] (analytic) = 1.2801976492238662885690883936544 y2[1] (numeric) = 1.2812022980561051123967131328579 absolute error = 0.0010046488322388238276247392035 relative error = 0.078476072257116163259563774902051 % h = 0.001 y1[1] (analytic) = 1.2801976492238662885690883936544 y1[1] (numeric) = 1.2831825491270251812252269095591 absolute error = 0.0029848999031588926561385159047 relative error = 0.23315930200063408961127564962537 % h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.6MB, time=29.96 NO POLE NO POLE x[1] = 0.285 y2[1] (analytic) = 1.2811574512952940216510983712452 y2[1] (numeric) = 1.2821786161576790847939534826699 absolute error = 0.0010211648623850631428551114247 relative error = 0.079706429631473518338210135089844 % h = 0.001 y1[1] (analytic) = 1.2811574512952940216510983712452 y1[1] (numeric) = 1.2841712328750761810878515227233 absolute error = 0.0030137815797821594367531514781 relative error = 0.23523896900690255788724972662435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.286 y2[1] (analytic) = 1.2821169722092938892259136459998 y2[1] (numeric) = 1.2831548325324861421632610171311 absolute error = 0.0010378603231922529373473711313 relative error = 0.080948957520143623515314470225006 % h = 0.001 y1[1] (analytic) = 1.2821169722092938892259136459998 y1[1] (numeric) = 1.2851597693484166515888616664445 absolute error = 0.0030427971391227623629480204447 relative error = 0.23732601666441815985305588338851 % h = 0.001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.6MB, time=30.18 NO POLE NO POLE x[1] = 0.287 y2[1] (analytic) = 1.2830762110063450572537401444227 y2[1] (numeric) = 1.2841309471758142919456140548269 absolute error = 0.0010547361694692346918739104042 relative error = 0.082203703912644579441583776538295 % h = 0.001 y1[1] (analytic) = 1.2830762110063450572537401444227 y1[1] (numeric) = 1.2861481575264874155463227561889 absolute error = 0.0030719465201423582925826117662 relative error = 0.23942042520864467414913167305195 % h = 0.001 TOP MAIN SOLVE Loop memory used=541.6MB, alloc=4.6MB, time=30.39 NO POLE NO POLE x[1] = 0.288 y2[1] (analytic) = 1.2840351667272088086199735950659 y2[1] (numeric) = 1.2851069600829530755687987917577 absolute error = 0.0010717933557442669488251966918 relative error = 0.083470716653040680406572732541435 % h = 0.001 y1[1] (analytic) = 1.2840351667272088086199735950659 y1[1] (numeric) = 1.2871363963887346445863398307855 absolute error = 0.0031012296615258359663662357196 relative error = 0.24152217492846028763015444534843 % h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.6MB, time=30.61 NO POLE NO POLE x[1] = 0.289 y2[1] (analytic) = 1.284993838412929502373836706576 y2[1] (numeric) = 1.2860828712491935734283881261962 absolute error = 0.0010890328362640710545514196202 relative error = 0.084750043440606220394226817866266 % h = 0.001 y1[1] (analytic) = 1.284993838412929502373836706576 y1[1] (numeric) = 1.2881244849146108919690373607244 absolute error = 0.0031306465016813895952006541484 relative error = 0.24363124616597300000284707351078 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.29 y2[1] (analytic) = 1.2859522251048355326839402055044 y2[1] (numeric) = 1.2870586806698284098678699882964 absolute error = 0.001106455564992877183929782792 relative error = 0.08604173183048653895636013174562 % h = 0.001 y1[1] (analytic) = 1.2859522251048355326839402055044 y1[1] (numeric) = 1.2891124220835761255544432780971 absolute error = 0.0031601969787405928705030725927 relative error = 0.24574761931633673597280718885627 % h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.6MB, time=30.82 NO POLE NO POLE x[1] = 0.291 y2[1] (analytic) = 1.286910325844540287509808778398 y2[1] (numeric) = 1.2880343883401517581579200176183 absolute error = 0.0011240624956114706481112392203 relative error = 0.087345829234356320108596513657698 % h = 0.001 y1[1] (analytic) = 1.286910325844540287509808778398 y1[1] (numeric) = 1.290100206875098760907252433365 absolute error = 0.003189881030558473397443654967 relative error = 0.2478712748275681617800900416417 % h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.6MB, time=31.03 NO POLE NO POLE x[1] = 0.292 y2[1] (analytic) = 1.287868139673943106988413246727 y2[1] (numeric) = 1.2890099942554593454748134318668 absolute error = 0.0011418545815162384864001851398 relative error = 0.088662382921075157385497441665188 % h = 0.001 y1[1] (analytic) = 1.287868139673943106988413246727 y1[1] (numeric) = 1.2910878382686566945394443984725 absolute error = 0.0032196985947135875510311517455 relative error = 0.25000219320036420301857018280224 % h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.6MB, time=31.25 NO POLE NO POLE x[1] = 0.293 y2[1] (analytic) = 1.2888256656352302415347505881947 y2[1] (numeric) = 1.2899854984110484578779709302829 absolute error = 0.0011598327758182163432203420882 relative error = 0.089991440017340398124178453614812 % h = 0.001 y1[1] (analytic) = 1.2888256656352302415347505881947 y1[1] (numeric) = 1.2920753152437383372897302511543 absolute error = 0.0032496496085080957549796629596 relative error = 0.25214035498792026064931904778723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.294 y2[1] (analytic) = 1.2897829027708758096555137039305 y2[1] (numeric) = 1.2909609008022179452866334752708 absolute error = 0.0011779980313421356311197713403 relative error = 0.091333047508337279978675151345842 % h = 0.001 y1[1] (analytic) = 1.2897829027708758096555137039305 y1[1] (numeric) = 1.2930626367798436478388026916114 absolute error = 0.0032797340089678381832889876809 relative error = 0.25428574079574912213336471411735 % h = 0.001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.6MB, time=31.46 NO POLE NO POLE x[1] = 0.295 y2[1] (analytic) = 1.2907398501236427554748931179768 y2[1] (numeric) = 1.2919362014242682264556607959942 absolute error = 0.0011963513006254709807676780174 relative error = 0.092687252238386372600657875144251 % h = 0.001 y1[1] (analytic) = 1.2907398501236427554748931179768 y1[1] (numeric) = 1.2940498018564851663593635600546 absolute error = 0.0033099517328424108844704420778 relative error = 0.25643833128150056462424709264595 % h = 0.001 TOP MAIN SOLVE Loop memory used=564.5MB, alloc=4.6MB, time=31.68 NO POLE NO POLE x[1] = 0.296 y2[1] (analytic) = 1.291696506736583805971553083346 y2[1] (numeric) = 1.2929114002725012939504484578306 absolute error = 0.0012148935359174879788953744846 relative error = 0.09405410091158833735580855600367 % h = 0.001 y1[1] (analytic) = 1.291696506736583805971553083346 y1[1] (numeric) = 1.2950368094531890482999025419351 absolute error = 0.0033403027166052423283494585891 relative error = 0.25859810715478164717574708755576 % h = 0.001 TOP MAIN SOLVE Loop memory used=568.4MB, alloc=4.6MB, time=31.89 NO POLE NO POLE x[1] = 0.297 y2[1] (analytic) = 1.2926528716530424279258248577527 y2[1] (numeric) = 1.2938864973422207191209583417339 absolute error = 0.0012336256891782911951334839812 relative error = 0.095433640092466017879261762863227 % h = 0.001 y1[1] (analytic) = 1.2926528716530424279258248577527 y1[1] (numeric) = 1.2960236585494960983012005670011 absolute error = 0.0033707868964536703753757092484 relative error = 0.26076504917697768893505230745885 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.298 y2[1] (analytic) = 1.2936089439166537845761602019079 y2[1] (numeric) = 1.2948614926287316570748573777206 absolute error = 0.0012525487120778724986971758127 relative error = 0.096825916206603874207972273392584 % h = 0.001 y1[1] (analytic) = 1.2936089439166537845761602019079 y1[1] (numeric) = 1.2970103481249628042445311286369 absolute error = 0.003401404208309019668370926729 relative error = 0.26293913816107393030642521327134 % h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.6MB, time=32.10 NO POLE NO POLE x[1] = 0.299 y2[1] (analytic) = 1.2945647225713456919838884439998 y2[1] (numeric) = 1.2958363861273408516497593768664 absolute error = 0.0012716635559951596658709328666 relative error = 0.098230975541284773162701337099839 % h = 0.001 y1[1] (analytic) = 1.2945647225713456919838884439998 y1[1] (numeric) = 1.2979968771591623714305324712562 absolute error = 0.0034321545878166794466440272564 relative error = 0.26512035497147787408516262723714 % h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.6MB, time=32.32 NO POLE NO POLE x[1] = 0.3 y2[1] (analytic) = 1.295520206661339575105320745685 y2[1] (numeric) = 1.2968111778333566403845648063771 absolute error = 0.0012909711720170652792440606921 relative error = 0.099648864246124147587510910160342 % h = 0.001 y1[1] (analytic) = 1.295520206661339575105320745685 y1[1] (numeric) = 1.2989832446316857568877233158371 absolute error = 0.0034630379703461817824025701521 relative error = 0.26730868052384230357627877803629 % h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.6MB, time=32.54 NO POLE NO POLE x[1] = 0.301 y2[1] (analytic) = 1.2964753952311514235702454975658 y2[1] (numeric) = 1.2977858677420889594898933524781 absolute error = 0.0013104725109375359196478549123 relative error = 0.10107962833370153699021727993882 % h = 0.001 y1[1] (analytic) = 1.2964753952311514235702454975658 y1[1] (numeric) = 1.2999694495221427038096345170011 absolute error = 0.0034940542909912802393890194353 relative error = 0.26950409578488897472690799344325 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.302 y2[1] (analytic) = 1.2974302873255927471658590657366 y2[1] (numeric) = 1.2987604558488493488176041160551 memory used=583.6MB, alloc=4.6MB, time=32.75 absolute error = 0.0013301685232566016517450503185 relative error = 0.10252331368018952206318043572665 % h = 0.001 y1[1] (analytic) = 1.2974302873255927471658590657366 y1[1] (numeric) = 1.3009554908101627761195287693526 absolute error = 0.003525203484570028953669703616 relative error = 0.27170658177223297931590824481293 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.303 y2[1] (analytic) = 1.2983848819897715310251764055494 y2[1] (numeric) = 1.2997349421489509568293982861696 absolute error = 0.0013500601591794258042218806202 relative error = 0.10397996602598006550009106661864 % h = 0.001 y1[1] (analytic) = 1.2983848819897715310251764055494 y1[1] (numeric) = 1.3019413674753963931616802061115 absolute error = 0.0035564854856248621365038005621 relative error = 0.27391611955420777625855346408493 % h = 0.001 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.6MB, time=32.97 NO POLE NO POLE x[1] = 0.304 y2[1] (analytic) = 1.2993391782690931905189663542671 y2[1] (numeric) = 1.3007093266377085455644991367711 absolute error = 0.001370148368615355045532782504 relative error = 0.10544963097630827146106097992419 % h = 0.001 y1[1] (analytic) = 1.2993391782690931905189663542671 y1[1] (numeric) = 1.302927078497515864518185459386 absolute error = 0.0035879002284226739992191051189 relative error = 0.27613269024969088809853135879567 % h = 0.001 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.6MB, time=33.18 NO POLE NO POLE x[1] = 0.305 y2[1] (analytic) = 1.3002931752092615258502567107484 y2[1] (numeric) = 1.3016836093104384956064041921297 absolute error = 0.0013904341011769697561474813813 relative error = 0.10693235400187357597532284915514 % h = 0.001 y1[1] (analytic) = 1.3002931752092615258502567107484 y1[1] (numeric) = 1.3039126228562164249502774787521 absolute error = 0.0036194476469548991000207680037 relative error = 0.27835627502793025977371480535125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=595.1MB, alloc=4.6MB, time=33.40 x[1] = 0.306 y2[1] (analytic) = 1.3012468718562796763504545077395 y2[1] (numeric) = 1.3026577901624588110487044067213 absolute error = 0.0014109183061791346982498989818 relative error = 0.10842818043945838050819934990027 % h = 0.001 y1[1] (analytic) = 1.3012468718562796763504545077395 y1[1] (numeric) = 1.3048979995312172694631131331228 absolute error = 0.0036511276749375931126586253833 relative error = 0.28058685510837127675634926341059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.307 y2[1] (analytic) = 1.3022002672564510744761271807312 y2[1] (numeric) = 1.3036318691890891244599652055108 absolute error = 0.0014316019326380499838380247796 relative error = 0.10993715549254414085670776946832 % h = 0.001 y1[1] (analytic) = 1.3022002672564510744761271807312 y1[1] (numeric) = 1.3058832075022625884930053502127 absolute error = 0.0036829402458115140168781694815 relative error = 0.28282441176048443968239648120091 % h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.6MB, time=33.61 NO POLE NO POLE x[1] = 0.308 y2[1] (analytic) = 1.30315336045638039950549063668 y2[1] (numeric) = 1.3046058463856507018476642307964 absolute error = 0.0014524859292703023421735941164 relative error = 0.1114593242319249234762219404138 % h = 0.001 y1[1] (analytic) = 1.30315336045638039950549063668 y1[1] (numeric) = 1.3068682457491226032160702782272 absolute error = 0.0037148852927422037105796415472 relative error = 0.28506892630359369259879650473601 % h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.6MB, time=33.83 NO POLE NO POLE x[1] = 0.309 y2[1] (analytic) = 1.3041061505029745309336505261852 y2[1] (numeric) = 1.3055797217474664476211806420019 absolute error = 0.0014735712444919166875301158167 relative error = 0.11299473159631844127901672216353 % h = 0.001 y1[1] (analytic) = 1.3041061505029745309336505261852 y1[1] (numeric) = 1.3078531132515946009772596857301 absolute error = 0.0037469627486200700436091595449 relative error = 0.28732038010670540197135611316198 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=606.5MB, alloc=4.6MB, time=34.04 x[1] = 0.31 y2[1] (analytic) = 1.305058636443443501565643323959 y2[1] (numeric) = 1.3065534952698609095538308150338 absolute error = 0.0014948588264174079881874910748 relative error = 0.11454342239297458088426912593425 % h = 0.001 y1[1] (analytic) = 1.305058636443443501565643323959 y1[1] (numeric) = 1.3088378089895039708387485479757 absolute error = 0.0037791725460604692731052240167 relative error = 0.28957875458833798360984272522259 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.311 y2[1] (analytic) = 1.3060108173253014503063241246284 y2[1] (numeric) = 1.3075271669481602837439452880523 absolute error = 0.0015163496228588334376211634239 relative error = 0.11610544129828143323818244606411 % h = 0.001 y1[1] (analytic) = 1.3060108173253014503063241246284 y1[1] (numeric) = 1.309822331942705239246647501323 absolute error = 0.0038115146174037889403233766946 relative error = 0.29184403121635217468065900095478 % h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.6MB, time=34.26 NO POLE NO POLE x[1] = 0.312 y2[1] (analytic) = 1.3069626921963675746461483640617 y2[1] (numeric) = 1.3085007367776924195749818007463 absolute error = 0.0015380445813248449288334366846 relative error = 0.1176808328583688394623333412066 % h = 0.001 y1[1] (analytic) = 1.3069626921963675746461483640617 y1[1] (numeric) = 1.3108066810910831058150095816885 absolute error = 0.0038439888947155311688612176268 relative error = 0.29411619150778194799119524021208 % h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.6MB, time=34.49 NO POLE NO POLE x[1] = 0.313 y2[1] (analytic) = 1.3079142601047670828418949805147 y2[1] (numeric) = 1.3094742047537868246746692744456 absolute error = 0.0015599446490197418327742939309 relative error = 0.11926964148970946372811462966192 % h = 0.001 y1[1] (analytic) = 1.3079142601047670828418949805147 y1[1] (numeric) = 1.311790855414553479226100398335 absolute error = 0.0038765953097863963842054178203 relative error = 0.29639521702866606574360469355585 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=617.9MB, alloc=4.6MB, time=34.70 x[1] = 0.314 y2[1] (analytic) = 1.3088655200989321457913788349557 y2[1] (numeric) = 1.3104475708717746698731775806547 absolute error = 0.001582050772842524081798745699 relative error = 0.12087191147971740489525656581907 % h = 0.001 y1[1] (analytic) = 1.3088655200989321457913788349557 y1[1] (numeric) = 1.3127748538930645132459006306425 absolute error = 0.0039093337941323674545217956868 relative error = 0.29868108939388026996932148625241 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.315 y2[1] (analytic) = 1.309816471227602848601200515934 y2[1] (numeric) = 1.3114208351269887941603079458471 absolute error = 0.0016043638993859455591074299131 relative error = 0.12248768698734435859285450589297 % h = 0.001 y1[1] (analytic) = 1.309816471227602848601200515934 y1[1] (numeric) = 1.3137586755065976428538094728588 absolute error = 0.0039422042789947942526089569248 relative error = 0.30097379026697010686914244631957 % h = 0.001 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.6MB, time=34.91 NO POLE NO POLE x[1] = 0.316 y2[1] (analytic) = 1.3107671125398281418465819613222 y2[1] (numeric) = 1.3123939975147637096416988406185 absolute error = 0.0016268849749355677951168792963 relative error = 0.12411701204367334136210911848225 % h = 0.001 y1[1] (analytic) = 1.3107671125398281418465819613222 y1[1] (numeric) = 1.3147423192351686204855173901864 absolute error = 0.0039752066953404786389354288642 relative error = 0.30327330135998438229712315154083 % h = 0.001 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.6MB, time=35.13 NO POLE NO POLE x[1] = 0.317 y2[1] (analytic) = 1.3117174430849667925223366371764 y2[1] (numeric) = 1.3133670580304356064940422015645 absolute error = 0.0016496149454688139717055643881 relative error = 0.12575993055250998842109463229084 % h = 0.001 y1[1] (analytic) = 1.3117174430849667925223366371764 y1[1] (numeric) = 1.3157257840588285523880162889258 absolute error = 0.0040083409738617598656796517494 relative error = 0.30557960443330924563989539584452 % h = 0.001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.6MB, time=35.35 NO POLE NO POLE x[1] = 0.318 y2[1] (analytic) = 1.3126674619126883346840233228225 y2[1] (numeric) = 1.3143400166693423579193048345181 absolute error = 0.0016725547566540232352815116956 relative error = 0.12741648629097143655330903456855 % h = 0.001 y1[1] (analytic) = 1.3126674619126883346840233228225 y1[1] (numeric) = 1.3167090689576649350857149437682 absolute error = 0.0040416070449766004016916209457 relative error = 0.307892681295502899356298446962 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.319 y2[1] (analytic) = 1.3136171680729740197783328610944 y2[1] (numeric) = 1.3153128734268235250979498480582 absolute error = 0.0016957053538495053196169869638 relative error = 0.12908672291007280356352564809771 % h = 0.001 y1[1] (analytic) = 1.3136171680729740197783328610944 y1[1] (numeric) = 1.3176921729118026919566272667068 absolute error = 0.0040750048388286721782944056124 relative error = 0.31021251380313093145543034572521 % h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.6MB, time=35.56 NO POLE NO POLE x[1] = 0.32 y2[1] (analytic) = 1.3145665606161177666617575434172 y2[1] (numeric) = 1.3162856282982203621411529664827 absolute error = 0.0017190676821025954793954230655 relative error = 0.13077068393531127568655614388013 % h = 0.001 y1[1] (analytic) = 1.3145665606161177666617575434172 y1[1] (numeric) = 1.3186750949014052099176007444236 absolute error = 0.0041085342852874432558432010064 relative error = 0.31253908386060226820436850255946 % h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.6MB, time=35.78 NO POLE NO POLE x[1] = 0.321 y2[1] (analytic) = 1.3155156385927271113065931111435 y2[1] (numeric) = 1.317258281278875821042008571725 absolute error = 0.0017426426861487097354154605815 relative error = 0.13246841276724781427694882557831 % h = 0.001 y1[1] (analytic) = 1.3155156385927271113065931111435 y1[1] (numeric) = 1.3196578339066753762175521143998 absolute error = 0.0041421953139482649109590032563 relative error = 0.31487237342000574436988139443635 % h = 0.001 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.6MB, time=35.99 NO POLE NO POLE x[1] = 0.322 y2[1] (analytic) = 1.3164644010537241561933236672222 y2[1] (numeric) = 1.3182308323641345566257203239861 absolute error = 0.0017664313104104004323966567639 relative error = 0.13417995268208649305038099751219 % h = 0.001 y1[1] (analytic) = 1.3164644010537241561933236672222 y1[1] (numeric) = 1.3206403889078566153376770944014 absolute error = 0.0041759878541324591443534271792 relative error = 0.31721236448094728831145566934726 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.323 y2[1] (analytic) = 1.3174128470503465193884401058919 y2[1] (numeric) = 1.3192032815493429314987712111494 absolute error = 0.0017904344989964121103311052575 relative error = 0.13590534683225147709055846153524 % h = 0.001 y1[1] (analytic) = 1.3174128470503465193884401058919 y1[1] (numeric) = 1.3216227588852339259976007254004 absolute error = 0.0042099118348874066091606195085 relative error = 0.31955903909038771925589583676053 % h = 0.001 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.6MB, time=36.20 NO POLE NO POLE x[1] = 0.324 y2[1] (analytic) = 1.3183609756341482833067429826609 y2[1] (numeric) = 1.3201756288298490209970678773499 absolute error = 0.001814653195700737690324894689 relative error = 0.13764463824696165477880675182457 % h = 0.001 y1[1] (analytic) = 1.3183609756341482833067429826609 y1[1] (numeric) = 1.322604942819134918266434634413 absolute error = 0.0042439671849866349596916517521 relative error = 0.32191237934248115409661736914261 % h = 0.001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.6MB, time=36.42 NO POLE NO POLE x[1] = 0.325 y2[1] (analytic) = 1.3193087858570009431571810623496 y2[1] (numeric) = 1.3211478742010026181330540813759 absolute error = 0.0018390883440016749758730190263 relative error = 0.13939786983280293374722569652704 % h = 0.001 y1[1] (analytic) = 1.3193087858570009431571810623496 y1[1] (numeric) = 1.3235869396899308507777072711624 absolute error = 0.0042781538329299076205262088128 relative error = 0.32427236737841402107354886762191 % h = 0.001 TOP MAIN SOLVE Loop memory used=652.3MB, alloc=4.6MB, time=36.64 NO POLE NO POLE x[1] = 0.326 y2[1] (analytic) = 1.3202562767710943550712770994355 y2[1] (numeric) = 1.3221200176581552385417881358936 absolute error = 0.0018637408870608834705110364581 relative error = 0.14116508437429821190027938922014 % h = 0.001 y1[1] (analytic) = 1.3202562767710943550712770994355 y1[1] (numeric) = 1.3245687484780376680471329209153 absolute error = 0.0043124717069433129758558214798 relative error = 0.32663898538624467770228535759984 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.327 y2[1] (analytic) = 1.3212034474289376839131927223542 y2[1] (numeric) = 1.3230920591966601254259791788043 absolute error = 0.0018886117677224415127864564501 relative error = 0.1429463245344750344940057720275 % h = 0.001 y1[1] (analytic) = 1.3212034474289376839131927223542 y1[1] (numeric) = 1.3255503681639170378921850452872 absolute error = 0.004346920734979353978992322933 relative error = 0.32901221560074363033379317740713 % h = 0.001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.6MB, time=36.85 NO POLE NO POLE x[1] = 0.328 y2[1] (analytic) = 1.3221502968833603507704846117713 y2[1] (numeric) = 1.3240639988118722544999771283665 absolute error = 0.0019137019285119037294925165952 relative error = 0.14474163285543094820665189860804 % h = 0.001 y1[1] (analytic) = 1.3221502968833603507704846117713 y1[1] (numeric) = 1.3265317977280773889524392532728 absolute error = 0.0043815008447170381819546415015 relative error = 0.33139204030323435273855770377992 % h = 0.001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.6MB, time=37.06 NO POLE NO POLE x[1] = 0.329 y2[1] (analytic) = 1.3230968241875129801246044821466 y2[1] (numeric) = 1.3250358364991483389327111740435 absolute error = 0.0019390123116353588081066918969 relative error = 0.14655105175889656307947069467287 % h = 0.001 y1[1] (analytic) = 1.3230968241875129801246044821466 y1[1] (numeric) = 1.3275130361510749483096509562274 absolute error = 0.0044162119635619681850464740808 relative error = 0.33377844182143470112158871715531 % h = 0.001 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.6MB, time=37.28 NO POLE NO POLE x[1] = 0.33 y2[1] (analytic) = 1.3240430283948683467001956961702 y2[1] (numeric) = 1.3260075722538468342895716553717 absolute error = 0.0019645438589784875893759592015 relative error = 0.14837462354679633315165081300606 % h = 0.001 y1[1] (analytic) = 1.3240430283948683467001956961702 y1[1] (numeric) = 1.328494082413514779206532513007 absolute error = 0.0044510540186464325063368168368 relative error = 0.33617140252929892298715494025015 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.331 y2[1] (analytic) = 1.3249889085592223219922396628531 y2[1] (numeric) = 1.3269792060713279434732301814836 absolute error = 0.0019902975121056214809905186305 relative error = 0.15021239040180706655889114891073 % h = 0.001 y1[1] (analytic) = 1.3249889085592223219922396628531 y1[1] (numeric) = 1.3294749354960518188631944249683 absolute error = 0.0044860269368294968709547621152 relative error = 0.33857090484686025728450957598626 % h = 0.001 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.6MB, time=37.49 NO POLE NO POLE x[1] = 0.332 y2[1] (analytic) = 1.3259344637346948204701054922043 y2[1] (numeric) = 1.3279507379469536216633928442629 absolute error = 0.0020162742122588011932873520586 relative error = 0.1520643943879141758109739118506 % h = 0.001 y1[1] (analytic) = 1.3259344637346948204701054922043 y1[1] (numeric) = 1.3304555943793919163902148950363 absolute error = 0.004521130644697095920109402832 relative error = 0.34097693124007412327819291346117 % h = 0.001 TOP MAIN SOLVE Loop memory used=671.4MB, alloc=4.6MB, time=37.71 NO POLE NO POLE x[1] = 0.333 y2[1] (analytic) = 1.3268796929757307454575567025243 y2[1] (numeric) = 1.3289221678760875812554813784602 absolute error = 0.0020424749003568357979246759359 relative error = 0.1539306774509656789098330231631 % h = 0.001 y1[1] (analytic) = 1.3268796929757307454575567025243 y1[1] (numeric) = 1.3314360580442928707973018205644 absolute error = 0.0045563650685621253397451180401 relative error = 0.34338946422066189559875664846178 % h = 0.001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.6MB, time=37.93 NO POLE NO POLE x[1] = 0.334 y2[1] (analytic) = 1.3278245953371009346877691003853 y2[1] (numeric) = 1.329893495854095296798237122452 absolute error = 0.0020689005169943621104680220667 relative error = 0.15581128141922396191605622330059 % h = 0.001 y1[1] (analytic) = 1.3278245953371009346877691003853 y1[1] (numeric) = 1.3324163254715654690965110462435 absolute error = 0.0045917301344645344087419458582 relative error = 0.34580848634595526294194786172062 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.335 y2[1] (analytic) = 1.3287691698739031055324142783622 y2[1] (numeric) = 1.3308647218763440099302426336847 absolute error = 0.0020955520024409043978283553225 relative error = 0.15770624800391531351849783126999 % h = 0.001 y1[1] (analytic) = 1.3287691698739031055324142783622 y1[1] (numeric) = 1.3333963956420745244989844608625 absolute error = 0.0046272257681714189665701825003 relative error = 0.3482339802187411678965189934615 % h = 0.001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.6MB, time=38.14 NO POLE NO POLE x[1] = 0.336 y2[1] (analytic) = 1.3297134156415627999038635015058 y2[1] (numeric) = 1.3318358459382027343153558132127 absolute error = 0.0021224302966399344114923117069 relative error = 0.15961561879977724210871282408086 % h = 0.001 y1[1] (analytic) = 1.3297134156415627999038635015058 y1[1] (numeric) = 1.334376267536739914704171280279 absolute error = 0.0046628518951771148003077787732 relative error = 0.35066592848710732539289402615103 % h = 0.001 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.6MB, time=38.36 NO POLE NO POLE x[1] = 0.337 y2[1] (analytic) = 1.3306573316958343288295670804365 y2[1] (numeric) = 1.3328068680350422605770513941088 absolute error = 0.0021495363392079317474843136723 relative error = 0.16153943528560358580925002270084 % h = 0.001 y1[1] (analytic) = 1.3306573316958343288295670804365 y1[1] (numeric) = 1.3353559401365376202804956185336 absolute error = 0.0046986084407032914509285380971 relative error = 0.35310431384428831727692081312707 % h = 0.001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.6MB, time=38.57 NO POLE NO POLE x[1] = 0.338 y2[1] (analytic) = 1.331600917092801716697664656756 y2[1] (numeric) = 1.3337777881622351612316646489011 absolute error = 0.0021768710694334445339999921451 relative error = 0.16347773882478742585246092730892 % h = 0.001 y1[1] (analytic) = 1.331600917092801716697664656756 y1[1] (numeric) = 1.3363354124225007631364332096262 absolute error = 0.0047344953296990464387685528702 relative error = 0.3555491190285122605248754437658 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.339 y2[1] (analytic) = 1.332544170888879645172882155245 y2[1] (numeric) = 1.3347486063151557956205321715727 absolute error = 0.0022044354262761504476500163277 relative error = 0.16543057066586181365438939005655 % h = 0.001 y1[1] (analytic) = 1.332544170888879645172882155245 y1[1] (numeric) = 1.3373146833757206450809599040769 absolute error = 0.0047705124868409999080777488319 relative error = 0.35800032682284804662775708630734 % h = 0.001 TOP MAIN SOLVE Loop memory used=690.4MB, alloc=4.6MB, time=38.78 NO POLE NO POLE x[1] = 0.34 y2[1] (analytic) = 1.3334870921408143967817714870308 y2[1] (numeric) = 1.3357193224891803148410245900452 absolute error = 0.0022322303483659180592531030144 relative error = 0.16739797194303832187650411263843 % h = 0.001 y1[1] (analytic) = 1.3334870921408143967817714870308 y1[1] (numeric) = 1.3382937519773477864723343270095 absolute error = 0.0048066598365333896905628399787 relative error = 0.36045792005505314968472126588517 % h = 0.001 TOP MAIN SOLVE Loop memory used=694.2MB, alloc=4.6MB, time=39.00 NO POLE NO POLE x[1] = 0.341 y2[1] (analytic) = 1.334429679905684798166349418561 y2[1] (numeric) = 1.3366899366796866666764660654606 absolute error = 0.0022602567740018685101166468996 relative error = 0.16937998367674342971651918551106 % h = 0.001 y1[1] (analytic) = 1.334429679905684798166349418561 y1[1] (numeric) = 1.3392726172085929649541768481302 absolute error = 0.0048429373029081667878274295692 relative error = 0.36292188159742200075724638529763 % h = 0.001 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.6MB, time=39.21 NO POLE NO POLE x[1] = 0.342 y2[1] (analytic) = 1.3353719332409031630051923528251 y2[1] (numeric) = 1.337660448882054600524935434971 absolute error = 0.0022885156411514375197430821459 relative error = 0.17137664677415275261831583053278 % h = 0.001 y1[1] (analytic) = 1.3353719332409031630051923528251 y1[1] (numeric) = 1.3402512780507282542778067786213 absolute error = 0.0048793448098250912726144257962 relative error = 0.36539219436663492604731284184946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.343 y2[1] (analytic) = 1.336313851204216234601044101807 y2[1] (numeric) = 1.3386308590916656723269438551499 absolute error = 0.0023170078874494377258997533429 relative error = 0.17338800202972312654002946900625 % h = 0.001 y1[1] (analytic) = 1.336313851204216234601044101807 y1[1] (numeric) = 1.3412297334850880632097994756372 absolute error = 0.0049158822808718286087553738302 relative error = 0.36786884132360764647449669879029 % h = 0.001 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.6MB, time=39.43 NO POLE NO POLE x[1] = 0.344 y2[1] (analytic) = 1.3372554328537061281339940626387 y2[1] (numeric) = 1.3396011673039032494919838035437 absolute error = 0.002345734450197121357989740905 relative error = 0.17541409012572255686869852003962 % h = 0.001 y1[1] (analytic) = 1.3372554328537061281339940626387 y1[1] (numeric) = 1.3422079824930701745237248017709 absolute error = 0.0049525496393640463897307391322 relative error = 0.37035180547334133623844089258228 % h = 0.001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.6MB, time=39.64 NO POLE NO POLE x[1] = 0.345 y2[1] (analytic) = 1.338196677247791272579283544357 y2[1] (numeric) = 1.3405713735141525158239442962975 absolute error = 0.0023746962663612432446607519405 relative error = 0.17745495163275804201948326060911 % h = 0.001 y1[1] (analytic) = 1.338196677247791272579283544357 y1[1] (numeric) = 1.3431860240561367840750281545595 absolute error = 0.0049893468083455114957446102025 relative error = 0.37284106986477323796466675517687 % h = 0.001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.6MB, time=39.85 NO POLE NO POLE x[1] = 0.346 y2[1] (analytic) = 1.3391375834452273522887983275334 y2[1] (numeric) = 1.3415414777178004764453871802046 absolute error = 0.0024038942725731241565888526712 relative error = 0.17951062701030128170735297919585 % h = 0.001 y1[1] (analytic) = 1.3391375834452273522887983275334 y1[1] (numeric) = 1.3441638571558155399580150498133 absolute error = 0.0050262737105881876692167222799 relative error = 0.37533661759062783204312755882808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.347 y2[1] (analytic) = 1.3400781505051082482353058753646 y2[1] (numeric) = 1.3425114799102359627206793579539 absolute error = 0.0024333294051277144853734825893 relative error = 0.18158115660721227982930587077788 % h = 0.001 y1[1] (analytic) = 1.3400781505051082482353058753646 y1[1] (numeric) = 1.3451414807737005817439000122899 absolute error = 0.0050633302685923335085941369253 relative error = 0.37783843178726855778028420183257 % h = 0.001 TOP MAIN SOLVE Loop memory used=713.3MB, alloc=4.6MB, time=40.07 NO POLE NO POLE x[1] = 0.348 y2[1] (analytic) = 1.3410183774868669789184959520651 y2[1] (numeric) = 1.3434813800868496371779758057774 absolute error = 0.0024630025999826582594798537123 relative error = 0.18366658066226085184562700498793 % h = 0.001 y1[1] (analytic) = 1.3410183774868669789184959520651 y1[1] (numeric) = 1.3461188938914535797988802979864 absolute error = 0.0051005164045866008803843459213 relative error = 0.38034649563455008399680139783972 % h = 0.001 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.6MB, time=40.28 NO POLE NO POLE x[1] = 0.349 y2[1] (analytic) = 1.3419582634502766409318837425973 y2[1] (numeric) = 1.3444511782430339984300482431339 absolute error = 0.0024929147927573574981645005366 relative error = 0.18576693930464604649940361431562 % h = 0.001 y1[1] (analytic) = 1.3419582634502766409318837425973 y1[1] (numeric) = 1.3470960954908047746811947440958 absolute error = 0.0051378320405281337493110014985 relative error = 0.38286079235567112671422115748315 % h = 0.001 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.6MB, time=40.50 NO POLE NO POLE x[1] = 0.35 y2[1] (analytic) = 1.3428978074554513491896349069176 y2[1] (numeric) = 1.3454208743741833860939543145027 absolute error = 0.0025230669187320369043194075851 relative error = 0.18788227255451349166450226798632 % h = 0.001 y1[1] (analytic) = 1.3428978074554513491896349069176 y1[1] (numeric) = 1.3480730845535540166161278154648 absolute error = 0.0051752770981026674264929085472 relative error = 0.38538130521702781158516930411549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=724.8MB, alloc=4.6MB, time=40.71 x[1] = 0.351 y2[1] (analytic) = 1.3438370085628471768123723419896 y2[1] (numeric) = 1.3463904684756939857095421438076 absolute error = 0.002553459912846808897169801818 relative error = 0.19001262032347067406346760544401 % h = 0.001 y1[1] (analytic) = 1.3438370085628471768123723419896 y1[1] (numeric) = 1.349049860061571805047918690201 absolute error = 0.0052128514987246282355463482114 relative error = 0.3879080175280675787327905908045 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.352 y2[1] (analytic) = 1.3447758658332630946710247658361 y2[1] (numeric) = 1.3473599605429638336567851224388 absolute error = 0.0025840947097007389857603566027 relative error = 0.19215802241510016254832559365605 % h = 0.001 y1[1] (analytic) = 1.3447758658332630946710247658361 y1[1] (numeric) = 1.3500264209968003282675350019078 absolute error = 0.0052505551635372335965102360717 relative error = 0.39044091264114362767618902373467 % h = 0.001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.6MB, time=40.93 NO POLE NO POLE x[1] = 0.353 y2[1] (analytic) = 1.345714378327841910587777579861 y2[1] (numeric) = 1.3483293505713928220719417922963 absolute error = 0.0026149722435509114841642124353 relative error = 0.19431851852547078458906415081793 % h = 0.001 y1[1] (analytic) = 1.345714378327841910587777579861 y1[1] (numeric) = 1.3510027663412545031152706318762 absolute error = 0.0052883880134125925274930520152 relative error = 0.39297997395136990002967258803769 % h = 0.001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.6MB, time=41.15 NO POLE NO POLE x[1] = 0.354 y2[1] (analytic) = 1.3466525451080712081931868085672 y2[1] (numeric) = 1.3492986385563827037625356857377 absolute error = 0.0026460934483114955693488771705 relative error = 0.19649414824364676556661886037471 % h = 0.001 y1[1] (analytic) = 1.3466525451080712081931868085672 y1[1] (numeric) = 1.3519788950770230147571267214341 absolute error = 0.0053263499689518065639399128669 relative error = 0.39552518489647659767456605345626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=736.2MB, alloc=4.6MB, time=41.37 x[1] = 0.355 y2[1] (analytic) = 1.3475903652357842854385172596347 y2[1] (numeric) = 1.3502678244933370971211499847793 absolute error = 0.0026774592575528116826327251446 relative error = 0.19868495105219484041950980857965 % h = 0.001 y1[1] (analytic) = 1.3475903652357842854385172596347 y1[1] (numeric) = 1.3529548061862693565339348525453 absolute error = 0.0053644409504850710954175929106 relative error = 0.39807652895666623411326224379987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.356 y2[1] (analytic) = 1.3485278377731610927623663921003 y2[1] (numeric) = 1.3512369083776614910380318623693 absolute error = 0.002709070604500398275665470269 relative error = 0.2008909663276893471458557516 % h = 0.001 y1[1] (analytic) = 1.3485278377731610927623663921003 y1[1] (numeric) = 1.3539304986512328698821811236659 absolute error = 0.0054026608780717771198147315656 relative error = 0.40063398965447021672603141960131 % h = 0.001 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.6MB, time=41.58 NO POLE NO POLE x[1] = 0.357 y2[1] (analytic) = 1.3494649617827291709106357260919 y2[1] (numeric) = 1.3522058902047632498125013690274 absolute error = 0.0027409284220340789018656429355 relative error = 0.20311223334121531161533230043697 % h = 0.001 y1[1] (analytic) = 1.3494649617827291709106357260919 y1[1] (numeric) = 1.3549059714542297843254896277984 absolute error = 0.0054410096715006134148539017065 relative error = 0.40319755055460595766190057862827 % h = 0.001 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.6MB, time=41.80 NO POLE NO POLE x[1] = 0.358 y2[1] (analytic) = 1.3504017363273645884089119742243 y2[1] (numeric) = 1.3531747699700516180631597286273 absolute error = 0.002773033642687029654247754403 relative error = 0.20534879125886953309874005864958 % h = 0.001 y1[1] (analytic) = 1.3504017363273645884089119742243 y1[1] (numeric) = 1.3558812235776542575357236206432 absolute error = 0.0054794872502896691268116464189 relative error = 0.40576719526383451110564985305301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=747.6MB, alloc=4.6MB, time=42.01 x[1] = 0.359 y2[1] (analytic) = 1.3513381604702928786863204223547 y2[1] (numeric) = 1.3541435476689377256368919075837 absolute error = 0.002805387198644846950571485229 relative error = 0.20760067914225967987620512458378 % h = 0.001 y1[1] (analytic) = 1.3513381604702928786863204223547 y1[1] (numeric) = 1.3568562540039794154626624487269 absolute error = 0.0055180935336865367763420263722 relative error = 0.40834290743081873467365210192876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.36 y2[1] (analytic) = 1.3522742332750899768499134359207 y2[1] (numeric) = 1.3551122232968345925166583221979 absolute error = 0.0028379900217446156667448862772 relative error = 0.20986793594900140423864655244971 % h = 0.001 y1[1] (analytic) = 1.3522742332750899768499134359207 y1[1] (numeric) = 1.3578310617157583925312120903875 absolute error = 0.0055568284406684156812986544668 relative error = 0.41092467074598197270190458838292 % h = 0.001 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.6MB, time=42.23 NO POLE NO POLE x[1] = 0.361 y2[1] (analytic) = 1.353209953805683156108657317552 y2[1] (numeric) = 1.3560807968491571337280705494116 absolute error = 0.0028708430434739776194132318596 relative error = 0.21215060053321348615101173915553 % h = 0.001 y1[1] (analytic) = 1.353209953805683156108657317552 y1[1] (numeric) = 1.3588056456956253719051069465252 absolute error = 0.0055956918899422157964496289732 relative error = 0.41351246894136725920016861516763 % h = 0.001 TOP MAIN SOLVE Loop memory used=755.3MB, alloc=4.6MB, time=42.44 NO POLE NO POLE x[1] = 0.362 y2[1] (analytic) = 1.3541453211263519638460810920458 y2[1] (numeric) = 1.357049268321322164244745906723 absolute error = 0.0029039471949702003986648146772 relative error = 0.21444871164601101479989976256259 % h = 0.001 y1[1] (analytic) = 1.3541453211263519638460810920458 y1[1] (numeric) = 1.3597800049262966258160603030741 absolute error = 0.0056346837999446619699792110283 relative error = 0.41610628579049703825664449097324 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=759.1MB, alloc=4.6MB, time=42.66 x[1] = 0.363 y2[1] (analytic) = 1.3550803343017291573406511461367 y2[1] (numeric) = 1.3580176377087484038924357675232 absolute error = 0.0029373034070192465517846213865 relative error = 0.2167623079359966172025629446918 % h = 0.001 y1[1] (analytic) = 1.3550803343017291573406511461367 y1[1] (numeric) = 1.3607541383905715559573206732248 absolute error = 0.0056738040888423986166695270881 relative error = 0.418706105108233399688065531887 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.364 y2[1] (analytic) = 1.3560149923968016391329360027619 y2[1] (numeric) = 1.3589859050068564822519224786272 absolute error = 0.0029709126100548431189864758653 relative error = 0.21909142794974974300889686638008 % h = 0.001 y1[1] (analytic) = 1.3560149923968016391329360027619 y1[1] (numeric) = 1.3617280450713337339405910145248 absolute error = 0.0057130526745320948076550117629 relative error = 0.42131191075063882774049628487763 % h = 0.001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.6MB, time=42.87 NO POLE NO POLE x[1] = 0.365 y2[1] (analytic) = 1.3569492944769113920386258627375 y2[1] (numeric) = 1.3599540702110689435606797472889 absolute error = 0.0030047757341575515220538845514 relative error = 0.22143611013231401458289723939314 % h = 0.001 y1[1] (analytic) = 1.3569492944769113920386258627375 y1[1] (numeric) = 1.362701723951551941815267604106 absolute error = 0.0057524294746405497766417413685 relative error = 0.42392368661483746065646710709311 % h = 0.001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.6MB, time=43.09 NO POLE NO POLE x[1] = 0.366 y2[1] (analytic) = 1.357883239607756413806471900903 y2[1] (numeric) = 1.360922133316810251613291365514 absolute error = 0.003038893709053837806819464611 relative error = 0.22379639282768265140517698329192 % h = 0.001 y1[1] (analytic) = 1.357883239607756413806471900903 y1[1] (numeric) = 1.3636751740142812126489551444341 absolute error = 0.0057919344065247988424832435311 relative error = 0.42654141663887685893436996012934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=770.5MB, alloc=4.6MB, time=43.30 x[1] = 0.367 y2[1] (analytic) = 1.3588168268553916514202106588722 y2[1] (numeric) = 1.3618900943195067946606231400124 absolute error = 0.0030732674641151432404124811402 relative error = 0.22617231427928197779349709843726 % h = 0.001 y1[1] (analytic) = 1.3588168268553916514202106588722 y1[1] (numeric) = 1.3646483942426638711682144621492 absolute error = 0.005831567387272219748003803277 relative error = 0.42916508480159028011627909258489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.368 y2[1] (analytic) = 1.3597500552862299350435392325448 y2[1] (numeric) = 1.3628579532145868903077428966667 absolute error = 0.0031078979283569552642036641219 relative error = 0.22856391263045302289386902586532 % h = 0.001 y1[1] (analytic) = 1.3597500552862299350435392325448 y1[1] (numeric) = 1.3656213836199305744584989537633 absolute error = 0.0058713283337006394149597212185 relative error = 0.43179467512245945795054549594331 % h = 0.001 TOP MAIN SOLVE Loop memory used=774.3MB, alloc=4.6MB, time=43.52 NO POLE NO POLE x[1] = 0.369 y2[1] (analytic) = 1.3606829239670429116072073094816 y2[1] (numeric) = 1.3638257099974807904105834289301 absolute error = 0.0031427860304378788033761194485 relative error = 0.23097122592493122185063270022037 % h = 0.001 y1[1] (analytic) = 1.3606829239670429116072073094816 y1[1] (numeric) = 1.3665941411294013527222357242041 absolute error = 0.0059112171623584411150284147225 relative error = 0.43443017166147788378564593572077 % h = 0.001 TOP MAIN SOLVE Loop memory used=778.2MB, alloc=4.6MB, time=43.73 NO POLE NO POLE x[1] = 0.37 y2[1] (analytic) = 1.3616154319649619780372924691272 y2[1] (numeric) = 1.3647933646636206859713432601137 absolute error = 0.0031779326986587079340507909865 relative error = 0.23339429210732422702000200438723 % h = 0.001 y1[1] (analytic) = 1.3616154319649619780372924691272 y1[1] (numeric) = 1.3675666657544866500940071574462 absolute error = 0.005951233789524672056714688319 relative error = 0.43707155851901458806184628704501 % h = 0.001 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.6MB, time=43.95 NO POLE NO POLE x[1] = 0.371 y2[1] (analytic) = 1.3625475783474792141237255176854 y2[1] (numeric) = 1.3657609172084407120326200900704 absolute error = 0.003213338860961497908894572385 relative error = 0.23583314902358783804789640206225 % h = 0.001 y1[1] (analytic) = 1.3625475783474792141237255176854 y1[1] (numeric) = 1.3685389564786883655117884527474 absolute error = 0.005991378131209151388062935062 relative error = 0.43971881983567841977726514377823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.372 y2[1] (analytic) = 1.3634793621824483150281329891974 y2[1] (numeric) = 1.3667283676273769525702717973393 absolute error = 0.0032490054449286375421388081419 relative error = 0.23828783442150005958944274762984 % h = 0.001 y1[1] (analytic) = 1.3634793621824483150281329891974 y1[1] (numeric) = 1.3695110122856008936431964553108 absolute error = 0.0060316501031525786150634661134 relative error = 0.44237193979218282181489752561764 % h = 0.001 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.6MB, time=44.17 NO POLE NO POLE x[1] = 0.373 y2[1] (analytic) = 1.364410782538085523430064305059 y2[1] (numeric) = 1.3676957159158674453849998683732 absolute error = 0.0032849333777819219549355633142 relative error = 0.24075838595113329540433324703707 % h = 0.001 y1[1] (analytic) = 1.364410782538085523430064305059 y1[1] (numeric) = 1.3704828321589121658657049065274 absolute error = 0.0060720496208266424356406014684 relative error = 0.44503090260921110002708027676969 % h = 0.001 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.6MB, time=44.39 NO POLE NO POLE x[1] = 0.374 y2[1] (analytic) = 1.3653418384829705613106714458277 y2[1] (numeric) = 1.3686629620693521869926501260369 absolute error = 0.0033211235863816256819786802092 relative error = 0.2432448411653246875192628766033 % h = 0.001 y1[1] (analytic) = 1.3653418384829705613106714458277 y1[1] (numeric) = 1.3714544150824046912997810363105 absolute error = 0.0061125765994341299891095904828 relative error = 0.4476956925472821839837507306808 % h = 0.001 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.6MB, time=44.61 NO POLE NO POLE x[1] = 0.375 y2[1] (analytic) = 1.3662725290860475613729093517163 y2[1] (numeric) = 1.3696301060832731375132256301364 absolute error = 0.0033575769972255761403162784201 relative error = 0.24574723752014460910594087411343 % h = 0.001 y1[1] (analytic) = 1.3662725290860475613729093517163 y1[1] (numeric) = 1.372425760039956597893898218424 absolute error = 0.0061532309539090365209888667077 relative error = 0.45036629390661687730066870430449 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.376 y2[1] (analytic) = 1.3672028534166259980973256316518 y2[1] (numeric) = 1.3705971479530742255586066233122 absolute error = 0.0033942945364482274612809916604 relative error = 0.24826561237536331968067482142944 % h = 0.001 y1[1] (analytic) = 1.3672028534166259980973256316518 y1[1] (numeric) = 1.3733968660155426735603792091201 absolute error = 0.0061940125989166754630535774683 relative error = 0.45304269102700459547353917511231 % h = 0.001 TOP MAIN SOLVE Loop memory used=797.2MB, alloc=4.6MB, time=44.82 NO POLE NO POLE x[1] = 0.377 y2[1] (analytic) = 1.368132810544381618432508525187 y2[1] (numeric) = 1.3715640876742013531189723962132 absolute error = 0.0034312771298197346864638710262 relative error = 0.25080000299491579118926097461723 % h = 0.001 y1[1] (analytic) = 1.368132810544381618432508525187 y1[1] (numeric) = 1.3743677319932354073610242898479 absolute error = 0.0062349214488537889285157646609 relative error = 0.45572486828767058915368937803733 % h = 0.001 TOP MAIN SOLVE Loop memory used=801.1MB, alloc=4.6MB, time=45.04 NO POLE NO POLE x[1] = 0.378 y2[1] (analytic) = 1.3690623995393573721192624268931 y2[1] (numeric) = 1.3725309252421024004479199464529 absolute error = 0.0034685257027450283286575195598 relative error = 0.25335044654736471349887950685878 % h = 0.001 y1[1] (analytic) = 1.3690623995393573721192624268931 y1[1] (numeric) = 1.3753383569572060307414784362693 absolute error = 0.0062759574178486586222160093762 relative error = 0.4584128101071436508106198272998 % h = 0.001 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.6MB, time=45.25 NO POLE NO POLE x[1] = 0.379 y2[1] (analytic) = 1.3699916194719643416475806491373 y2[1] (numeric) = 1.3734976606522272309462743064416 absolute error = 0.0035060411802628892986936573043 relative error = 0.25591698010636168777688686170583 % h = 0.001 y1[1] (analytic) = 1.3699916194719643416475806491373 y1[1] (numeric) = 1.376308739891725558813291438321 absolute error = 0.0063171204197612171657107891837 relative error = 0.46110650094312430273636420774759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.38 y2[1] (analytic) = 1.3709204694129826718454854663492 y2[1] (numeric) = 1.3744642939000276960445854157846 absolute error = 0.0035438244870450241990999494354 relative error = 0.25849964065110661619481812905304 % h = 0.001 y1[1] (analytic) = 1.3709204694129826718454854663492 y1[1] (numeric) = 1.3772788797811658316826246995959 absolute error = 0.0063584103681831598371392332467 relative error = 0.46380592529235346435615847971029 % h = 0.001 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.6MB, time=45.47 NO POLE NO POLE x[1] = 0.381 y2[1] (analytic) = 1.3718489484335624990988058520127 y2[1] (numeric) = 1.3754308249809576400843064145395 absolute error = 0.0035818765473951409855005625268 relative error = 0.26109846506680529635455892053937 % h = 0.001 y1[1] (analytic) = 1.3718489484335624990988058520127 y1[1] (numeric) = 1.3782487756100005558245582488807 absolute error = 0.006399827176438056725752396868 relative error = 0.46651106769048159681943518438514 % h = 0.001 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.6MB, time=45.68 NO POLE NO POLE x[1] = 0.382 y2[1] (analytic) = 1.3727770556052248802009636886848 y2[1] (numeric) = 1.3763972538904729051976482342324 absolute error = 0.0036201982852480249966845455476 relative error = 0.2637134901451252287925173107177 % h = 0.001 y1[1] (analytic) = 1.3727770556052248802009636886848 y1[1] (numeric) = 1.3792184263628063455019513022809 absolute error = 0.0064413707575814653009876135961 relative error = 0.46922191271193832285462510677131 % h = 0.001 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.6MB, time=45.89 NO POLE NO POLE x[1] = 0.383 y2[1] (analytic) = 1.3737047899998627208318396013306 y2[1] (numeric) = 1.3773635806240313361861053641452 absolute error = 0.0036587906241686153542657628146 relative error = 0.2663447525846496458767207103914 % h = 0.001 y1[1] (analytic) = 1.3737047899998627208318396013306 y1[1] (numeric) = 1.3801878310242637642278095209898 absolute error = 0.0064830410244010433959699196592 relative error = 0.47193844496980251988066543212218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.384 y2[1] (analytic) = 1.3746321506897417036647899351876 y2[1] (numeric) = 1.378329805177092785397647671005 absolute error = 0.0036976544873510817328577358174 relative error = 0.26899228899132977037107874082906 % h = 0.001 y1[1] (analytic) = 1.3746321506897417036647899351876 y1[1] (numeric) = 1.3811569885791583662701119174148 absolute error = 0.0065248378894166626053219822272 relative error = 0.47466064911567288437748159847479 % h = 0.001 TOP MAIN SOLVE Loop memory used=820.1MB, alloc=4.6MB, time=46.11 NO POLE NO POLE x[1] = 0.385 y2[1] (analytic) = 1.3755591367475012161008867712188 y2[1] (numeric) = 1.3792959275451191176025731508293 absolute error = 0.0037367907976179015016863796105 relative error = 0.27165613587893531190058998393245 % h = 0.001 y1[1] (analytic) = 1.3755591367475012161008867712188 y1[1] (numeric) = 1.3821258980123817381980501710625 absolute error = 0.0065667612648805220971633998437 relative error = 0.47738850983953896552702948089358 % h = 0.001 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.6MB, time=46.33 NO POLE NO POLE x[1] = 0.386 y2[1] (analytic) = 1.3764857472461552776294532449923 y2[1] (numeric) = 1.380261947723574214868016492309 absolute error = 0.0037762004774189372385632473167 relative error = 0.27433632966950320951102660255201 % h = 0.001 y1[1] (analytic) = 1.3764857472461552776294532449923 y1[1] (numeric) = 1.383094558308932540468632925304 absolute error = 0.0066088110627772628391796803117 relative error = 0.48012201186965266614575561811285 % h = 0.001 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.6MB, time=46.54 NO POLE NO POLE x[1] = 0.387 y2[1] (analytic) = 1.3774119812590934668139668085286 y2[1] (numeric) = 1.3812278657079239814311083317452 absolute error = 0.0038158844488305146171415232166 relative error = 0.27703290669378462847660497494361 % h = 0.001 y1[1] (analytic) = 1.3774119812590934668139668085286 y1[1] (numeric) = 1.3840629684539175490526074468944 absolute error = 0.0066509871948240822386406383658 relative error = 0.48286113997240020893855618425986 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.388 y2[1] (analytic) = 1.3783378378600818479024034492912 y2[1] (numeric) = 1.3821936814936363485707800801948 absolute error = 0.0038558436335545006683766309036 relative error = 0.27974590319169021946934139295612 % h = 0.001 y1[1] (analytic) = 1.3783378378600818479024034492912 y1[1] (numeric) = 1.3850311274325526970986508419055 absolute error = 0.0066932895724708491962473926143 relative error = 0.48560587895217456611349058959205 % h = 0.001 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.6MB, time=46.76 NO POLE NO POLE x[1] = 0.389 y2[1] (analytic) = 1.3792633161232638970610962560513 y2[1] (numeric) = 1.3831593950761812794782092041237 absolute error = 0.0038960789529173824171129480724 relative error = 0.28247535531273364816419826930849 % h = 0.001 y1[1] (analytic) = 1.3792633161232638970610962560513 y1[1] (numeric) = 1.3859990342301641166347828345491 absolute error = 0.0067357181069002195736865784978 relative error = 0.48835621365124835040563323654778 % h = 0.001 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.6MB, time=46.97 NO POLE NO POLE x[1] = 0.39 y2[1] (analytic) = 1.3801884151231614282311820978472 y2[1] (numeric) = 1.3841250064510307741258998415174 absolute error = 0.0039365913278693458947177436702 relative error = 0.28522129911647340331474692610232 % h = 0.001 y1[1] (analytic) = 1.3801884151231614282311820978472 y1[1] (numeric) = 1.3869666878321891803059519292189 absolute error = 0.0067782727090277520747698313717 relative error = 0.49111212894964716556752732916815 % h = 0.001 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.6MB, time=47.19 NO POLE NO POLE x[1] = 0.391 y2[1] (analytic) = 1.381113133934675518606710559668 y2[1] (numeric) = 1.3850905156136588741353936360509 absolute error = 0.0039773816789833555286830763829 relative error = 0.28798377057295289129490664484885 % h = 0.001 y1[1] (analytic) = 1.381113133934675518606710559668 y1[1] (numeric) = 1.3879340872241775431467465909646 absolute error = 0.0068209532895020245400360312966 relative error = 0.49387360976502341439273800413897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.392 y2[1] (analytic) = 1.3820374716330874337334896568294 y2[1] (numeric) = 1.3860559225595416676436056725831 absolute error = 0.0040184509264542339101160157537 relative error = 0.29076280556313882506336500533041 % h = 0.001 y1[1] (analytic) = 1.3820374716330874337334896568294 y1[1] (numeric) = 1.3889012313917921843881828955297 absolute error = 0.0068637597587047506546932387003 relative error = 0.49664064105253056234798868545722 % h = 0.001 TOP MAIN SOLVE Loop memory used=843.0MB, alloc=4.6MB, time=47.40 NO POLE NO POLE x[1] = 0.393 y2[1] (analytic) = 1.3829614272940595522277432292739 y2[1] (numeric) = 1.3870212272841572941677803979032 absolute error = 0.0040597999900977419400371686293 relative error = 0.29355843987935791546854039131558 % h = 0.001 y1[1] (analytic) = 1.3829614272940595522277432292739 y1[1] (numeric) = 1.3898681193208104492975199170397 absolute error = 0.0069066920267508970697766877658 relative error = 0.49941320780469785489830472703832 % h = 0.001 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.6MB, time=47.61 NO POLE NO POLE x[1] = 0.394 y2[1] (analytic) = 1.3838849999936362901136552972144 y2[1] (numeric) = 1.3879864297829859494690624113302 absolute error = 0.0041014297893496593554071141158 relative error = 0.29637070922573187277341266992083 % h = 0.001 y1[1] (analytic) = 1.3838849999936362901136552972144 y1[1] (numeric) = 1.3908347499971250910500539394122 absolute error = 0.0069497500034888009363986421978 relative error = 0.50219129505130548661848236097704 % h = 0.001 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.6MB, time=47.83 NO POLE NO POLE x[1] = 0.395 y2[1] (analytic) = 1.384808188808245024778877040654 y2[1] (numeric) = 1.3889515300515098904146770104394 absolute error = 0.0041433412432648656357999697854 relative error = 0.29919964921861072624122123800903 % h = 0.001 y1[1] (analytic) = 1.384808188808245024778877040654 y1[1] (numeric) = 1.3918011224067453126318423965863 absolute error = 0.0069929335985002878529653559323 relative error = 0.50497488785926022019304897529781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.396 y2[1] (analytic) = 1.3857309928146970185470724473521 y2[1] (numeric) = 1.3899165280852134398387153778733 absolute error = 0.0041855352705164212916429305212 relative error = 0.30204529538700446958490966321546 % h = 0.001 y1[1] (analytic) = 1.3857309928146970185470724473521 y1[1] (numeric) = 1.3927672355357978087723082667247 absolute error = 0.0070362427211007902252358193726 relative error = 0.50776397133247145341568306290579 % h = 0.001 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.6MB, time=48.04 NO POLE NO POLE x[1] = 0.397 y2[1] (analytic) = 1.3866534110901883418665790567684 y2[1] (numeric) = 1.3908814238795829914015192958796 absolute error = 0.0042280127893946495349402391112 relative error = 0.30490768317301304004528182463141 % h = 0.001 y1[1] (analytic) = 1.3866534110901883418665790567684 y1[1] (numeric) = 1.3937330883705278079056754666354 absolute error = 0.007079677280339466039096409867 relative error = 0.51055853061172773230781907152204 % h = 0.001 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.6MB, time=48.26 NO POLE NO POLE x[1] = 0.398 y2[1] (analytic) = 1.3875754427123007961142606114002 y2[1] (numeric) = 1.3918462174301070144476602759115 absolute error = 0.0042707747178062183333996645113 relative error = 0.3077868479322546388251245833122 % h = 0.001 y1[1] (analytic) = 1.3875754427123007961142606114002 y1[1] (numeric) = 1.3946986798973001141601856147921 absolute error = 0.0071232371849993180459250033919 relative error = 0.51335855087457370848487409925283 % h = 0.001 TOP MAIN SOLVE Loop memory used=862.1MB, alloc=4.6MB, time=48.48 NO POLE NO POLE x[1] = 0.399 y2[1] (analytic) = 1.3884970867590028360136288117384 y2[1] (numeric) = 1.3928109087322760588625079913206 absolute error = 0.0043138219732732228488791795822 relative error = 0.31068282493429240056904539647227 % h = 0.001 y1[1] (analytic) = 1.3884970867590028360136288117384 y1[1] (numeric) = 1.3956640091026001493740463544944 absolute error = 0.007166922343597313360417542756 relative error = 0.51616401733518753890720017597443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.4 y2[1] (analytic) = 1.3894183423086504916663117567957 y2[1] (numeric) = 1.3937754977815827599273829018778 absolute error = 0.0043571554729322682610711450821 relative error = 0.31359564936305941954146875157328 % h = 0.001 y1[1] (analytic) = 1.3894183423086504916663117567957 y1[1] (numeric) = 1.396629074973034995137061252915 absolute error = 0.0072107326643845034707494961193 relative error = 0.51897491524425872616148800176119 % h = 0.001 TOP MAIN SOLVE Loop memory used=865.9MB, alloc=4.6MB, time=48.69 NO POLE NO POLE x[1] = 0.401 y2[1] (analytic) = 1.3903392084399882901959470388174 y2[1] (numeric) = 1.3947399845735218431732879595622 absolute error = 0.0044007761335335529773409207448 relative error = 0.31652535631728214011813166238558 % h = 0.001 y1[1] (analytic) = 1.3903392084399882901959470388174 y1[1] (numeric) = 1.3975938764953344348568911170178 absolute error = 0.0072546680553461446609440782004 relative error = 0.52179122988886639742692573006979 % h = 0.001 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.6MB, time=48.90 NO POLE NO POLE x[1] = 0.402 y2[1] (analytic) = 1.3912596842321501770035778483565 y2[1] (numeric) = 1.3957043691035901292332142857726 absolute error = 0.0044446848714399522296364374161 relative error = 0.31947198081090211916951457411284 % h = 0.001 y1[1] (analytic) = 1.3912596842321501770035778483565 y1[1] (numeric) = 1.3985584126563519958488963936093 absolute error = 0.0072987284242018188453185452528 relative error = 0.52461294659235802028894993729566 % h = 0.001 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.6MB, time=49.12 NO POLE NO POLE x[1] = 0.403 y2[1] (analytic) = 1.3921797687646604366336308343958 y2[1] (numeric) = 1.3966686513672865386930157108338 absolute error = 0.004488882602626102059384876438 relative error = 0.32243555777349616787793870835453 % h = 0.001 y1[1] (analytic) = 1.3921797687646604366336308343958 y1[1] (numeric) = 1.3995226824430659914485101480984 absolute error = 0.0073429136784055548148793137026 relative error = 0.52744005071422855357191555857622 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=877.3MB, alloc=4.6MB, time=49.33 x[1] = 0.404 y2[1] (analytic) = 1.3930994611174346132495548536135 y2[1] (numeric) = 1.3976328313601120969408470673929 absolute error = 0.0045333702426774836912922137794 relative error = 0.32541612205069488049355299087746 % h = 0.001 y1[1] (analytic) = 1.3930994611174346132495548536135 y1[1] (numeric) = 1.4004866848425805631450909448933 absolute error = 0.0073872237251459498955360912798 relative error = 0.53027252765000003137045754110235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.405 y2[1] (analytic) = 1.3940187603707804307182001332327 y2[1] (numeric) = 1.3985969090775699390151611300291 absolute error = 0.0045781487067895082969609967964 relative error = 0.32841370840459955749812210030904 % h = 0.001 y1[1] (analytic) = 1.3940187603707804307182001332327 y1[1] (numeric) = 1.4014504188421267227362047817531 absolute error = 0.0074316584713462920180046485204 relative error = 0.5331103628311015784677195146133 % h = 0.001 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.6MB, time=49.55 NO POLE NO POLE x[1] = 0.406 y2[1] (analytic) = 1.3949376656053987123020177631507 y2[1] (numeric) = 1.3995608845151653144512590941354 absolute error = 0.0046232189097666021492413309847 relative error = 0.33142835151419753060941071826062 % h = 0.001 y1[1] (analytic) = 1.3949376656053987123020177631507 y1[1] (numeric) = 1.4024138834290633945012850608411 absolute error = 0.0074762178236646821992672976904 relative error = 0.53595354172474985533698414994938 % h = 0.001 TOP MAIN SOLVE Loop memory used=885.0MB, alloc=4.6MB, time=49.76 NO POLE NO POLE x[1] = 0.407 y2[1] (analytic) = 1.3958561759023842999581598252254 y2[1] (numeric) = 1.4005247576684055921263894878686 absolute error = 0.0046685817660212921682296626432 relative error = 0.33446008597577589702303661978667 % h = 0.001 y1[1] (analytic) = 1.3958561759023842999581598252254 y1[1] (numeric) = 1.403377077590878457393619410695 absolute error = 0.0075209016884941574354595854696 relative error = 0.5388020498338299309315563119182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=888.8MB, alloc=4.6MB, time=49.97 x[1] = 0.408 y2[1] (analytic) = 1.3967742903432269732435608606962 y2[1] (numeric) = 1.401488528532800265103390411709 absolute error = 0.0047142381895732918598295510128 relative error = 0.33750894630333367025293569541275 % h = 0.001 y1[1] (analytic) = 1.3967742903432269732435608606962 y1[1] (numeric) = 1.4043400003151897872496120058347 absolute error = 0.0075657099719628140060511451385 relative error = 0.54165587269677658147602385377348 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.409 y2[1] (analytic) = 1.3976920080098123678250817707338 y2[1] (numeric) = 1.4024521971038609554728700009204 absolute error = 0.0047601890940485876477882301866 relative error = 0.34057496692899235489604422632728 % h = 0.001 y1[1] (analytic) = 1.3976920080098123678250817707338 y1[1] (numeric) = 1.4053026505897462990142698642765 absolute error = 0.0076106425799339311891880935427 relative error = 0.54451499588745601348025218741284 % h = 0.001 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.6MB, time=50.19 NO POLE NO POLE x[1] = 0.41 y2[1] (analytic) = 1.3986093279844228935937976400511 y2[1] (numeric) = 1.4034157633771014191939200069565 absolute error = 0.0048064353926785256001223669054 relative error = 0.34365818220340495261145663378167 % h = 0.001 y1[1] (analytic) = 1.3986093279844228935937976400511 y1[1] (numeric) = 1.4062650274024289889818614378068 absolute error = 0.0076556994180060953880637977557 relative error = 0.54737940501504800920565783335675 % h = 0.001 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.6MB, time=50.41 NO POLE NO POLE x[1] = 0.411 y2[1] (analytic) = 1.3995262493497386523825113693651 y2[1] (numeric) = 1.404379227348037550933357394619 absolute error = 0.0048529779982988985508460252539 relative error = 0.34675862639616340656915939029509 % h = 0.001 y1[1] (analytic) = 1.3995262493497386523825113693651 y1[1] (numeric) = 1.4072271297412519770506956454953 absolute error = 0.0077008803915133246681842761302 relative error = 0.55024908572392849282145324487164 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=900.2MB, alloc=4.6MB, time=50.62 x[1] = 0.412 y2[1] (analytic) = 1.4004427711888383552855753992714 y2[1] (numeric) = 1.4053425890121873889034888525394 absolute error = 0.004899817823349033617913453268 relative error = 0.34987633369620449158847271965669 % h = 0.001 y1[1] (analytic) = 1.4004427711888383552855753992714 y1[1] (numeric) = 1.4081889565943635489909693375956 absolute error = 0.0077461854055251937053939383242 relative error = 0.55312402369355251549666054677689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.413 y2[1] (analytic) = 1.4013588925852002395801042057874 y2[1] (numeric) = 1.4063058483650711196983931153261 absolute error = 0.0049469557798708801182889095387 relative error = 0.35301133821221415715155003590485 % h = 0.001 y1[1] (analytic) = 1.4013588925852002395801042057874 y1[1] (numeric) = 1.4091505069500471987246310146859 absolute error = 0.0077916143648469591445268088985 relative error = 0.55600420463833765768175566439104 % h = 0.001 TOP MAIN SOLVE Loop memory used=904.1MB, alloc=4.6MB, time=50.84 NO POLE NO POLE x[1] = 0.414 y2[1] (analytic) = 1.4022746126227029852476606464264 y2[1] (numeric) = 1.4072690054022110831287159964947 absolute error = 0.0049943927795080978810553500683 relative error = 0.35616367397303033044268969824153 % h = 0.001 y1[1] (analytic) = 1.4022746126227029852476606464264 y1[1] (numeric) = 1.4101117797967226706162084656534 absolute error = 0.007837167174019685368547819227 relative error = 0.55888961430754784684182687554844 % h = 0.001 TOP MAIN SOLVE Loop memory used=907.9MB, alloc=4.6MB, time=51.05 NO POLE NO POLE x[1] = 0.415 y2[1] (analytic) = 1.4031899303856266310954996351939 y2[1] (numeric) = 1.4082320601191317770549730320816 absolute error = 0.0050421297335051459594733968877 relative error = 0.35933337492804418652980351382707 % h = 0.001 y1[1] (analytic) = 1.4031899303856266310954996351939 y1[1] (numeric) = 1.4110727741229470017735478279143 absolute error = 0.0078828437373203706780481927204 relative error = 0.56178023848517758891111332815582 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=911.7MB, alloc=4.6MB, time=51.26 x[1] = 0.416 y2[1] (analytic) = 1.4041048449586534904764530253388 y2[1] (numeric) = 1.4091950125113598622193546356253 absolute error = 0.0050901675527063717429016102865 relative error = 0.36252047494759989277016043631441 % h = 0.001 y1[1] (analytic) = 1.4041048449586534904764530253388 y1[1] (numeric) = 1.4120334889174155643574114140929 absolute error = 0.0079286439587620738809583887541 relative error = 0.56467606298983661174672975808159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.417 y2[1] (analytic) = 1.4050193554268690666065399800501 y2[1] (numeric) = 1.4101578625744241670760286659941 absolute error = 0.005138507147555100469488685944 relative error = 0.36572500782339283448848102397976 % h = 0.001 y1[1] (analytic) = 1.4050193554268690666065399800501 y1[1] (numeric) = 1.4129939231689631078988814912578 absolute error = 0.0079745677420940412923415112077 relative error = 0.56757707367463491886728374508309 % h = 0.001 TOP MAIN SOLVE Loop memory used=915.5MB, alloc=4.6MB, time=51.47 NO POLE NO POLE x[1] = 0.418 y2[1] (analytic) = 1.4059334608757629674793875135654 y2[1] (numeric) = 1.4111206103038556926199353103344 absolute error = 0.005187149428092725140547796769 relative error = 0.36894700726886632894159738220306 % h = 0.001 y1[1] (analytic) = 1.4059334608757629674793875135654 y1[1] (numeric) = 1.4139540758665648016235170417274 absolute error = 0.008020614990801834144129528162 relative error = 0.57048325642706825176995158440086 % h = 0.001 TOP MAIN SOLVE Loop memory used=919.3MB, alloc=4.6MB, time=51.69 NO POLE NO POLE x[1] = 0.419 y2[1] (analytic) = 1.4068471603912298203765462883469 y2[1] (numeric) = 1.4120832556951876172140691852163 absolute error = 0.0052360953039577968375228968694 relative error = 0.37218650691960683455021347367597 % h = 0.001 y1[1] (analytic) = 1.4068471603912298203765462883469 y1[1] (numeric) = 1.4149139459993372767812103784162 absolute error = 0.0080667856081074564046640900693 relative error = 0.57339459716890395912739845462757 % h = 0.001 TOP MAIN SOLVE Loop memory used=923.1MB, alloc=4.6MB, time=51.91 NO POLE NO POLE x[1] = 0.42 y2[1] (analytic) = 1.4077604530595701859727871580863 y2[1] (numeric) = 1.4130457987439553014152435598612 absolute error = 0.0052853456843851154424564017749 relative error = 0.37544354033373766234480079444279 % h = 0.001 y1[1] (analytic) = 1.4077604530595701859727871580863 y1[1] (numeric) = 1.4158735325565396689806903326942 absolute error = 0.0081130794969694830079031746079 relative error = 0.57631108185606727117370825203976 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.421 y2[1] (analytic) = 1.4086733379674914720354643513158 y2[1] (numeric) = 1.4140082394456962927983316061489 absolute error = 0.0053349014782048207628672548331 relative error = 0.37871814099231119653934345027377 % h = 0.001 y1[1] (analytic) = 1.4086733379674914720354643513158 y1[1] (numeric) = 1.4168328345275746605276185787766 absolute error = 0.0081594965600831884921542274608 relative error = 0.57923269647852797759622846102093 % h = 0.001 TOP MAIN SOLVE Loop memory used=926.9MB, alloc=4.6MB, time=52.12 NO POLE NO POLE x[1] = 0.422 y2[1] (analytic) = 1.4095858142021088467170315963406 y2[1] (numeric) = 1.4149705777959503307789795809192 absolute error = 0.0053847635938414840619479845786 relative error = 0.38201034229969963111350359667514 % h = 0.001 y1[1] (analytic) = 1.4095858142021088467170315963406 y1[1] (numeric) = 1.4177918509019895227652255057477 absolute error = 0.0082060366998806760481939094071 relative error = 0.58215942706018750725793595973632 % h = 0.001 TOP MAIN SOLVE Loop memory used=930.8MB, alloc=4.6MB, time=52.34 NO POLE NO POLE x[1] = 0.423 y2[1] (analytic) = 1.410497880850946151439797895052 y2[1] (numeric) = 1.4159328137902593514347868469073 absolute error = 0.0054349329393131999949889518553 relative error = 0.38532017758398422925081200645393 % h = 0.001 y1[1] (analytic) = 1.410497880850946151439797895052 y1[1] (numeric) = 1.4187505806694771584164318964566 absolute error = 0.0082526998185310069766340014046 relative error = 0.58509125965876640808259094135099 % h = 0.001 TOP MAIN SOLVE Loop memory used=934.6MB, alloc=4.6MB, time=52.55 NO POLE NO POLE x[1] = 0.424 y2[1] (analytic) = 1.4114095370019368133720100609405 y2[1] (numeric) = 1.4168949474241674923249476394802 absolute error = 0.0054854104222306789529375785397 relative error = 0.38864768009734311244769818457515 % h = 0.001 y1[1] (analytic) = 1.4114095370019368133720100609405 y1[1] (numeric) = 1.4197090228198771439264025216958 absolute error = 0.0082994858179403305543924607553 relative error = 0.58802818036569222544256838110142 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.425 y2[1] (analytic) = 1.4123207817434247574943495453043 y2[1] (numeric) = 1.4178569786932210973083494871758 absolute error = 0.0055361969497963398139999418715 relative error = 0.39199288301643758607555895209504 % h = 0.001 y1[1] (analytic) = 1.4123207817434247574943495453043 y1[1] (numeric) = 1.4206671763431767718044776082957 absolute error = 0.0083463945997520143101280629914 relative error = 0.59097017530598777739683991637936 % h = 0.001 TOP MAIN SOLVE Loop memory used=938.4MB, alloc=4.6MB, time=52.77 NO POLE NO POLE x[1] = 0.426 y2[1] (analytic) = 1.4132316141641653182559314852307 y2[1] (numeric) = 1.4188189075929687213601231948851 absolute error = 0.0055872934288034031041917096544 relative error = 0.3953558194427970081456227667744 % h = 0.001 y1[1] (analytic) = 1.4132316141641653182559314852307 y1[1] (numeric) = 1.4216250402295120929644279910329 absolute error = 0.0083934260653467747084965058022 relative error = 0.59391723063815982513412384691438 % h = 0.001 TOP MAIN SOLVE Loop memory used=942.2MB, alloc=4.6MB, time=52.98 NO POLE NO POLE x[1] = 0.427 y2[1] (analytic) = 1.4141420333533261508188943174277 y2[1] (numeric) = 1.4197807341189611353866392993625 absolute error = 0.0056387007656349845677449819348 relative error = 0.39873652240320220799409824013843 % h = 0.001 y1[1] (analytic) = 1.4141420333533261508188943174277 y1[1] (numeric) = 1.4225826134691689590619796105585 absolute error = 0.0084405801158428082430852931308 relative error = 0.59686933255408813698372741898653 % h = 0.001 TOP MAIN SOLVE Loop memory used=946.0MB, alloc=4.6MB, time=53.20 NO POLE NO POLE x[1] = 0.428 y2[1] (analytic) = 1.415052038400488141890668713393 y2[1] (numeric) = 1.4207424582667513310389459075995 absolute error = 0.0056904198662631891482771942065 relative error = 0.40213502485006746157299835926357 % h = 0.001 y1[1] (analytic) = 1.415052038400488141890668713393 y1[1] (numeric) = 1.4235398950525840648285528729101 absolute error = 0.0084878566520959229378841595171 relative error = 0.59982646727891494436407384565325 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.429 y2[1] (analytic) = 1.4159616283956463201430150037265 y2[1] (numeric) = 1.4217040800318945255246428294509 absolute error = 0.0057424516362482053816278257244 relative error = 0.40555135966182103000010584199851 % h = 0.001 y1[1] (analytic) = 1.4159616283956463201430150037265 y1[1] (numeric) = 1.4244968839703459904001622405705 absolute error = 0.008535255574699670257147236844 relative error = 0.60278862107093478804633684583205 % h = 0.001 TOP MAIN SOLVE Loop memory used=949.8MB, alloc=4.6MB, time=53.41 NO POLE NO POLE x[1] = 0.43 y2[1] (analytic) = 1.4168708024292107662169186726246 y2[1] (numeric) = 1.4226655994099481664181869167641 absolute error = 0.0057947969807374002012682441395 relative error = 0.4089855596432842679897888684207 % h = 0.001 y1[1] (analytic) = 1.4168708024292107662169186726246 y1[1] (numeric) = 1.425453579213196243640421280483 absolute error = 0.0085827767839854774235026078584 relative error = 0.60575578022148475311799806960563 % h = 0.001 TOP MAIN SOLVE Loop memory used=953.6MB, alloc=4.6MB, time=53.63 NO POLE NO POLE x[1] = 0.431 y2[1] (analytic) = 1.4177795595920075223124339177373 y2[1] (numeric) = 1.4236270163964719364696235221266 absolute error = 0.0058474568044644141571896043893 relative error = 0.41243765752604930875478916679811 % h = 0.001 y1[1] (analytic) = 1.4177795595920075223124339177373 y1[1] (numeric) = 1.4264099797720303024565982509273 absolute error = 0.00863042018002278014416433319 relative error = 0.60872793105483509103849782496411 % h = 0.001 TOP MAIN SOLVE Loop memory used=957.5MB, alloc=4.6MB, time=53.85 NO POLE NO POLE x[1] = 0.432 y2[1] (analytic) = 1.4186878989752795013625656856203 y2[1] (numeric) = 1.4245883309870277584117389912189 absolute error = 0.0059004320117482570491733055986 relative error = 0.41590768596885533193768512351726 % h = 0.001 y1[1] (analytic) = 1.4186878989752795013625656856203 y1[1] (numeric) = 1.4273660846378986571076671666977 absolute error = 0.0086781856626191557451014810774 relative error = 0.61170505992808022718646724047221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.433 y2[1] (analytic) = 1.4195958196706873957902810089753 y2[1] (numeric) = 1.4255495431771797997656291036342 absolute error = 0.0059537235064924039753480946589 relative error = 0.41939567755796342109948027274876 % h = 0.001 y1[1] (analytic) = 1.4195958196706873957902810089753 y1[1] (numeric) = 1.4283218928020078525032991406128 absolute error = 0.0087260731313204567130181316375 relative error = 0.61468715323103015230531059634963 % h = 0.001 TOP MAIN SOLVE Loop memory used=961.3MB, alloc=4.6MB, time=54.07 NO POLE NO POLE x[1] = 0.434 y2[1] (analytic) = 1.4205033207703105858477408887429 y2[1] (numeric) = 1.4265106529624944776446783779093 absolute error = 0.0060073321921838917969374891664 relative error = 0.42290166480753001726168124933584 % h = 0.001 y1[1] (analytic) = 1.4205033207703105858477408887429 y1[1] (numeric) = 1.4292774032557215304927386590189 absolute error = 0.008774082485410944644997770276 relative error = 0.61767419738610219626115023855251 % h = 0.001 TOP MAIN SOLVE Loop memory used=965.1MB, alloc=4.6MB, time=54.28 NO POLE NO POLE x[1] = 0.435 y2[1] (analytic) = 1.4214104013666480475368443818927 y2[1] (numeric) = 1.4274716603385404635569451573972 absolute error = 0.0060612589718924160201007755045 relative error = 0.42642568015997897496730810894673 % h = 0.001 y1[1] (analytic) = 1.4214104013666480475368443818927 y1[1] (numeric) = 1.430232614990561472142509309629 absolute error = 0.0088222136239134246056649277363 relative error = 0.62066617884821318253435346127642 % h = 0.001 TOP MAIN SOLVE Loop memory used=968.9MB, alloc=4.6MB, time=54.50 NO POLE NO POLE x[1] = 0.436 y2[1] (analytic) = 1.4223170605526192601101769744414 y2[1] (numeric) = 1.4284325653008886882059473945027 absolute error = 0.0061155047482694280957704200613 relative error = 0.42996775598637222729552289089147 % h = 0.001 y1[1] (analytic) = 1.4223170605526192601101769744414 y1[1] (numeric) = 1.4311875269982086400018933417694 absolute error = 0.008870466445589379891716367328 relative error = 0.62366308410467196187303120656482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.437 y2[1] (analytic) = 1.4232232974215651131514557388264 y2[1] (numeric) = 1.4293933678451123462898440517019 absolute error = 0.0061700704235472331383883128755 relative error = 0.43352792458677906623396848461431 % h = 0.001 y1[1] (analytic) = 1.4232232974215651131514557388264 y1[1] (numeric) = 1.4321421382705042203551293018801 absolute error = 0.0089188408489391072036735630537 relative error = 0.62666489967507232354403258664134 % h = 0.001 TOP MAIN SOLVE Loop memory used=972.7MB, alloc=4.6MB, time=54.71 NO POLE NO POLE x[1] = 0.438 y2[1] (analytic) = 1.4241291110672488132345641952656 y2[1] (numeric) = 1.4303540679667869012990070386656 absolute error = 0.0062249568995380880644428434 relative error = 0.43710621819064404478247832964028 % h = 0.001 y1[1] (analytic) = 1.4241291110672488132345641952656 y1[1] (numeric) = 1.4330964477994506654592718509411 absolute error = 0.0089673367322018522247076556755 relative error = 0.62967161211118628262405728678711 % h = 0.001 TOP MAIN SOLVE Loop memory used=976.5MB, alloc=4.6MB, time=54.93 NO POLE NO POLE x[1] = 0.439 y2[1] (analytic) = 1.425034500583856790160270218143 y2[1] (numeric) = 1.4313146656614900903119786057174 absolute error = 0.0062801650776333001517083875744 relative error = 0.44070266895715350713154730663641 % h = 0.001 y1[1] (analytic) = 1.425034500583856790160270218143 y1[1] (numeric) = 1.4340504545772127357666577353688 absolute error = 0.0090159539933559456063875172258 relative error = 0.63268320799685774178057005329785 % h = 0.001 TOP MAIN SOLVE Loop memory used=980.3MB, alloc=4.6MB, time=55.15 NO POLE NO POLE x[1] = 0.44 y2[1] (analytic) = 1.4259394650659996027697207507799 y2[1] (numeric) = 1.4322751609248019287898091147679 absolute error = 0.006335695858802326020088363988 relative error = 0.44431730897560075322884444377643 % h = 0.001 y1[1] (analytic) = 1.4259394650659996027697207507799 y1[1] (numeric) = 1.4350041575961185421309217488494 absolute error = 0.0090646925301189393612009980695 relative error = 0.63569967394789652599922791055871 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.441 y2[1] (analytic) = 1.4268440036087128443338075151701 y2[1] (numeric) = 1.4332355537523047153687701097861 absolute error = 0.006391550143591871034962594616 relative error = 0.44795017026574984401709785579087 % h = 0.001 y1[1] (analytic) = 1.4268440036087128443338075151701 y1[1] (numeric) = 1.435957555848660587995506389545 absolute error = 0.0091135522399477436616988743749 relative error = 0.63872099661197278872152168133737 % h = 0.001 TOP MAIN SOLVE Loop memory used=984.2MB, alloc=4.6MB, time=55.36 NO POLE NO POLE x[1] = 0.442 y2[1] (analytic) = 1.4277481153074580475174983273898 y2[1] (numeric) = 1.4341958441395830366514376097915 absolute error = 0.0064477288321249891339392824017 relative error = 0.45160128477819805359689074351332 % h = 0.001 y1[1] (analytic) = 1.4277481153074580475174983273898 y1[1] (numeric) = 1.4369106483274968115636087851312 absolute error = 0.0091625330200387640461104577414 relative error = 0.6417471626685117878632890004964 % h = 0.001 TOP MAIN SOLVE Loop memory used=988.0MB, alloc=4.6MB, time=55.57 NO POLE NO POLE x[1] = 0.443 y2[1] (analytic) = 1.4286517992581235889182290544272 y2[1] (numeric) = 1.4351560320822237719961405482803 absolute error = 0.0065042328241001830779114938531 relative error = 0.45527068439473697453827340827484 % h = 0.001 y1[1] (analytic) = 1.4286517992581235889182290544272 y1[1] (numeric) = 1.4378634340254516279485083271923 absolute error = 0.0092116347673280390302792727651 relative error = 0.64477815882858903019167650938785 % h = 0.001 TOP MAIN SOLVE Loop memory used=991.8MB, alloc=4.6MB, time=55.79 NO POLE NO POLE x[1] = 0.444 y2[1] (analytic) = 1.4295550545570255931774516741134 y2[1] (numeric) = 1.4361161175758160983047692839314 absolute error = 0.006561063018790505127317609818 relative error = 0.45895840092871228253561918105814 % h = 0.001 y1[1] (analytic) = 1.4295550545570255931774516741134 y1[1] (numeric) = 1.438815911935516971303218326621 absolute error = 0.0092608573784913781257666525076 relative error = 0.64781397183482578254501449048078 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.445 y2[1] (analytic) = 1.4304578803009088366644343266839 y2[1] (numeric) = 1.4370761006159514948089391083788 absolute error = 0.0066182203150426581445047816949 relative error = 0.46266446612538216657083103954199 % h = 0.001 y1[1] (analytic) = 1.4304578803009088366644343266839 y1[1] (numeric) = 1.4397680810508533369284048728394 absolute error = 0.0093102007499445002639705461555 relative error = 0.65085458846128494838691804082562 % h = 0.001 TOP MAIN SOLVE Loop memory used=995.6MB, alloc=4.6MB, time=56.01 NO POLE NO POLE x[1] = 0.446 y2[1] (analytic) = 1.4313602755869476507314096742436 y2[1] (numeric) = 1.4380359811982237478545036777808 absolute error = 0.0066757056112760971230940035372 relative error = 0.46638891166227443072083960203771 % h = 0.001 y1[1] (analytic) = 1.4313602755869476507314096742436 y1[1] (numeric) = 1.440719940364790823357515951879 absolute error = 0.0093596647778431726261062776354 relative error = 0.65389999551336730819274518129485 % h = 0.001 TOP MAIN SOLVE Loop memory used=999.4MB, alloc=4.6MB, time=56.22 NO POLE NO POLE x[1] = 0.447 y2[1] (analytic) = 1.4322622395127468245391683130648 y2[1] (numeric) = 1.4389957593182289556844132958658 absolute error = 0.006733519805482131145244982801 relative error = 0.47013176914954227371632126461982 % h = 0.001 y1[1] (analytic) = 1.4322622395127468245391683130648 y1[1] (numeric) = 1.4416714888708301744180637516271 absolute error = 0.0094092493580833498788954385623 relative error = 0.65695017982770812217332424496133 % h = 0.001 TOP MAIN SOLVE Loop memory used=1003.2MB, alloc=4.6MB, time=56.44 NO POLE NO POLE x[1] = 0.448 y2[1] (analytic) = 1.4331637711763425074521944131981 y2[1] (numeric) = 1.4399554349715655332199129770908 absolute error = 0.0067916637952230257677185638927 relative error = 0.47389307013031875232970661313824 % h = 0.001 y1[1] (analytic) = 1.4331637711763425074521944131981 y1[1] (numeric) = 1.442622725562643821268002956871 absolute error = 0.0094589543863013138158085436729 relative error = 0.66000512827207409384761067324275 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.449 y2[1] (analytic) = 1.4340648696762031110024411903364 y2[1] (numeric) = 1.4409150081538342168400752195069 absolute error = 0.0068501384776311058376340291705 relative error = 0.47767284608106993464184302439725 % h = 0.001 y1[1] (analytic) = 1.4340648696762031110024411903364 y1[1] (numeric) = 1.4435736494340769244061477121436 absolute error = 0.0095087797578738134037065218072 relative error = 0.66306482774526069298264715887773 % h = 0.001 TOP MAIN SOLVE Loop memory used=1007.1MB, alloc=4.6MB, time=56.65 NO POLE NO POLE x[1] = 0.45 y2[1] (analytic) = 1.4349655341112302104208442462319 y2[1] (numeric) = 1.4418744788606380691596624178941 absolute error = 0.0069089447494078587388181716622 relative error = 0.48147112841194674920812070785096 % h = 0.001 y1[1] (analytic) = 1.4349655341112302104208442462319 y1[1] (numeric) = 1.4445242594791484156555698068005 absolute error = 0.0095587253679182052347255605686 relative error = 0.6661292651769898364258810983331 % h = 0.001 TOP MAIN SOLVE Loop memory used=1010.9MB, alloc=4.6MB, time=56.87 NO POLE NO POLE x[1] = 0.451 y2[1] (analytic) = 1.4358657635807594457356712462275 y2[1] (numeric) = 1.442833847087582483805313848697 absolute error = 0.0069680835068230380696426024695 relative error = 0.48528794846713553611646747121947 % h = 0.001 y1[1] (analytic) = 1.4358657635807594457356712462275 y1[1] (numeric) = 1.4454745546920520401189205142339 absolute error = 0.0096087911112925943832492680064 relative error = 0.66919842752780792536153973795081 % h = 0.001 TOP MAIN SOLVE Loop memory used=1014.7MB, alloc=4.6MB, time=57.08 NO POLE NO POLE x[1] = 0.452 y2[1] (analytic) = 1.4367655571845614224368068356284 y2[1] (numeric) = 1.4437931128302751901900521592691 absolute error = 0.0070275556457137677532453236407 relative error = 0.48912333752520730590136336735115 % h = 0.001 y1[1] (analytic) = 1.4367655571845614224368068356284 y1[1] (numeric) = 1.4464245340671573981046183956597 absolute error = 0.0096589768825959756678115600313 relative error = 0.67227230178898423752937640298049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.453 y2[1] (analytic) = 1.4376649140228426117050721307038 y2[1] (numeric) = 1.4447522760843262582861042949157 absolute error = 0.0070873620614836465810321642119 relative error = 0.49297732679946571224992124745007 % h = 0.001 y1[1] (analytic) = 1.4376649140228426117050721307038 y1[1] (numeric) = 1.4473741965990109870228452584938 absolute error = 0.00970928257616837531777312779 relative error = 0.67535087498240967295068096973926 % h = 0.001 TOP MAIN SOLVE Loop memory used=1018.5MB, alloc=4.6MB, time=57.29 NO POLE NO POLE x[1] = 0.454 y2[1] (analytic) = 1.4385638331962462502056785550742 y2[1] (numeric) = 1.4457113368453481033960317982109 absolute error = 0.0071475036491018531903532431367 relative error = 0.49684994743829374440812226415374 % h = 0.001 y1[1] (analytic) = 1.4385638331962462502056785550742 y1[1] (numeric) = 1.44832354128233724325029233997 absolute error = 0.0097597080860909930446137848958 relative error = 0.67843413416049585171299446127089 % h = 0.001 TOP MAIN SOLVE Loop memory used=1022.3MB, alloc=4.6MB, time=57.51 NO POLE NO POLE x[1] = 0.455 y2[1] (analytic) = 1.4394623138058532394449162281053 y2[1] (numeric) = 1.4466702951089554909221654160574 absolute error = 0.0072079813031022514772491879521 relative error = 0.50074123052549914516748569953206 % h = 0.001 y1[1] (analytic) = 1.4394623138058532394449162281053 y1[1] (numeric) = 1.4492725671120395839625986683372 absolute error = 0.0098102533061863445176824402319 relative error = 0.68152206640607456237148149683549 % h = 0.001 TOP MAIN SOLVE Loop memory used=1026.1MB, alloc=4.6MB, time=57.73 NO POLE NO POLE x[1] = 0.456 y2[1] (analytic) = 1.4403603549531830446891775486958 y2[1] (numeric) = 1.4476291508707655411343389509532 absolute error = 0.0072687959175824964451614022574 relative error = 0.50465120708065856028478930480258 % h = 0.001 y1[1] (analytic) = 1.4403603549531830446891775486958 y1[1] (numeric) = 1.4502212730832014489334234367146 absolute error = 0.0098609181300184042442458880188 relative error = 0.68461465883229755953139548590827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.457 y2[1] (analytic) = 1.4412579557401945934454170555095 y2[1] (numeric) = 1.4485879041263977339359172939335 absolute error = 0.007329948386203140490500238424 relative error = 0.50857990805946042515993880364046 % h = 0.001 y1[1] (analytic) = 1.4412579557401945934454170555095 y1[1] (numeric) = 1.4511696581910873422990941084785 absolute error = 0.009911702450892748853677052969 relative error = 0.68771189858253670918252010732777 % h = 0.001 TOP MAIN SOLVE Loop memory used=1029.9MB, alloc=4.6MB, time=57.94 NO POLE NO POLE x[1] = 0.458 y2[1] (analytic) = 1.442155115269287173502149083267 y2[1] (numeric) = 1.4495465548714739136281135776627 absolute error = 0.0073914396021867401259644943957 relative error = 0.51252736435404659456971250616714 % h = 0.001 y1[1] (analytic) = 1.442155115269287173502149083267 y1[1] (numeric) = 1.4521177214311438742877718578999 absolute error = 0.0099626061618567007856227746329 relative error = 0.69081377283028448036288693123857 % h = 0.001 TOP MAIN SOLVE Loop memory used=1033.8MB, alloc=4.6MB, time=58.15 NO POLE NO POLE x[1] = 0.459 y2[1] (analytic) = 1.443051832643301330530085174175 y2[1] (numeric) = 1.4505051031016182936725903891645 absolute error = 0.0074532704583169631425052149895 relative error = 0.51649360679335272122787828920317 % h = 0.001 y1[1] (analytic) = 1.443051832643301330530085174175 y1[1] (numeric) = 1.453065461799000802912075835656 absolute error = 0.010013629155699472381990661481 relative error = 0.69392026877905478173545320326887 % h = 0.001 TOP MAIN SOLVE Loop memory used=1037.6MB, alloc=4.6MB, time=58.37 NO POLE NO POLE x[1] = 0.46 y2[1] (analytic) = 1.4439481069655197652415136439289 y2[1] (numeric) = 1.4514635488124574614523399826965 absolute error = 0.0075154418469376962108263387676 relative error = 0.52047866614344738891509470789616 % h = 0.001 y1[1] (analytic) = 1.4439481069655197652415136439289 y1[1] (numeric) = 1.4540128782904720756241076357928 absolute error = 0.0100647713249523103825939918639 relative error = 0.69703137366228414166777599248276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1041.4MB, alloc=4.6MB, time=58.58 x[1] = 0.461 y2[1] (analytic) = 1.4448439373396682301075241429856 y2[1] (numeric) = 1.4524218919996203830308384342992 absolute error = 0.0075779546599521529233142913136 relative error = 0.52448257310787000589506490637904 % h = 0.001 y1[1] (analytic) = 1.4448439373396682301075241429856 y1[1] (numeric) = 1.454959969901556870931817228728 absolute error = 0.0101160325618886408242930857424 relative error = 0.70014707474323323041103928182484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.462 y2[1] (analytic) = 1.4457393228699164256321804959556 y2[1] (numeric) = 1.4533801326587384079094686805773 absolute error = 0.0076408097888219822772881846217 relative error = 0.52850535832796746430661048905268 % h = 0.001 y1[1] (analytic) = 1.4457393228699164256321804959556 y1[1] (numeric) = 1.4559067356284406399756515139473 absolute error = 0.0101674127585242143434710179917 relative error = 0.70326735931488872298107932627734 % h = 0.001 TOP MAIN SOLVE Loop memory used=1045.2MB, alloc=4.6MB, time=58.81 NO POLE NO POLE x[1] = 0.463 y2[1] (analytic) = 1.446634262660878896182745545017 y2[1] (numeric) = 1.4543382707854452737832073853068 absolute error = 0.0077040081245663776004618402898 relative error = 0.53254705238322957119467180137846 % h = 0.001 y1[1] (analytic) = 1.446634262660878896182745545017 y1[1] (numeric) = 1.4568531744674961480644265361689 absolute error = 0.0102189118066172518816809911519 relative error = 0.70639221469986550135031089222054 % h = 0.001 TOP MAIN SOLVE Loop memory used=1049.0MB, alloc=4.6MB, time=59.03 NO POLE NO POLE x[1] = 0.464 y2[1] (analytic) = 1.4475287558176159253750621672001 y2[1] (numeric) = 1.4552963063753771112945705784982 absolute error = 0.0077675505577611859195084112981 relative error = 0.53660768579162325681672035721808 % h = 0.001 y1[1] (analytic) = 1.4475287558176159253750621672001 y1[1] (numeric) = 1.4577992854152845161693642999255 absolute error = 0.0102705295976685907943021327254 relative error = 0.70952162825030919456568299351143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1052.8MB, alloc=4.6MB, time=59.24 x[1] = 0.465 y2[1] (analytic) = 1.4484228014456344310131950802375 y2[1] (numeric) = 1.4562542394241724487858130135934 absolute error = 0.0078314379785380177726179333559 relative error = 0.54068728900992556583468765108526 % h = 0.001 y1[1] (analytic) = 1.4484228014456344310131950802375 y1[1] (numeric) = 1.4587450674685562623752350097455 absolute error = 0.010322266022921831362039929508 relative error = 0.71265558734779905541398762610441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.466 y2[1] (analytic) = 1.4493163986508888595824384974118 y2[1] (numeric) = 1.457212069927472217049376189521 absolute error = 0.0078956712765833574669376921092 relative error = 0.54478589243405543697627152508305 % h = 0.001 y1[1] (analytic) = 1.4493163986508888595824384974118 y1[1] (numeric) = 1.4596905196242523432875454564016 absolute error = 0.0103741209733634837051069589898 relative error = 0.71579407940325117226200894368966 % h = 0.001 TOP MAIN SOLVE Loop memory used=1056.6MB, alloc=4.6MB, time=59.46 NO POLE NO POLE x[1] = 0.467 y2[1] (analytic) = 1.4502095465397820802947951384674 y2[1] (numeric) = 1.4581697978809197540765799853917 absolute error = 0.0079602513411376737817848469243 relative error = 0.54890352639940427672337584385836 % h = 0.001 y1[1] (analytic) = 1.4502095465397820802947951384674 y1[1] (numeric) = 1.4606356408795051953947141640381 absolute error = 0.0104260943397231150999190255707 relative error = 0.71893709185682201470513348023389 % h = 0.001 TOP MAIN SOLVE Loop memory used=1060.5MB, alloc=4.6MB, time=59.67 NO POLE NO POLE x[1] = 0.468 y2[1] (analytic) = 1.4511022442191662786860325511832 y2[1] (numeric) = 1.459127423280160809804552856675 absolute error = 0.0080251790609945311185203054918 relative error = 0.55304022118116533255947069274636 % h = 0.001 y1[1] (analytic) = 1.4511022442191662786860325511832 y1[1] (numeric) = 1.4615804302316397763841738083888 absolute error = 0.0104781860124734976981412572056 relative error = 0.72208461217781231166414457930334 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1064.3MB, alloc=4.6MB, time=59.89 x[1] = 0.469 y2[1] (analytic) = 1.4519944907963438497634231466225 y2[1] (numeric) = 1.4600849461208435508613955427633 absolute error = 0.0080904553244997010979723961408 relative error = 0.55719600699466187128182788634723 % h = 0.001 y1[1] (analytic) = 1.4519944907963438497634231466225 y1[1] (numeric) = 1.4625248866781746064113413127526 absolute error = 0.0105303958818307566479181661301 relative error = 0.72523662786457126057599630156852 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.47 y2[1] (analytic) = 1.4528862853790682907032748003964 y2[1] (numeric) = 1.4610423663986185653095732369018 absolute error = 0.0081560810195502746062984365054 relative error = 0.56137091399567416785888949240367 % h = 0.001 y1[1] (analytic) = 1.4528862853790682907032748003964 y1[1] (numeric) = 1.463469009216822809320395925907 absolute error = 0.0105827238377545186171211255106 relative error = 0.72839312644440106633040391606537 % h = 0.001 TOP MAIN SOLVE Loop memory used=1068.1MB, alloc=4.6MB, time=60.11 NO POLE NO POLE x[1] = 0.471 y2[1] (analytic) = 1.4537776270755450930973593224828 y2[1] (numeric) = 1.461999684109138867387531170537 absolute error = 0.0082220570335937742901718480542 relative error = 0.56556497228076531028746458031845 % h = 0.001 y1[1] (analytic) = 1.4537776270755450930973593224828 y1[1] (numeric) = 1.4644127968454931538158054847116 absolute error = 0.0106351697699480607184461622288 relative error = 0.73155409547346180861009980340122 % h = 0.001 TOP MAIN SOLVE Loop memory used=1071.9MB, alloc=4.6MB, time=60.32 NO POLE NO POLE x[1] = 0.472 y2[1] (analytic) = 1.4546685149944326347473465492482 y2[1] (numeric) = 1.4629568992480599022495285652194 absolute error = 0.0082883842536272675021820159712 relative error = 0.5697782118876058258790207397356 % h = 0.001 y1[1] (analytic) = 1.4546685149944326347473465492482 y1[1] (numeric) = 1.4653562485622910945835409637788 absolute error = 0.0106877335678584598361944145306 relative error = 0.73471952253667663629858537254782 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1075.7MB, alloc=4.6MB, time=60.54 x[1] = 0.473 y2[1] (analytic) = 1.4555589482448430710063522633121 y2[1] (numeric) = 1.4639140118110395507036859062814 absolute error = 0.0083550635661964796973336429693 relative error = 0.57401066279529713437904133259267 % h = 0.001 y1[1] (analytic) = 1.4555589482448430710063522633121 y1[1] (numeric) = 1.4662993633655198133609193152767 absolute error = 0.0107404151206767423545670519646 relative error = 0.73788939524763728762516158138442 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.474 y2[1] (analytic) = 1.4564489259363432256667085997792 y2[1] (numeric) = 1.4648710217937381339482404936036 absolute error = 0.0084220958573949082815318938244 relative error = 0.57826235492469383329825619629953 % h = 0.001 y1[1] (analytic) = 1.4564489259363432256667085997792 y1[1] (numeric) = 1.4672421402536812599540145036698 absolute error = 0.0107932143173380342873059038906 relative error = 0.74106370124850993472294301547883 % h = 0.001 TOP MAIN SOLVE Loop memory used=1079.5MB, alloc=4.6MB, time=60.75 NO POLE NO POLE x[1] = 0.475 y2[1] (analytic) = 1.4573384471789554813930660511461 y2[1] (numeric) = 1.4658279291918184183060052258801 absolute error = 0.008489482012862936912939174734 relative error = 0.58253331813872482080952186485722 % h = 0.001 y1[1] (analytic) = 1.4573384471789554813930660511461 y1[1] (numeric) = 1.4681845782254771932015765430074 absolute error = 0.0108461310465217118085104918613 relative error = 0.74424242820994135128145338107434 % h = 0.001 TOP MAIN SOLVE Loop memory used=1083.3MB, alloc=4.6MB, time=60.97 NO POLE NO POLE x[1] = 0.476 y2[1] (analytic) = 1.4582275110831586696999366378509 y2[1] (numeric) = 1.4667847340009456199570255758955 absolute error = 0.0085572229177869502570889380446 relative error = 0.586823582242713261539226583358 % h = 0.001 y1[1] (analytic) = 1.4582275110831586696999366378509 y1[1] (numeric) = 1.4691266762798102218843982482259 absolute error = 0.010899165196651552184461610375 relative error = 0.74742556383096540198126386705821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1087.2MB, alloc=4.6MB, time=61.18 x[1] = 0.477 y2[1] (analytic) = 1.4591161167598889604727882670001 y2[1] (numeric) = 1.4677414362167874096694297154336 absolute error = 0.0086253194568984491966414484335 relative error = 0.59113317698469540055732472575257 % h = 0.001 y1[1] (analytic) = 1.4591161167598889604727882670001 y1[1] (numeric) = 1.4700684334157848455790693168523 absolute error = 0.0109523166558958851062810498522 relative error = 0.75061309583890985240397028496239 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.478 y2[1] (analytic) = 1.4600042633205407510318007582506 y2[1] (numeric) = 1.4686980358350139175284667495512 absolute error = 0.0086937725144731664966659913006 relative error = 0.59546213205573823084546396038605 % h = 0.001 y1[1] (analytic) = 1.4600042633205407510318007582506 y1[1] (numeric) = 1.4710098486327084954550572634724 absolute error = 0.0110055853121677444232565052218 relative error = 0.75380501198930349811661036497426 % h = 0.001 TOP MAIN SOLVE Loop memory used=1091.0MB, alloc=4.6MB, time=61.40 NO POLE NO POLE x[1] = 0.479 y2[1] (analytic) = 1.4608919498769675547373944731655 y2[1] (numeric) = 1.4696545328512977376637280210678 absolute error = 0.0087625829743301829263335479023 relative error = 0.59981047709025601949815591791163 % h = 0.001 y1[1] (analytic) = 1.4608919498769675547373944731655 y1[1] (numeric) = 1.471950920930092575014054636362 absolute error = 0.0110589710531250202766601631965 relative error = 0.75700130006578361163539922541746 % h = 0.001 TOP MAIN SOLVE Loop memory used=1094.8MB, alloc=4.6MB, time=61.62 NO POLE NO POLE x[1] = 0.48 y2[1] (analytic) = 1.4617791755414828891366429425886 y2[1] (numeric) = 1.4706109272613139329745464472461 absolute error = 0.0088317517198310438379035046575 relative error = 0.60417824166632569788755648407265 % h = 0.001 y1[1] (analytic) = 1.4617791755414828891366429425886 y1[1] (numeric) = 1.4728916493076535007705318537779 absolute error = 0.0111124737661706116338889111893 relative error = 0.7602019478800037059794090005186 % h = 0.001 TOP MAIN SOLVE Loop memory used=1098.6MB, alloc=4.6MB, time=61.83 NO POLE NO POLE x[1] = 0.481 y2[1] (analytic) = 1.4626659394268611636496813457004 y2[1] (numeric) = 1.4715672190607400398535688517664 absolute error = 0.008901279633878876203887506066 relative error = 0.6085654553060011209981644504962 % h = 0.001 y1[1] (analytic) = 1.4626659394268611636496813457004 y1[1] (numeric) = 1.4738320327653137428724349065588 absolute error = 0.0111660933384525792227535608584 relative error = 0.7634069432715416135305380606554 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.482 y2[1] (analytic) = 1.4635522406463385667952231544191 y2[1] (numeric) = 1.4725234082452560729084962562316 absolute error = 0.0089711675989175061132731018125 relative error = 0.61297214747562620111361640072621 % h = 0.001 y1[1] (analytic) = 1.4635522406463385667952231544191 y1[1] (numeric) = 1.4747720703032028656609670839009 absolute error = 0.0112198296568642988657439294818 relative error = 0.76661627410780787892180634603733 % h = 0.001 TOP MAIN SOLVE Loop memory used=1102.4MB, alloc=4.6MB, time=62.04 NO POLE NO POLE x[1] = 0.483 y2[1] (analytic) = 1.4644380783136139529542977177052 y2[1] (numeric) = 1.4734794948105445296819870965795 absolute error = 0.0090414164969305767276893788743 relative error = 0.61739834758614692101375067977563 % h = 0.001 y1[1] (analytic) = 1.4644380783136139529542977177052 y1[1] (numeric) = 1.4757117609216585681683937904501 absolute error = 0.0112736826080446152140960727449 relative error = 0.76982992828395446468167621154317 % h = 0.001 TOP MAIN SOLVE Loop memory used=1106.2MB, alloc=4.6MB, time=62.26 NO POLE NO POLE x[1] = 0.484 y2[1] (analytic) = 1.4653234515428497286713220221064 y2[1] (numeric) = 1.4744354787522903953697183309222 absolute error = 0.0091120272094406666983963088158 relative error = 0.62184408499342223181623339260727 % h = 0.001 y1[1] (analytic) = 1.4653234515428497286713220221064 y1[1] (numeric) = 1.4766511036212277245528094351868 absolute error = 0.0113276520783779958814874130804 relative error = 0.77304789372278376836773300011813 % h = 0.001 TOP MAIN SOLVE Loop memory used=1110.0MB, alloc=4.6MB, time=62.47 NO POLE NO POLE x[1] = 0.485 y2[1] (analytic) = 1.4662083594486727384916203275428 y2[1] (numeric) = 1.4753913600661811475365994064831 absolute error = 0.0091830006175084090449790789403 relative error = 0.62630938899853384057328390311799 % h = 0.001 y1[1] (analytic) = 1.4662083594486727384916203275428 y1[1] (numeric) = 1.4775900974026674244688052859757 absolute error = 0.0113817379539946859771849584329 relative error = 0.7762701583746579499286664764951 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.486 y2[1] (analytic) = 1.4670928011461751503345058408895 y2[1] (numeric) = 1.4763471387479067608311340544565 absolute error = 0.009254337601731610496628213567 relative error = 0.6307942888480948927104055665831 % h = 0.001 y1[1] (analytic) = 1.4670928011461751503345058408895 y1[1] (numeric) = 1.4785287412669460133729770981095 absolute error = 0.01143594012077086303847125722 relative error = 0.77949671021740856803907341198502 % h = 0.001 TOP MAIN SOLVE Loop memory used=1113.9MB, alloc=4.6MB, time=62.69 NO POLE NO POLE x[1] = 0.487 y2[1] (analytic) = 1.4679767757509153404010390543462 y2[1] (numeric) = 1.4773028147931597116979248827747 absolute error = 0.0093260390422443712968858284285 relative error = 0.6352988137345575543705187377184 % h = 0.001 y1[1] (analytic) = 1.4679767757509153404010390543462 y1[1] (numeric) = 1.4794670342152441327632112406948 absolute error = 0.0114902584643287923621721863486 relative error = 0.78272753725624652415715316592576 % h = 0.001 TOP MAIN SOLVE Loop memory used=1117.7MB, alloc=4.6MB, time=62.90 NO POLE NO POLE x[1] = 0.488 y2[1] (analytic) = 1.4688602823789187776155778409106 y2[1] (numeric) = 1.4782583881976349830883157379332 absolute error = 0.0093981058187162054727378970226 relative error = 0.63982299279651949970350676764031 % h = 0.001 y1[1] (analytic) = 1.4688602823789187776155778409106 y1[1] (numeric) = 1.4804049752489557603506879613054 absolute error = 0.0115446928700369827351101203948 relative error = 0.78596262752367231306089220729488 % h = 0.001 TOP MAIN SOLVE Loop memory used=1121.5MB, alloc=4.6MB, time=63.12 NO POLE NO POLE x[1] = 0.489 y2[1] (analytic) = 1.4697433201466789076002348654785 y2[1] (numeric) = 1.4792138589570300691691668081949 absolute error = 0.0094705388103511615689319427164 relative error = 0.64436685511902930811792105659859 % h = 0.001 y1[1] (analytic) = 1.4697433201466789076002348654785 y1[1] (numeric) = 1.4813425633696892501635403469713 absolute error = 0.0115992432230103425633054814928 relative error = 0.78920196907938657862383031069075 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.49 y2[1] (analytic) = 1.470625888171158036181358337188 y2[1] (numeric) = 1.4801692270670449800297574416706 absolute error = 0.0095433388958869438483991044826 relative error = 0.64893042973389077648844758853483 % h = 0.001 y1[1] (analytic) = 1.470625888171158036181358337188 y1[1] (numeric) = 1.4822797975792683725811074582725 absolute error = 0.0116539094081103363997491210845 relative error = 0.79244555001020097359697079029114 % h = 0.001 TOP MAIN SOLVE Loop memory used=1125.3MB, alloc=4.6MB, time=63.33 NO POLE NO POLE x[1] = 0.491 y2[1] (analytic) = 1.4715079855697882124271525965983 y2[1] (numeric) = 1.4811244925233822463868116539532 absolute error = 0.0096165069535940339596590573549 relative error = 0.65351374561996615128971406654777 % h = 0.001 y1[1] (analytic) = 1.4715079855697882124271525965983 y1[1] (numeric) = 1.4832166768797333542977200330714 absolute error = 0.0117086913099451418705674364731 relative error = 0.79569335842994932216883975089774 % h = 0.001 TOP MAIN SOLVE Loop memory used=1129.1MB, alloc=4.6MB, time=63.56 NO POLE NO POLE x[1] = 0.492 y2[1] (analytic) = 1.4723896114604721112155555001594 y2[1] (numeric) = 1.4820796553217469242876413011711 absolute error = 0.0096900438612748130720858010117 relative error = 0.65811683170347828560411312636873 % h = 0.001 y1[1] (analytic) = 1.4723896114604721112155555001594 y1[1] (numeric) = 1.4841532002733419182149570772457 absolute error = 0.0117635888128698069994015770863 relative error = 0.79894538247939908408111508119797 % h = 0.001 TOP MAIN SOLVE Loop memory used=1132.9MB, alloc=4.6MB, time=63.77 NO POLE NO POLE x[1] = 0.493 y2[1] (analytic) = 1.4732707649615839153314900341658 y2[1] (numeric) = 1.4830347154578465998114018955157 absolute error = 0.0097639504962626844799118613499 relative error = 0.66273971685831172592853246485575 % h = 0.001 y1[1] (analytic) = 1.4732707649615839153314900341658 y1[1] (numeric) = 1.4850893667625703232613115816704 absolute error = 0.0118186018009864079298215475046 relative error = 0.80220161032616311908263493666194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.494 y2[1] (analytic) = 1.4741514451919701970926080610182 y2[1] (numeric) = 1.4839896729273913937684560414967 absolute error = 0.0098382277354211966758479804785 relative error = 0.66738242990631273368221642114266 % h = 0.001 y1[1] (analytic) = 1.4741514451919701970926080610182 y1[1] (numeric) = 1.4860251753501144041382035276514 absolute error = 0.0118737301581442070455954666332 relative error = 0.80546203016461175050995790076966 % h = 0.001 TOP MAIN SOLVE Loop memory used=1136.8MB, alloc=4.6MB, time=63.99 NO POLE NO POLE x[1] = 0.495 y2[1] (analytic) = 1.4750316512709507995026445721214 y2[1] (numeric) = 1.4849445277260939663978394723802 absolute error = 0.0099128764551431668951949002588 relative error = 0.67204499961758824629543493423934 % h = 0.001 y1[1] (analytic) = 1.4750316512709507995026445721214 y1[1] (numeric) = 1.4869606250388906109912782670265 absolute error = 0.0119289737679398114886336949051 relative error = 0.80872663021578512678798301731254 % h = 0.001 TOP MAIN SOLVE Loop memory used=1140.6MB, alloc=4.6MB, time=64.20 NO POLE NO POLE x[1] = 0.496 y2[1] (analytic) = 1.475911382318319716931501294139 y2[1] (numeric) = 1.4858992798496695220628246674717 absolute error = 0.0099878975313498051313233733327 relative error = 0.67672745471080378273620421959398 % h = 0.001 y1[1] (analytic) = 1.475911382318319716931501294139 y1[1] (numeric) = 1.4878957148320370490059282882287 absolute error = 0.0119843325137173320744269940897 relative error = 0.81199539872730587964944759479161 % h = 0.001 TOP MAIN SOLVE Loop memory used=1144.4MB, alloc=4.6MB, time=64.42 NO POLE NO POLE x[1] = 0.497 y2[1] (analytic) = 1.4767906374543459753211789685932 y2[1] (numeric) = 1.4868539292938358139445770321191 absolute error = 0.0100632918394898386233980635259 relative error = 0.68142982385348029830998831103583 % h = 0.001 y1[1] (analytic) = 1.4767906374543459753211789685932 y1[1] (numeric) = 1.4888304437329145179259763057458 absolute error = 0.0120398062785685426047973371526 relative error = 0.81526832397329207787740423814494 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.498 y2[1] (analytic) = 1.4776694157997745119166780989527 y2[1] (numeric) = 1.4878084760543131487338986235289 absolute error = 0.0101390602545386368172205245762 relative error = 0.6861521356622899935451111584258 % h = 0.001 y1[1] (analytic) = 1.4776694157997745119166780989527 y1[1] (numeric) = 1.4897648107451075514944575376177 absolute error = 0.012095394945333039577779438665 relative error = 0.81854539425427047538003610332538 % h = 0.001 TOP MAIN SOLVE Loop memory used=1148.2MB, alloc=4.6MB, time=64.64 NO POLE NO POLE x[1] = 0.499 y2[1] (analytic) = 1.4785477164758270545209884343788 y2[1] (numeric) = 1.488762920126824391321054406711 absolute error = 0.0102152036509973368000659723322 relative error = 0.69089441870335108195452461572404 % h = 0.001 y1[1] (analytic) = 1.4785477164758270545209884343788 y1[1] (numeric) = 1.490698814872425456815438963879 absolute error = 0.0121510983965984022944505295002 relative error = 0.8218265978970900524124010365308 % h = 0.001 TOP MAIN SOLVE Loop memory used=1152.0MB, alloc=4.6MB, time=64.86 NO POLE NO POLE x[1] = 0.5 y2[1] (analytic) = 1.4794255386042030002732879352156 y2[1] (numeric) = 1.4897172615070949694836760260974 absolute error = 0.0102917229028919692103880908818 relative error = 0.69565670149252152144260776157429 % h = 0.001 y1[1] (analytic) = 1.4794255386042030002732879352156 y1[1] (numeric) = 1.4916324551189033536358132881886 absolute error = 0.012206916514700353362525352973 relative error = 0.82511192325483584876490119041099 % h = 0.001 TOP MAIN SOLVE Loop memory used=1155.8MB, alloc=4.6MB, time=65.07 NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 1.4803028813070802939494724420977 y2[1] (numeric) = 1.4906715001908528785727380796114 absolute error = 0.0103686188837725846232656375137 relative error = 0.70043901249569171410381693287439 % h = 0.001 y1[1] (analytic) = 1.4803028813070802939494724420977 y1[1] (numeric) = 1.4925657304888032135460052552835 absolute error = 0.0122628491817229195965328131858 relative error = 0.82840135870674308774345504298973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.502 y2[1] (analytic) = 1.4811797437071163057841377482187 y2[1] (numeric) = 1.4916256361738286861966018832055 absolute error = 0.0104458924667123804124641349868 relative error = 0.705241380129076179138262992069 % h = 0.001 y1[1] (analytic) = 1.4811797437071163057841377482187 y1[1] (numeric) = 1.4934986399866148990985279083571 absolute error = 0.0123188962794985933143901601384 relative error = 0.83169489265811158977150361815958 % h = 0.001 TOP MAIN SOLVE Loop memory used=1159.6MB, alloc=4.6MB, time=65.28 NO POLE NO POLE x[1] = 0.503 y2[1] (analytic) = 1.4820561249274487088131362528522 y2[1] (numeric) = 1.4925796694517555369031217151275 absolute error = 0.0105235445243068280899854622753 relative error = 0.71006383275950420358766206544559 % h = 0.001 y1[1] (analytic) = 1.4820561249274487088131362528522 y1[1] (numeric) = 1.4944311826170572028433263029859 absolute error = 0.0123750576896084940301900501337 relative error = 0.83499251354022047444911225554053 % h = 0.001 TOP MAIN SOLVE Loop memory used=1163.5MB, alloc=4.6MB, time=65.50 NO POLE NO POLE x[1] = 0.504 y2[1] (analytic) = 1.4829320240916963557358308536409 y2[1] (numeric) = 1.4935336000203691568598085304264 absolute error = 0.0106015759286728011239776767855 relative error = 0.71490639870470947557358766208269 % h = 0.001 y1[1] (analytic) = 1.4829320240916963557358308536409 y1[1] (numeric) = 1.4953633573850788862788461278216 absolute error = 0.0124313332933825305430152741807 relative error = 0.83829420981024314990953363857808 % h = 0.001 TOP MAIN SOLVE Loop memory used=1167.3MB, alloc=4.6MB, time=65.72 NO POLE NO POLE x[1] = 0.505 y2[1] (analytic) = 1.4838074403239601552961692154743 y2[1] (numeric) = 1.4944874278754078585320461374615 absolute error = 0.0106799875514477032358769219872 relative error = 0.71976910623361870469854509249469 % h = 0.001 y1[1] (analytic) = 1.4838074403239601552961692154743 y1[1] (numeric) = 1.4962951632958597187177646169205 absolute error = 0.0124877229718995634215954014462 relative error = 0.84159996995116258831867709683033 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.506 y2[1] (analytic) = 1.4846823727488239481817020349524 y2[1] (numeric) = 1.4954411530126125453593548294399 absolute error = 0.0107587802637885971776527944875 relative error = 0.7246519835666392342490928397859 % h = 0.001 y1[1] (analytic) = 1.4846823727488239481817020349524 y1[1] (numeric) = 1.4972265993548115160663210743031 absolute error = 0.0125442266059875678846190393507 relative error = 0.84490978247168688636798358630596 % h = 0.001 TOP MAIN SOLVE Loop memory used=1171.1MB, alloc=4.6MB, time=65.93 NO POLE NO POLE x[1] = 0.507 y2[1] (analytic) = 1.4855568204913553824396694014904 y2[1] (numeric) = 1.4963947754277267164296974652726 absolute error = 0.0108379549363713339900280637822 relative error = 0.72955505887594564981904938294561 % h = 0.001 y1[1] (analytic) = 1.4855568204913553824396694014904 y1[1] (numeric) = 1.4981576645675791795161842681249 absolute error = 0.0126008440762237970765148666345 relative error = 0.84822363590616510961623535310522 % h = 0.001 TOP MAIN SOLVE Loop memory used=1174.9MB, alloc=4.6MB, time=66.15 NO POLE NO POLE x[1] = 0.508 y2[1] (analytic) = 1.4864307826771067884092798390526 y2[1] (numeric) = 1.4973482951164964711518229953079 absolute error = 0.0109175124393896827425431562553 relative error = 0.73447836028576538894974732554435 % h = 0.001 y1[1] (analytic) = 1.4864307826771067884092798390526 y1[1] (numeric) = 1.4990883579400417341477938896909 absolute error = 0.0126575752629349457385140506383 relative error = 0.85154151881450341954083423296779 % h = 0.001 TOP MAIN SOLVE Loop memory used=1178.7MB, alloc=4.6MB, time=66.36 NO POLE NO POLE x[1] = 0.509 y2[1] (analytic) = 1.4873042584321160531693070963062 y2[1] (numeric) = 1.4983017120746705139256424287782 absolute error = 0.010997453642554460756335332472 relative error = 0.73942191587266335636332894135302 % h = 0.001 y1[1] (analytic) = 1.4873042584321160531693070963062 y1[1] (numeric) = 1.5000186784783133674441132114658 absolute error = 0.0127144200461973142748061151596 relative error = 0.8548634197820814821640629649977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.51 y2[1] (analytic) = 1.4881772468829074945001302376746 y2[1] (numeric) = 1.4992550262980001588106322410769 absolute error = 0.0110777794150926643105020034023 relative error = 0.74438575366582554934421781040647 % h = 0.001 y1[1] (analytic) = 1.4881772468829074945001302376746 y1[1] (numeric) = 1.5009486251887444677137300182161 absolute error = 0.0127713783058369732135997805415 relative error = 0.85818932741966915712479993127892 % h = 0.001 TOP MAIN SOLVE Loop memory used=1182.5MB, alloc=4.6MB, time=66.58 NO POLE NO POLE x[1] = 0.511 y2[1] (analytic) = 1.4890497471564927343593430733201 y2[1] (numeric) = 1.5002082377822393341922602202665 absolute error = 0.0111584906257465998329171469464 relative error = 0.74936990164734169780314949075173 % h = 0.001 y1[1] (analytic) = 1.4890497471564927343593430733201 y1[1] (numeric) = 1.5018781970779226624222428264727 absolute error = 0.0128284499214299280628997531526 relative error = 0.86151923036334346607108950733422 % h = 0.001 TOP MAIN SOLVE Loop memory used=1186.3MB, alloc=4.6MB, time=66.80 NO POLE NO POLE x[1] = 0.512 y2[1] (analytic) = 1.4899217583803715718700594525215 y2[1] (numeric) = 1.5011613465231445874464287535128 absolute error = 0.0112395881427730155763693009913 relative error = 0.75437438775248692353749955912981 % h = 0.001 y1[1] (analytic) = 1.4899217583803715718700594525215 y1[1] (numeric) = 1.5028073931526738564308693496188 absolute error = 0.0128856347723022845608098970973 relative error = 0.86485311727440583925387784882201 % h = 0.001 TOP MAIN SOLVE Loop memory used=1190.2MB, alloc=4.6MB, time=67.01 NO POLE NO POLE x[1] = 0.513 y2[1] (analytic) = 1.4907932796825328558210414322121 y2[1] (numeric) = 1.5021143525164750896019305554336 absolute error = 0.0113210728339422337808891232215 relative error = 0.75939923987000242318110927026498 % h = 0.001 y1[1] (analytic) = 1.4907932796825328558210414322121 y1[1] (numeric) = 1.5037362124200632701412141090944 absolute error = 0.0129429327375304143201726768823 relative error = 0.86819097683929963920710757794055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.514 y2[1] (analytic) = 1.4916643101914553566777778206244 y2[1] (numeric) = 1.5030672557579926400009118416552 absolute error = 0.0114029455665372833231340210308 relative error = 0.7644444858423751793163769438419 % h = 0.001 y1[1] (analytic) = 1.4916643101914553566777778206244 y1[1] (numeric) = 1.5046646538873964775451320364592 absolute error = 0.0130003436959411208673542158348 relative error = 0.87153279776952796040422459500552 % h = 0.001 TOP MAIN SOLVE Loop memory used=1194.0MB, alloc=4.6MB, time=67.22 NO POLE NO POLE x[1] = 0.515 y2[1] (analytic) = 1.4925348490361086381036410850348 y2[1] (numeric) = 1.5040200562434616709573379521746 absolute error = 0.0114852072073530328536968671398 relative error = 0.76951015346611670420105640923077 % h = 0.001 y1[1] (analytic) = 1.4925348490361086381036410850348 y1[1] (numeric) = 1.5055927165622204441786248563754 absolute error = 0.0130578675261118060749837713406 relative error = 0.87487856880157170378598625500681 % h = 0.001 TOP MAIN SOLVE Loop memory used=1197.8MB, alloc=4.6MB, time=67.44 NO POLE NO POLE x[1] = 0.516 y2[1] (analytic) = 1.4934048953459539279902511025232 y2[1] (numeric) = 1.504972753968649252413456430438 absolute error = 0.0115678586226953244232053279148 relative error = 0.77459627049204082054198184244206 % h = 0.001 y1[1] (analytic) = 1.4934048953459539279902511025232 y1[1] (numeric) = 1.5065203994523245649787069869587 absolute error = 0.0131155041063706369884558844355 relative error = 0.87822827869680792505927254126514 % h = 0.001 TOP MAIN SOLVE Loop memory used=1201.6MB, alloc=4.6MB, time=67.66 NO POLE NO POLE x[1] = 0.517 y2[1] (analytic) = 1.4942744482509449889961747234587 y2[1] (numeric) = 1.5059253489293250965942525653647 absolute error = 0.011650900678380107598077841906 relative error = 0.77970286462554048372782054282247 % h = 0.001 y1[1] (analytic) = 1.4942744482509449889961747234587 y1[1] (numeric) = 1.5074477015657417020421776413988 absolute error = 0.0131732533147967130460029179401 relative error = 0.88158191624142845567139076414207 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.518 y2[1] (analytic) = 1.4951435068815289885930906090811 y2[1] (numeric) = 1.5068778411212615626598924048671 absolute error = 0.011734334239732574066801795786 relative error = 0.78482996352686364991294104807155 % h = 0.001 y1[1] (analytic) = 1.4951435068815289885930906090811 y1[1] (numeric) = 1.5083746219107492222852357632738 absolute error = 0.0132311150292202336921451541927 relative error = 0.88493947024635879536912983809263 % h = 0.001 TOP MAIN SOLVE Loop memory used=1205.4MB, alloc=4.6MB, time=67.87 NO POLE NO POLE x[1] = 0.519 y2[1] (analytic) = 1.4960120703686473686185492970897 y2[1] (numeric) = 1.5078302305402336613561482507458 absolute error = 0.0118181601715862927375989536561 relative error = 0.78997759481138819432457290625922 % h = 0.001 y1[1] (analytic) = 1.4960120703686473686185492970897 y1[1] (numeric) = 1.5093011594958700350028743775726 absolute error = 0.0132890891272226663843250804829 relative error = 0.88830092954717727525656246768231 % h = 0.001 TOP MAIN SOLVE Loop memory used=1209.2MB, alloc=4.6MB, time=68.09 NO POLE NO POLE x[1] = 0.52 y2[1] (analytic) = 1.4968801378437367143344589425478 y2[1] (numeric) = 1.5087825171820190596628016461717 absolute error = 0.0119023793382823453283427036239 relative error = 0.79514578604989588414562584999099 % h = 0.001 y1[1] (analytic) = 1.4968801378437367143344589425478 y1[1] (numeric) = 1.5102273133298736293269908900981 absolute error = 0.0133471754861369149925319475503 relative error = 0.89166628300403449027031272801745 % h = 0.001 TOP MAIN SOLVE Loop memory used=1213.0MB, alloc=4.6MB, time=68.31 NO POLE NO POLE x[1] = 0.521 y2[1] (analytic) = 1.4977477084387296229904276756926 y2[1] (numeric) = 1.5097347010423980854400188683057 absolute error = 0.0119869926036684624495911926131 relative error = 0.8003345647688454103058294877455 % h = 0.001 y1[1] (analytic) = 1.4977477084387296229904276756926 y1[1] (numeric) = 1.5111530824217771115821498196499 absolute error = 0.0134053739830474885917221439573 relative error = 0.89503551950157299999570267798014 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.522 y2[1] (analytic) = 1.4986147812860555718910940133795 y2[1] (numeric) = 1.5106867821171537320726939399506 absolute error = 0.0120720008310981601815999265711 relative error = 0.80554395845064448249424938473412 % h = 0.001 y1[1] (analytic) = 1.4986147812860555718910940133795 y1[1] (numeric) = 1.512078465780846242537934400182 absolute error = 0.0134636844947906706468403868025 relative error = 0.8984086279488472967518649197496 % h = 0.001 TOP MAIN SOLVE Loop memory used=1216.9MB, alloc=4.6MB, time=68.52 NO POLE NO POLE x[1] = 0.523 y2[1] (analytic) = 1.4994813555186417859665772569024 y2[1] (numeric) = 1.5116387604020716631127541754773 absolute error = 0.0121574048834298771461769185749 relative error = 0.81077399453392099168673099487004 % h = 0.001 y1[1] (analytic) = 1.4994813555186417859665772569024 y1[1] (numeric) = 1.5130034624165964745568234439942 absolute error = 0.0135221068979546885902461870918 relative error = 0.90178559727924403987855853529737 % h = 0.001 TOP MAIN SOLVE Loop memory used=1220.7MB, alloc=4.6MB, time=68.74 NO POLE NO POLE x[1] = 0.524 y2[1] (analytic) = 1.5003474302699141048451803058119 y2[1] (numeric) = 1.5125906358929402169194232776225 absolute error = 0.0122432056230261120742429718106 relative error = 0.81602470041379324446241877615899 % h = 0.001 y1[1] (analytic) = 1.5003474302699141048451803058119 y1[1] (numeric) = 1.5139280713387939886365298119507 absolute error = 0.0135806410688798837913495061388 relative error = 0.90516641645040255516205371118469 % h = 0.001 TOP MAIN SOLVE Loop memory used=1224.5MB, alloc=4.6MB, time=68.95 NO POLE NO POLE x[1] = 0.525 y2[1] (analytic) = 1.5012130046737978494274778151016 y2[1] (numeric) = 1.5135424085855504112974370031154 absolute error = 0.0123294039117525618699591880138 relative error = 0.82129610344213927336419342606353 % h = 0.001 y1[1] (analytic) = 1.5012130046737978494274778151016 y1[1] (numeric) = 1.5148522915574567313457367927205 absolute error = 0.0136392868836588819182589776189 relative error = 0.90855107444413559834205572659108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.526 y2[1] (analytic) = 1.5020780778647186879609231217462 y2[1] (numeric) = 1.5144940784756959481332064164525 absolute error = 0.0124160006109772601722832947063 relative error = 0.82658823092786522753866496654683 % h = 0.001 y1[1] (analytic) = 1.5020780778647186879609231217462 y1[1] (numeric) = 1.515776122082855451652168650108 absolute error = 0.0136980442181367636912455283618 relative error = 0.9119395602663503816462219458822 % h = 0.001 TOP MAIN SOLVE Loop memory used=1228.3MB, alloc=4.6MB, time=69.17 NO POLE NO POLE x[1] = 0.527 y2[1] (analytic) = 1.5029426489776035016141078660558 y2[1] (numeric) = 1.5154456455591732180289237525122 absolute error = 0.0125029965815697164148158864564 relative error = 0.8319011101371728478722528497988 % h = 0.001 y1[1] (analytic) = 1.5029426489776035016141078660558 y1[1] (numeric) = 1.5166995619255147376419315556825 absolute error = 0.0137569129479112360278236896267 relative error = 0.91533186294696986230338614414878 % h = 0.001 TOP MAIN SOLVE Loop memory used=1232.1MB, alloc=4.6MB, time=69.39 NO POLE NO POLE x[1] = 0.528 y2[1] (analytic) = 1.5038067171478812495498087336605 y2[1] (numeric) = 1.5163971098317813049346059100754 absolute error = 0.0125903926839000553847971764149 relative error = 0.83723476829382603082087580629641 % h = 0.001 y1[1] (analytic) = 1.5038067171478812495498087336605 y1[1] (numeric) = 1.5176226100962140531290610831286 absolute error = 0.0138158929483328035792523494681 relative error = 0.91872797153985429199114302015818 % h = 0.001 TOP MAIN SOLVE Loop memory used=1235.9MB, alloc=4.6MB, time=69.60 NO POLE NO POLE x[1] = 0.529 y2[1] (analytic) = 1.504670281511483833495956245149 y2[1] (numeric) = 1.5173484712893219907780705996963 absolute error = 0.0126781897778381572821143545473 relative error = 0.8425892325794164851118632827098 % h = 0.001 y1[1] (analytic) = 1.504670281511483833495956245149 y1[1] (numeric) = 1.5185452656059887741542124010201 absolute error = 0.0138749840945049406582561558711 relative error = 0.92212787512272302617796223343501 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.53 y2[1] (analytic) = 1.5055333412048469618136610224661 y2[1] (numeric) = 1.5182997299275997600928401707568 absolute error = 0.0127663887227527982791791482907 relative error = 0.84796453013362848547788648628361 % h = 0.001 y1[1] (analytic) = 1.5055333412048469618136610224661 y1[1] (numeric) = 1.5194675274661312253714292620722 absolute error = 0.0139341862612842635577682396061 relative error = 0.92553156279707659232449585669984 % h = 0.001 TOP MAIN SOLVE Loop memory used=1239.8MB, alloc=4.6MB, time=69.81 NO POLE NO POLE x[1] = 0.531 y2[1] (analytic) = 1.5063958953649110130614334641129 y2[1] (numeric) = 1.5192508857424218046439681439246 absolute error = 0.0128549903775107915825346798117 relative error = 0.85336068805450272756398973620305 % h = 0.001 y1[1] (analytic) = 1.5063958953649110130614334641129 y1[1] (numeric) = 1.5203893946881917163219278493498 absolute error = 0.0139934993232807032604943852369 relative error = 0.92893902368811901591321587832243 % h = 0.001 TOP MAIN SOLVE Loop memory used=1243.6MB, alloc=4.6MB, time=70.03 NO POLE NO POLE x[1] = 0.532 y2[1] (analytic) = 1.5072579431291218990547332650042 y2[1] (numeric) = 1.5202019387295980280517834766347 absolute error = 0.0129439956004761289970502116305 relative error = 0.85877773339869928813018149579913 % h = 0.001 y1[1] (analytic) = 1.5072579431291218990547332650042 y1[1] (numeric) = 1.5213108662839795775938315034019 absolute error = 0.0140529231548576785390982383977 relative error = 0.93235024694468040327996943586692 % h = 0.001 TOP MAIN SOLVE Loop memory used=1247.4MB, alloc=4.6MB, time=70.25 NO POLE NO POLE x[1] = 0.533 y2[1] (analytic) = 1.5081194836354319274199857215036 y2[1] (numeric) = 1.5211528888849410504135475906122 absolute error = 0.0130334052495091229935618691086 relative error = 0.86421569318175969465351860015703 % h = 0.001 y1[1] (analytic) = 1.5081194836354319274199857215036 y1[1] (numeric) = 1.5222319412655641968667923188566 absolute error = 0.014112457630132269446806597353 relative error = 0.93576522173913978022546892699939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.534 y2[1] (analytic) = 1.508980516022300663642202267693 y2[1] (numeric) = 1.5221037362042662129230191918626 absolute error = 0.0131232201819655492808169241696 relative error = 0.86967459437836810841518628237842 % h = 0.001 y1[1] (analytic) = 1.508980516022300663642202267693 y1[1] (numeric) = 1.5231526186452760548404355646457 absolute error = 0.0141721026229753911982332969527 memory used=1251.2MB, alloc=4.6MB, time=70.47 relative error = 0.93918393726734818538914214064646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.535 y2[1] (analytic) = 1.5098410394286957926053431953273 y2[1] (numeric) = 1.5230544806833915824879219149661 absolute error = 0.0132134412546957898825787196388 relative error = 0.87515446392261162513974012262654 % h = 0.001 y1[1] (analytic) = 1.5098410394286957926053431953273 y1[1] (numeric) = 1.5240728974357077610455628487339 absolute error = 0.0142318580070119684402196534066 relative error = 0.94260638274855201737215419341276 % h = 0.001 TOP MAIN SOLVE Loop memory used=1255.0MB, alloc=4.6MB, time=70.69 NO POLE NO POLE x[1] = 0.536 y2[1] (analytic) = 1.5107010529940939796245610171836 y2[1] (numeric) = 1.5240051223181379563453098249301 absolute error = 0.0133040693240439767207488077465 relative error = 0.88065532870823969723543348406518 % h = 0.001 y1[1] (analytic) = 1.5107010529940939796245610171836 y1[1] (numeric) = 1.5249927766497150895370499160057 absolute error = 0.0142917236556211099124888988221 relative error = 0.9460325474253166346007784559854 % h = 0.001 TOP MAIN SOLVE Loop memory used=1258.8MB, alloc=4.6MB, time=70.90 NO POLE NO POLE x[1] = 0.537 y2[1] (analytic) = 1.511560555858481730969463441633 y2[1] (numeric) = 1.5249556611043288666748258112763 absolute error = 0.0133951052458471357053623696433 relative error = 0.88617721558892268166640484900401 % h = 0.001 y1[1] (analytic) = 1.511560555858481730969463441633 y1[1] (numeric) = 1.5259122553004180144673749368105 absolute error = 0.0143516994419362834979114951775 relative error = 0.94946242056345020692563792351606 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1262.6MB, alloc=4.6MB, time=71.12 x[1] = 0.538 y2[1] (analytic) = 1.5124195471623562538775354352446 y2[1] (numeric) = 1.5259060970377905852098479104642 absolute error = 0.0134865498754343313323124752196 relative error = 0.89172015137850951746944321979363 % h = 0.001 y1[1] (analytic) = 1.5124195471623562538775354352446 y1[1] (numeric) = 1.5268313324012017455397131135886 absolute error = 0.014411785238845491662177678344 relative error = 0.95289599145192781795666173418512 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.539 y2[1] (analytic) = 1.5132780260467263160568603600697 y2[1] (numeric) = 1.5268564301143521278465185941888 absolute error = 0.0135784040676258117896582341191 relative error = 0.89728416285128453691008589921061 % h = 0.001 y1[1] (analytic) = 1.5132780260467263160568603600697 y1[1] (numeric) = 1.5277500069657177633395334039929 absolute error = 0.0144719809189914472826730439232 relative error = 0.9563332494028158171379038819473 % h = 0.001 TOP MAIN SOLVE Loop memory used=1266.5MB, alloc=4.6MB, time=71.33 NO POLE NO POLE x[1] = 0.54 y2[1] (analytic) = 1.5141359916531131046772806829582 y2[1] (numeric) = 1.5278066603298452592506520625234 absolute error = 0.0136706686767321545733713795652 relative error = 0.902869276742223414254931011808 % h = 0.001 y1[1] (analytic) = 1.5141359916531131046772806829582 y1[1] (numeric) = 1.5286682780078848545436331309855 absolute error = 0.0145322863547717498663524480273 relative error = 0.95977418375119642057065271234329 % h = 0.001 TOP MAIN SOLVE Loop memory used=1270.3MB, alloc=4.6MB, time=71.55 NO POLE NO POLE x[1] = 0.541 y2[1] (analytic) = 1.514993443123551084849139265818 y2[1] (numeric) = 1.528756787680104497462514582326 absolute error = 0.013763344556553412613375316508 relative error = 0.90847551974724825611926657486368 % h = 0.001 y1[1] (analytic) = 1.514993443123551084849139265818 y1[1] (numeric) = 1.5295861445418901470055462235251 absolute error = 0.0145927014183390621564069577071 relative error = 0.96321878385509255959752064425705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1274.1MB, alloc=4.6MB, time=71.76 x[1] = 0.542 y2[1] (analytic) = 1.5158503796005888575887427581458 y2[1] (numeric) = 1.5297068121609671184994729127727 absolute error = 0.0138564325603782609107301546269 relative error = 0.91410291852348183733142827869176 % h = 0.001 y1[1] (analytic) = 1.5158503796005888575887427581458 y1[1] (numeric) = 1.5305036055821901447162608056719 absolute error = 0.0146532259816012871275180475261 relative error = 0.96666703909539297616444383412587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.543 y2[1] (analytic) = 1.51670680022729001726968912644 y2[1] (numeric) = 1.5306567337682731609565058613358 absolute error = 0.0139499335409831436868167348958 relative error = 0.91975149968950098623769889948629 % h = 0.001 y1[1] (analytic) = 1.51670680022729001726968912644 y1[1] (numeric) = 1.5314206601435117626391818272171 absolute error = 0.0147138599162217453694927007771 relative error = 0.97011893887577756398174129972653 % h = 0.001 TOP MAIN SOLVE Loop memory used=1277.9MB, alloc=4.6MB, time=71.98 NO POLE NO POLE x[1] = 0.544 y2[1] (analytic) = 1.5175627041472340085592018692383 y2[1] (numeric) = 1.5316065524978654306045740149833 absolute error = 0.014043848350631422045372145745 relative error = 0.92542128982558912335405295503624 % h = 0.001 y1[1] (analytic) = 1.5175627041472340085592018692383 y1[1] (numeric) = 1.5323373072408533614182744052998 absolute error = 0.0147746030936193528590725360615 relative error = 0.97357447262264295450958245707607 % h = 0.001 TOP MAIN SOLVE Loop memory used=1281.7MB, alloc=4.6MB, time=72.20 NO POLE NO POLE x[1] = 0.545 y2[1] (analytic) = 1.5184180905045169828386139815162 y2[1] (numeric) = 1.5325562683455895049868426928406 absolute error = 0.0141381778410725221482287113244 relative error = 0.93111231547398795725363033749397 % h = 0.001 y1[1] (analytic) = 1.5184180905045169828386139815162 y1[1] (numeric) = 1.5332535458894857819583235239022 absolute error = 0.014835455384968799119709542386 relative error = 0.97703362978502834679739120201083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1285.5MB, alloc=4.6MB, time=72.41 x[1] = 0.546 y2[1] (analytic) = 1.5192729584437526541071452480364 y2[1] (numeric) = 1.5335058813072937380127531680225 absolute error = 0.0142329228635410839056079199861 relative error = 0.93682460313914834156149173443818 % h = 0.001 y1[1] (analytic) = 1.5192729584437526541071452480364 y1[1] (numeric) = 1.5341693751049533798762457166144 absolute error = 0.014896416661200725769100468578 relative error = 0.98049639983454158021087369393499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.547 y2[1] (analytic) = 1.5201273071100731543681169619403 y2[1] (numeric) = 1.5344553913788292645499372078197 absolute error = 0.0143280842687561101818202458794 relative error = 0.94255817928798029691096620038395 % h = 0.001 y1[1] (analytic) = 1.5201273071100731543681169619403 y1[1] (numeric) = 1.5350847939030750598223883376344 absolute error = 0.0149574867930019054542713756941 relative error = 0.98396277226528544908449597960568 % h = 0.001 TOP MAIN SOLVE Loop memory used=1289.3MB, alloc=4.6MB, time=72.62 NO POLE NO POLE x[1] = 0.548 y2[1] (analytic) = 1.5209811356491298884967486824406 y2[1] (numeric) = 1.5354047985560500050139699829025 absolute error = 0.0144236629069201165172213004619 relative error = 0.94831307035010220169874678621515 % h = 0.001 y1[1] (analytic) = 1.5209811356491298884967486824406 y1[1] (numeric) = 1.5359998012999453096707520066181 absolute error = 0.0150186656508154211740033241775 relative error = 0.98743273659378425834135663341744 % h = 0.001 TOP MAIN SOLVE Loop memory used=1293.2MB, alloc=4.6MB, time=72.84 NO POLE NO POLE x[1] = 0.549 y2[1] (analytic) = 1.5218344432070943885886821638876 y2[1] (numeric) = 1.5363541028348126699559563976898 absolute error = 0.0145196596277182813672742338022 relative error = 0.95408930271808915545882320050416 % h = 0.001 y1[1] (analytic) = 1.5218344432070943885886821638876 y1[1] (numeric) = 1.5369143963119352345770717947131 absolute error = 0.0150799531048408459883896308255 relative error = 0.99090628235891061912649879289559 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1297.0MB, alloc=4.6MB, time=73.05 x[1] = 0.55 y2[1] (analytic) = 1.5226872289306591677883781077573 y2[1] (numeric) = 1.53730330421097676464794589552 absolute error = 0.0146160752803175968595677877627 relative error = 0.95988690274772051865836059089696 % h = 0.001 y1[1] (analytic) = 1.5226872289306591677883781077573 y1[1] (numeric) = 1.5378285779556935909036927019087 absolute error = 0.0151413490250344231153145941514 relative error = 0.99438339912181248350378543736445 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.551 y2[1] (analytic) = 1.5235394919670385735965319092362 y2[1] (numeric) = 1.5382524026804045936661707937568 absolute error = 0.0147129107133660200696388845206 relative error = 0.96570589675822663270174022736091 % h = 0.001 y1[1] (analytic) = 1.5235394919670385735965319092362 y1[1] (numeric) = 1.5387423452481478200101749597008 absolute error = 0.0152028532811092464136430504646 relative error = 0.99786407646584041727052159713568 % h = 0.001 TOP MAIN SOLVE Loop memory used=1300.8MB, alloc=4.6MB, time=73.27 NO POLE NO POLE x[1] = 0.552 y2[1] (analytic) = 1.5243912314639696406556550910571 y2[1] (numeric) = 1.5392013982389612654721032054634 absolute error = 0.0148101667749916248164481144063 relative error = 0.97154631103253472391217067520821 % h = 0.001 y1[1] (analytic) = 1.5243912314639696406556550910571 y1[1] (numeric) = 1.5396556972065050819085646780167 absolute error = 0.0152644657425354412529095869596 relative error = 1.0013483039964751099480474933877 % h = 0.001 TOP MAIN SOLVE Loop memory used=1304.6MB, alloc=4.6MB, time=73.49 NO POLE NO POLE x[1] = 0.553 y2[1] (analytic) = 1.525242446569712943012969639076 y2[1] (numeric) = 1.5401502908825146969913256057822 absolute error = 0.0149078443128017539783559667062 relative error = 0.97740817181751399524355650028094 % h = 0.001 y1[1] (analytic) = 1.525242446569712943012969639076 y1[1] (numeric) = 1.5405686328482532887822653413603 absolute error = 0.0153261862785403457692957022843 relative error = 1.0048360713412551210105474962303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1308.4MB, alloc=4.6MB, time=73.71 x[1] = 0.554 y2[1] (analytic) = 1.5260931364330534458597629767672 y2[1] (numeric) = 1.5410990806069356181902101026702 absolute error = 0.015005944173882172330447125903 relative error = 0.98329150532421990945867519118694 % h = 0.001 y1[1] (analytic) = 1.5260931364330534458597629767672 y1[1] (numeric) = 1.5414811511911621383674456462329 absolute error = 0.0153880147581086925076826694657 relative error = 1.0083273681497048614183213527037 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.555 y2[1] (analytic) = 1.5269433002033013567463518393519 y2[1] (numeric) = 1.5420477674080975766504014731549 absolute error = 0.015104467204796219904049633803 relative error = 0.98919633772813766749316135510756 % h = 0.001 y1[1] (analytic) = 1.5269433002033013567463518393519 y1[1] (numeric) = 1.5423932512532841471959191600503 absolute error = 0.0154499510499827904495673206984 relative error = 1.0118221840932628095257464779498 % h = 0.001 TOP MAIN SOLVE Loop memory used=1312.2MB, alloc=4.6MB, time=73.92 NO POLE NO POLE x[1] = 0.556 y2[1] (analytic) = 1.5277929370302929762718038326678 y2[1] (numeric) = 1.5429963512818769421410990277967 absolute error = 0.0152034142515839658692951951289 relative error = 0.99512269516942488570832988892897 % h = 0.001 y1[1] (analytic) = 1.5277929370302929762718038326678 y1[1] (numeric) = 1.5433049320529556836984312710203 absolute error = 0.0155119950226627074266274383525 relative error = 1.0153205088652099604381233220662 % h = 0.001 TOP MAIN SOLVE Loop memory used=1316.0MB, alloc=4.6MB, time=74.14 NO POLE NO POLE x[1] = 0.557 y2[1] (analytic) = 1.5286420460643915482475659871291 y2[1] (numeric) = 1.5439448322241529111891323675705 absolute error = 0.0153027861597613629415663804414 relative error = 1.0010706037531534757194862934921 % h = 0.001 y1[1] (analytic) = 1.5286420460643915482475659871291 y1[1] (numeric) = 1.5442161926087980011672888887604 absolute error = 0.0155741465444064529197229016313 relative error = 1.0188223321805985078955400218428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1319.9MB, alloc=4.6MB, time=74.35 x[1] = 0.558 y2[1] (analytic) = 1.5294906264564881093341501432183 y2[1] (numeric) = 1.5448932102308075116468260989106 absolute error = 0.0154025837743194023126759556923 relative error = 1.0070400895495507304700721351976 % h = 0.001 y1[1] (analytic) = 1.5294906264564881093341501432183 y1[1] (numeric) = 1.5451270319397182705772683468288 absolute error = 0.0156364054832301612431182036105 relative error = 1.0223276437761807577658178201293 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.559 y2[1] (analytic) = 1.530338677358002338150025531897 y2[1] (numeric) = 1.5458414852977256072576485742002 absolute error = 0.0155028079397232691076230423032 relative error = 1.0130311785942396202057764181812 % h = 0.001 y1[1] (analytic) = 1.530338677358002338150025531897 y1[1] (numeric) = 1.5460374490649106132637369508087 absolute error = 0.0156987717069082751137114189117 relative error = 1.0258364334103382722325051840653 % h = 0.001 TOP MAIN SOLVE Loop memory used=1323.7MB, alloc=4.6MB, time=74.56 NO POLE NO POLE x[1] = 0.56 y2[1] (analytic) = 1.531186197920883403851869441112 y2[1] (numeric) = 1.5467896574207949022196397265274 absolute error = 0.0156034594999114983677702854154 relative error = 1.0190438968884783019866088672715 % h = 0.001 y1[1] (analytic) = 1.531186197920883403851869441112 y1[1] (numeric) = 1.5469474430038571334569236091295 absolute error = 0.0157612450829737296050541680175 relative error = 1.0293486908630112437677762757203 % h = 0.001 TOP MAIN SOLVE Loop memory used=1327.5MB, alloc=4.6MB, time=74.78 NO POLE NO POLE x[1] = 0.561 y2[1] (analytic) = 1.5320331872976108141853273882178 y2[1] (numeric) = 1.5477377265959059457466130690795 absolute error = 0.0157045392982951315612856808617 relative error = 1.0250782703993988463588783940765 % h = 0.001 y1[1] (analytic) = 1.5320331872976108141853273882178 y1[1] (numeric) = 1.5478570127763289506712739784268 absolute error = 0.015823825478718136485946590209 relative error = 1.0328644059356280979839585213388 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1331.3MB, alloc=4.6MB, time=74.99 x[1] = 0.562 y2[1] (analytic) = 1.5328796446411952630054347476258 y2[1] (numeric) = 1.5486856928189521366271269310958 absolute error = 0.01580604817775687362169218347 relative error = 1.0311343250602451847930488860136 % h = 0.001 y1[1] (analytic) = 1.5328796446411952630054347476258 y1[1] (numeric) = 1.5487661574023872319488255509377 absolute error = 0.0158865127611919689433908033119 relative error = 1.0363835684510353244612645861202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.563 y2[1] (analytic) = 1.5337255691051794772658523133289 y2[1] (numeric) = 1.5496335560858297277812200038612 absolute error = 0.0159079869806502505153676905323 relative error = 1.0372120867706102814775544843073 % h = 0.001 y1[1] (analytic) = 1.5337255691051794772658523133289 y1[1] (numeric) = 1.5496748759023842239555381081985 absolute error = 0.0159493067972047466896857948696 relative error = 1.0399061682534275346531361862773 % h = 0.001 TOP MAIN SOLVE Loop memory used=1335.1MB, alloc=4.6MB, time=75.21 NO POLE NO POLE x[1] = 0.564 y2[1] (analytic) = 1.5345709598436390634760688071373 y2[1] (numeric) = 1.5505813163924378308149062717818 absolute error = 0.0160103565487987673388374646445 relative error = 1.043311581396672533042847266164 % h = 0.001 y1[1] (analytic) = 1.5345709598436390634760688071373 y1[1] (numeric) = 1.550583167296964284929514963159 absolute error = 0.0160122074533252214534461560217 relative error = 1.0434321952082777459744209548872 % h = 0.001 TOP MAIN SOLVE Loop memory used=1338.9MB, alloc=4.6MB, time=75.43 NO POLE NO POLE x[1] = 0.565 y2[1] (analytic) = 1.5354158160111833536257238754924 y2[1] (numeric) = 1.5515289737346784205724244051543 absolute error = 0.0161131577234950669467005296619 relative error = 1.0494328347714313997742212876156 % h = 0.001 y1[1] (analytic) = 1.5354158160111833536257238754924 y1[1] (numeric) = 1.5514910306070649164800504117494 absolute error = 0.016075214595881562854326536257 relative error = 1.046961639202267891181399118204 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1342.8MB, alloc=4.6MB, time=75.64 x[1] = 0.566 y2[1] (analytic) = 1.5362601367629562505752056506075 y2[1] (numeric) = 1.5524765281084563396862366928128 absolute error = 0.0162163913455000891110310422053 relative error = 1.0555758726949422718563078461661 % h = 0.001 y1[1] (analytic) = 1.5362601367629562505752056506075 y1[1] (numeric) = 1.5523984648539177952364388149361 absolute error = 0.0161383280909615446612331643286 relative error = 1.0504944901432195521564541291707 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.567 y2[1] (analytic) = 1.5371039212546370729116774854067 y2[1] (numeric) = 1.5534239795096793031247725944158 absolute error = 0.0163200582550422302130951090091 relative error = 1.0617407209345505741765671603217 % h = 0.001 y1[1] (analytic) = 1.5371039212546370729116774854067 y1[1] (numeric) = 1.5533054690590498043454807333787 absolute error = 0.016201547804412731433803247972 relative error = 1.0540307379600249172139407394751 % h = 0.001 TOP MAIN SOLVE Loop memory used=1346.6MB, alloc=4.6MB, time=75.86 NO POLE NO POLE x[1] = 0.568 y2[1] (analytic) = 1.5379471686424413992696890063077 y2[1] (numeric) = 1.5543713279342579027379119937187 absolute error = 0.016424159291816503468222987411 relative error = 1.0679274052251251131996110107614 % h = 0.001 y1[1] (analytic) = 1.5379471686424413992696890063077 y1[1] (numeric) = 1.5542120422442840648166215389524 absolute error = 0.0162648736018426655469325326447 relative error = 1.0575703726025779610475453635872 % h = 0.001 TOP MAIN SOLVE Loop memory used=1350.4MB, alloc=4.6MB, time=76.07 NO POLE NO POLE x[1] = 0.569 y2[1] (analytic) = 1.5387898780831219121155271633056 y2[1] (numeric) = 1.555318573378105611800203235768 absolute error = 0.0165286952949836996846760724624 relative error = 1.0741359512692906694087788244863 % h = 0.001 y1[1] (analytic) = 1.5387898780831219121155271633056 y1[1] (numeric) = 1.5551181834317409667136579306305 absolute error = 0.0163283053486190545981307673249 relative error = 1.0611133840417058464431570920355 % h = 0.001 TOP MAIN SOLVE Loop memory used=1354.2MB, alloc=4.6MB, time=76.29 NO POLE NO POLE x[1] = 0.57 y2[1] (analytic) = 1.5396320487339692409944634930788 y2[1] (numeric) = 1.5562657158371387895518110325444 absolute error = 0.0166336671031695485573475394656 relative error = 1.0803663847376598387960557875639 % h = 0.001 y1[1] (analytic) = 1.5396320487339692409944634930788 y1[1] (numeric) = 1.5560238916438392001919477865273 absolute error = 0.0163918429098699591974842934485 relative error = 1.0646597622691005468849734380449 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.571 y2[1] (analytic) = 1.540473679752812805240054347939 y2[1] (numeric) = 1.5572127553072766857371893231844 absolute error = 0.0167390755544638804971349752454 relative error = 1.0866187312690641268661654286376 % h = 0.001 y1[1] (analytic) = 1.540473679752812805240054347939 y1[1] (numeric) = 1.556929165903296786380058789287 absolute error = 0.016455486150483981140004441348 relative error = 1.0682094972972506891862529449616 % h = 0.001 TOP MAIN SOLVE Loop memory used=1358.0MB, alloc=4.6MB, time=76.50 NO POLE NO POLE x[1] = 0.572 y2[1] (analytic) = 1.5413147702980216561446513813949 y2[1] (numeric) = 1.5581596917844414451414741765113 absolute error = 0.0168449214864197889968227951164 relative error = 1.092893016470784298605490307993 % h = 0.001 y1[1] (analytic) = 1.5413147702980216561446513813949 y1[1] (numeric) = 1.5578340052331321081047912684634 absolute error = 0.0165192349351104519601398870685 relative error = 1.0717625791593736152797972321376 % h = 0.001 TOP MAIN SOLVE Loop memory used=1361.8MB, alloc=4.6MB, time=76.72 NO POLE NO POLE x[1] = 0.573 y2[1] (analytic) = 1.5421553195285053185902801198912 y2[1] (numeric) = 1.5591065252645581121245918252192 absolute error = 0.016951205736052793534311705328 relative error = 1.0991892659187799878513725642955 % h = 0.001 y1[1] (analytic) = 1.5421553195285053185902801198912 y1[1] (numeric) = 1.5587384086566649404585107110759 absolute error = 0.0165830891281596218682305911847 relative error = 1.0753189979093476623068980057921 % h = 0.001 TOP MAIN SOLVE Loop memory used=1365.6MB, alloc=4.6MB, time=76.94 NO POLE NO POLE x[1] = 0.574 y2[1] (analytic) = 1.5429953266037146321390449899122 y2[1] (numeric) = 1.5600532557435546351530769226651 absolute error = 0.0170579291398400030140319327529 relative error = 1.105507505157918569482320702977 % h = 0.001 y1[1] (analytic) = 1.5429953266037146321390449899122 y1[1] (numeric) = 1.559642375197517481207725400142 absolute error = 0.0166470485938028490686804102298 relative error = 1.0788787436216446601471200993911 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.575 y2[1] (analytic) = 1.5438347906836425915822197101162 y2[1] (numeric) = 1.5609998832173618713295961148475 absolute error = 0.0171650925337192797473764047313 relative error = 1.1118477597022032978346997490854 % h = 0.001 y1[1] (analytic) = 1.5438347906836425915822197101162 y1[1] (numeric) = 1.560545903879615381041844650681 absolute error = 0.0167111131959727894596249405648 relative error = 1.0824418063912626455349098247684 % h = 0.001 TOP MAIN SOLVE Loop memory used=1369.5MB, alloc=4.6MB, time=77.15 NO POLE NO POLE x[1] = 0.576 y2[1] (analytic) = 1.5446737109288251869471824994803 y2[1] (numeric) = 1.5619464076819135909201720217719 absolute error = 0.0172726967530884039729895222916 relative error = 1.1182100550350007147366083280543 % h = 0.001 y1[1] (analytic) = 1.5446737109288251869471824994803 y1[1] (numeric) = 1.5614489937271887736610531234562 absolute error = 0.0167752827983635867138706239759 relative error = 1.0860081763336587919126189007357 % h = 0.001 TOP MAIN SOLVE Loop memory used=1373.3MB, alloc=4.6MB, time=77.37 NO POLE NO POLE x[1] = 0.577 y2[1] (analytic) = 1.5455120865003422429613560945909 y2[1] (numeric) = 1.5628928291331464818791027240366 absolute error = 0.0173807426328042389177466294457 relative error = 1.1245944166092673305348479779424 % h = 0.001 y1[1] (analytic) = 1.5455120865003422429613560945909 y1[1] (numeric) = 1.5623516437647733057022367085719 absolute error = 0.016839557264431062740880613981 relative error = 1.0895778435846825541731180687935 % h = 0.001 TOP MAIN SOLVE Loop memory used=1377.1MB, alloc=4.6MB, time=77.59 NO POLE NO POLE x[1] = 0.578 y2[1] (analytic) = 1.546349916559818257972313112208 y2[1] (numeric) = 1.563839147567000154371571852106 absolute error = 0.017489231007181896399258739898 relative error = 1.1310008698477755814761666354817 % h = 0.001 y1[1] (analytic) = 1.546349916559818257972313112208 y1[1] (numeric) = 1.5632538530172111665018954839701 absolute error = 0.0169039364573929085295823717621 relative error = 1.0931507983005090274487412947502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.579 y2[1] (analytic) = 1.5471872002694232423232078370701 y2[1] (numeric) = 1.56478536297941714529394437738 absolute error = 0.0175981627099939029707365403099 relative error = 1.1374294401433390667893093775219 % h = 0.001 y1[1] (analytic) = 1.5471872002694232423232078370701 y1[1] (numeric) = 1.5641556205096521176949792678787 absolute error = 0.0169684202402288753717714308086 relative error = 1.0967270306575725191068512779042 % h = 0.001 TOP MAIN SOLVE Loop memory used=1380.9MB, alloc=4.6MB, time=77.80 NO POLE NO POLE x[1] = 0.58 y2[1] (analytic) = 1.5480239367918735561826960595765 y2[1] (numeric) = 1.5657314753663429227917432058143 absolute error = 0.0177075385744693666090471462378 relative error = 1.1438801528590370687998347441693 % h = 0.001 y1[1] (analytic) = 1.5480239367918735561826960595765 y1[1] (numeric) = 1.5650569452675545226485812993478 absolute error = 0.0170330084756809664658852397713 relative error = 1.1003065308525003331158499343393 % h = 0.001 TOP MAIN SOLVE Loop memory used=1384.7MB, alloc=4.6MB, time=78.02 NO POLE NO POLE x[1] = 0.581 y2[1] (analytic) = 1.548860125290432746828505133497 y2[1] (numeric) = 1.5666774847237258907753016764967 absolute error = 0.0178173594332931439467965429997 relative error = 1.1503530333284383593951539258025 % h = 0.001 y1[1] (analytic) = 1.548860125290432746828505133497 y1[1] (numeric) = 1.5659578263166863757294255971736 absolute error = 0.0170977010262536289009204636766 relative error = 1.1038892891020467659489736740247 % h = 0.001 TOP MAIN SOLVE Loop memory used=1388.5MB, alloc=4.6MB, time=78.24 NO POLE NO POLE x[1] = 0.582 y2[1] (analytic) = 1.5496957649289123853838169702094 y2[1] (numeric) = 1.5676233910475173934330870692417 absolute error = 0.0179276261186050080492700990323 relative error = 1.156848106855824296142822372581 % h = 0.001 y1[1] (analytic) = 1.5496957649289123853838169702094 y1[1] (numeric) = 1.5668582626831263314040835647531 absolute error = 0.0171624977542139460202665945437 relative error = 1.1074752956430273131967127398645 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.583 y2[1] (analytic) = 1.5505308548716729030056272331506 y2[1] (numeric) = 1.5685691943336717197426902269262 absolute error = 0.0180383394619988167370629937756 relative error = 1.1633653987164112113507585930839 % h = 0.001 y1[1] (analytic) = 1.5505308548716729030056272331506 y1[1] (numeric) = 1.5677582533932647331708554267333 absolute error = 0.0172273985215918301652281935827 relative error = 1.1110645407322530860621767064788 % h = 0.001 TOP MAIN SOLVE Loop memory used=1392.3MB, alloc=4.6MB, time=78.45 NO POLE NO POLE x[1] = 0.584 y2[1] (analytic) = 1.5513653942836244265242445441924 y2[1] (numeric) = 1.569514894578146107979476399957 absolute error = 0.0181495002945216814552318557646 relative error = 1.1699049341565720973437826616029 % h = 0.001 y1[1] (analytic) = 1.5513653942836244265242445441924 y1[1] (numeric) = 1.5686577974738046423222521027183 absolute error = 0.0172924031901802157980075585259 relative error = 1.1146570146464654369171945326643 % h = 0.001 TOP MAIN SOLVE Loop memory used=1396.2MB, alloc=4.6MB, time=78.67 NO POLE NO POLE x[1] = 0.585 y2[1] (analytic) = 1.5521993823302276135330940625129 y2[1] (numeric) = 1.5704604917769007502228924219316 absolute error = 0.0182611094466731366897983594187 relative error = 1.1764667383940575912166568670598 % h = 0.001 y1[1] (analytic) = 1.5521993823302276135330940625129 y1[1] (numeric) = 1.5695568939517628665370131437787 absolute error = 0.0173575116215352530039190812658 relative error = 1.1182527076822707931003874097023 % h = 0.001 TOP MAIN SOLVE Loop memory used=1400.0MB, alloc=4.6MB, time=78.89 NO POLE NO POLE x[1] = 0.586 y2[1] (analytic) = 1.553032818177494486927990346228 y2[1] (numeric) = 1.5714059859258987968604253272308 absolute error = 0.0183731677484043099324349810028 relative error = 1.1830508366182162623096726286217 % h = 0.001 y1[1] (analytic) = 1.553032818177494486927990346228 y1[1] (numeric) = 1.570455541854470988300596379065 absolute error = 0.017422723676976501372606032837 relative error = 1.1218516101560756981418861322195 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.587 y2[1] (analytic) = 1.5538657009919892688950449575815 y2[1] (numeric) = 1.5723513770211063610892075229651 absolute error = 0.0184856760291170921941625653836 relative error = 1.1896572539902142056387608935 % h = 0.001 y1[1] (analytic) = 1.5538657009919892688950449575815 y1[1] (numeric) = 1.5713537402095763931530749424655 absolute error = 0.017488039217587124258029984884 relative error = 1.1254537124040220596027819231483 % h = 0.001 TOP MAIN SOLVE Loop memory used=1403.8MB, alloc=4.6MB, time=79.10 NO POLE NO POLE x[1] = 0.588 y2[1] (analytic) = 1.5546980299408292143463748238537 y2[1] (numeric) = 1.5732966650584925234152636293829 absolute error = 0.0185986351176633090688888055292 relative error = 1.1962860156432539444981073440136 % h = 0.001 y1[1] (analytic) = 1.5546980299408292143463748238537 y1[1] (numeric) = 1.5722514880450432977633773729664 absolute error = 0.0175534581042140834170025491127 relative error = 1.1290590047819226027208006537208 % h = 0.001 TOP MAIN SOLVE Loop memory used=1407.6MB, alloc=4.6MB, time=79.32 NO POLE NO POLE x[1] = 0.589 y2[1] (analytic) = 1.5555298041916854438027779183523 y2[1] (numeric) = 1.5742418500340293361503941045413 absolute error = 0.018712045842343892347616186189 relative error = 1.202937146682792645439328497533 % h = 0.001 y1[1] (analytic) = 1.5555298041916854438027779183523 y1[1] (numeric) = 1.5731487843891537778288065071702 absolute error = 0.0176189801974683340260285888179 relative error = 1.1326674776651965290570752956979 % h = 0.001 TOP MAIN SOLVE Loop memory used=1411.4MB, alloc=4.6MB, time=79.54 NO POLE NO POLE x[1] = 0.59 y2[1] (analytic) = 1.5563610229127837757225433788758 y2[1] (numeric) = 1.575186931943691827906690770739 absolute error = 0.0188259090309080521841473918632 relative error = 1.2096106721867596488174098122901 % h = 0.001 y1[1] (analytic) = 1.5563610229127837757225433788758 y1[1] (numeric) = 1.5740456282705087957987729083044 absolute error = 0.0176846053577250200762295294286 relative error = 1.1362791214488053793422603099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.591 y2[1] (analytic) = 1.5571916852729055582755637349123 y2[1] (numeric) = 1.5761319107834580080886793619128 absolute error = 0.0189402255105524498131156270005 relative error = 1.2163066172057733180798218413439 % h = 0.001 y1[1] (analytic) = 1.5571916852729055582755637349123 y1[1] (numeric) = 1.5749420187180292284216786030103 absolute error = 0.017750333445123670146114868098 relative error = 1.1398939265471890997235845935083 % h = 0.001 TOP MAIN SOLVE Loop memory used=1415.2MB, alloc=4.6MB, time=79.76 NO POLE NO POLE x[1] = 0.592 y2[1] (analytic) = 1.5580217904413885005619174695279 y2[1] (numeric) = 1.5770767865493088713830842129075 absolute error = 0.0190549961079203708211667433796 relative error = 1.2230250067633572109615149391972 % h = 0.001 y1[1] (analytic) = 1.5580217904413885005619174695279 y1[1] (numeric) = 1.5758379547609568941138869252387 absolute error = 0.0178161643195683935519694557108 relative error = 1.1435118833942023106177766619092 % h = 0.001 TOP MAIN SOLVE Loop memory used=1419.0MB, alloc=4.6MB, time=79.97 NO POLE NO POLE x[1] = 0.593 y2[1] (analytic) = 1.5588513375881275032740906974331 y2[1] (numeric) = 1.5780215592372284022462102132423 absolute error = 0.0191702216491008989721195158092 relative error = 1.22976586585615557573484665211 % h = 0.001 y1[1] (analytic) = 1.5588513375881275032740906974331 y1[1] (numeric) = 1.5767334354288555801497142956964 absolute error = 0.0178820978407280768756235982633 relative error = 1.1471329824430507773781170088075 % h = 0.001 TOP MAIN SOLVE Loop memory used=1422.9MB, alloc=4.6MB, time=80.19 NO POLE NO POLE x[1] = 0.594 y2[1] (analytic) = 1.559680325883575488802007297074 y2[1] (numeric) = 1.5789662288432035793889371497158 absolute error = 0.0192859029596280905869298526418 relative error = 1.2365292194541481756499183505494 % h = 0.001 y1[1] (analytic) = 1.559680325883575488802007297074 y1[1] (numeric) = 1.5776284597516120696713797954859 absolute error = 0.0179481338680365808693724984119 relative error = 1.1507572141662280819871781530661 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.595 y2[1] (analytic) = 1.5605087544987442307800373917875 y2[1] (numeric) = 1.5799107953632243802593215639143 absolute error = 0.0194020408644801494792841721268 relative error = 1.243315092500864444687288527031 % h = 0.001 y1[1] (analytic) = 1.5605087544987442307800373917875 y1[1] (numeric) = 1.5785230267594371685178484238574 absolute error = 0.0180142722606929377378110320699 relative error = 1.154384569055452494990102821755 % h = 0.001 TOP MAIN SOLVE Loop memory used=1426.7MB, alloc=4.6MB, time=80.40 NO POLE NO POLE x[1] = 0.596 y2[1] (analytic) = 1.5613366226052051830751546330814 y2[1] (numeric) = 1.5808552587932837855228012524182 absolute error = 0.0195186361880786024476466193368 relative error = 1.2501235099135969777315891248529 % h = 0.001 y1[1] (analytic) = 1.5613366226052051830751546330814 y1[1] (numeric) = 1.5794171354828667318715039623517 absolute error = 0.0180805128776615487963493292703 relative error = 1.1580150376216040468865451167425 % h = 0.001 TOP MAIN SOLVE Loop memory used=1430.5MB, alloc=4.6MB, time=80.61 NO POLE NO POLE x[1] = 0.597 y2[1] (analytic) = 1.5621639293750903082154132979511 y2[1] (numeric) = 1.5817996191293777835399975392337 absolute error = 0.0196356897542874753245842412826 relative error = 1.2569544965836143582611979241156 % h = 0.001 y1[1] (analytic) = 1.5621639293750903082154132979511 y1[1] (numeric) = 1.5803107849527626907215874010518 absolute error = 0.0181468555776723825061741031007 relative error = 1.1616486103946617982026584460976 % h = 0.001 TOP MAIN SOLVE Loop memory used=1434.3MB, alloc=4.6MB, time=80.83 NO POLE NO POLE x[1] = 0.598 y2[1] (analytic) = 1.5629906739810929052579167718239 y2[1] (numeric) = 1.582743876367505374842110451718 absolute error = 0.0197532023864124695841936798941 relative error = 1.2638080773763733266358140350173 % h = 0.001 y1[1] (analytic) = 1.5629906739810929052579167718239 y1[1] (numeric) = 1.5812039742003140781433369171813 absolute error = 0.0182133002192211728854201453574 relative error = 1.1652852779236413074677575507723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.599 y2[1] (analytic) = 1.5638168555964684370954495492333 y2[1] (numeric) = 1.5836880305036685766039019330087 absolute error = 0.0198711749072001395084523837754 relative error = 1.2706842771317302920505445797008 % h = 0.001 y1[1] (analytic) = 1.5638168555964684370954495492333 y1[1] (numeric) = 1.5820967022570380553917654318872 absolute error = 0.0182798466605696182963158826539 relative error = 1.1689250307765322963235101996946 % h = 0.001 TOP MAIN SOLVE Loop memory used=1438.1MB, alloc=4.6MB, time=81.04 NO POLE NO POLE x[1] = 0.6 y2[1] (analytic) = 1.5646424733950353572009454456587 y2[1] (numeric) = 1.584632081533872427114262225719 absolute error = 0.0199896081388370699133167800603 relative error = 1.2775831206641521912119383317574 % h = 0.001 y1[1] (analytic) = 1.5646424733950353572009454456587 y1[1] (numeric) = 1.5829889681547809378090118077292 absolute error = 0.0183464947597455806080663620705 relative error = 1.1725678595402365109967271417434 % h = 0.001 TOP MAIN SOLVE Loop memory used=1441.9MB, alloc=4.6MB, time=81.26 NO POLE NO POLE x[1] = 0.601 y2[1] (analytic) = 1.5654675265511759358089652761314 y2[1] (numeric) = 1.5855760294541249902443545634141 absolute error = 0.0201085029029490544353892872827 relative error = 1.2845046327629266967782960755595 % h = 0.001 y1[1] (analytic) = 1.5654675265511759358089652761314 y1[1] (numeric) = 1.5838807709257192205442017871582 absolute error = 0.0184132443745432847352365110268 relative error = 1.1762137548205057793700167675052 % h = 0.001 TOP MAIN SOLVE Loop memory used=1445.7MB, alloc=4.6MB, time=81.48 NO POLE NO POLE x[1] = 0.602 y2[1] (analytic) = 1.5662920142398370855333578191989 y2[1] (numeric) = 1.5865198742604373599133333081449 absolute error = 0.020227860020600274379975488946 relative error = 1.2914488381923717785935473983976 % h = 0.001 y1[1] (analytic) = 1.5662920142398370855333578191989 y1[1] (numeric) = 1.5847721096023606040847548111131 absolute error = 0.0184800953625235185513969919142 relative error = 1.1798627072418802628877537255715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.603 y2[1] (analytic) = 1.5671159356365311864202784486542 y2[1] (numeric) = 1.5874636159488236645516306740785 absolute error = 0.0203476803122924781313522254243 relative error = 1.2984157616920446207310091905862 % h = 0.001 y1[1] (analytic) = 1.5671159356365311864202784486542 y1[1] (numeric) = 1.5856629832175450195980728967887 absolute error = 0.0185470475810138331777944481345 relative error = 1.1835147074476269025379785338514 % h = 0.001 TOP MAIN SOLVE Loop memory used=1449.6MB, alloc=4.6MB, time=81.69 NO POLE NO POLE x[1] = 0.604 y2[1] (analytic) = 1.5679392899173369104357403800814 y2[1] (numeric) = 1.5884072545153010715618071790374 absolute error = 0.020467964597964161126066798956 relative error = 1.3054054279769498973504319580787 % h = 0.001 y1[1] (analytic) = 1.5679392899173369104357403800814 y1[1] (numeric) = 1.5865533908044456540825477946376 absolute error = 0.0186141008871087436468074145562 relative error = 1.1871697460996780581539981025194 % h = 0.001 TOP MAIN SOLVE Loop memory used=1453.4MB, alloc=4.6MB, time=81.91 NO POLE NO POLE x[1] = 0.605 y2[1] (analytic) = 1.5687620762589000453868740447335 y2[1] (numeric) = 1.5893507899558897917769609675324 absolute error = 0.0205887136969897463900869227989 relative error = 1.3124178617377474103588958065802 % h = 0.001 y1[1] (analytic) = 1.5687620762589000453868740447335 y1[1] (numeric) = 1.5874433313965699753268226867543 absolute error = 0.0186812551376699299399486420208 relative error = 1.1908278138785703402825951176989 % h = 0.001 TOP MAIN SOLVE Loop memory used=1457.2MB, alloc=4.6MB, time=82.13 NO POLE NO POLE x[1] = 0.606 y2[1] (analytic) = 1.569584293838434318276070669554 y2[1] (numeric) = 1.5902942222666130839166911506567 absolute error = 0.0207099284281787656406204811027 relative error = 1.319453087640959091853338295273 % h = 0.001 y1[1] (analytic) = 1.569584293838434318276070669554 y1[1] (numeric) = 1.5883328040277607566762447319635 absolute error = 0.0187485101893264384001740624095 relative error = 1.1944889014833836338688774994943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.607 y2[1] (analytic) = 1.5704059418337222180871867092646 y2[1] (numeric) = 1.591237551443497259040610309992 absolute error = 0.0208316096097750409534236007274 relative error = 1.3265111303291753743097809442783 % h = 0.001 y1[1] (analytic) = 1.5704059418337222180871867092646 y1[1] (numeric) = 1.5892218077321971016054448071845 absolute error = 0.0188158658984748835182580979199 relative error = 1.1981529996316803130109077198952 % h = 0.001 TOP MAIN SOLVE Loop memory used=1461.0MB, alloc=4.6MB, time=82.35 NO POLE NO POLE x[1] = 0.608 y2[1] (analytic) = 1.5712270194231158180029863443854 y2[1] (numeric) = 1.5921807774825716849994013144714 absolute error = 0.020953758059455866996414970086 relative error = 1.3335920144212609314716696759937 % h = 0.001 y1[1] (analytic) = 1.5712270194231158180029863443854 y1[1] (numeric) = 1.5901103415443954680959808399793 absolute error = 0.0188833221212796500929944955939 relative error = 1.2018200990594446460403457195448 % h = 0.001 TOP MAIN SOLVE Loop memory used=1464.8MB, alloc=4.6MB, time=82.56 NO POLE NO POLE x[1] = 0.609 y2[1] (analytic) = 1.5720475257855375970529998278124 y2[1] (numeric) = 1.5931239003798687908834136009359 absolute error = 0.0210763745943311938304137731235 relative error = 1.3406957645125597928771565424948 % h = 0.001 y1[1] (analytic) = 1.5720475257855375970529998278124 y1[1] (numeric) = 1.5909984044992106928179811736084 absolute error = 0.018950878713673095764981345796 relative error = 1.205490190521022390188418572588 % h = 0.001 TOP MAIN SOLVE Loop memory used=1468.6MB, alloc=4.6MB, time=82.78 NO POLE NO POLE x[1] = 0.61 y2[1] (analytic) = 1.5728674601004812611909760321627 y2[1] (numeric) = 1.5940669201314240714687940709265 absolute error = 0.0211994600309428102778180387638 relative error = 1.3478224051750998349526254069512 % h = 0.001 y1[1] (analytic) = 1.5728674601004812611909760321627 y1[1] (numeric) = 1.5918859956318370151147244534146 absolute error = 0.0190185355313557539237484212519 relative error = 1.2091632647890605750995949887935 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.611 y2[1] (analytic) = 1.5736868215480125638011081205036 y2[1] (numeric) = 1.5950098367332760916611477580572 absolute error = 0.0213230151852635278600396375536 relative error = 1.3549719609577966515873024754224 % h = 0.001 y1[1] (analytic) = 1.5736868215480125638011081205036 y1[1] (numeric) = 1.5927731139778091007890925719391 absolute error = 0.0190862924297965369879844514355 relative error = 1.2128393126544474744583932863029 % h = 0.001 TOP MAIN SOLVE Loop memory used=1472.5MB, alloc=4.6MB, time=83.00 NO POLE NO POLE x[1] = 0.612 y2[1] (analytic) = 1.5745056093087701256322118343075 y2[1] (numeric) = 1.5959526501814664909367234221266 absolute error = 0.0214470408726963653045115878191 relative error = 1.3621444563866568070913933885442 % h = 0.001 y1[1] (analytic) = 1.5745056093087701256322118343075 y1[1] (numeric) = 1.5936597585730030656908332598345 absolute error = 0.019154149264232940058621425527 relative error = 1.2165183249262527649977876890496 % h = 0.001 TOP MAIN SOLVE Loop memory used=1476.3MB, alloc=4.6MB, time=83.22 NO POLE NO POLE x[1] = 0.613 y2[1] (analytic) = 1.5753238225639662541590364645238 y2[1] (numeric) = 1.596895360472039987781119227943 absolute error = 0.0215715379080737336220827634192 relative error = 1.369339915964980474427851653225 % h = 0.001 y1[1] (analytic) = 1.5753238225639662541590364645238 y1[1] (numeric) = 1.5945459284536374991035689603858 absolute error = 0.019222105889671244944532495862 relative error = 1.2202002924316678721606997731582 % h = 0.001 TOP MAIN SOLVE Loop memory used=1480.1MB, alloc=4.6MB, time=83.44 NO POLE NO POLE x[1] = 0.614 y2[1] (analytic) = 1.576141460495387762369889144524 y2[1] (numeric) = 1.5978379676010443841255036686589 absolute error = 0.0216965071056566217556145241349 relative error = 1.3765583641735634615956081981205 % h = 0.001 y1[1] (analytic) = 1.576141460495387762369889144524 y1[1] (numeric) = 1.5954316226562744869304886772786 absolute error = 0.0192901621608867245605995327546 relative error = 1.2238852060159465016890696789536 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.615 y2[1] (analytic) = 1.5769585222853967869797536773647 y2[1] (numeric) = 1.5987804715645305697803468952379 absolute error = 0.0218219492791337828005932178732 relative error = 1.3837998254708986290298784499808 % h = 0.001 y1[1] (analytic) = 1.5769585222853967869797536773647 y1[1] (numeric) = 1.5963168402178206346776595381644 absolute error = 0.0193583179324238476979058607997 relative error = 1.2275730565423453564179953909816 % h = 0.001 TOP MAIN SOLVE Loop memory used=1483.9MB, alloc=4.6MB, time=83.66 NO POLE NO POLE x[1] = 0.616 y2[1] (analytic) = 1.5777750071169316060680856843173 y2[1] (numeric) = 1.5997228723585525268666576155088 absolute error = 0.0219478652416209207985719311915 relative error = 1.3910643242933767008730112302413 % h = 0.001 y1[1] (analytic) = 1.5777750071169316060680856843173 y1[1] (numeric) = 1.5972015801755280902338948705654 absolute error = 0.0194265730585964841658091862481 relative error = 1.2312638348920650375554080395814 % h = 0.001 TOP MAIN SOLVE Loop memory used=1487.7MB, alloc=4.6MB, time=83.87 NO POLE NO POLE x[1] = 0.617 y2[1] (analytic) = 1.5785909141735074561404664369381 y2[1] (numeric) = 1.6006651699791673342447207281001 absolute error = 0.022074255805659878104254291162 relative error = 1.3983518850554864729572526429449 % h = 0.001 y1[1] (analytic) = 1.5785909141735074561404664369381 y1[1] (numeric) = 1.5980858415669955664461156417392 absolute error = 0.0194949273934881103056492048011 relative error = 1.2349575319641911297307168650077 % h = 0.001 TOP MAIN SOLVE Loop memory used=1491.5MB, alloc=4.6MB, time=84.09 NO POLE NO POLE x[1] = 0.618 y2[1] (analytic) = 1.579406242639217348613298311092 y2[1] (numeric) = 1.6016073644224351719403308583882 absolute error = 0.0222011217832178233270325472962 relative error = 1.4056625321500144203287676488509 % h = 0.001 y1[1] (analytic) = 1.579406242639217348613298311092 y1[1] (numeric) = 1.5989696234301693634891421702813 absolute error = 0.0195633807909520148758438591893 relative error = 1.2386541386756354690988092795451 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.619 y2[1] (analytic) = 1.5802209916987328857207253783037 y2[1] (numeric) = 1.6025494556844193255685169654429 absolute error = 0.0223284639856864398477915871392 relative error = 1.4129962899482437071302918808899 % h = 0.001 y1[1] (analytic) = 1.5802209916987328857207253783037 y1[1] (numeric) = 1.5998529248033443910288530744861 absolute error = 0.0196319331046115053081276961824 relative error = 1.2423536459610775937887294347116 % h = 0.001 TOP MAIN SOLVE Loop memory used=1495.3MB, alloc=4.6MB, time=84.30 NO POLE NO POLE x[1] = 0.62 y2[1] (analytic) = 1.5810351605373050758429632275822 y2[1] (numeric) = 1.6034914437611861907547531908035 absolute error = 0.0224562832238811149117899632213 relative error = 1.4203531828001526016478761390798 % h = 0.001 y1[1] (analytic) = 1.5810351605373050758429632275822 y1[1] (numeric) = 1.6007357447251651901776484808133 absolute error = 0.0197005841878601143346852532311 relative error = 1.2460560447729063759892829198947 % h = 0.001 TOP MAIN SOLVE Loop memory used=1499.2MB, alloc=4.6MB, time=84.52 NO POLE NO POLE x[1] = 0.621 y2[1] (analytic) = 1.581848748340765148255222689459 y2[1] (numeric) = 1.6044333286488052775536511217797 absolute error = 0.0225845803080401292984284323207 relative error = 1.4277332350346122993153355966089 % h = 0.001 y1[1] (analytic) = 1.581848748340765148255222689459 y1[1] (numeric) = 1.6016180822346269552411545752142 absolute error = 0.0197693338938618069859318857552 relative error = 1.2497613260811618349667257542321 % h = 0.001 TOP MAIN SOLVE Loop memory used=1503.0MB, alloc=4.6MB, time=84.73 NO POLE NO POLE x[1] = 0.622 y2[1] (analytic) = 1.5826617542955253672964127133811 y2[1] (numeric) = 1.6053751103433492148651286438311 absolute error = 0.02271335604782384756871593045 relative error = 1.4351364709595841564582247430527 % h = 0.001 y1[1] (analytic) = 1.5826617542955253672964127133811 y1[1] (numeric) = 1.6024999363710765552551066405647 absolute error = 0.0198381820755511879586939271836 relative error = 1.2534694808734771303125927556168 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.623 y2[1] (analytic) = 1.583474177588579845956808229827 y2[1] (numeric) = 1.6063167888408937548480505584507 absolute error = 0.0228426112523139088912423286237 relative error = 1.4425629148623163375474271766996 % h = 0.001 y1[1] (analytic) = 1.583474177588579845956808229827 y1[1] (numeric) = 1.6033813061742135553113477850275 absolute error = 0.0199071285856337093545395552005 relative error = 1.2571805001550207347226037467037 % h = 0.001 TOP MAIN SOLVE Loop memory used=1506.8MB, alloc=4.6MB, time=84.95 NO POLE NO POLE x[1] = 0.624 y2[1] (analytic) = 1.584286017407505358883869409543 y2[1] (numeric) = 1.6072583641375177773313361448474 absolute error = 0.0229723467300124184474667353044 relative error = 1.4500125910095398787207762297009 % h = 0.001 y1[1] (analytic) = 1.584286017407505358883869409543 y1[1] (numeric) = 1.6042621906840912376718806288242 absolute error = 0.0199761732765858787880112192812 relative error = 1.2608943749484387856104559575665 % h = 0.001 TOP MAIN SOLVE Loop memory used=1510.6MB, alloc=4.6MB, time=85.17 NO POLE NO POLE x[1] = 0.625 y2[1] (analytic) = 1.5850972729404621548053993141501 y2[1] (numeric) = 1.6081998362293032942225288456047 absolute error = 0.0231025632888411394171295314546 relative error = 1.4574855236476641703195077618197 % h = 0.001 y1[1] (analytic) = 1.5850972729404621548053993141501 y1[1] (numeric) = 1.6051425889411176226699092806412 absolute error = 0.0200453160006554678645099664911 relative error = 1.2646110962937976148631674749195 % h = 0.001 TOP MAIN SOLVE Loop memory used=1514.4MB, alloc=4.6MB, time=85.39 NO POLE NO POLE x[1] = 0.626 y2[1] (analytic) = 1.5859079433761947683692275150305 y2[1] (numeric) = 1.6091412051123354539138232583723 absolute error = 0.0232332617361406855445957433418 relative error = 1.4649817370029718611747899879433 % h = 0.001 y1[1] (analytic) = 1.5859079433761947683692275150305 y1[1] (numeric) = 1.6060224999860564893968089997193 absolute error = 0.0201145566098617210275814846888 relative error = 1.2683306552485264560474797371835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.627 y2[1] (analytic) = 1.5867180279040328313986078408783 y2[1] (numeric) = 1.6100824707827025456855446175398 absolute error = 0.0233644428786697142869367766615 relative error = 1.4725012552818131873680766100618 % h = 0.001 y1[1] (analytic) = 1.5867180279040328313986078408783 y1[1] (numeric) = 1.6069019228600283961739610055864 absolute error = 0.0201838949559955647753531647081 relative error = 1.2720530428873603283796569496717 % h = 0.001 TOP MAIN SOLVE Loop memory used=1518.2MB, alloc=4.6MB, time=85.60 NO POLE NO POLE x[1] = 0.628 y2[1] (analytic) = 1.5875275257138918835625189985835 y2[1] (numeric) = 1.6110236332364960041070759517324 absolute error = 0.0234961075226041205445569531489 relative error = 1.4800441026707997281775885059578 % h = 0.001 y1[1] (analytic) = 1.5875275257138918835625189985835 y1[1] (numeric) = 1.6077808566045117008083899643873 absolute error = 0.0202533308906198172458709658038 relative error = 1.2757782503022830967738369622602 % h = 0.001 TOP MAIN SOLVE Loop memory used=1522.0MB, alloc=4.6MB, time=85.82 NO POLE NO POLE x[1] = 0.629 y2[1] (analytic) = 1.5883364359962741824600573972178 y2[1] (numeric) = 1.6119646924698104134352281048689 absolute error = 0.0236282564735362309751707076511 relative error = 1.4876103033369975919118454867306 % h = 0.001 y1[1] (analytic) = 1.5883364359962741824600573972178 y1[1] (numeric) = 1.6086593002613435806311417488414 absolute error = 0.0203228642650693981710843516236 relative error = 1.2795062686024707072868916789796 % h = 0.001 TOP MAIN SOLVE Loop memory used=1525.9MB, alloc=4.6MB, time=86.04 NO POLE NO POLE x[1] = 0.63 y2[1] (analytic) = 1.5891447579422695131181120907946 y2[1] (numeric) = 1.6129056484787435120100478104271 absolute error = 0.0237608905364739988919357196325 relative error = 1.4951998814281200343198428775073 % h = 0.001 y1[1] (analytic) = 1.5891447579422695131181120907946 y1[1] (numeric) = 1.6095372528727210523173391380223 absolute error = 0.0203924949304515391992270472277 relative error = 1.2832370889142345972805455220502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1529.7MB, alloc=4.6MB, time=86.25 x[1] = 0.631 y2[1] (analytic) = 1.5899524907435559969015123421982 y2[1] (numeric) = 1.6138465012593961966480590104685 absolute error = 0.0238940105158401997465466682703 relative error = 1.502812861072719512256197604618 % h = 0.001 y1[1] (analytic) = 1.5899524907435559969015123421982 y1[1] (numeric) = 1.6104147134812019914868531933976 absolute error = 0.0204622227376459945853408511994 relative error = 1.2869707023809652796242779164827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.632 y2[1] (analytic) = 1.5907596335924008998348388981996 y2[1] (numeric) = 1.6147872508078725270329326128909 absolute error = 0.0240276172154716271980937146913 relative error = 1.510449266380379175268374796891 % h = 0.001 y1[1] (analytic) = 1.5907596335924008998348388981996 y1[1] (numeric) = 1.6112916811297061520845281188986 absolute error = 0.020532047537305252249689220699 relative error = 1.2907071001630761002653002624306 % h = 0.001 TOP MAIN SOLVE Loop memory used=1533.5MB, alloc=4.6MB, time=86.47 NO POLE NO POLE x[1] = 0.633 y2[1] (analytic) = 1.5915661856816614403350906538176 y2[1] (numeric) = 1.6157278971202797301035798822961 absolute error = 0.0241617114386182897684892284785 relative error = 1.5181091214419037977619483355986 % h = 0.001 y1[1] (analytic) = 1.5915661856816614403350906538176 y1[1] (numeric) = 1.6121681548615161855388974852035 absolute error = 0.0206019691798547452038068313859 relative error = 1.2944462734379471684946494845088 % h = 0.001 TOP MAIN SOLVE Loop memory used=1537.3MB, alloc=4.6MB, time=86.68 NO POLE NO POLE x[1] = 0.634 y2[1] (analytic) = 1.592372146204785596354398973423 y2[1] (numeric) = 1.6166684401927282044396646617835 absolute error = 0.0242962939879426080852656883605 relative error = 1.5257924503295101543887470288884 % h = 0.001 y1[1] (analytic) = 1.592372146204785596354398973423 y1[1] (numeric) = 1.6130441337202786596983297719167 absolute error = 0.0206719875154930633439307984937 relative error = 1.2981882133998694592411790564555 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1541.1MB, alloc=4.6MB, time=86.90 x[1] = 0.635 y2[1] (analytic) = 1.5931775143558129119319825259412 y2[1] (numeric) = 1.6176088800213315246445296249123 absolute error = 0.0244313656655186127125470989711 relative error = 1.5334992770970168412916918532382 % h = 0.001 y1[1] (analytic) = 1.5931775143558129119319825259412 y1[1] (numeric) = 1.6139196167500050775435412559098 absolute error = 0.0207421023941921656115587299686 relative error = 1.3019329112599890867279544587152 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.636 y2[1] (analytic) = 1.5939822893293753031545360822647 y2[1] (numeric) = 1.6185492166022064457255317590075 absolute error = 0.0245669272728311425709956767428 relative error = 1.5412296257800335458291387110475 % h = 0.001 y1[1] (analytic) = 1.5939822893293753031545360822647 y1[1] (numeric) = 1.6147946029950728956754143497573 absolute error = 0.0208123136656975925208782674926 relative error = 1.3056803582462517488282734009864 % h = 0.001 TOP MAIN SOLVE Loop memory used=1544.9MB, alloc=4.6MB, time=87.11 NO POLE NO POLE x[1] = 0.637 y2[1] (analytic) = 1.5947864703206978635242473145531 y2[1] (numeric) = 1.6194894499314729074717822829266 absolute error = 0.0247029796107750439475349683735 relative error = 1.5489835203961497673906051150943 % h = 0.001 y1[1] (analytic) = 1.5947864703206978635242473145531 y1[1] (numeric) = 1.6156690915002265425770595709541 absolute error = 0.020882621179528679052812256401 relative error = 1.3094305456033473414612318945246 % h = 0.001 TOP MAIN SOLVE Loop memory used=1548.7MB, alloc=4.6MB, time=87.33 NO POLE NO POLE x[1] = 0.638 y2[1] (analytic) = 1.5955900565255996687336362294726 y2[1] (numeric) = 1.620429580005254038829286204348 absolute error = 0.0248395234796543700956499748754 relative error = 1.5567609849451229919048778438805 % h = 0.001 y1[1] (analytic) = 1.5955900565255996687336362294726 y1[1] (numeric) = 1.6165430813105784366490594004358 absolute error = 0.0209530247849787679154231709632 relative error = 1.3131834645926547423694454529256 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1552.6MB, alloc=4.6MB, time=87.55 x[1] = 0.639 y2[1] (analytic) = 1.5963930471404945808464124606007 y2[1] (numeric) = 1.6213696068196761622734767235932 absolute error = 0.0249765596791815814270642629925 relative error = 1.5645620434090663226306716363038 % h = 0.001 y1[1] (analytic) = 1.5963930471404945808464124606007 y1[1] (numeric) = 1.6174165714716100040168323678483 absolute error = 0.0210235243311154231704199072476 relative error = 1.3169391064921867636242103994429 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.64 y2[1] (analytic) = 1.5971954413623920518835462392079 y2[1] (numeric) = 1.6223095303708687981791396929489 absolute error = 0.025114089008476746295593453741 relative error = 1.5723867197526355698092361287196 % h = 0.001 y1[1] (analytic) = 1.5971954413623920518835462392079 y1[1] (numeric) = 1.6182895610291726961090557810166 absolute error = 0.0210941196667806442255095418087 relative error = 1.3206974625965352722060535244621 % h = 0.001 TOP MAIN SOLVE Loop memory used=1556.4MB, alloc=4.6MB, time=87.76 NO POLE NO POLE x[1] = 0.641 y2[1] (analytic) = 1.5979972383888979268137494574101 y2[1] (numeric) = 1.6232493506549646691877233424173 absolute error = 0.0252521122660667423739738850072 relative error = 1.5802350379232158017475892054574 % h = 0.001 y1[1] (analytic) = 1.5979972383888979268137494574101 y1[1] (numeric) = 1.6191620490294890070060855981561 absolute error = 0.021164810640591080192336140746 relative error = 1.3244585242168164780112692325787 % h = 0.001 TOP MAIN SOLVE Loop memory used=1560.2MB, alloc=4.6MB, time=87.99 NO POLE NO POLE x[1] = 0.642 y2[1] (analytic) = 1.5987984374182152459475638332798 y2[1] (numeric) = 1.6241890676680997045720284847869 absolute error = 0.0253906302498844586244646515071 relative error = 1.5881070218511073598903894571348 % h = 0.001 y1[1] (analytic) = 1.5987984374182152459475638332798 y1[1] (numeric) = 1.6200340345191534905573120235452 absolute error = 0.0212355971009382446097481902654 relative error = 1.3282222826806163886376819051083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1564.0MB, alloc=4.6MB, time=88.21 x[1] = 0.643 y2[1] (analytic) = 1.599599037649145046734253783893 y2[1] (numeric) = 1.625128681406413044598274414888 absolute error = 0.025529643757267997864020630995 relative error = 1.5960026954497113404278482461314 % h = 0.001 y1[1] (analytic) = 1.599599037649145046734253783893 y1[1] (numeric) = 1.6209055165451337772663894906409 absolute error = 0.0213064788959887305321357067479 relative error = 1.3319887293319364303054975437919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.644 y2[1] (analytic) = 1.6003990382810871649607022094871 y2[1] (numeric) = 1.6260681918660470448855357198722 absolute error = 0.0256691535849598799248335103851 relative error = 1.603922082615714544976522690596 % h = 0.001 y1[1] (analytic) = 1.6003990382810871649607022094871 y1[1] (numeric) = 1.6217764941547715909432797809632 absolute error = 0.0213774558736844259825775714761 relative error = 1.3357578555311392342717229147765 % h = 0.001 TOP MAIN SOLVE Loop memory used=1567.8MB, alloc=4.6MB, time=88.42 NO POLE NO POLE x[1] = 0.645 y2[1] (analytic) = 1.6011984385140410353515079898995 y2[1] (numeric) = 1.6270075990431472807625452193365 absolute error = 0.025809160529106245411037229437 relative error = 1.6118652072292739028593244264666 % h = 0.001 y1[1] (analytic) = 1.6011984385140410353515079898995 y1[1] (numeric) = 1.6226469663957837651220471125087 absolute error = 0.0214485278817427297705391226092 relative error = 1.3395296526548945880992324409338 % h = 0.001 TOP MAIN SOLVE Loop memory used=1571.6MB, alloc=4.6MB, time=88.64 NO POLE NO POLE x[1] = 0.646 y2[1] (analytic) = 1.6019972375486064915694845932574 y2[1] (numeric) = 1.6279469029338625516218582560984 absolute error = 0.025949665385256060052373662841 relative error = 1.6198320931542003675006250200289 % h = 0.001 y1[1] (analytic) = 1.6019972375486064915694845932574 y1[1] (numeric) = 1.6235169323162632592433441179691 absolute error = 0.0215196947676567676738595247117 relative error = 1.3433041120961255511441530544683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1575.5MB, alloc=4.6MB, time=88.86 x[1] = 0.647 y2[1] (analytic) = 1.6027954345859845656157597964862 y2[1] (numeric) = 1.6288861035343448852713735604199 absolute error = 0.0260906689483603196556137639337 relative error = 1.6278227642381422894419371133923 % h = 0.001 y1[1] (analytic) = 1.6027954345859845656157597964862 y1[1] (numeric) = 1.6243863909646801746005277206327 absolute error = 0.0215909563786956089847679241465 relative error = 1.3470812252639547336278151817885 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.648 y2[1] (analytic) = 1.6035930288279782866286771176028 y2[1] (numeric) = 1.6298252008407495422832059124742 absolute error = 0.0262321720127712556545287948714 relative error = 1.635837244312768268473300524148 % h = 0.001 y1[1] (analytic) = 1.6035930288279782866286771176028 y1[1] (numeric) = 1.625255341389882770048344004536 absolute error = 0.0216623125619044834196668869332 relative error = 1.3508609835836507386620840482093 % h = 0.001 TOP MAIN SOLVE Loop memory used=1579.3MB, alloc=4.6MB, time=89.07 NO POLE NO POLE x[1] = 0.649 y2[1] (analytic) = 1.6043900194769934790807001609604 y2[1] (numeric) = 1.6307641948492350203399058298509 absolute error = 0.0263741753722415412592056688905 relative error = 1.6438755571939494873652043227134 % h = 0.001 y1[1] (analytic) = 1.6043900194769934790807001609604 y1[1] (numeric) = 1.6261237826410984774731212652042 absolute error = 0.0217337631641049983924211042438 relative error = 1.35464337849657476659943962054 % h = 0.001 TOP MAIN SOLVE Loop memory used=1583.1MB, alloc=4.6MB, time=89.29 NO POLE NO POLE x[1] = 0.65 y2[1] (analytic) = 1.6051864057360395603725216786059 y2[1] (numeric) = 1.6317030855559630585780215089015 absolute error = 0.0265166798199234982054998302956 relative error = 1.6519377266819415296756291125054 % h = 0.001 y1[1] (analytic) = 1.6051864057360395603725216786059 y1[1] (numeric) = 1.6269917137679349170234105181788 absolute error = 0.0218053080318953566508888395729 relative error = 1.3584284014601273810817158109415 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1586.9MB, alloc=4.6MB, time=89.51 x[1] = 0.651 y2[1] (analytic) = 1.6059821868087303378235797537072 y2[1] (numeric) = 1.6326418729570986419289982507383 absolute error = 0.0266596861483683041054184970311 relative error = 1.6600237765615656840965980759106 % h = 0.001 y1[1] (analytic) = 1.6059821868087303378235797537072 y1[1] (numeric) = 1.6278591338203809121000128344745 absolute error = 0.0218769470116505742764330807673 relative error = 1.3622160439476954361639401038147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.652 y2[1] (analytic) = 1.6067773618992848050581841156014 y2[1] (numeric) = 1.6335805570488100054574106047176 absolute error = 0.0268031951495252003992264891162 relative error = 1.6681337306023897377944805620855 % h = 0.001 y1[1] (analytic) = 1.6067773618992848050581841156014 y1[1] (numeric) = 1.628726041848807504104332965138 absolute error = 0.0219486799495226990461488495366 relative error = 1.3660062974485991638922335978276 % h = 0.001 TOP MAIN SOLVE Loop memory used=1590.7MB, alloc=4.6MB, time=89.72 NO POLE NO POLE x[1] = 0.653 y2[1] (analytic) = 1.6075719302125279377864562004034 y2[1] (numeric) = 1.6345191378272686386965224642594 absolute error = 0.026947207614740700910066263856 relative error = 1.6762676125589082611881978210736 % h = 0.001 y1[1] (analytic) = 1.6075719302125279377864562004034 y1[1] (numeric) = 1.629592436903968966943998811196 absolute error = 0.0220205066914410291575426107926 relative error = 1.3697991534680394217172386357701 % h = 0.001 TOP MAIN SOLVE Loop memory used=1594.5MB, alloc=4.6MB, time=89.93 NO POLE NO POLE x[1] = 0.654 y2[1] (analytic) = 1.6083658909538914889792871763013 y2[1] (numeric) = 1.6354576152886492899811703518818 absolute error = 0.0270917243347578010018831755805 relative error = 1.6844254461707223865994366740712 % h = 0.001 y1[1] (analytic) = 1.6083658909538914889792871763013 y1[1] (numeric) = 1.6304583180370038212946863904816 absolute error = 0.0220924270831123323153992141803 relative error = 1.3735946035270450991270367835952 % h = 0.001 TOP MAIN SOLVE Loop memory used=1598.3MB, alloc=4.6MB, time=90.15 NO POLE NO POLE x[1] = 0.655 y2[1] (analytic) = 1.609159243329414783436518758647 y2[1] (numeric) = 1.6363959894291299707779651323623 absolute error = 0.0272367460997151873414463737153 relative error = 1.6926072551627190831989831954422 % h = 0.001 y1[1] (analytic) = 1.609159243329414783436518758647 y1[1] (numeric) = 1.6313236842994358486170900491152 absolute error = 0.0221644409700210651805712904682 relative error = 1.3773926391624206828860039744343 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.656 y2[1] (analytic) = 1.6099519865457455117475522467268 y2[1] (numeric) = 1.6373342602448919600128073949737 absolute error = 0.0273822736991464482652551482469 relative error = 1.700813063245249930663344612481 % h = 0.001 y1[1] (analytic) = 1.6099519865457455117475522467268 y1[1] (numeric) = 1.632188534743175104927977762789 absolute error = 0.0222365481974295931804255160622 relative error = 1.3811932519266939802685222109326 % h = 0.001 TOP MAIN SOLVE Loop memory used=1602.2MB, alloc=4.6MB, time=90.36 NO POLE NO POLE x[1] = 0.657 y2[1] (analytic) = 1.6107441198101405236435918216702 y2[1] (numeric) = 1.6382724277321198083957117477851 absolute error = 0.0275283079219792847521199261149 relative error = 1.7090428941143093939459333501743 % h = 0.001 y1[1] (analytic) = 1.6107441198101405236435918216702 y1[1] (numeric) = 1.6330528684205189343242714714631 absolute error = 0.0223087486103784106806796497929 relative error = 1.3849964333880639996789283767434 % h = 0.001 TOP MAIN SOLVE Loop memory used=1606.0MB, alloc=4.6MB, time=90.58 NO POLE NO POLE x[1] = 0.658 y2[1] (analytic) = 1.6115356423304666207407287533185 y2[1] (numeric) = 1.6392104918870013427429352690661 absolute error = 0.0276748495565347220022065157476 relative error = 1.7172967714517126015572422080607 % h = 0.001 y1[1] (analytic) = 1.6115356423304666207407287533185 y1[1] (numeric) = 1.6339166843841529822590924906257 absolute error = 0.0223810420536863615183637373072 relative error = 1.3888021751303489880515305024993 % h = 0.001 TOP MAIN SOLVE Loop memory used=1609.8MB, alloc=4.6MB, time=90.80 NO POLE NO POLE x[1] = 0.659 y2[1] (analytic) = 1.6123265533152013486730737730358 y2[1] (numeric) = 1.6401484527057276702964053628842 absolute error = 0.0278218993905263216233315898484 relative error = 1.725574718925272629738643803106 % h = 0.001 y1[1] (analytic) = 1.6123265533152013486730737730358 y1[1] (numeric) = 1.6347799816871522085687121429013 absolute error = 0.0224534283719508598956383698655 relative error = 1.3926104687529346244269603190006 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.66 y2[1] (analytic) = 1.6131168519734337886151454793963 y2[1] (numeric) = 1.641086310184493183040442268044 absolute error = 0.0279694582110593944252967886477 relative error = 1.7338767601889772949047003972339 % h = 0.001 y1[1] (analytic) = 1.6131168519734337886151454793963 y1[1] (numeric) = 1.6356427593829819002493478555077 absolute error = 0.0225259074095481116342023761114 relative error = 1.3964213058707223691035581671251 % h = 0.001 TOP MAIN SOLVE Loop memory used=1613.6MB, alloc=4.6MB, time=91.01 NO POLE NO POLE x[1] = 0.661 y2[1] (analytic) = 1.6139065375148653481927232544241 y2[1] (numeric) = 1.6420240643194955620157714715776 absolute error = 0.0281175268046302138230482171535 relative error = 1.7422029188831654567191718021651 % h = 0.001 y1[1] (analytic) = 1.6139065375148653481927232544241 y1[1] (numeric) = 1.6365050165254986839827450718647 absolute error = 0.0225984790106333357900218174406 relative error = 1.400234678114077967764902375734 % h = 0.001 TOP MAIN SOLVE Loop memory used=1617.4MB, alloc=4.6MB, time=91.23 NO POLE NO POLE x[1] = 0.662 y2[1] (analytic) = 1.6146956091498105517813737796007 y2[1] (numeric) = 1.6429617151069357816308212800658 absolute error = 0.0282661059571252298494475004651 relative error = 1.750553218634702834160258970746 % h = 0.001 y1[1] (analytic) = 1.6146956091498105517813737796007 y1[1] (numeric) = 1.6373667521689515384094854295484 absolute error = 0.0226711430191409866281116499477 relative error = 1.4040505771287801099870001209208 % h = 0.001 TOP MAIN SOLVE Loop memory used=1621.2MB, alloc=4.6MB, time=91.45 NO POLE NO POLE x[1] = 0.663 y2[1] (analytic) = 1.6154840660891978301918608531767 y2[1] (numeric) = 1.6438992625430181139703008041398 absolute error = 0.0284151964538202837784399509631 relative error = 1.758927683057157336921018897837 % h = 0.001 y1[1] (analytic) = 1.6154840660891978301918608531767 y1[1] (numeric) = 1.6382279653679828061489617617583 absolute error = 0.0227438992787849759571009085816 relative error = 1.4078689945759692415310505979378 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.664 y2[1] (analytic) = 1.6162719075445703097416488234469 y2[1] (numeric) = 1.6448367066239501331010536135934 absolute error = 0.0285647990793798233594047901465 relative error = 1.7673263357509739144813323204247 % h = 0.001 y1[1] (analytic) = 1.6162719075445703097416488234469 y1[1] (numeric) = 1.639088655177629205564960585528 absolute error = 0.0228167476330588958233117620811 relative error = 1.4116899221320965298300741251586 % h = 0.001 TOP MAIN SOLVE Loop memory used=1625.0MB, alloc=4.6MB, time=91.66 NO POLE NO POLE x[1] = 0.665 y2[1] (analytic) = 1.6170591327280866007117105665481 y2[1] (numeric) = 1.6457740473459427193751823226175 absolute error = 0.0287149146178561186634717560694 relative error = 1.7757492003036489251782991841871 % h = 0.001 y1[1] (analytic) = 1.6170591327280866007117105665481 y1[1] (numeric) = 1.6399488206533228422757928470578 absolute error = 0.0228896879252362415640822805097 relative error = 1.4155133514888729820800726131213 % h = 0.001 TOP MAIN SOLVE Loop memory used=1628.9MB, alloc=4.6MB, time=91.88 NO POLE NO POLE x[1] = 0.666 y2[1] (analytic) = 1.6178457408525215851878515520396 y2[1] (numeric) = 1.6467112847052100637304393667569 absolute error = 0.0288655438526884785425878147173 relative error = 1.7841963002899040275924776897927 % h = 0.001 y1[1] (analytic) = 1.6178457408525215851878515520396 y1[1] (numeric) = 1.6408084608508922204079138027805 absolute error = 0.0229627199983706352200622507409 relative error = 1.4193392743532187153487477239154 % h = 0.001 TOP MAIN SOLVE Loop memory used=1632.7MB, alloc=4.6MB, time=92.10 NO POLE NO POLE x[1] = 0.667 y2[1] (analytic) = 1.6186317311312672042857621550066 y2[1] (numeric) = 1.6476484186979696719878792352826 absolute error = 0.029016687566702467702117080276 relative error = 1.792667659271859596557970708011 % h = 0.001 y1[1] (analytic) = 1.6186317311312672042857621550066 y1[1] (numeric) = 1.6416675748265632535919730240955 absolute error = 0.0230358436952960493062108690889 relative error = 1.4231676824472123781171530725098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.668 y2[1] (analytic) = 1.6194171027783332447590109897005 y2[1] (numeric) = 1.6485854493204423691467674247716 absolute error = 0.0291683465421091243877564350711 relative error = 1.8011633007992076660949982187954 % h = 0.001 y1[1] (analytic) = 1.6194171027783332447590109897005 y1[1] (numeric) = 1.64252616163696027570023562411 absolute error = 0.0231090588586270309412246344095 relative error = 1.4269985675080407226719960341404 % h = 0.001 TOP MAIN SOLVE Loop memory used=1636.5MB, alloc=4.6MB, time=92.31 NO POLE NO POLE x[1] = 0.669 y2[1] (analytic) = 1.6202018550083481249891926567879 y2[1] (numeric) = 1.649522376568852303676741381789 absolute error = 0.0293205215605041786875487250011 relative error = 1.8096832484093844015542759491061 % h = 0.001 y1[1] (analytic) = 1.6202018550083481249891926567879 y1[1] (numeric) = 1.6433842203391070513243159162233 absolute error = 0.0231823653307589263351232594354 relative error = 1.4308319212879483277686331753758 % h = 0.001 TOP MAIN SOLVE Loop memory used=1640.3MB, alloc=4.6MB, time=92.53 NO POLE NO POLE x[1] = 0.67 y2[1] (analytic) = 1.6209859870365596803574439141266 y2[1] (numeric) = 1.6504592004394269518072187046754 absolute error = 0.0294732134028672714497747905488 relative error = 1.8182275256277421032532483212203 % h = 0.001 y1[1] (analytic) = 1.6209859870365596803574439141266 y1[1] (numeric) = 1.6442417499904277859921648269672 absolute error = 0.0232557629538681056347209128406 relative error = 1.434667735554187470987121072869 % h = 0.001 TOP MAIN SOLVE Loop memory used=1644.1MB, alloc=4.6MB, time=92.75 NO POLE NO POLE x[1] = 0.671 y2[1] (analytic) = 1.6217694980788359479965428996171 y2[1] (numeric) = 1.6513959209283971218140478765573 absolute error = 0.0296264228495611738175049769402 relative error = 1.8267961559677207438749979434301 % h = 0.001 y1[1] (analytic) = 1.6217694980788359479965428996171 y1[1] (numeric) = 1.6450987496487481361232524991857 absolute error = 0.0233292515699121881267095995686 relative error = 1.4385060020889681502059913769863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.672 y2[1] (analytic) = 1.6225523873516659509228066540965 y2[1] (numeric) = 1.6523325380319969583033968038153 absolute error = 0.0297801506803310073805901497188 relative error = 1.835389162931019041891473944524 % h = 0.001 y1[1] (analytic) = 1.6225523873516659509228066540965 y1[1] (numeric) = 1.6459552183722962187208876363879 absolute error = 0.0234028310206302677980809822914 relative error = 1.4423467126894082536207154688982 % h = 0.001 TOP MAIN SOLVE Loop memory used=1647.9MB, alloc=4.6MB, time=92.97 NO POLE NO POLE x[1] = 0.673 y2[1] (analytic) = 1.6233346540721604815470028124424 y2[1] (numeric) = 1.65326905174646394649287443637 absolute error = 0.0299343976743034649458716239276 relative error = 1.8440065700077650732635472410618 % h = 0.001 y1[1] (analytic) = 1.6233346540721604815470028124424 y1[1] (numeric) = 1.6468111552197036208006152549495 absolute error = 0.0234765011475431392536124425071 relative error = 1.4461898591674838777361100025174 % h = 0.001 TOP MAIN SOLVE Loop memory used=1651.7MB, alloc=4.6MB, time=93.19 NO POLE NO POLE x[1] = 0.674 y2[1] (analytic) = 1.6241162974580528845634919520396 y2[1] (numeric) = 1.6542054620680389164898807482731 absolute error = 0.0300891646099860319263887962335 relative error = 1.8526484006766864236613121010311 % h = 0.001 y1[1] (analytic) = 1.6241162974580528845634919520396 y1[1] (numeric) = 1.6476665592500064085536346277653 absolute error = 0.0235502617919535239901426757257 relative error = 1.4500354333499797927642100683186 % h = 0.001 TOP MAIN SOLVE Loop memory used=1655.6MB, alloc=4.6MB, time=93.41 NO POLE NO POLE x[1] = 0.675 y2[1] (analytic) = 1.6248973167276998392168177095343 y2[1] (numeric) = 1.6551417689929660475671803592257 absolute error = 0.0302444522652662083503626496914 relative error = 1.8613146784052798834390098998213 % h = 0.001 y1[1] (analytic) = 1.6248973167276998392168177095343 y1[1] (numeric) = 1.6485214295226461362441793209677 absolute error = 0.0236241127949462970273616114334 relative error = 1.4538834270784400548614017160806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.676 y2[1] (analytic) = 1.6256777111000821409449623993491 y2[1] (numeric) = 1.6560779725174928724356950797847 absolute error = 0.0304002614174107314907326804356 relative error = 1.8700054266499806875899525269584 % h = 0.001 y1[1] (analytic) = 1.6256777111000821409449623993491 y1[1] (numeric) = 1.6493757650974708548398013444273 absolute error = 0.0236980539973887138948389450782 relative error = 1.4577338322091187646408601800925 % h = 0.001 TOP MAIN SOLVE Loop memory used=1659.4MB, alloc=4.6MB, time=93.62 NO POLE NO POLE x[1] = 0.677 y2[1] (analytic) = 1.6264574797948054823984864907691 y2[1] (numeric) = 1.6570140726378702815145106651618 absolute error = 0.0305565928430647991160241743927 relative error = 1.8787206688563313028978692672301 % h = 0.001 y1[1] (analytic) = 1.6264574797948054823984864907691 y1[1] (numeric) = 1.6502295650347361203735015569388 absolute error = 0.0237720852399306379750150661697 relative error = 1.4615866406129309713985844135566 % h = 0.001 TOP MAIN SOLVE Loop memory used=1663.2MB, alloc=4.6MB, time=93.84 NO POLE NO POLE x[1] = 0.678 y2[1] (analytic) = 1.6272366220321012338347709245244 y2[1] (numeric) = 1.6579500693503525271980930646693 absolute error = 0.0307134473182512933633221401449 relative error = 1.8874604284591497644921919229336 % h = 0.001 y1[1] (analytic) = 1.6272366220321012338347709245244 y1[1] (numeric) = 1.6510828283951060020366485882688 absolute error = 0.0238462063630047682018776637444 relative error = 1.4654418441754037224935525102606 % h = 0.001 TOP MAIN SOLVE Loop memory used=1667.0MB, alloc=4.6MB, time=94.05 NO POLE NO POLE x[1] = 0.679 y2[1] (analytic) = 1.6280151370328272228865818746926 y2[1] (numeric) = 1.65888596265119722812070945602 absolute error = 0.0308708256183700052341275813274 relative error = 1.8962247288826975640059282402583 % h = 0.001 y1[1] (analytic) = 1.6280151370328272228865818746926 y1[1] (numeric) = 1.6519355542396540900016286626032 absolute error = 0.0239204172068268671150467879106 relative error = 1.4692994347966272573247463213518 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.68 y2[1] (analytic) = 1.6287930240184685137041781874202 y2[1] (numeric) = 1.6598217525366653734180493558494 absolute error = 0.0310287285181968597138711684292 relative error = 1.9050135935408470915259531299839 % h = 0.001 y1[1] (analytic) = 1.6287930240184685137041781874202 y1[1] (numeric) = 1.6527877416298645029731688313796 absolute error = 0.0239947176113959892689906439594 relative error = 1.4731594043912063453500071137952 % h = 0.001 TOP MAIN SOLVE Loop memory used=1670.8MB, alloc=4.6MB, time=94.27 NO POLE NO POLE x[1] = 0.681 y2[1] (analytic) = 1.6295702822111381854701823544214 y2[1] (numeric) = 1.6607574390030213269860410999901 absolute error = 0.0311871567918831415158587455687 relative error = 1.913827045837248633516770508109 % h = 0.001 y1[1] (analytic) = 1.6295702822111381854701823544214 y1[1] (numeric) = 1.6536393896276328954672762480251 absolute error = 0.0240691074164947099970938936037 relative error = 1.4770217448882117675938875144027 % h = 0.001 TOP MAIN SOLVE Loop memory used=1674.6MB, alloc=4.6MB, time=94.48 NO POLE NO POLE x[1] = 0.682 y2[1] (analytic) = 1.6303469108335781102864365064475 y2[1] (numeric) = 1.6616930220465328317368589892011 absolute error = 0.0313461112129547214504224827536 relative error = 1.9226651091654969288900656064832 % h = 0.001 y1[1] (analytic) = 1.6303469108335781102864365064475 y1[1] (numeric) = 1.6544904972952674648167362427401 absolute error = 0.0241435864616893545302997362926 relative error = 1.4808864482311319410938582893168 % h = 0.001 TOP MAIN SOLVE Loop memory used=1678.5MB, alloc=4.6MB, time=94.70 NO POLE NO POLE x[1] = 0.683 y2[1] (analytic) = 1.6311229091091597304320655399362 y2[1] (numeric) = 1.6626285016634710138521163982251 absolute error = 0.0315055925543112834200508582889 relative error = 1.9315278069092972853836780965313 % h = 0.001 y1[1] (analytic) = 1.6311229091091597304320655399362 y1[1] (numeric) = 1.655341063695489957902112082179 absolute error = 0.0242181545863302274700465422428 relative error = 1.4847535063778246857364117728742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.684 y2[1] (analytic) = 1.631898276261884834991970118843 y2[1] (numeric) = 1.6635638778501103870332401482301 absolute error = 0.0316656015882255520412700293871 relative error = 1.9404151624426312584049801139605 % h = 0.001 y1[1] (analytic) = 1.631898276261884834991970118843 y1[1] (numeric) = 1.6561910878914366776071894266727 absolute error = 0.0242928116295518426152193078297 relative error = 1.488622911300469132936777030907 % h = 0.001 TOP MAIN SOLVE Loop memory used=1682.3MB, alloc=4.6MB, time=94.91 NO POLE NO POLE x[1] = 0.685 y2[1] (analytic) = 1.6326730115163863358549729232243 y2[1] (numeric) = 1.6644991506027288567490214448737 absolute error = 0.0318261390863425208940485216494 relative error = 1.949327199129921894485040051446 % h = 0.001 y1[1] (analytic) = 1.6326730115163863358549729232243 y1[1] (numeric) = 1.6570405689466594889978086265213 absolute error = 0.024367557430273153142835703297 relative error = 1.4924946549855177756181251711777 % h = 0.001 TOP MAIN SOLVE Loop memory used=1686.1MB, alloc=4.6MB, time=95.13 NO POLE NO POLE x[1] = 0.686 y2[1] (analytic) = 1.6334471140979290430808421464934 y2[1] (numeric) = 1.6654343199176077244803386864187 absolute error = 0.0319872058196786813994965399253 relative error = 1.9582639403261985414813925840994 % h = 0.001 y1[1] (analytic) = 1.6334471140979290430808421464934 y1[1] (numeric) = 1.6578895059251268252230281288545 absolute error = 0.0244423918271977821421859823611 relative error = 1.4963687294336486589482966455613 % h = 0.001 TOP MAIN SOLVE Loop memory used=1689.9MB, alloc=4.6MB, time=95.35 NO POLE NO POLE x[1] = 0.687 y2[1] (analytic) = 1.6342205832324104396354168743884 y2[1] (numeric) = 1.6663693857910316919620474485237 absolute error = 0.0321488025586212523266305741353 relative error = 1.9672254093772612276587175956211 % h = 0.001 y1[1] (analytic) = 1.6342205832324104396354168743884 y1[1] (numeric) = 1.6587378978912246931375623976138 absolute error = 0.0245173146588142535021455232254 relative error = 1.5002451266597177112942259744158 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.688 y2[1] (analytic) = 1.6349934181463614554930596105924 y2[1] (numeric) = 1.6673043482192888654220329545321 absolute error = 0.0323109300729274099289733439397 relative error = 1.9762116296198446117682552671715 % h = 0.001 y1[1] (analytic) = 1.6349934181463614554930596105924 y1[1] (numeric) = 1.6595857439097576786444378813549 absolute error = 0.0245923257633962231513782707625 relative error = 1.5041238386927112148563731103413 % h = 0.001 TOP MAIN SOLVE Loop memory used=1693.7MB, alloc=4.6MB, time=95.56 NO POLE NO POLE x[1] = 0.689 y2[1] (analytic) = 1.6357656180669472411056618466169 y2[1] (numeric) = 1.6682392071986707598174203422863 absolute error = 0.0324735891317235187117584956694 relative error = 1.985222624381781506238351365076 % h = 0.001 y1[1] (analytic) = 1.6357656180669472411056618466169 y1[1] (numeric) = 1.6604330430459499517568106967983 absolute error = 0.0246674249790027106511488501814 relative error = 1.5080048575756984154475946948403 % h = 0.001 TOP MAIN SOLVE Loop memory used=1697.5MB, alloc=4.6MB, time=95.78 NO POLE NO POLE x[1] = 0.69 y2[1] (analytic) = 1.6365371822219679402374292070087 y2[1] (numeric) = 1.6691739627254723030679380407061 absolute error = 0.0326367805035043628305088336974 relative error = 1.9942584169821659755801355064403 % h = 0.001 y1[1] (analytic) = 1.6365371822219679402374292070087 y1[1] (numeric) = 1.6612797943654462713778898303762 absolute error = 0.0247426121434783311404606233675 relative error = 1.5118881753657842708830027945523 % h = 0.001 TOP MAIN SOLVE Loop memory used=1701.3MB, alloc=4.6MB, time=95.99 NO POLE NO POLE x[1] = 0.691 y2[1] (analytic) = 1.6373081098398594621646733351585 y2[1] (numeric) = 1.6701086147959918402864295715826 absolute error = 0.0328005049561323781217562364241 relative error = 2.0033190307315160121039856841404 % h = 0.001 y1[1] (analytic) = 1.6373081098398594621646733351585 y1[1] (numeric) = 1.6621259969343129897979097954263 absolute error = 0.0248178870944535276332364602678 relative error = 1.5157737841340623374494633812359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.692 y2[1] (analytic) = 1.6380784001496942532398383199832 y2[1] (numeric) = 1.6710431634065311380065090942612 absolute error = 0.032964763256836884766670774278 relative error = 2.0124044889319357910341243862108 % h = 0.001 y1[1] (analytic) = 1.6380784001496942532398383199832 y1[1] (numeric) = 1.6629716498190390569070968191775 absolute error = 0.0248932496693448036672584991943 relative error = 1.5196616759655677939254818887124 % h = 0.001 TOP MAIN SOLVE Loop memory used=1705.2MB, alloc=4.6MB, time=96.20 NO POLE NO POLE x[1] = 0.693 y2[1] (analytic) = 1.638848052381182067818990099522 y2[1] (numeric) = 1.6719776085533953884073560131101 absolute error = 0.0331295561722133205883659135881 relative error = 2.0215148148772775071004250416617 % h = 0.001 y1[1] (analytic) = 1.638848052381182067818990099522 y1[1] (numeric) = 1.6638167520865370241235727712509 absolute error = 0.0249686997053549563045826717289 relative error = 1.5235518429592306026243086870142 % h = 0.001 TOP MAIN SOLVE Loop memory used=1709.0MB, alloc=4.6MB, time=96.42 NO POLE NO POLE x[1] = 0.694 y2[1] (analytic) = 1.639617065764670738551997914018 y2[1] (numeric) = 1.6729119502328932135356439699021 absolute error = 0.0332948844682224749836460558841 relative error = 2.0306500318533027946782820603189 % h = 0.001 y1[1] (analytic) = 1.639617065764670738551997914018 y1[1] (numeric) = 1.6646613028041440480351411840663 absolute error = 0.0250442370394733094831432700483 relative error = 1.5274442772278288069351733065091 % h = 0.001 TOP MAIN SOLVE Loop memory used=1712.8MB, alloc=4.6MB, time=96.64 NO POLE NO POLE x[1] = 0.695 y2[1] (analytic) = 1.6403854395311469460346375183712 y2[1] (numeric) = 1.6738461884413366695245995454729 absolute error = 0.0334607489101897234899620271017 relative error = 2.0398101631378437335392132019991 % h = 0.001 y1[1] (analytic) = 1.6403854395311469460346375183712 y1[1] (numeric) = 1.6655053010396228937538998552988 absolute error = 0.0251198615084759477192623369276 relative error = 1.5313389708979419648396227678983 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.696 y2[1] (analytic) = 1.641153172912236987821846501921 y2[1] (numeric) = 1.6747803231750412508101859972571 absolute error = 0.0336271502628042629883394953361 relative error = 2.0489952320009634422667192078928 % h = 0.001 y1[1] (analytic) = 1.641153172912236987821846501921 y1[1] (numeric) = 1.6663487458611629379826246633706 absolute error = 0.0251955729489259501607781614496 relative error = 1.5352359161099047178819964752101 % h = 0.001 TOP MAIN SOLVE Loop memory used=1716.6MB, alloc=4.6MB, time=96.85 NO POLE NO POLE x[1] = 0.697 y2[1] (analytic) = 1.6419202651402075468013627023692 y2[1] (numeric) = 1.6757143544303258943444073615509 absolute error = 0.0337940892901183475430446591817 relative error = 2.0582052617051162613838223508169 % h = 0.001 y1[1] (analytic) = 1.6419202651402075468013627023692 y1[1] (numeric) = 1.6671916363373811717918693688912 absolute error = 0.025271371197173624990506666522 relative error = 1.5391351050177604950751178527548 % h = 0.001 TOP MAIN SOLVE Loop memory used=1720.4MB, alloc=4.6MB, time=97.07 NO POLE NO POLE x[1] = 0.698 y2[1] (analytic) = 1.6426867154479664589269773402679 y2[1] (numeric) = 1.6766482822035129838057282515987 absolute error = 0.0339615667555465248787509113308 relative error = 2.0674402755053075282306426102114 % h = 0.001 y1[1] (analytic) = 1.6426867154479664589269773402679 y1[1] (numeric) = 1.6680339715373232031067263179759 absolute error = 0.025347256089356744179748977708 relative error = 1.5430365297892153512243213003598 % h = 0.001 TOP MAIN SOLVE Loop memory used=1724.2MB, alloc=4.6MB, time=97.29 NO POLE NO POLE x[1] = 0.699 y2[1] (analytic) = 1.643452523069063480310635140883 y2[1] (numeric) = 1.6775821064909283538066046848572 absolute error = 0.0341295834218648734959695439742 relative error = 2.0767002966492529456223473517243 % h = 0.001 y1[1] (analytic) = 1.643452523069063480310635140883 y1[1] (numeric) = 1.6688757505304642589021931074739 absolute error = 0.0254232274614007785915579665909 relative error = 1.5469401826055919391549621483959 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7 y2[1] (analytic) = 1.6442176872376910536726143513987 y2[1] (numeric) = 1.6785158272889012940981212750505 absolute error = 0.0342981400512102404255069236518 relative error = 2.085985348377537546309827490698 % h = 0.001 y1[1] (analytic) = 1.6442176872376910536726143513987 y1[1] (numeric) = 1.6697169723867101871060904173288 absolute error = 0.0254992851490191334334760659301 relative error = 1.5508460556617836153305771608427 % h = 0.001 TOP MAIN SOLVE Loop memory used=1728.0MB, alloc=4.6MB, time=97.50 NO POLE NO POLE x[1] = 0.701 y2[1] (analytic) = 1.6449822071886850741490202033442 y2[1] (numeric) = 1.6794494445937645537717301268943 absolute error = 0.0344672374050794796227099235501 relative error = 2.0952954539237742552575099462383 % h = 0.001 y1[1] (analytic) = 1.6449822071886850741490202033442 y1[1] (numeric) = 1.6705576361763984582084763615707 absolute error = 0.0255754289877133840594561582265 relative error = 1.5547541411662086783508738059007 % h = 0.001 TOP MAIN SOLVE Loop memory used=1731.9MB, alloc=4.6MB, time=97.72 NO POLE NO POLE x[1] = 0.702 y2[1] (analytic) = 1.6457460821575256544558260128154 y2[1] (numeric) = 1.6803829584018543454580867736389 absolute error = 0.0346368762443286910022607608235 relative error = 2.1046306365147620517448125500097 % h = 0.001 y1[1] (analytic) = 1.6457460821575256544558260128154 y1[1] (numeric) = 1.6713977409702991665765028568035 absolute error = 0.0256516588127735121206768439881 relative error = 1.5586644313407647398207280333385 % h = 0.001 TOP MAIN SOLVE Loop memory used=1735.7MB, alloc=4.6MB, time=97.94 NO POLE NO POLE x[1] = 0.703 y2[1] (analytic) = 1.6465093113803378894086967545133 y2[1] (numeric) = 1.6813163687095103495229784998555 absolute error = 0.0348070573291724601142817453422 relative error = 2.1139909193706437332898832664494 % h = 0.001 y1[1] (analytic) = 1.6465093113803378894086967545133 y1[1] (numeric) = 1.6722372858396160314736596555039 absolute error = 0.0257279744592781420649629009906 relative error = 1.5625769184207832270833627113989 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1739.5MB, alloc=4.6MB, time=98.15 x[1] = 0.704 y2[1] (analytic) = 1.6472718940938926197978305898392 y2[1] (numeric) = 1.6822496755130757182603403941707 absolute error = 0.0349777814191830984625098043315 relative error = 2.1233763257050632833864404132936 % h = 0.001 y1[1] (analytic) = 1.6472718940938926197978305898392 y1[1] (numeric) = 1.6730762698559873977823518409876 absolute error = 0.0258043757620947779845212511484 relative error = 1.5664915946549840173128622269261 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.705 y2[1] (analytic) = 1.6480338295356071956170544742679 y2[1] (numeric) = 1.6831828788088970800823544789389 absolute error = 0.035149049273289884465300004671 relative error = 2.1327868787253228450367443497564 % h = 0.001 y1[1] (analytic) = 1.6480338295356071956170544742679 y1[1] (numeric) = 1.6739146920914872364287567315237 absolute error = 0.0258808625558800408117022572558 relative error = 1.5704084523054302024631530847339 % h = 0.001 TOP MAIN SOLVE Loop memory used=1743.3MB, alloc=4.6MB, time=98.36 NO POLE NO POLE x[1] = 0.706 y2[1] (analytic) = 1.6487951169435462386464106149696 y2[1] (numeric) = 1.6841159785933245437066272661342 absolute error = 0.0353208616497783050602166511646 relative error = 2.1422226016325393020559836315617 % h = 0.001 y1[1] (analytic) = 1.6487951169435462386464106149696 y1[1] (numeric) = 1.674752551618626144508906292793 absolute error = 0.0259574346750799058624956778234 relative error = 1.5743274836474829845725456996134 % h = 0.001 TOP MAIN SOLVE Loop memory used=1747.1MB, alloc=4.6MB, time=98.58 NO POLE NO POLE x[1] = 0.707 y2[1] (analytic) = 1.6495557555564224043874711961547 y2[1] (numeric) = 1.6850489748627117023404410910378 absolute error = 0.0354932193062892979529698948831 relative error = 2.1516835176218004701156497263111 % h = 0.001 y1[1] (analytic) = 1.6495557555564224043874711961547 y1[1] (numeric) = 1.675589847510352345114941310687 absolute error = 0.0260340919539299407274701145323 relative error = 1.5782486809697567009248890008943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1750.9MB, alloc=4.6MB, time=98.80 x[1] = 0.708 y2[1] (analytic) = 1.6503157446135971433506194368912 y2[1] (numeric) = 1.6859818676134156378620745775978 absolute error = 0.0356661229998184945114551407066 relative error = 2.1611696498823208994858038480049 % h = 0.001 y1[1] (analytic) = 1.6503157446135971433506194368912 y1[1] (numeric) = 1.6764265788400526868604837303323 absolute error = 0.0261108342264555435098642934411 relative error = 1.5821720365740739785703370072557 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.709 y2[1] (analytic) = 1.6510750833550814616935356941786 y2[1] (numeric) = 1.6869146568417969249991875916436 absolute error = 0.035839573486715463305651897465 relative error = 2.1706810215975972914285071171508 % h = 0.001 y1[1] (analytic) = 1.6510750833550814616935356941786 y1[1] (numeric) = 1.6772627446815536431040737222007 absolute error = 0.0261876613264721814105380280221 relative error = 1.5860975427754210177106652223565 % h = 0.001 TOP MAIN SOLVE Loop memory used=1754.7MB, alloc=4.6MB, time=99.01 NO POLE NO POLE x[1] = 0.71 y2[1] (analytic) = 1.6518337710215366812101279728528 y2[1] (numeric) = 1.687847342544219635504266040448 absolute error = 0.0360135715226829542941380675952 relative error = 2.1802176559455635301870908946221 % h = 0.001 y1[1] (analytic) = 1.6518337710215366812101279728528 y1[1] (numeric) = 1.6780983441091223108696181922291 absolute error = 0.0262645730875856296594902193763 relative error = 1.5900251919019030034560045927239 % h = 0.001 TOP MAIN SOLVE Loop memory used=1758.6MB, alloc=4.6MB, time=99.23 NO POLE NO POLE x[1] = 0.711 y2[1] (analytic) = 1.6525918068542751986691468534576 y2[1] (numeric) = 1.6887799247170513423271218794457 absolute error = 0.0361881178627761436579750259881 relative error = 2.1897795760987453325083875849846 % h = 0.001 y1[1] (analytic) = 1.6525918068542751986691468534576 y1[1] (numeric) = 1.6789333761974674094627976100218 absolute error = 0.0263415693431922107936507565642 relative error = 1.5939549762946996454617818996386 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1762.4MB, alloc=4.6MB, time=99.44 x[1] = 0.712 y2[1] (analytic) = 1.6533491900952612445017254995287 y2[1] (numeric) = 1.6897124033566631237844436892372 absolute error = 0.0363632132614018792827181897085 relative error = 2.1993668052244145166275232734268 % h = 0.001 y1[1] (analytic) = 1.6533491900952612445017254995287 y1[1] (numeric) = 1.6797678400217402787823781874477 absolute error = 0.026418649926479034280652687919 relative error = 1.5978868883080208449565678704598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.713 y2[1] (analytic) = 1.6541059199871116408370860568158 y2[1] (numeric) = 1.6906447784594295677263931883329 absolute error = 0.0365388584723179268893071315171 relative error = 2.2089793664847428926373920632238 % h = 0.001 y1[1] (analytic) = 1.6541059199871116408370860568158 y1[1] (numeric) = 1.6806017346575358773253765992671 absolute error = 0.0264958146704242364882905424513 relative error = 1.601820920309062488673438032215 % h = 0.001 TOP MAIN SOLVE Loop memory used=1766.2MB, alloc=4.6MB, time=99.67 NO POLE NO POLE x[1] = 0.714 y2[1] (analytic) = 1.6548619957730965588856544087971 y2[1] (numeric) = 1.6915770500217287757002430494228 absolute error = 0.0367150542486322168145886406257 relative error = 2.2186172830369557761574877348424 % h = 0.001 y1[1] (analytic) = 1.6548619957730965588856544087971 y1[1] (numeric) = 1.681435059180893779885024597837 absolute error = 0.0265730634077972209993701890399 relative error = 1.6057570646779623691993464349995 % h = 0.001 TOP MAIN SOLVE Loop memory used=1770.0MB, alloc=4.6MB, time=99.89 NO POLE NO POLE x[1] = 0.715 y2[1] (analytic) = 1.655617416697140275668825905437 y2[1] (numeric) = 1.6925092180399423671110513892931 absolute error = 0.0368918013428020914422254838561 relative error = 2.2282805780334851272093611690105 % h = 0.001 y1[1] (analytic) = 1.655617416697140275668825905437 y1[1] (numeric) = 1.6822678126682991749404810354411 absolute error = 0.0266503959711588992716551300041 relative error = 1.6096953138077562312588988846938 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1773.8MB, alloc=4.6MB, time=100.10 x[1] = 0.716 y2[1] (analytic) = 1.6563721820038219300946253354824 y2[1] (numeric) = 1.6934412825104554833793683048516 absolute error = 0.0370691005066335532847429693692 relative error = 2.2379692746221223161986016833297 % h = 0.001 y1[1] (analytic) = 1.6563721820038219300946253354824 y1[1] (numeric) = 1.6830999941966838617372389703796 absolute error = 0.0267278121928619316426136348972 relative error = 1.613635660104333943450790286822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.717 y2[1] (analytic) = 1.6571262909383762783785050667013 y2[1] (numeric) = 1.6943732434296567920959698300689 absolute error = 0.0372469524912805137174647633676 relative error = 2.2476833959461705188959068431526 % h = 0.001 y1[1] (analytic) = 1.6571262909383762783785050667013 y1[1] (numeric) = 1.6839316028434272470571756966246 absolute error = 0.0268053119050509686786706299233 relative error = 1.6175780959863957949570401556465 % h = 0.001 TOP MAIN SOLVE Loop memory used=1777.6MB, alloc=4.6MB, time=100.32 NO POLE NO POLE x[1] = 0.718 y2[1] (analytic) = 1.6578797427466944488085259333295 y2[1] (numeric) = 1.6953051007939384911736146909939 absolute error = 0.0374253580472440423650887576644 relative error = 2.2574229651445967423025082430562 % h = 0.001 y1[1] (analytic) = 1.6578797427466944488085259333295 y1[1] (numeric) = 1.6847626376863573416771937016111 absolute error = 0.0268828949396628928686677682816 relative error = 1.6215226138854089167470213270805 % h = 0.001 TOP MAIN SOLVE Loop memory used=1781.4MB, alloc=4.6MB, time=100.54 NO POLE NO POLE x[1] = 0.719 y2[1] (analytic) = 1.6586325366753246958541661056053 y2[1] (numeric) = 1.6962368545996963129958192383577 absolute error = 0.0376043179243716171416531327524 relative error = 2.2671880053521834832779600361129 % h = 0.001 y1[1] (analytic) = 1.6586325366753246958541661056053 y1[1] (numeric) = 1.6855930978037517565154007225795 absolute error = 0.0269605611284270606612346169742 relative error = 1.6254692062455638268001294708131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1785.3MB, alloc=4.6MB, time=100.75 x[1] = 0.72 y2[1] (analytic) = 1.6593846719714731536180038326482 y2[1] (numeric) = 1.6971685048433295285626459396402 absolute error = 0.037783832871856374944642106992 relative error = 2.2769785396996800218010724355653 % h = 0.001 y1[1] (analytic) = 1.6593846719714731536180038326482 y1[1] (numeric) = 1.6864229822743386984637772388219 absolute error = 0.0270383103028655448457734061737 relative error = 1.6294178655237310988727851666076 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.721 y2[1] (analytic) = 1.6601361478830045886295206070606 y2[1] (numeric) = 1.6981000515212409516335008148393 absolute error = 0.0379639036382363630039802077787 relative error = 2.2867945913139533507275838512374 % h = 0.001 y1[1] (analytic) = 1.6601361478830045886295206070606 y1[1] (numeric) = 1.6872522901772979659062799052064 absolute error = 0.0271161422942933772767592981458 relative error = 1.6333685841894181543372961329641 % h = 0.001 TOP MAIN SOLVE Loop memory used=1789.1MB, alloc=4.6MB, time=100.97 NO POLE NO POLE x[1] = 0.722 y2[1] (analytic) = 1.6608869636584431519802719575123 y2[1] (numeric) = 1.6990314946298369428669352025551 absolute error = 0.0381445309713937908866632450428 relative error = 2.2966361833181387439010125743132 % h = 0.001 y1[1] (analytic) = 1.6608869636584431519802719575123 y1[1] (numeric) = 1.6880810205922619439213296014648 absolute error = 0.0271940569338187919410576439525 relative error = 1.6373213547247261766219347128623 % h = 0.001 TOP MAIN SOLVE Loop memory used=1792.9MB, alloc=4.6MB, time=101.19 NO POLE NO POLE x[1] = 0.723 y2[1] (analytic) = 1.6616371185469731307996737341996 y2[1] (numeric) = 1.6999628341655274139574472453742 absolute error = 0.0383257156185542831577735111746 relative error = 2.3065033388317899644660118137695 % h = 0.001 y1[1] (analytic) = 1.6616371185469731307996737341996 y1[1] (numeric) = 1.6889091725993165991676329419238 absolute error = 0.0272720540523434683679592077242 relative error = 1.6412761696243071477834049710361 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1796.7MB, alloc=4.6MB, time=101.40 x[1] = 0.724 y2[1] (analytic) = 1.6623866117984396990706524114553 y2[1] (numeric) = 1.7008940701247258317692784859227 absolute error = 0.0385074583262861326986260744674 relative error = 2.3163960809710291152264702420971 % h = 0.001 y1[1] (analytic) = 1.6623866117984396990706524114553 y1[1] (numeric) = 1.6897367452790024744522862616459 absolute error = 0.0273501334805627753816338501906 relative error = 1.6452330213953210067446847802234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.725 y2[1] (analytic) = 1.6631354426633496677844085919225 y2[1] (numeric) = 1.7018252025038492224672009673409 absolute error = 0.0386897598404995546827923754184 relative error = 2.3263144328486961328835538531369 % h = 0.001 y1[1] (analytic) = 1.6631354426633496677844085919225 y1[1] (numeric) = 1.690563737712315682980111267316 absolute error = 0.0274282950489660151957026753935 relative error = 1.6491919025573929287330311090753 % h = 0.001 TOP MAIN SOLVE Loop memory used=1800.5MB, alloc=4.6MB, time=101.62 NO POLE NO POLE x[1] = 0.726 y2[1] (analytic) = 1.6638836103928722344335435575901 y2[1] (numeric) = 1.702756231299318175644290234323 absolute error = 0.0388726209064459412107466767329 relative error = 2.3362584175744979279818736991407 % h = 0.001 y1[1] (analytic) = 1.6638836103928722344335435575901 y1[1] (numeric) = 1.6913901489807089022831717146687 absolute error = 0.0275065385878366678496281570786 relative error = 1.6531528056425707254547314116817 % h = 0.001 TOP MAIN SOLVE Loop memory used=1804.3MB, alloc=4.6MB, time=101.84 NO POLE NO POLE x[1] = 0.727 y2[1] (analytic) = 1.6646311142388397318427993746266 y2[1] (numeric) = 1.7036871565075568484466796332624 absolute error = 0.0390560422687171166038802586358 relative error = 2.3462280582551571723849877859102 % h = 0.001 y1[1] (analytic) = 1.6646311142388397318427993746266 y1[1] (numeric) = 1.6922159781660923678294206487961 absolute error = 0.0275848639272526359866212741695 relative error = 1.6571157231952823655449705964713 % h = 0.001 TOP MAIN SOLVE Loop memory used=1808.2MB, alloc=4.6MB, time=102.05 NO POLE NO POLE x[1] = 0.728 y2[1] (analytic) = 1.6653779534537483763366637213347 y2[1] (numeric) = 1.7046179781249929696952913124424 absolute error = 0.0392400246712445933586275911077 relative error = 2.3562233779945607360945038937971 % h = 0.001 y1[1] (analytic) = 1.6653779534537483763366637213347 y1[1] (numeric) = 1.6930412243508348663094279193084 absolute error = 0.0276632708970864899727641979737 relative error = 1.6610806477722936148329615598846 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.729 y2[1] (analytic) = 1.666124127290759015243091271684 y2[1] (numeric) = 1.7055486961480578440045393256179 absolute error = 0.0394245688572988287614480539339 relative error = 2.366244399893907775220143189176 % h = 0.001 y1[1] (analytic) = 1.666124127290759015243091271684 y1[1] (numeric) = 1.6938658866177647286001378590394 absolute error = 0.0277417593270057133570465873554 relative error = 1.6650475719426657959642577461777 % h = 0.001 TOP MAIN SOLVE Loop memory used=1812.0MB, alloc=4.6MB, time=102.27 NO POLE NO POLE x[1] = 0.73 y2[1] (analytic) = 1.6668696350036978737325941307615 y2[1] (numeric) = 1.7064793105731863558980002447459 absolute error = 0.0396096755694884821654061139844 relative error = 2.3762911470518574729012520272951 % h = 0.001 y1[1] (analytic) = 1.6668696350036978737325941307615 y1[1] (numeric) = 1.6946899640501708224046071927945 absolute error = 0.027820329046472948672013062033 relative error = 1.6690164882877136669239286773831 % h = 0.001 TOP MAIN SOLVE Loop memory used=1815.8MB, alloc=4.6MB, time=102.49 NO POLE NO POLE x[1] = 0.731 y2[1] (analytic) = 1.6676144758470573009919544831147 y2[1] (numeric) = 1.7074098213968169739210466900359 absolute error = 0.0397953455497596729290922069212 relative error = 2.3863636425646764349734111549696 % h = 0.001 y1[1] (analytic) = 1.6676144758470573009919544831147 y1[1] (numeric) = 1.6955134557318035445666734215334 absolute error = 0.0278989798847462435747189384187 relative error = 1.6729873894009634180060339249001 % h = 0.001 TOP MAIN SOLVE Loop memory used=1819.6MB, alloc=4.6MB, time=102.72 NO POLE NO POLE x[1] = 0.732 y2[1] (analytic) = 1.6683586490759965157318132803332 y2[1] (numeric) = 1.7083402286153917547504391879147 absolute error = 0.0399815795393952390186259075815 relative error = 2.3964619095263857421669874353231 % h = 0.001 y1[1] (analytic) = 1.6683586490759965157318132803332 y1[1] (numeric) = 1.6963363607468758130595041073585 absolute error = 0.0279777116708792973276908270253 relative error = 1.6769602678881107867765776051486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.733 y2[1] (analytic) = 1.6691021539463423510273894603448 y2[1] (numeric) = 1.7092705322253563473008717699226 absolute error = 0.0401683782790139962734823095778 relative error = 2.4065859710289076606177030689201 % h = 0.001 y1[1] (analytic) = 1.6691021539463423510273894603448 y1[1] (numeric) = 1.697158678180064058646977665749 absolute error = 0.0280565242337217076195882054042 relative error = 1.6809351163669792905788642129284 % h = 0.001 TOP MAIN SOLVE Loop memory used=1823.4MB, alloc=4.6MB, time=102.93 NO POLE NO POLE x[1] = 0.734 y2[1] (analytic) = 1.6698449897145899984915848577685 y2[1] (numeric) = 1.7102007322231599968284667279919 absolute error = 0.0403557425085699983368818702234 relative error = 2.4167358501622120124625609134985 % h = 0.001 y1[1] (analytic) = 1.6698449897145899984915848577685 y1[1] (numeric) = 1.6979804071165092162168464536326 absolute error = 0.0281354174019192177252615958641 relative error = 1.6849119274674785761319074961217 % h = 0.001 TOP MAIN SOLVE Loop memory used=1827.2MB, alloc=4.6MB, time=103.15 NO POLE NO POLE x[1] = 0.735 y2[1] (analytic) = 1.6705871556379037517797306322801 y2[1] (numeric) = 1.7111308286052555490312139439913 absolute error = 0.0405436729673517972514833117112 relative error = 2.4269115700144622082877617428049 % h = 0.001 y1[1] (analytic) = 1.6705871556379037517797306322801 y1[1] (numeric) = 1.6988015466418177157846331251301 absolute error = 0.02821439100391396400490249285 relative error = 1.6888906938315628857742671614274 % h = 0.001 TOP MAIN SOLVE Loop memory used=1831.0MB, alloc=4.6MB, time=103.36 NO POLE NO POLE x[1] = 0.736 y2[1] (analytic) = 1.671328650974117749425231710308 y2[1] (numeric) = 1.7120608213680994541463502138629 absolute error = 0.0407321703939817047211185035549 relative error = 2.437113153672160943188579971387 % h = 0.001 y1[1] (analytic) = 1.671328650974117749425231710308 y1[1] (numeric) = 1.6996220958420624731672114111343 absolute error = 0.0282934448679447237419797008263 relative error = 1.6928714081131896399074035194633 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.737 y2[1] (analytic) = 1.672069474981736717005366404475 y2[1] (numeric) = 1.7129907105081517710446739891216 absolute error = 0.0409212355264150540393075846466 relative error = 2.4473406242202955581945283446463 % h = 0.001 y1[1] (analytic) = 1.672069474981736717005366404475 y1[1] (numeric) = 1.7004420538037838803250226642997 absolute error = 0.0283725788220471633196562598247 relative error = 1.6968540629782781351943477669603 % h = 0.001 TOP MAIN SOLVE Loop memory used=1834.9MB, alloc=4.6MB, time=103.58 NO POLE NO POLE x[1] = 0.738 y2[1] (analytic) = 1.6728096269199367086364990450493 y2[1] (numeric) = 1.7139204960218761713217909609395 absolute error = 0.0411108691019394626852919158902 relative error = 2.4575940047424830688065391906221 % h = 0.001 y1[1] (analytic) = 1.6728096269199367086364990450493 y1[1] (numeric) = 1.7012614196139907953718796975213 absolute error = 0.028451792694054086735380652472 relative error = 1.7008386511046683580711854997618 % h = 0.001 TOP MAIN SOLVE Loop memory used=1838.7MB, alloc=4.6MB, time=103.79 NO POLE NO POLE x[1] = 0.739 y2[1] (analytic) = 1.6735491060485658477979641282533 y2[1] (numeric) = 1.7148501779057399433862859144921 absolute error = 0.0413010718571740955883217862388 relative error = 2.4678733183211148623863198917751 % h = 0.001 y1[1] (analytic) = 1.6735491060485658477979641282533 y1[1] (numeric) = 1.7020801923601615322513096315681 absolute error = 0.0285310863115956844533455033148 relative error = 1.7048251651820799131305432901461 % h = 0.001 TOP MAIN SOLVE Loop memory used=1842.5MB, alloc=4.6MB, time=104.01 NO POLE NO POLE x[1] = 0.74 y2[1] (analytic) = 1.6742879116281450674838811576082 y2[1] (numeric) = 1.7157797561562139965448162837034 absolute error = 0.0414918445280689290609351260952 relative error = 2.4781785880375010661315031019673 % h = 0.001 y1[1] (analytic) = 1.6742879116281450674838811576082 y1[1] (numeric) = 1.7028983711302448500783876562124 absolute error = 0.0286104595020997825945064986042 relative error = 1.7088135979120710659379527818279 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.741 y2[1] (analytic) = 1.6750260429198688496821600265609 y2[1] (numeric) = 1.7167092307697728650841228389939 absolute error = 0.041683187849904015401962812433 relative error = 2.4885098369720145873637077477298 % h = 0.001 y1[1] (analytic) = 1.6750260429198688496821600265609 y1[1] (numeric) = 1.7037159550126609421460137989572 absolute error = 0.0286899120927920924638537723963 relative error = 1.7128039420079978998436437922155 % h = 0.001 TOP MAIN SOLVE Loop memory used=1846.3MB, alloc=4.6MB, time=104.23 NO POLE NO POLE x[1] = 0.742 y2[1] (analytic) = 1.6757634991856059641799574634498 y2[1] (numeric) = 1.7176386017428947123499529431037 absolute error = 0.0418751025572887481699954796539 relative error = 2.4988670882042348278501548556483 % h = 0.001 y1[1] (analytic) = 1.6757634991856059641799574634498 y1[1] (numeric) = 1.7045329430963024245945849863118 absolute error = 0.028769443910696460414627522862 relative error = 1.7167961901949735863539874000457 % h = 0.001 TOP MAIN SOLVE Loop memory used=1850.1MB, alloc=4.6MB, time=104.44 NO POLE NO POLE x[1] = 0.743 y2[1] (analytic) = 1.676500279687900206694845733414 y2[1] (numeric) = 1.7185678690720613348228918125408 absolute error = 0.0420675893841611281280460791268 relative error = 2.5092503648130910738730425832563 % h = 0.001 y1[1] (analytic) = 1.676500279687900206694845733414 y1[1] (numeric) = 1.7053493344705353247440148745009 absolute error = 0.0288490547826351180491691410869 relative error = 1.7207903352098277686284719734934 % h = 0.001 TOP MAIN SOLVE Loop memory used=1853.9MB, alloc=4.6MB, time=104.66 NO POLE NO POLE x[1] = 0.744 y2[1] (analytic) = 1.6772363836899711363309554661397 y2[1] (numeric) = 1.7194970327537581661910972246833 absolute error = 0.0422606490637870298601417585436 relative error = 2.5196596898770055637544773425544 % h = 0.001 y1[1] (analytic) = 1.6772363836899711363309554661397 y1[1] (numeric) = 1.7061651282252000690870541195135 absolute error = 0.0289287445352289327560986533738 relative error = 1.7247863698010660576697495945923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.745 y2[1] (analytic) = 1.6779718104557148123593551533613 y2[1] (numeric) = 1.7204260927844742814199331130491 absolute error = 0.0424542823287594690605779596878 relative error = 2.5300950864740362345383824388907 % h = 0.001 y1[1] (analytic) = 1.6779718104557148123593551533613 y1[1] (numeric) = 1.7069803234506124709428639505049 absolute error = 0.0290085129948976585835087971436 relative error = 1.7287842867288296407759373961996 % h = 0.001 TOP MAIN SOLVE Loop memory used=1857.7MB, alloc=4.6MB, time=104.88 NO POLE NO POLE x[1] = 0.746 y2[1] (analytic) = 1.6787065592497045303219305358001 y2[1] (numeric) = 1.7213550491607024008184974957399 absolute error = 0.0426484899109978704965669599398 relative error = 2.5405565776820191495244620489467 % h = 0.001 y1[1] (analytic) = 1.6787065592497045303219305358001 y1[1] (numeric) = 1.7077949192375647177697961057606 absolute error = 0.0290883599878601874478655699605 relative error = 1.7327840787648550018259979827709 % h = 0.001 TOP MAIN SOLVE Loop memory used=1861.6MB, alloc=4.6MB, time=105.10 NO POLE NO POLE x[1] = 0.747 y2[1] (analytic) = 1.6794406293371915574580277757215 y2[1] (numeric) = 1.7222839018789388941030401845572 absolute error = 0.0428432725417473366450124088357 relative error = 2.5510441865787106083429864765672 % h = 0.001 y1[1] (analytic) = 1.6794406293371915574580277757215 y1[1] (numeric) = 1.70860891467732635813633238671 absolute error = 0.0291682853401348006783046109885 relative error = 1.7367857386924337529706553912174 % h = 0.001 TOP MAIN SOLVE Loop memory used=1865.4MB, alloc=4.6MB, time=105.31 NO POLE NO POLE x[1] = 0.748 y2[1] (analytic) = 1.6801740199841058674531249885306 y2[1] (numeric) = 1.7232126509356837844572657247926 absolute error = 0.043038630951577917004140736262 relative error = 2.5615579362419289412528843021205 % h = 0.001 y1[1] (analytic) = 1.6801740199841058674531249885306 y1[1] (numeric) = 1.709422308861645288349137282846 absolute error = 0.0292482888775394208960122943154 relative error = 1.7407892593063725773029279978236 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.749 y2[1] (analytic) = 1.6809067304570568745087973847929 y2[1] (numeric) = 1.7241412963274407525895170181962 absolute error = 0.0432345658703838780807196334033 relative error = 2.5720978497496959893393781281417 % h = 0.001 y1[1] (analytic) = 1.6809067304570568745087973847929 y1[1] (numeric) = 1.7102351008827487387371773188593 absolute error = 0.0293283704256918642283799340664 relative error = 1.7447946334129532820839774268388 % h = 0.001 TOP MAIN SOLVE Loop memory used=1869.2MB, alloc=4.6MB, time=105.53 NO POLE NO POLE x[1] = 0.75 y2[1] (analytic) = 1.6816387600233341667332419527799 y2[1] (numeric) = 1.7250698380507171407868350841392 absolute error = 0.0434310780273829740535931313593 relative error = 2.5826639501803782722811829701031 % h = 0.001 y1[1] (analytic) = 1.6816387600233341667332419527799 y1[1] (numeric) = 1.7110472898333442595908609748349 absolute error = 0.029408529810010092857619022055 relative error = 1.7488018538298929621015828994289 % h = 0.001 TOP MAIN SOLVE Loop memory used=1873.0MB, alloc=4.6MB, time=105.75 NO POLE NO POLE x[1] = 0.751 y2[1] (analytic) = 1.6823701079509082388516282910726 y2[1] (numeric) = 1.7259982761020239569658904165016 absolute error = 0.043628168151115718114262125429 relative error = 2.5932562606128278453510997974127 % h = 0.001 y1[1] (analytic) = 1.6823701079509082388516282910726 y1[1] (numeric) = 1.7118588748066207067551532309859 absolute error = 0.0294887668557124679035249399133 relative error = 1.752810913386304272740153614288 % h = 0.001 TOP MAIN SOLVE Loop memory used=1876.8MB, alloc=4.6MB, time=105.96 NO POLE NO POLE x[1] = 0.752 y2[1] (analytic) = 1.6831007735084312242355428809353 y2[1] (numeric) = 1.7269266104778758787207813963345 absolute error = 0.0438258369694446544852385153992 relative error = 2.6038748041265228473076811455071 % h = 0.001 y1[1] (analytic) = 1.6831007735084312242355428809353 y1[1] (numeric) = 1.7126698548962492268756189901101 absolute error = 0.0295690813878180026400761091748 relative error = 1.756821804922655812342787705593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.753 y2[1] (analytic) = 1.6838307559652376262507947690758 y2[1] (numeric) = 1.7278548411747912573676952228735 absolute error = 0.0440240852095536311169004537977 relative error = 2.6145196038017077408295209484912 % h = 0.001 y1[1] (analytic) = 1.6838307559652376262507947690758 y1[1] (numeric) = 1.7134802291963842422963498337534 absolute error = 0.0296494732311466160455550646776 relative error = 1.7608345212907326134474751157561 % h = 0.001 TOP MAIN SOLVE Loop memory used=1880.6MB, alloc=4.6MB, time=106.18 NO POLE NO POLE x[1] = 0.754 y2[1] (analytic) = 1.6845600545913450489228513130465 y2[1] (numeric) = 1.728782968189292121986426828008 absolute error = 0.0442229135979470730635755149615 relative error = 2.6251906827195332471376266346149 % h = 0.001 y1[1] (analytic) = 1.6845600545913450489228513130465 y1[1] (numeric) = 1.7142899968016644356087287719486 absolute error = 0.0297299422103193866858774589021 relative error = 1.764849055353596742481123382671 % h = 0.001 TOP MAIN SOLVE Loop memory used=1884.4MB, alloc=4.6MB, time=106.39 NO POLE NO POLE x[1] = 0.755 y2[1] (analytic) = 1.6852886686574549269191733239135 y2[1] (numeric) = 1.7297109915179041834587512418468 absolute error = 0.0444223228604492565395779179333 relative error = 2.6358880639621959764452679376959 % h = 0.001 y1[1] (analytic) = 1.6852886686574549269191733239135 y1[1] (numeric) = 1.7150991568072137338499878513673 absolute error = 0.0298104881497588069308145274538 relative error = 1.7688653999855480074966599073943 % h = 0.001 TOP MAIN SOLVE Loop memory used=1888.3MB, alloc=4.6MB, time=106.61 NO POLE NO POLE x[1] = 0.756 y2[1] (analytic) = 1.6860165974349532548477196239165 y2[1] (numeric) = 1.7306389111571568385036448795595 absolute error = 0.044622313722203583655925255643 relative error = 2.6466117706130777558686636609621 % h = 0.001 y1[1] (analytic) = 1.6860165974349532548477196239165 y1[1] (numeric) = 1.7159077083086422923505136927803 absolute error = 0.0298911108736890375027940688638 relative error = 1.7728835480720847735400317728577 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.757 y2[1] (analytic) = 1.686743840195911315870891720679 y2[1] (numeric) = 1.7315667271035831737093512222196 absolute error = 0.0448228869076718578384595015406 relative error = 2.6573618257568846564258646397761 % h = 0.001 y1[1] (analytic) = 1.686743840195911315870891720679 y1[1] (numeric) = 1.7167156504020474782288562358624 absolute error = 0.0299718102061361623579645151834 relative error = 1.7769034925098648852354846590866 % h = 0.001 TOP MAIN SOLVE Loop memory used=1892.1MB, alloc=4.6MB, time=106.83 NO POLE NO POLE x[1] = 0.758 y2[1] (analytic) = 1.6874703962130864096341899840818 y2[1] (numeric) = 1.7324944393537199695622863669223 absolute error = 0.0450240431406335599280963828405 relative error = 2.6681382524797857207452182431405 % h = 0.001 y1[1] (analytic) = 1.6874703962130864096341899840818 y1[1] (numeric) = 1.7175229821840148535333961776064 absolute error = 0.0300525859709284438992061935246 relative error = 1.7809252262066666961790558804283 % h = 0.001 TOP MAIN SOLVE Loop memory used=1895.9MB, alloc=4.6MB, time=107.04 NO POLE NO POLE x[1] = 0.759 y2[1] (analytic) = 1.6881962647599225795088533972068 y2[1] (numeric) = 1.733422047904107704472779924007 absolute error = 0.0452257831441851249639265268002 relative error = 2.678941073869551393098856786386 % h = 0.001 y1[1] (analytic) = 1.6881962647599225795088533972068 y1[1] (numeric) = 1.7183297027516191580296267999246 absolute error = 0.0301334379916965785207734027178 relative error = 1.7849487420813502047317630867296 % h = 0.001 TOP MAIN SOLVE Loop memory used=1899.7MB, alloc=4.6MB, time=107.26 NO POLE NO POLE x[1] = 0.76 y2[1] (analytic) = 1.6889214451105513391477556387697 y2[1] (numeric) = 1.7343495527512905587976467417723 absolute error = 0.0454281076407392196498911030026 relative error = 2.6897703130156916533707390572125 % h = 0.001 y1[1] (analytic) = 1.6889214451105513391477556387697 y1[1] (numeric) = 1.7191358112024252916320060924148 absolute error = 0.0302143660918739524842504536451 relative error = 1.788974033063818295805509757417 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.761 y2[1] (analytic) = 1.6896459365397923983538309412086 y2[1] (numeric) = 1.7352769538918164188595849416374 absolute error = 0.0456310173520240205057540004288 relative error = 2.7006259930095938565628906416527 % h = 0.001 y1[1] (analytic) = 1.6896459365397923983538309412086 y1[1] (numeric) = 1.7199413066344892964793352877551 absolute error = 0.0302953700946968981255043465465 relative error = 1.7930010920949780882362613066644 % h = 0.001 TOP MAIN SOLVE Loop memory used=1903.5MB, alloc=4.6MB, time=107.47 NO POLE NO POLE x[1] = 0.762 y2[1] (analytic) = 1.6903697383231543882603038560603 y2[1] (numeric) = 1.7362042513222368809633957492713 absolute error = 0.045834512999082492703091893211 relative error = 2.7115081369446602794376347352977 % h = 0.001 y1[1] (analytic) = 1.6903697383231543882603038560603 y1[1] (numeric) = 1.7207461881463593386526201397594 absolute error = 0.0303764498232049503923162836991 relative error = 1.7970299121267023873405714424169 % h = 0.001 TOP MAIN SOLVE Loop memory used=1907.3MB, alloc=4.6MB, time=107.69 NO POLE NO POLE x[1] = 0.763 y2[1] (analytic) = 1.6910928497368355858219977464571 y2[1] (numeric) = 1.7371314450391072554090206097869 absolute error = 0.0460385953022716695870228633298 relative error = 2.7224167679164453758877804971268 % h = 0.001 y1[1] (analytic) = 1.6910928497368355858219977464571 y1[1] (numeric) = 1.7215504548370766895343714877852 absolute error = 0.0304576051002411037123737413281 relative error = 1.8010604861217912422530574137337 % h = 0.001 TOP MAIN SOLVE Loop memory used=1911.2MB, alloc=4.6MB, time=107.90 NO POLE NO POLE x[1] = 0.764 y2[1] (analytic) = 1.6918152700577246376169975154955 y2[1] (numeric) = 1.7380585350389865705013910776767 absolute error = 0.0462432649812619328843935621812 relative error = 2.7333519090227927426209406098362 % h = 0.001 y1[1] (analytic) = 1.6918152700577246376169975154955 y1[1] (numeric) = 1.7223541058061767068083018659242 absolute error = 0.0305388357484520691913043504287 relative error = 1.8050928070539336076439349721412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.765 y2[1] (analytic) = 1.6925369985634012829579427688738 y2[1] (numeric) = 1.7389855213184375765570869747491 absolute error = 0.0464485227550362935991442058753 relative error = 2.7443135833639717967383834122426 % h = 0.001 y1[1] (analytic) = 1.6925369985634012829579427688738 y1[1] (numeric) = 1.7231571401536898150983751312361 absolute error = 0.0306201415902885321404323623623 relative error = 1.8091268679076691094172292954893 % h = 0.001 TOP MAIN SOLVE Loop memory used=1915.0MB, alloc=4.6MB, time=108.12 NO POLE NO POLE x[1] = 0.766 y2[1] (analytic) = 1.6932580345321370763122283005656 y2[1] (numeric) = 1.7399124038740267499077983119152 absolute error = 0.0466543693418896735955700113496 relative error = 2.7553018140428141667830876286235 % h = 0.001 y1[1] (analytic) = 1.6932580345321370763122283005656 y1[1] (numeric) = 1.7239595569801424862461663021965 absolute error = 0.0307015224480054099339380016309 relative error = 1.8131626616783499139917768084535 % h = 0.001 TOP MAIN SOLVE Loop memory used=1918.8MB, alloc=4.6MB, time=108.33 NO POLE NO POLE x[1] = 0.767 y2[1] (analytic) = 1.6939783772428961090303894813906 y2[1] (numeric) = 1.7408391827023242969005864732698 absolute error = 0.0468608054594281878701969918792 relative error = 2.7663166241648497988259591991505 % h = 0.001 y1[1] (analytic) = 1.6939783772428961090303894813906 y1[1] (numeric) = 1.7247613553865582192254890165295 absolute error = 0.0307829781436621101950995351389 relative error = 1.8172001813721027007686248144064 % h = 0.001 TOP MAIN SOLVE Loop memory used=1922.6MB, alloc=4.6MB, time=108.55 NO POLE NO POLE x[1] = 0.768 y2[1] (analytic) = 1.6946980259753357303819508221551 y2[1] (numeric) = 1.7417658577999041578949401635077 absolute error = 0.0470678318245684275129893413526 relative error = 2.7773580368384427791534898788836 % h = 0.001 y1[1] (analytic) = 1.6946980259753357303819508221551 y1[1] (numeric) = 1.7255625344744585196932482366772 absolute error = 0.0308645084991227893112974145221 relative error = 1.8212394200057907373899211603307 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.769 y2[1] (analytic) = 1.6954169800098072678980166755753 y2[1] (numeric) = 1.742692429163344011256621622323 absolute error = 0.0472754491535367433586049467477 relative error = 2.7884260751749268751144859839048 % h = 0.001 y1[1] (analytic) = 1.6954169800098072678980166755753 y1[1] (numeric) = 1.7263630933458638791754760513286 absolute error = 0.0309461133360566112774593757533 relative error = 1.825280370606976057395864820622 % h = 0.001 TOP MAIN SOLVE Loop memory used=1926.4MB, alloc=4.6MB, time=108.77 NO POLE NO POLE x[1] = 0.77 y2[1] (analytic) = 1.6961352386273567470198837344522 y2[1] (numeric) = 1.743618896789225277348298612045 absolute error = 0.0474836581618685303284148775928 relative error = 2.7995207622887407956778727873741 % h = 0.001 y1[1] (analytic) = 1.6961352386273567470198837344522 y1[1] (numeric) = 1.7271630311032947538875086426826 absolute error = 0.0310277924759380068676249082304 relative error = 1.8293230262138817398877603385897 % h = 0.001 TOP MAIN SOLVE Loop memory used=1930.2MB, alloc=4.6MB, time=108.98 NO POLE NO POLE x[1] = 0.771 y2[1] (analytic) = 1.696852801109725610052955677546 y2[1] (numeric) = 1.7445452606741331225169576873796 absolute error = 0.0476924595644075124640020098336 relative error = 2.8106421212975631732479854714217 % h = 0.001 y1[1] (analytic) = 1.696852801109725610052955677546 y1[1] (numeric) = 1.727962346849772543187262711458 absolute error = 0.031109545740046933134307033912 relative error = 1.8333673798753542908066845368534 % h = 0.001 TOP MAIN SOLVE Loop memory used=1934.0MB, alloc=4.6MB, time=109.20 NO POLE NO POLE x[1] = 0.772 y2[1] (analytic) = 1.6975696667393514344252410092942 y2[1] (numeric) = 1.7454715208146564630780942587445 absolute error = 0.0479018540753050286528532494503 relative error = 2.8217901753224472682781910893715 % h = 0.001 y1[1] (analytic) = 1.6975696667393514344252410092942 y1[1] (numeric) = 1.7287610396888205676605698750889 absolute error = 0.0311913729494691332353288657947 relative error = 1.837413424650826125438732830864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1937.9MB, alloc=4.6MB, time=109.41 x[1] = 0.773 y2[1] (analytic) = 1.6982858347993686502497158349369 y2[1] (numeric) = 1.7463976772073879692966749633071 absolute error = 0.0481118424080193190469591283702 relative error = 2.8329649474879553982181475535273 % h = 0.001 y1[1] (analytic) = 1.6982858347993686502497158349369 y1[1] (numeric) = 1.72955910872446504683752777905 absolute error = 0.0312732739250963965878119441131 relative error = 1.8414611536102781517592648832847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.774 y2[1] (analytic) = 1.6990013045736092571898340087447 y2[1] (numeric) = 1.747323729848924069364867860466 absolute error = 0.0483224252753148121750338517213 relative error = 2.8441664609222930923244951057974 % h = 0.001 y1[1] (analytic) = 1.6990013045736092571898340087447 y1[1] (numeric) = 1.7303565530612360765388268868512 absolute error = 0.0313552484876268193489928781065 relative error = 1.8455105598342024542300152525001 % h = 0.001 TOP MAIN SOLVE Loop memory used=1941.7MB, alloc=4.6MB, time=109.63 NO POLE NO POLE x[1] = 0.775 y2[1] (analytic) = 1.6997160753466035406274677899009 y2[1] (numeric) = 1.7482496787358649533765359711476 absolute error = 0.0485336033892614127490681812467 relative error = 2.8553947387574429738592929190009 % h = 0.001 y1[1] (analytic) = 1.6997160753466035406274677899009 y1[1] (numeric) = 1.7311533718041686058510121409179 absolute error = 0.031437296457565065223544351017 relative error = 1.8495616364135650776643741452379 % h = 0.001 TOP MAIN SOLVE Loop memory used=1945.5MB, alloc=4.6MB, time=109.84 NO POLE NO POLE x[1] = 0.776 y2[1] (analytic) = 1.7004301464035807871325628381541 y2[1] (numeric) = 1.7491755238648145772984896829289 absolute error = 0.0487453774612337901659268447748 relative error = 2.8666498041292983711950582867672 % h = 0.001 y1[1] (analytic) = 1.7004301464035807871325628381541 y1[1] (numeric) = 1.7319495640588034137296389143371 absolute error = 0.031519417655222626597076076183 relative error = 1.8536143764497689107775764125596 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1949.3MB, alloc=4.6MB, time=110.06 x[1] = 0.777 y2[1] (analytic) = 1.7011435170304699992337920796493 y2[1] (numeric) = 1.7501012652323806669384935456406 absolute error = 0.0489577482019106677047014659913 relative error = 2.8779316801777966593398381581113 % h = 0.001 y1[1] (analytic) = 1.7011435170304699992337920796493 y1[1] (numeric) = 1.7327451289311880852292829022953 absolute error = 0.031601611900718085995490822646 relative error = 1.8576687730546166690399635588165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.778 y2[1] (analytic) = 1.7018561865139006094894936723398 y2[1] (numeric) = 1.7510269028351747219100229847518 absolute error = 0.049170716321274112420529312412 relative error = 2.8892403900470523333903424314487 % h = 0.001 y1[1] (analytic) = 1.7018561865139006094894936723398 y1[1] (numeric) = 1.7335400655278779873593638319674 absolute error = 0.0316838790139773778698701596276 relative error = 1.8617248193502739764529037962048 % h = 0.001 TOP MAIN SOLVE Loop memory used=1953.1MB, alloc=4.6MB, time=110.27 NO POLE NO POLE x[1] = 0.779 y2[1] (analytic) = 1.7025681541412031938581790001042 y2[1] (numeric) = 1.7519524366698120195937664624919 absolute error = 0.0493842825286088257355874623877 relative error = 2.9005759568854898154157953121553 % h = 0.001 y1[1] (analytic) = 1.7025681541412031938581790001042 y1[1] (numeric) = 1.7343343729559372445647431006307 absolute error = 0.0317662188147340507065641005265 relative error = 1.8657825084692325458683691010609 % h = 0.001 TOP MAIN SOLVE Loop memory used=1956.9MB, alloc=4.6MB, time=110.49 NO POLE NO POLE x[1] = 0.78 y2[1] (analytic) = 1.7032794192004101843678973251179 y2[1] (numeric) = 1.7528778667329116190958686193222 absolute error = 0.0495984475325014347279712942043 relative error = 2.9119384038459759962698150312559 % h = 0.001 y1[1] (analytic) = 1.7032794192004101843678973251179 y1[1] (numeric) = 1.7351280503229397138300556838803 absolute error = 0.0318486311225295294621583587624 relative error = 1.8698418335542734574745758433209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1960.7MB, alloc=4.6MB, time=110.71 x[1] = 0.781 y2[1] (analytic) = 1.7039899809802565810837444291757 y2[1] (numeric) = 1.7538031930210963652029099310323 absolute error = 0.0498132120408397841191655018566 relative error = 2.9233277540859525138223131924008 % h = 0.001 y1[1] (analytic) = 1.7039899809802565810837444291757 y1[1] (numeric) = 1.7359210967369699594067368890046 absolute error = 0.0319311157567133783229924598289 relative error = 1.8739027877584305350714968954003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.782 y2[1] (analytic) = 1.7046998387701806633728032765141 y2[1] (numeric) = 1.7547284155309928923336184194049 absolute error = 0.0500285767608122289608151428908 relative error = 2.9347440307675677690981128346762 % h = 0.001 y1[1] (analytic) = 1.7046998387701806633728032765141 y1[1] (numeric) = 1.7367135113066242271617047628521 absolute error = 0.032013672536443563788901486338 relative error = 1.8779653642449538197614482119293 % h = 0.001 TOP MAIN SOLVE Loop memory used=1964.6MB, alloc=4.6MB, time=110.93 NO POLE NO POLE x[1] = 0.783 y2[1] (analytic) = 1.705408991860324700465805433254 y2[1] (numeric) = 1.7556535342592316284873089570643 absolute error = 0.0502445423989069280215035238103 relative error = 2.9461872570578086818037188432288 % h = 0.001 y1[1] (analytic) = 1.705408991860324700465805433254 y1[1] (numeric) = 1.7375052931410114185466591988698 absolute error = 0.0320963012806867180808537656158 relative error = 1.8820295561872731406813417346342 % h = 0.001 TOP MAIN SOLVE Loop memory used=1968.4MB, alloc=4.6MB, time=111.14 NO POLE NO POLE x[1] = 0.784 y2[1] (analytic) = 1.70611743954153566131480268186 y2[1] (numeric) = 1.7565785492024467991890457098016 absolute error = 0.0504611096609111378742430279416 relative error = 2.9576574561286321867184354843741 % h = 0.001 y1[1] (analytic) = 1.70611743954153566131480268186 y1[1] (numeric) = 1.7382964413497540641869590244347 absolute error = 0.0321790018082184028721563425747 relative error = 1.8860953567689617824045791479641 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=1972.2MB, alloc=4.6MB, time=111.36 x[1] = 0.785 y2[1] (analytic) = 1.7068251811053659237461389730047 y2[1] (numeric) = 1.7575034603572764314315232623522 absolute error = 0.0506782792519105076853842893475 relative error = 2.9691546511570964724208134616376 % h = 0.001 y1[1] (analytic) = 1.7068251811053659237461389730047 y1[1] (numeric) = 1.739086955042989297089038587118 absolute error = 0.0322617739376233733428996141133 relative error = 1.890162759183700248641937517869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.786 y2[1] (analytic) = 1.707532215844073982908013561925 y2[1] (numeric) = 1.7584282677203623576136619762877 absolute error = 0.0508960518762883747056484143627 relative error = 2.9806788653254919638162228610158 % h = 0.001 y1[1] (analytic) = 1.707532215844073982908013561925 y1[1] (numeric) = 1.7398768333313698254653255971281 absolute error = 0.0323446174872958425573120352031 relative error = 1.8942317566352401218721682183088 % h = 0.001 TOP MAIN SOLVE Loop memory used=1976.0MB, alloc=4.6MB, time=111.57 NO POLE NO POLE x[1] = 0.787 y2[1] (analytic) = 1.7082385430506251590119268817658 y2[1] (numeric) = 1.7593529712883502194759131313766 absolute error = 0.0511144282377250604639862496108 relative error = 2.9922301218214720499261885546036 % h = 0.001 y1[1] (analytic) = 1.7082385430506251590119268817658 y1[1] (numeric) = 1.7406660753260649051756222228669 absolute error = 0.0324275322754397461636953411011 relative error = 1.8983023423373680185343948154537 % h = 0.001 TOP MAIN SOLVE Loop memory used=1979.8MB, alloc=4.6MB, time=111.79 NO POLE NO POLE x[1] = 0.788 y2[1] (analytic) = 1.7089441620186923043673014125252 y2[1] (numeric) = 1.7602775710578894720322694044658 absolute error = 0.0513334090391971676649679919406 relative error = 3.0038084438381835583949909393247 % h = 0.001 y1[1] (analytic) = 1.7089441620186923043673014125252 y1[1] (numeric) = 1.7414546801387613117839116773063 absolute error = 0.0325105181200690074166102647811 relative error = 1.9023745095138696394157537665045 % h = 0.001 TOP MAIN SOLVE Loop memory used=1983.6MB, alloc=4.6MB, time=112.00 NO POLE NO POLE x[1] = 0.789 y2[1] (analytic) = 1.7096490720426565097085705110381 y2[1] (numeric) = 1.7612020670256333874989762426362 absolute error = 0.0515529949829768777904057315981 relative error = 3.0154138545743969781639271804981 % h = 0.001 y1[1] (analytic) = 1.7096490720426565097085705110381 y1[1] (numeric) = 1.7422426468816643122295527747479 absolute error = 0.0325935748390078025209822637098 relative error = 1.9064482513984939148690739270923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.79 y2[1] (analytic) = 1.7103532724176078098140288749692 y2[1] (numeric) = 1.7621264591882390592199396900911 absolute error = 0.0517731867706312494059108151219 relative error = 3.0270463772346364317585462870806 % h = 0.001 y1[1] (analytic) = 1.7103532724176078098140288749692 y1[1] (numeric) = 1.7430299746674986361118251804689 absolute error = 0.0326767022498908262977963054997 relative error = 1.9105235612349172444967369758949 % h = 0.001 TOP MAIN SOLVE Loop memory used=1987.4MB, alloc=4.6MB, time=112.22 NO POLE NO POLE x[1] = 0.791 y2[1] (analytic) = 1.711056762439345888415739022023 y2[1] (numeric) = 1.763050747542367405588826230951 absolute error = 0.051993985103021517173087208928 relative error = 3.0387060350293093986291152472089 % h = 0.001 y1[1] (analytic) = 1.711056762439345888415739022023 y1[1] (numeric) = 1.7438166626095094465867883197784 absolute error = 0.0327599001701635581710492977554 relative error = 1.9146004322767078309382009856201 % h = 0.001 TOP MAIN SOLVE Loop memory used=1991.3MB, alloc=4.6MB, time=112.45 NO POLE NO POLE x[1] = 0.792 y2[1] (analytic) = 1.7117595414043807823997888745235 y2[1] (numeric) = 1.7639749320846831739678502128408 absolute error = 0.0522153906803023915680613383173 relative error = 3.0503928511748361909795429785042 % h = 0.001 y1[1] (analytic) = 1.7117595414043807823997888745235 y1[1] (numeric) = 1.7446027098214633108754171581173 absolute error = 0.0328431684170825284756282835938 relative error = 1.9186788577872901074000035236035 % h = 0.001 TOP MAIN SOLVE Loop memory used=1995.1MB, alloc=4.6MB, time=112.66 NO POLE NO POLE x[1] = 0.793 y2[1] (analytic) = 1.7124616086099335852961962491652 y2[1] (numeric) = 1.76489901281185494460324441888 absolute error = 0.0524374042019213593070481697148 relative error = 3.0621068488937791835149838796824 % h = 0.001 y1[1] (analytic) = 1.7124616086099335852961962491652 y1[1] (numeric) = 1.7453881154176491703819783100219 absolute error = 0.0329265068077155850857820608567 relative error = 1.9227588310399092585683888801748 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.794 y2[1] (analytic) = 1.7131629633539371500577567620875 y2[1] (numeric) = 1.7658229897205551345374093584108 absolute error = 0.0526600263666179844796525963233 relative error = 3.0738480514149717985333631894703 % h = 0.001 y1[1] (analytic) = 1.7131629633539371500577567620875 y1[1] (numeric) = 1.7461728785128793104216101820454 absolute error = 0.0330099151589421603638534199579 relative error = 1.926840345317595834546026326775 % h = 0.001 TOP MAIN SOLVE Loop memory used=1998.9MB, alloc=4.6MB, time=112.87 NO POLE NO POLE x[1] = 0.795 y2[1] (analytic) = 1.713863604935036791127132370486 y2[1] (numeric) = 1.7667468628074600015177368495307 absolute error = 0.0528832578724232103906044790447 relative error = 3.0856164819736472477811120479193 % h = 0.001 y1[1] (analytic) = 1.713863604935036791127132370486 y1[1] (numeric) = 1.7469569982224903295560711030868 absolute error = 0.0330933932874535384289387326008 relative error = 1.9309233939131304574556027248953 % h = 0.001 TOP MAIN SOLVE Loop memory used=2002.7MB, alloc=4.6MB, time=113.09 NO POLE NO POLE x[1] = 0.796 y2[1] (analytic) = 1.7145635326525909857914784837286 y2[1] (numeric) = 1.7676706320692496479021034692318 absolute error = 0.0531070994166586621106249855032 relative error = 3.0974121638115670324884709978182 % h = 0.001 y1[1] (analytic) = 1.7145635326525909857914784837286 y1[1] (numeric) = 1.7477404736623441085366196450147 absolute error = 0.0331769410097531227451411612861 relative error = 1.9350079701290086203543833695507 % h = 0.001 TOP MAIN SOLVE Loop memory used=2006.5MB, alloc=4.6MB, time=113.30 NO POLE NO POLE x[1] = 0.797 y2[1] (analytic) = 1.7152627458066720748239082894086 y2[1] (numeric) = 1.7685942975026080245610294496904 absolute error = 0.0533315516959359497371211602818 relative error = 3.1092351201771492029948165427906 % h = 0.001 y1[1] (analytic) = 1.7152627458066720748239082894086 y1[1] (numeric) = 1.7485233039488287788529915869957 absolute error = 0.0332605581421567040290832975871 relative error = 1.9390940672774055781051396832547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.798 y2[1] (analytic) = 1.7159612436980669624110936529281 y2[1] (numeric) = 1.7695178591042229347764986019953 absolute error = 0.0535566154061559723654049490672 relative error = 3.1210853743255963793695861787616 % h = 0.001 y1[1] (analytic) = 1.7159612436980669624110936529281 y1[1] (numeric) = 1.7493054881988596908874382285408 absolute error = 0.0333442445007927284763445756127 relative error = 1.943181678680141329850141305796 % h = 0.001 TOP MAIN SOLVE Loop memory used=2010.3MB, alloc=4.6MB, time=113.52 NO POLE NO POLE x[1] = 0.799 y2[1] (analytic) = 1.7166590256282778153663026630705 y2[1] (numeric) = 1.7704413168707860381374348513544 absolute error = 0.0537822912425082227711321882839 relative error = 3.1329629495190235344295229214404 % h = 0.001 y1[1] (analytic) = 1.7166590256282778153663026630705 y1[1] (numeric) = 1.7500870255298803816727910089693 absolute error = 0.0334279999016025663064883458988 relative error = 1.9472707976686456927362032778368 % h = 0.001 TOP MAIN SOLVE Loop memory used=2014.2MB, alloc=4.6MB, time=113.73 NO POLE NO POLE x[1] = 0.8 y2[1] (analytic) = 1.7173560908995227616271746105814 y2[1] (numeric) = 1.771364670798992854431830970574 absolute error = 0.0540085798994700928046563599926 relative error = 3.1448678690265855405481306502583 % h = 0.001 y1[1] (analytic) = 1.7173560908995227616271746105814 y1[1] (numeric) = 1.7508679150598635422535176447609 absolute error = 0.0335118241603407806263430341795 relative error = 1.9513614175839234665400664197362 % h = 0.001 TOP MAIN SOLVE Loop memory used=2018.0MB, alloc=4.6MB, time=113.95 NO POLE NO POLE x[1] = 0.801 y2[1] (analytic) = 1.718052438814736588037533902042 y2[1] (numeric) = 1.7722879208855427675355251013654 absolute error = 0.0542354820708061794979911993234 relative error = 3.1568001561246044816484264645513 % h = 0.001 y1[1] (analytic) = 1.718052438814736588037533902042 y1[1] (numeric) = 1.7516481559073119846487352511158 absolute error = 0.0335957170925753966112013490738 relative error = 1.9554535317765196888446706865105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.802 y2[1] (analytic) = 1.7187480686775714374125451272789 y2[1] (numeric) = 1.7732110671271390292976206557995 absolute error = 0.0544629984495675918850755285206 relative error = 3.1687598340966967317652955880971 % h = 0.001 y1[1] (analytic) = 1.7187480686775714374125451272789 y1[1] (numeric) = 1.7524277471912596084161461699787 absolute error = 0.0336796785136881710036010426998 relative error = 1.9595471336064849804181572628458 % h = 0.001 TOP MAIN SOLVE Loop memory used=2021.8MB, alloc=4.6MB, time=114.16 NO POLE NO POLE x[1] = 0.803 y2[1] (analytic) = 1.7194429797923975048865122152131 y2[1] (numeric) = 1.7741341095204887634225451929981 absolute error = 0.054691129728091258536032977785 relative error = 3.180746926233899801558998050351 % h = 0.001 y1[1] (analytic) = 1.7194429797923975048865122152131 y1[1] (numeric) = 1.7532066880312723668158624837979 absolute error = 0.0337637082388748619293502685848 relative error = 1.9636422164433409804487054740339 % h = 0.001 TOP MAIN SOLVE Loop memory used=2025.6MB, alloc=4.6MB, time=114.38 NO POLE NO POLE x[1] = 0.804 y2[1] (analytic) = 1.7201371714643037335426253304078 y2[1] (numeric) = 1.7750570480623029693487438689272 absolute error = 0.0549198765979992358061185385194 relative error = 3.1927614558347989541566443053947 % h = 0.001 y1[1] (analytic) = 1.7201371714643037335426253304078 y1[1] (numeric) = 1.7539849775474492325730854523888 absolute error = 0.033847806083145499030460121981 relative error = 1.9677387736660458712895752559109 % h = 0.001 TOP MAIN SOLVE Loop memory used=2029.4MB, alloc=4.6MB, time=114.60 NO POLE NO POLE x[1] = 0.805 y2[1] (analytic) = 1.7208306429990985093239598806256 y2[1] (numeric) = 1.7759798827492965261240030599359 absolute error = 0.0551492397501980168000431793103 relative error = 3.204803446205653591693749011204 % h = 0.001 y1[1] (analytic) = 1.7208306429990985093239598806256 y1[1] (numeric) = 1.7547626148604231632386063694525 absolute error = 0.0339319718613246539146464888269 relative error = 1.9718367986629599923699849754759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.806 y2[1] (analytic) = 1.7215233937033103552250327244533 y2[1] (numeric) = 1.7769026135781881962773997634696 absolute error = 0.0553792198748778410523670390163 relative error = 3.216872920660523413923288271774 % h = 0.001 y1[1] (analytic) = 1.7215233937033103552250327244533 y1[1] (numeric) = 1.7555395990913620661460955955607 absolute error = 0.0340162053880517109210628711074 relative error = 1.9759362848318115429287078492043 % h = 0.001 TOP MAIN SOLVE Loop memory used=2033.2MB, alloc=4.6MB, time=114.81 NO POLE NO POLE x[1] = 0.807 y2[1] (analytic) = 1.7222154228841886247632213874979 y2[1] (numeric) = 1.7778252405457006296878723821756 absolute error = 0.0556098176615120049246509946777 relative error = 3.2289699025213943502550256325978 % h = 0.001 y1[1] (analytic) = 1.7222154228841886247632213874979 y1[1] (numeric) = 1.7563159293619697629651467857647 absolute error = 0.0341005064777811382019253982668 relative error = 1.9800372255796623732285180941238 % h = 0.001 TOP MAIN SOLVE Loop memory used=2037.0MB, alloc=4.6MB, time=115.03 NO POLE NO POLE x[1] = 0.808 y2[1] (analytic) = 1.7229067298497041947293528157898 y2[1] (numeric) = 1.7787477636485603674494085004122 absolute error = 0.0558410337988561727200556846224 relative error = 3.2410944151183042665832359070489 % h = 0.001 y1[1] (analytic) = 1.7229067298497041947293528157898 y1[1] (numeric) = 1.7570916047944869538490435924084 absolute error = 0.0341848749447827591196907766186 relative error = 1.9841396143228738639108602929692 % h = 0.001 TOP MAIN SOLVE Loop memory used=2040.9MB, alloc=4.6MB, time=115.25 NO POLE NO POLE x[1] = 0.809 y2[1] (analytic) = 1.7235973139085501572167689158648 y2[1] (numeric) = 1.779670182883497845732845264973 absolute error = 0.0560728689749476885160763491082 relative error = 3.2532464817894684482563433877387 % h = 0.001 y1[1] (analytic) = 1.7235973139085501572167689158648 y1[1] (numeric) = 1.7578666245116921811762163872363 absolute error = 0.0342693106031420239594474713715 relative error = 1.9882434444870728931513522843779 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.81 y2[1] (analytic) = 1.7242871743701425109281768525145 y2[1] (numeric) = 1.7805924982472473996442779846403 absolute error = 0.0563053238771048887161011321258 relative error = 3.2654261258814048605374020554741 % h = 0.001 y1[1] (analytic) = 1.7242871743701425109281768525145 y1[1] (numeric) = 1.7586409876369027928843568114732 absolute error = 0.0343538132667602819561799589587 relative error = 1.9923487095071178912779632277337 % h = 0.001 TOP MAIN SOLVE Loop memory used=2044.7MB, alloc=4.6MB, time=115.46 NO POLE NO POLE x[1] = 0.811 y2[1] (analytic) = 1.7249763105446208517595927974149 y2[1] (numeric) = 1.7815147097365472670800725659915 absolute error = 0.0565383991919264153204797685766 relative error = 3.2776333707490591878997799304901 % h = 0.001 y1[1] (analytic) = 1.7249763105446208517595927974149 y1[1] (numeric) = 1.7594146932939759053961582282233 absolute error = 0.0344383827493550536365654308084 relative error = 1.996455402827064982514934364451 % h = 0.001 TOP MAIN SOLVE Loop memory used=2048.5MB, alloc=4.6MB, time=115.68 NO POLE NO POLE x[1] = 0.812 y2[1] (analytic) = 1.7256647217428490626606885447446 y2[1] (numeric) = 1.7824368173481395925784774056947 absolute error = 0.0567720956052905299177888609501 relative error = 3.2898682397559296534978676099651 % h = 0.001 y1[1] (analytic) = 1.7256647217428490626606885447446 y1[1] (numeric) = 1.7601877406073093661356504182891 absolute error = 0.0345230188644603034749618735445 relative error = 2.0005635179001342135167304292097 % h = 0.001 TOP MAIN SOLVE Loop memory used=2052.3MB, alloc=4.6MB, time=115.89 NO POLE NO POLE x[1] = 0.813 y2[1] (analytic) = 1.7263524072764160027708511335054 y2[1] (numeric) = 1.7833588210787704311678303623485 absolute error = 0.0570064138023544283969792288431 relative error = 3.3021307562741916201481121950495 % h = 0.001 y1[1] (analytic) = 1.7263524072764160027708511335054 y1[1] (numeric) = 1.7609601287018427156340971283395 absolute error = 0.0346077214254267128632459948341 relative error = 2.004673048188675868357524679317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.814 y2[1] (analytic) = 1.7270393664576361958302663405423 y2[1] (numeric) = 1.7842807209251897522113564337442 absolute error = 0.0572413544675535563810900932019 relative error = 3.3144209436848219741511821246796 % h = 0.001 y1[1] (analytic) = 1.7270393664576361958302663405423 y1[1] (numeric) = 1.7617318567030581492244253492735 absolute error = 0.0346924902454219533941590087312 relative error = 2.0087839871641368696429301343874 % h = 0.001 TOP MAIN SOLVE Loop memory used=2056.1MB, alloc=4.6MB, time=116.11 NO POLE NO POLE x[1] = 0.815 y2[1] (analytic) = 1.7277255985995505178653376332361 y2[1] (numeric) = 1.7852025168841514432485517682564 absolute error = 0.0574769182846009253832141350203 relative error = 3.3267388253777232932815957963905 % h = 0.001 y1[1] (analytic) = 1.7277255985995505178653376332361 y1[1] (numeric) = 1.7625029237369814783231554726173 absolute error = 0.0347773251374309604578178393812 relative error = 2.0128963283070272654118938751305 % h = 0.001 TOP MAIN SOLVE Loop memory used=2059.9MB, alloc=4.6MB, time=116.33 NO POLE NO POLE x[1] = 0.816 y2[1] (analytic) = 1.7284111030159268841477528965088 y2[1] (numeric) = 1.7861242089524133138331496419004 absolute error = 0.0577131059364864296853967453916 relative error = 3.3390844247518478002666971614652 % h = 0.001 y1[1] (analytic) = 1.7284111030159268841477528965088 y1[1] (numeric) = 1.7632733289301830912988017438688 absolute error = 0.03486222591425620715104884736 relative error = 2.0170100651068868014978701643439 % h = 0.001 TOP MAIN SOLVE Loop memory used=2063.7MB, alloc=4.6MB, time=116.54 NO POLE NO POLE x[1] = 0.817 y2[1] (analytic) = 1.72909587902126093542651197513 y2[1] (numeric) = 1.7870457971267370993676640354327 absolute error = 0.0579499181054761639411520603027 relative error = 3.3514577652153211030724346294545 % h = 0.001 y1[1] (analytic) = 1.72909587902126093542651197513 y1[1] (numeric) = 1.764043071409778913925712703859 absolute error = 0.034947192388517978499200728729 relative error = 2.0211251910622515790195817498099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.818 y2[1] (analytic) = 1.7297799259307767234322287993561 y2[1] (numeric) = 1.7879672814038884649345064487138 absolute error = 0.0581873554731117415022776493577 relative error = 3.3638588701855657233089955008373 % h = 0.001 y1[1] (analytic) = 1.7297799259307767234322287993561 y1[1] (numeric) = 1.7648121503034313694223215824354 absolute error = 0.0350322243726546459900927830793 relative error = 2.0252416996806207966728670110669 % h = 0.001 TOP MAIN SOLVE Loop memory used=2067.6MB, alloc=4.6MB, time=116.76 NO POLE NO POLE x[1] = 0.819 y2[1] (analytic) = 1.7304632430604273956530225896556 y2[1] (numeric) = 1.7888886617806370091236715923984 absolute error = 0.0584254187202096134706490027428 relative error = 3.3762877630894244140649666641971 % h = 0.001 y1[1] (analytic) = 1.7304632430604273956530225896556 y1[1] (numeric) = 1.7655805647393503380727768830887 absolute error = 0.0351173216789229424197542934331 relative error = 2.0293595844784235774962936451212 % h = 0.001 TOP MAIN SOLVE Loop memory used=2071.4MB, alloc=4.6MB, time=116.98 NO POLE NO POLE x[1] = 0.82 y2[1] (analytic) = 1.7311458297268958793813133646877 y2[1] (numeric) = 1.7898099382537562678569875998712 absolute error = 0.0586641085268603884756742351835 relative error = 3.3887444673632832684743333426414 % h = 0.001 y1[1] (analytic) = 1.7311458297268958793813133646877 y1[1] (numeric) = 1.7663483138462941164309236725422 absolute error = 0.0352024841193982370496103078545 relative error = 2.0334788389809858797843973732409 % h = 0.001 TOP MAIN SOLVE Loop memory used=2075.2MB, alloc=4.6MB, time=117.20 NO POLE NO POLE x[1] = 0.821 y2[1] (analytic) = 1.7318276852475955650308377057945 y2[1] (numeric) = 1.7907311108200237182089264052026 absolute error = 0.0589034255724281531780886994081 relative error = 3.4012290064531946203162911518516 % h = 0.001 y1[1] (analytic) = 1.7318276852475955650308377057945 y1[1] (numeric) = 1.7671153967535703761056063657977 absolute error = 0.0352877115059748110747686600032 relative error = 2.0375994567224974918235767163218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.822 y2[1] (analytic) = 1.7325088089406709887232014610491 y2[1] (numeric) = 1.7916521794762207822239699357614 absolute error = 0.0591433705355497935007684747123 relative error = 3.4137414038149997379435325373746 % h = 0.001 y1[1] (analytic) = 1.7325088089406709887232014610491 y1[1] (numeric) = 1.7678818125910371221262640746912 absolute error = 0.0353730036503661334030626136421 relative error = 2.0417214312459791101268422535646 % h = 0.001 TOP MAIN SOLVE Loop memory used=2079.0MB, alloc=4.6MB, time=117.42 NO POLE NO POLE x[1] = 0.823 y2[1] (analytic) = 1.7331892001249985141432868023628 y2[1] (numeric) = 1.7925731442191328307305277709862 absolute error = 0.0593839440941343165872409686234 relative error = 3.4262816829144513128303766909993 % h = 0.001 y1[1] (analytic) = 1.7331892001249985141432868023628 y1[1] (numeric) = 1.7686475604891036508877898666455 absolute error = 0.0354583603641051367445030642827 relative error = 2.0458447561032495008447809718988 % h = 0.001 TOP MAIN SOLVE Loop memory used=2082.8MB, alloc=4.6MB, time=117.64 NO POLE NO POLE x[1] = 0.824 y2[1] (analytic) = 1.7338688581201870136628317803018 y2[1] (numeric) = 1.7934940050455491871514019216897 absolute error = 0.0596251469253621734885701413879 relative error = 3.4388498672273357440278422049393 % h = 0.001 y1[1] (analytic) = 1.7338688581201870136628317803018 y1[1] (numeric) = 1.7694126395787315076736255600262 absolute error = 0.0355437814585444940107937797244 relative error = 2.049969424854892744031253355413 % h = 0.001 TOP MAIN SOLVE Loop memory used=2086.6MB, alloc=4.6MB, time=117.86 NO POLE NO POLE x[1] = 0.825 y2[1] (analytic) = 1.7345477822465785487315012530908 y2[1] (numeric) = 1.7944147619522631313107943871467 absolute error = 0.0598669797056845825792931340559 relative error = 3.451445980239595219808513908475 % h = 0.001 y1[1] (analytic) = 1.7345477822465785487315012530908 y1[1] (numeric) = 1.7701770489914354437560639633008 absolute error = 0.03562926674485689502456271021 relative error = 2.0540954310702255604434927780372 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2090.4MB, alloc=4.6MB, time=118.07 x[1] = 0.826 y2[1] (analytic) = 1.7352259718252490495347687987877 y2[1] (numeric) = 1.795335414936071903237853150095 absolute error = 0.0601094431108228537030843513073 relative error = 3.4640700454474495977798294453757 % h = 0.001 y1[1] (analytic) = 1.7352259718252490495347687987877 y1[1] (numeric) = 1.770940787859284373072730747078 absolute error = 0.0357148160340353235379619482903 relative error = 2.0582227683272647205574235726805 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.827 y2[1] (analytic) = 1.735903426178008993917929952807 y2[1] (numeric) = 1.7962559639937767069667522726674 absolute error = 0.0603525378157677130488223198604 relative error = 3.4767220863575180847402070932619 % h = 0.001 y1[1] (analytic) = 1.735903426178008993917929952807 y1[1] (numeric) = 1.7717038553149023284782184210585 absolute error = 0.0358004291368933345602884682515 relative error = 2.0623514302126945354801558782487 % h = 0.001 TOP MAIN SOLVE Loop memory used=2094.3MB, alloc=4.6MB, time=118.29 NO POLE NO POLE x[1] = 0.828 y2[1] (analytic) = 1.7365801446274040855755678468317 y2[1] (numeric) = 1.7971764091221827143333017591602 absolute error = 0.0605962644947786287577339123285 relative error = 3.4894021264869407175482540003264 % h = 0.001 y1[1] (analytic) = 1.7365801446274040855755678468317 y1[1] (numeric) = 1.7724662504914694175698451719625 absolute error = 0.0358861058640653319942773251308 relative error = 2.0664814103218344294427520366128 % h = 0.001 TOP MAIN SOLVE Loop memory used=2098.1MB, alloc=4.6MB, time=118.51 NO POLE NO POLE x[1] = 0.829 y2[1] (analytic) = 1.7372561264967159315057930597084 y2[1] (numeric) = 1.7980967503180990687680828544409 absolute error = 0.0608406238213831372622897947325 relative error = 3.5021101893634996462711333221801 % h = 0.001 y1[1] (analytic) = 1.7372561264967159315057930597084 y1[1] (numeric) = 1.7732279725227227780865116036125 absolute error = 0.0359718460260068465807185439041 relative error = 2.0706127022586065935574909461461 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2101.9MB, alloc=4.6MB, time=118.73 x[1] = 0.83 y2[1] (analytic) = 1.7379313711099627187285802261381 y2[1] (numeric) = 1.7990169875783388890861044496973 absolute error = 0.0610856164683761703575242235592 relative error = 3.5148462985257402208740295863215 % h = 0.001 y1[1] (analytic) = 1.7379313711099627187285802261381 y1[1] (numeric) = 1.7739890205429575328796287065421 absolute error = 0.036057649432994814151048480404 relative error = 2.0747452996355037205249834013178 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.831 y2[1] (analytic) = 1.7386058777918998902675246848866 y2[1] (numeric) = 1.7999371208997192732729762701347 absolute error = 0.0613312431078193830054515852481 relative error = 3.5276104775230918827085338956502 % h = 0.001 y1[1] (analytic) = 1.7386058777918998902675246848866 y1[1] (numeric) = 1.7747493936870277444550906717721 absolute error = 0.0361435158951278541875659868855 relative error = 2.078879196073556819977613079847 % h = 0.001 TOP MAIN SOLVE Loop memory used=2105.7MB, alloc=4.6MB, time=118.94 NO POLE NO POLE x[1] = 0.832 y2[1] (analytic) = 1.7392796458680208203943431848106 y2[1] (numeric) = 1.8008571502790613022675945221375 absolute error = 0.0615775044110404818732513373269 relative error = 3.5404027499159888620536742115586 % h = 0.001 y1[1] (analytic) = 1.7392796458680208203943431848106 y1[1] (numeric) = 1.7755090910903473690852664517454 absolute error = 0.0362294452223265486909232669348 relative error = 2.0830143852023031141468945045825 % h = 0.001 TOP MAIN SOLVE Loop memory used=2109.5MB, alloc=4.6MB, time=119.16 NO POLE NO POLE x[1] = 0.833 y2[1] (analytic) = 1.739952674664557489135443404258 y2[1] (numeric) = 1.801777075713190043741335680326 absolute error = 0.061824401048632554605892276068 relative error = 3.5532231392759906829592408341983 % h = 0.001 y1[1] (analytic) = 1.739952674664557489135443404258 y1[1] (numeric) = 1.7762681118888912104899842608391 absolute error = 0.0363154372243337213545408565811 relative error = 2.0871508606597540135434510270732 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2113.3MB, alloc=4.6MB, time=119.38 x[1] = 0.834 y2[1] (analytic) = 1.7406249635084811560398877773265 y2[1] (numeric) = 1.8026968971989345558737540978589 absolute error = 0.0620719336904533998338663205324 relative error = 3.5660716691859024766370032292508 % h = 0.001 y1[1] (analytic) = 1.7406249635084811560398877773265 y1[1] (numeric) = 1.7770264552191958730854834983806 absolute error = 0.0364014917107147170455957210541 relative error = 2.0912886160923631723394226778781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.835 y2[1] (analytic) = 1.741296511727503033208077859075 y2[1] (numeric) = 1.8036166147331278911247791262549 absolute error = 0.0623201030056248579167012671799 relative error = 3.5789483632398951046413814410948 % h = 0.001 y1[1] (analytic) = 1.741296511727503033208077859075 y1[1] (numeric) = 1.7777841202183607148003088686774 absolute error = 0.0364876084908576815922310096024 relative error = 2.0954276451549946231442156255222 % h = 0.001 TOP MAIN SOLVE Loop memory used=2117.1MB, alloc=4.6MB, time=119.59 NO POLE NO POLE x[1] = 0.836 y2[1] (analytic) = 1.7419673186500749575804862010582 y2[1] (numeric) = 1.8045362283126071000034074339356 absolute error = 0.0625689096625321424229212328774 relative error = 3.5918532450436250930771233890967 % h = 0.001 y1[1] (analytic) = 1.7419673186500749575804862010582 y1[1] (numeric) = 1.7785411060240487994571217652341 absolute error = 0.0365737873739738418766355641759 relative error = 2.0995679415108909908656020051922 % h = 0.001 TOP MAIN SOLVE Loop memory used=2121.0MB, alloc=4.6MB, time=119.81 NO POLE NO POLE x[1] = 0.837 y2[1] (analytic) = 1.7426373836053900624857634485088 y2[1] (numeric) = 1.8054557379342132348328862156269 absolute error = 0.0628183543288231723471227671181 relative error = 3.6047863382143543790675482727137 % h = 0.001 y1[1] (analytic) = 1.7426373836053900624857634485088 y1[1] (numeric) = 1.7792974117744878487194042800708 absolute error = 0.036660028169097786233640831562 relative error = 2.1037094988316417853492710407398 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2124.8MB, alloc=4.6MB, time=120.03 x[1] = 0.838 y2[1] (analytic) = 1.743306705923383448447549111117 y2[1] (numeric) = 1.8063751435947913535123829876924 absolute error = 0.0630684376714079050648338765754 relative error = 3.6177476663810698707129460194772 % h = 0.001 y1[1] (analytic) = 1.743306705923383448447549111117 y1[1] (numeric) = 1.7800530366084711936020314938759 absolute error = 0.0367463306850877451544823827589 relative error = 2.107852310797151772491019711626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.839 y2[1] (analytic) = 1.7439752849347328532493152006504 y2[1] (numeric) = 1.807294445291190523275137667416 absolute error = 0.0633191603564576700258224667656 relative error = 3.6307372531846028217647731058747 % h = 0.001 y1[1] (analytic) = 1.7439752849347328532493152006504 y1[1] (numeric) = 1.7808079796653587255446879986224 absolute error = 0.036832694730625872295372797972 relative error = 2.1119963710956094235168537319419 % h = 0.001 TOP MAIN SOLVE Loop memory used=2128.6MB, alloc=4.6MB, time=120.24 NO POLE NO POLE x[1] = 0.84 y2[1] (analytic) = 1.7446431199708593212565726706296 y2[1] (numeric) = 1.8082136430202638244430926371995 absolute error = 0.0635705230494045031865199665699 relative error = 3.6437551222777480222373560720578 % h = 0.001 y1[1] (analytic) = 1.7446431199708593212565726706296 y1[1] (numeric) = 1.7815622400850778470471049012507 absolute error = 0.0369191201142185257905322306211 relative error = 2.1161416734234554421273473325817 % h = 0.001 TOP MAIN SOLVE Loop memory used=2132.4MB, alloc=4.6MB, time=120.46 NO POLE NO POLE x[1] = 0.841 y2[1] (analytic) = 1.7453102103639278719957713359055 y2[1] (numeric) = 1.8091327367788683541779964975922 absolute error = 0.0638225264149404821822251616867 relative error = 3.6568012973253828061749055468942 % h = 0.001 y1[1] (analytic) = 1.7453102103639278719957713359055 y1[1] (numeric) = 1.7823158170081244218650938550721 absolute error = 0.0370056066441965498693225191666 relative error = 2.1202882114853513692036832926814 % h = 0.001 TOP MAIN SOLVE Loop memory used=2136.2MB, alloc=4.6MB, time=120.67 NO POLE NO POLE x[1] = 0.842 y2[1] (analytic) = 1.7459765554468481679892246932965 y2[1] (numeric) = 1.8100517265638652302289772160281 absolute error = 0.0640751711170170622397525227316 relative error = 3.6698758020045858777877555082074 % h = 0.001 y1[1] (analytic) = 1.7459765554468481679892246932965 y1[1] (numeric) = 1.7830687095755637247663549646763 absolute error = 0.0370921541287155567771302713798 relative error = 2.1244359789941482647738628726266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.843 y2[1] (analytic) = 1.7466421545532751818453918084153 y2[1] (numeric) = 1.8109706123721195946765803811073 absolute error = 0.064328457818844412831188572692 relative error = 3.6829786600047559571678747348043 % h = 0.001 y1[1] (analytic) = 1.7466421545532751818453918084153 y1[1] (numeric) = 1.7838209169290313908450357103306 absolute error = 0.0371787623757562089996439019153 relative error = 2.1285849696708554669386387807053 % h = 0.001 TOP MAIN SOLVE Loop memory used=2140.0MB, alloc=4.6MB, time=120.89 NO POLE NO POLE x[1] = 0.844 y2[1] (analytic) = 1.7473070070176098626038491784596 y2[1] (numeric) = 1.8118893942005006176732682752253 absolute error = 0.0645823871828907550694190967657 relative error = 3.6961098950277302467898498716098 % h = 0.001 y1[1] (analytic) = 1.7473070070176098626038491784596 y1[1] (numeric) = 1.7845724382107343643940183391425 absolute error = 0.0372654311931245017901691606829 relative error = 2.132735177244609427457783079432 % h = 0.001 TOP MAIN SOLVE Loop memory used=2143.9MB, alloc=4.6MB, time=121.11 NO POLE NO POLE x[1] = 0.845 y2[1] (analytic) = 1.7479711121749998013342862260498 y2[1] (numeric) = 1.8128080720458815011803754813268 absolute error = 0.064836959870881699846089255277 relative error = 3.7092695307879027199997121380597 % h = 0.001 y1[1] (analytic) = 1.7479711121749998013342862260498 y1[1] (numeric) = 1.7853232725634518473339134726153 absolute error = 0.0373521603884520459996272465655 relative error = 2.1368865954526426236983560269435 % h = 0.001 TOP MAIN SOLVE Loop memory used=2147.7MB, alloc=4.6MB, time=121.32 NO POLE NO POLE x[1] = 0.846 y2[1] (analytic) = 1.7486344693613398959888588251738 y2[1] (numeric) = 1.8137266459051394827015167425342 absolute error = 0.0650921765437995867126579173604 relative error = 3.722457591012342232690172373451 % h = 0.001 y1[1] (analytic) = 1.7486344693613398959888588251738 y1[1] (numeric) = 1.7860734191305362471977379836633 absolute error = 0.0374389497691963512088791584895 relative error = 2.1410392180402525466476912746757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.847 y2[1] (analytic) = 1.7492970779132730155072360069414 y2[1] (numeric) = 1.8146451157751558390124427963854 absolute error = 0.065348037861882823505206789444 relative error = 3.7356740994409104593570417435752 % h = 0.001 y1[1] (analytic) = 1.7492970779132730155072360069414 y1[1] (numeric) = 1.7868228770559141246702555006645 absolute error = 0.0375257991426411091630194937231 relative error = 2.1451930387607707646948576254974 % h = 0.001 TOP MAIN SOLVE Loop memory used=2151.5MB, alloc=4.6MB, time=121.54 NO POLE NO POLE x[1] = 0.848 y2[1] (analytic) = 1.7499589371681906631736757401562 y2[1] (numeric) = 1.8155634816528158898873399083981 absolute error = 0.0656045444846252267136641682419 relative error = 3.7489190798263796547278479421812 % h = 0.001 y1[1] (analytic) = 1.7499589371681906631736757401562 y1[1] (numeric) = 1.7875716454840871406809582017191 absolute error = 0.0376127083158964775072824615629 relative error = 2.1493480513755320628853977177521 % h = 0.001 TOP MAIN SOLVE Loop memory used=2155.3MB, alloc=4.6MB, time=121.75 NO POLE NO POLE x[1] = 0.849 y2[1] (analytic) = 1.7506200464642336392254664296844 y2[1] (numeric) = 1.8164817435350090018215688326713 absolute error = 0.0658616970707753625961024029869 relative error = 3.7621925559345502421499090217642 % h = 0.001 y1[1] (analytic) = 1.7506200464642336392254664296844 y1[1] (numeric) = 1.788319723560133003049668868945 absolute error = 0.0376996770958993638242024392606 relative error = 2.1535042496538436573551795602992 % h = 0.001 TOP MAIN SOLVE Loop memory used=2159.1MB, alloc=4.6MB, time=121.97 NO POLE NO POLE x[1] = 0.85 y2[1] (analytic) = 1.7512804051402927027120715242355 y2[1] (numeric) = 1.8173999014186285917508389302275 absolute error = 0.066119496278335889038767405992 relative error = 3.7754945515443682299213989933727 % h = 0.001 y1[1] (analytic) = 1.7512804051402927027120715242355 y1[1] (numeric) = 1.7890671104297064126837424803841 absolute error = 0.0377867052894137099716709561486 relative error = 2.1576616273729544846502278227098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.851 y2[1] (analytic) = 1.7519400125360092326043153744632 y2[1] (numeric) = 1.8183179553005721307668131788018 absolute error = 0.0663779427645628981624978043386 relative error = 3.7888250904480424567452309590877 % h = 0.001 y1[1] (analytic) = 1.7519400125360092326043153744632 y1[1] (numeric) = 1.7898138052390400093258469259085 absolute error = 0.0378737927030307767215315514453 relative error = 2.1618201783180245656404282036351 % h = 0.001 TOP MAIN SOLVE Loop memory used=2162.9MB, alloc=4.6MB, time=122.19 NO POLE NO POLE x[1] = 0.852 y2[1] (analytic) = 1.7525988679917758881529492322585 y2[1] (numeric) = 1.8192359051777411478291398107855 absolute error = 0.066637037185965259676190578527 relative error = 3.802184196451161667481894696186 % h = 0.001 y1[1] (analytic) = 1.7525988679917758881529492322585 y1[1] (numeric) = 1.7905598071349453168513027434096 absolute error = 0.0379609391431694286983535111511 relative error = 2.1659798962820944437360200789461 % h = 0.001 TOP MAIN SOLVE Loop memory used=2166.7MB, alloc=4.6MB, time=122.41 NO POLE NO POLE x[1] = 0.853 y2[1] (analytic) = 1.7532569708487372684959370327215 y2[1] (numeric) = 1.8201537510470412334739063190457 absolute error = 0.0668967801983039649779692863242 relative error = 3.8155718933728114203737162151866 % h = 0.001 y1[1] (analytic) = 1.7532569708487372684959370327215 y1[1] (numeric) = 1.7913051152648136881139620825198 absolute error = 0.0380481444160764196180250497983 relative error = 2.1701407750660546971168099905437 % h = 0.001 TOP MAIN SOLVE Loop memory used=2170.6MB, alloc=4.6MB, time=122.62 NO POLE NO POLE x[1] = 0.854 y2[1] (analytic) = 1.7539143204487905715138013515826 y2[1] (numeric) = 1.8210714929053820435185115733521 absolute error = 0.0671571724565914720047102217695 relative error = 3.8289882050456908269093567778759 % h = 0.001 y1[1] (analytic) = 1.7539143204487905715138013515826 y1[1] (numeric) = 1.7920497287766172493396074151603 absolute error = 0.0381354083278266778258060635777 relative error = 2.1743028084786155246850513960174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.855 y2[1] (analytic) = 1.7545709161345862519323706827818 y2[1] (numeric) = 1.821989130749677302762951793165 absolute error = 0.0674182146150910508305811103832 relative error = 3.8424331553162291254937381033718 % h = 0.001 y1[1] (analytic) = 1.7545709161345862519323706827818 y1[1] (numeric) = 1.7927936468189098440658508253277 absolute error = 0.0382227306843235921334801425459 relative error = 2.1784659903362764054539444794111 % h = 0.001 TOP MAIN SOLVE Loop memory used=2174.4MB, alloc=4.6MB, time=122.84 NO POLE NO POLE x[1] = 0.856 y2[1] (analytic) = 1.7552267572495286786722699335127 y2[1] (numeric) = 1.82290666457684480868751612556 absolute error = 0.0676799073273161300152461920473 relative error = 3.8559067680447020900849689250166 % h = 0.001 y1[1] (analytic) = 1.7552267572495286786722699335127 y1[1] (numeric) = 1.7935368685408279766275150247238 absolute error = 0.0383101112912992979552450912111 relative error = 2.1826303144632958310847137436098 % h = 0.001 TOP MAIN SOLVE Loop memory used=2178.2MB, alloc=4.6MB, time=123.06 NO POLE NO POLE x[1] = 0.857 y2[1] (analytic) = 1.7558818431377767914444967872976 y2[1] (numeric) = 1.8238240943838064351468875800942 absolute error = 0.0679422512460296437023907927966 relative error = 3.869409067105348274956255605139 % h = 0.001 y1[1] (analytic) = 1.7558818431377767914444967872976 y1[1] (numeric) = 1.7942793930920917551864775561042 absolute error = 0.0383975499543149637419807688066 relative error = 2.1867957746916611112862205853797 % h = 0.001 TOP MAIN SOLVE Loop memory used=2182.0MB, alloc=4.6MB, time=123.28 NO POLE NO POLE x[1] = 0.858 y2[1] (analytic) = 1.7565361731442447565914273395692 y2[1] (numeric) = 1.8247414201674881360606450754517 absolute error = 0.0682052470232433794692177358825 relative error = 3.8829400763864850967372060858149 % h = 0.001 y1[1] (analytic) = 1.7565361731442447565914273395692 y1[1] (numeric) = 1.7950212196230058343049599625614 absolute error = 0.0384850464787610777135326229922 relative error = 2.1909623648610582517920631146845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.859 y2[1] (analytic) = 1.757189746614602622172595164811 y2[1] (numeric) = 1.8256586419248199491001623557444 absolute error = 0.0684688953102173269275671909334 relative error = 3.8964998197906247548853819679565 % h = 0.001 y1[1] (analytic) = 1.757189746614602622172595164811 y1[1] (numeric) = 1.795762347284460357061244018378 absolute error = 0.038572600669857734888648853567 relative error = 2.1951300788188419046311061397321 % h = 0.001 TOP MAIN SOLVE Loop memory used=2185.8MB, alloc=4.6MB, time=123.50 NO POLE NO POLE x[1] = 0.86 y2[1] (analytic) = 1.7578425628952769722945887295286 y2[1] (numeric) = 1.8265757596527359993718995373863 absolute error = 0.0687331967574590270773108078577 relative error = 3.910088321234589991735417887447 % h = 0.001 y1[1] (analytic) = 1.7578425628952769722945887295286 y1[1] (numeric) = 1.7965027752279318967067974355771 absolute error = 0.0386602123326549244122087060485 relative error = 2.1992989104200053904083705186945 % h = 0.001 TOP MAIN SOLVE Loop memory used=2189.6MB, alloc=4.6MB, time=123.71 NO POLE NO POLE x[1] = 0.861 y2[1] (analytic) = 1.7584946213334515806844128212126 y2[1] (numeric) = 1.8274927733481745030970830505075 absolute error = 0.0689981520147229224126702292949 relative error = 3.9237056046496296932695105124057 % h = 0.001 y1[1] (analytic) = 1.7584946213334515806844128212126 y1[1] (numeric) = 1.7972425026054843978637917798624 absolute error = 0.0387478812720328171793789586498 relative error = 2.2034688535271507923141929962651 % h = 0.001 TOP MAIN SOLVE Loop memory used=2193.4MB, alloc=4.6MB, time=123.93 NO POLE NO POLE x[1] = 0.862 y2[1] (analytic) = 1.7591459212770680635056604199826 y2[1] (numeric) = 1.8284096830080777712877697419251 absolute error = 0.0692637617310097077821093219425 relative error = 3.9373516939815343317495813401521 % h = 0.001 y1[1] (analytic) = 1.7591459212770680635056604199826 y1[1] (numeric) = 1.7979815285697701172619956502818 absolute error = 0.0388356072927020537563352302992 relative error = 2.2076399020104591215805452192172 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.863 y2[1] (analytic) = 1.7597964620748265314168421967984 y2[1] (numeric) = 1.8293264886293922134192909097466 absolute error = 0.0695300265545656820024487129482 relative error = 3.9510266131907512513479379437156 % h = 0.001 y1[1] (analytic) = 1.7597964620748265314168421967984 y1[1] (numeric) = 1.798719852274030564014026498662 absolute error = 0.0389233901992040325971843018636 relative error = 2.2118120497476605541043738773063 % h = 0.001 TOP MAIN SOLVE Loop memory used=2197.3MB, alloc=4.6MB, time=124.14 NO POLE NO POLE x[1] = 0.864 y2[1] (analytic) = 1.7604462430761862408712215799592 y2[1] (numeric) = 1.8302431902090683410990720427412 absolute error = 0.069796947132882100227850462782 relative error = 3.9647303862524997979097973267528 % h = 0.001 y1[1] (analytic) = 1.7604462430761862408712215799592 y1[1] (numeric) = 1.7994574728720974394279447876493 absolute error = 0.0390112297959111985567232076901 relative error = 2.2159852906240047379587928651218 % h = 0.001 TOP MAIN SOLVE Loop memory used=2201.1MB, alloc=4.6MB, time=124.36 NO POLE NO POLE x[1] = 0.865 y2[1] (analytic) = 1.7610952636313662446575040901144 y2[1] (numeric) = 1.8311597877440607717318240406818 absolute error = 0.0700645241126945270743199505674 relative error = 3.9784630371568862939775925110058 % h = 0.001 y1[1] (analytic) = 1.7610952636313662446575040901144 y1[1] (numeric) = 1.8001943895183935763561745100537 absolute error = 0.0390991258870273316986704199393 relative error = 2.2201596185322311715139230241287 % h = 0.001 TOP MAIN SOLVE Loop memory used=2204.9MB, alloc=4.6MB, time=124.58 NO POLE NO POLE x[1] = 0.866 y2[1] (analytic) = 1.7617435230913460416807304031469 y2[1] (numeric) = 1.8320762812313282321811016949309 absolute error = 0.070332758139982190500371291784 relative error = 3.9922245899090188602035593241028 % h = 0.001 y1[1] (analytic) = 1.7617435230913460416807304031469 y1[1] (numeric) = 1.8009306013679338780797344171265 absolute error = 0.0391870782765878363990040139796 relative error = 2.2243350273725396518901354228093 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.867 y2[1] (analytic) = 1.7623910208078662259827233600927 y2[1] (numeric) = 1.8329926706678335624272252116195 absolute error = 0.0706016498599673364445018515268 relative error = 4.0060150685291220842736944966769 % h = 0.001 y1[1] (analytic) = 1.7623910208078662259827233600927 y1[1] (numeric) = 1.801666107576326256726764629412 absolute error = 0.0392750867684600307440412693193 relative error = 2.228511511052560793467410283889 % h = 0.001 TOP MAIN SOLVE Loop memory used=2208.7MB, alloc=4.6MB, time=124.79 NO POLE NO POLE x[1] = 0.868 y2[1] (analytic) = 1.763037756133429135001439903703 y2[1] (numeric) = 1.8339089560505437192215605628478 absolute error = 0.0708711999171145842201206591448 relative error = 4.0198344970526515384627885392085 % h = 0.001 y1[1] (analytic) = 1.763037756133429135001439903703 y1[1] (numeric) = 1.8024009072997725712243336308923 absolute error = 0.0393631511663434362228937271893 relative error = 2.2326890634873266161754755907911 % h = 0.001 TOP MAIN SOLVE Loop memory used=2212.5MB, alloc=4.6MB, time=125.00 NO POLE NO POLE x[1] = 0.869 y2[1] (analytic) = 1.7636837284212994970685796823498 y2[1] (numeric) = 1.834825137376429779737154454423 absolute error = 0.0711414089551302826685747720732 relative error = 4.0336828995304081469368673717566 % h = 0.001 y1[1] (analytic) = 1.7636837284212994970685796823498 y1[1] (numeric) = 1.8031349996950695647825109752983 absolute error = 0.0394512712737700677139312929485 relative error = 2.2368676785992412032903371190287 % h = 0.001 TOP MAIN SOLVE Loop memory used=2216.3MB, alloc=4.6MB, time=125.22 NO POLE NO POLE x[1] = 0.87 y2[1] (analytic) = 1.7643289370255050781448028237228 y2[1] (numeric) = 1.8357412146424669452157197017368 absolute error = 0.071412277616961867070916878014 relative error = 4.0475603000286524039160252456772 % h = 0.001 y1[1] (analytic) = 1.7643289370255050781448028237228 y1[1] (numeric) = 1.8038683839196098019096913626879 absolute error = 0.0395394468941047237648885389651 relative error = 2.2410473503180514284637551606379 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.871 y2[1] (analytic) = 1.7649733813008373277919101431513 y2[1] (numeric) = 1.8366571878456345446109668084823 absolute error = 0.071683806544797216819056665331 relative error = 4.0614667226292184438072980493548 % h = 0.001 y1[1] (analytic) = 1.7649733813008373277919101431513 y1[1] (numeric) = 1.8046010591313826049581560746884 absolute error = 0.0396276778305452771662459315371 relative error = 2.2452280725808177517131625598413 % h = 0.001 TOP MAIN SOLVE Loop memory used=2220.1MB, alloc=4.6MB, time=125.44 NO POLE NO POLE x[1] = 0.872 y2[1] (analytic) = 1.7656170606028520243813398144258 y2[1] (numeric) = 1.8375730569829160382282775460068 absolute error = 0.071955996380064013846937731581 relative error = 4.0754021914296279644139105513603 % h = 0.001 y1[1] (analytic) = 1.7656170606028520243813398144258 y1[1] (numeric) = 1.8053330244889749901988580881733 absolute error = 0.0397159638861229658175182737475 relative error = 2.2494098393318850841004538738237 % h = 0.001 TOP MAIN SOLVE Loop memory used=2224.0MB, alloc=4.6MB, time=125.65 NO POLE NO POLE x[1] = 0.873 y2[1] (analytic) = 1.7662599742878699195383352946765 y2[1] (numeric) = 1.8384888220512990213607163342028 absolute error = 0.0722288477634291018223810395263 relative error = 4.0893667305432040043239334290534 % h = 0.001 y1[1] (analytic) = 1.7662599742878699195383352946765 y1[1] (numeric) = 1.8060642791515726034244175195847 absolute error = 0.0398043048637026838860822249082 relative error = 2.2535926445228537208290065323 % h = 0.001 TOP MAIN SOLVE Loop memory used=2227.8MB, alloc=4.6MB, time=125.87 NO POLE NO POLE x[1] = 0.874 y2[1] (analytic) = 1.7669021217129773818211400591947 y2[1] (numeric) = 1.8394044830477752279213752279462 absolute error = 0.0725023613347978461002351687515 relative error = 4.1033603640991845755781059815396 % h = 0.001 y1[1] (analytic) = 1.7669021217129773818211400591947 y1[1] (numeric) = 1.8067948222789606550793143856296 absolute error = 0.0398927005659832732581743264349 relative error = 2.2577764821125503424892218117956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2231.6MB, alloc=4.6MB, time=126.08 x[1] = 0.875 y2[1] (analytic) = 1.7675435022360270396345754670545 y2[1] (numeric) = 1.8403200399693405340720483162051 absolute error = 0.0727765377333134944374728491506 relative error = 4.1173831162428361527133181579487 % h = 0.001 y1[1] (analytic) = 1.7675435022360270396345754670545 y1[1] (numeric) = 1.807524653031524854916266000663 absolute error = 0.0399811507954978152816905336085 relative error = 2.2619613460669990841837962830262 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.876 y2[1] (analytic) = 1.768184115215638423377358844013 y2[1] (numeric) = 1.8412354928129949618482313440595 absolute error = 0.0730513775973565384708725000465 relative error = 4.1314350111355670192750008691746 % h = 0.001 y1[1] (analytic) = 1.768184115215638423377358844013 y1[1] (numeric) = 1.8082537705702523461777766667291 absolute error = 0.0400696553546139228004178227161 relative error = 2.2661472303593926722648531503821 % h = 0.001 TOP MAIN SOLVE Loop memory used=2235.4MB, alloc=4.6MB, time=126.30 NO POLE NO POLE x[1] = 0.877 y2[1] (analytic) = 1.7688239600111986068225196354215 y2[1] (numeric) = 1.842150841575742682780442370996 absolute error = 0.0733268815645440759579227355745 relative error = 4.1455160729550404728884464198004 % h = 0.001 y1[1] (analytic) = 1.7688239600111986068225196354215 y1[1] (numeric) = 1.8089821740567326393018476489633 absolute error = 0.0401582140455340324793280135418 relative error = 2.2703341289700636284159776000349 % h = 0.001 TOP MAIN SOLVE Loop memory used=2239.2MB, alloc=4.6MB, time=126.52 NO POLE NO POLE x[1] = 0.878 y2[1] (analytic) = 1.769463035982862847730272248788 y2[1] (numeric) = 1.8430660862545920215118592819674 absolute error = 0.0736030502717291737815870331794 relative error = 4.1596263258952878899758712209461 % h = 0.001 y1[1] (analytic) = 1.769463035982862847730272248788 y1[1] (numeric) = 1.8097098626531585451508357668548 absolute error = 0.0402468266702956974205635180668 relative error = 2.2745220358864555408131109238079 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2243.0MB, alloc=4.6MB, time=126.73 x[1] = 0.879 y2[1] (analytic) = 1.7701013424915552276927049731688 y2[1] (numeric) = 1.8439812268465554594122699708395 absolute error = 0.0738798843550002317195649976707 relative error = 4.1737657941668216512028406518113 % h = 0.001 y1[1] (analytic) = 1.7701013424915552276927049731688 y1[1] (numeric) = 1.8104368355223271077624492707445 absolute error = 0.0403354930307718800697442975757 relative error = 2.2787109451030944020991648094331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.88 y2[1] (analytic) = 1.770738878898969291209645130756 y2[1] (numeric) = 1.8448962633486496381883310189847 absolute error = 0.0741573844496803469786858882287 relative error = 4.1879345019967479287345009526589 % h = 0.001 y1[1] (analytic) = 1.770738878898969291209645130756 y1[1] (numeric) = 1.811163091827640536621870012873 absolute error = 0.040424212928671245412224882117 relative error = 2.2829008506215600139081197997797 % h = 0.001 TOP MAIN SOLVE Loop memory used=2246.9MB, alloc=4.6MB, time=126.95 NO POLE NO POLE x[1] = 0.881 y2[1] (analytic) = 1.771375644567568683995061384847 y2[1] (numeric) = 1.8458111957578953634901306949221 absolute error = 0.0744355511903266794950693100751 relative error = 4.2021324736288793363789052827667 % h = 0.001 y1[1] (analytic) = 1.771375644567568683995061384847 y1[1] (numeric) = 1.8118886307331071384539912633072 absolute error = 0.0405129861655384544589298784602 relative error = 2.287091746450457457675270543307 % h = 0.001 TOP MAIN SOLVE Loop memory used=2250.7MB, alloc=4.6MB, time=127.17 NO POLE NO POLE x[1] = 0.882 y2[1] (analytic) = 1.772011638860587790513364897848 y2[1] (numeric) = 1.8467260240713176085140521040499 absolute error = 0.0747143852107298180006872062019 relative error = 4.2163597333238474436915804897993 % h = 0.001 y1[1] (analytic) = 1.772011638860587790513364897848 y1[1] (numeric) = 1.8126134514033422485347608631572 absolute error = 0.0406018125427544580213959653092 relative error = 2.2912836266053886314711751015927 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2254.5MB, alloc=4.6MB, time=127.38 x[1] = 0.883 y2[1] (analytic) = 1.7726468611420323707449718030637 y2[1] (numeric) = 1.8476407482859455176019323206672 absolute error = 0.0749938871439131468569605176035 relative error = 4.2306163053592151551123576403385 % h = 0.001 y1[1] (analytic) = 1.7726468611420323707449718030637 y1[1] (numeric) = 1.8133375530035691615206197506483 absolute error = 0.0406906918615367907756479475846 relative error = 2.2954764851089238525977562654111 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.884 y2[1] (analytic) = 1.7732813107766801961804902247626 y2[1] (numeric) = 1.8485553683988124098365133376366 absolute error = 0.075274057622132213656023112874 relative error = 4.2449022140295889552023828825944 % h = 0.001 y1[1] (analytic) = 1.7732813107766801961804902247626 y1[1] (numeric) = 1.8140609346996200617950262398365 absolute error = 0.0407796239229398656145360150739 relative error = 2.2996703159905735256858895755772 % h = 0.001 TOP MAIN SOLVE Loop memory used=2258.3MB, alloc=4.6MB, time=127.60 NO POLE NO POLE x[1] = 0.885 y2[1] (analytic) = 1.7739149871300816850428958523849 y2[1] (numeric) = 1.8494698844069557826331806721991 absolute error = 0.0755548972768740975902848198142 relative error = 4.2592174836467310210461356798982 % h = 0.001 y1[1] (analytic) = 1.7739149871300816850428958523849 y1[1] (numeric) = 1.8147835956579369533310567770489 absolute error = 0.040868608527855268288160924664 relative error = 2.3038651132867598760346955655552 % h = 0.001 TOP MAIN SOLVE Loop memory used=2262.1MB, alloc=4.6MB, time=127.81 NO POLE NO POLE x[1] = 0.886 y2[1] (analytic) = 1.7745478895685605367370608467703 y2[1] (numeric) = 1.8503842963074173153279854696185 absolute error = 0.0758364067388567785909246228482 relative error = 4.2735621385396712028802087966019 % h = 0.001 y1[1] (analytic) = 1.7745478895685605367370608467703 y1[1] (numeric) = 1.8155055350455725890690742464937 absolute error = 0.0409576454770120523320133997234 relative error = 2.3080608710407887479336326572054 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2265.9MB, alloc=4.6MB, time=128.03 x[1] = 0.887 y2[1] (analytic) = 1.7751800174592143655260016289292 y2[1] (numeric) = 1.8512986040972428727619459494988 absolute error = 0.0761185866380285072359443205696 relative error = 4.2879362030548188740075485651387 % h = 0.001 y1[1] (analytic) = 1.7751800174592143655260016289292 y1[1] (numeric) = 1.8162267520301913998084552439157 absolute error = 0.0410467345709770342824536149865 relative error = 2.3122575833028214677093621656774 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.888 y2[1] (analytic) = 1.7758113701699153334332118751625 y2[1] (numeric) = 1.8522128077734825088616240427954 absolute error = 0.0764014376035671754284121676329 relative error = 4.3023397015560746510528148443414 % h = 0.001 y1[1] (analytic) = 1.7758113701699153334332118751625 y1[1] (numeric) = 1.8169472457800704226123680856757 absolute error = 0.0411358756101550891791562105132 relative error = 2.3164552441298467712402280214628 % h = 0.001 TOP MAIN SOLVE Loop memory used=2269.7MB, alloc=4.6MB, time=128.24 NO POLE NO POLE x[1] = 0.889 y2[1] (analytic) = 1.7764419470693107823704478162497 y2[1] (numeric) = 1.8531269073331904702159730707171 absolute error = 0.0766849602638796878455252544674 relative error = 4.3167726584249419856114976240497 % h = 0.001 y1[1] (analytic) = 1.7764419470693107823704478162497 y1[1] (numeric) = 1.8176670154641002287245936702014 absolute error = 0.0412250683947894463541458539517 relative error = 2.3206538475856527956820611137096 % h = 0.001 TOP MAIN SOLVE Loop memory used=2273.6MB, alloc=4.6MB, time=128.46 NO POLE NO POLE x[1] = 0.89 y2[1] (analytic) = 1.7770717475268238654903337129732 y2[1] (numeric) = 1.8540409027734251996494523198993 absolute error = 0.0769691552466013341591186069261 relative error = 4.3312350980606386283424213702647 % h = 0.001 y1[1] (analytic) = 1.7770717475268238654903337129732 y1[1] (numeric) = 1.8183860602517858509973816593974 absolute error = 0.0413143127249619855070479464242 relative error = 2.3248533877407991351498816159629 % h = 0.001 TOP MAIN SOLVE Loop memory used=2277.4MB, alloc=4.6MB, time=128.68 NO POLE NO POLE x[1] = 0.891 y2[1] (analytic) = 1.7777007709126541777631561554249 y2[1] (numeric) = 1.8549547940912493397914043714176 absolute error = 0.0772540231785951620282482159927 relative error = 4.3457270448802079665502788694142 % h = 0.001 y1[1] (analytic) = 1.7777007709126541777631561554249 y1[1] (numeric) = 1.8191043793132477108293347993095 absolute error = 0.0414036084005935330661786438846 relative error = 2.3290538586725889601009322902289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.892 y2[1] (analytic) = 1.7783290165977783857772166093547 y2[1] (numeric) = 1.8558685812837297366416910444019 absolute error = 0.0775395646859513508644744350472 relative error = 4.3602485233186302363018634502299 % h = 0.001 y1[1] (analytic) = 1.7783290165977783857772166093547 y1[1] (numeric) = 1.8198219718192225446123145521141 absolute error = 0.0414929552214441588350979427594 relative error = 2.3332552544650412001653315939104 % h = 0.001 TOP MAIN SOLVE Loop memory used=2281.2MB, alloc=4.6MB, time=128.90 NO POLE NO POLE x[1] = 0.893 y2[1] (analytic) = 1.7789564839539508567621124092591 y2[1] (numeric) = 1.85678226434793744313258381821 absolute error = 0.0778257803939865863704714089509 relative error = 4.3747995578289336101167119696819 % h = 0.001 y1[1] (analytic) = 1.7789564839539508567621124092591 y1[1] (numeric) = 1.820538836941064329686361565348 absolute error = 0.0415823529871134729242491560889 relative error = 2.3374575692088627901714874538663 % h = 0.001 TOP MAIN SOLVE Loop memory used=2285.0MB, alloc=4.6MB, time=129.12 NO POLE NO POLE x[1] = 0.894 y2[1] (analytic) = 1.7795831723537042868343171749836 y2[1] (numeric) = 1.8576958432809477226869046003191 absolute error = 0.0781126709272434358525874253355 relative error = 4.3893801728823051612699307760597 % h = 0.001 y1[1] (analytic) = 1.7795831723537042868343171749836 y1[1] (numeric) = 1.821254973850745209801624859207 absolute error = 0.0416718014970409229673076842234 relative error = 2.3416607970014209791142608382751 % h = 0.001 TOP MAIN SOLVE Loop memory used=2288.8MB, alloc=4.6MB, time=129.34 NO POLE NO POLE x[1] = 0.895 y2[1] (analytic) = 1.780209081170350328464432406308 y2[1] (numeric) = 1.8586093180798400527724127103022 absolute error = 0.0784002369094897243079803039942 relative error = 4.4039903929682017057420529413158 % h = 0.001 y1[1] (analytic) = 1.780209081170350328464432406308 y1[1] (numeric) = 1.8219703817208564200862939687201 absolute error = 0.0417613005505060916218615624121 relative error = 2.3458649319467157018147127672503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.896 y2[1] (analytic) = 1.7808342097779802171654827883184 y2[1] (numeric) = 1.8595226887416981284524339534654 absolute error = 0.078688478963717911286951165147 relative error = 4.4186302425944605228478673171335 % h = 0.001 y1[1] (analytic) = 1.7808342097779802171654827883184 y1[1] (numeric) = 1.822685059724609211519528634655 absolute error = 0.0418508499466289943540458463366 relative error = 2.3500699681553520130211091726533 % h = 0.001 TOP MAIN SOLVE Loop memory used=2292.6MB, alloc=4.6MB, time=129.56 NO POLE NO POLE x[1] = 0.897 y2[1] (analytic) = 1.7814585575514653974016285193201 y2[1] (numeric) = 1.8604359552636098659327276609394 absolute error = 0.0789773977121444685310991416193 relative error = 4.4332997462874099555732683496125 % h = 0.001 y1[1] (analytic) = 1.7814585575514653974016285193201 y1[1] (numeric) = 1.8233990070358357749083809951254 absolute error = 0.0419404494843703775067524758053 relative error = 2.3542758997445125837016950635142 % h = 0.001 TOP MAIN SOLVE Loop memory used=2296.4MB, alloc=4.6MB, time=129.77 NO POLE NO POLE x[1] = 0.898 y2[1] (analytic) = 1.7820821238664581477166687526331 y2[1] (numeric) = 1.861349117642667406104587576237 absolute error = 0.0792669937762092583879188236039 relative error = 4.4479989285919798916463000176482 % h = 0.001 y1[1] (analytic) = 1.7820821238664581477166687526331 y1[1] (numeric) = 1.8241122228289901643677055890518 absolute error = 0.0420300989625320166510368364187 relative error = 2.3584827208379302592805827907679 % h = 0.001 TOP MAIN SOLVE Loop memory used=2300.3MB, alloc=4.6MB, time=129.99 NO POLE NO POLE x[1] = 0.899 y2[1] (analytic) = 1.7827049080993922050817110238177 y2[1] (numeric) = 1.8622621758759671180841724715146 absolute error = 0.0795572677765749130024614476969 relative error = 4.4627278140718121263657076751579 % h = 0.001 y1[1] (analytic) = 1.7827049080993922050817110238177 y1[1] (numeric) = 1.8248247062791492203020528428774 absolute error = 0.0421197981797570152203418190597 relative error = 2.3626904255658606795689288508245 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9 y2[1] (analytic) = 1.7833269096274833884613823157136 y2[1] (numeric) = 1.8631751299606096027480623800047 absolute error = 0.0798482203331262142866800642911 relative error = 4.4774864273093706082074679103696 % h = 0.001 y1[1] (analytic) = 1.7833269096274833884613823157136 y1[1] (numeric) = 1.8255364565620134918885420732558 absolute error = 0.0422095469345301034271597575422 relative error = 2.3668990080650549601443996368369 % h = 0.001 TOP MAIN SOLVE Loop memory used=2304.1MB, alloc=4.6MB, time=130.21 NO POLE NO POLE x[1] = 0.901 y2[1] (analytic) = 1.7839481278287302215979581951327 y2[1] (numeric) = 1.8640879798936996962650363343193 absolute error = 0.0801398520649694746670781391866 relative error = 4.4922747929060515682269387214529 % h = 0.001 y1[1] (analytic) = 1.7839481278287302215979581951327 y1[1] (numeric) = 1.8262474728539081590597104008097 absolute error = 0.042299345025177937461752205677 relative error = 2.3711084624787324349327488558812 % h = 0.001 TOP MAIN SOLVE Loop memory used=2307.9MB, alloc=4.6MB, time=130.43 NO POLE NO POLE x[1] = 0.902 y2[1] (analytic) = 1.7845685620819145550127872371293 y2[1] (numeric) = 1.8650007256723464736240675035656 absolute error = 0.0804321635904319186112802664363 relative error = 4.5070929354822935342714602815361 % h = 0.001 y1[1] (analytic) = 1.7845685620819145550127872371293 y1[1] (numeric) = 1.8269577543317839539853343335082 absolute error = 0.0423891922498693989725470963789 relative error = 2.3753187829565534597461479949381 % h = 0.001 TOP MAIN SOLVE Loop memory used=2311.7MB, alloc=4.6MB, time=130.64 NO POLE NO POLE x[1] = 0.903 y2[1] (analytic) = 1.7851882117666021872243887354735 y2[1] (numeric) = 1.8659133672936632521585316254549 absolute error = 0.0807251555270610649341428899814 relative error = 4.5219408796776872310154402626541 % h = 0.001 y1[1] (analytic) = 1.7851882117666021872243887354735 y1[1] (numeric) = 1.8276673001732180820522211427247 absolute error = 0.0424790884066158948278324072512 relative error = 2.379529963654592276533726254688 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.904 y2[1] (analytic) = 1.7858070762631434851826024812843 y2[1] (numeric) = 1.8668259047547675950666246328372 absolute error = 0.0810188284916241098840221515529 relative error = 4.5368186501510853668271770431019 % h = 0.001 y1[1] (analytic) = 1.7858070762631434851826024812843 y1[1] (numeric) = 1.8283761095564151423409675206182 absolute error = 0.0425690332932716571583650393339 relative error = 2.3837419987353099381005877927277 % h = 0.001 TOP MAIN SOLVE Loop memory used=2315.5MB, alloc=4.6MB, time=130.86 NO POLE NO POLE x[1] = 0.905 y2[1] (analytic) = 1.7864251549526740039181701757212 y2[1] (numeric) = 1.8677383380527813149279853773437 absolute error = 0.0813131831001073110098152016225 relative error = 4.5517262715807123084739090721137 % h = 0.001 y1[1] (analytic) = 1.7864251549526740039181701757212 y1[1] (numeric) = 1.8290841816602080475986833741257 absolute error = 0.0426590267075340436805131984045 relative error = 2.3879548823675272930523819432338 % h = 0.001 TOP MAIN SOLVE Loop memory used=2319.3MB, alloc=4.6MB, time=131.08 NO POLE NO POLE x[1] = 0.906 y2[1] (analytic) = 1.787042447217115105407128827208 y2[1] (numeric) = 1.8686506671848304772165193560779 absolute error = 0.0816082199677153718093905288699 relative error = 4.5666637686642736446688291453266 % h = 0.001 y1[1] (analytic) = 1.787042447217115105407128827208 y1[1] (numeric) = 1.8297915156640589437066789785666 absolute error = 0.0427490684469438382995501513586 relative error = 2.392168608726398030723306322781 % h = 0.001 TOP MAIN SOLVE Loop memory used=2323.1MB, alloc=4.6MB, time=131.29 NO POLE NO POLE x[1] = 0.907 y2[1] (analytic) = 1.7876589524391745766493972688437 y2[1] (numeric) = 1.8695628921480454038094193505575 absolute error = 0.0819039397088708271600220817138 relative error = 4.5816311661190656394610682919158 % h = 0.001 y1[1] (analytic) = 1.7876589524391745766493972688437 y1[1] (numeric) = 1.8304981107480601286421140826345 absolute error = 0.0428391583088855519927168137908 relative error = 2.3963831719933817858462234084342 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.908 y2[1] (analytic) = 1.7882746700023472469609377174681 y2[1] (numeric) = 1.8704750129395606764923788903755 absolute error = 0.0822003429372134295314411729074 relative error = 4.596628488682084576466935325144 % h = 0.001 y1[1] (analytic) = 1.7882746700023472469609377174681 y1[1] (numeric) = 1.8312039660929349709326079263954 absolute error = 0.0429292960905877239716702089273 relative error = 2.4005985663562173027243682986236 % h = 0.001 TOP MAIN SOLVE Loop memory used=2327.0MB, alloc=4.6MB, time=131.51 NO POLE NO POLE x[1] = 0.909 y2[1] (analytic) = 1.78888959929091560447887508227 y2[1] (numeric) = 1.8713870295565151404609944573195 absolute error = 0.0824974302655995359821193750495 relative error = 4.6116557611101359949379948010184 % h = 0.001 y1[1] (analytic) = 1.78888959929091560447887508227 y1[1] (numeric) = 1.8319090808800388276028095048157 absolute error = 0.0430194815891232231239344225457 relative error = 2.4048147860088956586649189557742 % h = 0.001 TOP MAIN SOLVE Loop memory used=2330.8MB, alloc=4.6MB, time=131.72 NO POLE NO POLE x[1] = 0.91 y2[1] (analytic) = 1.7895037396899504118789575178716 y2[1] (numeric) = 1.8722989419960519078183523489643 absolute error = 0.0827952023061014959393948310927 relative error = 4.6267130081799438186588781014306 % h = 0.001 y1[1] (analytic) = 1.7895037396899504118789575178716 y1[1] (numeric) = 1.832613454291359961611927781316 absolute error = 0.0431097146014095497329702634444 relative error = 2.409031825151633546435490296702 % h = 0.001 TOP MAIN SOLVE Loop memory used=2334.6MB, alloc=4.6MB, time=131.95 NO POLE NO POLE x[1] = 0.911 y2[1] (analytic) = 1.7901170905853113213047425044789 y2[1] (numeric) = 1.8732107502553183610687961240326 absolute error = 0.0830936596700070397640536195537 relative error = 4.6418002546882593786650495473167 % h = 0.001 y1[1] (analytic) = 1.7901170905853113213047425044789 y1[1] (numeric) = 1.8333170855095204587812219288802 absolute error = 0.0431999949242091374764794244013 relative error = 2.4132496779908466155054000578791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.912 y2[1] (analytic) = 1.7907296513636474885078935259636 y2[1] (numeric) = 1.8741224543314661566078705551035 absolute error = 0.0833928029678186680999770291399 relative error = 4.6569175254519703307680917918928 % h = 0.001 y1[1] (analytic) = 1.7907296513636474885078935259636 y1[1] (numeric) = 1.83401997371777714421045205035 absolute error = 0.0432903223541296557025585243864 relative error = 2.4174683387391228718343374326059 % h = 0.001 TOP MAIN SOLVE Loop memory used=2338.4MB, alloc=4.6MB, time=132.16 NO POLE NO POLE x[1] = 0.913 y2[1] (analytic) = 1.7913414214123981861989732056309 y2[1] (numeric) = 1.8750340542216512282084380175369 absolute error = 0.083692632809253042009464811906 relative error = 4.6720648453082094688734321828324 % h = 0.001 y1[1] (analytic) = 1.7913414214123981861989732056309 y1[1] (numeric) = 1.8347221181000224981822912046962 absolute error = 0.0433806966876243119833179990653 relative error = 2.4216878016151961359718450707875 % h = 0.001 TOP MAIN SOLVE Loop memory used=2342.2MB, alloc=4.6MB, time=132.38 NO POLE NO POLE x[1] = 0.914 y2[1] (analytic) = 1.7919524001197934166081195489314 y2[1] (numeric) = 1.8759455499230337905029632467775 absolute error = 0.0839931498032403738948436978461 relative error = 4.687242239114463435072804254473 % h = 0.001 y1[1] (analytic) = 1.7919524001197934166081195489314 y1[1] (numeric) = 1.8354235178407855715536999422873 absolute error = 0.0434711177209921549455803933559 relative error = 2.4259080608439195592318011645013 % h = 0.001 TOP MAIN SOLVE Loop memory used=2346.0MB, alloc=4.6MB, time=132.59 NO POLE NO POLE x[1] = 0.915 y2[1] (analytic) = 1.7925625868748545232549927324916 y2[1] (numeric) = 1.8768569414327783424619623994987 absolute error = 0.0842943545579238192069696670071 relative error = 4.7024497317486813274911259559033 % h = 0.001 y1[1] (analytic) = 1.7925625868748545232549927324916 y1[1] (numeric) = 1.836124172125232900633264929463 absolute error = 0.0435615852503783773782721969714 relative error = 2.4301291106562391977068610281832 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.916 y2[1] (analytic) = 1.7931719810673948019273806695674 y2[1] (numeric) = 1.8777682287480536708686123573507 absolute error = 0.0845962476806588689412316877833 relative error = 4.717687348109383206864878578075 % h = 0.001 y1[1] (analytic) = 1.7931719810673948019273806695674 y1[1] (numeric) = 1.8368240801391694215435036210755 absolute error = 0.0436520990717746196161229515081 relative error = 2.4343509452891676438885868362172 % h = 0.001 TOP MAIN SOLVE Loop memory used=2349.8MB, alloc=4.6MB, time=132.81 NO POLE NO POLE x[1] = 0.917 y2[1] (analytic) = 1.7937805820880201108678523733656 y2[1] (numeric) = 1.8786794118660328537895162153846 absolute error = 0.084898829778012742921663842019 relative error = 4.7329551131157685028264875528663 % h = 0.001 y1[1] (analytic) = 1.7937805820880201108678523733656 y1[1] (numeric) = 1.837523241069039384067137319077 absolute error = 0.0437426589810192731992849457114 relative error = 2.4385735589857577156597600172828 % h = 0.001 TOP MAIN SOLVE Loop memory used=2353.7MB, alloc=4.6MB, time=133.03 NO POLE NO POLE x[1] = 0.918 y2[1] (analytic) = 1.7943883893281294801678489316321 y2[1] (numeric) = 1.8795904907838932640416209005363 absolute error = 0.0852021014557637838737719689042 relative error = 4.7482530517078243208666382995831 % h = 0.001 y1[1] (analytic) = 1.7943883893281294801678489316321 y1[1] (numeric) = 1.8382216541019272649763353357101 absolute error = 0.043833264773797784808486404078 relative error = 2.4427969459950762024261332385149 % h = 0.001 TOP MAIN SOLVE Loop memory used=2357.5MB, alloc=4.6MB, time=133.25 NO POLE NO POLE x[1] = 0.919 y2[1] (analytic) = 1.7949954021799157203686026984643 y2[1] (numeric) = 1.8805014654988165726552828688702 absolute error = 0.0855060633189008522866801704059 relative error = 4.7635811888464336509439070308469 % h = 0.001 y1[1] (analytic) = 1.7949954021799157203686026984643 y1[1] (numeric) = 1.8389193184255586808439333613988 absolute error = 0.0439239162456429604753306629345 relative error = 2.4470211005721776681556379582558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.92 y2[1] (analytic) = 1.7956016200363660302682761024816 y2[1] (numeric) = 1.8814123360079887523334778336052 absolute error = 0.0858107159716227220652017311236 relative error = 4.7789395495134834787085478406007 % h = 0.001 y1[1] (analytic) = 1.7956016200363660302682761024816 y1[1] (numeric) = 1.839616233228301300335629520043 absolute error = 0.0440146131919352700673534175614 relative error = 2.4512460169780783110938191976447 % h = 0.001 TOP MAIN SOLVE Loop memory used=2361.3MB, alloc=4.6MB, time=133.46 NO POLE NO POLE x[1] = 0.921 y2[1] (analytic) = 1.7962070422912626039347122642647 y2[1] (numeric) = 1.8823231023086000809071504792704 absolute error = 0.0861160600173374769724382150057 relative error = 4.7943281587119728003047534242048 % h = 0.001 y1[1] (analytic) = 1.7962070422912626039347122642647 y1[1] (numeric) = 1.840312397699165755982161978082 absolute error = 0.0441053554079031520474497138173 relative error = 2.4554716894797298799250214934046 % h = 0.001 TOP MAIN SOLVE Loop memory used=2365.1MB, alloc=4.6MB, time=133.67 NO POLE NO POLE x[1] = 0.922 y2[1] (analytic) = 1.7968116683391832369231904103635 y2[1] (numeric) = 1.8832337643978451447867001206683 absolute error = 0.0864220960586619078635097103048 relative error = 4.8097470414661205417131973654458 % h = 0.001 y1[1] (analytic) = 1.7968116683391832369231904103635 y1[1] (numeric) = 1.8410078110278065554304723584224 absolute error = 0.0441961426886233185072819480589 relative error = 2.4596981123499936461495989610297 % h = 0.001 TOP MAIN SOLVE Loop memory used=2368.9MB, alloc=4.6MB, time=133.89 NO POLE NO POLE x[1] = 0.923 y2[1] (analytic) = 1.797415497575501931698579866169 y2[1] (numeric) = 1.884144322272922842409598268659 absolute error = 0.08672882469742091071101840249 relative error = 4.8251962228214733835931710100857 % h = 0.001 y1[1] (analytic) = 1.797415497575501931698579866169 y1[1] (numeric) = 1.8417024724045229921728595961122 absolute error = 0.0442869748290210604742797299432 relative error = 2.4639252798676144324481680330267 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.924 y2[1] (analytic) = 1.7980185293963895022612872055464 y2[1] (numeric) = 1.8850547759310363876841340681174 absolute error = 0.087036246534646885422846862571 relative error = 4.8406757278450134925811474725395 % h = 0.001 y1[1] (analytic) = 1.7980185293963895022612872055464 y1[1] (numeric) = 1.8423963810202600557531292594939 absolute error = 0.0443778516238705534918420539475 relative error = 2.4681531863171946968046637554608 % h = 0.001 TOP MAIN SOLVE Loop memory used=2372.7MB, alloc=4.6MB, time=134.11 NO POLE NO POLE x[1] = 0.925 y2[1] (analytic) = 1.7986207631988141779763919313308 y2[1] (numeric) = 1.8859651253693933134292835767608 absolute error = 0.08734436217057913545289164543 relative error = 4.8561855816252661600001392344928 % h = 0.001 y1[1] (analytic) = 1.7986207631988141779763919313308 y1[1] (numeric) = 1.843089536066609341448743748481 absolute error = 0.0444687728677951634723518171502 relative error = 2.4723818259891686721606995417997 % h = 0.001 TOP MAIN SOLVE Loop memory used=2376.6MB, alloc=4.6MB, time=134.32 NO POLE NO POLE x[1] = 0.926 y2[1] (analytic) = 1.7992221983805422066053668576022 y2[1] (numeric) = 1.8868753705852054748106988568913 absolute error = 0.0876531722046632682053319992891 relative error = 4.8717258092724073489317640339374 % h = 0.001 y1[1] (analytic) = 1.7992221983805422066053668576022 y1[1] (numeric) = 1.8437819367358099594279791705716 absolute error = 0.0445597383552677528226123129694 relative error = 2.4766111931797765613744660092115 % h = 0.001 TOP MAIN SOLVE Loop memory used=2380.4MB, alloc=4.6MB, time=134.54 NO POLE NO POLE x[1] = 0.927 y2[1] (analytic) = 1.7998228343401384565397801620681 y2[1] (numeric) = 1.8877855115756890527728128554522 absolute error = 0.0879626772355505962330326933841 relative error = 4.887296435918371150600496254708 % h = 0.001 y1[1] (analytic) = 1.7998228343401384565397801620681 y1[1] (numeric) = 1.8444735822207494433810950852482 absolute error = 0.0446507478806109868413149231801 relative error = 2.4808412821910387872581369742249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.928 y2[1] (analytic) = 1.8004226704769670182363768749028 memory used=2384.2MB, alloc=4.6MB, time=134.76 y2[1] (numeric) = 1.8886955483380645574670560511542 absolute error = 0.0882728778610975392306791762514 relative error = 4.9028974867169571510171577526885 % h = 0.001 y1[1] (analytic) = 1.8004226704769670182363768749028 y1[1] (numeric) = 1.8451644717149646586245236985023 absolute error = 0.0447418012379976403881468235995 relative error = 2.4850720873307302974684798743913 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.929 y2[1] (analytic) = 1.8010217061911918048529383690117 y2[1] (numeric) = 1.8896054808695568316761808507896 absolute error = 0.0885837746783650268232424817779 relative error = 4.918528986843937708826292940192 % h = 0.001 y1[1] (analytic) = 1.8010217061911918048529383690117 y1[1] (numeric) = 1.8458546044126427096770854813773 absolute error = 0.0448328982214509048241471123656 relative error = 2.4893036029123549240260938252702 % h = 0.001 TOP MAIN SOLVE Loop memory used=2388.0MB, alloc=4.6MB, time=134.99 NO POLE NO POLE x[1] = 0.93 y2[1] (analytic) = 1.8016199408837771520843192159106 y2[1] (numeric) = 1.8905153091673950542346897202206 absolute error = 0.08889536828361790215037050431 relative error = 4.9341909614971651452996779386149 % h = 0.001 y1[1] (analytic) = 1.8016199408837771520843192159106 y1[1] (numeric) = 1.8465439795086218473072385796342 absolute error = 0.0449240386248446952229193637236 relative error = 2.4935358232551197972394212305816 % h = 0.001 TOP MAIN SOLVE Loop memory used=2391.8MB, alloc=4.6MB, time=135.20 NO POLE NO POLE x[1] = 0.931 y2[1] (analytic) = 1.8022173739564884171980615712348 y2[1] (numeric) = 1.8914250332288127434453630388972 absolute error = 0.0892076592723243262473014676624 relative error = 4.9498834358966788474158326456079 % h = 0.001 y1[1] (analytic) = 1.8022173739564884171980615712348 y1[1] (numeric) = 1.8472325961983923750503697759165 absolute error = 0.0450152222419039578523082046817 relative error = 2.4977687426839098138103983515592 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2395.6MB, alloc=4.6MB, time=135.42 x[1] = 0.932 y2[1] (analytic) = 1.802814004811892577268988054311 y2[1] (numeric) = 1.8923346530510477604918826701381 absolute error = 0.0895206482391551832228946158271 relative error = 4.9656064352848122849630375925395 % h = 0.001 y1[1] (analytic) = 1.802814004811892577268988054311 y1[1] (numeric) = 1.8479204536780975551951351611237 absolute error = 0.0451064488662049779261471068127 relative error = 2.5020023555292621588993265234683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.933 y2[1] (analytic) = 1.8034098328533588266121748872515 y2[1] (numeric) = 1.8932441686313423128475472427866 absolute error = 0.0898343357779834862353723555351 relative error = 4.9813599849262999426010044348237 % h = 0.001 y1[1] (analytic) = 1.8034098328533588266121748872515 y1[1] (numeric) = 1.8486075511445345142378590680901 absolute error = 0.0451977182911756876256841808386 relative error = 2.5062366561273408819272587951414 % h = 0.001 TOP MAIN SOLVE Loop memory used=2399.4MB, alloc=4.6MB, time=135.63 NO POLE NO POLE x[1] = 0.934 y2[1] (analytic) = 1.8040048574850591734137078606457 y2[1] (numeric) = 1.8941535799669429576800751432406 absolute error = 0.0901487224818837842663672825949 relative error = 4.9971441101083841678140097687956 % h = 0.001 y1[1] (analytic) = 1.8040048574850591734137078606457 y1[1] (numeric) = 1.849293887795155147804000218117 absolute error = 0.0452890303100959743902923574713 relative error = 2.510471638819911525894906676262 % h = 0.001 TOP MAIN SOLVE Loop memory used=2403.3MB, alloc=4.6MB, time=135.85 NO POLE NO POLE x[1] = 0.935 y2[1] (analytic) = 1.8045990781119690355586244951433 y2[1] (numeric) = 1.895062887055100605252491220242 absolute error = 0.0904638089431315696938667250987 relative error = 5.0129588361409219356859766486634 % h = 0.001 y1[1] (analytic) = 1.8045990781119690355586244951433 y1[1] (numeric) = 1.8499794628280670250356944294141 absolute error = 0.0453803847160979894770699342708 relative error = 2.5147072979543158099977784190115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2407.1MB, alloc=4.6MB, time=136.07 x[1] = 0.936 y2[1] (analytic) = 1.8051924941398678356554465710368 y2[1] (numeric) = 1.8959720898930705223200932082091 absolute error = 0.0907795957532026866646466371723 relative error = 5.0288041883564915314256766330538 % h = 0.001 y1[1] (analytic) = 1.8051924941398678356554465710368 y1[1] (numeric) = 1.8506642754420342924443836360697 absolute error = 0.0454717813021664567889370650329 relative error = 2.5189436278834463653179638494016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.937 y2[1] (analytic) = 1.8057851049753395952567080013595 y2[1] (numeric) = 1.8968811884781123355234938782896 absolute error = 0.0910960835027727402667858769301 relative error = 5.0446801921104991515679273682044 % h = 0.001 y1[1] (analytic) = 1.8057851049753395952567080013595 y1[1] (numeric) = 1.8513483248364785772275413667953 absolute error = 0.0455632198611389819708333654358 relative error = 2.5231806229657215233736812125677 % h = 0.001 TOP MAIN SOLVE Loop memory used=2410.9MB, alloc=4.6MB, time=136.29 NO POLE NO POLE x[1] = 0.938 y2[1] (analytic) = 1.8063769100257735282748838280223 y2[1] (numeric) = 1.8977901828074900347777349297186 absolute error = 0.0914132727817165065028511016963 relative error = 5.0605868727812854247743765614393 % h = 0.001 y1[1] (analytic) = 1.8063769100257735282748838280223 y1[1] (numeric) = 1.8520316102114798900485052343715 absolute error = 0.0456547001857063617736214063492 relative error = 2.5274182775650601573083988180425 % h = 0.001 TOP MAIN SOLVE Loop memory used=2414.7MB, alloc=4.6MB, time=136.50 NO POLE NO POLE x[1] = 0.939 y2[1] (analytic) = 1.8069679086993646335931269251073 y2[1] (numeric) = 1.898699072878471976657468637471 absolute error = 0.0917311641791073430643417123637 relative error = 5.0765242557702318531551926610119 % h = 0.001 y1[1] (analytic) = 1.8069679086993646335931269251073 y1[1] (numeric) = 1.8527141307677775272784273894612 absolute error = 0.0457462220684128936853004643539 relative error = 2.5316565860508565755020384793776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2418.5MB, alloc=4.6MB, time=136.72 x[1] = 0.94 y2[1] (analytic) = 1.8075581004051142868702197986342 y2[1] (numeric) = 1.899607858688330887778203275611 absolute error = 0.0920497582832166009079834769768 relative error = 5.0924923665018671750307255836906 % h = 0.001 y1[1] (analytic) = 1.8075581004051142868702197986342 y1[1] (numeric) = 1.8533958857067709726993542962517 absolute error = 0.0458377853016566858291344976175 relative error = 2.5358955427979554673874588494326 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.941 y2[1] (analytic) = 1.8081474845528308315391496778929 y2[1] (numeric) = 1.9005165402343438681736083391576 absolute error = 0.0923690556815130366344586612647 relative error = 5.1084912304239736500499573682945 % h = 0.001 y1[1] (analytic) = 1.8081474845528308315391496778929 y1[1] (numeric) = 1.8540768742305207986674475922436 absolute error = 0.0459293896776899671282979143507 relative error = 2.5401351421866269012561047727273 % h = 0.001 TOP MAIN SOLVE Loop memory used=2422.3MB, alloc=4.6MB, time=136.94 NO POLE NO POLE x[1] = 0.942 y2[1] (analytic) = 1.8087360605531301689987158998209 y2[1] (numeric) = 1.9014251175137923946688755907061 absolute error = 0.0926890569606622256701596908852 relative error = 5.1245208730076932675803326281304 % h = 0.001 y1[1] (analytic) = 1.8087360605531301689987158998209 y1[1] (numeric) = 1.854757095541749566735358200411 absolute error = 0.0460210349886193977366423005901 relative error = 2.5443753786025413738373937200927 % h = 0.001 TOP MAIN SOLVE Loop memory used=2426.1MB, alloc=4.6MB, time=137.15 NO POLE NO POLE x[1] = 0.943 y2[1] (analytic) = 1.8093238278174363479975793948635 y2[1] (numeric) = 1.902333590523962324250131961471 absolute error = 0.0930097627065259762525525666075 relative error = 5.1405813197476338792813420780626 % h = 0.001 y1[1] (analytic) = 1.8093238278174363479975793948635 y1[1] (numeric) = 1.8554365488438427277327662689285 absolute error = 0.046112721026406379735186874065 relative error = 2.5486162464367449114370922539475 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2430.0MB, alloc=4.6MB, time=137.37 x[1] = 0.944 y2[1] (analytic) = 1.8099107857579821532101648903185 y2[1] (numeric) = 1.9032419592621438974299003398465 absolute error = 0.093331173504161744219735449528 relative error = 5.1566725961619752567720291695805 % h = 0.001 y1[1] (analytic) = 1.8099107857579821532101648903185 y1[1] (numeric) = 1.8561152333408495213040999216793 absolute error = 0.0462044475828673680939350313608 relative error = 2.5528577400856342224206143049506 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.945 y2[1] (analytic) = 1.8104969337878096930038272553123 y2[1] (numeric) = 1.9041502237256317416086042840137 absolute error = 0.0936532899378220486047770287014 relative error = 5.1727947277925750753003999296401 % h = 0.001 y1[1] (analytic) = 1.8104969337878096930038272553123 y1[1] (numeric) = 1.8567931482374838749024462118417 absolute error = 0.0462962144496741818986189565294 relative error = 2.5570998539509319008278488373914 % h = 0.001 TOP MAIN SOLVE Loop memory used=2433.8MB, alloc=4.6MB, time=137.59 NO POLE NO POLE x[1] = 0.946 y2[1] (analytic) = 1.8110822713207709863966942202884 y2[1] (numeric) = 1.905058383911724874432112698565 absolute error = 0.0939761125909538880354184782766 relative error = 5.1889477402050748243205394152638 % h = 0.001 y1[1] (analytic) = 1.8110822713207709863966942202884 y1[1] (numeric) = 1.8574702927391253022386680809831 absolute error = 0.0463880214183543158419738606947 relative error = 2.561342582439661680906797252805 % h = 0.001 TOP MAIN SOLVE Loop memory used=2437.6MB, alloc=4.6MB, time=137.81 NO POLE NO POLE x[1] = 0.947 y2[1] (analytic) = 1.8116667977715285492055985132169 y2[1] (numeric) = 1.9059664398177267071453205185579 absolute error = 0.094299642046198157939722005341 relative error = 5.2051316589890056458810747145322 % h = 0.001 y1[1] (analytic) = 1.8116667977715285492055985132169 y1[1] (numeric) = 1.8581466660518198011847415372825 absolute error = 0.0464798682802912519791430240656 relative error = 2.5655859199641237423539706418157 % h = 0.001 TOP MAIN SOLVE Loop memory used=2441.4MB, alloc=4.6MB, time=138.02 NO POLE NO POLE x[1] = 0.948 y2[1] (analytic) = 1.8122505125555559793835132646391 y2[1] (numeric) = 1.9068743914409450479417614478589 absolute error = 0.0946238788853890685582481832198 relative error = 5.2213465097578941017264740966164 % h = 0.001 y1[1] (analytic) = 1.8122505125555559793835132646391 y1[1] (numeric) = 1.8588222673822807511303276787469 absolute error = 0.0465717548267247717468144141078 relative error = 2.5698298609418700660501637560624 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.949 y2[1] (analytic) = 1.8128334150891385415459053441629 y2[1] (numeric) = 1.9077822387786921053092488020912 absolute error = 0.0949488236895535637633434579283 relative error = 5.2375923181493678700105346876567 % h = 0.001 y1[1] (analytic) = 1.8128334150891385415459053441629 y1[1] (numeric) = 1.8594970959378898097915946005883 absolute error = 0.0466636808487512682456892564254 relative error = 2.574074399795679840080886346841 % h = 0.001 TOP MAIN SOLVE Loop memory used=2445.2MB, alloc=4.6MB, time=138.24 NO POLE NO POLE x[1] = 0.95 y2[1] (analytic) = 1.8134155047893737506854221021026 y2[1] (numeric) = 1.9086899818282844913715405099563 absolute error = 0.0952744770389107406861184078537 relative error = 5.2538691098252613725192868768955 % h = 0.001 y1[1] (analytic) = 1.8134155047893737506854221021026 y1[1] (numeric) = 1.860171150926697809471304640282 absolute error = 0.0467556461373240587858825381794 relative error = 2.5783195309535349158313933180511 % h = 0.001 TOP MAIN SOLVE Loop memory used=2449.0MB, alloc=4.6MB, time=138.45 NO POLE NO POLE x[1] = 0.951 y2[1] (analytic) = 1.8139967810741719550743278016264 y2[1] (numeric) = 1.9095976205870432252260243301621 absolute error = 0.0956008395128712701516965285357 relative error = 5.2701769104717213332984324883025 % h = 0.001 y1[1] (analytic) = 1.8139967810741719550743278016264 y1[1] (numeric) = 1.8608444315574256527691828292362 absolute error = 0.0468476504832536976948550276098 relative error = 2.5825652488485953139469129796857 % h = 0.001 TOP MAIN SOLVE Loop memory used=2452.8MB, alloc=4.6MB, time=138.67 NO POLE NO POLE x[1] = 0.952 y2[1] (analytic) = 1.8145772433622569183541068390228 y2[1] (numeric) = 1.9105051550522937362774193446542 absolute error = 0.0959279116900368179233125056314 relative error = 5.28651574579931226957833553832 % h = 0.001 y1[1] (analytic) = 1.8145772433622569183541068390228 y1[1] (numeric) = 1.8615169370394652077415828364678 absolute error = 0.046939693677208289387475997445 relative error = 2.5868115479191747799493275774708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.953 y2[1] (analytic) = 1.815156891073166400811651662531 y2[1] (numeric) = 1.91141258522136586756748979232 absolute error = 0.096255694148199466755838129789 relative error = 5.3028856415431219158874990913296 % h = 0.001 y1[1] (analytic) = 1.815156891073166400811651662531 y1[1] (numeric) = 1.8621886665828802025094671071937 absolute error = 0.0470317755097138016978154446627 relative error = 2.591058422608716389302212225697 % h = 0.001 TOP MAIN SOLVE Loop memory used=2456.7MB, alloc=4.6MB, time=138.88 NO POLE NO POLE x[1] = 0.954 y2[1] (analytic) = 1.8157357236272527398414541135974 y2[1] (numeric) = 1.9123199110915938791007673108076 absolute error = 0.0965841874643411392593131972102 relative error = 5.319286623462866582243389272019 % h = 0.001 y1[1] (analytic) = 1.8157357236272527398414541135974 y1[1] (numeric) = 1.862859619398407119313718317821 absolute error = 0.0471238957711543794722642042236 relative error = 2.5953058673657682017167873966291 % h = 0.001 TOP MAIN SOLVE Loop memory used=2460.5MB, alloc=4.6MB, time=139.10 NO POLE NO POLE x[1] = 0.955 y2[1] (analytic) = 1.8163137404456834295932197284128 y2[1] (numeric) = 1.913227132660316451166277657583 absolute error = 0.0969133922146330215730579291702 relative error = 5.3357187173429964473074078506172 % h = 0.001 y1[1] (analytic) = 1.8163137404456834295932197284128 y1[1] (numeric) = 1.8635297946974560880167996884409 absolute error = 0.0472160542517726584235799600281 relative error = 2.5995538766439589644919862328866 % h = 0.001 TOP MAIN SOLVE Loop memory used=2464.3MB, alloc=4.6MB, time=139.32 NO POLE NO POLE x[1] = 0.956 y2[1] (analytic) = 1.8168909409504416998043253521668 y2[1] (numeric) = 1.9141342499248766876552679848319 absolute error = 0.0972433089744349878509426326651 relative error = 5.352181948992800787388767933639 % h = 0.001 y1[1] (analytic) = 1.8168909409504416998043253521668 y1[1] (numeric) = 1.8641991916921117790497821146096 absolute error = 0.0473082507416700792454567624428 relative error = 2.6038024449019738646824811605968 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.957 y2[1] (analytic) = 1.8174673245643270938165412336083 y2[1] (numeric) = 1.9150412628826221193749307463003 absolute error = 0.097573938318295025558389512692 relative error = 5.3686763442465131421799931228434 % h = 0.001 y1[1] (analytic) = 1.8174673245643270938165412336083 y1[1] (numeric) = 1.8648678095951342958037565019286 absolute error = 0.0474004850308072019872152683203 relative error = 2.6080515666035303298891546035398 % h = 0.001 TOP MAIN SOLVE Loop memory used=2468.1MB, alloc=4.6MB, time=139.53 NO POLE NO POLE x[1] = 0.958 y2[1] (analytic) = 1.8180428907109560457764395832387 y2[1] (numeric) = 1.9159481715309047073581203176622 absolute error = 0.0979052808199486615816807344235 relative error = 5.3852019289634164181047390002255 % h = 0.001 y1[1] (analytic) = 1.8180428907109560457764395832387 y1[1] (numeric) = 1.86553564761996006646465010972 absolute error = 0.0474927569090040206882105264813 relative error = 2.6123012362173538774671360431425 % h = 0.001 TOP MAIN SOLVE Loop memory used=2471.9MB, alloc=4.6MB, time=139.75 NO POLE NO POLE x[1] = 0.959 y2[1] (analytic) = 1.8186176388147624570189123947776 y2[1] (numeric) = 1.9168549758670808461690584154989 absolute error = 0.0982373370523183891501460207213 relative error = 5.4017587290279479301566269101096 % h = 0.001 y1[1] (analytic) = 1.8186176388147624570189123947776 y1[1] (numeric) = 1.8662027049807027352904661339256 absolute error = 0.047585066165940278271553739148 relative error = 2.6165514482171540119471622481503 % h = 0.001 TOP MAIN SOLVE Loop memory used=2475.7MB, alloc=4.6MB, time=139.97 NO POLE NO POLE x[1] = 0.96 y2[1] (analytic) = 1.8191915683009982716332221464304 y2[1] (numeric) = 1.9177616758885113672050244034764 absolute error = 0.098570107587513095571802257046 relative error = 5.4183467703498043831057836939533 % h = 0.001 y1[1] (analytic) = 1.8191915683009982716332221464304 y1[1] (numeric) = 1.8668689808921540533299661842456 absolute error = 0.0476774125911557816967440378152 relative error = 2.6208021970816001704666492229975 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.961 y2[1] (analytic) = 1.8197646785957340512110098159569 y2[1] (numeric) = 1.9186682715925615419940265778133 absolute error = 0.0989035929968274907830167618564 relative error = 5.434966078864046792947797242271 % h = 0.001 y1[1] (analytic) = 1.8197646785957340512110098159569 y1[1] (numeric) = 1.8675344745697847685818157364705 absolute error = 0.0477697959740507173708059205136 relative error = 2.6250534772942977160074933066054 % h = 0.001 TOP MAIN SOLVE Loop memory used=2479.6MB, alloc=4.6MB, time=140.18 NO POLE NO POLE x[1] = 0.962 y2[1] (analytic) = 1.820336969125859548775685461578 y2[1] (numeric) = 1.9195747629766010854884505276426 absolute error = 0.0992377938507415367127650660646 relative error = 5.451616680531205349467826415438 % h = 0.001 y1[1] (analytic) = 1.820336969125859548775685461578 y1[1] (numeric) = 1.8681991852297455155932130679501 absolute error = 0.0478622161038859668175276063721 relative error = 2.6293052833437639782382449059355 % h = 0.001 TOP MAIN SOLVE Loop memory used=2483.4MB, alloc=4.6MB, time=140.40 NO POLE NO POLE x[1] = 0.963 y2[1] (analytic) = 1.8209084393190842818926274393802 y2[1] (numeric) = 1.9204811500380041593546806693859 absolute error = 0.0995727107189198774620532300057 relative error = 5.4682986013373842207906450038591 % h = 0.001 y1[1] (analytic) = 1.8209084393190842818926274393802 y1[1] (numeric) = 1.868863112088867704497022612181 absolute error = 0.0479546727697834226043951728008 relative error = 2.6335576097234043417589215814436 % h = 0.001 TOP MAIN SOLVE Loop memory used=2487.2MB, alloc=4.6MB, time=140.62 NO POLE NO POLE x[1] = 0.964 y2[1] (analytic) = 1.8214790886039381049596171470655 y2[1] (numeric) = 1.9213874327741493752586910577775 absolute error = 0.099908344170211270299073910712 relative error = 5.4850118672943663007854529032664 % h = 0.001 y1[1] (analytic) = 1.8214790886039381049596171470655 y1[1] (numeric) = 1.8695262543646644094864340975888 absolute error = 0.0480471657607263045268169505233 relative error = 2.6378104509314883815473476277746 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.965 y2[1] (analytic) = 1.8220489164097717806769370036593 y2[1] (numeric) = 1.9222936111824197981476015796997 absolute error = 0.1002446947726480174706645760404 relative error = 5.5017565044397179001923535264746 % h = 0.001 y1[1] (analytic) = 1.8220489164097717806769370036593 y1[1] (numeric) = 1.87018861127533125672616926572 absolute error = 0.0481396948655594760492322620607 relative error = 2.6420638014711260454065249226244 % h = 0.001 TOP MAIN SOLVE Loop memory used=2491.0MB, alloc=4.6MB, time=140.84 NO POLE NO POLE x[1] = 0.966 y2[1] (analytic) = 1.8226179221667575506965601951263 y2[1] (numeric) = 1.9231996852602029495271956405198 absolute error = 0.1005817630934453988306354453935 relative error = 5.5185325388368933823354746136626 % h = 0.001 y1[1] (analytic) = 1.8226179221667575506965601951263 y1[1] (numeric) = 1.8708501820397473116992583952511 absolute error = 0.0482322598729897610026982001248 relative error = 2.646317655850243883213154661873 % h = 0.001 TOP MAIN SOLVE Loop memory used=2494.8MB, alloc=4.6MB, time=141.06 NO POLE NO POLE x[1] = 0.967 y2[1] (analytic) = 1.8231861053058897054498615367527 y2[1] (numeric) = 1.9241056550048908107353954561517 absolute error = 0.100919549699001105285533919399 relative error = 5.5353399965753397442857999940371 % h = 0.001 y1[1] (analytic) = 1.8231861053058897054498615367527 y1[1] (numeric) = 1.8715109658774759659884092904649 absolute error = 0.0483248605715862605385477537122 relative error = 2.6505720085815613227680416710421 % h = 0.001 TOP MAIN SOLVE Loop memory used=2498.6MB, alloc=4.6MB, time=141.28 NO POLE NO POLE x[1] = 0.968 y2[1] (analytic) = 1.8237534652589851531532796246302 y2[1] (numeric) = 1.9250115204138798262116910676012 absolute error = 0.101258055154894673058411442971 relative error = 5.5521789037706011443348824478218 % h = 0.001 y1[1] (analytic) = 1.8237534652589851531532796246302 y1[1] (numeric) = 1.8721709620087658234909918261345 absolute error = 0.0484174967497806703377122015043 relative error = 2.6548268541825669920497222931357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.969 y2[1] (analytic) = 1.8243200014586839879913612706282 y2[1] (numeric) = 1.925917281484570906762519198298 absolute error = 0.1015972800258869187711579276698 relative error = 5.5690492865644233766387225742573 % h = 0.001 y1[1] (analytic) = 1.8243200014586839879913612706282 y1[1] (numeric) = 1.8728301696545515860666615750955 absolute error = 0.0485101681958675980753003044673 relative error = 2.6590821871754950876732634119895 % h = 0.001 TOP MAIN SOLVE Loop memory used=2502.4MB, alloc=4.6MB, time=141.49 NO POLE NO POLE x[1] = 0.97 y2[1] (analytic) = 1.8248857133384500574766200378563 y2[1] (numeric) = 1.9268229382143694328225880780611 absolute error = 0.1019372248759193753459680402048 relative error = 5.5859511711248582938892254444163 % h = 0.001 y1[1] (analytic) = 1.8248857133384500574766200378563 y1[1] (numeric) = 1.8734885880364549386166464801786 absolute error = 0.0486028746980048811400264423223 relative error = 2.6633380020873017893567839901583 % h = 0.001 TOP MAIN SOLVE Loop memory used=2506.3MB, alloc=4.6MB, time=141.72 NO POLE NO POLE x[1] = 0.971 y2[1] (analytic) = 1.8254506003325715289856415168064 y2[1] (numeric) = 1.927728490600685257712144361096 absolute error = 0.1022778902681137287265028442896 relative error = 5.6028845836463681788687857631133 % h = 0.001 y1[1] (analytic) = 1.8254506003325715289856415168064 y1[1] (numeric) = 1.8741462163767854335937209686113 absolute error = 0.0486956160442139046080794518049 relative error = 2.6675942934496417201988515914543 % h = 0.001 TOP MAIN SOLVE Loop memory used=2510.1MB, alloc=4.6MB, time=141.94 NO POLE NO POLE x[1] = 0.972 y2[1] (analytic) = 1.8260146618761614554708688061158 y2[1] (numeric) = 1.9286339386409327108901782689775 absolute error = 0.1026192767647712554193094628617 relative error = 5.6198495503499300657417032383278 % h = 0.001 y1[1] (analytic) = 1.8260146618761614554708688061158 y1[1] (numeric) = 1.8748030538985413749418923444843 absolute error = 0.0487883920223799194710235383685 relative error = 2.6718510557988444525705047322202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.973 y2[1] (analytic) = 1.8265778974051583403475024862134 y2[1] (numeric) = 1.9295392823325306012035630931296 absolute error = 0.1029613849273722608560606069162 relative error = 5.6368460974831400119342928155007 % h = 0.001 y1[1] (analytic) = 1.8265778974051583403475024862134 y1[1] (numeric) = 1.8754590998254107014648247334153 absolute error = 0.0488812024202523611173222472019 relative error = 2.6761082836758910594262475730475 % h = 0.001 TOP MAIN SOLVE Loop memory used=2513.9MB, alloc=4.6MB, time=142.15 NO POLE NO POLE x[1] = 0.974 y2[1] (analytic) = 1.8271403063563267015549501989961 y2[1] (numeric) = 1.9304445216729022201321251948795 absolute error = 0.1033042153165755185771749958834 relative error = 5.6538742513203173214537293350279 % h = 0.001 y1[1] (analytic) = 1.8271403063563267015549501989961 y1[1] (numeric) = 1.8761143533817718696220262931229 absolute error = 0.0489740470254451680670760941268 relative error = 2.6803659716263907108389564346972 % h = 0.001 TOP MAIN SOLVE Loop memory used=2517.7MB, alloc=4.6MB, time=142.37 NO POLE NO POLE x[1] = 0.975 y2[1] (analytic) = 1.8277018881672576347922617721328 y2[1] (numeric) = 1.93134965665947534502964064473 absolute error = 0.1036477684922177102373788725972 relative error = 5.6709340381626087204938529708076 % h = 0.001 y1[1] (analytic) = 1.8277018881672576347922617721328 y1[1] (numeric) = 1.876768813792694735751825844256 absolute error = 0.0490669256254371009595640721232 relative error = 2.6846241142005573155642279098036 % h = 0.001 TOP MAIN SOLVE Loop memory used=2521.5MB, alloc=4.6MB, time=142.59 NO POLE NO POLE x[1] = 0.976 y2[1] (analytic) = 1.8282626422763693759269866526067 y2[1] (numeric) = 1.9322546872896822423607546460668 absolute error = 0.1039920450133128664337679934601 relative error = 5.688025484338092486174360463274 % h = 0.001 y1[1] (analytic) = 1.8282626422763693759269866526067 y1[1] (numeric) = 1.8774224802839414377201655175011 absolute error = 0.0491598380075720617931788648944 relative error = 2.6888827059531862074402859560194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.977 y2[1] (analytic) = 1.8288225681229078625768912406878 y2[1] (numeric) = 1.9331596135609596709338198920948 absolute error = 0.104337045438051808356928651407 relative error = 5.7051486162018825292580176291573 % h = 0.001 y1[1] (analytic) = 1.8288225681229078625768912406878 y1[1] (numeric) = 1.8780753520819672759942364557139 absolute error = 0.0492527839590594134173452150261 relative error = 2.6931417414436308764301503072338 % h = 0.001 TOP MAIN SOLVE Loop memory used=2525.3MB, alloc=4.6MB, time=142.80 NO POLE NO POLE x[1] = 0.978 y2[1] (analytic) = 1.8293816651469472948639745426626 y2[1] (numeric) = 1.9340644354707488851296500083793 absolute error = 0.1046827703238015902656754657167 relative error = 5.7223034601362324316887508706558 % h = 0.001 y1[1] (analytic) = 1.8293816651469472948639745426626 y1[1] (numeric) = 1.8787274284139215941399850535941 absolute error = 0.0493457632669742992760105109315 relative error = 2.6974012152357797441133508389359 % h = 0.001 TOP MAIN SOLVE Loop memory used=2529.1MB, alloc=4.6MB, time=143.02 NO POLE NO POLE x[1] = 0.979 y2[1] (analytic) = 1.8299399327893906953402213883531 y2[1] (numeric) = 1.9349691530164956381261842369521 absolute error = 0.105029220227104942785962848599 relative error = 5.7394900425506394397917093756895 % h = 0.001 y1[1] (analytic) = 1.8299399327893906953402213883531 y1[1] (numeric) = 1.8793787085076486587425176622398 absolute error = 0.0494387757182579634022962738867 relative error = 2.7016611218980329834350521812601 % h = 0.001 TOP MAIN SOLVE Loop memory used=2533.0MB, alloc=4.6MB, time=143.23 NO POLE NO POLE x[1] = 0.98 y2[1] (analytic) = 1.8304973704919704680845332877192 y2[1] (numeric) = 1.9358737661956501851190595215348 absolute error = 0.1053763957036797170345262338156 relative error = 5.7567083898819484139746353576829 % h = 0.001 y1[1] (analytic) = 1.8304973704919704680845332877192 y1[1] (numeric) = 1.8800291915916885387484321317806 absolute error = 0.0495318210997180706638988440614 relative error = 2.7059214560032793825210299000869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.981 y2[1] (analytic) = 1.8310539776972489569702778296585 y2[1] (numeric) = 1.9367782750056672865380861570242 absolute error = 0.1057242973084183295678083273657 relative error = 5.7739585285944557357681369858135 % h = 0.001 y1[1] (analytic) = 1.8310539776972489569702778296585 y1[1] (numeric) = 1.8806788768952779842291050122002 absolute error = 0.0496248991980290272588271825417 relative error = 2.7101822121288732523675139734764 % h = 0.001 TOP MAIN SOLVE Loop memory used=2536.8MB, alloc=4.6MB, time=143.45 NO POLE NO POLE x[1] = 0.982 y2[1] (analytic) = 1.831609753848619003102898355503 y2[1] (numeric) = 1.9376826794440062112596231699849 absolute error = 0.1060729255953872081567248144819 relative error = 5.7912404851800131730407275634931 % h = 0.001 y1[1] (analytic) = 1.831609753848619003102898355503 y1[1] (numeric) = 1.8813277636483513045639636804126 absolute error = 0.0497180097997323014610653249096 relative error = 2.7144433848566113782154870873373 % h = 0.001 TOP MAIN SOLVE Loop memory used=2540.6MB, alloc=4.6MB, time=143.66 NO POLE NO POLE x[1] = 0.983 y2[1] (analytic) = 1.8321646983903045014270264696466 y2[1] (numeric) = 1.9385869795081307398148496004976 absolute error = 0.106422281117826238387823130851 relative error = 5.8085542861581317042227749836398 % h = 0.001 y1[1] (analytic) = 1.8321646983903045014270264696466 y1[1] (numeric) = 1.8819758510815412460427731106563 absolute error = 0.0498111526912367446157466410097 relative error = 2.7187049687727100144195944722588 % h = 0.001 TOP MAIN SOLVE Loop memory used=2544.4MB, alloc=4.6MB, time=143.88 NO POLE NO POLE x[1] = 0.984 y2[1] (analytic) = 1.8327188107673609565025407802402 y2[1] (numeric) = 1.939491175195509167593927859318 absolute error = 0.1067723644281482110913870790778 relative error = 5.8258999580760853023717974820597 % h = 0.001 y1[1] (analytic) = 1.8327188107673609565025407802402 y1[1] (numeric) = 1.8826231384261798688859674553178 absolute error = 0.0499043276588189123834266750776 relative error = 2.7229669584677819226223886121081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2548.2MB, alloc=4.6MB, time=144.09 x[1] = 0.985 y2[1] (analytic) = 1.8332720904256760374490160939396 y2[1] (numeric) = 1.9403952665036143080460553379147 absolute error = 0.1071231760779382705970392439751 relative error = 5.8432775275090146799098451859287 % h = 0.001 y1[1] (analytic) = 1.8332720904256760374490160939396 y1[1] (numeric) = 1.883269624914299423682057054383 absolute error = 0.0499975344886233862330409604434 relative error = 2.7272293485368134530451961856257 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.986 y2[1] (analytic) = 1.8338245368119701320580081203051 y2[1] (numeric) = 1.9412992534299234958754004525707 absolute error = 0.1074747166179533638173923322656 relative error = 5.860687021060030994862021871186 % h = 0.001 y1[1] (analytic) = 1.8338245368119701320580081203051 y1[1] (numeric) = 1.88391530977863322724114194385 absolute error = 0.0500907729666630951831338235449 relative error = 2.7314921335791416687074560643821 % h = 0.001 TOP MAIN SOLVE Loop memory used=2552.0MB, alloc=4.6MB, time=144.31 NO POLE NO POLE x[1] = 0.987 y2[1] (analytic) = 1.8343761493737969000726195736126 y2[1] (numeric) = 1.9422031359719185902329193073531 absolute error = 0.1078269865981216901602997337405 relative error = 5.8781284653603195194235276616025 % h = 0.001 y1[1] (analytic) = 1.8343761493737969000726195736126 y1[1] (numeric) = 1.8845601922526165378635633866159 absolute error = 0.0501840428788196377909438130033 relative error = 2.7357553081984315123869360951594 % h = 0.001 TOP MAIN SOLVE Loop memory used=2555.8MB, alloc=4.6MB, time=144.53 NO POLE NO POLE x[1] = 0.988 y2[1] (analytic) = 1.8349269275595438256337943925575 y2[1] (numeric) = 1.9431069141270859779040491643817 absolute error = 0.1081799865675421522702547718242 relative error = 5.895601887069243271680941082812 % h = 0.001 y1[1] (analytic) = 1.8349269275595438256337943925575 y1[1] (numeric) = 1.8852042715703874300227254035686 absolute error = 0.0502773440108436043889310110111 relative error = 2.7400188670026530161337927512503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2559.7MB, alloc=4.6MB, time=144.74 x[1] = 0.989 y2[1] (analytic) = 1.8354768708184327688927876316028 y2[1] (numeric) = 1.9440105878929165764922749134568 absolute error = 0.108533717074483807599487281854 relative error = 5.9131073128744466113118078875935 % h = 0.001 y1[1] (analytic) = 1.8354768708184327688927876316028 y1[1] (numeric) = 1.8858475469667876684611187378826 absolute error = 0.0503706761483548995683311062798 relative error = 2.7442828046040585531519915566787 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.99 y2[1] (analytic) = 1.8360259786005205167892594115471 y2[1] (numeric) = 1.9449141572669058375985647367395 absolute error = 0.1088881786663853208093053251924 relative error = 5.9306447694919588000849643544086 % h = 0.001 y1[1] (analytic) = 1.8360259786005205167892594115471 y1[1] (numeric) = 1.8864900176773635816985801418229 absolute error = 0.0504640390768430649093207302758 relative error = 2.7485471156191601318621574790291 % h = 0.001 TOP MAIN SOLVE Loop memory used=2563.5MB, alloc=4.6MB, time=144.96 NO POLE NO POLE x[1] = 0.991 y2[1] (analytic) = 1.8365742503566993329944421512648 y2[1] (numeric) = 1.9458176222465537499966711678176 absolute error = 0.1092433718898544170022290165528 relative error = 5.9482142836662975279823942907303 % h = 0.001 y1[1] (analytic) = 1.8365742503566993329944421512648 y1[1] (numeric) = 1.8871316829383669349518203327142 absolute error = 0.0505574325816676019573781814494 relative error = 2.7528117946687067319604732611428 % h = 0.001 TOP MAIN SOLVE Loop memory used=2567.3MB, alloc=4.6MB, time=145.17 NO POLE NO POLE x[1] = 0.992 y2[1] (analytic) = 1.8371216855386975070188311374976 y2[1] (numeric) = 1.9467209828293648428042937481314 absolute error = 0.1095992972906673357854626106338 relative error = 5.9658158821705724057618017069297 % h = 0.001 y1[1] (analytic) = 1.8371216855386975070188311374976 y1[1] (numeric) = 1.8877725419867558024642544231216 absolute error = 0.050650856448058295445423285624 relative error = 2.7570768363776616822887899288306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2571.1MB, alloc=4.6MB, time=145.39 x[1] = 0.993 y2[1] (analytic) = 1.8376682835990799024838493250508 y2[1] (numeric) = 1.9476242390128481886500994873816 absolute error = 0.1099559554137682861662501623308 relative error = 5.9834495918065884247774750271069 % h = 0.001 y1[1] (analytic) = 1.8376682835990799024838493250508 y1[1] (numeric) = 1.8884125940601954392451690897287 absolute error = 0.0507443104611155367613197646779 relative error = 2.7613422353751800803316574818482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.994 y2[1] (analytic) = 1.8382140439912485045569380957782 y2[1] (numeric) = 1.9485273907945174068365973381926 absolute error = 0.1103133468032689022796592424144 relative error = 6.0011154394049493848754237311194 % h = 0.001 y1[1] (analytic) = 1.8382140439912485045569380957782 y1[1] (numeric) = 1.8890518383970591522172612058708 absolute error = 0.0508377944058106476603231100926 relative error = 2.7656079862945862531565250570571 % h = 0.001 TOP MAIN SOLVE Loop memory used=2574.9MB, alloc=4.6MB, time=145.60 NO POLE NO POLE x[1] = 0.995 y2[1] (analytic) = 1.8387589661694429665495265413068 y2[1] (numeric) = 1.9494304381718906664988628989608 absolute error = 0.110671472002447699949336357654 relative error = 6.0188134518251612911771844400851 % h = 0.001 y1[1] (analytic) = 1.8387589661694429665495265413068 y1[1] (numeric) = 1.8896902742364291707715831242026 absolute error = 0.0509313080669862042220565828958 relative error = 2.7698740837733512596138986578189 % h = 0.001 TOP MAIN SOLVE Loop memory used=2578.7MB, alloc=4.6MB, time=145.82 NO POLE NO POLE x[1] = 0.996 y2[1] (analytic) = 1.8393030495887411556773326715804 y2[1] (numeric) = 1.9503333811424906897591095624764 absolute error = 0.111030331553749534081776890896 relative error = 6.0365436559557357205651206262963 % h = 0.001 y1[1] (analytic) = 1.8393030495887411556773326715804 y1[1] (numeric) = 1.8903279008180975167289302585365 absolute error = 0.0510248512293563610515975869561 relative error = 2.7741405224530704336147808798716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2582.5MB, alloc=4.6MB, time=146.03 x[1] = 0.997 y2[1] (analytic) = 1.839846293705059697982450788966 y2[1] (numeric) = 1.9512362197038447548771023315726 absolute error = 0.1113899259987850568946515426066 relative error = 6.0543060787142931586804783115418 % h = 0.001 y1[1] (analytic) = 1.839846293705059697982450788966 y1[1] (numeric) = 1.8909647173825668737067070774886 absolute error = 0.0511184236775071757242562885226 relative error = 2.7784072969794409683032509427853 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.998 y2[1] (analytic) = 1.8403886979751545224166801058793 y2[1] (numeric) = 1.9521389538534846993964105267246 absolute error = 0.1117502558783301769797304208453 relative error = 6.0721007470476663082439092769049 % h = 0.001 y1[1] (analytic) = 1.8403886979751545224166801058793 y1[1] (numeric) = 1.8916007231710514558903080872102 absolute error = 0.0512120251958969334736279813309 relative error = 2.7826744020022395409425747663993 % h = 0.001 TOP MAIN SOLVE Loop memory used=2586.4MB, alloc=4.6MB, time=146.25 NO POLE NO POLE x[1] = 0.999 y2[1] (analytic) = 1.8409302618566214040855505226477 y2[1] (numeric) = 1.9530415835889469232864956141939 absolute error = 0.1121113217323255192009450915462 relative error = 6.0899276879320033695066334047899 % h = 0.001 y1[1] (analytic) = 1.8409302618566214040855505226477 y1[1] (numeric) = 1.8922359174254778762080508461613 absolute error = 0.0513056555688564721225003235136 relative error = 2.7869418321752999783337638228259 % h = 0.001 TOP MAIN SOLVE Loop memory used=2590.2MB, alloc=4.6MB, time=146.47 NO POLE NO POLE x[1] = 1 y2[1] (analytic) = 1.8414709848078965066525023216303 y2[1] (numeric) = 1.9539441089077723920806303869909 absolute error = 0.1124731240998758854281280653606 relative error = 6.1077869283728712936388827737049 % h = 0.001 y1[1] (analytic) = 1.8414709848078965066525023216303 y1[1] (numeric) = 1.8928702993884860139086985216049 absolute error = 0.0513993145805895072561961999746 relative error = 2.7912095821564909625860280571504 % h = 0.001 TOP MAIN SOLVE Loop memory used=2594.0MB, alloc=4.6MB, time=146.69 NO POLE NO POLE x[1] = 1.001 y2[1] (analytic) = 1.8420108662882569239026773734589 y2[1] (numeric) = 1.9548465298075066400096457346103 absolute error = 0.1128356635192497161069683611514 relative error = 6.1256784954053590098607519910043 % h = 0.001 y1[1] (analytic) = 1.8420108662882569239026773734589 y1[1] (numeric) = 1.8935038683034298815406099652599 absolute error = 0.051493002015172957637932591801 relative error = 2.7954776466076937770590923127572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.002 y2[1] (analytic) = 1.842549905757821220465780291656 y2[1] (numeric) = 1.9557488462856997731315012411798 absolute error = 0.1131989405278785526657209495238 relative error = 6.1436024160941806271190719414731 % h = 0.001 y1[1] (analytic) = 1.842549905757821220465780291656 y1[1] (numeric) = 1.8941366234143784913315557543484 absolute error = 0.0515867176565572708657754626924 relative error = 2.7997460201947800922978674296554 % h = 0.001 TOP MAIN SOLVE Loop memory used=2597.8MB, alloc=4.6MB, time=146.91 NO POLE NO POLE x[1] = 1.003 y2[1] (analytic) = 1.8430881026775499716974688128113 y2[1] (numeric) = 1.9566510583399064724566758553544 absolute error = 0.1135629556623565007592070425431 relative error = 6.1615587175337786111124276147299 % h = 0.001 y1[1] (analytic) = 1.8430881026775499716974688128113 y1[1] (numeric) = 1.8947685639661167209682391141128 absolute error = 0.0516804612885667492707703013015 relative error = 2.8040146975875897917804865166111 % h = 0.001 TOP MAIN SOLVE Loop memory used=2601.6MB, alloc=4.6MB, time=147.12 NO POLE NO POLE x[1] = 1.004 y2[1] (analytic) = 1.8436254565092463027187335209743 y2[1] (numeric) = 1.9575531659676859970693748789807 absolute error = 0.1139277094584396943506413580064 relative error = 6.1795474268484269374649549144066 % h = 0.001 y1[1] (analytic) = 1.8436254565092463027187335209743 y1[1] (numeric) = 1.8953996892041461787745611087526 absolute error = 0.0517742326948998760558275877783 relative error = 2.8082836734599088373012338383859 % h = 0.001 TOP MAIN SOLVE Loop memory used=2605.4MB, alloc=4.6MB, time=147.34 NO POLE NO POLE x[1] = 1.005 y2[1] (analytic) = 1.844161966715556426612727876925 y2[1] (numeric) = 1.9584551691666021872445495252578 absolute error = 0.1142932024510457606318216483328 relative error = 6.1975685711923342218480763127142 % h = 0.001 y1[1] (analytic) = 1.844161966715556426612727876925 y1[1] (numeric) = 1.8960299983746860682876699596464 absolute error = 0.0518680316591296416749420827214 relative error = 2.8125529424894471738104083188438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.006 y2[1] (analytic) = 1.8446976327599701817785103555398 y2[1] (numeric) = 1.9593570679342234675607253008219 absolute error = 0.1146594351742532857822149452821 relative error = 6.2156221777497468278478708575939 % h = 0.001 y1[1] (analytic) = 1.8446976327599701817785103555398 y1[1] (numeric) = 1.8966594907246740522308348226763 absolute error = 0.0519618579647038704523244671365 relative error = 2.8168224993578166735336758469001 % h = 0.001 TOP MAIN SOLVE Loop memory used=2609.3MB, alloc=4.6MB, time=147.55 NO POLE NO POLE x[1] = 1.007 y2[1] (analytic) = 1.8452324541068215684411613375549 y2[1] (numeric) = 1.9602588622681228500086354698912 absolute error = 0.1150264081613012815674741323363 relative error = 6.2337082737350519533743203323483 % h = 0.001 y1[1] (analytic) = 1.8452324541068215684411613375549 y1[1] (numeric) = 1.897288165501767115882184830462 absolute error = 0.0520557113949455474410234929071 relative error = 2.8210923387505091191939743957432 % h = 0.001 TOP MAIN SOLVE Loop memory used=2613.1MB, alloc=4.6MB, time=147.77 NO POLE NO POLE x[1] = 1.008 y2[1] (analytic) = 1.8457664302212892843177382456532 y2[1] (numeric) = 1.9611605521658779370956558623196 absolute error = 0.1153941219445886527779176166664 relative error = 6.2518268863928806964072302732392 % h = 0.001 y1[1] (analytic) = 1.8457664302212892843177382456532 y1[1] (numeric) = 1.8979160219543424298383546803391 absolute error = 0.0521495917330531455206164346859 relative error = 2.8253624553568742261595434351385 % h = 0.001 TOP MAIN SOLVE Loop memory used=2616.9MB, alloc=4.6MB, time=147.99 NO POLE NO POLE x[1] = 1.009 y2[1] (analytic) = 1.8462995605693972594385332589671 y2[1] (numeric) = 1.9620621376250709249460372911228 absolute error = 0.1157625770556736655075040321557 relative error = 6.2699780429982111008721920336599 % h = 0.001 y1[1] (analytic) = 1.8462995605693972594385332589671 y1[1] (numeric) = 1.8985430593314982121720785249787 absolute error = 0.0522434987621009527335452660116 relative error = 2.8296328438700977033421542407301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.01 y2[1] (analytic) = 1.846831844618015190123098784782 y2[1] (numeric) = 1.9629636186432886063969318487624 absolute error = 0.1161317740252734162738330639804 relative error = 6.2881617708564711834385301103638 % h = 0.001 y1[1] (analytic) = 1.846831844618015190123098784782 y1[1] (numeric) = 1.8991692768830545899827743996479 absolute error = 0.0523374322650393998596756148659 relative error = 2.8339034989871793526701204933689 % h = 0.001 TOP MAIN SOLVE Loop memory used=2620.7MB, alloc=4.6MB, time=148.20 NO POLE NO POLE x[1] = 1.011 y2[1] (analytic) = 1.8473632818348590721105067114598 y2[1] (numeric) = 1.9638649952181223740902093551976 absolute error = 0.1165017133832633019797026437378 relative error = 6.306378097303641942029767481928 % h = 0.001 y1[1] (analytic) = 1.8473632818348590721105067114598 y1[1] (numeric) = 1.899794673859554460339161898245 absolute error = 0.0524313920246953882286551867852 relative error = 2.8381744154089112069611690233383 % h = 0.001 TOP MAIN SOLVE Loop memory used=2624.5MB, alloc=4.6MB, time=148.42 NO POLE NO POLE x[1] = 1.012 y2[1] (analytic) = 1.8478938716884917328433083123683 y2[1] (numeric) = 1.9647662673471682235600602344437 absolute error = 0.1168723956586764907167519220754 relative error = 6.3246270497063603468357407184042 % h = 0.001 y1[1] (analytic) = 1.8478938716884917328433083123683 y1[1] (numeric) = 1.9004192495122643506129562894176 absolute error = 0.0525253778237726177696479770493 relative error = 2.8424455878398557060207486989288 % h = 0.001 TOP MAIN SOLVE Loop memory used=2628.3MB, alloc=4.6MB, time=148.63 NO POLE NO POLE x[1] = 1.013 y2[1] (analytic) = 1.8484236136483233629046625169003 y2[1] (numeric) = 1.9656674350280267563163811001101 absolute error = 0.1172438213797033934117185832098 relative error = 6.3429086554620223146141060695979 % h = 0.001 y1[1] (analytic) = 1.8484236136483233629046625169003 y1[1] (numeric) = 1.9010430030931752782026827442783 absolute error = 0.052619389444851915298020227378 relative error = 2.846717010988323910791851294721 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.014 y2[1] (analytic) = 1.8489525071846120466081011114986 y2[1] (numeric) = 1.9665684982583031829239393341283 absolute error = 0.1176159910736911363158382226297 relative error = 6.3612229419988856670675975933722 % h = 0.001 y1[1] (analytic) = 1.8489525071846120466081011114986 y1[1] (numeric) = 1.9016659338550036096466548284761 absolute error = 0.0527134266703915630385537169775 relative error = 2.8509886795663537553829117111523 % h = 0.001 TOP MAIN SOLVE Loop memory used=2632.1MB, alloc=4.6MB, time=148.85 NO POLE NO POLE x[1] = 1.015 y2[1] (analytic) = 1.8494805517684642917394002809662 y2[1] (numeric) = 1.967469457035607326077312946622 absolute error = 0.1179889052671430343379126656558 relative error = 6.3795699367761730740820286110792 % h = 0.001 y1[1] (analytic) = 1.8494805517684642917394002809662 y1[1] (numeric) = 1.9022880410511919191241618936602 absolute error = 0.052807489282727627384761612694 relative error = 2.8552605882896883368008461624727 % h = 0.001 TOP MAIN SOLVE Loop memory used=2636.0MB, alloc=4.6MB, time=149.06 NO POLE NO POLE x[1] = 1.016 y2[1] (analytic) = 1.850007746871835558450028748234 y2[1] (numeric) = 1.9683703113575536236716020086184 absolute error = 0.1183625644857180652215732603844 relative error = 6.3979496672841749826086683411517 % h = 0.001 y1[1] (analytic) = 1.850007746871835558450028748234 y1[1] (numeric) = 1.9029093239359098463439104866839 absolute error = 0.0529015770640742878938817384499 relative error = 2.8595327318777542422167759137474 % h = 0.001 TOP MAIN SOLVE Loop memory used=2639.8MB, alloc=4.6MB, time=149.28 NO POLE NO POLE x[1] = 1.017 y2[1] (analytic) = 1.8505340919675307873016436191816 y2[1] (numeric) = 1.9692710612217611318689079530505 absolute error = 0.1187369692542303445672643338689 relative error = 6.4163621610443525319732764304352 % h = 0.001 y1[1] (analytic) = 1.8505340919675307873016436191816 y1[1] (numeric) = 1.9035297817640549538187653792443 absolute error = 0.0529956897965241665171217600627 relative error = 2.8638051050536399135924708381598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.018 y2[1] (analytic) = 1.8510595865292049264611058880601 y2[1] (numeric) = 1.9701717066258535281605770432542 absolute error = 0.1191121200966486016994711551941 relative error = 6.4348074456094404563927392427441 % h = 0.001 y1[1] (analytic) = 1.8510595865292049264611058880601 y1[1] (numeric) = 1.9041494137912535835258363060326 absolute error = 0.0530898272620486570647304179725 relative error = 2.8680777025440740494960314919279 % h = 0.001 TOP MAIN SOLVE Loop memory used=2643.6MB, alloc=4.6MB, time=149.50 NO POLE NO POLE x[1] = 1.019 y2[1] (analytic) = 1.8515842300313634580454884085451 y2[1] (numeric) = 1.9710722475674591144252043119243 absolute error = 0.1194880175360956563797159033792 relative error = 6.4532855485635499754789231427197 % h = 0.001 y1[1] (analytic) = 1.8515842300313634580454884085451 y1[1] (numeric) = 1.9047682192738617129509569858842 absolute error = 0.0531839892424982549054685773391 relative error = 2.8723505190794040439358105748267 % h = 0.001 TOP MAIN SOLVE Loop memory used=2647.4MB, alloc=4.6MB, time=149.72 NO POLE NO POLE x[1] = 1.02 y2[1] (analytic) = 1.8521080219493629236165499854554 y2[1] (numeric) = 1.9719726840442108199823942772566 absolute error = 0.1198646620948478963658442918012 relative error = 6.471796497522271673508041597181 % h = 0.001 y1[1] (analytic) = 1.8521080219493629236165499854554 y1[1] (numeric) = 1.9053861974689658105166034878646 absolute error = 0.0532781755196028869000535024092 relative error = 2.8766235493935744620420545679816 % h = 0.001 TOP MAIN SOLVE Loop memory used=2651.2MB, alloc=4.6MB, time=149.93 NO POLE NO POLE x[1] = 1.021 y2[1] (analytic) = 1.8526309617594114488241500927072 y2[1] (numeric) = 1.9728730160537462046422747467699 absolute error = 0.1202420542943347558181246540627 relative error = 6.4903403201327783682325246732443 % h = 0.001 y1[1] (analytic) = 1.8526309617594114488241500927072 y1[1] (numeric) = 1.9060033476343836903922994927062 absolute error = 0.053372385874972241568149399999 relative error = 2.8808967882241055524262240259151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.022 y2[1] (analytic) = 1.8531530489385692671980795741338 y2[1] (numeric) = 1.9737732435937074617507600230764 absolute error = 0.1206201946551381945526804489426 relative error = 6.5089170440739279700110814104079 % h = 0.001 y1[1] (analytic) = 1.8531530489385692671980795741338 y1[1] (numeric) = 1.9066196690286653666865564895245 absolute error = 0.0534666200900960994884769153907 relative error = 2.8851702303120717960484264555346 % h = 0.001 TOP MAIN SOLVE Loop memory used=2655.0MB, alloc=4.6MB, time=150.15 NO POLE NO POLE x[1] = 1.023 y2[1] (analytic) = 1.8536742829647492430877835353817 y2[1] (numeric) = 1.9746733666617414212305598296419 absolute error = 0.1209990836969921781427762942602 relative error = 6.5275266970563663320313575500618 % h = 0.001 y1[1] (analytic) = 1.8536742829647492430877835353817 y1[1] (numeric) = 1.9072351609110939070193974382844 absolute error = 0.0535608779463446639316139029027 relative error = 2.8894438704020804914238689493308 % h = 0.001 TOP MAIN SOLVE Loop memory used=2658.8MB, alloc=4.6MB, time=150.38 NO POLE NO POLE x[1] = 1.024 y2[1] (analytic) = 1.854194663316717393749453487206 y2[1] (numeric) = 1.9755733852554995526179302783608 absolute error = 0.1213787219387821588684767911548 relative error = 6.5461693068226300923983131885291 % h = 0.001 y1[1] (analytic) = 1.854194663316717393749453487206 y1[1] (numeric) = 1.9078498225416862854745129200649 absolute error = 0.0536551592249688917250594328589 relative error = 2.8937177032422503759997087617901 % h = 0.001 TOP MAIN SOLVE Loop memory used=2662.7MB, alloc=4.6MB, time=150.62 NO POLE NO POLE x[1] = 1.025 y2[1] (analytic) = 1.8547141894740934105799666531149 y2[1] (numeric) = 1.976473299372637968095163204553 absolute error = 0.1217591098985445575151965514381 relative error = 6.5648449011472495088601770472016 % h = 0.001 y1[1] (analytic) = 1.8547141894740934105799666531149 y1[1] (numeric) = 1.9084636531811942349300992897764 absolute error = 0.0537494637071008243501326366615 relative error = 2.8979917235841902835341488358337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2666.5MB, alloc=4.6MB, time=150.83 x[1] = 1.026 y2[1] (analytic) = 1.8552328609173511794971512074687 y2[1] (numeric) = 1.9773731090108174255188101987816 absolute error = 0.1221402480934662460216589913129 relative error = 6.5835535078368512869425761937559 % h = 0.001 y1[1] (analytic) = 1.8552328609173511794971512074687 y1[1] (numeric) = 1.909076652091105098767428839624 absolute error = 0.0538437911737539192702776321553 relative error = 2.9022659261829778373100919078943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.027 y2[1] (analytic) = 1.8557506771278193004658570638093 y2[1] (numeric) = 1.9782728141677033314436376686806 absolute error = 0.1225221370398840309777806048713 relative error = 6.6022951547302614022601921705731 % h = 0.001 y1[1] (analytic) = 1.8557506771278193004658570638093 y1[1] (numeric) = 1.9096888185336426819562024762783 absolute error = 0.053938141405823381490345412469 relative error = 2.9065403057971381790161312548738 % h = 0.001 TOP MAIN SOLVE Loop memory used=2670.3MB, alloc=4.6MB, time=151.05 NO POLE NO POLE x[1] = 1.028 y2[1] (analytic) = 1.8562676375876816061693126873962 y2[1] (numeric) = 1.9791724148409657441423092677816 absolute error = 0.1229047772532841379729965803854 relative error = 6.6210698696986079177740565588396 % h = 0.001 y1[1] (analytic) = 1.8562676375876816061693126873962 y1[1] (numeric) = 1.9103001517717681015157359104152 absolute error = 0.054032514184086495346423223019 relative error = 2.9108148571886227331281184013789 % h = 0.001 TOP MAIN SOLVE Loop memory used=2674.1MB, alloc=4.6MB, time=151.27 NO POLE NO POLE x[1] = 1.029 y2[1] (analytic) = 1.8567837417799776798252492606312 y2[1] (numeric) = 1.9800719110282793766207920321298 absolute error = 0.1232881692483016967955427714986 relative error = 6.6398776806454237967613709992393 % h = 0.001 y1[1] (analytic) = 1.8567837417799776798252492606312 y1[1] (numeric) = 1.9109106510691806363510308540141 absolute error = 0.0541269092892029565257815933829 relative error = 2.9150895751227880066250081906172 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2677.9MB, alloc=4.6MB, time=151.50 x[1] = 1.03 y2[1] (analytic) = 1.8572989891886033721462743852944 y2[1] (numeric) = 1.9809713027273235996294825692845 absolute error = 0.1236723135387202274832081839901 relative error = 6.6587186155067497122635185702917 % h = 0.001 y1[1] (analytic) = 1.8572989891886033721462743852944 y1[1] (numeric) = 1.9115203156903185764627832185644 absolute error = 0.05422132650171520431650883327 relative error = 2.9193644543683744238731395440855 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.031 y2[1] (analytic) = 1.8578133792983113174439783612591 y2[1] (numeric) = 1.9818705899357824446700496481106 absolute error = 0.1240572106374711272260712868515 relative error = 6.6775927022512368537767251644492 % h = 0.001 y1[1] (analytic) = 1.8578133792983113174439783612591 y1[1] (numeric) = 1.912129144900360071530380806116 absolute error = 0.0543157656020487540864024448569 relative error = 2.9236394896974851965135660031124 % h = 0.001 TOP MAIN SOLVE Loop memory used=2681.7MB, alloc=4.6MB, time=151.71 NO POLE NO POLE x[1] = 1.032 y2[1] (analytic) = 1.8583269115947114488762569376219 y2[1] (numeric) = 1.9827697726513446069979895415825 absolute error = 0.1244428610566331581217326039606 relative error = 6.6964999688802497319486310683121 % h = 0.001 y1[1] (analytic) = 1.8583269115947114488762569376219 y1[1] (numeric) = 1.9127371379652239788669434849289 absolute error = 0.054410226370512529990686547307 relative error = 2.9279146758855652281875037669497 % h = 0.001 TOP MAIN SOLVE Loop memory used=2685.5MB, alloc=4.6MB, time=151.93 NO POLE NO POLE x[1] = 1.033 y2[1] (analytic) = 1.85883958556427151283733528897 y2[1] (numeric) = 1.9836688508717034486208904786384 absolute error = 0.1248292653074319357835551896684 relative error = 6.715440443427968982042844316765 % h = 0.001 y1[1] (analytic) = 1.85883958556427151283733528897 y1[1] (numeric) = 1.9133442941515707107454593423196 absolute error = 0.0545047085872991979081240533496 relative error = 2.9321900077113800539354164253486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2689.4MB, alloc=4.6MB, time=152.15 x[1] = 1.034 y2[1] (analytic) = 1.8593514006943175824899788268026 y2[1] (numeric) = 1.9845678245945570012924025649491 absolute error = 0.1252164239002394188024237381465 relative error = 6.7344141539614941669323685222694 % h = 0.001 y1[1] (analytic) = 1.8593514006943175824899788268026 y1[1] (numeric) = 1.9139506127268030810950708091777 absolute error = 0.0545992120324854986050919823751 relative error = 2.9364654799569948141057049374195 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.035 y2[1] (analytic) = 1.8598623564730345704393773139402 y2[1] (numeric) = 1.9854666938176079695019095362889 absolute error = 0.1256043373445733990625322223487 relative error = 6.7534211285809465803816287486832 % h = 0.001 y1[1] (analytic) = 1.8598623564730345704393773139402 y1[1] (numeric) = 1.9145560929590671515665652535267 absolute error = 0.0546937364860325811271879395865 relative error = 2.9407410874077532626094186399172 % h = 0.001 TOP MAIN SOLVE Loop memory used=2693.2MB, alloc=4.6MB, time=152.37 NO POLE NO POLE x[1] = 1.036 y2[1] (analytic) = 1.8603724523894667405481896080782 y2[1] (numeric) = 1.9863654585385637334598987120313 absolute error = 0.1259930061490969929117091039531 relative error = 6.7724613954195720513756595758202 % h = 0.001 y1[1] (analytic) = 1.8603724523894667405481896080782 y1[1] (numeric) = 1.9151607341172530769661250444313 absolute error = 0.0547882817277863364179354363531 relative error = 2.9450168248522568093578481859433 % h = 0.001 TOP MAIN SOLVE Loop memory used=2697.0MB, alloc=4.6MB, time=152.59 NO POLE NO POLE x[1] = 1.037 y2[1] (analytic) = 1.8608816879335182188922372194854 y2[1] (numeric) = 1.9872641187551363520790255201245 absolute error = 0.1263824308216181331867883006391 relative error = 6.7915349826438437502538697553159 % h = 0.001 y1[1] (analytic) = 1.8608816879335182188922372194854 y1[1] (numeric) = 1.91576453547099595005639259251 absolute error = 0.0548828475374777311641553730246 relative error = 2.9492926870823435967203043264808 % h = 0.001 TOP MAIN SOLVE Loop memory used=2700.8MB, alloc=4.6MB, time=152.80 NO POLE NO POLE x[1] = 1.038 y2[1] (analytic) = 1.8613900625959535038563357271943 y2[1] (numeric) = 1.9881626744650425659508689687439 absolute error = 0.1267726118690890620945332415496 relative error = 6.81064191845356499740465776271 % h = 0.001 y1[1] (analytic) = 1.8613900625959535038563357271943 y1[1] (numeric) = 1.9163674962906766457239063792941 absolute error = 0.0549774336947231418675706520998 relative error = 2.953568668893067609839827361013 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.039 y2[1] (analytic) = 1.861897575868397975369753957895 y2[1] (numeric) = 1.9890611256660038003183744436612 absolute error = 0.1271635497976058249486204857662 relative error = 6.829782231081972075276022074383 % h = 0.001 y1[1] (analytic) = 1.861897575868397975369753957895 y1[1] (numeric) = 1.9169696158474226645119644946826 absolute error = 0.0550720399790246891422105367876 relative error = 2.9578447650826778206450109066854 % h = 0.001 TOP MAIN SOLVE Loop memory used=2704.6MB, alloc=4.6MB, time=153.02 NO POLE NO POLE x[1] = 1.04 y2[1] (analytic) = 1.8624042272433384032807916921162 y2[1] (numeric) = 1.9899594723557461680439802142193 absolute error = 0.1275552451124077647631885221031 relative error = 6.8489559487958370444561891132199 % h = 0.001 y1[1] (analytic) = 1.8624042272433384032807916921162 y1[1] (numeric) = 1.9175708934131089755179727097785 absolute error = 0.0551666661697705722371810176623 relative error = 2.9621209704525973653965603765708 % h = 0.001 TOP MAIN SOLVE Loop memory used=2708.4MB, alloc=4.6MB, time=153.23 NO POLE NO POLE x[1] = 1.041 y2[1] (analytic) = 1.8629100162141234548699675231574 y2[1] (numeric) = 1.9908577145320004725734240346532 absolute error = 0.1279476983178770177034565114958 relative error = 6.8681630998955705645771704844035 % h = 0.001 y1[1] (analytic) = 1.8629100162141234548699675231574 y1[1] (numeric) = 1.9181713282603588586543346214513 absolute error = 0.0552613120462354037843670982939 relative error = 2.9663972798074027556076412240275 % h = 0.001 TOP MAIN SOLVE Loop memory used=2712.3MB, alloc=4.6MB, time=153.45 NO POLE NO POLE x[1] = 1.042 y2[1] (analytic) = 1.863414942274964201501309355628 y2[1] (numeric) = 1.9917558521925022108952262313549 absolute error = 0.1283409099175380093939168757269 relative error = 6.8874037127153247207930593341836 % h = 0.001 y1[1] (analytic) = 1.863414942274964201501309355628 y1[1] (numeric) = 1.9187709196625447462719419150566 absolute error = 0.0553559773875805447706325594286 relative error = 2.9706736879548031221775046096891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.043 y2[1] (analytic) = 1.8639190049209346244112408923424 y2[1] (numeric) = 1.9926538853349915764958456705405 absolute error = 0.1287348804140569520846047781981 relative error = 6.9066778156230958565837833817122 % h = 0.001 y1[1] (analytic) = 1.8639190049209346244112408923424 y1[1] (numeric) = 1.9193696668937890641453233028541 absolute error = 0.0554506619728544397340824105117 relative error = 2.9749501897056194925783086883515 % h = 0.001 TOP MAIN SOLVE Loop memory used=2716.1MB, alloc=4.6MB, time=153.66 NO POLE NO POLE x[1] = 1.044 y2[1] (analytic) = 1.8644222036479721196345583207306 y2[1] (numeric) = 1.993551813957213462310505004643 absolute error = 0.1291296103092413426759466839124 relative error = 6.9259854370208274136339493681592 % h = 0.001 y1[1] (analytic) = 1.8644222036479721196345583207306 y1[1] (numeric) = 1.9199675692289650718185112078016 absolute error = 0.055545365580992952183952887071 relative error = 2.9792267798737641009354822018274 % h = 0.001 TOP MAIN SOLVE Loop memory used=2719.9MB, alloc=4.6MB, time=153.88 NO POLE NO POLE x[1] = 1.045 y2[1] (analytic) = 1.8649245379528780020669922728253 y2[1] (numeric) = 1.994449638056917463669681599623 absolute error = 0.1295251001040394616026893267977 relative error = 6.9453266053445127795353403117012 % h = 0.001 y1[1] (analytic) = 1.8649245379528780020669922728253 y1[1] (numeric) = 1.9205646259436977023106857755589 absolute error = 0.0556400879908197002436935027336 relative error = 2.9835034532762197308424035094374 % h = 0.001 TOP MAIN SOLVE Loop memory used=2723.7MB, alloc=4.6MB, time=154.10 NO POLE NO POLE x[1] = 1.046 y2[1] (analytic) = 1.8654260073333180086638509963099 y2[1] (numeric) = 1.9953473576318578812412605492636 absolute error = 0.1299213502985398725774095529537 relative error = 6.9647013490642981440605630221046 % h = 0.001 y1[1] (analytic) = 1.8654260073333180086638509963099 y1[1] (numeric) = 1.9211608363143644011806563117217 absolute error = 0.0557348289810463925168053154118 relative error = 2.9877802047330190907505925965993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.047 y2[1] (analytic) = 1.8659266112878228007742415380223 y2[1] (numeric) = 1.996244972679793723968346186393 absolute error = 0.1303183613919709231941046483707 relative error = 6.9841096966845853647542887887298 % h = 0.001 y1[1] (analytic) = 1.8659266112878228007742415380223 y1[1] (numeric) = 1.9217561996180959649492407565096 absolute error = 0.0558295883302731641749992184873 relative error = 2.9920570290672242217770359827699 % h = 0.001 TOP MAIN SOLVE Loop memory used=2727.5MB, alloc=4.6MB, time=154.31 NO POLE NO POLE x[1] = 1.048 y2[1] (analytic) = 1.8664263493157884656103666057382 y2[1] (numeric) = 1.9971424831984887120027285048601 absolute error = 0.1307161338827002463923618991219 relative error = 7.0035516767441348425874849816803 % h = 0.001 y1[1] (analytic) = 1.8664263493157884656103666057382 y1[1] (numeric) = 1.9223507151327773788786043253623 absolute error = 0.0559243658169889132682377196241 relative error = 2.9963339211049059377706848089879 % h = 0.001 TOP MAIN SOLVE Loop memory used=2731.3MB, alloc=4.6MB, time=154.53 NO POLE NO POLE x[1] = 1.049 y2[1] (analytic) = 1.8669252209174770168513956389767 y2[1] (numeric) = 1.9980398891857112796340009099737 absolute error = 0.131114668268234262782605270997 relative error = 7.0230273178161684084189994717557 % h = 0.001 y1[1] (analytic) = 1.8669252209174770168513956389767 y1[1] (numeric) = 1.9229443821370486541076189611503 absolute error = 0.0560191612195716372562233221736 relative error = 3.0006108756751232974805847312618 % h = 0.001 TOP MAIN SOLVE Loop memory used=2735.1MB, alloc=4.6MB, time=154.75 NO POLE NO POLE x[1] = 1.05 y2[1] (analytic) = 1.8674232255940168943814094850003 y2[1] (numeric) = 1.9989371906392345782143257190079 absolute error = 0.1315139650452176838329162340076 relative error = 7.0425366485084722210078332527691 % h = 0.001 y1[1] (analytic) = 1.8674232255940168943814094850003 y1[1] (numeric) = 1.9235371999103056641423057619802 absolute error = 0.0561139743162887697608962769799 relative error = 3.0048878876099031086685125853251 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.051 y2[1] (analytic) = 1.8679203628474034631609189421053 y2[1] (numeric) = 1.9998343875568364790788438372679 absolute error = 0.1319140247094330159179248951626 relative error = 7.0620796974634996773184194132265 % h = 0.001 y1[1] (analytic) = 1.8679203628474034631609189421053 y1[1] (numeric) = 1.9241291677327009807004230678704 absolute error = 0.0562088048852975175395041257651 relative error = 3.0091649517442194640094091290929 % h = 0.001 TOP MAIN SOLVE Loop memory used=2739.0MB, alloc=4.6MB, time=154.96 NO POLE NO POLE x[1] = 1.052 y2[1] (analytic) = 1.8684166321804995112314582987262 y2[1] (numeric) = 2.0007314799362995764617250391109 absolute error = 0.1323148477558000652302667403847 relative error = 7.0816564933584743358602186265622 % h = 0.001 y1[1] (analytic) = 1.8684166321804995112314582987262 y1[1] (numeric) = 1.9247202848851447089092634098908 absolute error = 0.0563036527046451976778051111646 relative error = 3.0134420629159733086233095183515 % h = 0.001 TOP MAIN SOLVE Loop memory used=2742.8MB, alloc=4.6MB, time=155.18 NO POLE NO POLE x[1] = 1.053 y2[1] (analytic) = 1.8689120330970357468527558638018 y2[1] (numeric) = 2.0016284677754111904078552872191 absolute error = 0.1327164346783754435550994234173 relative error = 7.1012670649054928538019425835346 % h = 0.001 y1[1] (analytic) = 1.8689120330970357468527558638018 y1[1] (numeric) = 1.9253105506493053218557230466989 absolute error = 0.0563985175522695750029671828971 relative error = 3.0177192159659720390828835364238 % h = 0.001 TOP MAIN SOLVE Loop memory used=2746.6MB, alloc=4.6MB, time=155.40 NO POLE NO POLE x[1] = 1.054 y2[1] (analytic) = 1.8694065651016112947719843512738 y2[1] (numeric) = 2.002525351071963369680157527327 absolute error = 0.1331187859703520749081731760532 relative error = 7.1209114408516279385997272505183 % h = 0.001 y1[1] (analytic) = 1.8694065651016112947719843512738 y1[1] (numeric) = 1.9258999643076104944877083357636 absolute error = 0.0564933992059991997157239844898 relative error = 3.0219964057379091337411059868674 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.055 y2[1] (analytic) = 1.8699002276996941916245948495095 y2[1] (numeric) = 2.0034221298237528946625423995188 absolute error = 0.1335219021240587030379475500093 relative error = 7.1405896499790313148775974774323 % h = 0.001 y1[1] (analytic) = 1.8699002276996941916245948495095 y1[1] (numeric) = 1.9264885251432479368659437099475 absolute error = 0.056588297443553745241348860438 relative error = 3.0262736270783438142239840769895 % h = 0.001 TOP MAIN SOLVE Loop memory used=2750.4MB, alloc=4.6MB, time=155.61 NO POLE NO POLE x[1] = 1.056 y2[1] (analytic) = 1.8703930203976218804662389748547 y2[1] (numeric) = 2.0043188040285812802584853111237 absolute error = 0.133925783630959399792246336269 relative error = 7.1603017211050367072975932725503 % h = 0.001 y1[1] (analytic) = 1.8703930203976218804662389748547 y1[1] (numeric) = 1.9270762324401662267652465545184 absolute error = 0.0566832120425443462990075796637 relative error = 3.0305508748366807379336730765089 % h = 0.001 TOP MAIN SOLVE Loop memory used=2754.2MB, alloc=4.6MB, time=155.83 NO POLE NO POLE x[1] = 1.057 y2[1] (analytic) = 1.8708849427026017044352846774374 y2[1] (numeric) = 2.0052153736842547787852263201595 absolute error = 0.1343304309816530743499416427221 relative error = 7.1800476830822628401559659828749 % h = 0.001 y1[1] (analytic) = 1.8708849427026017044352846774374 y1[1] (numeric) = 1.9276630854830756416243348050796 absolute error = 0.0567781427804739371890501276422 relative error = 3.0348281438651497214077140367852 % h = 0.001 TOP MAIN SOLVE Loop memory used=2758.0MB, alloc=4.6MB, time=156.04 NO POLE NO POLE x[1] = 1.058 y2[1] (analytic) = 1.8713759941227113995454320367466 y2[1] (numeric) = 2.0061118387885843828635892821943 absolute error = 0.1347358446658729833181572454477 relative error = 7.1998275647987164544408996422922 % h = 0.001 y1[1] (analytic) = 1.8713759941227113995454320367466 y1[1] (numeric) = 1.9282490835574489898432336133473 absolute error = 0.0568730894347375902978015766007 relative error = 3.0391054290187854943805279094204 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.059 y2[1] (analytic) = 1.871866174166899586607936254411 y2[1] (numeric) = 2.007008199339385828303416717428 absolute error = 0.135142025172486241695480463017 relative error = 7.2196413951778953430862688502285 % h = 0.001 y1[1] (analytic) = 1.871866174166899586607936254411 y1[1] (numeric) = 1.9288342259495224414273479551594 absolute error = 0.0569680517826228548194117007484 relative error = 3.0433827251554074843936990152391 % h = 0.001 TOP MAIN SOLVE Loop memory used=2761.8MB, alloc=4.6MB, time=156.26 NO POLE NO POLE x[1] = 1.06 y2[1] (analytic) = 1.8723554823449862622829459219974 y2[1] (numeric) = 2.0079044553344795969846168587229 absolute error = 0.1355489729894933347016709367255 relative error = 7.239489203178891405155009694894 % h = 0.001 y1[1] (analytic) = 1.8723554823449862622829459219974 y1[1] (numeric) = 1.9294185119462963579772685835769 absolute error = 0.0570630296013100956943226615795 relative error = 3.0476600271355996318019774930397 % h = 0.001 TOP MAIN SOLVE Loop memory used=2765.7MB, alloc=4.6MB, time=156.48 NO POLE NO POLE x[1] = 1.061 y2[1] (analytic) = 1.8728439181676632892594655125299 y2[1] (numeric) = 2.0088006067716909197338193452517 absolute error = 0.1359566886040276304743538327218 relative error = 7.2593710177964937196847544135242 % h = 0.001 y1[1] (analytic) = 1.8728439181676632892594655125299 y1[1] (numeric) = 1.9300019408355361220233792594317 absolute error = 0.0571580226678728327639137469018 relative error = 3.0519373298226902350223251092387 % h = 0.001 TOP MAIN SOLVE Loop memory used=2769.5MB, alloc=4.6MB, time=156.70 NO POLE NO POLE x[1] = 1.062 y2[1] (analytic) = 1.8733314811464948855634519158083 y2[1] (numeric) = 2.0096966536488497791966360303684 absolute error = 0.1363651725023548936331841145601 relative error = 7.2792868680612916399274636610562 % h = 0.001 y1[1] (analytic) = 1.8733314811464948855634519158083 y1[1] (numeric) = 1.9305845119057729657043337221855 absolute error = 0.0572530307592780801408818063772 relative error = 3.0562146280827318258737216411985 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.063 y2[1] (analytic) = 1.8738181707939181129935557094709 y2[1] (numeric) = 2.0105925959637909127055233762546 absolute error = 0.1367744251698727997119676667837 relative error = 7.2992367830397779087138824145437 % h = 0.001 y1[1] (analytic) = 1.8738181707939181129935557094709 y1[1] (numeric) = 1.9311662244463047987884713954939 absolute error = 0.057348053652386685794915686023 relative error = 3.060491916784481074855839965913 % h = 0.001 TOP MAIN SOLVE Loop memory used=2773.3MB, alloc=4.6MB, time=156.91 NO POLE NO POLE x[1] = 1.064 y2[1] (analytic) = 1.8743039866232433646840187301006 y2[1] (numeric) = 2.0114884337143538151432429118385 absolute error = 0.1371844470911104504592241817379 relative error = 7.3192207918344517956727466481537 % h = 0.001 y1[1] (analytic) = 1.8743039866232433646840187301006 y1[1] (numeric) = 1.9317470777471970360372413544135 absolute error = 0.0574430911239536713532226243129 relative error = 3.0647691907993787262150869986528 % h = 0.001 TOP MAIN SOLVE Loop memory used=2777.1MB, alloc=4.6MB, time=157.12 NO POLE NO POLE x[1] = 1.065 y2[1] (analytic) = 1.8747889281486548517942403815169 y2[1] (numeric) = 2.0123841668983827418019162344392 absolute error = 0.1375952387497278900076758529223 relative error = 7.3392389235839222570337779487911 % h = 0.001 y1[1] (analytic) = 1.8747889281486548517942403815169 y1[1] (numeric) = 1.9323270710992834239097046147528 absolute error = 0.0575381429506285721154642332359 relative error = 3.069046445001529562646894740095 % h = 0.001 TOP MAIN SOLVE Loop memory used=2780.9MB, alloc=4.6MB, time=157.34 NO POLE NO POLE x[1] = 1.066 y2[1] (analytic) = 1.875272994885211089324525990729 y2[1] (numeric) = 2.013279795513726711237671039544 absolute error = 0.138006800628515621913145048815 relative error = 7.3592912074630111187426221804235 % h = 0.001 y1[1] (analytic) = 1.875272994885211089324525990729 y1[1] (numeric) = 1.932906203794166866607185339644 absolute error = 0.057633208908955777282659348915 relative error = 3.0733236742676823994835309119396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2784.7MB, alloc=4.6MB, time=157.56 x[1] = 1.067 y2[1] (analytic) = 1.8757561863488453810575313958413 y2[1] (numeric) = 2.014175319558239508120874667086 absolute error = 0.1384191332093941270633432712447 relative error = 7.3793776726828562836150161224069 % h = 0.001 y1[1] (analytic) = 1.8757561863488453810575313958413 y1[1] (numeric) = 1.9334844751242202514571420940075 absolute error = 0.0577282887753748703996106981662 relative error = 3.0776008734772101082170819974086 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.068 y2[1] (analytic) = 1.8762385020563663036249188245075 y2[1] (numeric) = 2.0150707390297796860819516565563 absolute error = 0.1388322369734133824570328320488 relative error = 7.3994983484910149632566026793961 % h = 0.001 y1[1] (analytic) = 1.8762385020563663036249188245075 y1[1] (numeric) = 1.9340618843825872736353308141879 absolute error = 0.0578233823262209700104119896804 relative error = 3.0818780375120896692076429604709 % h = 0.001 TOP MAIN SOLVE Loop memory used=2788.5MB, alloc=4.6MB, time=157.78 NO POLE NO POLE x[1] = 1.069 y2[1] (analytic) = 1.876719941525458189698739996318 y2[1] (numeric) = 2.0159660539262105705527818072516 absolute error = 0.1392461124007523808540418109336 relative error = 7.4196532641715669354739607637949 % h = 0.001 y1[1] (analytic) = 1.876719941525458189698739996318 y1[1] (numeric) = 1.934638430863183260225331697665 absolute error = 0.057918489337725070526591701347 relative error = 3.0861551612568822534271275034182 % h = 0.001 TOP MAIN SOLVE Loop memory used=2792.4MB, alloc=4.6MB, time=158.00 NO POLE NO POLE x[1] = 1.07 y2[1] (analytic) = 1.8772005042746816103070632577768 y2[1] (numeric) = 2.016861264245400261603675243932 absolute error = 0.1396607599707186512966119861552 relative error = 7.4398424490452178279015702629501 % h = 0.001 y1[1] (analytic) = 1.8772005042746816103070632577768 y1[1] (numeric) = 1.9352141138606959936145127563801 absolute error = 0.0580136095860143833074494986033 relative error = 3.090432239598713333089490442966 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2796.2MB, alloc=4.6MB, time=158.22 x[1] = 1.071 y2[1] (analytic) = 1.8776801898234738562733624342827 y2[1] (numeric) = 2.0177563699852216367759209921407 absolute error = 0.140076180161747780502558557858 relative error = 7.4600659324694024285685955984284 % h = 0.001 y1[1] (analytic) = 1.8776801898234738562733624342827 y1[1] (numeric) = 1.9357889326705865342255033168705 absolute error = 0.0581087428471126779521408825878 relative error = 3.0947092674272528210185296469717 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.072 y2[1] (analytic) = 1.8781589976921494187791859597638 y2[1] (numeric) = 2.0186513711435523539099055714181 absolute error = 0.1404923734514029351307196116543 relative error = 7.4803237438383880241285432411048 % h = 0.001 y1[1] (analytic) = 1.8781589976921494187791859597638 y1[1] (numeric) = 1.9363628865890900425822512910698 absolute error = 0.058203888896940623803065331306 relative error = 3.0989862396346952386048089842139 % h = 0.001 TOP MAIN SOLVE Loop memory used=2800.0MB, alloc=4.6MB, time=158.44 NO POLE NO POLE x[1] = 1.073 y2[1] (analytic) = 1.8786369274019004690496257213382 y2[1] (numeric) = 2.019546267718274853968798118628 absolute error = 0.1409093403163743849191723972898 relative error = 7.5006159125833777664740291394726 % h = 0.001 y1[1] (analytic) = 1.8786369274019004690496257213382 y1[1] (numeric) = 1.9369359749132166007097385833118 absolute error = 0.0582990475113161316601128619736 relative error = 3.1032631511157399122036159044301 % h = 0.001 TOP MAIN SOLVE Loop memory used=2803.8MB, alloc=4.6MB, time=158.65 NO POLE NO POLE x[1] = 1.074 y2[1] (analytic) = 1.8791139784747973371611059335712 y2[1] (numeric) = 2.0204410597072763638577985576028 absolute error = 0.1413270812324790266966926240316 relative error = 7.520942468172614068458081327442 % h = 0.001 y1[1] (analytic) = 1.8791139784747973371611059335712 y1[1] (numeric) = 1.9375081969407520328664295417651 absolute error = 0.0583942184659546957053236081939 relative error = 3.1075399967675711978262375920739 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=2807.6MB, alloc=4.6MB, time=158.87 x[1] = 1.075 y2[1] (analytic) = 1.8795901504337889899710132345797 y2[1] (numeric) = 2.0213357471084488992389453353084 absolute error = 0.1417455966746599092679321007287 relative error = 7.541303440111482029442600978568 % h = 0.001 y1[1] (analytic) = 1.8795901504337889899710132345797 y1[1] (numeric) = 1.9380795519702587256085279062317 absolute error = 0.058489401536469735637514671652 relative error = 3.111816771489838733977208131417 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.076 y2[1] (analytic) = 1.8800654428027035081686900743944 y2[1] (numeric) = 2.0222303299196892673414792487265 absolute error = 0.1421648871169857591727891743321 relative error = 7.5616988579426128913938118435495 % h = 0.001 y1[1] (analytic) = 1.8800654428027035081686900743944 y1[1] (numeric) = 1.9386500393010764471851182489582 absolute error = 0.0585845964983729390164281745638 relative error = 3.1160934701846377224905457889494 % h = 0.001 TOP MAIN SOLVE Loop memory used=2811.4MB, alloc=4.6MB, time=159.08 NO POLE NO POLE x[1] = 1.077 y2[1] (analytic) = 1.8805398551062485624473143446251 y2[1] (numeric) = 2.0231248081388990697677598906529 absolute error = 0.1425849530326505073204455460278 relative error = 7.5821287512459875262437433247699 % h = 0.001 y1[1] (analytic) = 1.8805398551062485624473143446251 y1[1] (numeric) = 1.9392196582333231662632684508346 absolute error = 0.0586798031270746038159541062095 relative error = 3.1203700877564892372183643683183 % h = 0.001 TOP MAIN SOLVE Loop memory used=2815.2MB, alloc=4.6MB, time=159.30 NO POLE NO POLE x[1] = 1.078 y2[1] (analytic) = 1.8810133868700118887961890775899 y2[1] (numeric) = 2.0240191817639847052947312466178 absolute error = 0.1430057948939728164985421690279 relative error = 7.6025931496390399552360163829931 % h = 0.001 y1[1] (analytic) = 1.8810133868700118887961890775899 y1[1] (numeric) = 1.9397884080678958699821703020971 absolute error = 0.0587750211978839811859812245072 relative error = 3.1246466191123205604256056295909 % h = 0.001 TOP MAIN SOLVE Loop memory used=2819.1MB, alloc=4.6MB, time=159.52 NO POLE NO POLE x[1] = 1.079 y2[1] (analytic) = 1.8814860376204617629129669226588 y2[1] (numeric) = 2.0249134507928573726709329791413 absolute error = 0.1434274131723956097579660564825 relative error = 7.6230920827767609009734340149248 % h = 0.001 y1[1] (analytic) = 1.8814860376204617629129669226588 y1[1] (numeric) = 1.9403562881064713813353958643985 absolute error = 0.0588702504860096184224289417397 relative error = 3.1289230591614455467450009946636 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.08 y2[1] (analytic) = 1.8819578068849474737353349876248 y2[1] (numeric) = 2.0258076152234330734090539395539 absolute error = 0.1438498083384855996737189519291 relative error = 7.6436255803518013728841191647002 % h = 0.001 y1[1] (analytic) = 1.8819578068849474737353349876248 y1[1] (numeric) = 1.9409232976515071758803477798711 absolute error = 0.0589654907665597021450127922463 relative error = 3.1331994028155450145467301910348 % h = 0.001 TOP MAIN SOLVE Loop memory used=2822.9MB, alloc=4.6MB, time=159.74 NO POLE NO POLE x[1] = 1.081 y2[1] (analytic) = 1.8824286941916997960916865134587 y2[1] (numeric) = 2.0267016750536326145740244516262 absolute error = 0.1442729808619328184823379381675 relative error = 7.6641936720945762868221926145337 % h = 0.001 y1[1] (analytic) = 1.8824286941916997960916865134587 y1[1] (numeric) = 1.9414894360062421977739822625772 absolute error = 0.0590607418145424016822957491185 relative error = 3.1374756449886471645776021225131 % h = 0.001 TOP MAIN SOLVE Loop memory used=2826.7MB, alloc=4.6MB, time=159.95 NO POLE NO POLE x[1] = 1.082 y2[1] (analytic) = 1.8828986990698314624703067318156 y2[1] (numeric) = 2.0275956302813816115666439152774 absolute error = 0.1446969312115501490963371834618 relative error = 7.6847963877733681195182416193957 % h = 0.001 y1[1] (analytic) = 1.8828986990698314624703067318156 y1[1] (numeric) = 1.9420547024746976751338840585213 absolute error = 0.0591560034048662126635773267057 relative error = 3.1417517805971080257249391046784 % h = 0.001 TOP MAIN SOLVE Loop memory used=2830.5MB, alloc=4.6MB, time=160.17 NO POLE NO POLE x[1] = 1.083 y2[1] (analytic) = 1.8833678210493376339066011361452 y2[1] (numeric) = 2.0284894809046104909027402826552 absolute error = 0.14512165985527285699613914651 relative error = 7.705433757194430598594096785154 % h = 0.001 y1[1] (analytic) = 1.8833678210493376339066011361452 y1[1] (numeric) = 1.9426190963616779347237732121865 absolute error = 0.0592512753123403008171720760413 relative error = 3.1460278045595919277606996711081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.084 y2[1] (analytic) = 1.8838360596610963699878952792174 y2[1] (numeric) = 2.0293832269212544929878579629117 absolute error = 0.1455471672601581229999626836943 relative error = 7.7261058102020924288557099181624 % h = 0.001 y1[1] (analytic) = 1.8838360596610963699878952792174 y1[1] (numeric) = 1.9431826169727712159625240303567 absolute error = 0.0593465573116748459746287511393 relative error = 3.1503037117970520009217274496555 % h = 0.001 TOP MAIN SOLVE Loop memory used=2834.3MB, alloc=4.6MB, time=160.38 NO POLE NO POLE x[1] = 1.085 y2[1] (analytic) = 1.8843034144368690979753360923033 y2[1] (numeric) = 2.0302768683292536748874707160324 absolute error = 0.1459734538923845769121346237291 relative error = 7.7468125766788610555772092753994 % h = 0.001 y1[1] (analytic) = 1.8843034144368690979753360923033 y1[1] (numeric) = 1.9437452636143504842557771877901 absolute error = 0.0594418491774813862804410954868 relative error = 3.1545794972327107021823641326079 % h = 0.001 TOP MAIN SOLVE Loop memory used=2838.1MB, alloc=4.6MB, time=160.59 NO POLE NO POLE x[1] = 1.086 y2[1] (analytic) = 1.8847698849093010810424256041483 y2[1] (numeric) = 2.0311704051265529130927161001147 absolute error = 0.1464005202172518320502904959664 relative error = 7.7675540865455264654885007972575 % h = 0.001 y1[1] (analytic) = 1.8847698849093010810424256041483 y1[1] (numeric) = 1.9443070355935742436492264741242 absolute error = 0.0595371506842731626068008699759 relative error = 3.1588551557920403680760133268881 % h = 0.001 TOP MAIN SOLVE Loop memory used=2842.0MB, alloc=4.6MB, time=160.81 NO POLE NO POLE x[1] = 1.087 y2[1] (analytic) = 1.8852354706119218856297188212437 y2[1] (numeric) = 2.032063837311101906281648040534 absolute error = 0.1468283666991800206519292192903 relative error = 7.7883303697612650261780844884719 % h = 0.001 y1[1] (analytic) = 1.8852354706119218856297188212437 y1[1] (numeric) = 1.9448679322183873488026622372139 absolute error = 0.0596324616064654631729434159702 relative error = 3.1631306824027437939225890762115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.088 y2[1] (analytic) = 1.8857001710791458479152184147362 y2[1] (numeric) = 2.0329571648808551780760040934811 absolute error = 0.1472569938017093301607856787449 relative error = 7.8091414563237433646220641062767 % h = 0.001 y1[1] (analytic) = 1.8857001710791458479152184147362 y1[1] (numeric) = 1.9454279527975218162838541349316 absolute error = 0.0597277817183759683686357201954 relative error = 3.1674060719947348393191281028445 % h = 0.001 TOP MAIN SOLVE Loop memory used=2845.8MB, alloc=4.6MB, time=161.02 NO POLE NO POLE x[1] = 1.089 y2[1] (analytic) = 1.8861639858462725393999997436219 y2[1] (numeric) = 2.0338503878337720797934839804055 absolute error = 0.1476864019874995403934842367836 relative error = 7.8299873762692222855496456975039 % h = 0.001 y1[1] (analytic) = 1.8861639858462725393999997436219 y1[1] (numeric) = 1.945987096640497635181356365294 absolute error = 0.0598231107942250957813566216721 relative error = 3.1716813195001190597511883279129 % h = 0.001 TOP MAIN SOLVE Loop memory used=2849.6MB, alloc=4.6MB, time=161.25 NO POLE NO POLE x[1] = 1.09 y2[1] (analytic) = 1.886626914449487231608600628636 y2[1] (numeric) = 2.034743506167816793195535973954 absolute error = 0.148116591718329561586935345318 relative error = 7.85086815967266073035474627836 % h = 0.001 y1[1] (analytic) = 1.886626914449487231608600628636 y1[1] (numeric) = 1.9465453630576235770353191036214 absolute error = 0.0599184486081363454267184749854 relative error = 3.1759564198531743641829980028473 % h = 0.001 TOP MAIN SOLVE Loop memory used=2853.4MB, alloc=4.6MB, time=161.47 NO POLE NO POLE x[1] = 1.091 y2[1] (analytic) = 1.8870889564258613599037111764894 y2[1] (numeric) = 2.0356365198809583332306477200498 absolute error = 0.1485475634550969733269365435604 relative error = 7.8717838366478197772626680505148 % h = 0.001 y1[1] (analytic) = 1.8870889564258613599037111764894 y1[1] (numeric) = 1.9471027513599980050853904352811 absolute error = 0.0600137949341366451816792587917 relative error = 3.1802313679903316984846598254998 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.092 y2[1] (analytic) = 1.8875501113133529864146998397988 y2[1] (numeric) = 2.0365294289711705507731380848236 absolute error = 0.1489793176578175643584382450248 relative error = 7.8927344373473666834601359763521 % h = 0.001 y1[1] (analytic) = 1.8875501113133529864146998397988 y1[1] (numeric) = 1.9476592608595096828347936334201 absolute error = 0.0601091495461566964200937936213 relative error = 3.1845061588501557545550527299149 % h = 0.001 TOP MAIN SOLVE Loop memory used=2857.2MB, alloc=4.6MB, time=161.69 NO POLE NO POLE x[1] = 1.093 y2[1] (analytic) = 1.8880103786508072620795127842255 y2[1] (numeric) = 2.0374222334364321353574466191699 absolute error = 0.1494118547856248732779338349444 relative error = 7.9137199919629789698963472729048 % h = 0.001 y1[1] (analytic) = 1.8880103786508072620795127842255 y1[1] (numeric) = 1.9482148908688385819296651929492 absolute error = 0.0602045122180313198501524087237 relative error = 3.1887807873733257049994106334178 % h = 0.001 TOP MAIN SOLVE Loop memory used=2861.0MB, alloc=4.6MB, time=161.91 NO POLE NO POLE x[1] = 1.094 y2[1] (analytic) = 1.8884697579779568877994845209589 y2[1] (numeric) = 2.0383149332747266179079172377768 absolute error = 0.1498451752967697301084327168179 relative error = 7.9347405307254485494620404103931 % h = 0.001 y1[1] (analytic) = 1.8884697579779568877994845209589 y1[1] (numeric) = 1.9487696407014566893527395949017 absolute error = 0.0602998827234998015532550739428 relative error = 3.1930552485026159632208923056572 % h = 0.001 TOP MAIN SOLVE Loop memory used=2864.8MB, alloc=4.6MB, time=162.12 NO POLE NO POLE x[1] = 1.095 y2[1] (analytic) = 1.888928248835422574706598649776 y2[1] (numeric) = 2.0392075284840423734640727135473 absolute error = 0.1502792796486197987574740637713 relative error = 7.9557960839047858992529584953705 % h = 0.001 y1[1] (analytic) = 1.888928248835422574706598649776 y1[1] (numeric) = 1.949323509671628813930467339157 absolute error = 0.060395260836206239223868689381 relative error = 3.1973295371828769687857896962581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.096 y2[1] (analytic) = 1.8893858507647135035427384454507 y2[1] (numeric) = 2.0401000190623726239013765924127 absolute error = 0.150714168297659120358638146962 relative error = 7.9768866818103242776234574632124 % h = 0.001 y1[1] (analytic) = 1.8893858507647135035427384454507 y1[1] (numeric) = 1.9498764970944133921526533483872 absolute error = 0.0604906463296998886099149029365 relative error = 3.2016036483610159979223535278297 % h = 0.001 TOP MAIN SOLVE Loop memory used=2868.7MB, alloc=4.6MB, time=162.34 NO POLE NO POLE x[1] = 1.097 y2[1] (analytic) = 1.8898425633082277831504679083043 y2[1] (numeric) = 2.040992405007715440647479137618 absolute error = 0.1511498416994876574970112293137 relative error = 7.9980123547908239867353932781426 % h = 0.001 y1[1] (analytic) = 1.8898425633082277831504679083043 y1[1] (numeric) = 1.9504286022856632933037034119597 absolute error = 0.0605860389774355101532355036554 relative error = 3.205877576985977999013544733847 % h = 0.001 TOP MAIN SOLVE Loop memory used=2872.5MB, alloc=4.6MB, time=162.56 NO POLE NO POLE x[1] = 1.098 y2[1] (analytic) = 1.8902983860092529080748847881513 y2[1] (numeric) = 2.0418846863180737473939439166471 absolute error = 0.1515863003088208393190591284958 relative error = 8.0191731332345766813068143242323 % h = 0.001 y1[1] (analytic) = 1.8902983860092529080748847881513 y1[1] (numeric) = 1.9509798245620266239045669054025 absolute error = 0.0606814385527737158296821172512 relative error = 3.2101513180087264529443484033483 % h = 0.001 TOP MAIN SOLVE Loop memory used=2876.3MB, alloc=4.6MB, time=162.77 NO POLE NO POLE x[1] = 1.099 y2[1] (analytic) = 1.8907533184119662152760879798278 y2[1] (numeric) = 2.0427768629914553228034516480461 absolute error = 0.1520235445794891075273636682183 relative error = 8.0403690475695097242643853469126 % h = 0.001 y1[1] (analytic) = 1.8907533184119662152760879798278 y1[1] (numeric) = 1.9515301632409475314644645889182 absolute error = 0.0607768448289813161883766090904 relative error = 3.2144248663822242581646132911639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.1 y2[1] (analytic) = 1.8912073600614353399518025778717 y2[1] (numeric) = 2.0436689350258728032124779294965 absolute error = 0.1524615749644374632606753516248 relative error = 8.0616001282632905900028776537629 % h = 0.001 y1[1] (analytic) = 1.8912073600614353399518025778717 y1[1] (numeric) = 1.952079617640667007541490857312 absolute error = 0.0608722575792316675896882794403 relative error = 3.2186982170614146403287046701171 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y2 , x , 4 ) = y1 - 1.0; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 1000 Total Elapsed Time memory used=2880.1MB, alloc=4.6MB, time=162.99 = 2 Minutes 42 Seconds Elapsed Time(since restart) = 2 Minutes 42 Seconds Expected Time Remaining = 10 Minutes 50 Seconds Optimized Time Remaining = 10 Minutes 50 Seconds Time to Timeout = 12 Minutes 17 Seconds Percent Done = 20.02 % > quit memory used=2880.2MB, alloc=4.6MB, time=162.99