|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y2(ind_var); > omniout_float(ALWAYS,"y2[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y2[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > ; > analytic_val_y := exact_soln_y1(ind_var); > omniout_float(ALWAYS,"y1[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y1[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[2] := relerr; > else > array_last_rel_error[2] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y2(ind_var); omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y2[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "); analytic_val_y := exact_soln_y1(ind_var); omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y1[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[2] := relerr else array_last_rel_error[2] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y2_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y1_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y2_higher[1,m]) < glob_small_float) or (abs(array_y2_higher[1,m-1]) < glob_small_float) or (abs(array_y2_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y2_higher[1,m]/array_y2_higher[1,m-1]; > rm1 := array_y2_higher[1,m-1]/array_y2_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[1,1] := rcs; > array_real_pole[1,2] := ord_no; > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[1,1] := glob_large_float; > array_real_pole[1,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 1 > #IN RADII REAL EQ = 2 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 2 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_y1_higher[1,m]) < glob_small_float) or (abs(array_y1_higher[1,m-1]) < glob_small_float) or (abs(array_y1_higher[1,m-2]) < glob_small_float ))) do # do number 2 > m := m - 1; > od;# end do number 2 > ; > if (m > 10) then # if number 1 > rm0 := array_y1_higher[1,m]/array_y1_higher[1,m-1]; > rm1 := array_y1_higher[1,m-1]/array_y1_higher[1,m-2]; > hdrc := convfloat(m-1)*rm0-convfloat(m-2)*rm1; > if (abs(hdrc) > glob_small_float) then # if number 2 > rcs := glob_h/hdrc; > ord_no := convfloat(m-1)*rm0/hdrc - convfloat(m) + 2.0; > array_real_pole[2,1] := rcs; > array_real_pole[2,2] := ord_no; > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 2 > else > array_real_pole[2,1] := glob_large_float; > array_real_pole[2,2] := glob_large_float; > fi;# end if 1 > ; > #BOTTOM RADII REAL EQ = 2 > #TOP RADII COMPLEX EQ = 1 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y2_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y2_higher[1,m]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y2_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y2_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y2_higher[1,m])/(array_y2_higher[1,m-1]); > rm1 := (array_y2_higher[1,m-1])/(array_y2_higher[1,m-2]); > rm2 := (array_y2_higher[1,m-2])/(array_y2_higher[1,m-3]); > rm3 := (array_y2_higher[1,m-3])/(array_y2_higher[1,m-4]); > rm4 := (array_y2_higher[1,m-4])/(array_y2_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > #TOP RADII COMPLEX EQ = 2 > #Computes radius of convergence for complex conjugate pair of poles. > #from 6 adjacent Taylor series terms > #Also computes r_order of poles. > #Due to Manuel Prieto. > #With a correction by Dennis J. Darland > n := glob_max_terms - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y1_higher[1,n]) > glob_small_float) then # if number 2 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 2 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 2 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > elif (abs(array_y1_higher[1,m]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y1_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y1_higher[1,m-5]) >= (glob_large_float)) then # if number 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > rm0 := (array_y1_higher[1,m])/(array_y1_higher[1,m-1]); > rm1 := (array_y1_higher[1,m-1])/(array_y1_higher[1,m-2]); > rm2 := (array_y1_higher[1,m-2])/(array_y1_higher[1,m-3]); > rm3 := (array_y1_higher[1,m-3])/(array_y1_higher[1,m-4]); > rm4 := (array_y1_higher[1,m-4])/(array_y1_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 4 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 5 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 6 > if (rcs > 0.0) then # if number 7 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 7 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > fi;# end if 4 > ; > array_complex_pole[2,1] := rad_c; > array_complex_pole[2,2] := ord_no; > fi;# end if 3 > ; > #BOTTOM RADII COMPLEX EQ = 2 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 3 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 1 > found := false; > #TOP WHICH RADII EQ = 2 > if not found and ((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float)) and ((array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > found := true; > array_type_pole[2] := 2; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] <> glob_large_float) and (array_real_pole[2,2] <> glob_large_float) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float) or (array_complex_pole[2,1] <= 0.0 ) or (array_complex_pole[2,2] <= 0.0))) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and (((array_real_pole[2,1] = glob_large_float) or (array_real_pole[2,2] = glob_large_float)) and ((array_complex_pole[2,1] = glob_large_float) or (array_complex_pole[2,2] = glob_large_float))) then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > found := true; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_real_pole[2,1] < array_complex_pole[2,1]) and (array_real_pole[2,1] > 0.0) and (array_real_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_real_pole[2,1]; > array_poles[2,2] := array_real_pole[2,2]; > found := true; > array_type_pole[2] := 1; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found and ((array_complex_pole[2,1] <> glob_large_float) and (array_complex_pole[2,2] <> glob_large_float) and (array_complex_pole[2,1] > 0.0) and (array_complex_pole[2,2] > 0.0)) then # if number 3 > array_poles[2,1] := array_complex_pole[2,1]; > array_poles[2,2] := array_complex_pole[2,2]; > array_type_pole[2] := 2; > found := true; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 4 > ; > fi;# end if 3 > ; > if not found then # if number 3 > array_poles[2,1] := glob_large_float; > array_poles[2,2] := glob_large_float; > array_type_pole[2] := 3; > if (glob_display_flag) then # if number 4 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 4 > ; > fi;# end if 3 > ; > #BOTTOM WHICH RADII EQ = 2 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 3 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #TOP WHICH RADIUS EQ = 2 > if array_pole[1] > array_poles[2,1] then # if number 3 > array_pole[1] := array_poles[2,1]; > array_pole[2] := array_poles[2,2]; > fi;# end if 3 > ; > #BOTTOM WHICH RADIUS EQ = 2 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y2_higher[1, m]) < glob_small_float or abs(array_y2_higher[1, m - 1]) < glob_small_float or abs(array_y2_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[1, 1] := rcs; array_real_pole[1, 2] := ord_no else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if else array_real_pole[1, 1] := glob_large_float; array_real_pole[1, 2] := glob_large_float end if; n := glob_max_terms; m := n - 2; while 10 <= m and (abs(array_y1_higher[1, m]) < glob_small_float or abs(array_y1_higher[1, m - 1]) < glob_small_float or abs(array_y1_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; hdrc := convfloat(m - 1)*rm0 - convfloat(m - 2)*rm1; if glob_small_float < abs(hdrc) then rcs := glob_h/hdrc; ord_no := convfloat(m - 1)*rm0/hdrc - convfloat(m) + 2.0; array_real_pole[2, 1] := rcs; array_real_pole[2, 2] := ord_no else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if else array_real_pole[2, 1] := glob_large_float; array_real_pole[2, 2] := glob_large_float end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y2_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y2_higher[1, m]) or glob_large_float <= abs(array_y2_higher[1, m - 1]) or glob_large_float <= abs(array_y2_higher[1, m - 2]) or glob_large_float <= abs(array_y2_higher[1, m - 3]) or glob_large_float <= abs(array_y2_higher[1, m - 4]) or glob_large_float <= abs(array_y2_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y2_higher[1, m]/array_y2_higher[1, m - 1]; rm1 := array_y2_higher[1, m - 1]/array_y2_higher[1, m - 2]; rm2 := array_y2_higher[1, m - 2]/array_y2_higher[1, m - 3]; rm3 := array_y2_higher[1, m - 3]/array_y2_higher[1, m - 4]; rm4 := array_y2_higher[1, m - 4]/array_y2_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; n := glob_max_terms - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y1_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float elif glob_large_float <= abs(array_y1_higher[1, m]) or glob_large_float <= abs(array_y1_higher[1, m - 1]) or glob_large_float <= abs(array_y1_higher[1, m - 2]) or glob_large_float <= abs(array_y1_higher[1, m - 3]) or glob_large_float <= abs(array_y1_higher[1, m - 4]) or glob_large_float <= abs(array_y1_higher[1, m - 5]) then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else rm0 := array_y1_higher[1, m]/array_y1_higher[1, m - 1]; rm1 := array_y1_higher[1, m - 1]/array_y1_higher[1, m - 2]; rm2 := array_y1_higher[1, m - 2]/array_y1_higher[1, m - 3]; rm3 := array_y1_higher[1, m - 3]/array_y1_higher[1, m - 4]; rm4 := array_y1_higher[1, m - 4]/array_y1_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[2, 1] := glob_large_float; array_complex_pole[2, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[2, 1] := rad_c; array_complex_pole[2, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; found := false; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; found := true; array_type_pole[2] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[2, 1] <> glob_large_float and array_real_pole[2, 2] <> glob_large_float and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float or array_complex_pole[2, 1] <= 0. or array_complex_pole[2, 2] <= 0.) then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[2, 1] = glob_large_float or array_real_pole[2, 2] = glob_large_float) and ( array_complex_pole[2, 1] = glob_large_float or array_complex_pole[2, 2] = glob_large_float) then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; found := true; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[2, 1] < array_complex_pole[2, 1] and 0. < array_real_pole[2, 1] and 0. < array_real_pole[2, 2] then array_poles[2, 1] := array_real_pole[2, 1]; array_poles[2, 2] := array_real_pole[2, 2]; found := true; array_type_pole[2] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[2, 1] <> glob_large_float and array_complex_pole[2, 2] <> glob_large_float and 0. < array_complex_pole[2, 1] and 0. < array_complex_pole[2, 2] then array_poles[2, 1] := array_complex_pole[2, 1]; array_poles[2, 2] := array_complex_pole[2, 2]; array_type_pole[2] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[2, 1] := glob_large_float; array_poles[2, 2] := glob_large_float; array_type_pole[2] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; if array_poles[2, 1] < array_pole[1] then array_pole[1] := array_poles[2, 1]; array_pole[2] := array_poles[2, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 3 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y2[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y2[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > ; > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y1[iii]) > array_norms[iii]) then # if number 4 > array_norms[iii] := abs(array_y1[iii]); > fi;# end if 4 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y2[iii]) then array_norms[iii] := abs(array_y2[iii]) end if; iii := iii + 1 end do; iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y1[iii]) then array_norms[iii] := abs(array_y1[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre add $eq_no = 1 i = 1 > array_tmp1[1] := array_const_0D0[1] + array_y1[1]; > #emit pre sub $eq_no = 1 i = 1 > array_tmp2[1] := (array_tmp1[1] - (array_const_2D0[1])); > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y2_set_initial[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y2[2] := temporary; > array_y2_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #emit pre diff $eq_no = 2 i = 1 > array_tmp4[1] := array_y2_higher[6,1]; > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y1_set_initial[2,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y1[2] := temporary; > array_y1_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre add $eq_no = 1 i = 2 > array_tmp1[2] := array_const_0D0[2] + array_y1[2]; > #emit pre sub $eq_no = 1 i = 2 > array_tmp2[2] := (array_tmp1[2] - (array_const_2D0[2])); > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y2_set_initial[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y2[3] := temporary; > array_y2_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #emit pre diff $eq_no = 2 i = 2 > array_tmp4[2] := array_y2_higher[6,2]; > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y1_set_initial[2,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y1[3] := temporary; > array_y1_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre add $eq_no = 1 i = 3 > array_tmp1[3] := array_const_0D0[3] + array_y1[3]; > #emit pre sub $eq_no = 1 i = 3 > array_tmp2[3] := (array_tmp1[3] - (array_const_2D0[3])); > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y2_set_initial[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y2[4] := temporary; > array_y2_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #emit pre diff $eq_no = 2 i = 3 > array_tmp4[3] := array_y2_higher[6,3]; > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y1_set_initial[2,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y1[4] := temporary; > array_y1_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre add $eq_no = 1 i = 4 > array_tmp1[4] := array_const_0D0[4] + array_y1[4]; > #emit pre sub $eq_no = 1 i = 4 > array_tmp2[4] := (array_tmp1[4] - (array_const_2D0[4])); > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y2_set_initial[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y2[5] := temporary; > array_y2_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #emit pre diff $eq_no = 2 i = 4 > array_tmp4[4] := array_y2_higher[6,4]; > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y1_set_initial[2,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y1[5] := temporary; > array_y1_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre add $eq_no = 1 i = 5 > array_tmp1[5] := array_const_0D0[5] + array_y1[5]; > #emit pre sub $eq_no = 1 i = 5 > array_tmp2[5] := (array_tmp1[5] - (array_const_2D0[5])); > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y2_set_initial[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y2[6] := temporary; > array_y2_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y2_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #emit pre diff $eq_no = 2 i = 5 > array_tmp4[5] := array_y2_higher[6,5]; > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y1_set_initial[2,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp4[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y1[6] := temporary; > array_y1_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y1_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit add $eq_no = 1 > array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; > #emit sub $eq_no = 1 > array_tmp2[kkk] := (array_tmp1[kkk] - (array_const_2D0[kkk])); > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y2[kkk + order_d] := temporary; > array_y2_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y2_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > #emit diff $eq_no = 2 > array_tmp4[kkk] := array_y2_higher[6,kkk]; > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_set_initial[2,kkk + order_d] then # if number 2 > temporary := array_tmp4[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y1[kkk + order_d] := temporary; > array_y1_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y1_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; array_tmp1[1] := array_const_0D0[1] + array_y1[1]; array_tmp2[1] := array_tmp1[1] - array_const_2D0[1]; if not array_y2_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y2[2] := temporary; array_y2_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp4[1] := array_y2_higher[6, 1]; if not array_y1_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[1]*glob_h*factorial_3(0, 1); array_y1[2] := temporary; array_y1_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := array_const_0D0[2] + array_y1[2]; array_tmp2[2] := array_tmp1[2] - array_const_2D0[2]; if not array_y2_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y2[3] := temporary; array_y2_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp4[2] := array_y2_higher[6, 2]; if not array_y1_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[2]*glob_h*factorial_3(1, 2); array_y1[3] := temporary; array_y1_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := array_const_0D0[3] + array_y1[3]; array_tmp2[3] := array_tmp1[3] - array_const_2D0[3]; if not array_y2_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y2[4] := temporary; array_y2_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp4[3] := array_y2_higher[6, 3]; if not array_y1_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[3]*glob_h*factorial_3(2, 3); array_y1[4] := temporary; array_y1_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := array_const_0D0[4] + array_y1[4]; array_tmp2[4] := array_tmp1[4] - array_const_2D0[4]; if not array_y2_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y2[5] := temporary; array_y2_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp4[4] := array_y2_higher[6, 4]; if not array_y1_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[4]*glob_h*factorial_3(3, 4); array_y1[5] := temporary; array_y1_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := array_const_0D0[5] + array_y1[5]; array_tmp2[5] := array_tmp1[5] - array_const_2D0[5]; if not array_y2_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y2[6] := temporary; array_y2_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y2_higher[2, 5] := temporary end if end if; kkk := 6; array_tmp4[5] := array_y2_higher[6, 5]; if not array_y1_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[5]*glob_h*factorial_3(4, 5); array_y1[6] := temporary; array_y1_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y1_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := array_const_0D0[kkk] + array_y1[kkk]; array_tmp2[kkk] := array_tmp1[kkk] - array_const_2D0[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y2[kkk + order_d] := temporary; array_y2_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y2_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; array_tmp4[kkk] := array_y2_higher[6, kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[2, kkk + order_d] then temporary := array_tmp4[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y1[kkk + order_d] := temporary; array_y1_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y1_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > 2.0 + sin(x); > end; exact_soln_y1 := proc(x) 2.0 + sin(x) end proc > exact_soln_y2 := proc(x) > 2.0 - cos(x); > end; exact_soln_y2 := proc(x) 2.0 - cos(x) end proc > exact_soln_y2p := proc(x) > sin(x); > end; exact_soln_y2p := proc(x) sin(x) end proc > exact_soln_y2pp := proc(x) > cos(x); > end; exact_soln_y2pp := proc(x) cos(x) end proc > exact_soln_y2ppp := proc(x) > -sin(x); > end; exact_soln_y2ppp := proc(x) -sin(x) end proc > exact_soln_y2pppp := proc(x) > -cos(x); > end; exact_soln_y2pppp := proc(x) -cos(x) end proc > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > glob_iolevel, > INFO, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > glob_max_terms, > #Top Generate Globals Decl > MAX_UNCHANGED, > glob_no_eqs, > glob_max_trunc_err, > glob_hmin_init, > glob_reached_optimal_h, > glob_log10relerr, > glob_relerr, > glob_not_yet_finished, > glob_max_minutes, > glob_max_rel_trunc_err, > glob_dump_analytic, > glob_clock_sec, > glob_html_log, > glob_current_iter, > glob_small_float, > glob_max_opt_iter, > glob_optimal_expect_sec, > glob_abserr, > glob_almost_1, > glob_log10_abserr, > glob_hmin, > glob_optimal_done, > centuries_in_millinium, > djd_debug2, > glob_log10normmin, > glob_log10abserr, > glob_curr_iter_when_opt, > glob_start, > glob_warned2, > glob_large_float, > glob_h, > glob_disp_incr, > years_in_century, > glob_normmax, > glob_max_sec, > glob_smallish_float, > glob_log10_relerr, > glob_look_poles, > days_in_year, > glob_dump, > glob_optimal_clock_start_sec, > glob_not_yet_start_msg, > glob_clock_start_sec, > glob_display_flag, > glob_percent_done, > glob_iter, > glob_orig_start_sec, > glob_warned, > glob_max_hours, > glob_last_good_h, > min_in_hour, > sec_in_min, > djd_debug, > glob_unchanged_h_cnt, > glob_optimal_start, > glob_max_iter, > glob_hmax, > glob_initial_pass, > hours_in_day, > glob_subiter_method, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_5, > array_const_1, > array_const_0D0, > array_const_2D0, > #END CONST > array_last_rel_error, > array_m1, > array_x, > array_type_pole, > array_y2_init, > array_y2, > array_y1, > array_pole, > array_norms, > array_y1_init, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_1st_rel_error, > array_y2_set_initial, > array_real_pole, > array_y1_set_initial, > array_y2_higher_work2, > array_y2_higher_work, > array_y2_higher, > array_complex_pole, > array_y1_higher_work2, > array_y1_higher_work, > array_y1_higher, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_iolevel := 5; > INFO := 2; > DEBUGMASSIVE := 4; > DEBUGL := 3; > ALWAYS := 1; > glob_max_terms := 30; > MAX_UNCHANGED := 10; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_hmin_init := 0.001; > glob_reached_optimal_h := false; > glob_log10relerr := 0.0; > glob_relerr := 0.1e-10; > glob_not_yet_finished := true; > glob_max_minutes := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_dump_analytic := false; > glob_clock_sec := 0.0; > glob_html_log := true; > glob_current_iter := 0; > glob_small_float := 0.1e-50; > glob_max_opt_iter := 10; > glob_optimal_expect_sec := 0.1; > glob_abserr := 0.1e-10; > glob_almost_1 := 0.9990; > glob_log10_abserr := 0.1e-10; > glob_hmin := 0.00000000001; > glob_optimal_done := false; > centuries_in_millinium := 10.0; > djd_debug2 := true; > glob_log10normmin := 0.1; > glob_log10abserr := 0.0; > glob_curr_iter_when_opt := 0; > glob_start := 0; > glob_warned2 := false; > glob_large_float := 9.0e100; > glob_h := 0.1; > glob_disp_incr := 0.1; > years_in_century := 100.0; > glob_normmax := 0.0; > glob_max_sec := 10000.0; > glob_smallish_float := 0.1e-100; > glob_log10_relerr := 0.1e-10; > glob_look_poles := false; > days_in_year := 365.0; > glob_dump := false; > glob_optimal_clock_start_sec := 0.0; > glob_not_yet_start_msg := true; > glob_clock_start_sec := 0.0; > glob_display_flag := true; > glob_percent_done := 0.0; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_warned := false; > glob_max_hours := 0.0; > glob_last_good_h := 0.1; > min_in_hour := 60.0; > sec_in_min := 60.0; > djd_debug := true; > glob_unchanged_h_cnt := 0; > glob_optimal_start := 0.0; > glob_max_iter := 1000; > glob_hmax := 1.0; > glob_initial_pass := true; > hours_in_day := 24.0; > 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/mtest9_revpostode.ode#################"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.5;"); > omniout_str(ALWAYS,"x_end := 10.0;"); > omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);"); > omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);"); > omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);"); > omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); > omniout_str(ALWAYS,"array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 10;"); > omniout_str(ALWAYS,"glob_subiter_method := 3;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > 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,"2.0 + sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2 := proc(x)"); > omniout_str(ALWAYS,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2p := proc(x)"); > omniout_str(ALWAYS,"sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)"); > omniout_str(ALWAYS,"cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2ppp := proc(x)"); > omniout_str(ALWAYS,"-sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_y2pppp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_y2_init:= Array(1..(max_terms + 1),[]); > array_y2:= Array(1..(max_terms + 1),[]); > array_y1:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y1_init:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y2_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_real_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_set_initial := Array(1..(3+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work2 := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher_work := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_y2_higher := Array(1..(6+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(2+ 1) ,(1..3+ 1),[]); > array_y1_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y1_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(2+ 1) ,(1..3+ 1),[]); > 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_m1[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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1_init[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_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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 <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher[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 <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher[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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_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_5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_5[1] := 5; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.5; > x_end := 10.0; > array_y1_init[0 + 1] := exact_soln_y1(x_start); > array_y2_init[0 + 1] := exact_soln_y2(x_start); > array_y2_init[1 + 1] := exact_soln_y2p(x_start); > array_y2_init[2 + 1] := exact_soln_y2pp(x_start); > array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); > array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); > glob_h := 0.00001 ; > glob_look_poles := true; > glob_max_iter := 10; > glob_subiter_method := 3; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > 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] := true; > array_y2_set_initial[1,6] := false; > array_y2_set_initial[1,7] := false; > array_y2_set_initial[1,8] := false; > array_y2_set_initial[1,9] := false; > array_y2_set_initial[1,10] := false; > array_y2_set_initial[1,11] := false; > array_y2_set_initial[1,12] := false; > array_y2_set_initial[1,13] := false; > array_y2_set_initial[1,14] := false; > array_y2_set_initial[1,15] := false; > array_y2_set_initial[1,16] := false; > array_y2_set_initial[1,17] := false; > array_y2_set_initial[1,18] := false; > array_y2_set_initial[1,19] := false; > array_y2_set_initial[1,20] := false; > array_y2_set_initial[1,21] := false; > array_y2_set_initial[1,22] := false; > array_y2_set_initial[1,23] := false; > array_y2_set_initial[1,24] := false; > array_y2_set_initial[1,25] := false; > array_y2_set_initial[1,26] := false; > array_y2_set_initial[1,27] := false; > array_y2_set_initial[1,28] := false; > array_y2_set_initial[1,29] := false; > array_y2_set_initial[1,30] := false; > array_y1_set_initial[2,1] := true; > array_y1_set_initial[2,2] := false; > array_y1_set_initial[2,3] := false; > array_y1_set_initial[2,4] := false; > array_y1_set_initial[2,5] := false; > array_y1_set_initial[2,6] := false; > array_y1_set_initial[2,7] := false; > array_y1_set_initial[2,8] := false; > array_y1_set_initial[2,9] := false; > array_y1_set_initial[2,10] := false; > array_y1_set_initial[2,11] := false; > array_y1_set_initial[2,12] := false; > array_y1_set_initial[2,13] := false; > array_y1_set_initial[2,14] := false; > array_y1_set_initial[2,15] := false; > array_y1_set_initial[2,16] := false; > array_y1_set_initial[2,17] := false; > array_y1_set_initial[2,18] := false; > array_y1_set_initial[2,19] := false; > array_y1_set_initial[2,20] := false; > array_y1_set_initial[2,21] := false; > array_y1_set_initial[2,22] := false; > array_y1_set_initial[2,23] := false; > array_y1_set_initial[2,24] := false; > array_y1_set_initial[2,25] := false; > array_y1_set_initial[2,26] := false; > array_y1_set_initial[2,27] := false; > array_y1_set_initial[2,28] := false; > array_y1_set_initial[2,29] := false; > array_y1_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 5; > #Start Series array_y2 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y2[term_no] := array_y2_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y2_higher[r_order,term_no] := array_y2_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > order_diff := 1; > #Start Series array_y1 > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y1[term_no] := array_y1_init[term_no] * glob_h ^ (term_no - 1) / factorial_1(term_no - 1); > term_no := term_no + 1; > od;# end do number 2 > ; > rows := order_diff; > r_order := 1; > while (r_order <= rows) do # do number 2 > term_no := 1; > while (term_no <= (rows - r_order + 1)) do # do number 3 > it := term_no + r_order - 1; > array_y1_higher[r_order,term_no] := array_y1_init[it]* (glob_h ^ (term_no - 1)) / ((factorial_1(term_no - 1))); > term_no := term_no + 1; > od;# end do number 3 > ; > r_order := r_order + 1; > od;# end do number 2 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > start_array_y2(); > if (abs(array_y2_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y2_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > start_array_y1(); > if (abs(array_y1_higher[1,1]) > glob_small_float) then # if number 3 > tmp := abs(array_y1_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 4 > glob_log10normmin := log10norm; > fi;# end if 4 > fi;# end if 3 > ; > display_alot(current_iter) > ; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := 0; > glob_iter := 0; > omniout_str(DEBUGL," "); > glob_reached_optimal_h := true; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > while ((glob_current_iter < glob_max_iter) and (array_x[1] <= x_end ) and ((convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec)) < convfloat(glob_max_sec))) do # do number 2 > #left paren 0001C > omniout_str(INFO," "); > omniout_str(INFO,"TOP MAIN SOLVE Loop"); > glob_iter := glob_iter + 1; > glob_clock_sec := elapsed_time_seconds(); > glob_current_iter := glob_current_iter + 1; > if glob_subiter_method = 1 then # if number 3 > atomall(); > elif glob_subiter_method = 2 then # if number 4 > subiter := 1; > while subiter <= 2 do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > else > subiter := 1; > while subiter <= 2 + glob_max_terms do # do number 3 > atomall(); > subiter := subiter + 1; > od;# end do number 3 > ; > fi;# end if 4 > ; > if (glob_look_poles) then # if number 4 > #left paren 0004C > check_for_pole(); > fi;# end if 4 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y2 > order_diff := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 6; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[6,iii] := array_y2_higher[6,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 6; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 5; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 5; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[5,iii] := array_y2_higher[5,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[4,iii] := array_y2_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 6; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 6; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 5; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y2[term_no] := array_y2_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > #Jump Series array_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #END SUM AND ADJUST EQ =2 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y1[term_no] := array_y1_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 4 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 4 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 4 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 4 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(INFO,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-15T23:42:31-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9_rev") > ; > logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 5 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 5 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"mtest9_rev diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9_rev maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff(y1,x,1) = diff(y2,x,5);") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 5 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if glob_html_log then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `subiter` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, subiter; global glob_iolevel, INFO, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_max_terms, MAX_UNCHANGED, glob_no_eqs, glob_max_trunc_err, glob_hmin_init, glob_reached_optimal_h, glob_log10relerr, glob_relerr, glob_not_yet_finished, glob_max_minutes, glob_max_rel_trunc_err, glob_dump_analytic, glob_clock_sec, glob_html_log, glob_current_iter, glob_small_float, glob_max_opt_iter, glob_optimal_expect_sec, glob_abserr, glob_almost_1, glob_log10_abserr, glob_hmin, glob_optimal_done, centuries_in_millinium, djd_debug2, glob_log10normmin, glob_log10abserr, glob_curr_iter_when_opt, glob_start, glob_warned2, glob_large_float, glob_h, glob_disp_incr, years_in_century, glob_normmax, glob_max_sec, glob_smallish_float, glob_log10_relerr, glob_look_poles, days_in_year, glob_dump, glob_optimal_clock_start_sec, glob_not_yet_start_msg, glob_clock_start_sec, glob_display_flag, glob_percent_done, glob_iter, glob_orig_start_sec, glob_warned, glob_max_hours, glob_last_good_h, min_in_hour, sec_in_min, djd_debug, glob_unchanged_h_cnt, glob_optimal_start, glob_max_iter, glob_hmax, glob_initial_pass, hours_in_day, glob_subiter_method, array_const_5, array_const_1, array_const_0D0, array_const_2D0, array_last_rel_error, array_m1, array_x, array_type_pole, array_y2_init, array_y2, array_y1, array_pole, array_norms, array_y1_init, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_1st_rel_error, array_y2_set_initial, array_real_pole, array_y1_set_initial, array_y2_higher_work2, array_y2_higher_work, array_y2_higher, array_complex_pole, array_y1_higher_work2, array_y1_higher_work, array_y1_higher, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_iolevel := 5; INFO := 2; DEBUGMASSIVE := 4; DEBUGL := 3; ALWAYS := 1; glob_max_terms := 30; MAX_UNCHANGED := 10; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_hmin_init := 0.001; glob_reached_optimal_h := false; glob_log10relerr := 0.; glob_relerr := 0.1*10^(-10); glob_not_yet_finished := true; glob_max_minutes := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; glob_clock_sec := 0.; glob_html_log := true; glob_current_iter := 0; glob_small_float := 0.1*10^(-50); glob_max_opt_iter := 10; glob_optimal_expect_sec := 0.1; glob_abserr := 0.1*10^(-10); glob_almost_1 := 0.9990; glob_log10_abserr := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_optimal_done := false; centuries_in_millinium := 10.0; djd_debug2 := true; glob_log10normmin := 0.1; glob_log10abserr := 0.; glob_curr_iter_when_opt := 0; glob_start := 0; glob_warned2 := false; glob_large_float := 0.90*10^101; glob_h := 0.1; glob_disp_incr := 0.1; years_in_century := 100.0; glob_normmax := 0.; glob_max_sec := 10000.0; glob_smallish_float := 0.1*10^(-100); glob_log10_relerr := 0.1*10^(-10); glob_look_poles := false; days_in_year := 365.0; glob_dump := false; glob_optimal_clock_start_sec := 0.; glob_not_yet_start_msg := true; glob_clock_start_sec := 0.; glob_display_flag := true; glob_percent_done := 0.; glob_iter := 0; glob_orig_start_sec := 0.; glob_warned := false; glob_max_hours := 0.; glob_last_good_h := 0.1; min_in_hour := 60.0; sec_in_min := 60.0; djd_debug := true; glob_unchanged_h_cnt := 0; glob_optimal_start := 0.; glob_max_iter := 1000; glob_hmax := 1.0; glob_initial_pass := true; hours_in_day := 24.0; 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/mtest9_revpostode.ode#################"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.5;"); omniout_str(ALWAYS, "x_end := 10.0;"); omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);"); omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);"); omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);") ; omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);") ; omniout_str(ALWAYS, "array_y2_init[3 + 1] := exact_soln_y2ppp(x_start);"); omniout_str(ALWAYS, "array_y2_init[4 + 1] := exact_soln_y2pppp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 10;"); omniout_str(ALWAYS, "glob_subiter_method := 3;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); 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, "2.0 + sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2 := proc(x)"); omniout_str(ALWAYS, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2p := proc(x)"); omniout_str(ALWAYS, "sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)"); omniout_str(ALWAYS, "cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2ppp := proc(x)"); omniout_str(ALWAYS, "-sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_y2pppp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_last_rel_error := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_y2_init := Array(1 .. max_terms + 1, []); array_y2 := Array(1 .. max_terms + 1, []); array_y1 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y1_init := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y2_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_real_pole := Array(1 .. 3, 1 .. 4, []); array_y1_set_initial := Array(1 .. 4, 1 .. max_terms + 1, []); array_y2_higher_work2 := Array(1 .. 7, 1 .. max_terms + 1, []); array_y2_higher_work := Array(1 .. 7, 1 .. max_terms + 1, []); array_y2_higher := Array(1 .. 7, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 3, 1 .. 4, []); array_y1_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y1_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y1_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 3, 1 .. 4, []); 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_m1[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_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1_init[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_1st_rel_error[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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 <= 6 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher[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 <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[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; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_y2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y2[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_5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_5[term] := 0.; term := term + 1 end do; array_const_5[1] := 5; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.5; x_end := 10.0; array_y1_init[1] := exact_soln_y1(x_start); array_y2_init[1] := exact_soln_y2(x_start); array_y2_init[2] := exact_soln_y2p(x_start); array_y2_init[3] := exact_soln_y2pp(x_start); array_y2_init[4] := exact_soln_y2ppp(x_start); array_y2_init[5] := exact_soln_y2pppp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; glob_h := 0.001; 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] := true; array_y2_set_initial[1, 6] := false; array_y2_set_initial[1, 7] := false; array_y2_set_initial[1, 8] := false; array_y2_set_initial[1, 9] := false; array_y2_set_initial[1, 10] := false; array_y2_set_initial[1, 11] := false; array_y2_set_initial[1, 12] := false; array_y2_set_initial[1, 13] := false; array_y2_set_initial[1, 14] := false; array_y2_set_initial[1, 15] := false; array_y2_set_initial[1, 16] := false; array_y2_set_initial[1, 17] := false; array_y2_set_initial[1, 18] := false; array_y2_set_initial[1, 19] := false; array_y2_set_initial[1, 20] := false; array_y2_set_initial[1, 21] := false; array_y2_set_initial[1, 22] := false; array_y2_set_initial[1, 23] := false; array_y2_set_initial[1, 24] := false; array_y2_set_initial[1, 25] := false; array_y2_set_initial[1, 26] := false; array_y2_set_initial[1, 27] := false; array_y2_set_initial[1, 28] := false; array_y2_set_initial[1, 29] := false; array_y2_set_initial[1, 30] := false; array_y1_set_initial[2, 1] := true; array_y1_set_initial[2, 2] := false; array_y1_set_initial[2, 3] := false; array_y1_set_initial[2, 4] := false; array_y1_set_initial[2, 5] := false; array_y1_set_initial[2, 6] := false; array_y1_set_initial[2, 7] := false; array_y1_set_initial[2, 8] := false; array_y1_set_initial[2, 9] := false; array_y1_set_initial[2, 10] := false; array_y1_set_initial[2, 11] := false; array_y1_set_initial[2, 12] := false; array_y1_set_initial[2, 13] := false; array_y1_set_initial[2, 14] := false; array_y1_set_initial[2, 15] := false; array_y1_set_initial[2, 16] := false; array_y1_set_initial[2, 17] := false; array_y1_set_initial[2, 18] := false; array_y1_set_initial[2, 19] := false; array_y1_set_initial[2, 20] := false; array_y1_set_initial[2, 21] := false; array_y1_set_initial[2, 22] := false; array_y1_set_initial[2, 23] := false; array_y1_set_initial[2, 24] := false; array_y1_set_initial[2, 25] := false; array_y1_set_initial[2, 26] := false; array_y1_set_initial[2, 27] := false; array_y1_set_initial[2, 28] := false; array_y1_set_initial[2, 29] := false; array_y1_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 5; term_no := 1; while term_no <= order_diff do array_y2[term_no] := array_y2_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y2_higher[r_order, term_no] := array_y2_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; order_diff := 1; term_no := 1; while term_no <= order_diff do array_y1[term_no] := array_y1_init[term_no]*glob_h^(term_no - 1)/ factorial_1(term_no - 1); term_no := term_no + 1 end do; rows := order_diff; r_order := 1; while r_order <= rows do term_no := 1; while term_no <= rows - r_order + 1 do it := term_no + r_order - 1; array_y1_higher[r_order, term_no] := array_y1_init[it]* glob_h^(term_no - 1)/factorial_1(term_no - 1); term_no := term_no + 1 end do; r_order := r_order + 1 end do; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); start_array_y2(); if glob_small_float < abs(array_y2_higher[1, 1]) then tmp := abs(array_y2_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); start_array_y1(); if glob_small_float < abs(array_y1_higher[1, 1]) then tmp := abs(array_y1_higher[1, 1]); log10norm := log10(tmp); if log10norm < glob_log10normmin then glob_log10normmin := log10norm end if end if; display_alot(current_iter); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 5; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[6, iii] := array_y2_higher[6, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 6; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 6; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 6; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-15T23:42:31-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9_rev"); logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "mtest9_rev diffeq.mxt"); logitem_str(html_log_file, "mtest9_rev maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/mtest9_revpostode.ode################# diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.5; x_end := 10.0; array_y1_init[0 + 1] := exact_soln_y1(x_start); array_y2_init[0 + 1] := exact_soln_y2(x_start); array_y2_init[1 + 1] := exact_soln_y2p(x_start); array_y2_init[2 + 1] := exact_soln_y2pp(x_start); array_y2_init[3 + 1] := exact_soln_y2ppp(x_start); array_y2_init[4 + 1] := exact_soln_y2pppp(x_start); glob_h := 0.00001 ; glob_look_poles := true; glob_max_iter := 10; glob_subiter_method := 3; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y1 := proc(x) 2.0 + sin(x); end; exact_soln_y2 := proc(x) 2.0 - cos(x); end; exact_soln_y2p := proc(x) sin(x); end; exact_soln_y2pp := proc(x) cos(x); end; exact_soln_y2ppp := proc(x) -sin(x); end; exact_soln_y2pppp := proc(x) -cos(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.001 x[1] = 0.5 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.001 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.501 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228973023595716096962371645635 absolute error = 3.9964315912251e-18 relative error = 3.5590357041799818917528935659069e-16 % h = 0.001 y1[1] (analytic) = 2.4803028813070802939494724420977 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008773427028772936761845068821 relative error = 0.035372401874360924089566086208289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.502 y2[1] (analytic) = 1.1233780437121404920409717621522 y2[1] (numeric) = 1.1233780437121403641161663103213 absolute error = 1.279248054518309e-16 relative error = 1.1387511636698049527321551304247e-14 % h = 0.001 y1[1] (analytic) = 2.4811797437071163057841377482187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0017542051029133055108498130031 relative error = 0.070700444309300938093178385518425 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.44 NO POLE NO POLE x[1] = 0.503 y2[1] (analytic) = 1.1238596616865926064215271335312 y2[1] (numeric) = 1.1238596616865916346964672953222 absolute error = 9.717250598382090e-16 relative error = 8.6463202921610960949418515093497e-14 % h = 0.001 y1[1] (analytic) = 2.4820561249274487088131362528522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0026305863232457085398483176366 relative error = 0.10598415953719021627869493626097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.504 y2[1] (analytic) = 1.1243421558013100225170503558855 y2[1] (numeric) = 1.1243421558013059264282111875027 absolute error = 4.0960888391683828e-15 relative error = 3.6430981601407017699748432374480e-13 % h = 0.001 y1[1] (analytic) = 2.4829320240916963557358308536409 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035064854874933554625429184253 relative error = 0.14122357976256294749295818319025 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.505 y2[1] (analytic) = 1.1248255255737986658179668865485 y2[1] (numeric) = 1.124825525573786161740578682083 absolute error = 1.25040773882044655e-14 relative error = 1.1116459489862533014706793539627e-12 % h = 0.001 y1[1] (analytic) = 2.4838074403239601552961692154743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0043819017197571550228812802587 relative error = 0.17641873716207358683165415092659 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.506 y2[1] (analytic) = 1.1253097705206888041164464559634 y2[1] (numeric) = 1.1253097705206576805008601015673 absolute error = 3.11236155863543961e-14 relative error = 2.7657820452365999314295612731972e-12 % h = 0.001 y1[1] (analytic) = 2.4846823727488239481817020349524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0052568341446209479084140997368 relative error = 0.2115696638844533806737925932691 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.9MB, time=0.98 NO POLE NO POLE x[1] = 0.507 y2[1] (analytic) = 1.1257948901577355308760949947039 y2[1] (numeric) = 1.1257948901576682400144553957437 absolute error = 6.72908616395989602e-14 relative error = 5.9771866285670219323854670962975e-12 % h = 0.001 y1[1] (analytic) = 2.4855568204913553824396694014904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0061312818871523821663814662748 relative error = 0.24667639205046716400687694163286 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.508 y2[1] (analytic) = 1.1262808839998192494768208161278 y2[1] (numeric) = 1.1262808839996880150248741416841 absolute error = 1.312344519466744437e-13 relative error = 1.1652018054378653982694624370328e-11 % h = 0.001 y1[1] (analytic) = 2.4864307826771067884092798390526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.007005244072903788135991903837 relative error = 0.28173895375287042897210788637658 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.509 y2[1] (analytic) = 1.126767751560946158334390809836 y2[1] (numeric) = 1.1267677515607095977137355437444 absolute error = 2.365606206552660916e-13 relative error = 2.0994621147752175134343597888834e-11 % h = 0.001 y1[1] (analytic) = 2.4873042584321160531693070963062 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0078787198279130528960191610906 relative error = 0.31675738105636666356223183993781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.51 y2[1] (analytic) = 1.1272554923542487368941915264245 y2[1] (numeric) = 1.1272554923538479977007684335643 absolute error = 4.007391934230928602e-13 relative error = 3.5549988103065944200239348593181e-11 % h = 0.001 y1[1] (analytic) = 2.4881772468829074945001302376746 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008751708278704494226842302459 relative error = 0.35173170599756495940790535457244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=11.4MB, alloc=3.9MB, time=1.49 x[1] = 0.511 y2[1] (analytic) = 1.1277441058919862324987091598053 y2[1] (numeric) = 1.1277441058913406420438112700674 absolute error = 6.455904548978897379e-13 relative error = 5.7246183023697709038133538255325e-11 % h = 0.001 y1[1] (analytic) = 2.4890497471564927343593430733201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0096242085522897340860551381045 relative error = 0.38666196058493788759169880261458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.512 y2[1] (analytic) = 1.1282335916855451481282415596589 y2[1] (numeric) = 1.1282335916845473752388121394612 absolute error = 9.977728894294201977e-13 relative error = 8.8436729484253273713900937808655e-11 % h = 0.001 y1[1] (analytic) = 2.4899217583803715718700594525215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0104962197761685715967715173059 relative error = 0.42154817679877964143210727811901 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.513 y2[1] (analytic) = 1.1287239492454397310143545333464 y2[1] (numeric) = 1.1287239492439504592198287552371 absolute error = 1.4892717945257781093e-12 relative error = 1.3194296050166803556963687023898e-10 % h = 0.001 y1[1] (analytic) = 2.4907932796825328558210414322121 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0113677410783298555477534969965 relative error = 0.45639038659116444518317374841848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.514 y2[1] (analytic) = 1.1292151780813124621255938238659 y2[1] (numeric) = 1.1292151780791545733590284581703 absolute error = 2.1578887665653656956e-12 relative error = 1.9109633030543453821668290298872e-10 % h = 0.001 y1[1] (analytic) = 2.4916643101914553566777778206244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0122387715872523564044898854088 relative error = 0.4911886218859052275985589770279 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.515 y2[1] (analytic) = 1.1297072777019345465249632781811 y2[1] (numeric) = 1.12970727769888681446668821632 absolute error = 3.0477320582750618611e-12 relative error = 2.6978068730112092719404051664209e-10 % h = 0.001 y1[1] (analytic) = 2.4925348490361086381036410850348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0131093104319056378303531498192 relative error = 0.5259429145785125593121146588246 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=2.01 NO POLE NO POLE x[1] = 0.516 y2[1] (analytic) = 1.1302002476152064045986788484863 y2[1] (numeric) = 1.1302002476109966967911946250292 absolute error = 4.2097078074842234571e-12 relative error = 3.7247450762526124546953832005182e-10 % h = 0.001 y1[1] (analytic) = 2.4934048953459539279902511025232 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0139793567417509277169631673076 relative error = 0.5606532965361538529902305589296 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.517 y2[1] (analytic) = 1.1306940873281581641557071976931 y2[1] (numeric) = 1.1306940873224561520190439069248 absolute error = 5.7020121366632907683e-12 relative error = 5.0429308869361866809505202241791e-10 % h = 0.001 y1[1] (analytic) = 2.4942744482509449889961747234587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0148489096467419887228867882431 relative error = 0.59531979959761282521443323237872 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.518 y2[1] (analytic) = 1.1311887963469501533975968096429 y2[1] (numeric) = 1.1311887963393595292748419119177 absolute error = 7.5906241227548977252e-12 relative error = 6.7103070214874685469833382583942e-10 % h = 0.001 y1[1] (analytic) = 2.4951435068815289885930906090811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0157179682773259883198026738655 relative error = 0.62994245557324921905591312628167 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.519 y2[1] (analytic) = 1.1316843741768733947581086342535 y2[1] (numeric) = 1.1316843741669235951213041172024 absolute error = 9.9497996368045170511e-12 relative error = 8.7920270561670239858508448512629e-10 % h = 0.001 y1[1] (analytic) = 2.4960120703686473686185492970897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0165865317644443683452613618741 relative error = 0.6645212962449587863068485349416 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=3.9MB, time=2.53 NO POLE NO POLE x[1] = 0.52 y2[1] (analytic) = 1.1321808203223500996121524280115 y2[1] (numeric) = 1.1321808203094875335592556272576 absolute error = 1.28625660528968007539e-11 relative error = 1.1360876126866926788887946083009e-09 % h = 0.001 y1[1] (analytic) = 2.4968801378437367143344589425478 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0174545992395337140611710073322 relative error = 0.69905635336613352833657899470403 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.521 y2[1] (analytic) = 1.1326781342869341638535340809147 y2[1] (numeric) = 1.1326781342705129460276311738457 absolute error = 1.64212178259029070690e-11 relative error = 1.4497691205313780838993891625955e-09 % h = 0.001 y1[1] (analytic) = 2.4977477084387296229904276756926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.018322169834526622717139740477 relative error = 0.73354765866162219454385727487693 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.522 y2[1] (analytic) = 1.1331763155733116643410183521593 y2[1] (numeric) = 1.133176315552583851403475116013 absolute error = 2.07278129375432361463e-11 relative error = 1.8291780945894853766377648320273e-09 % h = 0.001 y1[1] (analytic) = 2.4986147812860555718910940133795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0191892426818525716178060781639 relative error = 0.76799524382769103737957814754559 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.523 y2[1] (analytic) = 1.133675363683301356212210568549 y2[1] (numeric) = 1.1336753636574066860019414400897 absolute error = 2.58946702102691284593e-11 relative error = 2.2841345097363297270984737912638e-09 % h = 0.001 y1[1] (analytic) = 2.4994813555186417859665772569024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0200558169144387856932893216868 relative error = 0.80239914053198482291754360789496 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=3.9MB, time=3.06 NO POLE NO POLE x[1] = 0.524 y2[1] (analytic) = 1.134175278117855171064759971788 y2[1] (numeric) = 1.13417527808581030357629375969 absolute error = 3.20448674884662120980e-11 relative error = 2.8253893473717864488146139728092e-09 % h = 0.001 y1[1] (analytic) = 2.5003474302699141048451803058119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0209218916657111045718923705963 relative error = 0.83675938041348809595397817241225 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.525 y2[1] (analytic) = 1.1346760583770587160043865334936 y2[1] (numeric) = 1.1346760583377459753179053157118 absolute error = 3.93127406864812177818e-11 relative error = 3.4646664478591995601679747345454e-09 % h = 0.001 y1[1] (analytic) = 2.5012130046737978494274778151016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.021787466069594849154189879886 relative error = 0.87107599508248669861965431007077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.526 y2[1] (analytic) = 1.135177703960131773559232189945 y2[1] (numeric) = 1.1351777039122873898562589763369 absolute error = 4.78443837029732136081e-11 relative error = 4.2147043177526627557257281746367e-09 % h = 0.001 y1[1] (analytic) = 2.5020780778647186879609231217462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0226525392605156876876351865306 relative error = 0.90534901612052954149162696626603 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.527 y2[1] (analytic) = 1.1356802143654288024600365822581 y2[1] (numeric) = 1.1356802143076306532589472370312 absolute error = 5.77981492010893452269e-11 relative error = 5.0892978912540590312042186574573e-09 % h = 0.001 y1[1] (analytic) = 2.5029426489776035016141078660558 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0235171103734005013408199308402 relative error = 0.9395784750803906261947075261474 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.0MB, time=3.58 NO POLE NO POLE x[1] = 0.528 y2[1] (analytic) = 1.1361835890904394392856365218521 y2[1] (numeric) = 1.1361835890210942890316722205442 absolute error = 6.93451502539643013079e-11 relative error = 6.1033402453451978712143861671488e-09 % h = 0.001 y1[1] (analytic) = 2.5038067171478812495498087336605 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0243811785436782492765207984449 relative error = 0.97376440348603131848593143841097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.529 y2[1] (analytic) = 1.1366878276317890009732875357502 y2[1] (numeric) = 1.1366878275491192381182456769095 absolute error = 8.26697628550418588407e-11 relative error = 7.2728642680443433955661990116202e-09 % h = 0.001 y1[1] (analytic) = 2.504670281511483833495956245149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0252447429072808332226683099334 relative error = 1.0079068328325628708183900876048 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.53 y2[1] (analytic) = 1.1371929294852389881933049814358 y2[1] (numeric) = 1.1371929293872688589005889834444 absolute error = 9.79701292927159979914e-11 relative error = 8.6150842792403829836699138019396e-09 % h = 0.001 y1[1] (analytic) = 2.5055333412048469618136610224661 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0261078026006439615403730872505 relative error = 1.042005794586209193383906368475 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.531 y2[1] (analytic) = 1.1376988941456875895875213566629 y2[1] (numeric) = 1.1376988940302289271987331447503 absolute error = 1.154586623887882119126e-10 relative error = 1.0148437603561843472019507283895e-08 % h = 0.001 y1[1] (analytic) = 2.5063958953649110130614334641129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0269703567607080127881455288973 relative error = 1.0760613201842698726371347848636 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=30.5MB, alloc=4.0MB, time=4.13 x[1] = 0.532 y2[1] (analytic) = 1.138205721107170186871055565808 y2[1] (numeric) = 1.1382057209718076362708187927123 absolute error = 1.353625506002367730957e-10 relative error = 1.1892626094741920866350061657138e-08 % h = 0.001 y1[1] (analytic) = 2.5072579431291218990547332650042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0278324045249188987814453297886 relative error = 1.1100734410350834363067607743614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.533 y2[1] (analytic) = 1.1387134098628598607968890410339 y2[1] (numeric) = 1.1387134097049355968130961864994 absolute error = 1.579242639837928545345e-10 relative error = 1.3868657610944649443247738245995e-08 % h = 0.001 y1[1] (analytic) = 2.5081194836354319274199857215036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.028693945031228927146697786288 relative error = 1.1440421885179908639025603534242 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.534 y2[1] (analytic) = 1.1392219599050678979827427537335 y2[1] (numeric) = 1.1392219597216658369599252125646 absolute error = 1.834020610228175411689e-10 relative error = 1.6098887440521296957581391040888e-08 % h = 0.001 y1[1] (analytic) = 2.508980516022300663642202267693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0295549774180976633689143324774 relative error = 1.1779675939832993417301600923899 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.535 y2[1] (analytic) = 1.1397313707252442985997482894172 y2[1] (numeric) = 1.1397313705131738022837753846447 absolute error = 2.120704963159729047725e-10 relative error = 1.8607059677670034240010904963685e-08 % h = 0.001 y1[1] (analytic) = 2.5098410394286957926053431953273 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0304155008244927923320552601117 relative error = 1.211849688752246261428408871237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.536 y2[1] (analytic) = 1.1402416418139782849224052974161 y2[1] (numeric) = 1.1402416415697573557952258437604 absolute error = 2.442209291271794536557e-10 relative error = 2.1418348547475889585605201294029e-08 % h = 0.001 y1[1] (analytic) = 2.5107010529940939796245610171836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.031275514389890979351273081968 relative error = 1.2456885041169634610473368412739 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.0MB, time=4.65 NO POLE NO POLE x[1] = 0.537 y2[1] (analytic) = 1.1407527726609988107393167654858 y2[1] (numeric) = 1.1407527723808367779429653582163 absolute error = 2.801620327963514072695e-10 relative error = 2.4559399679811960821711452251050e-08 % h = 0.001 y1[1] (analytic) = 2.511560555858481730969463441633 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0321350172542787306961755064174 relative error = 1.2794840713404417076877335311725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.538 y2[1] (analytic) = 1.1412647627551750716241927086173 y2[1] (numeric) = 1.1412647624349547666137923236009 absolute error = 3.202203050104003850164e-10 relative error = 2.8058371331586820623881426203049e-08 % h = 0.001 y1[1] (analytic) = 2.5124195471623562538775354352446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.032994008558153253604247500029 relative error = 1.3132364216564954207264260941613 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.539 y2[1] (analytic) = 1.1417776115845170160666120010952 y2[1] (numeric) = 1.1417776112197764371326147627865 absolute error = 3.647405789339972383087e-10 relative error = 3.1944975556827013347411501295589e-08 % h = 0.001 y1[1] (analytic) = 2.5132780260467263160568603600697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0338524874425233157835724248541 relative error = 1.346945586269727634654380302806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.54 y2[1] (analytic) = 1.1422913186361758574620312210822 y2[1] (numeric) = 1.1422913182220893222624503259293 absolute error = 4.140865351995808951529e-10 relative error = 3.6250519324087504183275863412490e-08 % h = 0.001 y1[1] (analytic) = 2.5141359916531131046772806829582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0347104530489101044039927477426 relative error = 1.3806115963554952005577810653469 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.0MB, time=5.17 NO POLE NO POLE x[1] = 0.541 y2[1] (analytic) = 1.1428058833964445869605285177651 y2[1] (numeric) = 1.1428058829278033722044262904695 absolute error = 4.686412147561022272956e-10 relative error = 4.1007945580686903658269625567168e-08 % h = 0.001 y1[1] (analytic) = 2.514993443123551084849139265818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0355679045193480845758513306024 relative error = 1.414234483059874225275275969045 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.542 y2[1] (analytic) = 1.1433213053507584871737696523608 y2[1] (numeric) = 1.1433213048219509545977795611311 absolute error = 5.288075325759900912297e-10 relative error = 4.6251874263268252206176299731652e-08 % h = 0.001 y1[1] (analytic) = 2.5158503796005888575887427581458 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0364248409963858573154548229302 relative error = 1.4478142774996257472675846581109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.543 y2[1] (analytic) = 1.1438375839836956467396825060591 y2[1] (numeric) = 1.1438375833886868545198566699219 absolute error = 5.950087922198258361372e-10 relative error = 5.2018643254190110568581165927099e-08 % h = 0.001 y1[1] (analytic) = 2.51670680022729001726968912644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0372812616230870169964011912244 relative error = 1.4813510107621616482386887333922 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.544 y2[1] (analytic) = 1.1443547187789774757443254902696 y2[1] (numeric) = 1.1443547181112882744861137761337 absolute error = 6.676892012582117141359e-10 relative error = 5.8346349283256661969756470778293e-08 % h = 0.001 y1[1] (analytic) = 2.5175627041472340085592018692383 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0381371655430310082859139340227 relative error = 1.5148447139055107995508213241878 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.0MB, time=5.70 NO POLE NO POLE x[1] = 0.545 y2[1] (analytic) = 1.1448727092194692220004344373497 y2[1] (numeric) = 1.1448727084721548344501166663422 absolute error = 7.473143875503177710075e-10 relative error = 6.5274888774299491180630107260169e-08 % h = 0.001 y1[1] (analytic) = 2.5184180905045169828386139815162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0389925519003139825653260463006 relative error = 1.548295417958285442478472536587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.546 y2[1] (analytic) = 1.1453915547871804881821316933069 y2[1] (numeric) = 1.1453915539528085718035407544069 absolute error = 8.343719163785909389000e-10 relative error = 7.2845998636127663572328145765780e-08 % h = 0.001 y1[1] (analytic) = 2.5192729584437526541071452480364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0398474198395496538338573128208 relative error = 1.5817031539196478013496166344112 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.547 y2[1] (analytic) = 1.1459112549632657498152802778119 y2[1] (numeric) = 1.1459112540338939413761710814713 absolute error = 9.293718084391091963406e-10 relative error = 8.1103296997366683894528023985370e-08 % h = 0.001 y1[1] (analytic) = 2.5201273071100731543681169619403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0407017685058701540948290267247 relative error = 1.6150679527592769286253490645899 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.548 y2[1] (analytic) = 1.1464318092280248741229651212096 y2[1] (numeric) = 1.1464318081951778154359023159626 absolute error = 1.0328470586870628052470e-09 relative error = 9.0092323884710869629615624089630e-08 % h = 0.001 y1[1] (analytic) = 2.5209811356491298884967486824406 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041555597044926888223460747225 relative error = 1.6483898454173357809720963064167 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.0MB, time=6.23 NO POLE NO POLE x[1] = 0.549 y2[1] (analytic) = 1.1469532170609036397255825330915 y2[1] (numeric) = 1.146953215915549483688738753592 absolute error = 1.1453541560368437794995e-09 relative error = 9.9860581844117627206174715170316e-08 % h = 0.001 y1[1] (analytic) = 2.5218344432070943885886821638876 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.042408904602891388315394228672 relative error = 1.6816688628044385253835290098796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.55 y2[1] (analytic) = 1.1474754779404942571950182023822 y2[1] (numeric) = 1.1474754766730206532787943173546 absolute error = 1.2674736039162238850276e-09 relative error = 1.1045757650447607093970242858435e-07 % h = 0.001 y1[1] (analytic) = 2.5226872289306591677883781077573 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0432616903264561675150901725417 relative error = 1.7149050358016180744122689999509 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.551 y2[1] (analytic) = 1.1479985913445358904623931748063 y2[1] (numeric) = 1.1479985899447254487882925575294 absolute error = 1.3998104416741006172769e-09 relative error = 1.2193485708328637414163453383014e-07 % h = 0.001 y1[1] (analytic) = 2.5235394919670385735965319092362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0441139533628355733232439740206 relative error = 1.7480983952602938495744334681979 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.552 y2[1] (analytic) = 1.1485225567499151790788564000321 y2[1] (numeric) = 1.1485225552069204122375666516792 absolute error = 1.5429947668412897483529e-09 relative error = 1.3434605683389018923731526529230e-07 % h = 0.001 y1[1] (analytic) = 2.5243912314639696406556550910571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0449656928597666403823671558415 relative error = 1.7812489720022397719930050577058 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=49.5MB, alloc=4.0MB, time=6.77 x[1] = 0.553 y2[1] (analytic) = 1.1490473736326667613289015877443 y2[1] (numeric) = 1.1490473719349845030850594046507 absolute error = 1.6976822582438421830936e-09 relative error = 1.4774693343379641879876018897131e-07 % h = 0.001 y1[1] (analytic) = 2.525242446569712943012969639076 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0458169079655099427396817038604 relative error = 1.8143567968195524793489545796575 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.554 y2[1] (analytic) = 1.1495730414679737981956852593716 y2[1] (numeric) = 1.1495730396034190982273232485745 absolute error = 1.8645546999683620107971e-09 relative error = 1.6219540931365056196833440053716e-07 % h = 0.001 y1[1] (analytic) = 2.5260931364330534458597629767672 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0466675978288504455864750415516 relative error = 1.8474219004746197682119737872459 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.555 y2[1] (analytic) = 1.150099559730168498177822030195 y2[1] (numeric) = 1.1500995576858479919990202428652 absolute error = 2.0443205061788017873298e-09 relative error = 1.7775161192639980066629485464989e-07 % h = 0.001 y1[1] (analytic) = 2.5269433002033013567463518393519 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0475177615990983564730639041363 relative error = 1.8804443137000892608255989824759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.556 y2[1] (analytic) = 1.1506269278927326429571323050854 y2[1] (numeric) = 1.150626925655017396172922074221 absolute error = 2.2377152467842102308644e-09 relative error = 1.9447791395620992708049404567576e-07 % h = 0.001 y1[1] (analytic) = 2.5277929370302929762718038326678 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0483673984260899759985158974522 relative error = 1.9134240671988372954244222515677 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.557 y2[1] (analytic) = 1.1511551454282981139168167201663 y2[1] (numeric) = 1.1511551429827959399599100566243 absolute error = 2.4455021739569066635420e-09 relative error = 2.1243897346669414807331658596099e-07 % h = 0.001 y1[1] (analytic) = 2.5286420460643915482475659871291 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0492165074601885479742780519135 relative error = 1.946361191643938039163995822631 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.0MB, time=7.30 NO POLE NO POLE x[1] = 0.558 y2[1] (analytic) = 1.1516842118086474195095308122717 y2[1] (numeric) = 1.1516842091401746700089751313412 absolute error = 2.6684727495005556809305e-09 relative error = 2.3170177398801773315433507323963e-07 % h = 0.001 y1[1] (analytic) = 2.5294906264564881093341501432183 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0500650878522851090608622080027 relative error = 1.9792557176786328227469364228357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.559 y2[1] (analytic) = 1.1522141265047142234748325481675 y2[1] (numeric) = 1.1522141235972670504072178669217 absolute error = 2.9074471730676146812458e-09 relative error = 2.5233566454244640040112937125557e-07 % h = 0.001 y1[1] (analytic) = 2.530338677358002338150025531897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0509131387537993378767375966814 relative error = 2.0121076759162996958316305894297 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.56 y2[1] (analytic) = 1.1527448889865838739054744961337 y2[1] (numeric) = 1.1527448858233089626798484591997 absolute error = 3.1632749112256260369340e-09 relative error = 2.7441239960791025901346767538929e-07 % h = 0.001 y1[1] (analytic) = 2.531186197920883403851869441112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0517606593166804035785815058964 relative error = 2.0449170969404232023128286671607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.561 y2[1] (analytic) = 1.153276498723493933162011573659 y2[1] (numeric) = 1.1532764952866587057901867312931 absolute error = 3.4368352273718248423659e-09 relative error = 2.9800617901915904790373703432270e-07 % h = 0.001 y1[1] (analytic) = 2.5320331872976108141853273882178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0526076486934078139120394530022 relative error = 2.0776840113045643745662947124054 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.0MB, time=7.83 NO POLE NO POLE x[1] = 0.562 y2[1] (analytic) = 1.1538089551838347086351944566842 y2[1] (numeric) = 1.1538089514547969961396621336035 absolute error = 3.7290377124955323230807e-09 relative error = 3.2319368780608832670873468208395e-07 % h = 0.001 y1[1] (analytic) = 2.5328796446411952630054347476258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0534541060369922627321468124102 relative error = 2.1104084495323309457525517291988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.563 y2[1] (analytic) = 1.1543422578351497843556178880455 y2[1] (numeric) = 1.1543422537943269675678137438164 absolute error = 4.0408228167878041442291e-09 relative error = 3.5005413596882018870401421693270e-07 % h = 0.001 y1[1] (analytic) = 2.5337255691051794772658523133289 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0543000305009764769925643781133 relative error = 2.143090442117347779277626592704 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.564 y2[1] (analytic) = 1.1548764061441365534500922755128 y2[1] (numeric) = 1.1548764017709741713522902669013 absolute error = 4.3731623820978020086115e-09 relative error = 3.7866929818912597416316436021516e-07 % h = 0.001 y1[1] (analytic) = 2.5345709598436390634760688071373 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0551454212394360632027808719217 relative error = 2.1757300195232275145115566796189 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.565 y2[1] (analytic) = 1.1554113995766467514442061230971 y2[1] (numeric) = 1.1554113948495865762088500351116 absolute error = 4.7270601752353560879855e-09 relative error = 4.0912355347778236758271489018801e-07 % h = 0.001 y1[1] (analytic) = 2.5354158160111833536257238754924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0559902774069803533524359402768 relative error = 2.2083272121835414278682706306582 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.0MB, time=8.35 NO POLE NO POLE x[1] = 0.566 y2[1] (analytic) = 1.1559472375976869904105459931083 y2[1] (numeric) = 1.1559472324941345682913610079844 absolute error = 5.1035524221191849851239e-09 relative error = 4.4150392475745616274150225663225e-07 % h = 0.001 y1[1] (analytic) = 2.5362601367629562505752056506075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0568345981587532503019177153919 relative error = 2.2408820505017905083532988261491 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.567 y2[1] (analytic) = 1.1564839196714192939620398507875 y2[1] (numeric) = 1.1564839141677109511918007723409 absolute error = 5.5037083427702390784466e-09 relative error = 4.7590011838071687563606138794095e-07 % h = 0.001 y1[1] (analytic) = 2.5371039212546370729116774854067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0576783826504340726383895501911 relative error = 2.2733945648513767466886050699314 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.568 y2[1] (analytic) = 1.157021445261161633089888798216 y2[1] (numeric) = 1.157021439332530945940256542286 absolute error = 5.9286306871496322559300e-09 relative error = 5.1240456358278027678649408422451e-07 % h = 0.001 y1[1] (analytic) = 2.5379471686424413992696890063077 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0585216300382383989964010710921 relative error = 2.3058647855755746371266596580326 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.569 y2[1] (analytic) = 1.1575598138293884628455513596132 y2[1] (numeric) = 1.1575598074499321910049251592086 absolute error = 6.3794562718406262004046e-09 relative error = 5.5111245186858980109577058700382e-07 % h = 0.001 y1[1] (analytic) = 2.5387898780831219121155271633056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.05936433947891891184223922809 relative error = 2.3382927429875028910686954649239 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.0MB, time=8.87 NO POLE NO POLE x[1] = 0.57 y2[1] (analytic) = 1.158099024837731259866243636084 y2[1] (numeric) = 1.1580990179803747422921130917814 absolute error = 6.8573565175741305443026e-09 relative error = 5.9212177633384667522858433901231e-07 % h = 0.001 y1[1] (analytic) = 2.5396320487339692409944634930788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0602065101297662407211755578632 relative error = 2.3706784673700963616049029207394 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.571 y2[1] (analytic) = 1.158639077746979060743417804361 y2[1] (numeric) = 1.1586390703834410731462364359611 absolute error = 7.3635379875971813683999e-09 relative error = 6.3553337091960347921129750944765e-07 % h = 0.001 y1[1] (analytic) = 2.540473679752812805240054347939 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0610481411486098049667664127234 relative error = 2.4030219889760781780971267856779 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.572 y2[1] (analytic) = 1.1591799720170790012336805911064 y2[1] (numeric) = 1.1591799641178360743498209149881 absolute error = 7.8992429268838596761183e-09 relative error = 6.8145094960003973050262303111130e-07 % h = 0.001 y1[1] (analytic) = 2.5413147702980216561446513813949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0618892316938186558713634461793 relative error = 2.4353233380279320899274274619847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.573 y2[1] (analytic) = 1.1597217071071368563116125119018 y2[1] (numeric) = 1.1597216986413870541235018793869 absolute error = 8.4657498021881106325149e-09 relative error = 7.2998114550304194500650515907324e-07 % h = 0.001 y1[1] (analytic) = 2.5421553195285053185902801198912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0627297809243023183169921846756 relative error = 2.467582544717875018538662228083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=68.6MB, alloc=4.0MB, time=9.40 x[1] = 0.574 y2[1] (analytic) = 1.1602642824754175810639478221502 y2[1] (numeric) = 1.1602642734110437381260243069658 absolute error = 9.0643738429379235151844e-09 relative error = 7.8123354996321449025604646161770e-07 % h = 0.001 y1[1] (analytic) = 2.5429953266037146321390449899122 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0635697879995116318657570546966 relative error = 2.4997996392078298168960272420956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.575 y2[1] (analytic) = 1.1608076975793458524245742857562 y2[1] (numeric) = 1.1608076878828782694542428028169 absolute error = 9.6964675829703314829393e-09 relative error = 8.3532075150695140115374273326135e-07 % h = 0.001 y1[1] (analytic) = 2.5438347906836425915822197101162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0644092520794395913089317749006 relative error = 2.5319746516293982355012794525378 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.576 y2[1] (analytic) = 1.1613519518755066117498110266296 y2[1] (numeric) = 1.1613519415120852086431215993162 absolute error = 1.03634214031066894273134e-08 relative error = 8.9235837476920317807309290798064e-07 % h = 0.001 y1[1] (analytic) = 2.5446737109288251869471824994803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0652481723246221866738945642647 relative error = 2.5641076120838340940941286808358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.577 y2[1] (analytic) = 1.1618970448196456082334218877795 y2[1] (numeric) = 1.1618970337529815336657345561237 absolute error = 1.10666640745676873316558e-08 relative error = 9.5246511934157643067532825274992e-07 % h = 0.001 y1[1] (analytic) = 2.5455120865003422429613560945909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0660865478961392426880681593753 relative error = 2.5961985506420166581780541127425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.578 y2[1] (analytic) = 1.162442975866669943160820883031 y2[1] (numeric) = 1.1624429640590066399332651601833 absolute error = 1.18076633032275557228477e-08 relative error = 1.0157627985514080683393048305269e-06 % h = 0.001 y1[1] (analytic) = 2.546349916559818257972313112208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0669243779556152576990251769924 relative error = 2.628247497344424219510556262531 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.0MB, time=9.93 NO POLE NO POLE x[1] = 0.579 y2[1] (analytic) = 1.1629897444706486150019254872046 y2[1] (numeric) = 1.1629897318827223402950065257226 absolute error = 1.25879262747069189614820e-08 relative error = 1.0823763781714595695101866858895e-06 % h = 0.001 y1[1] (analytic) = 2.5471872002694232423232078370701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0677616616652202420499199018545 relative error = 2.6602544822011078797006051644972 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.58 y2[1] (analytic) = 1.16353735008481306534211267195 y2[1] (numeric) = 1.1635373366758128650383613942532 absolute error = 1.34090002003037512776968e-08 relative error = 1.1524340150598806874123405494702e-06 % h = 0.001 y1[1] (analytic) = 2.5480239367918735561826960595765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0685983981876705559094081243609 relative error = 2.6922195351916655360587881093964 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.581 y2[1] (analytic) = 1.1640857921615577256507317563242 y2[1] (numeric) = 1.1640857778890848618888421345706 absolute error = 1.42724728637618896217536e-08 relative error = 1.2260670957300957683143062698452e-06 % h = 0.001 y1[1] (analytic) = 2.548860125290432746828505133497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0694345866862297465552171982814 relative error = 2.724142686265216068848395688654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.582 y2[1] (analytic) = 1.1646350701524405648866273036464 y2[1] (numeric) = 1.1646350549724673960100707427541 absolute error = 1.51799731688765565608923e-08 relative error = 1.3034102748502696707493281464582e-06 % h = 0.001 y1[1] (analytic) = 2.5496957649289123853838169702094 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0702702263247093851105290349938 relative error = 2.7560239653403737290884132455654 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.0MB, time=10.45 NO POLE NO POLE x[1] = 0.583 y2[1] (analytic) = 1.165185183508183637940124459152 y2[1] (numeric) = 1.1651851673750119500037788421669 absolute error = 1.61331716879363456169851e-08 relative error = 1.3846015136720140796566093225912e-06 % h = 0.001 y1[1] (analytic) = 2.5505308548716729030056272331506 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.071105316267469902732339297935 relative error = 2.7878634023052227260621060694901 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.584 y2[1] (analytic) = 1.1657361316786736349109282865074 y2[1] (numeric) = 1.1657361145448924239098076834562 absolute error = 1.71337812110011206030512e-08 relative error = 1.4697821183879988081896832965331e-06 % h = 0.001 y1[1] (analytic) = 2.5513653942836244265242445441924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0719398556794214262509566089768 relative error = 2.8196610270172920136876008158076 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.585 y2[1] (analytic) = 1.1662879141129624312213878253303 y2[1] (numeric) = 1.166287895929405135206108144553 absolute error = 1.81835572960152796807773e-08 relative error = 1.5590967784181364718130688992125e-06 % h = 0.001 y1[1] (analytic) = 2.5521993823302276135330940625129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0727738437260246132598061272973 relative error = 2.8514168693035302749095727003818 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.586 y2[1] (analytic) = 1.1668405302592676385645747564984 y2[1] (numeric) = 1.1668405109749688188087407306722 absolute error = 1.92842988197558340258262e-08 relative error = 1.6526936046240127041533064151578e-06 % h = 0.001 y1[1] (analytic) = 2.553032818177494486927990346228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0736072795732914866547024110124 relative error = 2.8831309589602811032738480119188 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.0MB, time=10.98 NO POLE NO POLE x[1] = 0.587 y2[1] (analytic) = 1.1673939795649731566866257272142 y2[1] (numeric) = 1.1673939591271246270718755743125 absolute error = 2.04378485296147501529017e-08 relative error = 1.7507241674512378617619025894479e-06 % h = 0.001 y1[1] (analytic) = 2.5538657009919892688950449575815 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0744401623877862686217570223659 relative error = 2.9148033257532583808494244187152 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.588 y2[1] (analytic) = 1.1679482614766297260027965535271 y2[1] (numeric) = 1.1679482398305361297877924352566 absolute error = 2.16460935962150041182705e-08 relative error = 1.8533435349993999353634309869858e-06 % h = 0.001 y1[1] (analytic) = 2.5546980299408292143463748238537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0752724913366262140730868886381 relative error = 2.9464339994175218516650974269552 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.589 y2[1] (analytic) = 1.1685033754399554810466756843086 y2[1] (numeric) = 1.168503352528989314186880700571 absolute error = 2.29109661668597949837376e-08 relative error = 1.9607103110193021481825722819279e-06 % h = 0.001 y1[1] (analytic) = 2.5555298041916854438027779183523 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0761042655874824435294899831367 relative error = 2.9780230096574528898305601861543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.59 y2[1] (analytic) = 1.1690593208998365047520034775093 y2[1] (numeric) = 1.1690592966653925849376393846061 absolute error = 2.42344439198143640929032e-08 relative error = 2.0729866728371724774471100147809e-06 % h = 0.001 y1[1] (analytic) = 2.5563610229127837757225433788758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0769354843085807754492554436602 relative error = 3.0095703861467304615145156424937 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.0MB, time=11.51 NO POLE NO POLE x[1] = 0.591 y2[1] (analytic) = 1.1696160973003273835665430069271 y2[1] (numeric) = 1.1696160716817767641466771289963 absolute error = 2.56185506194198658779308e-08 relative error = 2.1903384092055360830341558906666e-06 % h = 0.001 y1[1] (analytic) = 2.5571916852729055582755637349123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0777661466687025580022757996967 relative error = 3.0410761585283072799550048232859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.592 y2[1] (analytic) = 1.1701737040846517633974472856612 y2[1] (numeric) = 1.1701736770192950913587122026597 absolute error = 2.70653566720387350830015e-08 relative error = 2.3129349580804453673444019579756e-06 % h = 0.001 y1[1] (analytic) = 2.5580217904413885005619174695279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0785962518371855002886295343123 relative error = 3.0725403564143861526798128044012 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.593 y2[1] (analytic) = 1.1707321406952029063875669609314 y2[1] (numeric) = 1.1707321121182232235565725017985 absolute error = 2.85769796828309944591329e-08 relative error = 2.4409494443247661227388837431058e-06 % h = 0.001 y1[1] (analytic) = 2.5588513375881275032740906974331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0794257989839245030008027622175 relative error = 3.103963009386396520117464677924 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.594 y2[1] (analytic) = 1.1712914065735442485221417040005 y2[1] (numeric) = 1.1712913764179592351611955498985 absolute error = 3.01555850133609461541020e-08 relative error = 2.5745587173372219471393389530249e-06 % h = 0.001 y1[1] (analytic) = 2.559680325883575488802007297074 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0802547872793724885287193618584 relative error = 3.1353441469949711847819676087763 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=87.7MB, alloc=4.0MB, time=12.03 x[1] = 0.595 y2[1] (analytic) = 1.1718515011604099580653176885558 y2[1] (numeric) = 1.1718514693570236180316284977296 absolute error = 3.18033863400336891908262e-08 relative error = 2.7139433886069028245623593994840e-06 % h = 0.001 y1[1] (analytic) = 2.5605087544987442307800373917875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0810832158945412305067494565719 relative error = 3.1666837987599232302170918568458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.596 y2[1] (analytic) = 1.172412423895705494825932721079 y2[1] (numeric) = 1.1724123903730592814650281233456 absolute error = 3.35226462133609045977334e-08 relative error = 2.8592878691929474753169552436195e-06 % h = 0.001 y1[1] (analytic) = 2.5613366226052051830751546330814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0819110840010021828018666978658 relative error = 3.1979819941702231288886134550952 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.597 y2[1] (analytic) = 1.1729741742185081702520097574644 y2[1] (numeric) = 1.172974138902831552196660832084 absolute error = 3.53156766180553489253804e-08 relative error = 3.0107804071291127802321558807728e-06 % h = 0.001 y1[1] (analytic) = 2.5621639293750903082154132979511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0827383907708873079421253627355 relative error = 3.2292387626839760382155640842174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.598 y2[1] (analytic) = 1.1735367515670677083533987114403 y2[1] (numeric) = 1.1735367143822281743999026565663 absolute error = 3.71848395339534960548740e-08 relative error = 3.1686131247529472744865442458321e-06 % h = 0.001 y1[1] (analytic) = 2.5629906739810929052579167718239 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0835651353768899049846288366083 relative error = 3.2604541337283992839341495806934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.599 y2[1] (analytic) = 1.1741001553788068074520056321979 y2[1] (numeric) = 1.1741001162462593096862392566979 absolute error = 3.91325474977657663755000e-08 relative error = 3.3329820559592893892746650758697e-06 % h = 0.001 y1[1] (analytic) = 2.5638168555964684370954495492333 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0843913169922654368221616140177 relative error = 3.2916281366998000299906074678557 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.0MB, time=12.58 NO POLE NO POLE x[1] = 0.6 y2[1] (analytic) = 1.1746643850903217027590475010446 y2[1] (numeric) = 1.1746643439290575371052659196681 absolute error = 4.11612641656537815813765e-08 relative error = 3.5040871833778147935580859879562e-06 % h = 0.001 y1[1] (analytic) = 2.5646424733950353572009454456587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0852169347908323569276575104431 relative error = 3.3227608009635531341618759185234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.601 y2[1] (analytic) = 1.1752294401373827297787700698751 y2[1] (numeric) = 1.17522939686387785314468755995 absolute error = 4.32735048766340825099251e-08 relative error = 3.6821324754743608534047463712396e-06 % h = 0.001 y1[1] (analytic) = 2.5654675265511759358089652761314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0860419879469729355356773409158 relative error = 3.3538521558540791886055416535691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.602 y2[1] (analytic) = 1.1757953199549348885380653377883 y2[1] (numeric) = 1.1757952744830976717303187193006 absolute error = 4.54718372168077466184877e-08 relative error = 3.8673259235757598828122066604227e-06 % h = 0.001 y1[1] (analytic) = 2.5662920142398370855333578191989 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0868664756356340852600698839833 relative error = 3.3849022306748227445431224633943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.603 y2[1] (analytic) = 1.1763620239770984086414244362806 y2[1] (numeric) = 1.1763619762182168242260835667609 absolute error = 4.77588815844153408695197e-08 relative error = 4.0598795788179165073345514560156e-06 % h = 0.001 y1[1] (analytic) = 2.5671159356365311864202784486542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0876903970323281861469905134386 relative error = 3.4159110546982307202833213189365 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.0MB, time=13.10 NO POLE NO POLE x[1] = 0.604 y2[1] (analytic) = 1.1769295516371693151506608681084 y2[1] (numeric) = 1.1769295014998575594340158986556 absolute error = 5.01373117557166449694528e-08 relative error = 4.2600095890168681001843192620531e-06 % h = 0.001 y1[1] (analytic) = 2.5679392899173369104357403800814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0885137513131339101624524448658 relative error = 3.4468786571657309917944634260815 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.605 y2[1] (analytic) = 1.177497902367619995288838220145 y2[1] (numeric) = 1.1774978497577645435942591385934 absolute error = 5.26098554516945790815516e-08 relative error = 4.4679362354625708796579920535269e-06 % h = 0.001 y1[1] (analytic) = 2.5687620762589000453868740447335 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0893365376546970451135861095179 relative error = 3.4778050672877111650378950822063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.606 y2[1] (analytic) = 1.1780670756000997659678356463513 y2[1] (numeric) = 1.1780670204208048603850663374669 absolute error = 5.51792949055827693088844e-08 relative error = 4.6838839696351578766343883715683e-06 % h = 0.001 y1[1] (analytic) = 2.569584293838434318276070669554 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0901587552342313180027827343384 relative error = 3.5086903142434975292766838268634 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.607 y2[1] (analytic) = 1.1786370707654354421389835933405 y2[1] (numeric) = 1.1786370129169680109228001734525 absolute error = 5.78484674312161834198880e-08 relative error = 4.9080814498434185914191204450909e-06 % h = 0.001 y1[1] (analytic) = 2.5704059418337222180871867092646 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.090980403229519217813898774049 relative error = 3.5395344271813341905765131501844 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.0MB, time=13.65 NO POLE NO POLE x[1] = 0.608 y2[1] (analytic) = 1.1792078872936319059662014179512 y2[1] (numeric) = 1.1792078266733659137619329520105 absolute error = 6.06202659922042684659407e-08 relative error = 5.1407615777852537602567520239646e-06 % h = 0.001 y1[1] (analytic) = 2.5712270194231158180029863443854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0918014808189128177296984091698 relative error = 3.5703374352183623847182119436167 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.609 y2[1] (analytic) = 1.1797795246138726768210677237362 y2[1] (numeric) = 1.1797794611162329048950466058852 absolute error = 6.34976397719260211178510e-08 relative error = 5.3821615350298622433058361881207e-06 % h = 0.001 y1[1] (analytic) = 2.5720475257855375970529998278124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0926219871813345967797118925968 relative error = 3.6010993674405999687438989579265 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.61 y2[1] (analytic) = 1.1803519821545204820992534213452 y2[1] (numeric) = 1.1803519156709257377528326951047 absolute error = 6.64835947443464207262405e-08 relative error = 5.6325228194214206276751149326696e-06 % h = 0.001 y1[1] (analytic) = 2.5728674601004812611909760321627 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0934419214962782609176880969471 relative error = 3.6318202529029210903612557840579 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.611 y2[1] (analytic) = 1.1809252593431178288577466964165 y2[1] (numeric) = 1.1809251897619235832040924069809 absolute error = 6.95811942456536542894356e-08 relative error = 5.8920912814040197111547718488005e-06 % h = 0.001 y1[1] (analytic) = 2.5736868215480125638011081205036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.094261282943809563527820185288 relative error = 3.6625001206290360344329683037879 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.0MB, time=14.17 NO POLE NO POLE x[1] = 0.612 y2[1] (analytic) = 1.1814993556063875762722982477992 y2[1] (numeric) = 1.1814992828128280295557365561097 absolute error = 7.27935595467165616916895e-08 relative error = 6.1611171602676255944503664983205e-06 % h = 0.001 y1[1] (analytic) = 2.5745056093087701256322118343075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0950800707045671253589238990919 relative error = 3.6931389996114712457808961797835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.613 y2[1] (analytic) = 1.1820742703702335089145143387088 y2[1] (numeric) = 1.1820741942463630825527855843708 absolute error = 7.61238704263617287543380e-08 relative error = 6.4398551203148366619455612644929e-06 % h = 0.001 y1[1] (analytic) = 2.5753238225639662541590364645238 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0958982839597632538857485293082 relative error = 3.7237369188115495275370427794905 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.614 y2[1] (analytic) = 1.1826500030597409108480243837716 y2[1] (numeric) = 1.1826499234843751653783695609279 absolute error = 7.95753657454696548228437e-08 relative error = 6.7285642869482112731898383570718e-06 % h = 0.001 y1[1] (analytic) = 2.576141460495387762369889144524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0967159218911847620966012093084 relative error = 3.7542939071593704142759039646728 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.615 y2[1] (analytic) = 1.1832265530991771405431489758368 y2[1] (numeric) = 1.1832264699478331186537281822285 absolute error = 8.31513440218894207936083e-08 relative error = 7.0275082826779445193379935880058e-06 % h = 0.001 y1[1] (analytic) = 2.5769585222853967869797536773647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0975329836811937867064657421491 relative error = 3.7848099935537907191652734394429 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=106.8MB, alloc=4.0MB, time=14.70 x[1] = 0.616 y2[1] (analytic) = 1.1838039199119922066094934379379 y2[1] (numeric) = 1.1838038330568282004382107720039 absolute error = 8.68551640061712826659340e-08 relative error = 7.3369552630496759205690631628517e-06 % h = 0.001 y1[1] (analytic) = 2.5777750071169316060680856843173 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0983494685127286057947977491017 relative error = 3.8152852068624052543750748447606 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.617 y2[1] (analytic) = 1.1843821029208193443458911678558 y2[1] (numeric) = 1.1843820122305740862292762812695 absolute error = 9.06902452581166148865863e-08 relative error = 7.6571779524922134519936680194446e-06 % h = 0.001 y1[1] (analytic) = 2.5785909141735074561404664369381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0991653755693044558671785017225 relative error = 3.8457195759215277239862765276675 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.618 y2[1] (analytic) = 1.1849611015474755931071202253905 y2[1] (numeric) = 1.1849610068874068689624932883244 absolute error = 9.46600687241446269370661e-08 relative error = 7.9884536800849627866335654078763e-06 % h = 0.001 y1[1] (analytic) = 2.579406242639217348613298311092 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0999807040350143483400103758764 relative error = 3.8761131295361717886444239095876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.619 y2[1] (analytic) = 1.1855409152129623744868157956707 y2[1] (numeric) = 1.1855408164447850590115399987517 absolute error = 9.87681773154752757969190e-08 relative error = 8.3310644152448541346367116482967e-06 % h = 0.001 y1[1] (analytic) = 2.5802209916987328857207253783037 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1007954530945298854474374430881 relative error = 3.9064658964800323012047966410118 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.62 y2[1] (analytic) = 1.1861215433374660713160003456393 y2[1] (numeric) = 1.1861214403192895841882042454183 absolute error = 1.030181764871277961002210e-07 relative error = 8.6852968033325625378916531677419e-06 % h = 0.001 y1[1] (analytic) = 2.5810351605373050758429632275822 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1016096219331020755696752923666 relative error = 3.9367779054954667126186632703545 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.0MB, time=15.23 NO POLE NO POLE x[1] = 0.621 y2[1] (analytic) = 1.1867029853403586074766524752305 y2[1] (numeric) = 1.1867028779266237897423834884751 absolute error = 1.074137348177342689867554e-07 relative error = 9.0514422011778209485394112942781e-06 % h = 0.001 y1[1] (analytic) = 2.581848748340765148255222689459 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1024232097365621479819347542434 relative error = 3.9670491852934766473125649841116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.622 y2[1] (analytic) = 1.1872852406401980285297346497202 y2[1] (numeric) = 1.1872851286816134383620848153567 absolute error = 1.119585845901676498343635e-07 relative error = 9.4297967125236288784677806911502e-06 % h = 0.001 y1[1] (analytic) = 2.5826617542955253672964127133811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1032362156913223670231247781655 relative error = 3.9972797645536896473150121040467 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.623 y2[1] (analytic) = 1.1878683086547290831570991852689 y2[1] (numeric) = 1.1878681919982067101734249407817 absolute error = 1.166565223729836742444872e-07 relative error = 9.8206612233891628546273644460728e-06 % h = 0.001 y1[1] (analytic) = 2.583474177588579845956808229827 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1040486389843768456835202946114 relative error = 4.0274696719243410843874224667694 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.624 y2[1] (analytic) = 1.1884521888008838054166910457999 y2[1] (numeric) = 1.1884520672894742027406302067526 absolute error = 1.215114096026760608390473e-07 relative error = 1.0224341437351198351851022564245e-05 % h = 0.001 y1[1] (analytic) = 2.584286017407505358883869409543 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1048604788033023586105814743274 relative error = 4.0576189360222562394185695718972 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.0MB, time=15.76 NO POLE NO POLE x[1] = 0.625 y2[1] (analytic) = 1.1890368804947820978104651960589 y2[1] (numeric) = 1.1890367539676089310660365825557 absolute error = 1.265271731667444286135032e-07 relative error = 1.0641147910743856300707027625499e-05 % h = 0.001 y1[1] (analytic) = 2.5850972729404621548053993141501 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1056717343362591545321113789345 relative error = 4.0877275854328325483442404789218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.626 y2[1] (analytic) = 1.189622383151732315164435442986 y2[1] (numeric) = 1.1896222514439263275900896647613 absolute error = 1.317078059875743457782247e-07 relative error = 1.1071396087776490682692265673327e-05 % h = 0.001 y1[1] (analytic) = 2.5859079433761947683692275150305 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1064824047719917680959395798149 relative error = 4.1177956487100220138562288703778 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.627 y2[1] (analytic) = 1.1902086961862318493202708853993 y2[1] (numeric) = 1.1902085591288642421913446772234 absolute error = 1.370573676071289262081759e-07 relative error = 1.1515406335569537128697059401777e-05 % h = 0.001 y1[1] (analytic) = 2.5867180279040328313986078408783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1072924892998298311253199056627 relative error = 4.1478231543763137821672074915037 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.628 y2[1] (analytic) = 1.1907958190119677146378552804441 y2[1] (numeric) = 1.1907956764319829421864664710801 absolute error = 1.425799847724513888093640e-07 relative error = 1.1973503979108145829070305962466e-05 % h = 0.001 y1[1] (analytic) = 2.5875275257138918835625189985835 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1081019871096888832892310633679 relative error = 4.1778101309227168841004363351864 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.0MB, time=16.29 NO POLE NO POLE x[1] = 0.629 y2[1] (analytic) = 1.1913837510418171343082238242947 y2[1] (numeric) = 1.1913836027619651123302295247533 absolute error = 1.482798520219779942995414e-07 relative error = 1.2446019336113425444706383419491e-05 % h = 0.001 y1[1] (analytic) = 2.5883364359962741824600573972178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1089108973920711821867694620022 relative error = 4.2077566068087431397756684770144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.63 y2[1] (analytic) = 1.1919724916878481274762910342229 y2[1] (numeric) = 1.1919723375266158548155179439487 absolute error = 1.541612322726607730902742e-07 relative error = 1.2933287751831128078289122808145e-05 % h = 0.001 y1[1] (analytic) = 2.5891447579422695131181120907946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.109719219338066512844824155579 relative error = 4.2376626104623902261650143896036 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.631 y2[1] (analytic) = 1.1925620403613200971727826093538 y2[1] (numeric) = 1.192561880132862689273325461656 absolute error = 1.602284574078994571476978e-07 relative error = 1.3435649633737608723088524720731e-05 % h = 0.001 y1[1] (analytic) = 2.5899524907435559969015123421982 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1105269521393529966282244069826 relative error = 4.2675281702801249067949178897863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.632 y2[1] (analytic) = 1.1931523964726844190547833382246 y2[1] (numeric) = 1.1931522299867555527727554381488 absolute error = 1.664859288662820279000758e-07 relative error = 1.3953450486162895953440290782023e-05 % h = 0.001 y1[1] (analytic) = 2.5907596335924008998348388981996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.111334094988197899561550962984 relative error = 4.2973533146268664228727826073781 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.0MB, time=16.82 NO POLE NO POLE x[1] = 0.633 y2[1] (analytic) = 1.1937435594315850309543123126502 y2[1] (numeric) = 1.1937433864934667998210208609844 absolute error = 1.729381182311332914516658e-07 relative error = 1.4487040944830713956175093737015e-05 % h = 0.001 y1[1] (analytic) = 2.5915661856816614403350906538176 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.112140647077458440061802718602 relative error = 4.3271380718359700451191670220827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.634 y2[1] (analytic) = 1.1943355286468590232343358993664 y2[1] (numeric) = 1.1943353490572912023634443450042 absolute error = 1.795895678208708915543622e-07 relative error = 1.5036776811315299325731934113203e-05 % h = 0.001 y1[1] (analytic) = 2.592372146204785596354398973423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1129466076005825960811110382074 relative error = 4.3568824702092107855888387062452 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.635 y2[1] (analytic) = 1.1949283035265372299516281134903 y2[1] (numeric) = 1.1949281170816459497834581323333 absolute error = 1.864448912801681699811570e-07 relative error = 1.5603019087414859357420291652100e-05 % h = 0.001 y1[1] (analytic) = 2.5931775143558129119319825259412 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1137519757516099116586945907256 relative error = 4.3865865380167672687663444477524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.636 y2[1] (analytic) = 1.1955218834778448208258872309833 y2[1] (numeric) = 1.1955216899690706489026040923809 absolute error = 1.935087741719232831386024e-07 relative error = 1.6186134009441521873217653417544e-05 % h = 0.001 y1[1] (analytic) = 2.5939822893293753031545360822647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1145567507251723028812481470491 relative error = 4.416250303497205761224112420087 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=125.8MB, alloc=4.0MB, time=17.35 x[1] = 0.637 y2[1] (analytic) = 1.1961162679072018940145166710524 y2[1] (numeric) = 1.1961160671212273239805337218398 absolute error = 2.007859745700339829492126e-07 relative error = 1.6786493082427629902538004724156e-05 % h = 0.001 y1[1] (analytic) = 2.5947864703206978635242473145531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1153609317164948632509593793375 relative error = 4.4458737948574643591334555272216 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.638 y2[1] (analytic) = 1.1967114562202240696924773737563 y2[1] (numeric) = 1.1967112479389004167150081446869 absolute error = 2.082813236529774692290694e-07 relative error = 1.7404473114248237816513296049036e-05 % h = 0.001 y1[1] (analytic) = 2.5955900565255996687336362294726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.116164517921396668460348294257 relative error = 4.4754570402728373329211914910751 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.639 y2[1] (analytic) = 1.1973074478217230844366180930148 y2[1] (numeric) = 1.197307231821996786241898112183 absolute error = 2.159997262981947199808318e-07 relative error = 1.8040456249659668778431120387181e-05 % h = 0.001 y1[1] (analytic) = 2.5963930471404945808464124606007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1169675085362915805731245253851 relative error = 4.505000067886959628366935179818 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.64 y2[1] (analytic) = 1.1979042421157073864138892207397 y2[1] (numeric) = 1.1979040181695457091351840028726 absolute error = 2.239461616772787052178671e-07 relative error = 1.8694830004253996625001118034397e-05 % h = 0.001 y1[1] (analytic) = 2.5971954413623920518835462392079 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1177699027581890516102583039923 relative error = 4.5345029058117915234384521083715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.641 y2[1] (analytic) = 1.198501838505382731372844953923 y2[1] (numeric) = 1.1985016063796988794069558225843 absolute error = 2.321256838519658891313387e-07 relative error = 1.9367987298329318533018078634426e-05 % h = 0.001 y1[1] (analytic) = 2.5979972383888979268137494574101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1185716997846949265404615221945 relative error = 4.5639655821276034401647889889422 % h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.0MB, time=17.88 NO POLE NO POLE x[1] = 0.642 y2[1] (analytic) = 1.1991002363931527794378378132311 y2[1] (numeric) = 1.1990999958497304085074132044304 absolute error = 2.405434223709304246088007e-07 relative error = 2.0060326490675688053688646067930e-05 % h = 0.001 y1[1] (analytic) = 2.5987984374182152459475638332798 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1193728988140122456742758980642 relative error = 4.5933881248829609108492176815203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.643 y2[1] (analytic) = 1.1996994351806196927053087189588 y2[1] (numeric) = 1.1996991859760368253248654088071 absolute error = 2.492045828673804433101517e-07 relative error = 2.0772251412276581312328749101287e-05 % h = 0.001 y1[1] (analytic) = 2.599599037649145046734253783893 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1201734990449420464609658486774 relative error = 4.6227705620947096979263429028712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.644 y2[1] (analytic) = 1.2002994342685847336415750281037 y2[1] (numeric) = 1.2002991761541370761857313233947 absolute error = 2.581144476574558437047090e-07 relative error = 2.1504171399925772374261621818599e-05 % h = 0.001 y1[1] (analytic) = 2.6003990382810871649607022094871 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1209734996768841646874142742715 relative error = 4.6521129217479610667700316098188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.645 y2[1] (analytic) = 1.2009002330570488642815181348221 y2[1] (numeric) = 1.2008999657786725248545394631571 absolute error = 2.672783763394269786716650e-07 relative error = 2.2256501329759496968490989178380e-05 % h = 0.001 y1[1] (analytic) = 2.6011984385140410353515079898995 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1217728999098380350782200546839 relative error = 4.681415231796077210761123089686 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.0MB, time=18.43 NO POLE NO POLE x[1] = 0.646 y2[1] (analytic) = 1.2015018309452133462275714356296 y2[1] (numeric) = 1.2015015542434069525339279703422 absolute error = 2.767018063936936434652874e-07 relative error = 2.3029661650703786939032991009736e-05 % h = 0.001 y1[1] (analytic) = 2.6019972375486064915694845932574 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1225716989444034912961966580418 relative error = 4.7106775201606568279261734796457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.647 y2[1] (analytic) = 1.2021042273314803414484086604078 y2[1] (numeric) = 1.2021039409412265578646446144819 absolute error = 2.863902537835837640459259e-07 relative error = 2.3824078417836860959606594709984e-05 % h = 0.001 y1[1] (analytic) = 2.6027954345859845656157597964862 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1233698959817815653424718612706 relative error = 4.7398998147315208484607767087401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.648 y2[1] (analytic) = 1.2027074216134535138767317705792 y2[1] (numeric) = 1.2027071252641399569255467923918 absolute error = 2.963493135569511849781874e-07 relative error = 2.4640183325666460200649078200981e-05 % h = 0.001 y1[1] (analytic) = 2.6035930288279782866286771176028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1241674902237752863553891823872 relative error = 4.769082143366698312453285723345 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.649 y2[1] (analytic) = 1.203311413187938631805556826712 y2[1] (numeric) = 1.2033111066032781832336015281715 absolute error = 3.065846604485719552985405e-07 relative error = 2.5478413741322020778285505351274e-05 % h = 0.001 y1[1] (analytic) = 2.6043900194769934790807001609604 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1249644808727904788074122257448 relative error = 4.7982245338924123971270333305875 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.0MB, time=18.95 NO POLE NO POLE x[1] = 0.65 y2[1] (analytic) = 1.2039162014509441710823954293201 y2[1] (numeric) = 1.2039158843488946877438854732044 absolute error = 3.171020494833385099561157e-07 relative error = 2.6339212737661577942885327543259e-05 % h = 0.001 y1[1] (analytic) = 2.6051864057360395603725216786059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1257608671318365600992337433903 relative error = 4.8273270141030665929214210861246 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.651 y2[1] (analytic) = 1.2045217857976819191007285387257 y2[1] (numeric) = 1.2045214578903653388495849061578 absolute error = 3.279073165802511436325679e-07 relative error = 2.7223029126293300080131071346011e-05 % h = 0.001 y1[1] (analytic) = 2.6059821868087303378235797537072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1265566482045273375502918184916 relative error = 4.8563896117612310277345073747963 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.652 y2[1] (analytic) = 1.2051281656225675795881686825627 y2[1] (numeric) = 1.205127826616188422381995732983 absolute error = 3.390063791572061729495797e-07 relative error = 2.8130317490511553700052695028470e-05 % h = 0.001 y1[1] (analytic) = 2.6067773618992848050581841156014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1273518232950818047848961803858 relative error = 4.8854123545976289386519821965807 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.653 y2[1] (analytic) = 1.2057353403192213781907057628076 y2[1] (numeric) = 1.205734989913984641610523486915 absolute error = 3.504052367365801822758926e-07 relative error = 2.9061538218147403679194124289458e-05 % h = 0.001 y1[1] (analytic) = 2.6075719302125279377864562004034 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1281463916083249375131682651878 relative error = 4.9143952703111232904896661877052 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=141.1MB, alloc=4.0MB, time=19.49 x[1] = 0.654 y2[1] (analytic) = 1.2063433092804686688524308781435 y2[1] (numeric) = 1.2063429471704971172426833284729 absolute error = 3.621099715516097475496706e-07 relative error = 3.0017157534333456097926464599817e-05 % h = 0.001 y1[1] (analytic) = 2.6083658909538914889792871763013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1289403523496884887059992410857 relative error = 4.9433383865687035404789150896414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.655 y2[1] (analytic) = 1.2069520718983405409901317819836 y2[1] (numeric) = 1.2069516977715913874241000454595 absolute error = 3.741267491535660317365241e-07 relative error = 3.0997647534182954078855937091876e-05 % h = 0.001 y1[1] (analytic) = 2.609159243329414783436518758647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1297337047252117831632308234314 relative error = 4.9722417310054725484265482387333 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.656 y2[1] (analytic) = 1.207561627564074427462152801609 y2[1] (numeric) = 1.2075612411022554077385080529615 absolute error = 3.864618190197236447486475e-07 relative error = 3.2003486215383040083245094922043e-05 % h = 0.001 y1[1] (analytic) = 2.6099519865457455117475522467268 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1305264479415425114742643115112 relative error = 5.0011053312246336316831506982117 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.657 y2[1] (analytic) = 1.2081719756681147133309112496125 y2[1] (numeric) = 1.2081715765465995512077513933496 absolute error = 3.991215151621231598562629e-07 relative error = 3.3035157510702101160326994012387e-05 % h = 0.001 y1[1] (analytic) = 2.6107441198101405236435918216702 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1313185812059375233703038864546 relative error = 5.029929214797477764255823404278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=144.9MB, alloc=4.0MB, time=20.02 x[1] = 0.658 y2[1] (analytic) = 1.2087831156001133454184615651814 y2[1] (numeric) = 1.2087827034878566082917837362783 absolute error = 4.121122567371266778289031e-07 relative error = 3.4093151320411116669296422573621e-05 % h = 0.001 y1[1] (analytic) = 2.6115356423304666207407287533185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1321101037262636204674408181029 relative error = 5.0587134092633709194036741604268 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.659 y2[1] (analytic) = 1.2093950467489304426544976297072 y2[1] (numeric) = 1.209394621308381786888668378686 absolute error = 4.254405486557658292510212e-07 relative error = 3.5177963544618931005565640065103e-05 % h = 0.001 y1[1] (analytic) = 2.6123265533152013486730737730358 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1329010147109983483997858378202 relative error = 5.0874579421297415550565545014021 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.66 y2[1] (analytic) = 1.2100077685026349072161829087698 y2[1] (numeric) = 1.2100073293896527123345782447949 absolute error = 4.391129821948816046639749e-07 relative error = 3.6290096115521376861529407096256e-05 % h = 0.001 y1[1] (analytic) = 2.6131168519734337886151454793963 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1336913133692307883418575441807 relative error = 5.116162840872068241399753371776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.661 y2[1] (analytic) = 1.2106212802485050364591972807178 y2[1] (numeric) = 1.2106208271122694274037958861113 absolute error = 4.531362356090554013946065e-07 relative error = 3.7430057029564177537552429766997e-05 % h = 0.001 y1[1] (analytic) = 2.6139065375148653481927232544241 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1344809989106623479194353192085 relative error = 5.1448281329338674299695582360836 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.662 y2[1] (analytic) = 1.2112355813730291356393886208484 y2[1] (numeric) = 1.2112351138559543923087134814251 absolute error = 4.675170747433306751394233e-07 relative error = 3.8598360379519559791129125099128e-05 % h = 0.001 y1[1] (analytic) = 2.6146956091498105517813737796007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1352700705456075515080858443851 relative error = 5.1734538457266813636067876698688 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.0MB, time=20.55 NO POLE NO POLE x[1] = 0.663 y2[1] (analytic) = 1.2118506712619061314244164195866 y2[1] (numeric) = 1.2118501889995524846998328368104 absolute error = 4.822623536467245835827762e-07 relative error = 3.9795526386476511671129215623734e-05 % h = 0.001 y1[1] (analytic) = 2.6154840660891978301918608531767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1360585274849948299185729179611 relative error = 5.2020400066300661266175866853581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.664 y2[1] (analytic) = 1.2124665493000461861947739230711 y2[1] (numeric) = 1.2124660519210309996657653856249 absolute error = 4.973790151865290085374462e-07 relative error = 4.1022081431744622729693299679597e-05 % h = 0.001 y1[1] (analytic) = 2.6162719075445703097416488234469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1368463689403673094683608882313 relative error = 5.230586642991579834492957034435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.665 y2[1] (analytic) = 1.2130832148715713131335744951767 y2[1] (numeric) = 1.2130827019974796497332321885103 absolute error = 5.128740916634003423066664e-07 relative error = 4.2278558088671446936639549868778e-05 % h = 0.001 y1[1] (analytic) = 2.6170591327280866007117105665481 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1376335941238836004384226313325 relative error = 5.2590937821267709625406695162698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.666 y2[1] (analytic) = 1.213700667359815992104487111237 y2[1] (numeric) = 1.2137001386051105648670639333922 absolute error = 5.287547054272374231778448e-07 relative error = 4.3565495154373331540148534692407e-05 % h = 0.001 y1[1] (analytic) = 2.6178457408525215851878515520396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.138420202248318584914563616824 relative error = 5.2875614513191668127853739102098 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.1MB, time=21.07 NO POLE NO POLE x[1] = 0.667 y2[1] (analytic) = 1.2143189061473277863172051055833 y2[1] (numeric) = 1.2143183611192582924702009354801 absolute error = 5.450280694938470041701032e-07 relative error = 4.4883437681379658022969483412931e-05 % h = 0.001 y1[1] (analytic) = 2.6186317311312672042857621550066 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.139206192527064204012474219791 relative error = 5.3159896778202621184948845676121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.668 y2[1] (analytic) = 1.2149379306158679597798315074841 y2[1] (numeric) = 1.2149373689143797973836931372674 absolute error = 5.617014881623961383702167e-07 relative error = 4.6232937009190444195401888496295e-05 % h = 0.001 y1[1] (analytic) = 2.6194171027783332447590109897005 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1399915641741302444857230544849 relative error = 5.3443784888495077856927759417571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.669 y2[1] (analytic) = 1.2155577401464120955375635131482 y2[1] (numeric) = 1.2155571613640544618867001085312 absolute error = 5.787823576336508634046170e-07 relative error = 4.7614550795747259344814489409678e-05 % h = 0.001 y1[1] (analytic) = 2.6202018550083481249891926567879 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1407763164041451247159047215723 relative error = 5.3727279115942997710195724244993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.67 y2[1] (analytic) = 1.2161783341191507146970578551619 y2[1] (numeric) = 1.2161777378409840856964910463327 absolute error = 5.962781666290005668088292e-07 relative error = 4.9028843048817407226435961896245e-05 % h = 0.001 y1[1] (analytic) = 2.6209859870365596803574439141266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.141560448432356680084155978911 relative error = 5.4010379732099680953069608041498 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.1MB, time=21.60 NO POLE NO POLE x[1] = 0.671 y2[1] (analytic) = 1.2167997119134898962358580450436 y2[1] (numeric) = 1.2167990977169928859684447750169 absolute error = 6.141964970102674132700267e-07 relative error = 5.0476384157291334531552415768829e-05 % h = 0.001 y1[1] (analytic) = 2.6217694980788359479965428996171 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1423439594746329477232549644015 relative error = 5.4293087008197659922315914731123 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.672 y2[1] (analytic) = 1.2174218729080518975962636795423 y2[1] (numeric) = 1.2174212403630274972960497462127 absolute error = 6.325450244003002139333296e-07 relative error = 5.1957750922393225307044403284929e-05 % h = 0.001 y1[1] (analytic) = 2.6225523873516659509228066540965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1431268487474629506495187188809 relative error = 5.4575401215148591914171662082766 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.673 y2[1] (analytic) = 1.2180448164806757760630212168607 y2[1] (numeric) = 1.2180441651491569717109040388328 absolute error = 6.513315188043521171780279e-07 relative error = 5.3473526588804744624357458576258e-05 % h = 0.001 y1[1] (analytic) = 2.6233346540721604815470028124424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1439091154679574812737148772268 relative error = 5.4857322623543153353556359339891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.674 y2[1] (analytic) = 1.2186685420084180109242148451658 y2[1] (numeric) = 1.2186678714445727786827153590739 absolute error = 6.705638452322414994860919e-07 relative error = 5.5024300875701897606494750198234e-05 % h = 0.001 y1[1] (analytic) = 2.6241162974580528845634919520396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.144690758853849884290204016824 relative error = 5.5138851503650935295204513687649 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=160.2MB, alloc=4.1MB, time=22.13 x[1] = 0.675 y2[1] (analytic) = 1.219293048867553126414735282546 y2[1] (numeric) = 1.2192923586175888051193010404165 absolute error = 6.902499643212954342421295e-07 relative error = 5.6610670007704972718417086071690e-05 % h = 0.001 y1[1] (analytic) = 2.6248973167276998392168177095343 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1454717781234968389435297743187 relative error = 5.5419988125420340250469228649757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.676 y2[1] (analytic) = 1.2199183364335743154417035649992 y2[1] (numeric) = 1.2199176260356413553665880436251 absolute error = 7.103979329600751155213741e-07 relative error = 5.8233236745741541009305612992942e-05 % h = 0.001 y1[1] (analytic) = 2.6256777111000821409449623993491 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1462521724958791406716744641335 relative error = 5.5700732758478480333568530873214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.677 y2[1] (analytic) = 1.2205444040811940640912260970796 y2[1] (numeric) = 1.220543673065289151208612956748 absolute error = 7.310159049128826131403316e-07 relative error = 5.9892610417822485764456993289262e-05 % h = 0.001 y1[1] (analytic) = 2.6264574797948054823984864907691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1470319411906024821251985555535 relative error = 5.5981085672131076721067074535381 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.678 y2[1] (analytic) = 1.2211712511843447769158564585004 y2[1] (numeric) = 1.2211704990722133318675219951173 absolute error = 7.521121314450483344633831e-07 relative error = 6.1589406949731039780112086901207e-05 % h = 0.001 y1[1] (analytic) = 2.6272366220321012338347709245244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1478110834278982335614829893088 relative error = 5.6261047135362360418406824912812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.679 y2[1] (analytic) = 1.221798877116179403002138679282 y2[1] (numeric) = 1.2217981034212174540035710013491 absolute error = 7.736949619489985676779329e-07 relative error = 6.3324248895624810216240491746603e-05 % h = 0.001 y1[1] (analytic) = 2.6280151370328272228865818746926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.148589598428624222613293939477 relative error = 5.6540617416834974327321214608247 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.1MB, time=22.66 NO POLE NO POLE x[1] = 0.68 y2[1] (analytic) = 1.2224272812490720628176059159557 y2[1] (numeric) = 1.2224264854762274917151254453434 absolute error = 7.957728445711024804706123e-07 relative error = 6.5097765468550773710188961725016e-05 % h = 0.001 y1[1] (analytic) = 2.6287930240184685137041781874202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1493674854142655134308902522046 relative error = 5.6819796784889876607988097660643 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.681 y2[1] (analytic) = 1.2230564629546186758366076818755 y2[1] (numeric) = 1.223055644600291836538660424284 absolute error = 8.183543268392979472575915e-07 relative error = 6.6910592570873227148126045029021e-05 % h = 0.001 y1[1] (analytic) = 2.6295702822111381854701823544214 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1501447436069351851968944192058 relative error = 5.7098585507546245329797598387687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.682 y2[1] (analytic) = 1.223686421603637588944338005864 y2[1] (numeric) = 1.2236855801555812974487606626387 absolute error = 8.414480562914955773432253e-07 relative error = 6.8763372824614682191354896012975e-05 % h = 0.001 y1[1] (analytic) = 2.6303469108335781102864365064475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1509213722293751100131485712319 relative error = 5.7376983852501384404631663449404 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.683 y2[1] (analytic) = 1.2243171565661702056184361152149 y2[1] (numeric) = 1.224316291503389100858120512159 absolute error = 8.650627811047603156030559e-07 relative error = 7.0656755601709694340797119857213e-05 % h = 0.001 y1[1] (analytic) = 2.6311229091091597304320655399362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1516973705049567301587776047206 relative error = 5.7654992087130630796572777399649 % h = 0.001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.1MB, time=23.21 NO POLE NO POLE x[1] = 0.684 y2[1] (analytic) = 1.2249486672114816158875304615069 y2[1] (numeric) = 1.2249477780041308906175439518804 absolute error = 8.892073507252699865096265e-07 relative error = 7.2591397054171619995250884408953e-05 % h = 0.001 y1[1] (analytic) = 2.631898276261884834991970118843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1524727376576818347186821836274 relative error = 5.7932610478487263001979894029834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.685 y2[1] (analytic) = 1.2255809529080612270660961307334 y2[1] (numeric) = 1.2255800390173447280159445881224 absolute error = 9.138907164990501515426110e-07 relative error = 7.4567960144172297617373750505178e-05 % h = 0.001 y1[1] (analytic) = 2.6326730115163863358549729232243 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1532474729121833355816849880087 relative error = 5.8209839293302410793890168227644 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.686 y2[1] (analytic) = 1.2262140130236233952649949029474 y2[1] (numeric) = 1.2262130739016910917803456544881 absolute error = 9.391219323034846492484593e-07 relative error = 7.6587114674034651765715646048145e-05 % h = 0.001 y1[1] (analytic) = 2.6334471140979290430808421464934 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1540215754937260428075542112778 relative error = 5.8486678797984966224725545998463 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.687 y2[1] (analytic) = 1.2268478469251080576770664509304 y2[1] (numeric) = 1.2268468820149528780758800118647 absolute error = 9.649101551796011864390657e-07 relative error = 7.8649537316138221381507794713414e-05 % h = 0.001 y1[1] (analytic) = 2.6342205832324104396354168743884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1547950446282074393621289391728 relative error = 5.8763129258621495881303683844685 % h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.1MB, time=23.75 NO POLE NO POLE x[1] = 0.688 y2[1] (analytic) = 1.2274824539786813656371383923497 y2[1] (numeric) = 1.2274814627140354005057901484233 absolute error = 9.912646459651313482439264e-07 relative error = 8.0755911642737616335283047497340e-05 % h = 0.001 y1[1] (analytic) = 2.6349934181463614554930596105924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1555678795421584552197716753768 relative error = 5.9039190940976154386173022996708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.689 y2[1] (analytic) = 1.2281178335497363184558221354451 y2[1] (numeric) = 1.2281168153549663901114281796187 absolute error = 1.0181947699283443939558264e-06 relative error = 8.2906928155693908840740794603983e-05 % h = 0.001 y1[1] (analytic) = 2.6357656180669472411056618466169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1563400794627442408323739114013 relative error = 5.9314864110490599139312139156503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.69 y2[1] (analytic) = 1.2287539850028933980264606845022 y2[1] (numeric) = 1.2287529392928959953722558481898 absolute error = 1.0457099974026542048363124e-06 relative error = 8.5103284316118968931560094880296e-05 % h = 0.001 y1[1] (analytic) = 2.6365371822219679402374292070087 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1571116436177649399641412717931 relative error = 5.9590149032283906294253724576355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.691 y2[1] (analytic) = 1.2293909077020012042045937982186 y2[1] (numeric) = 1.2293898338820967822058445241592 absolute error = 1.0738199044219987492740594e-06 relative error = 8.7345684573932755771090580441939e-05 % h = 0.001 y1[1] (analytic) = 2.6373081098398594621646733351585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1578825712356564618913853999429 relative error = 5.9865045971152487962713736570507 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.1MB, time=24.29 NO POLE NO POLE x[1] = 0.692 y2[1] (analytic) = 1.2300286010101370909593051215486 y2[1] (numeric) = 1.2300274984759637339678752048335 absolute error = 1.1025341733569914299167151e-06 relative error = 8.9634840397333579124995437635384e-05 % h = 0.001 y1[1] (analytic) = 2.6380784001496942532398383199832 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1586528615454912529665503847676 relative error = 6.0139555191570010641826365071518 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.693 y2[1] (analytic) = 1.2306670642896078032958151397345 y2[1] (numeric) = 1.2306659324270142514521385148031 absolute error = 1.1318625935518436766249314e-06 relative error = 9.1971470302181347872971190846709e-05 % h = 0.001 y1[1] (analytic) = 2.638848052381182067818990099522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1594225137769790675457021643064 relative error = 6.0413676957687314858105531718217 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.694 y2[1] (analytic) = 1.2313062969019501149486830319832 y2[1] (numeric) = 1.2313051350868881528905347059423 absolute error = 1.1618150619620581483260409e-06 relative error = 9.4356299881293824967608804824033e-05 % h = 0.001 y1[1] (analytic) = 2.639617065764670738551997914018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1601915271604677382787099788024 relative error = 6.0687411533332336022273634317269 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.695 y2[1] (analytic) = 1.2319462982079314668449797316401 y2[1] (numeric) = 1.2319451058063476739530736574094 absolute error = 1.1924015837928919060742307e-06 relative error = 9.6790061833655910766278148157698e-05 % h = 0.001 y1[1] (analytic) = 2.6403854395311469460346375183712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1609599009269439457613495831556 relative error = 6.0960759182010026489118193485249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=179.2MB, alloc=4.1MB, time=24.82 x[1] = 0.696 y2[1] (analytic) = 1.2325870675675506063367937297397 y2[1] (numeric) = 1.2325858439352774677478748756464 absolute error = 1.2236322731385889188540933e-06 relative error = 9.9273495993541979165599436439779e-05 % h = 0.001 y1[1] (analytic) = 2.641153172912236987821846501921 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1617276343080339875485585667054 relative error = 6.123372016690227881655694296687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.697 y2[1] (analytic) = 1.2332286043400382272024303894814 y2[1] (numeric) = 1.2332273488226846048211674943794 absolute error = 1.2555173536223812628951020e-06 relative error = 0.00010180734935955129345759960273691 % h = 0.001 y1[1] (analytic) = 2.6419202651402075468013627023692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1624947265360045465280747671536 relative error = 6.1506294750867850218111731668764 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.698 y2[1] (analytic) = 1.2338709078838576104156647704838 y2[1] (numeric) = 1.2338696198166985731572902746182 absolute error = 1.2880671590372583744958656e-06 relative error = 0.00010439237612355653130202751954653 % h = 0.001 y1[1] (analytic) = 2.6426867154479664589269773402679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1632611768437634586536894050523 relative error = 6.1778483196442288203011373962789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.699 y2[1] (analytic) = 1.234513977556705265682407193618 y2[1] (numeric) = 1.2345126562645712781786916046565 absolute error = 1.3212921339875037155889615e-06 relative error = 0.00010702933769956545067050908361265 % h = 0.001 y1[1] (analytic) = 2.643452523069063480310635140883 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1640269844648604800373472056674 relative error = 6.2050285765837857398163295425691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7 y2[1] (analytic) = 1.2351578127155115737441400098081 y2[1] (numeric) = 1.235156457512677042745929500072 absolute error = 1.3552028345309982105097361e-06 relative error = 0.00010971900275249573106525254281057 % h = 0.001 y1[1] (analytic) = 2.6442176872376910536726143513987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1647921486334880533993264161831 relative error = 6.2321702720943467546253474014694 % h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.1MB, time=25.35 NO POLE NO POLE x[1] = 0.701 y2[1] (analytic) = 1.2358024127164414294474832694162 y2[1] (numeric) = 1.2358010229065126071576716037262 absolute error = 1.3898099288222898116656900e-06 relative error = 0.00011246214722686302674785678974938 % h = 0.001 y1[1] (analytic) = 2.6449822071886850741490202033442 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1655566685844820738757322681286 relative error = 6.2592734323324602674253771851652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.702 y2[1] (analytic) = 1.2364477769148948855792462226979 y2[1] (numeric) = 1.2364463517906971291506951857645 absolute error = 1.4251241977564285510369334e-06 relative error = 0.00011525955437538227113242271602378 % h = 0.001 y1[1] (analytic) = 2.6457460821575256544558260128154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1663205435533226541825380775998 relative error = 6.2863380834223251426635290430358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.703 y2[1] (analytic) = 1.2370939046655077974663208163335 y2[1] (numeric) = 1.2370924435089721838998871436161 absolute error = 1.4611565356135664336727174e-06 relative error = 0.00011811201478748227390161393727528 % h = 0.001 y1[1] (analytic) = 2.6465093113803378894086967545133 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1670837727761348891354088192977 relative error = 6.313364251455783855760586228899 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.704 y2[1] (analytic) = 1.2377407953221524683397725861917 y2[1] (numeric) = 1.2377392974042017640182440019943 absolute error = 1.4979179507043215285841974e-06 relative error = 0.00012102032641773365479454998075955 % h = 0.001 y1[1] (analytic) = 2.6472718940938926197978305898392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1678463554896896195245426546236 relative error = 6.340351962492315757670921513011 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.1MB, time=25.88 NO POLE NO POLE x[1] = 0.705 y2[1] (analytic) = 1.2383884482379382954624835822915 y2[1] (numeric) = 1.238386912818372279556871912896 absolute error = 1.5354195660159056116693955e-06 relative error = 0.00012398529461419016039143906583506 % h = 0.001 y1[1] (analytic) = 2.6480338295356071956170544742679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1686082909314041953437665390523 relative error = 6.3673012425590304542142710145098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.706 y2[1] (analytic) = 1.2390368627652124170197011983717 y2[1] (numeric) = 1.2390352890925925580049866556023 absolute error = 1.5736726198590147145427694e-06 relative error = 0.00012700773214664341258166145770044 % h = 0.001 y1[1] (analytic) = 2.6487951169435462386464106149696 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.169369578339343238373122679754 relative error = 6.3942121176506612996169865033523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.707 y2[1] (analytic) = 1.2396860382555603597718460155734 y2[1] (numeric) = 1.2396844255670938442899136366779 absolute error = 1.6126884665154819323788955e-06 relative error = 0.00013008845923479113974959618130596 % h = 0.001 y1[1] (analytic) = 2.6495557555564224043874711961547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1701302169522194041141832609391 relative error = 6.421084613729559003702312401921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.708 y2[1] (analytic) = 1.2403359740598066874689310074817 y2[1] (numeric) = 1.2403343215812298007770878899715 absolute error = 1.6524785768866918431175102e-06 relative error = 0.00013322830357631894404583822034671 % h = 0.001 y1[1] (analytic) = 2.6503157446135971433506194368912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1708902060093941430773315016756 relative error = 6.4479187567256853521711532183191 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.1MB, time=26.41 NO POLE NO POLE x[1] = 0.709 y2[1] (analytic) = 1.2409866695280156500259436921618 y2[1] (numeric) = 1.2409849764734765072700540766157 absolute error = 1.6930545391427558896155461e-06 relative error = 0.00013642810037489566043057903753938 % h = 0.001 y1[1] (analytic) = 2.6510750833550814616935356941786 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.171649544750878461420247758963 relative error = 6.4747145725366070394167109778115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.71 y2[1] (analytic) = 1.2416381240094918334585420558604 y2[1] (numeric) = 1.241636389581432461010466485027 absolute error = 1.7344280593724480755708334e-06 relative error = 0.00013968869236808236548081700774009 % h = 0.001 y1[1] (analytic) = 2.6518337710215366812101279728528 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1724082324173336809368400376372 relative error = 6.5014720870274896133182803981574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.711 y2[1] (analytic) = 1.2422903368527808105784143127322 y2[1] (numeric) = 1.2422885602418185766780890309057 absolute error = 1.7766109622339003252818265e-06 relative error = 0.00014301092985515509624372602029505 % h = 0.001 y1[1] (analytic) = 2.6525918068542751986691468534576 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.173166268250072198395858918242 relative error = 6.5281913260310915314613920915587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.712 y2[1] (analytic) = 1.2429433074056697924476518052839 y2[1] (numeric) = 1.2429414877904781863907952572361 absolute error = 1.8196151916060568565480478e-06 relative error = 0.0001463956707248413416949383174046 % h = 0.001 y1[1] (analytic) = 2.6533491900952612445017254995287 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1739236514910582442284375643131 relative error = 6.5548723153477583282333909822048 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.1MB, time=26.95 NO POLE NO POLE x[1] = 0.713 y2[1] (analytic) = 1.2435970350151882805914835912195 y2[1] (numeric) = 1.2435951715623770397045683342863 absolute error = 1.8634528112408869152569332e-06 relative error = 0.00014984378048297037162269311245352 % h = 0.001 y1[1] (analytic) = 2.6541059199871116408370860568158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1746803813829086405637981216002 relative error = 6.5815150807454168922454284169874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.714 y2[1] (analytic) = 1.2442515190276087199687205040045 y2[1] (numeric) = 1.2442496108916033036135010596083 absolute error = 1.9081360054163552194443962e-06 relative error = 0.00015335613228003747000676477086673 % h = 0.001 y1[1] (analytic) = 2.6548619957730965588856544087971 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1754364571688935586123664735815 relative error = 6.6081196479595698535337321295107 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.715 y2[1] (analytic) = 1.2449067587884471526992557167609 y2[1] (numeric) = 1.2449048051113675625497958580379 absolute error = 1.9536770795901494598587230e-06 relative error = 0.00015693360693868214219481665352921 % h = 0.001 y1[1] (analytic) = 2.655617416697140275668825905437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1761918780929372753955379702214 relative error = 6.6346860426932900799948983070395 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.716 y2[1] (analytic) = 1.2455627536424638725479680820458 y2[1] (numeric) = 1.245560753554002818383764781695 absolute error = 2.0000884610541642033003508e-06 relative error = 0.00016057709298108036739832974337244 % h = 0.001 y1[1] (analytic) = 2.6563721820038219300946253354824 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1769466433996189298213374002668 relative error = 6.6612142906172152825118245181599 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=198.3MB, alloc=4.1MB, time=27.48 x[1] = 0.717 y2[1] (analytic) = 1.2462195029336640801643737636656 y2[1] (numeric) = 1.2462174555509644904238295099832 absolute error = 2.0473826995897405442536824e-06 relative error = 0.00016428748665625097023553307314644 % h = 0.001 y1[1] (analytic) = 2.6571262909383762783785050667013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1777007523341732781052171314857 relative error = 6.687704417369542728228771198571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.718 y2[1] (analytic) = 1.2468770060052985390773709209283 y2[1] (numeric) = 1.24687491043283041541652134959 absolute error = 2.0955724681236608495713383e-06 relative error = 0.00016806569196727618723981812929043 % h = 0.001 y1[1] (analytic) = 2.6578797427466944488085259333295 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1784542041424914485352379981139 relative error = 6.7141564485560240614359027755712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.719 y2[1] (analytic) = 1.2475352621998642324444214506442 y2[1] (numeric) = 1.2475331175293008475464812344869 absolute error = 2.1446705633848979402161573e-06 relative error = 0.00017191262069843650642895716222807 % h = 0.001 y1[1] (analytic) = 2.6586325366753246958541661056053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1792069980711216955808781703897 relative error = 6.7405704097499602315255173507357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.72 y2[1] (analytic) = 1.248194270859105020554513037748 y2[1] (numeric) = 1.2481920761691984584364597259291 absolute error = 2.1946899065621180533118189e-06 relative error = 0.00017582919244225986019306978899823 % h = 0.001 y1[1] (analytic) = 2.6593846719714731536180038326482 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1799591333672701533447158974326 relative error = 6.7669463264921965274840261676881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.721 y2[1] (analytic) = 1.2488540313240122990842440116342 y2[1] (numeric) = 1.2488517856804683371473170124559 absolute error = 2.2456435439619369269991783e-06 relative error = 0.00017981633462648525390769915143548 % h = 0.001 y1[1] (analytic) = 2.6601361478830045886295206070606 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.180710609278801588356232671845 relative error = 6.7932842242911177183855908795733 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.1MB, time=28.00 NO POLE NO POLE x[1] = 0.722 y2[1] (analytic) = 1.249514542934825658106372752177 y2[1] (numeric) = 1.2495122453901779901780229098903 absolute error = 2.2975446476679283498422867e-06 relative error = 0.0001838749825409409148125750899999 % h = 0.001 y1[1] (analytic) = 2.6608869636584431519802719575123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1814614250542401517069840222967 relative error = 6.819584128622643299355167911546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.723 y2[1] (analytic) = 1.2501758050310335418501726369398 y2[1] (numeric) = 1.2501734546245173414656568613393 absolute error = 2.3504065162003845157756005e-06 relative error = 0.00018800607936433704781666288769272 % h = 0.001 y1[1] (analytic) = 2.6616371185469731307996737341996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.182211579942770130526385798984 relative error = 6.8458460649302228424705449994247 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.724 y2[1] (analytic) = 1.2508378169513739092129327692739 y2[1] (numeric) = 1.2508354127087987323854079371937 absolute error = 2.4042425751768275248320802e-06 relative error = 0.00019221057619097328699593097620581 % h = 0.001 y1[1] (analytic) = 2.6623866117984396990706524114553 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1829610731942366987973644762397 relative error = 6.8720700586248314520747852889943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.725 y2[1] (analytic) = 1.2515005780338348950219439758613 y2[1] (numeric) = 1.2514981189674569217505748351282 absolute error = 2.4590663779732713691407331e-06 relative error = 0.00019648943205736093364192685932508 % h = 0.001 y1[1] (analytic) = 2.6631354426633496677844085919225 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1837099040591466675111206567069 relative error = 6.898256135084965323972319213603 % h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.1MB, time=28.53 NO POLE NO POLE x[1] = 0.726 y2[1] (analytic) = 1.2521640876156554720463088117698 y2[1] (numeric) = 1.2521615727240490858125658801015 absolute error = 2.5148916063862337429316683e-06 relative error = 0.00020084361396876007379673653297922 % h = 0.001 y1[1] (analytic) = 2.6638836103928722344335435575901 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1844580717886692341602556223745 relative error = 6.9244043196566374079837437428849 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.727 y2[1] (analytic) = 1.2528283450333261137579135612673 y2[1] (numeric) = 1.252825773301254818260899024356 absolute error = 2.5717320712954970145369113e-06 relative error = 0.00020527409692563167027322849605806 % h = 0.001 y1[1] (analytic) = 2.6646311142388397318427993746266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.185205575634636731569511439411 relative error = 6.9505146376533731733362025251764 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.728 y2[1] (analytic) = 1.2534933496225894578408994734763 y2[1] (numeric) = 1.2534907200208761302232018474181 absolute error = 2.6296017133276176976260582e-06 relative error = 0.00020978186395000472620865820279824 % h = 0.001 y1[1] (analytic) = 2.6653779534537483763366637213347 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1859524148495453760633757861191 relative error = 6.9765871143562064763680289425739 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.729 y2[1] (analytic) = 1.2541591007184409704489697234547 y2[1] (numeric) = 1.2541564122038374502652115560981 absolute error = 2.6885146035201837581673566e-06 relative error = 0.00021436790611175861923474475420748 % h = 0.001 y1[1] (analytic) = 2.666124127290759015243091271684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1866985886865560149698033364684 relative error = 7.0026217750136755300281371729956 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.1MB, time=29.07 NO POLE NO POLE x[1] = 0.73 y2[1] (analytic) = 1.2548255976551296112098678414497 y2[1] (numeric) = 1.2548228491701856243907749844901 absolute error = 2.7484849439868190928569596e-06 relative error = 0.00021903322255482070736823821277512 % h = 0.001 y1[1] (analytic) = 2.6668696350036978737325941307615 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1874440963994948734593061955459 relative error = 7.028618644841818974652444020332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.731 y2[1] (analytic) = 1.2554928397661584989763626059028 y2[1] (numeric) = 1.2554900302390899160418485939721 absolute error = 2.8095270685829345140119307e-06 relative error = 0.00022377882052327930973278657439534 % h = 0.001 y1[1] (analytic) = 2.6676144758470573009919544831147 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1881889372428543007186665478991 relative error = 7.0545777490241720495013965443032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.732 y2[1] (analytic) = 1.2561608263842855783230736492765 y2[1] (numeric) = 1.256157954728842006098498473206 absolute error = 2.8716554435722245751760705e-06 relative error = 0.00022860571538741216721559774917041 % h = 0.001 y1[1] (analytic) = 2.6683586490759965157318132803332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1889331104717935154585253451176 relative error = 7.0804991127117628645444674077163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.733 y2[1] (analytic) = 1.2568295568415242867884712799312 y2[1] (numeric) = 1.2568266219568559928789003381377 absolute error = 2.9348846682939095709417935e-06 relative error = 0.00023351493066963049014098713129893 % h = 0.001 y1[1] (analytic) = 2.6691021539463423510273894603448 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1896766153421393507541015251292 relative error = 7.1063827610231087719792613735486 % h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.1MB, time=29.61 NO POLE NO POLE x[1] = 0.734 y2[1] (analytic) = 1.2574990304691442228613832781104 y2[1] (numeric) = 1.2574960312396683921393395319968 absolute error = 2.9992294758307220437461136e-06 relative error = 0.00023850749807033870200741978928485 % h = 0.001 y1[1] (analytic) = 2.6698449897145899984915848577685 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1904194511103869982182969225529 relative error = 7.1322287190442128369746525391931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.735 y2[1] (analytic) = 1.2581692465976718147113406795812 y2[1] (numeric) = 1.2581661818929381370742110252969 absolute error = 3.0647047336776371296542843e-06 relative error = 0.00024358445749370999028511093728274 % h = 0.001 y1[1] (analytic) = 2.6705871556379037517797306322801 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1911616170337007515064426970645 relative error = 7.1580370118285604071291427029629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.736 y2[1] (analytic) = 1.2588402045568909896620938166407 y2[1] (numeric) = 1.2588370732314465783160194158354 absolute error = 3.1313254444113460744008053e-06 relative error = 0.00024874685707337777720765564149643 % h = 0.001 y1[1] (analytic) = 2.671328650974117749425231710308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1919031123699147491519437750924 relative error = 7.1838076643971157801373967309282 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.737 y2[1] (analytic) = 1.2595119036758438444076291430284 y2[1] (numeric) = 1.2595087045690974839353789286936 absolute error = 3.1991067463604722502143348e-06 relative error = 0.00025399575319804322541353273899896 % h = 0.001 y1[1] (analytic) = 2.672069474981736717005366404475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1926439363775337167320784692594 relative error = 7.2095407017383189691596709422136 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=217.4MB, alloc=4.1MB, time=30.14 x[1] = 0.738 y2[1] (analytic) = 1.2601843432828313159700166267826 y2[1] (numeric) = 1.2601810752189170394410134162368 absolute error = 3.2680639142765290032105458e-06 relative error = 0.00025933221053699889520168540154239 % h = 0.001 y1[1] (analytic) = 2.6728096269199367086364990450493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1933840883157337083632111098337 relative error = 7.2352361488080825653906053707657 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.739 y2[1] (analytic) = 1.2608575227054138533984167532507 y2[1] (numeric) = 1.260854184493053847779756358114 absolute error = 3.3382123600056186603951367e-06 relative error = 0.00026475730206556867205973830064351 % h = 0.001 y1[1] (analytic) = 2.6735491060485658477979641282533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1941235674443628475246761930377 relative error = 7.2608940305297886973256003032031 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.74 y2[1] (analytic) = 1.2615314412704120902085754393012 y2[1] (numeric) = 1.2615280317027789293365508612583 absolute error = 3.4095676331608720245780429e-06 relative error = 0.00027027210909046408500378531098361 % h = 0.001 y1[1] (analytic) = 2.6742879116281450674838811576082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1948623730239420672105932223926 relative error = 7.2865143717942860862247417481814 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.741 y2[1] (analytic) = 1.2622060983039075175621344192991 y2[1] (numeric) = 1.2622026161584857219344496598865 absolute error = 3.4821454217956276847594126e-06 relative error = 0.0002758777212750571381350910003841 % h = 0.001 y1[1] (analytic) = 2.6750260429198688496821600265609 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1956005043156658494088720913453 relative error = 7.3120971974598871972759794748446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.742 y2[1] (analytic) = 1.2628814931312431581850839235906 y2[1] (numeric) = 1.2628779371696900808346151154993 absolute error = 3.5559615530773504688080913e-06 relative error = 0.00028157523666456977967151075814896 % h = 0.001 y1[1] (analytic) = 2.6757634991856059641799574634498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1963379605814029639066695282342 relative error = 7.3376425323523654859609949787623 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.1MB, time=30.67 NO POLE NO POLE x[1] = 0.743 y2[1] (analytic) = 1.2635576250770242410246837310994 y2[1] (numeric) = 1.2635539940450302787363192168814 absolute error = 3.6310319939622883645142180e-06 relative error = 0.00028736576171118013454996801569122 % h = 0.001 y1[1] (analytic) = 2.676500279687900206694845733414 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1970747410836972064215577981984 relative error = 7.3631504012649527391289252053945 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.744 y2[1] (analytic) = 1.2642344934651188766441779391716 y2[1] (numeric) = 1.2642307860922670057769435801012 absolute error = 3.7073728518708672343590704e-06 relative error = 0.00029325041129904562852095176284498 % h = 0.001 y1[1] (analytic) = 2.6772363836899711363309554661397 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1978108450857681360576675309241 relative error = 7.3886208289583365102848310959776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.745 y2[1] (analytic) = 1.2649120976186587333546280560096 y2[1] (numeric) = 1.2649083126182833695319794485112 absolute error = 3.7850003753638226486074984e-06 relative error = 0.00029923030876924313346673261437117 % h = 0.001 y1[1] (analytic) = 2.6779718104557148123593551533613 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1985462718515118120860672181457 relative error = 7.4140538401606576486015180307971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.746 y2[1] (analytic) = 1.2655904368600397140831882839174 y2[1] (numeric) = 1.2655865729290848950150276927477 absolute error = 3.8639309548190681605911697e-06 relative error = 0.00030530658594462626547186253061514 % h = 0.001 y1[1] (analytic) = 2.6787065592497045303219305358001 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1992810206455015300486426005845 relative error = 7.4394494595675079211650280426061 % h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.1MB, time=31.21 NO POLE NO POLE x[1] = 0.747 y2[1] (analytic) = 1.266269510510922633977146125141 y2[1] (numeric) = 1.2662655663297995246777988107308 absolute error = 3.9441811231092993473144102e-06 relative error = 0.000311480383154599968957542149413 % h = 0.001 y1[1] (analytic) = 2.6794406293371915574580277757215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2000150907329885571847398405059 relative error = 7.4648077118419277279658312704014 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.748 y2[1] (analytic) = 1.2669493178922338987430507063167 y2[1] (numeric) = 1.2669452921246776184101129276646 absolute error = 4.0257675562803329377786521e-06 relative error = 0.00031775284925981252196063166566687 % h = 0.001 y1[1] (analytic) = 2.6801740199841058674531249885306 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.200748481379902867179837053315 relative error = 7.4901286216144039091494465333956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.749 y2[1] (analytic) = 1.2676298583241661837202504824584 y2[1] (numeric) = 1.267625749617091953539899796037 absolute error = 4.1087070742301803506864214e-06 relative error = 0.00032412514167676509939346954722205 % h = 0.001 y1[1] (analytic) = 2.6809067304570568745087973847929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2014811918528538742355094495773 relative error = 7.5154122134828676440419181386171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.75 y2[1] (analytic) = 1.2683111311261791136881612469999 y2[1] (numeric) = 1.2683069381095377248331987956198 absolute error = 4.1930166413888549624513801e-06 relative error = 0.00033059842640233903286226860713322 % h = 0.001 y1[1] (analytic) = 2.6816387600233341667332419527799 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2022132214191311664599540175643 relative error = 7.5406585120126924414672681059768 % h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.1MB, time=31.74 NO POLE NO POLE x[1] = 0.751 y2[1] (analytic) = 1.2689931356169999434065846406836 y2[1] (numeric) = 1.2689888569036325444941589334687 absolute error = 4.2787133673989124257072149e-06 relative error = 0.00033717387803824090734970617338674 % h = 0.001 y1[1] (analytic) = 2.6823701079509082388516282910726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.202944569346705238578340355857 relative error = 7.5658675417366922208757299131905 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.752 y2[1] (analytic) = 1.2696758711146242388883966190315 y2[1] (numeric) = 1.2696715053001164421650388439233 absolute error = 4.3658145077967233577751082e-06 relative error = 0.00034385267981536563678143568895124 % h = 0.001 y1[1] (analytic) = 2.6831007735084312242355428809353 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2036752349042282239622549457197 relative error = 7.5910393271551194838032516427375 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.753 y2[1] (analytic) = 1.270359336936316559403924605769 y2[1] (numeric) = 1.2703548825988518649262067886071 absolute error = 4.4543374646944777178171619e-06 relative error = 0.00035063602361807766219664674903364 % h = 0.001 y1[1] (analytic) = 2.6838307559652376262507947690758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2044052173610346259775068338602 relative error = 7.6161738927356635751844330655286 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.754 y2[1] (analytic) = 1.2710435323986111402163313278786 y2[1] (numeric) = 1.2710389880988236772961406564274 absolute error = 4.5442997874629201906714512e-06 relative error = 0.00035752511000841041792951223005254 % h = 0.001 y1[1] (analytic) = 2.6845600545913450489228513130465 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2051345159871420486495633778309 relative error = 7.6412712629134490340427327336982 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.1MB, time=32.27 NO POLE NO POLE x[1] = 0.755 y2[1] (analytic) = 1.2717284568173125760473225969591 y2[1] (numeric) = 1.2717238210981391612314279635755 absolute error = 4.6357191734148158946333836e-06 relative error = 0.00036452114825018421288141115646598 % h = 0.001 y1[1] (analytic) = 2.6852886686574549269191733239135 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2058631300532519266458853886979 relative error = 7.666331462091034033083447590102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.756 y2[1] (analytic) = 1.2724141095074965052724955712377 y2[1] (numeric) = 1.2724093808940280161267658535265 absolute error = 4.7286134684891457297177112e-06 relative error = 0.00037162535633304267562322831988102 % h = 0.001 y1[1] (analytic) = 2.6860165974349532548477196239165 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2065910588307502545744316887009 relative error = 7.6913545146384089067166289464939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.757 y2[1] (analytic) = 1.2731004897835102948456433029448 y2[1] (numeric) = 1.2730956667828423588149610970394 absolute error = 4.8230006679360306822059054e-06 relative error = 0.00037883896099640791371283324699261 % h = 0.001 y1[1] (analytic) = 2.686743840195911315870891720679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2073183015917083155976037854634 relative error = 7.7163404448929947670387549487574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.758 y2[1] (analytic) = 1.2737875969589737259513306468032 y2[1] (numeric) = 1.273782678060056723566930092157 absolute error = 4.9188989170023844005546462e-06 relative error = 0.00038616319775335453924505769921488 % h = 0.001 y1[1] (analytic) = 2.6874703962130864096341899840818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2080448576088834093609020488662 relative error = 7.7412892771596422073036308473205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=236.5MB, alloc=4.1MB, time=32.81 x[1] = 0.759 y2[1] (analytic) = 1.274475430346779680385055877114 y2[1] (numeric) = 1.2744704140202680620916988642062 absolute error = 5.0163265116182933570129078e-06 relative error = 0.00039359931091440271427014954023763 % h = 0.001 y1[1] (analytic) = 2.6881962647599225795088533972068 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2087707261557195792355654619912 relative error = 7.7662010357106300924146345369539 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.76 y2[1] (analytic) = 1.275163989259094827660311633333 y2[1] (numeric) = 1.2751588739571957435364030657975 absolute error = 5.1153018990841239085675355e-06 relative error = 0.00040114855361123037132180850430291 % h = 0.001 y1[1] (analytic) = 2.6889214451105513391477556387697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2094959065063483388744677035541 relative error = 7.7910757447856644359720659339063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.761 y2[1] (analytic) = 1.2758532730073603128418580871366 y2[1] (numeric) = 1.2758480571636815544862879768256 absolute error = 5.2158436787583555701103110e-06 relative error = 0.00040881218782030476588753416205051 % h = 0.001 y1[1] (analytic) = 2.6896459365397923983538309412086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.210220397935589398080543005993 relative error = 7.81591342859187736341099483257 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.762 y2[1] (analytic) = 1.2765432809022924451045204977583 y2[1] (numeric) = 1.2765379629316896989647085044688 absolute error = 5.3179706027461398119932895e-06 relative error = 0.00041659148438643351923216592843771 % h = 0.001 y1[1] (analytic) = 2.6903697383231543882603038560603 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2109441997189513879870159208447 relative error = 7.8407141113038261607666329400224 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.763 y2[1] (analytic) = 1.2772340122538833870168225968583 y2[1] (numeric) = 1.2772285905523067984331291831895 absolute error = 5.4217015765885836934136688e-06 relative error = 0.00042448772304623531155019830122448 % h = 0.001 y1[1] (analytic) = 2.6910928497368355858219977464571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2116673111326325855487098112415 relative error = 7.8654778170634924086058818376643 % h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.1MB, time=33.34 NO POLE NO POLE x[1] = 0.764 y2[1] (analytic) = 1.277925466371401844548766519348 y2[1] (numeric) = 1.2779199393157418917911241747338 absolute error = 5.5270556599527576423446142e-06 relative error = 0.00043250219245153038697374032210883 % h = 0.001 y1[1] (analytic) = 2.6918152700577246376169975154955 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2123897314535216373437095802799 relative error = 7.8902045699802812006653296762428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.765 y2[1] (analytic) = 1.2786176425633937578030692724491 y2[1] (numeric) = 1.2786120085113264353763772681318 absolute error = 5.6340520673224266920043173e-06 relative error = 0.00044063619019265103350088620611513 % h = 0.001 y1[1] (analytic) = 2.6925369985634012829579427688738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2131114599591982826846548336582 relative error = 7.9148943941310204467375854862449 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.766 y2[1] (analytic) = 1.2793105401376829924691650118068 y2[1] (numeric) = 1.2793047974275143029646818796975 absolute error = 5.7427101686895044831321093e-06 relative error = 0.00044889102282167220243380380240093 % h = 0.001 y1[1] (analytic) = 2.6932580345321370763122283005656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.21383249592793407603894036535 relative error = 7.9395473135599602593494510919709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.767 y2[1] (analytic) = 1.2800041584013720319992816707128 y2[1] (numeric) = 1.2799983053518817857699410530287 absolute error = 5.8530494902462293406176841e-06 relative error = 0.00045726800587556243342705957518713 % h = 0.001 y1[1] (analytic) = 2.6939783772428961090303894813906 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.214552838638693108757101546175 relative error = 7.9641633522787724237770367666475 % h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.1MB, time=33.88 NO POLE NO POLE x[1] = 0.768 y2[1] (analytic) = 1.2806984966608426705058997664195 y2[1] (numeric) = 1.2806925315711275924441674590071 absolute error = 5.9650897150780617323074124e-06 relative error = 0.00046576846389925525274461369451981 % h = 0.001 y1[1] (analytic) = 2.6946980259753357303819508221551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2152724873711327301086628869395 relative error = 7.9887425342665499509445279695173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.769 y2[1] (analytic) = 1.2813935542217567063799004861449 y2[1] (numeric) = 1.2813874753710728490774833957984 absolute error = 6.0788506838573024170903465e-06 relative error = 0.00047439373046864121380856776910308 % h = 0.001 y1[1] (analytic) = 2.6954169800098072678980166755753 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2159914414056042676247287403597 relative error = 8.0132848834698067127549067764678 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.77 y2[1] (analytic) = 1.2820893303890566366287094346757 y2[1] (numeric) = 1.282083136036661099198120788852 absolute error = 6.1943523955374305886458237e-06 relative error = 0.00048314514821348075059416197334976 % h = 0.001 y1[1] (analytic) = 2.6961352386273567470198837344522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2167097000231537467465957992366 relative error = 8.0377904238024771594025229649946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.771 y2[1] (analytic) = 1.2827858244669663519337417054856 y2[1] (numeric) = 1.2827795128519583037724211909013 absolute error = 6.3116150080481613205145843e-06 relative error = 0.00049202406884023801588373047734307 % h = 0.001 y1[1] (analytic) = 2.696852801109725610052955677546 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2174272625055226097796677423304 relative error = 8.0622591791459161182189961544647 % h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.1MB, time=34.41 NO POLE NO POLE x[1] = 0.772 y2[1] (analytic) = 1.2834830357589918324264532179796 y2[1] (numeric) = 1.2834766051001528412048357819635 absolute error = 6.4306588389912216174360161e-06 relative error = 0.00050103185315483587783736549453708 % h = 0.001 y1[1] (analytic) = 2.6975696667393514344252410092942 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2181441281351484341519530740786 relative error = 8.0866911733488986736055119455824 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.773 y2[1] (analytic) = 1.2841809635679218441823025448716 y2[1] (numeric) = 1.2841744120635555073379253693398 absolute error = 6.5515043663368443771755318e-06 relative error = 0.00051016987108533224976994441050775 % h = 0.001 y1[1] (analytic) = 2.6982858347993686502497158349369 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2188602961951656499764278997213 relative error = 8.1110864302276201276061516608929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.774 y2[1] (analytic) = 1.2848796071958286364319267357915 y2[1] (numeric) = 1.2848729330235995154523603876153 absolute error = 6.6741722291209795663481762e-06 relative error = 0.00051943950170451792944297417775675 % h = 0.001 y1[1] (analytic) = 2.6990013045736092571898340087447 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2195757659694062569165460735291 relative error = 8.1354449735656960406784670727505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.775 y2[1] (analytic) = 1.2855789659440686394888339260045 y2[1] (numeric) = 1.2855721672608404962669208986588 absolute error = 6.7986832281432219130273457e-06 relative error = 0.00052884213325243612558543580187604 % h = 0.001 y1[1] (analytic) = 2.6997160753466035406274677899009 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2202905367424005403541798546853 relative error = 8.1597668271141623522190784288308 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=251.7MB, alloc=4.1MB, time=34.94 x[1] = 0.776 y2[1] (analytic) = 1.2862790391132831633929148026071 y2[1] (numeric) = 1.2862721140549564979384965916231 absolute error = 6.9250583266654544182109840e-06 relative error = 0.00053837916315882385075050314973439 % h = 0.001 y1[1] (analytic) = 2.7004301464035807871325628381541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2210046077993777868592749029385 relative error = 8.1840520145914755804036361594389 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.777 y2[1] (analytic) = 1.2869798260033990972690742847478 y2[1] (numeric) = 1.2869727726847479860620867829449 absolute error = 7.0533186511112069875018029e-06 relative error = 0.00054805199806547536099469924986439 % h = 0.001 y1[1] (analytic) = 2.7011435170304699992337920796493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2217179784262669989605041444337 relative error = 8.2083005596835131009020438881901 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.778 y2[1] (analytic) = 1.2876813259136296094002840592981 y2[1] (numeric) = 1.2876741424281378436708004163448 absolute error = 7.1834854917657294836429533e-06 relative error = 0.00055786205384852782423277329216351 % h = 0.001 y1[1] (analytic) = 2.7018561865139006094894936723398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2224306479096976092162057371242 relative error = 8.23251248604357350403139277924 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.779 y2[1] (analytic) = 1.28838353814247484801435589898 y2[1] (numeric) = 1.2883762225621713712358560628272 absolute error = 7.3155803034767784998361528e-06 relative error = 0.00056781075564066940047536864034449 % h = 0.001 y1[1] (analytic) = 2.7025681541412031938581790001042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2231426155370001935848910648886 relative error = 8.2566878172923770299106048529499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=255.5MB, alloc=4.1MB, time=35.48 x[1] = 0.78 y2[1] (analytic) = 1.2890864619877226427837349762354 y2[1] (numeric) = 1.2890790123630162866665819206804 absolute error = 7.4496247063561171530555550e-06 relative error = 0.00057789953785326991849744099297984 % h = 0.001 y1[1] (analytic) = 2.7032794192004101843678973251179 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2238538805962071840946093899023 relative error = 8.2808265770180660811823256988019 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.781 y2[1] (analytic) = 1.289790096746449207037611673102 y2[1] (numeric) = 1.2897825111059627253104158154767 absolute error = 7.5856404864817271958576253e-06 relative error = 0.00058812984419843433481341224587558 % h = 0.001 y1[1] (analytic) = 2.7039899809802565810837444291757 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2245644423760535808104564939601 relative error = 8.3049287887762058128691450221179 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.782 y2[1] (analytic) = 1.2904944417150198406856496750424 y2[1] (numeric) = 1.2904867180654232399529052000721 absolute error = 7.7236495966007327444749703e-06 relative error = 0.00059850312771097916215024568882208 % h = 0.001 y1[1] (analytic) = 2.7046998387701806633728032765141 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2252743001659776630995153412985 relative error = 8.3289944760897847989327566910316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.783 y2[1] (analytic) = 1.2911994961890896338526274250576 y2[1] (numeric) = 1.2911916325149328008177071546066 absolute error = 7.8636741568330349202704510e-06 relative error = 0.0006090208507703320559120380608178 % h = 0.001 y1[1] (analytic) = 2.705408991860324700465805433254 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2259834532561217001925174980384 relative error = 8.3530236624492157751061984146479 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.784 y2[1] (analytic) = 1.2919052594636041712232893035015 y2[1] (numeric) = 1.2918972537271487955665883865041 absolute error = 8.0057364553756567009169974e-06 relative error = 0.00061968448512235474841938058572255 % h = 0.001 y1[1] (analytic) = 2.70611743954153566131480268186 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2266919009373326610415147466444 relative error = 8.3770163713123364575708348937478 % h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.1MB, time=36.01 NO POLE NO POLE x[1] = 0.785 y2[1] (analytic) = 1.2926117308328002370967021888034 y2[1] (numeric) = 1.2926035809738510292994252304724 absolute error = 8.1498589492077972769583310e-06 relative error = 0.00063049551190108952198368115497623 % h = 0.001 y1[1] (analytic) = 2.7068251811053659237461389730047 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2273996425011629234728510377891 relative error = 8.4009726261044104370512672540994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.786 y2[1] (analytic) = 1.293318909590206521149412344802 y2[1] (numeric) = 1.293310613525941724554203648503 absolute error = 8.2960642647965952086962990e-06 relative error = 0.00064145542165042941314090113506513 % h = 0.001 y1[1] (analytic) = 2.707532215844073982908013561925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2281066772398709826347256267094 relative error = 8.4248924502181281479028658109598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.787 y2[1] (analytic) = 1.2940267950286443249066968715924 y2[1] (numeric) = 1.2940183506534455213070192298715 absolute error = 8.4443751988035996776417209e-06 relative error = 0.0006525657143457123416207797814342 % h = 0.001 y1[1] (analytic) = 2.7082385430506251590119268817658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2288130044464221587386389465502 relative error = 8.4487758670136079117681327336798 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.788 y2[1] (analytic) = 1.2947353864402282689212032486917 y2[1] (numeric) = 1.2947267916255094769720771911373 absolute error = 8.5948147187919491260575544e-06 relative error = 0.00066382789941523935886663561594138 % h = 0.001 y1[1] (analytic) = 2.7089441620186923043673014125252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2295186234144893040940134773096 relative error = 8.4726228998183970553796059933374 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.1MB, time=36.55 NO POLE NO POLE x[1] = 0.789 y2[1] (analytic) = 1.2954446831163670006582697919461 y2[1] (numeric) = 1.2954359357104030664016923761436 absolute error = 8.7474059639342565774158025e-06 relative error = 0.00067524349576171721214728557244465 % h = 0.001 y1[1] (analytic) = 2.7096490720426565097085705110381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2302235334384535094352825758225 relative error = 8.4964335719274731020885160956598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.79 y2[1] (analytic) = 1.296154684347763903087219138915 y2[1] (numeric) = 1.2961457821755181818862892560176 absolute error = 8.9021722457212009298828974e-06 relative error = 0.00068681403178362542151654700456761 % h = 0.001 y1[1] (analytic) = 2.7103532724176078098140288749692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2309277338134048095407409397536 relative error = 8.5202079066032450366999025382318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.791 y2[1] (analytic) = 1.2968653894244178039779161714986 y2[1] (numeric) = 1.2968563302873691331544019291704 absolute error = 9.0591370486708235142423282e-06 relative error = 0.00069854104539650806807722510445231 % h = 0.001 y1[1] (analytic) = 2.711056762439345888415739022023 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2316312238351428881424510868074 relative error = 8.5439459270755546431963876966559 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.792 y2[1] (analytic) = 1.2975767976356236859018810793109 y2[1] (numeric) = 1.2975675793115926473726741212969 absolute error = 9.2183240310385292069580140e-06 relative error = 0.00071042608405419049319547693450757 % h = 0.001 y1[1] (analytic) = 2.7117595414043807823997888745235 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2323340028001777821265009393079 relative error = 8.5676476565416779149342919509374 % h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.1MB, time=37.07 NO POLE NO POLE x[1] = 0.793 y2[1] (analytic) = 1.2982889082699733969372475627432 y2[1] (numeric) = 1.2982795285129478691458591853759 absolute error = 9.3797570255277913883773673e-06 relative error = 0.00072247070476992110948802300190372 % h = 0.001 y1[1] (analytic) = 2.7124616086099335852961962491652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2330360700057305850229083139496 relative error = 8.5913131181663265368972553225627 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.794 y2[1] (analytic) = 1.2990017206153563620768554708199 y2[1] (numeric) = 1.2989921771553163605168201016701 absolute error = 9.5434600400015600353691498e-06 relative error = 0.00073467647413743852556888824949912 % h = 0.001 y1[1] (analytic) = 2.7131629633539371500577567620875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2337374247497341497844688268719 relative error = 8.6149423350816494395940077162244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.795 y2[1] (analytic) = 1.2997152339589602953387664658126 y2[1] (numeric) = 1.2997055245017021009665294777261 absolute error = 9.7094572581943722369880865e-06 relative error = 0.00074704496835196418769423596115351 % h = 0.001 y1[1] (analytic) = 2.713863604935036791127132370486 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2344380663308337908538444352704 relative error = 8.6385353303872344241884020600185 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.796 y2[1] (analytic) = 1.3004294475872719125784906041565 y2[1] (numeric) = 1.3004195698142314874140695483744 absolute error = 9.8777730404251644210557821e-06 relative error = 0.00075957777323112074258345128711918 % h = 0.001 y1[1] (analytic) = 2.7145635326525909857914784837286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.235137994048387985518190548513 relative error = 8.6620921271501098584512922253465 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=270.8MB, alloc=4.1MB, time=37.61 x[1] = 0.797 y2[1] (analytic) = 1.3011443607860776450022110215024 y2[1] (numeric) = 1.3011343123541533342166321757293 absolute error = 1.00484319243107855788457731e-05 relative error = 0.00077227648423577632682197624124704 % h = 0.001 y1[1] (analytic) = 2.7152627458066720748239082894086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.235837207202469074550620354193 relative error = 8.6856127484047464431253005950171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.798 y2[1] (analytic) = 1.3018599728404643533802932087375 y2[1] (numeric) = 1.301849751381838873169518849189 absolute error = 1.02214586254802107743595485e-05 relative error = 0.00078514270649081498936653587376071 % h = 0.001 y1[1] (analytic) = 2.7159612436980669624110936529281 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2365357050938639621378057177125 relative error = 8.7090972171530590482949785464574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.799 y2[1] (analytic) = 1.3025762830348200429603646655274 y2[1] (numeric) = 1.3025658861567817535061406854357 absolute error = 1.03968780382894542239800917e-05 relative error = 0.00079817805480583345477636778576658 % h = 0.001 y1[1] (analytic) = 2.7166590256282778153663026630705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2372334870240748150930147278549 relative error = 8.7325455563644086193563169384766 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8 y2[1] (analytic) = 1.3032932906528345790792500183577 y2[1] (numeric) = 1.3032827159375980418980184284354 absolute error = 1.05747152365371812315899223e-05 relative error = 0.00081138415369576443588491455468198 % h = 0.001 y1[1] (analytic) = 2.7173560908995227616271746105814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2379305522953197613538866753658 relative error = 8.7559577889756041521810129460799 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.801 y2[1] (analytic) = 1.3040109949775004034730459911998 y2[1] (numeric) = 1.3040002399820262224547824494379 absolute error = 1.07549954741810182635417619e-05 relative error = 0.00082476263740142670570520362735844 % h = 0.001 y1[1] (analytic) = 2.718052438814736588037533902042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2386269002105335877642459668264 relative error = 8.7793339378909047370723442904032 % h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.1MB, time=38.14 NO POLE NO POLE x[1] = 0.802 y2[1] (analytic) = 1.3047293952911132512846199187868 y2[1] (numeric) = 1.304718457546927196724172746977 absolute error = 1.09377441860545604471718098e-05 relative error = 0.00083831514991000213942886349233266 % h = 0.001 y1[1] (analytic) = 2.7187480686775714374125451272789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2393225300733684371392571920633 relative error = 8.8026740259820216711109420713074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.803 y2[1] (analytic) = 1.3054484908752728687678147950589 y2[1] (numeric) = 1.3054373678882842836920389468704 absolute error = 1.11229869885850757758481885e-05 relative error = 0.00085204334497543993843345029969125 % h = 0.001 y1[1] (analytic) = 2.7194429797923975048865122152131 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2400174411881945046132242799975 relative error = 8.8259780760881206384901890403286 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.804 y2[1] (analytic) = 1.3061682810108837316876431526351 y2[1] (numeric) = 1.3061569702612032197823403022196 absolute error = 1.13107496805119053028504155e-05 relative error = 0.00086594888613878824925552875827629 % h = 0.001 y1[1] (analytic) = 2.7201371714643037335426253304078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2407116328601007332693373951922 relative error = 8.849246111015823958442401263151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.805 y2[1] (analytic) = 1.3068887649781557644157513731752 y2[1] (numeric) = 1.3068772639199121588571456934101 absolute error = 1.15010582436055586056797651e-05 relative error = 0.00088003344674845339151780683078528 % h = 0.001 y1[1] (analytic) = 2.7208306429990985093239598806256 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.24140510439489550905067194541 relative error = 8.8724781535392129003583777250567 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.1MB, time=38.67 NO POLE NO POLE x[1] = 0.806 y2[1] (analytic) = 1.3076099420566050597204353332294 y2[1] (numeric) = 1.3075982481177616722166336281111 absolute error = 1.16939388433875038017051183e-05 relative error = 0.00089429870998038690981760962398342 % h = 0.001 y1[1] (analytic) = 2.7215233937033103552250327244533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2420978550991073549517447892377 relative error = 8.8956742263998300657043245416278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.807 y2[1] (analytic) = 1.3083318115250545992504875956188 y2[1] (numeric) = 1.3083199221072247485990922412758 absolute error = 1.18894178298506513953543430e-05 relative error = 0.00090874636885820066559113570976522 % h = 0.001 y1[1] (analytic) = 2.7222154228841886247632213874979 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2427898842799856244899334522823 relative error = 8.9188343523066818363415780619723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.808 y2[1] (analytic) = 1.3090543726616349747121556625597 y2[1] (numeric) = 1.3090422851398967941809192951413 absolute error = 1.20875217381805312363674184e-05 relative error = 0.00092337812627321018596331363110439 % h = 0.001 y1[1] (analytic) = 2.7229067298497041947293528157898 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2434811912455011944560648805742 relative error = 8.941958553936240888855964304158 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.809 y2[1] (analytic) = 1.3097776247437851097384901136346 y2[1] (numeric) = 1.3097653364664956325766221792286 absolute error = 1.22882772894771618679344060e-05 relative error = 0.00093819569500440648757671028875521 % h = 0.001 y1[1] (analytic) = 2.7235973139085501572167689158648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2441717753043471569434809806492 relative error = 8.9650468539324487745050408544903 % h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.1MB, time=39.20 NO POLE NO POLE x[1] = 0.81 y2[1] (analytic) = 1.3105015670482529824503607593199 y2[1] (numeric) = 1.3104890753368615048388179103425 absolute error = 1.24917113914776115428489774e-05 relative error = 0.00095320079773835659436488025465196 % h = 0.001 y1[1] (analytic) = 2.7242871743701425109281768525145 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2448616357659395106548889172989 relative error = 8.9880992749067185643928716046333 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.811 y2[1] (analytic) = 1.311226198851096348708418249117 y2[1] (numeric) = 1.3112135009999570694582331325717 absolute error = 1.26978511392792501851165453e-05 relative error = 0.00096839516708903296919583052011538 % h = 0.001 y1[1] (analytic) = 2.7249763105446208517595927974149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2455507719404178514863048621993 relative error = 9.0111158394379375594833845055669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.812 y2[1] (analytic) = 1.3119515194276834660552778823829 y2[1] (numeric) = 1.3119386127038674023637041172888 absolute error = 1.29067238160636915737650941e-05 relative error = 0.00098378054561757208025995186710734 % h = 0.001 y1[1] (analytic) = 2.7256647217428490626606885447446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.246239183138646062387400609529 relative error = 9.0340965700724700650647578958337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.813 y2[1] (analytic) = 1.3126775280526938183472016797382 y2[1] (numeric) = 1.3126644096957999969221767631503 absolute error = 1.31183568938214250249165879e-05 relative error = 0.00099935868585196232401388172310267 % h = 0.001 y1[1] (analytic) = 2.7263524072764160027708511335054 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2469268686722130024975631982898 relative error = 9.0570414893241602292786719256079 % h = 0.001 TOP MAIN SOLVE Loop memory used=286.1MB, alloc=4.1MB, time=39.73 NO POLE NO POLE x[1] = 0.814 y2[1] (analytic) = 1.3134042240001188410745540834314 y2[1] (numeric) = 1.3133908912220847639387065960966 absolute error = 1.33327780340771358474873348e-05 relative error = 0.0010151313503066615274173577643777 % h = 0.001 y1[1] (analytic) = 2.7270393664576361958302663405423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2476138278534331955569784053267 relative error = 9.0799506196743349453296481587468 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.815 y2[1] (analytic) = 1.3141316065432626473703059662622 y2[1] (numeric) = 1.314118056528174031656458769352 absolute error = 1.35500150886157138471969102e-05 relative error = 0.0010311003115021442531142417327365 % h = 0.001 y1[1] (analytic) = 2.7277255985995505178653376332361 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2483000599953475175920496980205 relative error = 9.1028239835718068169910826039731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.816 y2[1] (analytic) = 1.314859674954742754705860940622 y2[1] (numeric) = 1.3148459048586425457567080634246 absolute error = 1.37700961002089491528771974e-05 relative error = 0.0010472673519843791321115846498105 % h = 0.001 y1[1] (analytic) = 2.7284111030159268841477528965088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2489855644117238838744649612932 relative error = 9.1256616034328771870259552151183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.817 y2[1] (analytic) = 1.315588428506490812273477271886 y2[1] (numeric) = 1.3155744354571874693588388861064 absolute error = 1.39930493033429146383857796e-05 relative error = 0.0010636342643442364494019121885474 % h = 0.001 y1[1] (analytic) = 2.72909587902126093542651197513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2496703404170579351532240399144 relative error = 9.1484635016413392281415723200789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=289.9MB, alloc=4.1MB, time=40.26 x[1] = 0.818 y2[1] (analytic) = 1.316317866469753329054558013794 y2[1] (numeric) = 1.3163036475666283830203452724733 absolute error = 1.42189031249460342127413207e-05 relative error = 0.0010802028512368262088538783602124 % h = 0.001 y1[1] (analytic) = 2.7297799259307767234322287993561 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2503543873265737231589408641405 relative error = 9.1712297005484810960990675007284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.819 y2[1] (analytic) = 1.3170479881150924025730812975917 y2[1] (numeric) = 1.3170335404289072847368308848851 absolute error = 1.44476861851178362504127066e-05 relative error = 0.001096974925400766904565112756269 % h = 0.001 y1[1] (analytic) = 2.7304632430604273956530225896556 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.25103770445622439537973465444 relative error = 9.1939602224730891445997511623412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.82 y2[1] (analytic) = 1.3177787927123864483334420215631 y2[1] (numeric) = 1.3177641132850885899420090129855 absolute error = 1.46794272978583914330085776e-05 relative error = 0.0011139523096773852267285166343301 % h = 0.001 y1[1] (analytic) = 2.7311458297268958793813133646877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2517202911226928791080254294721 relative error = 9.2166550897014512015717594130151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.821 y2[1] (analytic) = 1.3185102795308309299419755031717 y2[1] (numeric) = 1.318495365375359131507702573702 absolute error = 1.49141554717984342729294697e-05 relative error = 0.001131136837029846930909492387598 % h = 0.001 y1[1] (analytic) = 2.7318276852475955650308377057945 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2524021466433925647575497705789 relative error = 9.239314324487359906481808932105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.822 y2[1] (analytic) = 1.3192424478389390899114329723498 y2[1] (numeric) = 1.3192272959390281597438441112461 absolute error = 1.51518999109301675888611037e-05 relative error = 0.0011485303505622191004666659340663 % h = 0.001 y1[1] (analytic) = 2.7325088089406709887232014610491 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2530832703364679884499135258335 relative error = 9.2619379490521161082982162534957 % h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.1MB, time=40.79 NO POLE NO POLE x[1] = 0.823 y2[1] (analytic) = 1.3199752969045426811476781015192 y2[1] (numeric) = 1.3199599042145273423984757971132 absolute error = 1.53926900153387492023044060e-05 relative error = 0.0011661347035384640326726278354 % h = 0.001 y1[1] (analytic) = 2.7331892001249985141432868023628 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2537636615207955138699988671472 relative error = 9.2845259855845323237326873357101 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.824 y2[1] (analytic) = 1.3207088259947926991178730857087 y2[1] (numeric) = 1.3206931894394107646577494300824 absolute error = 1.56365553819344601236556263e-05 relative error = 0.001183951759401364979904123901153 % h = 0.001 y1[1] (analytic) = 2.7338688581201870136628317803018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2544433195159840133895438450862 relative error = 9.3070784562409362553897264479548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.825 y2[1] (analytic) = 1.3214430343761601146994221046441 y2[1] (numeric) = 1.3214271508503549291459264362168 absolute error = 1.58835258051855534956684273e-05 relative error = 0.0012019833917913839780730156809441 % h = 0.001 y1[1] (analytic) = 2.7345477822465785487315012530908 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2551222436423755484582133178752 relative error = 9.3295953831451743694538522803886 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.826 y2[1] (analytic) = 1.3221779213144366077089393179268 y2[1] (numeric) = 1.3221617876831587559253778688634 absolute error = 1.61336312778517835614490634e-05 relative error = 0.0012202314845654519952602526243579 % h = 0.001 y1[1] (analytic) = 2.7352259718252490495347687987877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2558004332210460492614808635721 relative error = 9.3520767883886155325461437994853 % h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.1MB, time=41.35 NO POLE NO POLE x[1] = 0.827 y2[1] (analytic) = 1.3229134860747353011105078643946 y2[1] (numeric) = 1.3228970991727435824965844086531 absolute error = 1.63869019917186139234557415e-05 relative error = 0.0012386979318156916342950978852693 % h = 0.001 y1[1] (analytic) = 2.735903426178008993917929952807 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2564778875738059936446420175914 relative error = 9.3745226940301547073829687268813 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.828 y2[1] (analytic) = 1.3236497279214914959024956574681 y2[1] (numeric) = 1.3236330845531531637981363635006 absolute error = 1.66433683383321043592939675e-05 relative error = 0.0012573846378880726237909758506475 % h = 0.001 y1[1] (analytic) = 2.7365801446274040855755678468317 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2571546060232010853022799116161 relative error = 9.3969331220962167068710736332696 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.829 y2[1] (analytic) = 1.3243866461184634066821930897261 y2[1] (numeric) = 1.3243697430575536722067336686046 absolute error = 1.69030609097344754594211215e-05 relative error = 0.0012762935174010003329076082852042 % h = 0.001 y1[1] (analytic) = 2.7372561264967159315057930597084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2578305878925129312325051244928 relative error = 9.4193080945807600062745365197812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.83 y2[1] (analytic) = 1.3251242399287328978875370821356 y2[1] (numeric) = 1.3251070739182336975371858864475 absolute error = 1.71660104992003503511956881e-05 relative error = 0.0012954264952638375458566260027273 % h = 0.001 y1[1] (analytic) = 2.7379313711099627187285802261381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2585058325057597184552922909225 relative error = 9.441647633445280613090400418174 % h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.1MB, time=41.88 NO POLE NO POLE x[1] = 0.831 y2[1] (analytic) = 1.3258625086147062207151852362717 y2[1] (numeric) = 1.3258450763666042470424122067958 absolute error = 1.74322481019736727730294759e-05 relative error = 0.0013147855066953597329046302090574 % h = 0.001 y1[1] (analytic) = 2.7386058777918998902675246848866 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.259180339187696889994236749671 relative error = 9.4639517606188159942711199902844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.832 y2[1] (analytic) = 1.3266014514381147507142031715169 y2[1] (numeric) = 1.3265837496331987454134414466997 absolute error = 1.77018049160053007617248172e-05 relative error = 0.0013343724972421440553537816220958 % h = 0.001 y1[1] (analytic) = 2.7392796458680208203943431848106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.259854107263817820121055249595 relative error = 9.4862204979979490604332623567348 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.833 y2[1] (analytic) = 1.3273410676600157260546274536119 y2[1] (numeric) = 1.3273230929476730347794120504934 absolute error = 1.79747123426912752154031185e-05 relative error = 0.0013541894227968923426954619192962 % h = 0.001 y1[1] (analytic) = 2.739952674664557489135443404258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2605271360603544888621554690424 relative error = 9.508453867446812206693208447026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.834 y2[1] (analytic) = 1.3280813565407929864701658460576 y2[1] (numeric) = 1.328063105538805374707572089795 absolute error = 1.82510019876117625937562626e-05 relative error = 0.001374238249616688280837430986313 % h = 0.001 y1[1] (analytic) = 2.7406249635084811560398877773265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2611994249042781557665998421109 relative error = 9.5306518907970914097719020481735 % h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.1MB, time=42.43 NO POLE NO POLE x[1] = 0.835 y2[1] (analytic) = 1.3288223173401577128742959417292 y2[1] (numeric) = 1.3288037866344964422032792635063 absolute error = 1.85307056612706710166782229e-05 relative error = 0.001394520954341189050999241265765 % h = 0.001 y1[1] (analytic) = 2.741296511727503033208077859075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2618709731233000329347899238594 relative error = 9.5528145898480303810119904488806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.836 y2[1] (analytic) = 1.3295639493171491676490225586661 y2[1] (numeric) = 1.3295451354617693317100008978132 absolute error = 1.88138553798359390216608529e-05 relative error = 0.0014150395240107516595545163428926 % h = 0.001 y1[1] (analytic) = 2.7419673186500749575804862010582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2625417800458719573071982658426 relative error = 9.5749419863664347749519931413972 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.837 y2[1] (analytic) = 1.3303062517301354356055536113409 y2[1] (numeric) = 1.3302871512467695551093139461854 absolute error = 1.91004833658804962396651555e-05 relative error = 0.0014357959560844941997721027429336 % h = 0.001 y1[1] (analytic) = 2.7426373836053900624857634485088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2632118450011870622124755132932 relative error = 9.5970341020866764531034234652651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.838 y2[1] (analytic) = 1.3310492238368141656161534967937 y2[1] (numeric) = 1.3310298332147650417209049893765 absolute error = 1.93906220491238952485074172e-05 relative error = 0.0014567922584582922870711100879532 % h = 0.001 y1[1] (analytic) = 2.743306705923383448447549111117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2638811673191804481742611759014 relative error = 9.6190909587106978025780723670068 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=308.9MB, alloc=4.1MB, time=42.96 x[1] = 0.839 y2[1] (analytic) = 1.3317928648942133129164323638407 y2[1] (numeric) = 1.331773180590146138302570235424 absolute error = 1.96843040671746138621284167e-05 relative error = 0.0014780304494827109100575141103406 % h = 0.001 y1[1] (analytic) = 2.7439752849347328532493152006504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2645497463305298529760272654348 relative error = 9.6411125779080161092139436184842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.84 y2[1] (analytic) = 1.3325371741586918820773289631291 y2[1] (numeric) = 1.3325171925964256090502155196492 absolute error = 1.99815622662730271134434799e-05 relative error = 0.0014995125579808719402523576805615 % h = 0.001 y1[1] (analytic) = 2.7446431199708593212565726706296 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.265217581366656320983284735414 relative error = 9.6630989813157279848496058955976 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.841 y2[1] (analytic) = 1.3332821508859406706460441061175 y2[1] (numeric) = 1.3332618684562386355978563046573 absolute error = 2.02824297020350481878014602e-05 relative error = 0.0015212406232662575440536961245456 % h = 0.001 y1[1] (analytic) = 2.7453102103639278719957713359055 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2658846717597248717224834006899 relative error = 9.6850501905385138483979990786157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.842 y2[1] (analytic) = 1.3340277943309830134551810921098 y2[1] (numeric) = 1.3340072073913428170176176803374 absolute error = 2.05869396401964375634117724e-05 relative error = 0.0015432166951604497410963433087149 % h = 0.001 y1[1] (analytic) = 2.7459765554468481679892246932965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2665510168426451677159367580809 relative error = 9.7069662271486424603720000075688 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.843 y2[1] (analytic) = 1.334774103748175527599348794266 y2[1] (numeric) = 1.3347532086226181698197343638626 absolute error = 2.08951255573577796144304034e-05 relative error = 0.0015654428340108063537852333485864 % h = 0.001 y1[1] (analytic) = 2.7466421545532751818453918084153 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2672166159490721815721038731997 relative error = 9.7288471126859755105153167211015 % h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.1MB, time=43.49 NO POLE NO POLE x[1] = 0.844 y2[1] (analytic) = 1.3355210783912088580784824280462 y2[1] (numeric) = 1.3354998713700671279525506996897 absolute error = 2.12070211417301259317283565e-05 relative error = 0.0015879211107080735933798677970695 % h = 0.001 y1[1] (analytic) = 2.7473070070176098626038491784596 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.267881468413406862330561243244 relative error = 9.7506928686579722581935399364642 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.845 y2[1] (analytic) = 1.3362687175131084241071363588314 y2[1] (numeric) = 1.3362471948528145428025206595595 absolute error = 2.15226602938813046156992719e-05 relative error = 0.0016106536067039355285989198485158 % h = 0.001 y1[1] (analytic) = 2.7479711121749998013342862260498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2685455735707968010609982908342 relative error = 9.7725035165396942252014362026548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.846 y2[1] (analytic) = 1.3370170203662351660890026394896 y2[1] (numeric) = 1.3369951782891076831942078424967 absolute error = 2.18420771274828947947969929e-05 relative error = 0.0016336424140285006832956637505567 % h = 0.001 y1[1] (analytic) = 2.7486344693613398959888588251738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2692089307571368957155708899582 relative error = 9.7942790777738099406438187892222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.847 y2[1] (analytic) = 1.3377659862022862932559083034306 y2[1] (numeric) = 1.3377438208963162353902854748098 absolute error = 2.21653059700578656228286208e-05 relative error = 0.001656889635307726010326538871626 % h = 0.001 y1[1] (analytic) = 2.7492970779132730155072360069414 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2698715393090700152339480717258 relative error = 9.8160195737705997375485799708115 % h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.1MB, time=44.03 NO POLE NO POLE x[1] = 0.848 y2[1] (analytic) = 1.3385156142722960319705437742155 y2[1] (numeric) = 1.3384931218909323030915364100912 absolute error = 2.24923813637288790073641243e-05 relative error = 0.0016803973837807784892968932181899 % h = 0.001 y1[1] (analytic) = 2.7499589371681906631736757401562 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2705333985639876629003878049406 relative error = 9.837725025907960600871711943055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.849 y2[1] (analytic) = 1.3392659038266363746921740890535 y2[1] (numeric) = 1.3392430804885704074368531292172 absolute error = 2.28233380659672553209598363e-05 relative error = 0.0017041677833173345964198296212868 % h = 0.001 y1[1] (analytic) = 2.7506200464642336392254664296844 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2711945078600306389521784944688 relative error = 9.8593954555314110665553831699381 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.85 y2[1] (analytic) = 1.3400168541150178296045839705385 y2[1] (numeric) = 1.339993695903967487003237740348 absolute error = 2.31582110503426013462301905e-05 relative error = 0.0017282029684348178952661493577926 % h = 0.001 y1[1] (analytic) = 2.7512804051402927027120715242355 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2718548665360897024387835890199 relative error = 9.8810308839540961713013725271652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.851 y2[1] (analytic) = 1.3407684643864901709055071187424 y2[1] (numeric) = 1.3407449673509828978058019789277 absolute error = 2.34970355072730997051398147e-05 relative error = 0.0017525050843155749977157015873884 % h = 0.001 y1[1] (analytic) = 2.7519400125360092326043153744632 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2725144739318062323310274392476 relative error = 9.9026313324567924527233951810239 % h = 0.001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.1MB, time=44.56 NO POLE NO POLE x[1] = 0.852 y2[1] (analytic) = 1.3415207338894431897567894342973 y2[1] (numeric) = 1.3414968940425984132977672076843 absolute error = 2.38398468447764590222266130e-05 relative error = 0.0017770762868239901449430526736172 % h = 0.001 y1[1] (analytic) = 2.7525988679917758881529492322585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2731733293875728878796612970429 relative error = 9.9241968222879129995430817391055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.853 y2[1] (analytic) = 1.3422736618716074458945352223685 y2[1] (numeric) = 1.3422494751909182243704644166295 absolute error = 2.41866806892215240708057390e-05 relative error = 0.0018019187425235386587833371292129 % h = 0.001 y1[1] (analytic) = 2.7532569708487372684959370327215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2738314322445342682226490975059 relative error = 9.9457273746635125514955958382273 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.854 y2[1] (analytic) = 1.3430272475800550198984847674316 y2[1] (numeric) = 1.3430027100071689393533342230591 absolute error = 2.45375728860805451505443725e-05 relative error = 0.0018270346286937795143274902189557 % h = 0.001 y1[1] (analytic) = 2.7539143204487905715138013515826 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.274488781844587571240513416367 relative error = 9.9672230107672926486120950074975 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.855 y2[1] (analytic) = 1.3437814902612002661198710095412 y2[1] (numeric) = 1.3437565977016995840139268715527 absolute error = 2.48925595006821059441379885e-05 relative error = 0.0018524261333472872850898428062521 % h = 0.001 y1[1] (analytic) = 2.7545709161345862519323706827818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2751453775303832516590827475662 relative error = 9.9886837517506068295474553709929 % h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.1MB, time=45.09 NO POLE NO POLE x[1] = 0.856 y2[1] (analytic) = 1.3445363891608005662670023942965 y2[1] (numeric) = 1.3445111374839816015579022339738 absolute error = 2.52516768189647091001603227e-05 relative error = 0.001878095455246523712575329639678 % h = 0.001 y1[1] (analytic) = 2.7552267572495286786722699335127 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2758012186453256783989819982971 relative error = 10.010109618732465878622892546008 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.857 y2[1] (analytic) = 1.3452919435239570836478183109831 y2[1] (numeric) = 1.3452663285626088526290298094698 absolute error = 2.56149613482310187885015133e-05 relative error = 0.0019040448039206491525483743625248 % h = 0.001 y1[1] (analytic) = 2.7558818431377767914444967872976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.276456304533573791171208852082 relative error = 10.03150063279954312125431896016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.858 y2[1] (analytic) = 1.3460481525951155180686628763995 y2[1] (numeric) = 1.3460221701452976153091887244719 absolute error = 2.59824498179027594741519276e-05 relative error = 0.001930276399682274150770917453403 % h = 0.001 y1[1] (analytic) = 2.7565361731442447565914273395692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2771106345400417563181394043536 relative error = 10.052856815006179767438481764173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.859 y2[1] (analytic) = 1.3468050156180668613885221656564 y2[1] (numeric) = 1.3467786614388865851183677326953 absolute error = 2.63541791802762701544329611e-05 relative error = 0.0019567924736441514014330968114988 % h = 0.001 y1[1] (analytic) = 2.757189746614602622172595164811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2777642080103996218993072295954 relative error = 10.074178186374390302970125568308 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=328.0MB, alloc=4.1MB, time=45.61 x[1] = 0.86 y2[1] (analytic) = 1.3475625318359481537279693357761 y2[1] (numeric) = 1.347535801649336875014665215139 absolute error = 2.67301866112787133041206371e-05 relative error = 0.0019835952677358083419468255496377 % h = 0.001 y1[1] (analytic) = 2.7578425628952769722945887295286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.278417024291073972021300794313 relative error = 10.095464767893867928064620389059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.861 y2[1] (analytic) = 1.3483207004912432403320614332074 y2[1] (numeric) = 1.3482935899817320153942891800859 absolute error = 2.71105095112249377722531215e-05 relative error = 0.0020106870347201206382099866715791 % h = 0.001 y1[1] (analytic) = 2.7584946213334515806844128212126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.279069082729248580411124885997 relative error = 10.116716580521990043061687470593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.862 y2[1] (analytic) = 1.3490795208257835290864310224247 y2[1] (numeric) = 1.3490520256402779540915572631028 absolute error = 2.74951855055749948737593219e-05 relative error = 0.0020380700382098268148772313163247 % h = 0.001 y1[1] (analytic) = 2.7591459212770680635056604199826 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.279720382672865063232372484767 relative error = 10.13793364518382378088704405207 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.863 y2[1] (analytic) = 1.3498389920807487486858151195816 y2[1] (numeric) = 1.3498111078283030563788967270404 absolute error = 2.78842524456923069183925412e-05 relative error = 0.0020657465526839842855924746691808 % h = 0.001 y1[1] (analytic) = 2.7597964620748265314168421967984 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2803709234706235311435542615828 relative error = 10.159115982772131585949972699269 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.864 y2[1] (analytic) = 1.3505991134966677074542632627533 y2[1] (numeric) = 1.3505708357482581049668444620332 absolute error = 2.82777484096024874188007201e-05 relative error = 0.0020937188635043670385481827917166 % h = 0.001 y1[1] (analytic) = 2.7604462430761862408712215799592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2810207044719832405979336447436 relative error = 10.180263614147376839156001516383 % h = 0.001 TOP MAIN SOLVE Loop memory used=331.8MB, alloc=4.1MB, time=46.15 NO POLE NO POLE x[1] = 0.865 y2[1] (analytic) = 1.3513598843134190528162658986232 y2[1] (numeric) = 1.3513312086017163000040469854997 absolute error = 2.86757117027528122189131235e-05 relative error = 0.0021219892669318052331374841443351 % h = 0.001 y1[1] (analytic) = 2.7610952636313662446575040901144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2816697250271632443842161548988 relative error = 10.201376560137729528715058413238 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.866 y2[1] (analytic) = 1.3521213037702320314180436145485 y2[1] (numeric) = 1.3520922255893732590772604421422 absolute error = 2.90781808587723407831724063e-05 relative error = 0.0021505600701424669638570718799273 % h = 0.001 y1[1] (analytic) = 2.7617435230913460416807304031469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2823179844871430414074424679313 relative error = 10.222454841539071966426635633953 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.867 y2[1] (analytic) = 1.3528833711056872498982370947791 y2[1] (numeric) = 1.3528538859110470172113506039469 absolute error = 2.94851946402326868864908322e-05 relative error = 0.0021794335912440824480018370787399 % h = 0.001 y1[1] (analytic) = 2.7623910208078662259827233600927 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2829654822036632257094354248771 relative error = 10.24349847911500454912466996698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.868 y2[1] (analytic) = 1.3536460855577174363072370302028 y2[1] (numeric) = 1.3536161887656780268692928701839 absolute error = 2.98967920394094379441600189e-05 relative error = 0.0022086121592921108940662394679352 % h = 0.001 y1[1] (analytic) = 2.763037756133429135001439903703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2836122175292261347281519684874 relative error = 10.264507493596851564966009463156 % h = 0.001 TOP MAIN SOLVE Loop memory used=335.7MB, alloc=4.1MB, time=46.69 NO POLE NO POLE x[1] = 0.869 y2[1] (analytic) = 1.3544094463636082021743925623504 y2[1] (numeric) = 1.3543791333513291579521722674072 absolute error = 3.03130122790442222202949432e-05 relative error = 0.0022380981143058503081326309255771 % h = 0.001 y1[1] (analytic) = 2.7636837284212994970685796823498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2842581898170964967952917471342 relative error = 10.28548190568366704424749909902 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.87 y2[1] (analytic) = 1.3551734527599988052223361945172 y2[1] (numeric) = 1.3551427188651856977991834494546 absolute error = 3.07338948131074231527450626e-05 relative error = 0.0022678938072844904958831486239993 % h = 0.001 y1[1] (analytic) = 2.7643289370255050781448028237228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2849033984213020778715148885072 relative error = 10.306421736042240654437875647675 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.871 y2[1] (analytic) = 1.3559381039828829127276624557362 y2[1] (numeric) = 1.3559069445035553511876306974479 absolute error = 3.11594793275615400317582883e-05 relative error = 0.002298001600223109518219438671039 % h = 0.001 y1[1] (analytic) = 2.7649733813008373277919101431513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2855478426966343275186222079357 relative error = 10.327327005307103639111816069062 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.872 y2[1] (analytic) = 1.3567033992676093655271969569926 y2[1] (numeric) = 1.3566718094618682403329279197928 absolute error = 3.15898057411251942690371998e-05 relative error = 0.0023284238661286138588134094002523 % h = 0.001 y1[1] (analytic) = 2.7656170606028520243813398144258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2861915219986490241080518792102 relative error = 10.348197734080534800474634016756 % h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.1MB, time=47.23 NO POLE NO POLE x[1] = 0.873 y2[1] (analytic) = 1.3574693378488829426690918334692 y2[1] (numeric) = 1.3574373129346769048885986521787 absolute error = 3.20249142060377804931812905e-05 relative error = 0.0023591629890356225622424938330489 % h = 0.001 y1[1] (analytic) = 2.7662599742878699195383352946765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2868344356836669192650473594609 relative error = 10.369033942932566525167265589351 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.874 y2[1] (analytic) = 1.3582359189607651267079829217956 y2[1] (numeric) = 1.358203454115656301946276057579 absolute error = 3.24648451088247617068642166e-05 relative error = 0.0023902213640222956016845764598603 % h = 0.001 y1[1] (analytic) = 2.7669021217129773818211400591947 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2874765831087743815478521239791 relative error = 10.389835652400990853042328241819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.875 y2[1] (analytic) = 1.359003141836674869643443377204 y2[1] (numeric) = 1.3589702321976038060357029262511 absolute error = 3.29096390710636077404509529e-05 relative error = 0.0024216013972261067354608579910966 % h = 0.001 y1[1] (analytic) = 2.7675435022360270396345754670545 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2881179636318240393612875318389 relative error = 10.410602882991365588603175826304 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.876 y2[1] (analytic) = 1.3597710057093893595009677922045 y2[1] (numeric) = 1.359737646372439209124731675736 absolute error = 3.33593369501503762361164685e-05 relative error = 0.0024533055058595611120195455306458 % h = 0.001 y1[1] (analytic) = 2.768184115215638423377358844013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2887585766114354231040709087974 relative error = 10.431335655177020454799008063334 % h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.1MB, time=47.77 NO POLE NO POLE x[1] = 0.877 y2[1] (analytic) = 1.3605395098110447875547202358586 y2[1] (numeric) = 1.3605056958312047206193243508589 absolute error = 3.38139798400669353958849997e-05 relative error = 0.0024853361182258578832494132351562 % h = 0.001 y1[1] (analytic) = 2.7688239600111986068225196354215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2893984214069956065492317002059 relative error = 10.452033989399063288870224363298 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.878 y2[1] (analytic) = 1.3613086533731371161912789909656 y2[1] (numeric) = 1.3612743797640649673635526237286 absolute error = 3.42736090721488277263672370e-05 relative error = 0.0025176956737344980863000316551577 % h = 0.001 y1[1] (analytic) = 2.769463035982862847730272248788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2900374973786598474569843135724 relative error = 10.472697906066386279939339835383 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.879 y2[1] (analytic) = 1.3620784356265228474136101254846 y2[1] (numeric) = 1.362043697360306993639597793738 absolute error = 3.47382662158537740123317466e-05 relative error = 0.0025503866229168380543648619668533 % h = 0.001 y1[1] (analytic) = 2.7701013424915552276927049731688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2906758038873522274194170379532 relative error = 10.493327425555672248043905546588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.88 y2[1] (analytic) = 1.3628488558014197919845013942779 y2[1] (numeric) = 1.3628136478083402611677507875638 absolute error = 3.52079930795308167506067141e-05 relative error = 0.0025834114274415886171545043734306 % h = 0.001 y1[1] (analytic) = 2.770738878898969291209645130756 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2913133402947662909363571955404 relative error = 10.513922568211400964308995638046 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=347.1MB, alloc=4.1MB, time=48.30 x[1] = 0.881 y2[1] (analytic) = 1.3636199131274078392086873278103 y2[1] (numeric) = 1.3635842302956966491064121591666 absolute error = 3.56828317111901022751686437e-05 relative error = 0.0026167725601302603520502293126728 % h = 0.001 y1[1] (analytic) = 2.771375644567568683995061384847 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2919501059633656837217734496314 relative error = 10.534483354345855511957940779423 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.882 y2[1] (analytic) = 1.3643916068334297273528957257406 y2[1] (numeric) = 1.3643554440090304540520920897908 absolute error = 3.61628243992733008036359498e-05 relative error = 0.0026504725049725551471825544073256 % h = 0.001 y1[1] (analytic) = 2.772011638860587790513364897848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2925861002563847902400769626324 relative error = 10.555009804239128687861100655412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.883 y2[1] (analytic) = 1.3651639361477918147030451354242 y2[1] (numeric) = 1.3651272881341183900394103879648 absolute error = 3.66480136734246636347474594e-05 relative error = 0.0026845137571417043379261109216032 % h = 0.001 y1[1] (analytic) = 2.7726468611420323707449718030637 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2932213225378293704716838678481 relative error = 10.575501938139129444323577741384 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.884 y2[1] (analytic) = 1.3659369002981648512578222581931 y2[1] (numeric) = 1.3658997618558595885410964895008 absolute error = 3.71384423052627167257686923e-05 relative error = 0.0027188988230097536785404201457215 % h = 0.001 y1[1] (analytic) = 2.7732813107766801961804902247626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.293855772172477195907202289547 relative error = 10.59595977626158937081388054835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.885 y2[1] (analytic) = 1.3667104985115847510578675899006 y2[1] (numeric) = 1.3666728643582755984679894574949 absolute error = 3.76341533091525898781324057e-05 relative error = 0.0027536302201627954109165229781706 % h = 0.001 y1[1] (analytic) = 2.7739149871300816850428958523849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2944894485258786847696079171693 relative error = 10.616383338790069215336646811076 % h = 0.001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.1MB, time=48.84 NO POLE NO POLE x[1] = 0.886 y2[1] (analytic) = 1.3674847300144533651497969666091 y2[1] (numeric) = 1.3674465948245103861690379823271 absolute error = 3.81351899429789807589842820e-05 relative error = 0.0027887104774161476926117251709544 % h = 0.001 y1[1] (analytic) = 2.7745478895685605367370608467703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2951223509643575364637729115547 relative error = 10.636772645875965445153635767425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.887 y2[1] (analytic) = 1.3682595940325392551842860514642 y2[1] (numeric) = 1.3682209524368303354313003816613 absolute error = 3.86415957089197529856698029e-05 relative error = 0.0028241421348294816465690862185784 % h = 0.001 y1[1] (analytic) = 2.7751800174592143655260016289292 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2957544788550113652527136937136 relative error = 10.65712771763851684655829374219 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.888 y2[1] (analytic) = 1.3690350897909784676474441647341 y2[1] (numeric) = 1.3689959363766242474799446004453 absolute error = 3.91534143542201674995642888e-05 relative error = 0.0028599277437218962951247416456214 % h = 0.001 y1[1] (analytic) = 2.7758113701699153334332118751625 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2963858315657123331599239399469 relative error = 10.677448574164811163410288715048 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.889 y2[1] (analytic) = 1.369811216514275308724703225707 y2[1] (numeric) = 1.3697715458244033409782482109108 absolute error = 3.96706898719677464550147962e-05 relative error = 0.0028960698666869416411047568716082 % h = 0.001 y1[1] (analytic) = 2.7764419470693107823704478162497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2970164084651077820971598810341 relative error = 10.697735235509791774137497429935 % h = 0.001 TOP MAIN SOLVE Loop memory used=354.7MB, alloc=4.1MB, time=49.37 NO POLE NO POLE x[1] = 0.89 y2[1] (analytic) = 1.3705879734263031197964469426198 y2[1] (numeric) = 1.3705477799598012520275984125733 absolute error = 4.01934665018677688485300465e-05 relative error = 0.0029325710776075901590040150150705 % h = 0.001 y1[1] (analytic) = 2.7770717475268238654903337129732 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2976462089226208652170457777576 relative error = 10.717987721696264406914012902407 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.891 y2[1] (analytic) = 1.3713653597503050535646047550548 y2[1] (numeric) = 1.3713246379615740341674920322322 absolute error = 4.07217887310193971127228226e-05 relative error = 0.0029694339616711569594226919176601 % h = 0.001 y1[1] (analytic) = 2.7777007709126541777631561554249 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2982752323084511774898682202093 relative error = 10.738206052714903892723820912406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.892 y2[1] (analytic) = 1.3721433747088948508094344022757 y2[1] (numeric) = 1.3721021190076001583755355239708 absolute error = 4.12557012946924338988783049e-05 relative error = 0.0030066611153841688901112183991739 % h = 0.001 y1[1] (analytic) = 2.7783290165977783857772166093547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2989034779935753855039286741391 relative error = 10.758390248524260956020871242713 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.893 y2[1] (analytic) = 1.3729220175240576177757163607833 y2[1] (numeric) = 1.3728802222748805130674449691562 absolute error = 4.17952491771047082713916271e-05 relative error = 0.0030442551465871828371423221673176 % h = 0.001 y1[1] (analytic) = 2.7789564839539508567621124092591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2995309453497478564888244740435 relative error = 10.77854032905076904269734304801 % h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.1MB, time=49.90 NO POLE NO POLE x[1] = 0.894 y2[1] (analytic) = 1.373701287417150604187582764963 y2[1] (numeric) = 1.3736589469395384040970460764396 absolute error = 4.23404776122000905366885234e-05 relative error = 0.0030822186744695534898888302642356 % h = 0.001 y1[1] (analytic) = 2.7795831723537042868343171749836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.300157633749501286561029239768 relative error = 10.798656314188751185072973826444 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.895 y2[1] (analytic) = 1.3744811836089039818912027960585 y2[1] (numeric) = 1.3744382921768195547562741817559 absolute error = 4.28914320844271349286143026e-05 relative error = 0.0031205543295841508336384463977891 % h = 0.001 y1[1] (analytic) = 2.780209081170350328464432406308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3007835425661473281911444710924 relative error = 10.818738223800426903619388024426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.896 y2[1] (analytic) = 1.3752617053194216241245458968532 y2[1] (numeric) = 1.375218257161092105775174248324 absolute error = 4.34481583295183493716485292e-05 relative error = 0.0031592647538620276338217461811062 % h = 0.001 y1[1] (analytic) = 2.7808342097779802171654827883184 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3014086711737772168921948531028 relative error = 10.838786077715919145134424346859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.897 y2[1] (analytic) = 1.3760428517681818854134435423582 y2[1] (numeric) = 1.3759988410658466153219008666465 absolute error = 4.40107023352700915426757117e-05 relative error = 0.003198352600627037175967206373929 % h = 0.001 y1[1] (analytic) = 2.7814585575514653974016285193201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3020330189472623971283405841045 relative error = 10.858799895733261257082520378351 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=362.4MB, alloc=4.1MB, time=50.42 x[1] = 0.898 y2[1] (analytic) = 1.3768246221740383820931696705131 y2[1] (numeric) = 1.3767800430636960590027182545101 absolute error = 4.45791103423230904514160030e-05 relative error = 0.0032378205346104015256272518532279 % h = 0.001 y1[1] (analytic) = 2.7820821238664581477166687526331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3026565852622551474433808174175 relative error = 10.878779697618403997818269157053 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.899 y2[1] (analytic) = 1.3776070157552207734547592513822 y2[1] (numeric) = 1.3775618623263758298620002569853 absolute error = 4.51534288449435927589943969e-05 relative error = 0.0032776712319652305726421149445733 % h = 0.001 y1[1] (analytic) = 2.7827049080993922050817110238177 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3032793694951892048084230886021 relative error = 10.898725503105222582411314890871 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9 y2[1] (analytic) = 1.3783900317293355435152838485929 y2[1] (numeric) = 1.3783442980247437383822303464265 absolute error = 4.57337045918051330535021664e-05 relative error = 0.0033179073802809921242238059049881 % h = 0.001 y1[1] (analytic) = 2.7833269096274833884613823157136 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.303901371023280388188094380498 relative error = 10.91863733189552376379180407652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.901 y2[1] (analytic) = 1.3791736693133667834113024028072 y2[1] (numeric) = 1.3791273493287800124840016224719 absolute error = 4.63199845867709273007803353e-05 relative error = 0.003358531678597933311450740195672 % h = 0.001 y1[1] (analytic) = 2.7839481278287302215979581951327 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3045225892245272213246702599171 relative error = 10.938515203659052948936653884742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=366.2MB, alloc=4.1MB, time=50.95 x[1] = 0.902 y2[1] (analytic) = 1.3799579277236769744147048438388 y2[1] (numeric) = 1.3799110154075872975260168120436 absolute error = 4.69123160896768886880317952e-05 relative error = 0.0033995468374214535738646063045143 % h = 0.001 y1[1] (analytic) = 2.7845685620819145550127872371293 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3051430234777115547394993019137 relative error = 10.958359138033501349817941820303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.903 y2[1] (analytic) = 1.380742806176007771570165515639 y2[1] (numeric) = 1.3806952954293906563050882693477 absolute error = 4.75107466171152650772462913e-05 relative error = 0.0034409555787364294869549376219319 % h = 0.001 y1[1] (analytic) = 2.7851882117666021872243887354735 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3057626731623991869511008002579 relative error = 10.978169154624513168835759362738 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.904 y2[1] (analytic) = 1.3815283038854807879534227767624 y2[1] (numeric) = 1.3814801885615375690561379758741 absolute error = 4.81153239432188972848008883e-05 relative error = 0.0034827606360214916974036213404125 % h = 0.001 y1[1] (analytic) = 2.7858070762631434851826024812843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3063815376589404849093145460687 relative error = 10.997945273005692818458907553547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.905 y2[1] (analytic) = 1.3823144200665983795496005180982 y2[1] (numeric) = 1.3822656939704979334521975403965 absolute error = 4.87260961004460974029777017e-05 relative error = 0.003524964754263254231041286282557 % h = 0.001 y1[1] (analytic) = 2.7864251549526740039181701757212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3069996163484710036448822405056 relative error = 11.017687512718612174797844327024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.906 y2[1] (analytic) = 1.3831011539332444307507867196122 y2[1] (numeric) = 1.3830518108218640646044081989727 absolute error = 4.93431113803661463785206395e-05 relative error = 0.0035675706899704964385402089163683 % h = 0.001 y1[1] (analytic) = 2.787042447217115105407128827208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3076169086129121051338408919924 relative error = 11.037395893272817864835321795661 % h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.1MB, time=51.49 NO POLE NO POLE x[1] = 0.907 y2[1] (analytic) = 1.3838885046986851404720835485838 y2[1] (numeric) = 1.3838385382803506950620208149442 absolute error = 4.99664183344454100627336396e-05 relative error = 0.0036105812111882978439341111283062 % h = 0.001 y1[1] (analytic) = 2.7876589524391745766493972688437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3082334138349715763761093336281 relative error = 11.057070434145838587041176706266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.908 y2[1] (analytic) = 1.3846764715755698088853428833566 y2[1] (numeric) = 1.3846258755097949748123958789364 absolute error = 5.05960657748340729470044202e-05 relative error = 0.0036539990975121261611140442286045 % h = 0.001 y1[1] (analytic) = 2.7882746700023472469609377174681 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3088491313981442466876497822525 relative error = 11.076711154783192465098758890113 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.909 y2[1] (analytic) = 1.3854650537759316247698005289301 y2[1] (numeric) = 1.3854138216731564712810035088587 absolute error = 5.12321027751534887970200714e-05 relative error = 0.0036978271401018787435015089859226 % h = 0.001 y1[1] (analytic) = 2.78888959929091560447887508227 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3094640606867126042055871470544 relative error = 11.096318074598394434471500748796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.91 y2[1] (analytic) = 1.3862542505111884534788217738253 y2[1] (numeric) = 1.3862023759325171693314234499043 absolute error = 5.18745786712841473983239210e-05 relative error = 0.0037420681416958777321451009872436 % h = 0.001 y1[1] (analytic) = 2.7895037396899504118789575178716 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.310078201085747411605669582656 relative error = 11.115891212972963661539145657316 % h = 0.001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.1MB, time=52.04 NO POLE NO POLE x[1] = 0.911 y2[1] (analytic) = 1.3870440609921436255219703215436 y2[1] (numeric) = 1.3869915374490814712653450745503 absolute error = 5.25235430621542566252469933e-05 relative error = 0.0037867249166248191675253419518873 % h = 0.001 y1[1] (analytic) = 2.7901170905853113213047425044789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3106915519811083210314545692633 relative error = 11.135430589256430995034164636675 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.912 y2[1] (analytic) = 1.387834484428986725761612014616 y2[1] (numeric) = 1.3877813053831761968225673825577 absolute error = 5.31790458105289390446320583e-05 relative error = 0.0038318002908256763303840101555054 % h = 0.001 y1[1] (analytic) = 2.7907296513636474885078935259636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.311304112759444488234605590748 relative error = 11.154936222766346449509898759956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.913 y2[1] (analytic) = 1.3886255200312943832232641547054 y2[1] (numeric) = 1.3885716788942505831809990009713 absolute error = 5.38411370438000422651537341e-05 relative error = 0.0038772971018555575769192648285204 % h = 0.001 y1[1] (analytic) = 2.7913414214123981861989732056309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3119158828081951859256852704153 relative error = 11.174408132788286720572969518052 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.914 y2[1] (analytic) = 1.3894171670080310615189006084766 y2[1] (numeric) = 1.3893626571408762849566581841199 absolute error = 5.45098671547765622424243567e-05 relative error = 0.0039232181989055189337062185612165 % h = 0.001 y1[1] (analytic) = 2.7919524001197934166081195489314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3125268615155904163348316137158 relative error = 11.193846338575862731613500793778 % h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.1MB, time=52.56 NO POLE NO POLE x[1] = 0.915 y2[1] (analytic) = 1.390209424567549849882422275997 y2[1] (numeric) = 1.3901542392807473742036728136161 absolute error = 5.51852868024756787494623809e-05 relative error = 0.0039695664428143317177143974916586 % h = 0.001 y1[1] (analytic) = 2.7925625868748545232549927324916 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.313137048270651522981704797276 relative error = 11.213250859350727211767694185639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.916 y2[1] (analytic) = 1.3910022919175932548165018862618 y2[1] (numeric) = 1.3909464244706803404142803983564 absolute error = 5.58674469129144022214879054e-05 relative error = 0.0040163447060822054467987882157857 % h = 0.001 y1[1] (analytic) = 2.7931719810673948019273806695674 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3137464424631918016540927343518 relative error = 11.232621714302582304848294194797 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.917 y2[1] (analytic) = 1.3917957682652939923500114730661 y2[1] (numeric) = 1.3917392118666140905188280745212 absolute error = 5.65563986799018311833985449e-05 relative error = 0.0040635558728844663060399524737788 % h = 0.001 y1[1] (analytic) = 2.7937805820880201108678523733656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.31435504348381711059456443815 relative error = 11.251958922589187208979471250428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.918 y2[1] (analytic) = 1.3925898528171757809052402738607 y2[1] (numeric) = 1.3925326006236099488857726055748 absolute error = 5.72521935658320194676682859e-05 relative error = 0.0041112028390851914353010425416041 % h = 0.001 y1[1] (analytic) = 2.7943883893281294801678489316321 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3149628507239264798945609964165 relative error = 11.271262503336365846673638709412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=381.4MB, alloc=4.1MB, time=53.09 x[1] = 0.919 y2[1] (analytic) = 1.3933845447791541347741101844421 y2[1] (numeric) = 1.3933265898958516573216803822653 absolute error = 5.79548833024774524298021768e-05 relative error = 0.00415928851225079930335552090107 % h = 0.001 y1[1] (analytic) = 2.7949954021799157203686026984643 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3155698635757127200953147632487 relative error = 11.290532475638014565088704835516 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.92 y2[1] (analytic) = 1.3941798433565371582025952933256 y2[1] (numeric) = 1.3941211788366453750712274226249 absolute error = 5.86645198917831313678707007e-05 relative error = 0.0042078158116635964339190237932363 % h = 0.001 y1[1] (analytic) = 2.7956016200363660302682761024816 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.316176081432163029994988167266 relative error = 11.309768858556109866205242351083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.921 y2[1] (analytic) = 1.3949757477540263400825514114488 y2[1] (numeric) = 1.3949163665984196788171993719694 absolute error = 5.93811556066612653520394794e-05 relative error = 0.0042567876683352807488921586776386 % h = 0.001 y1[1] (analytic) = 2.7962070422912626039347122642647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3167815036870596036614243290491 relative error = 11.328971671120716166664036469614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.922 y2[1] (analytic) = 1.3957722571757173492501609054418 y2[1] (numeric) = 1.3957121523327255626804915028986 absolute error = 6.01048429917865696694025432e-05 relative error = 0.0043062070250204017940881368280621 % h = 0.001 y1[1] (analytic) = 2.7968116683391832369231904103635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3173861297349802366499024751479 relative error = 11.348140932329993587005447370691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.923 y2[1] (analytic) = 1.3965693708251008303901975360864 y2[1] (numeric) = 1.3965085351902364382201087152963 absolute error = 6.08356348643921700888207901e-05 relative error = 0.0043560768362297781126800629817708 % h = 0.001 y1[1] (analytic) = 2.797415497575501931698579866169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3179899589712989314252919309534 relative error = 11.367276661150205770052994878714 % h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.1MB, time=53.62 NO POLE NO POLE x[1] = 0.924 y2[1] (analytic) = 1.3973670879050632005453153977649 y2[1] (numeric) = 1.39730551432074813443316553633 absolute error = 6.15735843150661121498614349e-05 relative error = 0.0044064000682438720315574804165989 % h = 0.001 y1[1] (analytic) = 2.7980185293963895022612872055464 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3185929907921865019879992703308 relative error = 11.386378876515727728184541663484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.925 y2[1] (analytic) = 1.3981654076178874462295654496762 y2[1] (numeric) = 1.3981030888731788977548861204512 absolute error = 6.23187447085484746793292250e-05 relative error = 0.0044571796991261221257304501497589 % h = 0.001 y1[1] (analytic) = 2.7986207631988141779763919313308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3191952245946111777031039961152 relative error = 11.40544759732905371923541660328 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.926 y2[1] (analytic) = 1.3989643291652539211453425253694 y2[1] (numeric) = 1.3989012579955693920586042493953 absolute error = 6.30711696845290867382759741e-05 relative error = 0.004508418718736233625862074197712 % h = 0.001 y1[1] (analytic) = 2.7992221983805422066053668576022 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3197966597763392063320789223866 relative error = 11.424482842460805150778782049361 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.927 y2[1] (analytic) = 1.3997638517482411445029651037137 y2[1] (numeric) = 1.3997000208350826986557633321815 absolute error = 6.38309131584458472017715322e-05 relative error = 0.0045601201287434270339470016790272 % h = 0.001 y1[1] (analytic) = 2.7998228343401384565397801620681 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3203972957359354562664922268525 relative error = 11.443484630749738512529507614047 % h = 0.001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.1MB, time=54.16 NO POLE NO POLE x[1] = 0.928 y2[1] (analytic) = 1.4005639745673265999420895217925 y2[1] (numeric) = 1.4004993765380043162959164051129 absolute error = 6.45980293222836461731166796e-05 relative error = 0.0046122869426396452120841305883115 % h = 0.001 y1[1] (analytic) = 2.8004226704769670182363768749028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3209971318727640179630889396872 relative error = 11.462452981002753336618768782354 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.929 y2[1] (analytic) = 1.4013646968223875350541597083728 y2[1] (numeric) = 1.4012993242497421611667261317765 absolute error = 6.53725726453738874335765963e-05 relative error = 0.0046649221857527192092164835975168 % h = 0.001 y1[1] (analytic) = 2.8010217061911918048529383690117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3215961675869888045796504337961 relative error = 11.481387911994900185487541128929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.93 y2[1] (analytic) = 1.402166017712701761505092915567 y2[1] (numeric) = 1.4020998631148265668939648030432 absolute error = 6.61545978751946111281125238e-05 relative error = 0.004718028895259493090630140504899 % h = 0.001 y1[1] (analytic) = 2.8016199408837771520843192159106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.322194402279574151811031280695 relative error = 11.500289442469388667148110217096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.931 y2[1] (analytic) = 1.4029679364369484557574013260696 y2[1] (numeric) = 1.4029009922769102845415143370677 absolute error = 6.69441600381712158869890019e-05 relative error = 0.0047716101201989080349171994183979 % h = 0.001 y1[1] (analytic) = 2.8022173739564884171980615712348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3227918353522854169247736360192 relative error = 11.519157591137595477563663374874 % h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.1MB, time=54.68 NO POLE NO POLE x[1] = 0.932 y2[1] (analytic) = 1.4037704521932089603909488139114 y2[1] (numeric) = 1.4037027108787684826113662792888 absolute error = 6.77413144404777795825346226e-05 relative error = 0.0048256689214850459630150594826382 % h = 0.001 y1[1] (analytic) = 2.802814004811892577268988054311 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3233884662076895769957001190954 relative error = 11.537992376679072469896972492766 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.933 y2[1] (analytic) = 1.4045735641789675860215415380431 y2[1] (numeric) = 1.4045050180622987470436218024289 absolute error = 6.85461166688389779197356142e-05 relative error = 0.0048802083719201329638359175642019 % h = 0.001 y1[1] (analytic) = 2.8034098328533588266121748872515 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3239842942491558263388869520359 relative error = 11.556793817741554750380116779881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.934 y2[1] (analytic) = 1.4053772715911124138165504502244 y2[1] (numeric) = 1.4053079129685210812164917064945 absolute error = 6.93586225913326000587437299e-05 relative error = 0.0049352315562075027808962945319309 % h = 0.001 y1[1] (analytic) = 2.8040048574850591734137078606457 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3245793188808561731404199254301 relative error = 11.575561932940968800558131057383 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.935 y2[1] (analytic) = 1.4061815736259360986067632016613 y2[1] (numeric) = 1.4061113947375779059462964187759 absolute error = 7.01788883581926604667828854e-05 relative error = 0.0049907415709645206242467010835705 % h = 0.001 y1[1] (analytic) = 2.8045990781119690355586244951433 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3251735395077660352853365599277 relative error = 11.594296740861440625660398671 % h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.1MB, time=55.22 NO POLE NO POLE x[1] = 0.936 y2[1] (analytic) = 1.4069864694791366725936623366093 y2[1] (numeric) = 1.4069154625087340594874659938472 absolute error = 7.10069704026131061963427621e-05 relative error = 0.0050467415247354675718862639832572 % h = 0.001 y1[1] (analytic) = 2.8051924941398678356554465710368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3257669555356648353821586358212 relative error = 11.612998260055303928854538476572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.937 y2[1] (analytic) = 1.4077919583458183496513260657285 y2[1] (numeric) = 1.4077201154203767975325401135666 absolute error = 7.18429254415521187859521619e-05 relative error = 0.0051032345380043858247263066516295 % h = 0.001 y1[1] (analytic) = 2.8057851049753395952567080013595 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3263595663711365949834200661439 relative error = 11.631666509043108311138462603602 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.938 y2[1] (analytic) = 1.4085980394204923302221473173594 y2[1] (numeric) = 1.4085253526100157932121680870759 absolute error = 7.26868104765370099792302835e-05 relative error = 0.0051602237432078850790405602837944 % h = 0.001 y1[1] (analytic) = 2.8063769100257735282748838280223 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3269513714215705280015958928067 relative error = 11.650301506313627496627205840977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.939 y2[1] (analytic) = 1.409404711897077606805566171065 y2[1] (numeric) = 1.4093311732142831370951088508011 absolute error = 7.35386827944697104573202639e-05 relative error = 0.0052177122847479102802079169546533 % h = 0.001 y1[1] (analytic) = 2.8069679086993646335931269251073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3275423700951616333198389898917 relative error = 11.668903270323867582992048525319 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=400.5MB, alloc=4.1MB, time=55.76 x[1] = 0.94 y2[1] (analytic) = 1.410211974968901770039010184776 y2[1] (numeric) = 1.4101375763689333371882309684518 absolute error = 7.43985999684328507792163242e-05 relative error = 0.0052757033190044710214164722786123 % h = 0.001 y1[1] (analytic) = 2.8075581004051142868702197986342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3281325618009112865969318634186 relative error = 11.687471819499075316810372755571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.941 y2[1] (analytic) = 1.4110198278287018153702365346646 y2[1] (numeric) = 1.4109445612088433189365126310217 absolute error = 7.52666198584964337239036429e-05 relative error = 0.0053342000143483328508550851750378 % h = 0.001 y1[1] (analytic) = 2.8081474845528308315391496778929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3287219459486278312658617426773 relative error = 11.706007172232746393585606615963 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.942 y2[1] (analytic) = 1.4118282696686249503202692954725 y2[1] (numeric) = 1.4117521268680124252230416567882 absolute error = 7.61428006125250972276386843e-05 relative error = 0.0053932055511536707507708536609158 % h = 0.001 y1[1] (analytic) = 2.8087360605531301689987158998209 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3293105219489271687254279646053 relative error = 11.724509346886633782197522873436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.943 y2[1] (analytic) = 1.4126372996802294023361245984231 y2[1] (numeric) = 1.4125602724795624163690154913127 absolute error = 7.70272006669859671091071104e-05 relative error = 0.0054527231218106850516178117851727 % h = 0.001 y1[1] (analytic) = 2.8093238278174363479975793948635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3298982892132333477242914596479 relative error = 11.742978361790756073544067333187 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.944 y2[1] (analytic) = 1.41344691705448522723251581406 y2[1] (numeric) = 1.4133689971757374701337412074405 absolute error = 7.79198787477570987746066195e-05 relative error = 0.0055127559307381800443638400887794 % h = 0.001 y1[1] (analytic) = 2.8099107857579821532101648903185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3304852471537791529368769551029 relative error = 11.761414235243405853136797697275 % h = 0.001 TOP MAIN SOLVE Loop memory used=404.3MB, alloc=4.1MB, time=56.28 NO POLE NO POLE x[1] = 0.945 y2[1] (analytic) = 1.4142571209817751182217303183736 y2[1] (numeric) = 1.4141783000879041817146355053007 absolute error = 7.88208938709365070948130729e-05 relative error = 0.0055733071943961055538592944418141 % h = 0.001 y1[1] (analytic) = 2.8104969337878096930038272553123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3310713951836066927305393200967 relative error = 11.779816985511158097412916384683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.946 y2[1] (analytic) = 1.4150679106518952155308688124071 y2[1] (numeric) = 1.4149881803465515637472247123064 absolute error = 7.97303053436517836441001007e-05 relative error = 0.0056343801412980617360022410806168 % h = 0.001 y1[1] (analytic) = 2.8110822713207709863966942202884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3316567327165679861234062850728 relative error = 11.798186630828878593527780346215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.947 y2[1] (analytic) = 1.4158792852540559166056375781701 y2[1] (numeric) = 1.4157986370812910463051447831544 absolute error = 8.06481727648703004927950157e-05 relative error = 0.005695978012023767361261483538656 % h = 0.001 y1[1] (analytic) = 2.8116667977715285492055985132169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3322412591673255489323105780013 relative error = 11.816523189399732382392667453412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.948 y2[1] (analytic) = 1.4166912439768826868998834671338 y2[1] (numeric) = 1.4166096694208564769001412998256 absolute error = 8.15745560262099997421673082e-05 relative error = 0.0057581040592314918469398242224018 % h = 0.001 y1[1] (analytic) = 2.8122505125555559793835132646391 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3328249739513529791102253294235 relative error = 11.834826679395192224723472565874 % h = 0.001 TOP MAIN SOLVE Loop memory used=408.1MB, alloc=4.1MB, time=56.81 NO POLE NO POLE x[1] = 0.949 y2[1] (analytic) = 1.4175037860084168712500608318425 y2[1] (numeric) = 1.4174212764931041204820694715846 absolute error = 8.25095153127507679913602579e-05 relative error = 0.005820761547670451300376264939532 % h = 0.001 y1[1] (analytic) = 2.8128334150891385415459053441629 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3334078764849355412726174089473 relative error = 11.853097118955047089866896895646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.95 y2[1] (analytic) = 1.4183169105361165058338190262395 y2[1] (numeric) = 1.41823345742501265943889413498 absolute error = 8.34531111038463949248912595e-05 relative error = 0.005883953754193168835097159343248 % h = 0.001 y1[1] (analytic) = 2.8134155047893737506854221021026 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.333989966185170750412134166887 relative error = 11.871334526187410667171581799125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.951 y2[1] (analytic) = 1.4191306167468571307118985161905 y2[1] (numeric) = 1.4190462113426831935966897538442 absolute error = 8.44054041739371152087623463e-05 relative error = 0.0059476839677677994217327322152883 % h = 0.001 y1[1] (analytic) = 2.8139967810741719550743278016264 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3345712424699689548010398664108 relative error = 11.889538919168729899672522645768 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.952 y2[1] (analytic) = 1.419944903826932602952523058373 y2[1] (numeric) = 1.4198595373713392402196404192936 absolute error = 8.53664555933627328826390794e-05 relative error = 0.0060119554894904195353169174550268 % h = 0.001 y1[1] (analytic) = 2.8145772433622569183541068390228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3351517047580539180808189038072 relative error = 11.907710315943793539857979947351 % h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.1MB, time=57.34 NO POLE NO POLE x[1] = 0.953 y2[1] (analytic) = 1.4207597709620559103374748232099 y2[1] (numeric) = 1.4206734346353267340100398497283 absolute error = 8.63363267291763274349734816e-05 relative error = 0.0060767716325972818603851846564342 % h = 0.001 y1[1] (analytic) = 2.815156891073166400811651662531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3357313524689634005383637273154 relative error = 11.925848734525740727288983490874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.954 y2[1] (analytic) = 1.4215752173373599856490387558386 y2[1] (numeric) = 1.4214879022581140271082913908325 absolute error = 8.73150792459585407473650061e-05 relative error = 0.0061421357224770353150769648552144 % h = 0.001 y1[1] (analytic) = 2.8157357236272527398414541135974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3363101850230497395681661783818 relative error = 11.943954192896069587842400811363 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.955 y2[1] (analytic) = 1.4223912421373985215370018882395 y2[1] (numeric) = 1.4223029393622918890929080155741 absolute error = 8.83027751066324440938726654e-05 relative error = 0.006208051096682910655236494663955 % h = 0.001 y1[1] (analytic) = 2.8163137404456834295932197284128 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3368882018414804293199317931972 relative error = 11.962026709004645854349413976456 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.956 y2[1] (analytic) = 1.4232078445461467859648927355918 y2[1] (numeric) = 1.423118545069573506980512324205 absolute error = 8.92994765732789843804113868e-05 relative error = 0.0062745211049448719192884166295848 % h = 0.001 y1[1] (analytic) = 2.8168909409504416998043253521668 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3374654023462386995310374169512 relative error = 11.980066300769711508402118342213 % h = 0.001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.1MB, time=57.88 NO POLE NO POLE x[1] = 0.957 y2[1] (analytic) = 1.4240250237470024382346453306867 y2[1] (numeric) = 1.423934718500794485225836544261 absolute error = 9.03052462079530088087864257e-05 relative error = 0.0063415491091817339744423467327191 % h = 0.001 y1[1] (analytic) = 2.8174673245643270938165412336083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3380417859601240935432532983927 relative error = 11.998072986077893443101823687374 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.958 y2[1] (analytic) = 1.4248427789227863455888718718004 y2[1] (numeric) = 1.4247514587759128457217225305616 absolute error = 9.13201468734998671493412388e-05 relative error = 0.0064091384835132464245538893255963 % h = 0.001 y1[1] (analytic) = 2.8180428907109560457764395832387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3386173521067530455031516480231 relative error = 12.016046782784212146523501950666 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.959 y2[1] (analytic) = 1.4256611092557434003899273818234 y2[1] (numeric) = 1.4255687650140090277991217652104 absolute error = 9.23442417343725908056166130e-05 relative error = 0.0064772926142721441397382895727333 % h = 0.001 y1[1] (analytic) = 2.8186176388147624570189123947776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.339192100210559456745624459562 relative error = 12.033987708712090405671686691323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.96 y2[1] (analytic) = 1.4264800139275433378749491996481 y2[1] (numeric) = 1.4263866363332858882270953575948 absolute error = 9.33775942574496478538420533e-05 relative error = 0.0065460149000161646675971057595336 % h = 0.001 y1[1] (analytic) = 2.8191915683009982716332221464304 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3397660296967952713599342112148 relative error = 12.051895781653362030703987375677 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=419.6MB, alloc=4.1MB, time=58.42 x[1] = 0.961 y2[1] (analytic) = 1.4272994921192815544860535488458 y2[1] (numeric) = 1.4272050718510687012128140443861 absolute error = 9.44202682128532732395044597e-05 relative error = 0.0066153087515400327856780016780926 % h = 0.001 y1[1] (analytic) = 2.8197646785957340512110098159569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3403391399915310509377218807413 relative error = 12.069771019368280599199236671347 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.962 y2[1] (analytic) = 1.4281195430114799267748708535018 y2[1] (numeric) = 1.4280240706838051584015581895394 absolute error = 9.54723276747683733126639624e-05 relative error = 0.0066851775918874124545430447052243 % h = 0.001 y1[1] (analytic) = 2.820336969125859548775685461578 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3409114305216565485023975263624 relative error = 12.087613439585528220248141113821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.963 y2[1] (analytic) = 1.4289401657840876308806008967442 y2[1] (numeric) = 1.4288436319470653688767177842938 absolute error = 9.65338370222620038831124504e-05 relative error = 0.0067556248563628264305717914629204 % h = 0.001 y1[1] (analytic) = 2.8209084393190842818926274393802 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3414829007148812816193395041646 relative error = 12.105423060002224318145154807288 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.964 y2[1] (analytic) = 1.4297613596164819625807683439772 y2[1] (numeric) = 1.4296637547555418591597924471722 absolute error = 9.76048609401034209758968050e-05 relative error = 0.0068266539925435437973719911640222 % h = 0.001 y1[1] (analytic) = 2.8214790886039381049596171470655 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3420535499997351046863292118499 relative error = 12.123199898283934435461142240683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.965 y2[1] (analytic) = 1.4305831236874691579138585801337 y2[1] (numeric) = 1.4304844382230495732103914239814 absolute error = 9.86854644195847034671561523e-05 relative error = 0.006898268460291435674412980022335 % h = 0.001 y1[1] (analytic) = 2.8220489164097717806769370036593 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3426233778055687804036490684437 relative error = 12.140943972064679055277239850195 % h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.1MB, time=58.96 NO POLE NO POLE x[1] = 0.966 y2[1] (analytic) = 1.4314054571752852143730132383785 y2[1] (numeric) = 1.4313056814625258724262335878121 absolute error = 9.97757127593419467796505664e-05 relative error = 0.0069704717317647993612348195432425 % h = 0.001 y1[1] (analytic) = 2.8226179221667575506965601951263 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3431923835625545504232722599107 relative error = 12.158655298946942442361166649562 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.967 y2[1] (analytic) = 1.4322283592575967126699642266353 y2[1] (numeric) = 1.432127483586030535643147439039 absolute error = 0.0001008756715661770268167875963 relative error = 0.0070432672914301511753199894470781 % h = 0.001 y1[1] (analytic) = 2.8231861053058897054498615367527 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3437605667016867051765736015371 relative error = 12.176333896501681503068072088021 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.968 y2[1] (analytic) = 1.4330518291115016390683844880724 y2[1] (numeric) = 1.4329498437047457591350711053204 absolute error = 0.000101985406755879933313382752 relative error = 0.0071166586360739882414440238142973 % h = 0.001 y1[1] (analytic) = 2.8237534652589851531532796246302 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3443279266547821528799916894146 relative error = 12.193979782268334663748844291454 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.969 y2[1] (analytic) = 1.4338758659135302082858331622636 y2[1] (numeric) = 1.4337727609289761566140523415988 absolute error = 0.0001031049845540516717808206648 relative error = 0.0071906492748145194900469179093747 % h = 0.001 y1[1] (analytic) = 2.8243200014586839879913612706282 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3448944628544809877180733354126 relative error = 12.211592973754830767449634003948 % h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.1MB, time=59.49 NO POLE NO POLE x[1] = 0.97 y2[1] (analytic) = 1.4347004688396456869634722451501 y2[1] (numeric) = 1.4345962343681487592302485301003 absolute error = 0.0001042344714969277332237150498 relative error = 0.0072652427291133661218884754605367 % h = 0.001 y1[1] (analytic) = 2.8248857133384500574766200378563 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3454601747342470572033321026407 relative error = 12.229173488437597988687178882994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.971 y2[1] (analytic) = 1.4355256370652452177027312781524 y2[1] (numeric) = 1.4354202631308130155719266803351 absolute error = 0.0001053739344322021308045978173 relative error = 0.0073404425327872317959680511183883 % h = 0.001 y1[1] (analytic) = 2.8254506003325715289856415168064 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3460250617283685287123535815908 relative error = 12.246721343761572766085339320889 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.972 y2[1] (analytic) = 1.4363513697651606436680960298383 y2[1] (numeric) = 1.4362448463246407916654634290972 absolute error = 0.0001065234405198520026326007411 relative error = 0.0074162522320195427974024139229138 % h = 0.001 y1[1] (analytic) = 2.8260146618761614554708688061158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3465891232719584551975808709002 relative error = 12.264236557140208752659080675839 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.973 y2[1] (analytic) = 1.4371776661136593337551965674268 y2[1] (numeric) = 1.4370699830564263709753450404644 absolute error = 0.0001076830572329627798515269624 relative error = 0.0074926753853720584416647533602899 % h = 0.001 y1[1] (analytic) = 2.8265778974051583403475024862134 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3471523588009553400742145509978 relative error = 12.281719145955485783532957707705 % h = 0.001 TOP MAIN SOLVE Loop memory used=431.0MB, alloc=4.1MB, time=60.03 NO POLE NO POLE x[1] = 0.974 y2[1] (analytic) = 1.4380045252844450083233695501071 y2[1] (numeric) = 1.4378956724320864544041674057986 absolute error = 0.0001088528523585539192021443085 relative error = 0.0075697155637964519712932120588079 % h = 0.001 y1[1] (analytic) = 2.8271403063563267015549501989961 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3477147677521237012816622637805 relative error = 12.299169127557918860881975133604 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.975 y2[1] (analytic) = 1.4388319464506585654918690116816 y2[1] (numeric) = 1.4387219135566601602926360437453 absolute error = 0.0001100328939984051992329679363 relative error = 0.0076473763506458622008787988780274 % h = 0.001 y1[1] (analytic) = 2.8277018881672576347922617721328 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3482763495630546345189738369172 relative error = 12.316586519266567155883513556413 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.976 y2[1] (analytic) = 1.4396599287848789079988993363884 y2[1] (numeric) = 1.4395487055343090244195661002342 absolute error = 0.0001112232505698835793332361542 relative error = 0.0077256613416864161658401521999133 % h = 0.001 y1[1] (analytic) = 2.8282626422763693759269866526067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3488371036721663756536987173911 relative error = 12.333971338369043027469822583032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.977 y2[1] (analytic) = 1.4404884714591237706226435689417 y2[1] (numeric) = 1.4403760474683170000018823484786 absolute error = 0.0001124239908067706207612204631 relative error = 0.0078045741451087230301864279431046 % h = 0.001 y1[1] (analytic) = 2.8288225681229078625768912406878 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3493970295187048623036033054722 relative error = 12.351323602121521057671392747765 % h = 0.001 TOP MAIN SOLVE Loop memory used=434.8MB, alloc=4.1MB, time=60.56 NO POLE NO POLE x[1] = 0.978 y2[1] (analytic) = 1.4413175736448505481634596378282 y2[1] (numeric) = 1.4412039384610904576946191889758 absolute error = 0.0001136351837600904688404488524 relative error = 0.007884118381539339508159617741207 % h = 0.001 y1[1] (analytic) = 2.8293816651469472948639745426626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.349956126542744294590686607447 relative error = 12.368643327748747103342324897523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.979 y2[1] (analytic) = 1.4421472345129571239864165097351 y2[1] (numeric) = 1.4420323776141581855909206495071 absolute error = 0.000114856898798938395495860228 relative error = 0.0079642976840522070543339023341458 % h = 0.001 y1[1] (analytic) = 2.8299399327893906953402213883531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3505143941851876950669334531375 relative error = 12.385930532444047364059619988651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.98 y2[1] (analytic) = 1.4429774532337826991233417326401 y2[1] (numeric) = 1.4428613640281713892220403851375 absolute error = 0.0001160892056113099013013475026 relative error = 0.0080451156981800610764322508676532 % h = 0.001 y1[1] (analytic) = 2.8304973704919704680845332877192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3510718318877674678112453525036 relative error = 12.403185233369337465989113798188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.981 y2[1] (analytic) = 1.4438082289771086219335512655861 y2[1] (numeric) = 1.4436908968029036915573416782159 absolute error = 0.0001173321742049303762095873702 relative error = 0.008126576081925812424799429825064 % h = 0.001 y1[1] (analytic) = 2.8310539776972489569702778296585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3516284390930459566969898944429 relative error = 12.420407447655131561511579873773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=438.7MB, alloc=4.1MB, time=61.09 x[1] = 0.982 y2[1] (analytic) = 1.4446395609121592183224319344801 y2[1] (numeric) = 1.4445209750372511330042974383752 absolute error = 0.0001185858749080853181344961049 relative error = 0.0082086825057739014121459242838527 % h = 0.001 y1[1] (analytic) = 2.831609753848619003102898355503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3521842152444160028296104202874 relative error = 12.437597192400551444403320144884 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.983 y2[1] (analytic) = 1.4454714482076026225170462954026 y2[1] (numeric) = 1.4453515978292321714084902025322 absolute error = 0.0001198503783704511085560928704 relative error = 0.0082914386527016246168490384093322 % h = 0.001 y1[1] (analytic) = 2.8321646983903045014270264696466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.352739159786101501153738534431 relative error = 12.454754484673335680366356001541 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.984 y2[1] (analytic) = 1.4463038900315516083979291298914 y2[1] (numeric) = 1.4461827642759876820536121348874 absolute error = 0.000121125755563926344316995004 relative error = 0.0083748482181904347227656708230527 % h = 0.001 y1[1] (analytic) = 2.8327188107673609565025407802402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3532932721631579562292528450246 relative error = 12.471879341509848752704123324131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.985 y2[1] (analytic) = 1.4471368855515644213862442404742 y2[1] (numeric) = 1.4470144734737809576614650269253 absolute error = 0.0001224120777834637247792135489 relative error = 0.0084589149102372136481759926993707 % h = 0.001 y1[1] (analytic) = 2.8332720904256760374490160939396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.353846551821473037175728158724 relative error = 12.488971779915090222939362927146 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.986 y2[1] (analytic) = 1.4479704339346456108854696593607 y2[1] (numeric) = 1.4478467245179977083919602974143 absolute error = 0.0001237094166479024935093619464 relative error = 0.0085436424493655192161385305371951 % h = 0.001 y1[1] (analytic) = 2.8338245368119701320580081203051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3543989982077671317847201850895 relative error = 12.506031816862703906171683169521 % h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.1MB, time=61.64 NO POLE NO POLE x[1] = 0.987 y2[1] (analytic) = 1.4488045343472468632767788286789 y2[1] (numeric) = 1.4486795165031460618431189924066 absolute error = 0.0001250178441008014336598362723 relative error = 0.0086290345686368056181950105715254 % h = 0.001 y1[1] (analytic) = 2.8343761493737969000726195736126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.354950610769593899799331638397 relative error = 12.523059469294987060973054092611 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.988 y2[1] (analytic) = 1.4496391859552678354672847569453 y2[1] (numeric) = 1.4495128485228565630510717852384 absolute error = 0.0001263374324112724162129717069 relative error = 0.0087150950136616179230177959482156 % h = 0.001 y1[1] (analytic) = 2.8349269275595438256337943925575 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3555013889553408253605064573419 relative error = 12.540054754122899593620272382406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.989 y2[1] (analytic) = 1.4504743879240569889903136035916 y2[1] (numeric) = 1.4503467196698821744900589765297 absolute error = 0.0001276682541748145002546270619 relative error = 0.0088018275426107608812438790632536 % h = 0.001 y1[1] (analytic) = 2.8354768708184327688927876316028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3560513322142297686194996963872 relative error = 12.557017688226073276464213723396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.99 y2[1] (analytic) = 1.4513101394184124246568735913464 y2[1] (numeric) = 1.4511811290360982760724304941845 absolute error = 0.0001290103823141485844430971619 relative error = 0.0088892359262264422773872187332914 % h = 0.001 y1[1] (analytic) = 2.8360259786005205167892594115471 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3566004399963175165159714763315 relative error = 12.573948288452820980236463725889 % h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.1MB, time=62.16 NO POLE NO POLE x[1] = 0.991 y2[1] (analytic) = 1.4521464396025827177574845950707 y2[1] (numeric) = 1.4520160757125026651486458933905 absolute error = 0.0001303638900800526088387016802 relative error = 0.0089773239478333910793657721214363 % h = 0.001 y1[1] (analytic) = 2.8365742503566993329944421512648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3571487117524963327211542160492 relative error = 12.590846571620145920094690574926 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.992 y2[1] (analytic) = 1.4529832876402677538135332052885 y2[1] (numeric) = 1.4528515587892155565072743566194 absolute error = 0.0001317288510521973062588486691 relative error = 0.0090660954033499506358209030733355 % h = 0.001 y1[1] (analytic) = 2.8371216855386975070188311374976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.357696146934494506745543202282 relative error = 12.607712554513750915208891875328 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.993 y2[1] (analytic) = 1.4538206826946195648773175151265 y2[1] (numeric) = 1.4536875773554795823749946936267 absolute error = 0.0001331053391399825023228214998 relative error = 0.0091555541012991471710449890027902 % h = 0.001 y1[1] (analytic) = 2.8376682835990799024838493250508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3582427449948769022105613898352 relative error = 12.624546253888047661691414862026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.994 y2[1] (analytic) = 1.4546586239282431663799453306873 y2[1] (numeric) = 1.4545241304996597924165953414519 absolute error = 0.0001344934285833739633499892354 relative error = 0.00924570386281973382696803503813 % h = 0.001 y1[1] (analytic) = 2.8382140439912485045569380957782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3587885053870455042836501605626 relative error = 12.641347686466166018674413216221 % h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.1MB, time=62.69 NO POLE NO POLE x[1] = 0.995 y2[1] (analytic) = 1.4554971105031973945262489570286 y2[1] (numeric) = 1.4553612173092436537349743644183 absolute error = 0.0001358931939537407912745926103 relative error = 0.009336548521677210501285974573171 % h = 0.001 y1[1] (analytic) = 2.8387589661694429665495265413068 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3593334275652399662762386060912 relative error = 12.658116868939963307339165183617 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.996 y2[1] (analytic) = 1.4563361415809957442358791649033 y2[1] (numeric) = 1.4561988368708410508711394541332 absolute error = 0.0001373047101546933647397107701 relative error = 0.0094280919242748197304421260053838 % h = 0.001 y1[1] (analytic) = 2.8393030495887411556773326715804 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3598775109845381554040447363648 relative error = 12.674853817970033622702436539963 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.997 y2[1] (analytic) = 1.4571757163226072076297403972349 y2[1] (numeric) = 1.4570369882701842858042079294876 absolute error = 0.0001387280524229218255324677473 relative error = 0.0095203379296645188657990238303342 % h = 0.001 y1[1] (analytic) = 2.839846293705059697982450788966 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3604207551008566977091628537504 relative error = 12.691558550185717157965828198815 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.998 y2[1] (analytic) = 1.4580158338884571130609287289657 y2[1] (numeric) = 1.4578756705921280779514067366565 absolute error = 0.0001401632963290351095219923092 relative error = 0.0096132904095579287909605850859721 % h = 0.001 y1[1] (analytic) = 2.8403886979751545224166801058793 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3609631593709515221433921706637 relative error = 12.708231082185109541234801915319 % h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.1MB, time=63.23 NO POLE NO POLE x[1] = 0.999 y2[1] (analytic) = 1.4588564934384279646893335494061 y2[1] (numeric) = 1.4587148829206495641680724490988 absolute error = 0.0001416105177784005212611003073 relative error = 0.0097069532483372594278243454047017 % h = 0.001 y1[1] (analytic) = 2.8409302618566214040855505226477 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3615047232524184038122625874321 relative error = 12.724871430535071184414828616052 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1 y2[1] (analytic) = 1.459697694131860282599063392557 y2[1] (numeric) = 1.4595546243388482987476512675572 absolute error = 0.0001430697930119838514121249998 relative error = 0.0098013303430662122785603402326044 % h = 0.001 y1[1] (analytic) = 2.8414709848078965066525023216303 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3620454462036935063792143864147 relative error = 12.74147961177123664409285238639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.001 y2[1] (analytic) = 1.4605394351275534434578557980464 y2[1] (numeric) = 1.4603948939289462534216990200583 absolute error = 0.0001445411986071900361567779881 relative error = 0.0098964256035008602503271507962476 % h = 0.001 y1[1] (analytic) = 2.8420108662882569239026773734589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3625853276840539236293894382433 relative error = 12.758055642398023994213009081703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.002 y2[1] (analytic) = 1.4613817155837665217176305433427 y2[1] (numeric) = 1.4612356907722878173598811619127 absolute error = 0.00014602481147870435774938143 relative error = 0.0099922429521005050091467189388908 % h = 0.001 y1[1] (analytic) = 2.842549905757821220465780291656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3631243671536182201924923564404 relative error = 12.774599538888644210356281905063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=457.7MB, alloc=4.1MB, time=63.76 x[1] = 1.003 y2[1] (analytic) = 1.4622245346582191313553450467597 y2[1] (numeric) = 1.4620770139493397971699727757147 absolute error = 0.000147520708879334185372271045 relative error = 0.010088786324038512108967794409226 % h = 0.001 y1[1] (analytic) = 2.8430881026775499716974688128113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3636625640733469714241808775957 relative error = 12.791111317685110565434517119844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.004 y2[1] (analytic) = 1.4630678915080922681533102004696 y2[1] (numeric) = 1.4629188625396914168978585713426 absolute error = 0.000149028968400851255451629127 relative error = 0.01018605966721312414155334939681 % h = 0.001 y1[1] (analytic) = 2.8436254565092463027187335209743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3641999179050433024454455857587 relative error = 12.807590995198248036609961348992 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.005 y2[1] (analytic) = 1.4639117852900291525181243532775 y2[1] (numeric) = 1.4637612356220543180275328859586 absolute error = 0.0001505496679748344905914673189 relative error = 0.010284066942258252152430013069202 % h = 0.001 y1[1] (analytic) = 2.844161966715556426612727876925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3647364281113534263394399417094 relative error = 12.82403858780770272325221766133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.006 y2[1] (analytic) = 1.4647562151601360728373826242936 y2[1] (numeric) = 1.4646041322742625594810996840088 absolute error = 0.0001520828858735133562829402848 relative error = 0.01038281212255424556773757913369 % h = 0.001 y1[1] (analytic) = 2.8446976327599701817785103555398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3652720941557671815052224203242 relative error = 12.840454111861951275745250867654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.007 y2[1] (analytic) = 1.4656011802739832293733181908644 y2[1] (numeric) = 1.4654475515732726176187725572231 absolute error = 0.0001536287007106117545456336413 relative error = 0.010482299194238640876413957400618 % h = 0.001 y1[1] (analytic) = 2.8452324541068215684411613375549 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3658069155026185681678734023393 relative error = 12.856837583678310334957803152915 % h = 0.001 TOP MAIN SOLVE Loop memory used=461.5MB, alloc=4.1MB, time=64.30 NO POLE NO POLE x[1] = 1.008 y2[1] (analytic) = 1.4664466797866055786925316571923 y2[1] (numeric) = 1.4662914925951633862388747246153 absolute error = 0.000155187191442192453656932577 relative error = 0.010582532156216889311745610805217 % h = 0.001 y1[1] (analytic) = 2.8457664302212892843177382456532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3663408916170862840444503104376 relative error = 12.873189019542945982191309363741 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.009 y2[1] (analytic) = 1.467292712852503678630964073983 y2[1] (numeric) = 1.467135954415136176577839032483 absolute error = 0.0001567584373675020531250415 relative error = 0.010683515020173063775905577300329 % h = 0.001 y1[1] (analytic) = 2.8462995605693972594385332589671 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3668740219651942591652453237515 relative error = 12.889508435710883199420126960964 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.01 y2[1] (analytic) = 1.4681392786256445337932686442208 y2[1] (numeric) = 1.4679809361075147173102079544079 absolute error = 0.0001583425181298164830606898129 relative error = 0.010785251810580545250690656555261 % h = 0.001 y1[1] (analytic) = 2.846831844618015190123098784782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3674063060138121898498108495664 relative error = 12.905795848406015339639618842126 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.011 y2[1] (analytic) = 1.4689863762594624415857356157674 y2[1] (numeric) = 1.4688264367457451545486335912555 absolute error = 0.0001599395137172870371020245119 relative error = 0.010887746564712688937256278213614 % h = 0.001 y1[1] (analytic) = 2.8473632818348590721105067114598 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3679377432306560718372187762442 relative error = 12.922051273821113607138347947521 % h = 0.001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.1MB, time=64.83 NO POLE NO POLE x[1] = 1.012 y2[1] (analytic) = 1.4698340049068598387819243279326 y2[1] (numeric) = 1.469672455402396051843877671175 absolute error = 0.0001615495044637869380466567576 relative error = 0.010991003332653470367231997048317 % h = 0.001 y1[1] (analytic) = 2.8478938716884917328433083123683 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3684683330842887325700203771527 relative error = 12.938274728117836547511360792789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.013 y2[1] (analytic) = 1.4706821637202081486201558464534 y2[1] (numeric) = 1.4705189911491583901848115495998 absolute error = 0.0001631725710497584353442968536 relative error = 0.011095026177308111727182513763293 % h = 0.001 y1[1] (analytic) = 2.8484236136483233629046625169003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3689980750441203626313745816847 relative error = 12.95446622742673954723225282928 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.014 y2[1] (analytic) = 1.4715308518513486284320190894609 y2[1] (numeric) = 1.4713660430568455679984162092469 absolute error = 0.000164808794503060433602880214 relative error = 0.011199819174413688637958633727481 % h = 0.001 y1[1] (analytic) = 2.8489525071846120466081011114986 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.369526968580409046334813176283 relative error = 12.970625787847284342602421828244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.015 y2[1] (analytic) = 1.472380068451593217801042815998 y2[1] (numeric) = 1.4722136101953934011497822601174 absolute error = 0.0001664582561998166512605558806 relative error = 0.011305386412549717630059681937467 % h = 0.001 y1[1] (analytic) = 2.8494805517684642917394002809662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3700550131642612914661123457506 relative error = 12.98675342544784853789662632419 % h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.1MB, time=65.37 NO POLE NO POLE x[1] = 1.016 y2[1] (analytic) = 1.4732298126717253872506853184886 y2[1] (numeric) = 1.4730616916338601229421099394961 absolute error = 0.0001681210378652643085753789925 relative error = 0.011411731993148724555703626522903 % h = 0.001 y1[1] (analytic) = 2.850007746871835558450028748234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3705822082676325581767408130184 relative error = 13.002849156265735132524674544174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.017 y2[1] (analytic) = 1.4740800836620009874607931312371 y2[1] (numeric) = 1.4739102864404263841167091119518 absolute error = 0.0001697972215746033440840192853 relative error = 0.011518860030506794177873556610766 % h = 0.001 y1[1] (analytic) = 2.8505340919675307873016436191816 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.371108553363327787028355683966 relative error = 13.018912996307182057029775201237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.018 y2[1] (analytic) = 1.4749308805721490990116795385718 y2[1] (numeric) = 1.4747593936823952528529992693371 absolute error = 0.0001714868897538461586802692347 relative error = 0.011626774651794101176179248742506 % h = 0.001 y1[1] (analytic) = 2.8510595865292049264611058880601 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3716340479250019261878179528445 relative error = 13.034944961547371717744785049455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.019 y2[1] (analytic) = 1.4757822025513728826549731386242 y2[1] (numeric) = 1.4756090124261922147685095307886 absolute error = 0.0001731901251806678864636078356 relative error = 0.01173547999706542280894037077996 % h = 0.001 y1[1] (analytic) = 2.8515842300313634580454884085451 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3721586914271604577722004733295 relative error = 13.050945067930440549928289192668 % h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.1MB, time=65.89 NO POLE NO POLE x[1] = 1.02 y2[1] (analytic) = 1.4766340487483504301103861919662 y2[1] (numeric) = 1.4764591417373651729188786427267 absolute error = 0.0001749070109852571915075492395 relative error = 0.011844980219270633470463447451055 % h = 0.001 y1[1] (analytic) = 2.8521080219493629236165499854554 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3726824833451599233432620502398 relative error = 13.066913331369488579203148816855 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.021 y2[1] (analytic) = 1.4774864183112356153875519584076 y2[1] (numeric) = 1.4773097806805844477978549788557 absolute error = 0.0001766376306511675896969795519 relative error = 0.01195527948426518138204807962034 % h = 0.001 y1[1] (analytic) = 2.8526309617594114488241500927072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3732054231552084485508621574916 relative error = 13.082849767746588991120847284876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.022 y2[1] (analytic) = 1.4783393103876589466320797001881 y2[1] (numeric) = 1.4781609283196427773372965401638 absolute error = 0.0001783820680161692947831600243 relative error = 0.012066381970820547654819103114101 % h = 0.001 y1[1] (analytic) = 2.8531530489385692671980795741338 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3737275103343662669247916389182 relative error = 13.098754392912797708675659399691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.023 y2[1] (analytic) = 1.4791927241247284184949755055798 y2[1] (numeric) = 1.4790125837174553169071709549231 absolute error = 0.0001801404072731015878045506567 relative error = 0.012178291870634687962040424563909 % h = 0.001 y1[1] (analytic) = 2.8536742829647492430877835353817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3742487443605462428144956001661 relative error = 13.114627222688162977593360115685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=476.8MB, alloc=4.1MB, time=66.43 x[1] = 1.024 y2[1] (analytic) = 1.4800466586690303650245765635492 y2[1] (numeric) = 1.4798647459360596393155554786895 absolute error = 0.0001819127329707257090210848597 relative error = 0.012291013388342457058123213780321 % h = 0.001 y1[1] (analytic) = 2.854194663316717393749453487206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3747691247125143934761655519904 relative error = 13.130468272861734959219878065323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.025 y2[1] (analytic) = 1.4809011131666303130801459976169 y2[1] (numeric) = 1.4807174140366157348086369943029 absolute error = 0.000183699130014578271509003314 relative error = 0.012404550741526016381095996987481 % h = 0.001 y1[1] (analytic) = 2.8547141894740934105799666531149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3752886508698904103066787178993 relative error = 13.146277559191575330835985977277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.026 y2[1] (analytic) = 1.4817560867630738362662748453913 y2[1] (numeric) = 1.481570587079406011070712011887 absolute error = 0.0001854996836678251955628335043 relative error = 0.012518908160725224974857014443542 % h = 0.001 y1[1] (analytic) = 2.8552328609173511794971512074687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3758073223131481792238632722531 relative error = 13.162055097404766893224804400418 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.027 y2[1] (analytic) = 1.4826115786033874093872372494439 y2[1] (numeric) = 1.4824242641238352932241866688494 absolute error = 0.0001873144795521161630505805945 relative error = 0.012634089889448013967080011325927 % h = 0.001 y1[1] (analytic) = 2.8557506771278193004658570638093 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3763251385236163001925691285937 relative error = 13.177800903197423185319577122801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=480.6MB, alloc=4.1MB, time=66.96 x[1] = 1.028 y2[1] (analytic) = 1.4834675878320792634204444052437 y2[1] (numeric) = 1.4832784442284308238295767298815 absolute error = 0.0001891436036484395908676753622 relative error = 0.012750100184180744838193454581701 % h = 0.001 y1[1] (analytic) = 2.8562676375876816061693126873962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3768420989834786058960247521806 relative error = 13.193514992234698105759856294169 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.029 y2[1] (analytic) = 1.4843241135931402410081422927682 y2[1] (numeric) = 1.4841331264508422628855075869588 absolute error = 0.0001909871422979781226347058094 relative error = 0.012866943314398551716400041252571 % h = 0.001 y1[1] (analytic) = 2.8567837417799776798252492606312 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3773582031757746795519613254156 relative error = 13.209197380150795541184912531271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.03 y2[1] (analytic) = 1.4851811550300446524664977001626 y2[1] (numeric) = 1.4849883098478416878287142593405 absolute error = 0.0001928451822029646377834408221 relative error = 0.012984623562575667933248317451119 % h = 0.001 y1[1] (analytic) = 2.8572989891886033721462743852944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3778734505844003718729864500788 relative error = 13.224848082548979001093860215981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.031 y2[1] (analytic) = 1.4860387112857511323112165304354 y2[1] (numeric) = 1.4858439934753235935340413935698 absolute error = 0.0001947178104275387771751368656 relative error = 0.013103145224195737073811292865519 % h = 0.001 y1[1] (analytic) = 2.8578133792983113174439783612591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3783878406941083171706904260435 relative error = 13.240467115001581259102660793387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.032 y2[1] (analytic) = 1.4868967815027034962988378656402 y2[1] (numeric) = 1.4867001763883048923144432634736 absolute error = 0.0001966051143986039843946021666 relative error = 0.013222512607762108755068143769417 % h = 0.001 y1[1] (analytic) = 2.8583269115947114488762569376219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3789013729905084486029690024063 relative error = 13.256054493050014000428837148847 % h = 0.001 TOP MAIN SOLVE Loop memory used=484.4MB, alloc=4.1MB, time=67.50 NO POLE NO POLE x[1] = 1.033 y2[1] (analytic) = 1.4877553648228315989828467473245 y2[1] (numeric) = 1.4875568576409249139209837701629 absolute error = 0.0001985071819066850618629771616 relative error = 0.013342730034808119365624479686882 % h = 0.001 y1[1] (analytic) = 2.85883958556427151283733528897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3794140469600685125640473537544 relative error = 13.27161023220477747543540009674 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.034 y2[1] (analytic) = 1.4886144603875521917837481172009 y2[1] (numeric) = 1.4884140362864454055428364420325 absolute error = 0.0002004241011067862409116751684 relative error = 0.013463801839907357999444234652874 % h = 0.001 y1[1] (analytic) = 2.8593514006943175824899788268026 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.379925862090114582216690891587 relative error = 13.287134347945470159066153656605 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.035 y2[1] (analytic) = 1.489474067337769781572243848041 y2[1] (numeric) = 1.489271711377250531807284434761 absolute error = 0.00020235596051924976495941328 relative error = 0.013585732370683917815802064910257 % h = 0.001 y1[1] (analytic) = 2.8598623564730345704393773139402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3804368178688315701660893787246 relative error = 13.302626855720798416005209132335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.036 y2[1] (analytic) = 1.4903341848138774897646542816844 y2[1] (numeric) = 1.4901298819648468747797205313111 absolute error = 0.0002043028490306149849337503733 relative error = 0.013708525987822633057199220136702 % h = 0.001 y1[1] (analytic) = 2.8603724523894667405481896080782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3809469137852637402749016728626 relative error = 13.318087770948586171394199054106 % h = 0.001 TOP MAIN SOLVE Loop memory used=488.2MB, alloc=4.1MB, time=68.02 NO POLE NO POLE x[1] = 1.037 y2[1] (analytic) = 1.4911948119557579119297251788145 y2[1] (numeric) = 1.4909885470998634339636471419291 absolute error = 0.0002062648558944779660780368854 relative error = 0.013832187065079301956518236073867 % h = 0.001 y1[1] (analytic) = 2.8608816879335182188922372194854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3814561493293152186189492842698 relative error = 13.33351710901578458694134079869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.038 y2[1] (analytic) = 1.4920559479027839779059604737648 y2[1] (numeric) = 1.4918477058320516263006763041454 absolute error = 0.0002082420707323516052841696194 relative error = 0.013956719989290895764222501368698 % h = 0.001 y1[1] (analytic) = 2.8613900625959535038563357271943 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3819645239917505035830477919787 relative error = 13.348914885278481742257156178489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.039 y2[1] (analytic) = 1.4929175917938198124286207170946 y2[1] (numeric) = 1.4927073572102852861705296827742 absolute error = 0.0002102345835345262580910343204 relative error = 0.0140821291603857541259358116528 % h = 0.001 y1[1] (analytic) = 2.861897575868397975369753957895 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3824720372641949750964660226794 relative error = 13.364281115061912321252307491061 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.04 y2[1] (analytic) = 1.4937797427672215962655265790078 y2[1] (numeric) = 1.4935675002825606653910385699136 absolute error = 0.0002122424846609308744880090942 relative error = 0.014208418991393767040264467797972 % h = 0.001 y1[1] (analytic) = 2.8624042272433384032807916921162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3829786886391354030075037569006 relative error = 13.379615813660467303433662455958 % h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.1MB, time=68.55 NO POLE NO POLE x[1] = 1.041 y2[1] (analytic) = 1.4946423999608384278608062778836 y2[1] (numeric) = 1.4944281340959964332181438849456 absolute error = 0.000214265864841994642662392938 relative error = 0.014335593908456543626250333067601 % h = 0.001 y1[1] (analytic) = 2.8629100162141234548699675231574 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3834844776099204545966795879418 relative error = 13.394918996337703659935350141982 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.042 y2[1] (analytic) = 1.4955055625120131854857252902416 y2[1] (numeric) = 1.495289257696833676345896174536 absolute error = 0.0002163048151795091398291157056 relative error = 0.014463658350837567929367564155147 % h = 0.001 y1[1] (analytic) = 2.863414942274964201501309355628 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3839894036707612012280214204124 relative error = 13.410190678326354054122217412702 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.043 y2[1] (analytic) = 1.4963692295575833898957361913855 y2[1] (numeric) = 1.4961508701304358989064556126346 absolute error = 0.0002183594271474909892805787509 relative error = 0.014592616770932341994498503672624 % h = 0.001 y1[1] (analytic) = 2.8639190049209346244112408923424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3844934663167316241379529571268 relative error = 13.425430874828336546603740598504 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.044 y2[1] (analytic) = 1.4972334002338820674928859697464 y2[1] (numeric) = 1.497012970441289022470092000475 absolute error = 0.0002204297925930450227939692714 relative error = 0.014722473634278516433845494609232 % h = 0.001 y1[1] (analytic) = 2.8644222036479721196345583207306 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.384996665043769119361270385515 relative error = 13.440639601014764304497090047191 % h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.1MB, time=69.09 NO POLE NO POLE x[1] = 1.045 y2[1] (analytic) = 1.4980980736767386139927176525903 y2[1] (numeric) = 1.4978755576730013860451847665747 absolute error = 0.0002225160037372279475328860156 relative error = 0.014853233419566008717255179824994 % h = 0.001 y1[1] (analytic) = 2.8649245379528780020669922728253 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3854989993486750017937043376097 relative error = 13.455816872025955314778685918841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.046 y2[1] (analytic) = 1.4989632490214796585948025762604 y2[1] (numeric) = 1.4987386308683037460782229667351 absolute error = 0.0002246181531759125165796095253 relative error = 0.014984900618647109411950210331118 % h = 0.001 y1[1] (analytic) = 2.8654260073333180086638509963099 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3860004687291150083905630610943 relative error = 13.470962702971442101564222082398 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.047 y2[1] (analytic) = 1.499828925402929928656039130494 y2[1] (numeric) = 1.4996021890690492764538052840415 absolute error = 0.0002267363338806522022338464525 relative error = 0.01511747973654657659818023306293 % h = 0.001 y1[1] (analytic) = 2.8659266112878228007742415380223 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3865010726836198005009536028067 relative error = 13.486077108929981447157771247582 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.048 y2[1] (analytic) = 1.5006951019554131148658533035871 y2[1] (numeric) = 1.500466231316213568494640028863 absolute error = 0.0002288706391995463712132747241 relative error = 0.015250975291471718686819590462199 % h = 0.001 y1[1] (analytic) = 2.8664263493157884656103666057382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3870008107115854653370786705226 relative error = 13.501160104949564116711218534308 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=499.7MB, alloc=4.1MB, time=69.62 x[1] = 1.049 y2[1] (analytic) = 1.5015617778127527369224358532785 y2[1] (numeric) = 1.5013307566498946309615451388527 absolute error = 0.0002310211628581059608907144258 relative error = 0.015385391814822465864453368452831 % h = 0.001 y1[1] (analytic) = 2.8669252209174770168513956389767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3874996823132740165781077037611 relative error = 13.516211706047424586335902549331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.05 y2[1] (analytic) = 1.5024289521082730097091504271879 y2[1] (numeric) = 1.5021957641093128900534481789476 absolute error = 0.0002331879989601196557022482403 relative error = 0.01552073385120143039100630420733 % h = 0.001 y1[1] (analytic) = 2.8674232255940168943814094850003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3879976869898138941081215497847 relative error = 13.531231927210050774508972714008 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.051 y2[1] (analytic) = 1.5032966239747997099702464564727 y2[1] (numeric) = 1.5030612527328111894073863413684 absolute error = 0.0002353712419885205628601151043 relative error = 0.015657005958423955974480638141708 % h = 0.001 y1[1] (analytic) = 2.8679203628474034631609189421053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3884948242432004628876310068897 relative error = 13.546220783393193776617599074756 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.052 y2[1] (analytic) = 1.5041647925446610434850101470624 y2[1] (numeric) = 1.5039272215578547900985064456199 absolute error = 0.0002375709868062533865037014425 relative error = 0.015794212707528156446879293249514 % h = 0.001 y1[1] (analytic) = 2.8684166321804995112314582987262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3889910935762965109581703635106 relative error = 13.561178289521877602484796136266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.053 y2[1] (analytic) = 1.5050334569496885127394863943916 y2[1] (numeric) = 1.5047936696210313706400649384906 absolute error = 0.000239787328657142099421455901 relative error = 0.015932358682784943964899816933694 % h = 0.001 y1[1] (analytic) = 2.8689120330970357468527558638018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3894864944928327465794679285862 relative error = 13.576104460490408916721245393888 % h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.1MB, time=70.17 NO POLE NO POLE x[1] = 1.054 y2[1] (analytic) = 1.5059026163212177850949039499833 y2[1] (numeric) = 1.505660595958051026983427894053 absolute error = 0.0002420203631667581114760559303 relative error = 0.016071448481708046958492352619998 % h = 0.001 y1[1] (analytic) = 2.8694065651016112947719843512738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3899810264974082944986964160582 relative error = 13.590999311162386781748122213001 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.055 y2[1] (analytic) = 1.5067722697900895614519356715277 y2[1] (numeric) = 1.5065279996037462725180710136635 absolute error = 0.0002442701863432889338646578642 relative error = 0.016211486715064018049881547944149 % h = 0.001 y1[1] (analytic) = 2.8699002276996941916245948495095 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3904746890954911913513069142939 relative error = 13.605862856370712403336551516647 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.056 y2[1] (analytic) = 1.5076424164866504454099251922705 y2[1] (numeric) = 1.5073958795920720380715796259623 absolute error = 0.0002465368945784073383455663082 relative error = 0.016352478006882232165157780214086 % h = 0.001 y1[1] (analytic) = 2.8703930203976218804662389748547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3909674817934188801929510396391 relative error = 13.620695110917598878509933405366 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.057 y2[1] (analytic) = 1.508513055540753812920210850555 y2[1] (numeric) = 1.5082642349561056719096486868735 absolute error = 0.0002488205846481410105621636815 relative error = 0.016494426994464875060047414284513 % h = 0.001 y1[1] (analytic) = 2.8708849427026017044352846774374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3914594040983987041619967422218 relative error = 13.635496089574580945655994352151 % h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.1MB, time=70.71 NO POLE NO POLE x[1] = 1.058 y2[1] (analytic) = 1.5093841860817606824326772262677 y2[1] (numeric) = 1.5091330647280469397360827796051 absolute error = 0.0002511213537137426965944466626 relative error = 0.016637338328396922480975030243789 % h = 0.001 y1[1] (analytic) = 2.8713759941227113995454320367466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.391950455518508399272144101531 relative error = 13.650265807082524736696031997584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.059 y2[1] (analytic) = 1.5102558072385405855346641377078 y2[1] (numeric) = 1.5100023679392180246927961146489 absolute error = 0.0002534392993225608418680230589 relative error = 0.016781216672556110182032694001708 % h = 0.001 y1[1] (analytic) = 2.871866174166899586607936254411 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3924406355626965863346483191954 relative error = 13.665004278151637531159431822814 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.06 y2[1] (analytic) = 1.5111279181394724380813624600436 y2[1] (numeric) = 1.5108721436200635273598125297808 absolute error = 0.0002557745194089107215499302628 relative error = 0.016926066704122895017972419615052 % h = 0.001 y1[1] (analytic) = 2.8723554823449862622829459219974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3929299437407832620096579867818 relative error = 13.679711517461477512012142107955 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.061 y2[1] (analytic) = 1.5120005179124454118168256350344 y2[1] (numeric) = 1.5117423908001504657552654900604 absolute error = 0.000258127112294946061560144974 relative error = 0.017071893113590407332838014209345 % h = 0.001 y1[1] (analytic) = 2.8728439181676632892594655125299 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3934183795634602889861775773143 relative error = 13.694387539660963523088399597656 % h = 0.001 TOP MAIN SOLVE Loop memory used=511.1MB, alloc=4.1MB, time=71.25 NO POLE NO POLE x[1] = 1.062 y2[1] (analytic) = 1.5128736056848598064847252510766 y2[1] (numeric) = 1.5126131085081682753353980878313 absolute error = 0.0002604971766915311493271632453 relative error = 0.017218700604774394863351529499555 % h = 0.001 y1[1] (analytic) = 2.8733314811464948855634519158083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3939059425422918852901639805927 relative error = 13.70903235936838482797560220115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.063 y2[1] (analytic) = 1.513747180583627922427978582893 y2[1] (numeric) = 1.5134842957719288089945630427208 absolute error = 0.0002628848116991134334155401722 relative error = 0.01736649389482315837566759549161 % h = 0.001 y1[1] (analytic) = 2.8738181707939181129935557094709 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3943926321897151127202677742553 relative error = 13.723645991171410870202826857969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.064 y2[1] (analytic) = 1.5146212417351749336763754913097 y2[1] (numeric) = 1.5143559516183663370652227016403 absolute error = 0.0002652901168085966111527896694 relative error = 0.01751527771422747925360600575625 % h = 0.001 y1[1] (analytic) = 2.8743039866232433646840187301006 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.394878448019040364410730794885 relative error = 13.738228449627101034584090409494 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.065 y2[1] (analytic) = 1.5154957882654397615213315955666 y2[1] (numeric) = 1.515228075073537547317949038785 absolute error = 0.0002677131919022142033825567816 relative error = 0.017665056806830539255969086468695 % h = 0.001 y1[1] (analytic) = 2.8747889281486548517942403815169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3953633895444518515209524463013 relative error = 13.752779749261914409568048937689 % h = 0.001 TOP MAIN SOLVE Loop memory used=514.9MB, alloc=4.1MB, time=71.78 NO POLE NO POLE x[1] = 1.066 y2[1] (analytic) = 1.5163708192998759485768941434805 y2[1] (numeric) = 1.5161006651626215449614236556339 absolute error = 0.0002701541372544036154704878466 relative error = 0.017815835929837832660045637356512 % h = 0.001 y1[1] (analytic) = 2.875272994885211089324525990729 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3958474562810080890512380555134 relative error = 13.767299904571719550446426572701 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.067 y2[1] (analytic) = 1.5172463339634525333261265185295 y2[1] (numeric) = 1.51697372090991985264243778095 absolute error = 0.0002726130535326806836887375795 relative error = 0.017967619853827071007897607707898 % h = 0.001 y1[1] (analytic) = 2.8757561863488453810575313958413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3963306477446423807842434606257 relative error = 13.781788930021804243274058237107 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.068 y2[1] (analytic) = 1.5181223313806549251519968375448 y2[1] (numeric) = 1.5178472413388564104458922707801 absolute error = 0.0002750900417985147061045667647 relative error = 0.018120413362758080671519188629006 % h = 0.001 y1[1] (analytic) = 2.8762385020563663036249188245075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3968129634521633033516308892919 relative error = 13.796246840046885269354022193669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.069 y2[1] (analytic) = 1.5189988106754857798518956081959 y2[1] (numeric) = 1.5187212254719775758947976084549 absolute error = 0.000277585203508203957097999741 relative error = 0.018274221253982693452450689366429 % h = 0.001 y1[1] (analytic) = 2.876719941525458189698739996318 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3972944029212551894254520611024 relative error = 13.810673649051118170141927602206 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=518.8MB, alloc=4.1MB, time=72.32 x[1] = 1.07 y2[1] (analytic) = 1.5198757709714658756349069318241 y2[1] (numeric) = 1.5195956723309521239502739045891 absolute error = 0.000280098640513751684633027235 relative error = 0.018429048338254630430921444611716 % h = 0.001 y1[1] (analytic) = 2.8772005042746816103070632577768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3977749656704786100337753225612 relative error = 13.825069371408107012424009576331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.071 y2[1] (analytic) = 1.5207532113916349896009572544251 y2[1] (numeric) = 1.5204705809365712470115508970811 absolute error = 0.000282630455063742589406357344 relative error = 0.018584899439739379279087095935184 % h = 0.001 y1[1] (analytic) = 2.8776801898234738562733624342827 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3982546512192708560000744990671 relative error = 13.839434021460914153624269469556 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.072 y2[1] (analytic) = 1.521631131058552774700965186707 y2[1] (numeric) = 1.5213459503087485549159679511133 absolute error = 0.0002851807498042197849972355937 relative error = 0.018741779396024065252416928163622 % h = 0.001 y1[1] (analytic) = 2.8781589976921494187791859597638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3987334590879464185058980245482 relative error = 13.853767613522070007096481318876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.073 y2[1] (analytic) = 1.5225095290942996371771154331449 y2[1] (numeric) = 1.522221779466520074938974059152 absolute error = 0.0002877496277795622381413739929 relative error = 0.01889969305812731607277654428543 % h = 0.001 y1[1] (analytic) = 2.8786369274019004690496257213382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3992113887976974687763377861226 relative error = 13.868070161873582807257466539809 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=522.6MB, alloc=4.1MB, time=72.85 x[1] = 1.074 y2[1] (analytic) = 1.5233884046204776144823793898327 y2[1] (numeric) = 1.5230980674280442517941278409473 absolute error = 0.0002903371924333626882515488854 relative error = 0.019058645290509120916240054734183 % h = 0.001 y1[1] (analytic) = 2.8791139784747973371611059335712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3996884398705943368878179983556 relative error = 13.882341680766948374418618106245 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.075 y2[1] (analytic) = 1.5242677567582112536784044916836 y2[1] (numeric) = 1.5239748132106019476330975435333 absolute error = 0.0002929435476093060453069481503 relative error = 0.019218640971080683718154161823735 % h = 0.001 y1[1] (analytic) = 2.8795901504337889899710132345797 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4001646118295859896977252993641 relative error = 13.89658218442315987917323256844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.076 y2[1] (analytic) = 1.5251475846281484903108939111643 y2[1] (numeric) = 1.5248520158305964420456610412278 absolute error = 0.0002955687975520482652328699365 relative error = 0.019379684991214271007464061908228 % h = 0.001 y1[1] (analytic) = 2.8800654428027035081686900743944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4006399041985005078954021391788 relative error = 13.910791687032717606197783369688 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.077 y2[1] (analytic) = 1.5260278873504615277615977332555 y2[1] (numeric) = 1.5257296743035534320597058356326 absolute error = 0.0002982130469080957018918976229 relative error = 0.019541782255753054481797989063643 % h = 0.001 y1[1] (analytic) = 2.8805398551062485624473143446251 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4011143165020455621740264094095 relative error = 13.924970202755638717325842023343 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.078 y2[1] (analytic) = 1.5269086640448477170760362547213 y2[1] (numeric) = 1.5266077876441210321412290556335 absolute error = 0.0003008764007266849348071990878 relative error = 0.019704937683020948534293508936517 % h = 0.001 y1[1] (analytic) = 2.8810133868700118887961890775899 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4015878482658088885229011423743 relative error = 13.939117745721467013753924813691 % h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.1MB, time=73.38 NO POLE NO POLE x[1] = 1.079 y2[1] (analytic) = 1.527789913830530437266075580037 y2[1] (numeric) = 1.5274863548660697741943374573999 absolute error = 0.0003035589644606630717381226371 relative error = 0.01986915620483244294263436212321 % h = 0.001 y1[1] (analytic) = 2.8814860376204617629129669226588 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4020604990162587626396789874432 relative error = 13.953234330029282697239111793402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.08 y2[1] (analytic) = 1.528671635826259976086475211474 y2[1] (numeric) = 1.5283653749822926075612474243853 absolute error = 0.0003062608439673685252277870887 relative error = 0.020034442766502430930251776412814 % h = 0.001 y1[1] (analytic) = 2.8819578068849474737353349876248 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4025322682807444734620470524092 relative error = 13.96731996974771213014885197341 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.081 y2[1] (analytic) = 1.5295538291503144112845268568664 y2[1] (numeric) = 1.5292448470048048990222849673271 absolute error = 0.0003089821455095122622418895393 relative error = 0.020200802326856032809128739126094 % h = 0.001 y1[1] (analytic) = 2.8824286941916997960916865134587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4030031555874967958183985782431 relative error = 13.981374678914937594223933745115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.082 y2[1] (analytic) = 1.5304364929205004923219032054952 y2[1] (numeric) = 1.5301247699447444327958857242464 absolute error = 0.0003117229757560595260174812488 relative error = 0.020368239858238415413129767124144 % h = 0.001 y1[1] (analytic) = 2.8828986990698314624703067318156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4034731604656284621970187966 relative error = 13.995398471538707047916162746046 % h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.1MB, time=73.92 NO POLE NO POLE x[1] = 1.083 y2[1] (analytic) = 1.5313196262541545225678349503138 y2[1] (numeric) = 1.5310051428123714105385949604484 absolute error = 0.0003144834417831120292399898654 relative error = 0.020536760346524607530262255164836 % h = 0.001 y1[1] (analytic) = 2.8833678210493376339066011361452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4039422824451346336333132009296 relative error = 14.009391361596343882162850585282 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.084 y2[1] (analytic) = 1.5322032282681432419627338634115 y2[1] (numeric) = 1.531885964617068451345067568522 absolute error = 0.0003172636510747906176662948895 relative error = 0.02070636879112931154175854593591 % h = 0.001 y1[1] (analytic) = 2.8838360596610963699878952792174 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4044105210568933697146073440018 relative error = 14.023353363034756674460777090851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.085 y2[1] (analytic) = 1.533087298078864710151379261166 y2[1] (numeric) = 1.5327672343673405917480680683401 absolute error = 0.0003200637115241184033111928259 relative error = 0.020877070205016711475350468679832 % h = 0.001 y1[1] (analytic) = 2.8843034144368690979753360923033 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4048778758326660977020481570877 relative error = 14.037284489770448941102846034278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.086 y2[1] (analytic) = 1.5339718348022491900847847259714 y2[1] (numeric) = 1.5336489510708152857184706070594 absolute error = 0.000322883731433904366314118912 relative error = 0.021048869614710277679590260458839 % h = 0.001 y1[1] (analytic) = 2.8847698849093010810424256041483 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4053443463050980807691376689327 relative error = 14.051184755689528887441209634203 % h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.1MB, time=74.45 NO POLE NO POLE x[1] = 1.087 y2[1] (analytic) = 1.5348568375537600320898614827493 y2[1] (numeric) = 1.5345311137342424046652589591206 absolute error = 0.0003257238195176274246025236287 relative error = 0.021221772060302568325553536170262 % h = 0.001 y1[1] (analytic) = 2.8852354706119218856297188212437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4058099320077188853564308860281 relative error = 14.065054174647719156041190548065 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.088 y2[1] (analytic) = 1.5357423054483945584059943606521 y2[1] (numeric) = 1.5354137213634942374355265262482 absolute error = 0.0003285840849003209704678344039 relative error = 0.021395782595465027941741332251773 % h = 0.001 y1[1] (analytic) = 2.8857001710791458479152184147362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4062746324749428476419304795206 relative error = 14.078892760470366572590881534724 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.089 y2[1] (analytic) = 1.5366282376006849481876458034578 y2[1] (numeric) = 1.5362967729635654903144763374505 absolute error = 0.0003314646371194578731694660073 relative error = 0.021570906287457783187479236164922 % h = 0.001 y1[1] (analytic) = 2.8861639858462725393999997436219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4067384472420695391267118084063 relative error = 14.092700526952451889431852518305 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.09 y2[1] (analytic) = 1.5375146331246991229721029261249 y2[1] (numeric) = 1.5371802675385732870254210490199 absolute error = 0.000334365586125835946681877105 relative error = 0.021747148217139436069592250218144 % h = 0.001 y1[1] (analytic) = 2.886626914449487231608600628636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4072013758452842313353126934204 relative error = 14.106477487858599526576942410629 % h = 0.001 TOP MAIN SOLVE Loop memory used=537.8MB, alloc=4.1MB, time=74.98 NO POLE NO POLE x[1] = 1.091 y2[1] (analytic) = 1.5384014911340416326114821498343 y2[1] (numeric) = 1.5380642040917571687297829445325 absolute error = 0.0003372870422844638816992053018 relative error = 0.021924513478976854806614345796483 % h = 0.001 y1[1] (analytic) = 2.8870889564258613599037111764894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4076634178216583596304232412738 relative error = 14.12022365692308731008165876332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.092 y2[1] (analytic) = 1.5392888107418545416681054835882 y2[1] (numeric) = 1.5389485816254790940270939348484 absolute error = 0.0003402291163754476410115487398 relative error = 0.022103007181054962544271663057497 % h = 0.001 y1[1] (analytic) = 2.8875501113133529864146998397988 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4081245727091499861414119045832 relative error = 14.13393904784985620763625212706 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.093 y2[1] (analytic) = 1.5401765910608183162723620570624 y2[1] (numeric) = 1.5398333991412234389549955581115 absolute error = 0.0003431919195948773173664989509 relative error = 0.022282634445086524125458022926257 % h = 0.001 y1[1] (analytic) = 2.8880103786508072620795127842255 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4085848400466042618062248490099 relative error = 14.147623674312520061246073901432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.094 y2[1] (analytic) = 1.5410648312031527114421680469252 y2[1] (numeric) = 1.5407186556395969969892389797496 absolute error = 0.0003461755635557144529290671756 relative error = 0.022463400406421931117400863298683 % h = 0.001 y1[1] (analytic) = 2.8884697579779568877994845209589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4090442193737538875261965857433 relative error = 14.16127754995437531686836647022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=541.6MB, alloc=4.1MB, time=75.53 x[1] = 1.095 y2[1] (analytic) = 1.5419535302806176588631376772364 y2[1] (numeric) = 1.5416043501203289790436849924744 absolute error = 0.000349180160288679819452684762 relative error = 0.022645310214058985298194910331249 % h = 0.001 y1[1] (analytic) = 2.888928248835422574706598649776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4095027102312195744333107145604 relative error = 14.174900688388410750874172541114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.096 y2[1] (analytic) = 1.5428426874045141551285775138303 y2[1] (numeric) = 1.5424904815822710134703040162815 absolute error = 0.0003522058222431416582734975488 relative error = 0.022828369030652680804359869044236 % h = 0.001 y1[1] (analytic) = 2.8893858507647135035427384454507 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4099603121605105032694505102351 relative error = 14.188493103197317193204586851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.097 y2[1] (analytic) = 1.5437323016856851504384158127608 y2[1] (numeric) = 1.5433770490233971460591760984503 absolute error = 0.0003552526622880043792397143105 relative error = 0.023012582032524985140557185166805 % h = 0.001 y1[1] (analytic) = 2.8898425633082277831504679083043 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4104170247040247828771799730887 relative error = 14.202054807933497247091107765787 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.098 y2[1] (analytic) = 1.5446223722345164377561782239551 y2[1] (numeric) = 1.5442640514408038400384909135442 absolute error = 0.0003583207937125977176873104109 relative error = 0.023197954409674619252079512861524 % h = 0.001 y1[1] (analytic) = 2.8902983860092529080748847881513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4108728474050499078015968529357 relative error = 14.215585816119075005210378802466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.099 y2[1] (analytic) = 1.5455128981609375424231206931733 y2[1] (numeric) = 1.5451514878307099760745477634105 absolute error = 0.0003614103302275663485729297628 relative error = 0.023384491365786836860204939980751 % h = 0.001 y1[1] (analytic) = 2.8907533184119662152760879798278 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4113277798077632150028000446122 relative error = 14.229086141245905762144140737992 % h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.1MB, time=76.06 NO POLE NO POLE x[1] = 1.1 y2[1] (analytic) = 1.5464038785744226122286299482153 y2[1] (numeric) = 1.5460393571884568522717555771802 absolute error = 0.0003645213859657599568743710351 relative error = 0.023572198118243203259986294089633 % h = 0.001 y1[1] (analytic) = 2.8912073600614353399518025778717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4117818214572323396785146426561 relative error = 14.242555796775585723015743750369 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.101 y2[1] (analytic) = 1.5472953125839913079360014990487 y2[1] (numeric) = 1.5469276585085081841726329112684 absolute error = 0.0003676540754831237633685877803 relative error = 0.023761079898131373779523998063482 % h = 0.001 y1[1] (analytic) = 2.8916605105036186704697067677687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4122349718994156701964188325531 relative error = 14.255994796139461708175095968752 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.102 y2[1] (analytic) = 1.5481871992982096942627046261544 y2[1] (numeric) = 1.5478163907844501047578079493739 absolute error = 0.0003708085137595895048966767805 relative error = 0.023951141950254872099248983408796 % h = 0.001 y1[1] (analytic) = 2.8921127692853658024090056214744 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4126872306811628021357176862588 relative error = 14.269403152738640853804449897538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.103 y2[1] (analytic) = 1.5490795378251911313142433768984 y2[1] (numeric) = 1.5487055530089911644460185024795 absolute error = 0.0003739848161999668682248744189 relative error = 0.024142389533142868629220121269976 % h = 0.001 y1[1] (analytic) = 2.8925641359544179917107977556764 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4131385973502149914375098204608 relative error = 14.282780879944000308317951430671 % h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.1MB, time=76.59 NO POLE NO POLE x[1] = 1.104 y2[1] (analytic) = 1.5499723272725971664707221361436 y2[1] (numeric) = 1.5495951441739623310941120088519 absolute error = 0.0003771830986348353766101272917 relative error = 0.02433482791905995914191851551882 % h = 0.001 y1[1] (analytic) = 2.8930146100594086069367817024688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4135890714552056066634937672532 relative error = 14.296127991096196924428397593169 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.105 y2[1] (analytic) = 1.5508655667476384267252238846103 y2[1] (numeric) = 1.5504851632703169899970455340416 absolute error = 0.0003804034773214367281783505687 relative error = 0.024528462394015943857498837526301 % h = 0.001 y1[1] (analytic) = 2.8934641911498635806358497337686 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.414038652545660580362561798553 relative error = 14.309444499505676946755168743109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.106 y2[1] (analytic) = 1.551759255357075511473108806681 y2[1] (numeric) = 1.551375609288130943887885770883 absolute error = 0.000383646068944567585223035798 relative error = 0.024723298257775607177935687586828 % h = 0.001 y1[1] (analytic) = 2.8939128787762018598181177729194 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4144873401719988595448298377038 relative error = 14.322730418452685694847818745712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.107 y2[1] (analytic) = 1.5526533922072198857513404584262 y2[1] (numeric) = 1.5522664812166024129378090394945 absolute error = 0.0003869109906174728135314189317 relative error = 0.024919340823868498265980762270422 % h = 0.001 y1[1] (analytic) = 2.8943606724897358555359409194884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4149351338855328552626529842728 relative error = 14.335985761187277241500322597552 % h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.1MB, time=77.12 NO POLE NO POLE x[1] = 1.108 y2[1] (analytic) = 1.5535479764039347739269462565986 y2[1] (numeric) = 1.5531577780440520347561012872782 absolute error = 0.0003901983598827391708449693204 relative error = 0.025116595419598712664324408470116 % h = 0.001 y1[1] (analytic) = 2.8948075718426718915714650062808 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4153820332384688912981770710652 relative error = 14.349210540929324086231495139864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.109 y2[1] (analytic) = 1.5544430070526360538337186002104 y2[1] (numeric) = 1.5540494987579228643901580889202 absolute error = 0.0003935082947131894435605112902 relative error = 0.025315067386054675149832972379014 % h = 0.001 y1[1] (analytic) = 2.8952535763881106522302655010551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4158280377839076519569775658395 relative error = 14.362404770868526823807606861294 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.11 y2[1] (analytic) = 1.5553384832582931513562624880664 y2[1] (numeric) = 1.5549416423447803743254846463904 absolute error = 0.000396840913512777030777841676 relative error = 0.025514762078118924017211223302891 % h = 0.001 y1[1] (analytic) = 2.8956986856800476292406259593394 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4162731470758446289673380241238 relative error = 14.375568464164423807683733358837 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.111 y2[1] (analytic) = 1.5562344041254299354604950482804 y2[1] (numeric) = 1.5558342077903124544856957889427 absolute error = 0.0004001963351174809747992593377 relative error = 0.02571568486447789698591706612784 % h = 0.001 y1[1] (analytic) = 2.8961428992733735677580091291065 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4167173606691705674847211938909 relative error = 14.38870163394640080824088380689 % h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.1MB, time=77.66 NO POLE NO POLE x[1] = 1.112 y2[1] (analytic) = 1.5571307687581256136697019493493 y2[1] (numeric) = 1.5567271940793294122325159731148 absolute error = 0.0004035746787962014371859762345 relative error = 0.025917841127631718923633770607425 % h = 0.001 y1[1] (analytic) = 2.896586216723874911474274702875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4171606781196719112009867676594 relative error = 14.401804293313700665696460784858 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.113 y2[1] (analytic) = 1.5580275762600156279852552168044 y2[1] (numeric) = 1.5576206001957639723657792827283 absolute error = 0.0004069760642516556194759340761 relative error = 0.026121236263903991579083058202155 % h = 0.001 y1[1] (analytic) = 2.8970286375882342468311986080539 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4176030989840312465579106728383 relative error = 14.414876455335432937566109039389 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.114 y2[1] (analytic) = 1.5589248257342925512510965347952 y2[1] (numeric) = 1.5585144251226712771234294288887 absolute error = 0.0004104006116212741276671059065 relative error = 0.026325875683451585516440615586819 % h = 0.001 y1[1] (analytic) = 2.8974701614240307463378496220504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4180446228198277460645616868348 relative error = 14.427918133050583540555514214601 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.115 y2[1] (analytic) = 1.5598225162837069839610896681975 y2[1] (numeric) = 1.5594086678422288861815197499853 absolute error = 0.0004138484414780977795699182122 relative error = 0.026531764810274434443093966072687 % h = 0.001 y1[1] (analytic) = 2.8979107877897406109913799948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4184852491855376107180920595844 relative error = 14.44092933946802438676121427829 % h = 0.001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.1MB, time=78.20 NO POLE NO POLE x[1] = 1.116 y2[1] (analytic) = 1.5607206470105684515083451979695 y2[1] (numeric) = 1.5603033273357367766542132116915 absolute error = 0.000417319674831674854131986278 relative error = 0.026738909082225332121961143233096 % h = 0.001 y1[1] (analytic) = 2.8983505162447375118007876579656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.41892497764053451152749972275 relative error = 14.453910087566523014059986310554 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.117 y2[1] (analytic) = 1.5616192170167463018756203205038 y2[1] (numeric) = 1.5611984025836173430937824069643 absolute error = 0.0004208144331289587818379135395 relative error = 0.026947313951019732059067292190918 % h = 0.001 y1[1] (analytic) = 2.8987893463492930304132084970801 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4193638077450900301399205618645 relative error = 14.466860390294752210566869509386 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.118 y2[1] (analytic) = 1.5625182254036706037658960206517 y2[1] (numeric) = 1.5620938925654153974906095560448 absolute error = 0.0004243328382552062752864646069 relative error = 0.027156984882245550156555190778672 % h = 0.001 y1[1] (analytic) = 2.8992272776645770988422980603767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4198017390603740985690101251611 relative error = 14.479780260571299633042381711744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.119 y2[1] (analytic) = 1.5634176712723330451722334879172 y2[1] (numeric) = 1.5629897962597981692731865064579 absolute error = 0.0004278750125348758990469814593 relative error = 0.027367927355372970520784752068917 % h = 0.001 y1[1] (analytic) = 2.8996643097526584382982629759624 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4202387711484554380249750407468 relative error = 14.49266971128467741912998143446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=564.5MB, alloc=4.1MB, time=78.73 x[1] = 1.12 y2[1] (analytic) = 1.5643175537232878323860112060389 y2[1] (numeric) = 1.5638861126445553053081147330124 absolute error = 0.0004314410787325270778964730265 relative error = 0.027580146863764254614655858059695 % h = 0.001 y1[1] (analytic) = 2.9001004421765049971191032473392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4206749035723019968458153121236 relative error = 14.505528755293331793305320413083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.121 y2[1] (analytic) = 1.5652178718566525894426437077979 y2[1] (numeric) = 1.564782840696598869900105337801 absolute error = 0.0004350311600537195425383699969 relative error = 0.027793648914683553942768398969026 % h = 0.001 y1[1] (analytic) = 2.9005356744999843878026274960677 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4211101358957813875293395608521 relative error = 14.518357405425652666419322864492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.122 y2[1] (analytic) = 1.5661186247721092580038825494078 y2[1] (numeric) = 1.5656799793919633447919790502002 absolute error = 0.0004386453801459132119034992076 relative error = 0.02800843902930672645751316969979 % h = 0.001 y1[1] (analytic) = 2.9009700062878643231388041195943 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4215444676836613228655161843787 relative error = 14.531155674479983228717617226753 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.123 y2[1] (analytic) = 1.5670198115689049976757996222608 y2[1] (numeric) = 1.5665775277058056291646662268705 absolute error = 0.0004422838630993685111333953903 relative error = 0.028224522742731156873667321267166 % h = 0.001 y1[1] (analytic) = 2.9014034371058130514420122319265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4219778985016100511687242967109 relative error = 14.543923575224629536219333943342 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.124 y2[1] (analytic) = 1.5679214313458530867615524841214 y2[1] (numeric) = 1.5674754846124050396372068517562 absolute error = 0.0004459467334480471243456323652 relative error = 0.02844190560398558107854839668852 % h = 0.001 y1[1] (analytic) = 2.9018359665203997908827571549424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4224104279161967906094692197268 relative error = 14.55666112039787009033876896442 % h = 0.001 TOP MAIN SOLVE Loop memory used=568.4MB, alloc=4.1MB, time=79.26 NO POLE NO POLE x[1] = 1.125 y2[1] (analytic) = 1.5688234832013338234480309570783 y2[1] (numeric) = 1.5683738490851633102667505360855 absolute error = 0.0004496341161705131812804209928 relative error = 0.02866059317603991482426161403701 % h = 0.001 y1[1] (analytic) = 2.9022675940990951629184161286548 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4228420554948921626451281934392 relative error = 14.569368322707965410633897041327 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.126 y2[1] (analytic) = 1.5697259662332954274254838056815 y2[1] (numeric) = 1.5692726200966045925485565183705 absolute error = 0.000453346136690834876927287311 relative error = 0.0288805910358150868880560101069 % h = 0.001 y1[1] (analytic) = 2.9026983194102716248225808097203 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4232727808060686245492928745047 relative error = 14.58204519483316760056620159781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.127 y2[1] (analytic) = 1.5706288795392549419392238757145 y2[1] (numeric) = 1.5701717966183754554159936644072 absolute error = 0.0004570829208794865232302113073 relative error = 0.029101904774192876886286342624529 % h = 0.001 y1[1] (analytic) = 2.9031281420232039013125640288867 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4237026034190009010392760936711 relative error = 14.594691749421729906156768978598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.128 y2[1] (analytic) = 1.571532222216299136272509641971 y2[1] (numeric) = 1.5710713776212448852405404672754 absolute error = 0.0004608445950542510319691746956 relative error = 0.02932453999602575792695928241131 % h = 0.001 y1[1] (analytic) = 2.903557061508069415274639179909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4241315229038664150013512446934 relative error = 14.607307999091916267424074208877 % h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.1MB, time=79.79 NO POLE NO POLE x[1] = 1.129 y2[1] (analytic) = 1.5724359933610854086597006822295 y2[1] (numeric) = 1.5719713620751042858317850473389 absolute error = 0.0004646312859811228279156348906 relative error = 0.029548502320146744285324425374179 % h = 0.001 y1[1] (analytic) = 2.9039850774359487175865815147284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4245595388317457173132935795128 relative error = 14.619893956432010862489363052576 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.13 y2[1] (analytic) = 1.5733401920698426896287841643465 y2[1] (numeric) = 1.5728717489489674784374251522453 absolute error = 0.0004684431208752111913590121012 relative error = 0.029773797379379244286453033193492 % h = 0.001 y1[1] (analytic) = 2.9044121893788259160370815224114 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4249866507746229157637935871958 relative error = 14.632449634000327644236011139538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.131 y2[1] (analytic) = 1.5742448174383723457723690040154 y2[1] (numeric) = 1.5737725372109707017432681569261 absolute error = 0.0004722802274016440291008470893 relative error = 0.030000430820546918578230185894548 % h = 0.001 y1[1] (analytic) = 2.9048383969095891033416014724691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4254128583053861030683135372535 relative error = 14.644975044325219869409715246907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.132 y2[1] (analytic) = 1.5751498685620490839462439222745 y2[1] (numeric) = 1.5746737258283726118732310635967 absolute error = 0.0004761427336764720730128586778 relative error = 0.030228408304483543977669215321047 % h = 0.001 y1[1] (analytic) = 2.9052636996020307842542471067375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4258381609978277839809591715219 relative error = 14.657470199905089620046844474831 % h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.1MB, time=80.34 NO POLE NO POLE x[1] = 1.133 y2[1] (analytic) = 1.5760553445358218558945952042796 y2[1] (numeric) = 1.5755753137675542823893405017564 absolute error = 0.0004800307682675735052547025232 relative error = 0.030457735506042883072940899774257 % h = 0.001 y1[1] (analytic) = 2.9056880970308483017752273679812 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4262625584266453015019394327656 relative error = 14.669935113208397317118750056306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.134 y2[1] (analytic) = 1.5769612444542147633009795341995 y2[1] (numeric) = 1.5764772999940192042917327281884 absolute error = 0.0004839444601955590092468060111 relative error = 0.030688418114108559762993952749086 % h = 0.001 y1[1] (analytic) = 2.9061115887716442624534759577981 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4266860501674412621801880225825 relative error = 14.68236979667367122628030189174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.135 y2[1] (analytic) = 1.5778675674113279632641468553367 y2[1] (numeric) = 1.5773796834723932860186536269597 absolute error = 0.000487883938934677245493228377 relative error = 0.030920461831603940916127846933443 % h = 0.001 y1[1] (analytic) = 2.906534174400926960784009421237 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4271086357967239605107214860214 relative error = 14.694774262709516955611387606256 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.136 y2[1] (analytic) = 1.578774312500838574197807779727 y2[1] (numeric) = 1.5782824631664248534464587094213 absolute error = 0.0004918493344137207513490703057 relative error = 0.031153872375502024328363993451378 % h = 0.001 y1[1] (analytic) = 2.9069558534961108026995973608071 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4275303148919078024263094255915 relative error = 14.707148523694626945240575997864 % h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.1MB, time=80.87 NO POLE NO POLE x[1] = 1.137 y2[1] (analytic) = 1.5796814788160015821534396475239 y2[1] (numeric) = 1.5791856380389846498896131142079 absolute error = 0.000495840777016932263826533316 relative error = 0.031388655476835333161946759974443 % h = 0.001 y1[1] (analytic) = 2.9073766256355167281563212882432 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4279510870313137278830333530276 relative error = 14.719492591977789948740611182977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.138 y2[1] (analytic) = 1.5805890654496507475652249134399 y2[1] (numeric) = 1.5800892070520658361006916072383 absolute error = 0.0004998583975849114645333062016 relative error = 0.031624816880705817043791774717272 % h = 0.001 y1[1] (analytic) = 2.9077964903983726328125995285035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4283709517941696325393115932879 relative error = 14.731806479877900506185866558341 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.139 y2[1] (analytic) = 1.5814970714941995124162151153795 y2[1] (numeric) = 1.580993169166783990270378581715 absolute error = 0.0005039023274155221458365336645 relative error = 0.031862362346294760003185440125322 % h = 0.001 y1[1] (analytic) = 2.9082154473648137888012564970109 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4287899087606107885279685617953 relative error = 14.744090199683968408762348890875 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.14 y2[1] (analytic) = 1.5824054960416419078248132591774 y2[1] (numeric) = 1.5818975233433771080274680581246 absolute error = 0.0005079726982647997973452010528 relative error = 0.032101297646872695427526584955837 % h = 0.001 y1[1] (analytic) = 2.9086334961158832645942155781022 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4292079575116802643209276428866 relative error = 14.756343763655128154821302424947 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=583.6MB, alloc=4.1MB, time=81.43 x[1] = 1.141 y2[1] (analytic) = 1.5833143381835534620506670330335 y2[1] (numeric) = 1.5828022685412056024388636842373 absolute error = 0.0005120696423478596118033487962 relative error = 0.03234162856980932821438873016967 % h = 0.001 y1[1] (analytic) = 2.909050636233532343959395740028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4296250976293293436861078048124 relative error = 14.768567184020648397267920866119 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.142 y2[1] (analytic) = 1.5842235970110921089190648458288 y2[1] (numeric) = 1.5837074037187523040095787351074 absolute error = 0.0005161932923398049094861107214 relative error = 0.032583360916583464297669546570712 % h = 0.001 y1[1] (analytic) = 2.9094668673006209440093929296424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4300413286964179437361049944268 relative error = 14.780760472979941382177131466925 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.143 y2[1] (analytic) = 1.5851332716149990966629262650005 y2[1] (numeric) = 1.584612927833622460682736113073 absolute error = 0.0005203437813766359801901519275 relative error = 0.032826500502792947725082754289463 % h = 0.001 y1[1] (analytic) = 2.9098821889009180323415281981339 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4304566502967150320682402629183 relative error = 14.792923642702572378528870209505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.144 y2[1] (analytic) = 1.5860433610855998971814780120622 y2[1] (numeric) = 1.5855188398425437378395683477561 absolute error = 0.0005245212430561593419096643061 relative error = 0.033071053158164605463736969477035 % h = 0.001 y1[1] (analytic) = 2.910296600619102043268845417787 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4308710620148990429955574825714 relative error = 14.805056705328269098955720257866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=587.4MB, alloc=4.1MB, time=81.95 x[1] = 1.145 y2[1] (analytic) = 1.5869538645128051157147062571694 y2[1] (numeric) = 1.5864251387013662182994175960626 absolute error = 0.0005287258114388974152886611068 relative error = 0.033317024726564200110035855740131 % h = 0.001 y1[1] (analytic) = 2.9107101020407612931416423588084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4312845634365582928683544235928 relative error = 14.817159672966931111396237444335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.146 y2[1] (analytic) = 1.5878647809861114009326755383524 y2[1] (numeric) = 1.5873318233650624023197356421823 absolute error = 0.0005329576210489986129398961701 relative error = 0.033564421066006390679624399881673 % h = 0.001 y1[1] (analytic) = 2.9111226927523943947591198047236 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.431697154148191394485831869508 relative error = 14.829232557698639241547736566725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.147 y2[1] (analytic) = 1.5887761095946023554388042161757 y2[1] (numeric) = 1.5882388927877272075960838975888 absolute error = 0.0005372168068751478427203185869 relative error = 0.033813248048664701652597217318582 % h = 0.001 y1[1] (analytic) = 2.9115343723414106708707342947284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4321088337372076705974463595128 relative error = 14.841275371573664966012760709851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.148 y2[1] (analytic) = 1.5896878494269494466861859606218 y2[1] (numeric) = 1.5891463459225779692621334010397 absolute error = 0.0005415035043714774240525595821 relative error = 0.03406351156088150044867651430305 % h = 0.001 y1[1] (analytic) = 2.9119451403961305667668409916768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4325196017919275664935530564612 relative error = 14.853288126612479796033902673448 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.149 y2[1] (analytic) = 1.590599999571412918306046353956 y2[1] (numeric) = 1.5900541817219544398896648185763 absolute error = 0.0005458178494584784163815353797 relative error = 0.034315217503177983506559706051594 % h = 0.001 y1[1] (analytic) = 2.9123549965057860619582140850978 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4329294579015830616849261498822 relative error = 14.86527083480576465171209289358 % h = 0.001 TOP MAIN SOLVE Loop memory used=591.2MB, alloc=4.1MB, time=82.49 NO POLE NO POLE x[1] = 1.15 y2[1] (analytic) = 1.5915125591158427018474232811901 y2[1] (numeric) = 1.590962399137318789488568443524 absolute error = 0.0005501599785239123588548376661 relative error = 0.034568371790264171141129723547208 % h = 0.001 y1[1] (analytic) = 2.9127639402605210809440330497537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4333384016563180806707451145381 relative error = 14.877223508114419226603911991951 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.151 y2[1] (analytic) = 1.5924255271476793289271593685416 y2[1] (numeric) = 1.591870997119255605506844196492 absolute error = 0.0005545300284237234203151720496 relative error = 0.034822980351048911351714751281698 % h = 0.001 y1[1] (analytic) = 2.913171971251391903067923991789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4337464326471889027946360565734 relative error = 14.889146158469571342593928282896 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.152 y2[1] (analytic) = 1.5933389027539548437892943199711 y2[1] (numeric) = 1.5927799746174718928306016253733 absolute error = 0.0005589281364829509586926945978 relative error = 0.035079049128649892754078534925146 % h = 0.001 y1[1] (analytic) = 2.9135790890703675714616462264618 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4341535504661645711883582912462 relative error = 14.901038797772586294938501216469 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.153 y2[1] (analytic) = 1.594252685021293716272944592482 y2[1] (numeric) = 1.5936893305807970737840599053449 absolute error = 0.0005633544404966424888846871371 relative error = 0.035336584080403666808317495367488 % h = 0.001 y1[1] (analytic) = 2.9139852933103303010760151438061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4345597547061273008027272085905 relative error = 14.912901437895076187377930843948 % h = 0.001 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.1MB, time=83.03 NO POLE NO POLE x[1] = 1.154 y2[1] (analytic) = 1.5951668730359137551877574423796 y2[1] (numeric) = 1.5945990639571829881295478388676 absolute error = 0.000567809078730767058209603512 relative error = 0.035595591177875679514336695647964 % h = 0.001 y1[1] (analytic) = 2.9143905835650758857986533313354 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4349650449608728855253653961198 relative error = 14.924734090678909257214270964383 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.155 y2[1] (analytic) = 1.5960814658836270220960259671097 y2[1] (numeric) = 1.5955091736937038930675038556862 absolute error = 0.0005722921899231290285221114235 relative error = 0.035856076406870312746073242034829 % h = 0.001 y1[1] (analytic) = 2.9147949594293141046581628360706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.435369420825111104384874900855 relative error = 14.93653676793621919025255965335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.156 y2[1] (analytic) = 1.5969964626498407455005513606404 y2[1] (numeric) = 1.5964196587365564632364760128292 absolute error = 0.0005768039132842822640753478112 relative error = 0.036118045767440935395132973041468 % h = 0.001 y1[1] (analytic) = 2.9151984204986691271143123617542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4357728818944661268410244265386 relative error = 14.948309481449414425503655393232 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.157 y2[1] (analytic) = 1.5979118624195582354373381945989 y2[1] (numeric) = 1.5973305180310597907131219946092 absolute error = 0.0005813443884984447242161999897 relative error = 0.03638150527389996449400431102567 % h = 0.001 y1[1] (analytic) = 2.9156009663696799174338341110968 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4361754277654769171605461758812 relative error = 14.96005224297118744954730002363 % h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.1MB, time=83.56 NO POLE NO POLE x[1] = 1.158 y2[1] (analytic) = 1.5988276642773797984722081325456 y2[1] (numeric) = 1.5982417505216553850122091126225 absolute error = 0.0005859137557244134599990199231 relative error = 0.036646460954828936488511933760471 % h = 0.001 y1[1] (analytic) = 2.9160025966398006381514258972928 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4365770580355976378781379620772 relative error = 14.97176506422452408045446121643 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.159 y2[1] (analytic) = 1.5997438673075036531004170808466 y2[1] (numeric) = 1.5991533551519071730866143057494 absolute error = 0.0005905121555964800138027750972 relative error = 0.036912918853088588828672478208547 % h = 0.001 y1[1] (analytic) = 2.9164033109074010526155550638374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4369777723031980523422671286218 relative error = 14.983447956902712741168437158156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.16 y2[1] (analytic) = 1.600660470593726845548360376606 y2[1] (numeric) = 1.600065330864501499327324140154 absolute error = 0.000595139729225346221036236452 relative error = 0.037180885025828952046614828862738 % h = 0.001 y1[1] (analytic) = 2.9168031087717669266186616668743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4373775701675639263453737316587 relative error = 14.995100932669353722244634597836 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.161 y2[1] (analytic) = 1.6015774732194461659764502110262 y2[1] (numeric) = 1.6009776766012471255634348092843 absolute error = 0.0005997966181990404130154017419 relative error = 0.037450365544499452489728678368839 % h = 0.001 y1[1] (analytic) = 2.9172019898331004291113592899035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4377764512288974288380713546879 relative error = 15.006724003158368433849358397253 % h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.1MB, time=84.08 NO POLE NO POLE x[1] = 1.162 y2[1] (analytic) = 1.602494874267659065082249085398 y2[1] (numeric) = 1.6018903913030752310621521338723 absolute error = 0.0006044829645838340200969515257 relative error = 0.037721366494859025876706991889488 % h = 0.001 y1[1] (analytic) = 2.9175999536925205320002327766828 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4381744150883175317269448414672 relative error = 15.018317179974008646918376207668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.163 y2[1] (analytic) = 1.6034126728209645711029426966612 y2[1] (numeric) = 1.6028034739100394125287915619337 absolute error = 0.0006091989109251585741511347275 relative error = 0.037993893976986241843650768489919 % h = 0.001 y1[1] (analytic) = 2.917996999952063409028833084559 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4385714613478604087555451493434 relative error = 15.0298804746908657233764458981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.164 y2[1] (analytic) = 1.6043308679615642072162352501407 y2[1] (numeric) = 1.6037169233613156841067781687682 absolute error = 0.0006139446002485231094570813725 relative error = 0.038267954105289439646908085127627 % h = 0.001 y1[1] (analytic) = 2.9183931282146828337414703772652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4389675896104798334681824420496 relative error = 15.041413898853879835319415880521 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.165 y2[1] (analytic) = 1.6052494587712629093387497986382 y2[1] (numeric) = 1.6046307385952024773776466569594 absolute error = 0.0006187201760604319611031416788 relative error = 0.038543553008516875188823842060965 % h = 0.001 y1[1] (analytic) = 2.9187883380842505765294073934265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4393627994800475762561194582109 relative error = 15.052917463978349173060929522482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=606.5MB, alloc=4.1MB, time=84.62 x[1] = 1.166 y2[1] (analytic) = 1.6061684443314699443210158095567 y2[1] (numeric) = 1.6055449185491206413610413563747 absolute error = 0.000623525782349302959974453182 relative error = 0.038820696829766879532081913874335 % h = 0.001 y1[1] (analytic) = 2.9191826291655568007590560446127 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4397570905613538004857681093971 relative error = 15.064391181549939141946184412708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.167 y2[1] (analytic) = 1.6070878237231998285381257651454 y2[1] (numeric) = 1.6064594621596134425147162241655 absolute error = 0.0006283615635863860234095409799 relative error = 0.039099391726498029067827558442191 % h = 0.001 y1[1] (analytic) = 2.9195760010643104579817811147742 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4401504624601074577084931795586 relative error = 15.075835063024691547835615355781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.168 y2[1] (analytic) = 1.6080075960270732468751422052864 y2[1] (numeric) = 1.6073743683623465647345348447669 absolute error = 0.0006332276647266821406073605195 relative error = 0.039379643870539327502264958332697 % h = 0.001 y1[1] (analytic) = 2.9199684533871396822249158512909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4405429147829366819516279160753 relative error = 15.087249119829033771161786623443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.169 y2[1] (analytic) = 1.6089277603233179721063362274918 y2[1] (numeric) = 1.6082896360921081093544704298981 absolute error = 0.0006381242312098627518657975937 relative error = 0.039661459448100399825932675107402 % h = 0.001 y1[1] (analytic) = 2.9203599857415921833635951566516 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.440934447137389183090307221436 relative error = 15.098633363359787929463194187547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.17 y2[1] (analytic) = 1.6098483156917697846673380649495 y2[1] (numeric) = 1.609205264282808595146605818562 absolute error = 0.0006430514089611895207322463875 relative error = 0.0399448446597816984293685982461 % h = 0.001 y1[1] (analytic) = 2.920750597736135639573013008962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4413250591319326392997250737464 relative error = 15.109987804984180028299092408644 % h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.1MB, time=85.15 NO POLE NO POLE x[1] = 1.171 y2[1] (analytic) = 1.6107692612118733928192799705438 y2[1] (numeric) = 1.6101212518674809583211334770455 absolute error = 0.0006480093443924344981464934983 relative error = 0.040229805720584721528385676470059 % h = 0.001 y1[1] (analytic) = 2.9211402889801580888607116590592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4417147503759550885874237238436 relative error = 15.121312456039849100449871960091 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.172 y2[1] (analytic) = 1.6116905959626833532040112427848 y2[1] (numeric) = 1.6110375977782805525263554989193 absolute error = 0.0006529981844028006776557438655 relative error = 0.040516348859922244061690341149749 % h = 0.001 y1[1] (analytic) = 2.9215290590839683196785110719728 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4421035204797653194052231367572 relative error = 15.132607327834856333307926635294 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.173 y2[1] (analytic) = 1.6126123190228649917894648385082 y2[1] (numeric) = 1.6119543009464851488486836050381 absolute error = 0.0006580180763798429407812334701 relative error = 0.040804480321628561223087078739329 % h = 0.001 y1[1] (analytic) = 2.9219169076587962606136880008392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4424913690545932603404000656236 relative error = 15.143872431647694184364356121143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.174 y2[1] (analytic) = 1.6135344294706953252042546270552 y2[1] (numeric) = 1.6128713603024949358126391435404 absolute error = 0.0006630691682003893916154835148 relative error = 0.04109420636396974479002509240594 % h = 0.001 y1[1] (analytic) = 2.9223038343167933691590150021193 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4428782957125903688857270669037 relative error = 15.155107778727295484697259828446 % h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.1MB, time=85.69 NO POLE NO POLE x[1] = 1.175 y2[1] (analytic) = 1.6144569263840639824605819514124 y2[1] (numeric) = 1.6137887747758325193808530898485 absolute error = 0.0006681516082314630797288615639 relative error = 0.041385533259653912409756421819244 % h = 0.001 y1[1] (analytic) = 2.9226898386710330195612706221156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4432643000668300192879826869 relative error = 15.166313380293042530367783456191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.176 y2[1] (analytic) = 1.6153798088404741270645297734828 y2[1] (numeric) = 1.6147065432951429229540660466688 absolute error = 0.000673265545331204110463726814 relative error = 0.04167846729584151000388927450021 % h = 0.001 y1[1] (analytic) = 2.923074920335510889747832906309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4436493817313078894745449710934 relative error = 15.177489247534776161630485135317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.177 y2[1] (analytic) = 1.6163030759170433795128222932681 y2[1] (numeric) = 1.6156246647881935873711282439914 absolute error = 0.0006784111288497921416940492767 relative error = 0.041973014774155607451635671638437 % h = 0.001 y1[1] (analytic) = 2.9234590789251453473309693049552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4440335403209423470576813697396 relative error = 15.188635391612804829864991755226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.178 y2[1] (analytic) = 1.6172267266905047401751275452828 y2[1] (numeric) = 1.6165431381818743709089995390904 absolute error = 0.0006835885086303692661280061924 relative error = 0.042269182010692207711568836049184 % h = 0.001 y1[1] (analytic) = 2.923842314055777834689436970682 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4444167754515748344161490354664 relative error = 15.199751823657913652136318427241 % h = 0.001 TOP MAIN SOLVE Loop memory used=617.9MB, alloc=4.1MB, time=86.22 NO POLE NO POLE x[1] = 1.179 y2[1] (analytic) = 1.6181507602372075125609800899718 y2[1] (numeric) = 1.6174619624021975492827494165237 absolute error = 0.0006887978350099632782306734481 relative error = 0.042566975336030569541223058721271 % h = 0.001 y1[1] (analytic) = 2.9242246253441732531270083665204 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4447990867399702528537204313048 relative error = 15.210838554771373453291624989149 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.18 y2[1] (analytic) = 1.6190751756331182269704005332872 y2[1] (numeric) = 1.6183811363742978156455569881331 absolute error = 0.0006940392588204113248435451541 relative error = 0.042866401095243543973387083356824 % h = 0.001 y1[1] (analytic) = 2.9246060124080203461075380258748 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4451804738038173458342500906592 relative error = 15.22189559602494979550158300887 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.181 y2[1] (analytic) = 1.6199999719538215645272882238809 y2[1] (numeric) = 1.6193006590224322805887109930443 absolute error = 0.0006993129313892839385772308366 relative error = 0.043167465647907924707461354205549 % h = 0.001 y1[1] (analytic) = 2.924986474865932081566187229398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4455609362617290812928992941824 relative error = 15.232922958460911995154924908427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.182 y2[1] (analytic) = 1.620925148274521281594663094598 y2[1] (numeric) = 1.6202205292699804721416097976669 absolute error = 0.0007046190045408094530532969311 relative error = 0.043470175368114812573769790879975 % h = 0.001 y1[1] (analytic) = 2.9253660123374460332964242875787 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4459404737332430330231363523631 relative error = 15.243920653092042127015143606988 % h = 0.001 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.1MB, time=86.75 NO POLE NO POLE x[1] = 1.183 y2[1] (analytic) = 1.621850703670041134570832233106 y2[1] (numeric) = 1.6211407460394443357717613956943 absolute error = 0.0007099576305967987990708374117 relative error = 0.04377453664447999422823809355962 % h = 0.001 y1[1] (analytic) = 2.9257446244430247614124190420718 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4463190858388217611391311068562 relative error = 15.254888690901644015548706478734 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.184 y2[1] (analytic) = 1.6227766372148258050655563855695 y2[1] (numeric) = 1.6220613082524482343847834081039 absolute error = 0.0007153289623775706807729774656 relative error = 0.044080555880154335234372952124057 % h = 0.001 y1[1] (analytic) = 2.9261223108040561918864511234096 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.446696772199853191613163188194 relative error = 15.265827082843552213334541443168 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.185 y2[1] (analytic) = 1.6237029479829418254552912172827 y2[1] (numeric) = 1.622982214829738948324403083157 absolute error = 0.0007207331532028771308881341257 relative error = 0.044388239492834187688999942493085 % h = 0.001 y1[1] (analytic) = 2.926499071042853995160952427717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4470735324386509948876644925014 relative error = 15.276735839842140966464945657029 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.186 y2[1] (analytic) = 1.6246296350480785048165777750938 y2[1] (numeric) = 1.6239034646911856753724572963986 absolute error = 0.0007261703568928294441204786952 relative error = 0.044697593914771812547742350816077 % h = 0.001 y1[1] (analytic) = 2.9268749047826579638348052004202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4474493661784549635615172652046 relative error = 15.28761497279233316684845856356 % h = 0.001 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.1MB, time=87.30 NO POLE NO POLE x[1] = 1.187 y2[1] (analytic) = 1.6255566974835488552366562183088 y2[1] (numeric) = 1.6248250567557800307488925506578 absolute error = 0.000731640727768824487763667651 relative error = 0.04500862559278581680574868069291 % h = 0.001 y1[1] (analytic) = 2.9272498116476343894235180406812 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4478242730434313891502301054656 relative error = 15.298464492559609291325630981405 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.188 y2[1] (analytic) = 1.6264841343622905185003765075383 y2[1] (numeric) = 1.6257469899416360471117649760474 absolute error = 0.0007371444206544713886115314909 relative error = 0.045321340988271605688703178471758 % h = 0.001 y1[1] (analytic) = 2.9276237912628764381929030664147 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4481982526586734379196151311991 relative error = 15.30928440998001632750901048722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.189 y2[1] (analytic) = 1.6274119447568666931524793646539 y2[1] (numeric) = 1.6266692631659901745572403299642 absolute error = 0.0007426815908765185952390346897 relative error = 0.045635746577211850008681365097513 % h = 0.001 y1[1] (analytic) = 2.9279968432544045260658784062408 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4485713046502015257925904710252 relative error = 15.320074735860176686259050568002 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.19 y2[1] (analytic) = 1.6283401277394670619343204416495 y2[1] (numeric) = 1.6275918753452012806195939970889 absolute error = 0.0007482523942657813147264445606 relative error = 0.045951848850186968838941298902138 % h = 0.001 y1[1] (analytic) = 2.9283689672491666926020211116027 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4489434286449636923287331763871 relative error = 15.330835480977297100708036896421 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=629.4MB, alloc=4.1MB, time=87.83 x[1] = 1.191 y2[1] (analytic) = 1.6292686823819087195941102617622 y2[1] (numeric) = 1.628514825394750650271210989386 absolute error = 0.0007538569871580693228992723762 relative error = 0.046269654312385627661271120100432 % h = 0.001 y1[1] (analytic) = 2.9287401628750389740494965095271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4493146242708359737762085743115 relative error = 15.341566656079177511744508620002 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.192 y2[1] (analytic) = 1.6301976077556371010697421226884 y2[1] (numeric) = 1.6294381122292419859225859461039 absolute error = 0.0007594955263951151471561765845 relative error = 0.046589169483615252139044352523204 % h = 0.001 y1[1] (analytic) = 2.9291104297608257754689909441298 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4496848911566227751957030089142 relative error = 15.352268271884219939871035758083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.193 y2[1] (analytic) = 1.6311269029317269100432797791466 y2[1] (numeric) = 1.630361734762401407422323133775 absolute error = 0.0007651681693255026209566453716 relative error = 0.046910400898312557668666470071266 % h = 0.001 y1[1] (analytic) = 2.929479767536260241929275782964 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4500542289320572416559878477484 relative error = 15.362940339081437343348595673793 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.194 y2[1] (analytic) = 1.6320565669808830478661763503744 y2[1] (numeric) = 1.6312856919070774520571364462154 absolute error = 0.000770875073805595809039904159 relative error = 0.047233355105554094861629381519569 % h = 0.001 y1[1] (analytic) = 2.9298481758320046287740314926789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4504226372278016285007435574633 relative error = 15.373582868330462462541172137262 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.195 y2[1] (analytic) = 1.63298659897344154285429552742 y2[1] (numeric) = 1.6322099825752410745518494045251 absolute error = 0.0007766163982004683024461228949 relative error = 0.047558038669066811108924756438971 % h = 0.001 y1[1] (analytic) = 2.9302156542796506709595615171946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.450790115675447670686273581979 relative error = 15.384195870261556650374579725487 % h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.1MB, time=88.36 NO POLE NO POLE x[1] = 1.196 y2[1] (analytic) = 1.6339169979793704799518057852832 y2[1] (numeric) = 1.6331346056779856470693951570882 absolute error = 0.000782392301384832882410628195 relative error = 0.047884458167238628379102514231527 % h = 0.001 y1[1] (analytic) = 2.9305822025117199514630266207112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4511566639075169511897386854956 relative error = 15.394779355475618688823894219112 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.197 y2[1] (analytic) = 1.6348477630682709307630179360904 y2[1] (numeric) = 1.6340595601255269592108164795725 absolute error = 0.0007882029427439715522014565179 relative error = 0.048212620193129037400797335796563 % h = 0.001 y1[1] (analytic) = 2.9309478201616642687608312873475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4515222815574612684875433521319 relative error = 15.40533333454419359134424626149 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.198 y2[1] (analytic) = 1.6357788933093778839512359915417 y2[1] (numeric) = 1.6349848448272032180152657749297 absolute error = 0.000794048482174665935970216612 relative error = 0.048542531354479708380083740027809 % h = 0.001 y1[1] (analytic) = 2.9313125068638660033767946990539 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4518869682596630031035067638383 relative error = 15.415857818009481391160110845974 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.199 y2[1] (analytic) = 1.6367103877715611760036909358589 y2[1] (numeric) = 1.6359104586914750479600050733954 absolute error = 0.0007999290800861280436858624635 relative error = 0.048874198273725118402559103795557 % h = 0.001 y1[1] (analytic) = 2.9316762622536384834997397436597 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4522507236494354832264518084441 relative error = 15.426352816384345915328599198323 % h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.1MB, time=88.90 NO POLE NO POLE x[1] = 1.2 y2[1] (analytic) = 1.6376422455233264223616266443769 y2[1] (numeric) = 1.636836400625925490960406032489 absolute error = 0.0008058448974009314012206118879 relative error = 0.049207627588003195669594000387592 % h = 0.001 y1[1] (analytic) = 2.9320390859672263496701344354948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4526135473630233493968465002792 relative error = 15.436818340152323544492632327205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.201 y2[1] (analytic) = 1.6385744656328159489146068177702 y2[1] (numeric) = 1.637762669537260006369949937014 absolute error = 0.0008117960955559425446568807562 relative error = 0.049542825949165980717730395815762 % h = 0.001 y1[1] (analytic) = 2.9324009776418059185354210619766 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.452975439037602918262133126761 relative error = 15.447254399767631958240246932338 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.202 y2[1] (analytic) = 1.6395070471678097238581114376854 y2[1] (numeric) = 1.6386892643313064709802276990576 absolute error = 0.0008177828365032528778837386278 relative error = 0.049879800023790304769750581875131 % h = 0.001 y1[1] (analytic) = 2.9327619369154855456736693008611 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4533363983112825454003813656455 relative error = 15.457661005655178865986654491182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.203 y2[1] (analytic) = 1.6404399891957262899134908862618 y2[1] (numeric) = 1.639616183913015179020939857991 absolute error = 0.0008238052827111108925510282708 relative error = 0.05021855649318848536548324620495 % h = 0.001 y1[1] (analytic) = 2.9331219634273059874851904845377 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4536964248231029872119025493221 relative error = 15.468038168210570723296043196884 % h = 0.001 TOP MAIN SOLVE Loop memory used=640.8MB, alloc=4.1MB, time=89.43 NO POLE NO POLE x[1] = 1.204 y2[1] (analytic) = 1.6413732907836236969093455096614 y2[1] (numeric) = 1.6405434271864588421598965804692 absolute error = 0.0008298635971648547494489291922 relative error = 0.050559102053419039419957790155202 % h = 0.001 y1[1] (analytic) = 2.9334810568172407621517511197817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4540555182130377618784631845661 relative error = 15.478385897800121433560479996551 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.205 y2[1] (analytic) = 1.6423069509982004347233980443092 y2[1] (numeric) = 1.6414709930548325895030176604311 absolute error = 0.0008359579433678452203803838781 relative error = 0.05090144341529741385606391207238 % h = 0.001 y1[1] (analytic) = 2.9338392167261965096630247037822 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4544136781219935093897367685666 relative error = 15.488704204760861034953636285401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.206 y2[1] (analytic) = 1.6432409689057963665839259640468 y2[1] (numeric) = 1.6423988804204539675943325190995 absolute error = 0.0008420884853423989895934449473 relative error = 0.051245587304406733958420582875015 % h = 0.001 y1[1] (analytic) = 2.9341964427960133509099218100225 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4547709041918103506366338748069 relative error = 15.498993099400544372577425853316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.207 y2[1] (analytic) = 1.6441753435723936627298204468466 y2[1] (numeric) = 1.643327088184762940415980204981 absolute error = 0.0008482553876307223138402418656 relative error = 0.051591540461108569594706860116971 % h = 0.001 y1[1] (analytic) = 2.9345527346694652458444393507144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4551271960652622455711514154988 relative error = 15.509252591997659755720007461021 % h = 0.001 TOP MAIN SOLVE Loop memory used=644.6MB, alloc=4.1MB, time=89.97 NO POLE NO POLE x[1] = 1.208 y2[1] (analytic) = 1.6451100740636177344283383011036 y2[1] (numeric) = 1.6442556152483218893882093938662 absolute error = 0.0008544588152958450401289072374 relative error = 0.051939309640553719450256521832821 % h = 0.001 y1[1] (analytic) = 2.9349080919902603507056708559653 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4554825533860573504323829207497 relative error = 15.51948269280143760014396694802 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.209 y2[1] (analytic) = 1.6460451594447381683496128338324 y2[1] (numeric) = 1.6451844605108156133693783888296 absolute error = 0.0008606989339225549802344450028 relative error = 0.052288901612693013421269259887801 % h = 0.001 y1[1] (analytic) = 2.9352625144030413743116205436987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4558369757988383740383326084831 relative error = 15.529683412031859055323855048745 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.21 y2[1] (analytic) = 1.6469805987806696612969892863352 y2[1] (numeric) = 1.6461136228710513286559551202295 absolute error = 0.0008669759096183326410341661057 relative error = 0.05264032316228813331154315974822 % h = 0.001 y1[1] (analytic) = 2.9356160015533859334164648885436 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.456190462949182933143176953328 relative error = 15.53985475987966461655261712163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.211 y2[1] (analytic) = 1.6479163911359729552922501070842 y2[1] (numeric) = 1.6470431012269586689825171457081 absolute error = 0.0008732899090142863097329613761 relative error = 0.052993581088922451977186416796071 % h = 0.001 y1[1] (analytic) = 2.9359685530878069071329063324602 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4565430144836039068596183972446 relative error = 15.549996746506362721836809782986 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=648.5MB, alloc=4.1MB, time=90.52 x[1] = 1.212 y2[1] (analytic) = 1.6488525355748557730147949766699 y2[1] (numeric) = 1.6479728944755896855217516501915 absolute error = 0.0008796410992660874930433264784 relative error = 0.053348682207011891063320704221727 % h = 0.001 y1[1] (analytic) = 2.9363201686537527904192647147783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4568946300495497901459767795627 relative error = 15.560109382044238333500856988405 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.213 y2[1] (analytic) = 1.6497890311611737535938401457143 y2[1] (numeric) = 1.6489030015131188468844554458896 absolute error = 0.0008860296480549067093846998247 relative error = 0.053705633345815797476344320786245 % h = 0.001 y1[1] (analytic) = 2.9366708478996080466309529345866 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.457245309295405046357664999371 relative error = 15.570192676596361504420954423709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.214 y2[1] (analytic) = 1.6507258769584313887527012936274 y2[1] (numeric) = 1.6498334212348430391195349722964 absolute error = 0.000892455723588349633166321331 relative error = 0.054064441349447838734880214020924 % h = 0.001 y1[1] (analytic) = 2.9370205904746934591359842940259 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4575950518704904588626963588103 relative error = 15.580246640236595928809586159924 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.215 y2[1] (analytic) = 1.6516630720297829593042237640016 y2[1] (numeric) = 1.6507641525351815657140062961896 absolute error = 0.000898919494601393590217467812 relative error = 0.054425113076886917342092202165976 % h = 0.001 y1[1] (analytic) = 2.9373693960292664819941599070089 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4579438574250634817208719717933 relative error = 15.590271283009607477471971397333 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.216 y2[1] (analytic) = 1.6526006154380334719964236812925 y2[1] (numeric) = 1.6516951943076761475929951116308 absolute error = 0.0009054211303573244034285696617 relative error = 0.054787655401988104321612211942848 % h = 0.001 y1[1] (analytic) = 2.9377172642145215896995854942074 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4582917256103185894262975589918 relative error = 15.600266614930872717456111776828 % h = 0.001 memory used=652.3MB, alloc=4.1MB, time=91.05 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.217 y2[1] (analytic) = 1.6535385062456395967074031032222 y2[1] (numeric) = 1.6526265454449909231197367399655 absolute error = 0.0009119608006486735876663632567 relative error = 0.055152075213493592058882115209053 % h = 0.001 y1[1] (analytic) = 2.938064194682590625986167821821 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4586386560783876257128798866054 relative error = 15.610232645986687416018461177621 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.218 y2[1] (analytic) = 1.6544767435147106039886020140696 y2[1] (numeric) = 1.6535582048389124480955761298231 absolute error = 0.0009185386757981558930258842465 relative error = 0.055518379415043666589275791373823 % h = 0.001 y1[1] (analytic) = 2.938410187086543151695741978658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4589846484823401514224540434424 relative error = 15.620169386134175028827590153184 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.219 y2[1] (analytic) = 1.6554153263070093029554496156717 y2[1] (numeric) = 1.6544901713803496957599678571169 absolute error = 0.0009251549266596071954817585548 relative error = 0.055886574925187699473930369490879 % h = 0.001 y1[1] (analytic) = 2.9387552410803867917084816234314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4593297024761837914351936882158 relative error = 15.630076845301295172328566187257 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.22 y2[1] (analytic) = 1.6563542536839529795244770255648 y2[1] (numeric) = 1.6554224439593340567904761250441 absolute error = 0.0009318097246189227340009005207 relative error = 0.056256668677395159403780220546516 % h = 0.001 y1[1] (analytic) = 2.9390993563190675809352452718884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4596738177148645806619573366728 relative error = 15.639955033386852080191118783231 % h = 0.001 TOP MAIN SOLVE Loop memory used=656.1MB, alloc=4.1MB, time=91.58 NO POLE NO POLE x[1] = 1.221 y2[1] (analytic) = 1.6572935247066143349959531452297 y2[1] (numeric) = 1.6563550214650193393027747640857 absolute error = 0.000938503241594995693178381144 relative error = 0.05662866762006664367185318122309 % h = 0.001 y1[1] (analytic) = 2.9394425324584703093715126314552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4600169938542673090982246962396 relative error = 15.649803960260503043765005038022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.222 y2[1] (analytic) = 1.6582331384357224249811051158837 y2[1] (numeric) = 1.6572879027856817688506472320066 absolute error = 0.0009452356500406561304578838771 relative error = 0.057002578716544929653455701510122 % h = 0.001 y1[1] (analytic) = 2.9397847691554188662125659294917 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4603592305512158659392779942761 relative error = 15.659623635762766836466336800467 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.223 y2[1] (analytic) = 1.6591730939316635986729844346777 y2[1] (numeric) = 1.6582210868087199884259866138557 absolute error = 0.000952007122943610246997820822 relative error = 0.057378408945126046433442124961981 % h = 0.001 y1[1] (analytic) = 2.94012606606767658302957212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4607005274634735827562841847844 relative error = 15.669414069705032122018974778654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.224 y2[1] (analytic) = 1.6601133902544824384600394605093 y2[1] (numeric) = 1.6591545724206550584587956219656 absolute error = 0.0009588178338273800012438385437 relative error = 0.057756165299070366719333137351804 % h = 0.001 y1[1] (analytic) = 2.9404664228539465760062227927368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4610408842497435757329348575212 relative error = 15.67917527186956584647543804563 % h = 0.001 TOP MAIN SOLVE Loop memory used=659.9MB, alloc=4.1MB, time=92.12 NO POLE NO POLE x[1] = 1.225 y2[1] (analytic) = 1.6610540264638826998814546959592 y2[1] (numeric) = 1.6600883585071304568171865959529 absolute error = 0.0009656679567522430642681000063 relative error = 0.058135854786613719178619562433023 % h = 0.001 y1[1] (analytic) = 2.9408058391738720872355895481154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4613803005696690869623016128998 relative error = 15.688907252009521613942119302616 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.226 y2[1] (analytic) = 1.6619950016192282519233168900892 y2[1] (numeric) = 1.6610224439529120788073815027181 absolute error = 0.0009725576663161731159353873711 relative error = 0.058517484430978521338160147319571 % h = 0.001 y1[1] (analytic) = 2.9411443146880368250768535410717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4617187760838338248035656058561 relative error = 15.69861001984894804593393699843 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.227 y2[1] (analytic) = 1.6629363147795440176546676660131 y2[1] (numeric) = 1.6619568276418882371737119364456 absolute error = 0.0009794871376557804809557295675 relative error = 0.058901061270384933183155769663798 % h = 0.001 y1[1] (analytic) = 2.9414818490579653035715688371935 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4620563104537623032982809019779 relative error = 15.708283585082797124283894977508 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.228 y2[1] (analytic) = 1.6638779650035169152025020372686 y2[1] (numeric) = 1.6628915084570696620986191186036 absolute error = 0.000986456546447253103882918665 relative error = 0.059286592358062031592757619718187 % h = 0.001 y1[1] (analytic) = 2.9418184419461231809191201648767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4623929033419201806458322296611 relative error = 15.717927957376932517533358741452 % h = 0.001 TOP MAIN SOLVE Loop memory used=663.7MB, alloc=4.1MB, time=92.65 NO POLE NO POLE x[1] = 1.229 y2[1] (analytic) = 1.6648199513494967990647718380677 y2[1] (numeric) = 1.6638264852805895012026538979442 absolute error = 0.0009934660689072978621179401235 relative error = 0.059674084762259005748943366475047 % h = 0.001 y1[1] (analytic) = 2.9421540930159175970110365880794 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4627285544117145967377486528638 relative error = 15.727543146368137890729194665124 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.23 y2[1] (analytic) = 1.6657622728754974017604527545023 y2[1] (numeric) = 1.6647617569937033195444767505034 absolute error = 0.0010005158817940822159760039989 relative error = 0.060063545566256373654873114321825 % h = 0.001 y1[1] (analytic) = 2.9424888019316975100238235653892 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4630632633274945097505356301736 relative error = 15.73712916166412519855425461241 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.231 y2[1] (analytic) = 1.6667049286391972758157333067154 y2[1] (numeric) = 1.6656973224767890996208577796011 absolute error = 0.0010076061624081761948755271143 relative error = 0.060454981868377219898516098664755 % h = 0.001 y1[1] (analytic) = 2.9428225683587540320699768025983 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4633970297545510317966888673827 relative error = 15.746686012843542961718023353452 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.232 y2[1] (analytic) = 1.6676479176979407360853837959275 y2[1] (numeric) = 1.666633180609347241366676715841 absolute error = 0.0010147370885934947187070800865 relative error = 0.060848400781998454796919561122979 % h = 0.001 y1[1] (analytic) = 2.9431553919633207639068422478012 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4637298533591177636335543125856 relative error = 15.756213709455984526534579999151 % h = 0.001 TOP MAIN SOLVE Loop memory used=667.5MB, alloc=4.1MB, time=93.18 NO POLE NO POLE x[1] = 1.233 y2[1] (analytic) = 1.6685912391087388024083628950293 y2[1] (numeric) = 1.6675693302700005621549229171108 absolute error = 0.0010219088387382402534399779185 relative error = 0.061243809435562095056073091435705 % h = 0.001 y1[1] (analytic) = 2.9434872724125741287029875201834 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4640617338083711284296995849678 relative error = 15.765712261021996307615357344425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.234 y2[1] (analytic) = 1.6695348919282701425967192272101 y2[1] (numeric) = 1.6685057703364942967966953685821 absolute error = 0.001029121591775845800023858628 relative error = 0.061641214972586566080904928409821 % h = 0.001 y1[1] (analytic) = 2.9438182093746337048617510061568 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4643926707704307045884630709412 relative error = 15.775181677033086013604514553705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.235 y2[1] (analytic) = 1.6704788752128820157568449438006 y2[1] (numeric) = 1.6694424996856960975412026827102 absolute error = 0.0010363755271859182156422610904 relative error = 0.062040624551678026069531281092631 % h = 0.001 y1[1] (analytic) = 2.9441482025185625579016357993198 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4647226639143595576283478641042 relative error = 15.784621966951730855885069035014 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.236 y2[1] (analytic) = 1.6714231880185912159421379801556 y2[1] (numeric) = 1.6703795171935960340757630992345 absolute error = 0.0010436708249951818663748809211 relative error = 0.062442045346541712025465667498979 % h = 0.001 y1[1] (analytic) = 2.9444772515143675713932166038778 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4650517129101645711199286686622 relative error = 15.794033140211385740184262637243 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=671.4MB, alloc=4.1MB, time=93.71 x[1] = 1.237 y2[1] (analytic) = 1.6723678294010850161361293369909 y2[1] (numeric) = 1.6713168217353065935258044851781 absolute error = 0.0010510076657784226103248518128 relative error = 0.062845484545993307821082576285656 % h = 0.001 y1[1] (analytic) = 2.9448053560329997769522286646428 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4653798174287967766789407294272 relative error = 15.803415206216491441006965473289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.238 y2[1] (analytic) = 1.673312798415722112565131404128 y2[1] (numeric) = 1.6722544121850626804548643348482 absolute error = 0.0010583862306594321102670692798 relative error = 0.063250949353970334445218440944626 % h = 0.001 y1[1] (analytic) = 2.9451325157463546832885087305517 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4657069771421516830152207953361 relative error = 15.812768174342482758826247724281 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.239 y2[1] (analytic) = 1.6742580941175335693394630140758 y2[1] (numeric) = 1.6731922874162216168645897698356 absolute error = 0.0010658067013119524748732442402 relative error = 0.063658446989543562567382980287402 % h = 0.001 y1[1] (analytic) = 2.9454587303272726043104590027897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4660331917230696040371710675741 relative error = 15.822092053935796659960575721453 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.24 y2[1] (analytic) = 1.6752037155612237634223065843026 y2[1] (numeric) = 1.6741304463012631421947375390153 absolute error = 0.0010732692599606212275690452873 relative error = 0.064067984686928447550645407151327 % h = 0.001 y1[1] (analytic) = 2.9457839994495389862847059630818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4663584608453359860114180278662 relative error = 15.831386854313880399067413436996 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.241 y2[1] (analytic) = 1.6761496618011713299252523794216 y2[1] (numeric) = 1.6750688877117894133231740185459 absolute error = 0.0010807740893819166020783608757 relative error = 0.064479569695496587044852844036981 % h = 0.001 y1[1] (analytic) = 2.9461083227878847340506269225208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4666827841836817337773389873052 relative error = 15.840652584765199624183334247774 % h = 0.001 TOP MAIN SOLVE Loop memory used=675.2MB, alloc=4.1MB, time=94.24 NO POLE NO POLE x[1] = 1.242 y2[1] (analytic) = 1.6770959318914301077295845978224 y2[1] (numeric) = 1.67600761051852500456587521187 absolute error = 0.0010883213729051031637093859524 relative error = 0.064893209279787201291432512253677 % h = 0.001 y1[1] (analytic) = 2.9464317000179865362894180764331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4670061614137835360161301412175 relative error = 15.849889254549246464241070470671 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.243 y2[1] (analytic) = 1.678042524885730085432363661543 y2[1] (numeric) = 1.6769466135913169076769267497142 absolute error = 0.0010959112944131777554369118288 relative error = 0.065308910719518636270624885693814 % h = 0.001 y1[1] (analytic) = 2.9467541308164671898473787962413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4673285922122641895740908610257 relative error = 15.859096872896547598994249709929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.244 y2[1] (analytic) = 1.6789894398374783476163587633775 y2[1] (numeric) = 1.6778858957991345318485238900888 absolute error = 0.0011035440383438157678348732887 relative error = 0.065726681309599889821592023663669 % h = 0.001 y1[1] (analytic) = 2.9470756148608959231130878350644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4676500762566929228397998998488 relative error = 15.868275449008672311280887509567 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.245 y2[1] (analytic) = 1.6799366757997600214428844013667 y2[1] (numeric) = 1.678825456010069703710971518288 absolute error = 0.0011112197896903177319128830787 relative error = 0.06614652836014216086544372401299 % h = 0.001 y1[1] (analytic) = 2.9473961518297887184481480699102 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4679706132255857181748601346946 relative error = 15.87742499205824052155702517249 % h = 0.001 TOP MAIN SOLVE Loop memory used=679.0MB, alloc=4.1MB, time=94.78 NO POLE NO POLE x[1] = 1.246 y2[1] (analytic) = 1.6808842318253392235665943079135 y2[1] (numeric) = 1.67976529309133666733268414689 absolute error = 0.0011189387340025562339101610235 relative error = 0.066568459196470421860823971262309 % h = 0.001 y1[1] (analytic) = 2.9477157414026086336711773497374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4682902027984056333978894145218 relative error = 15.886545511188930804632219896102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.247 y2[1] (analytic) = 1.6818321069666600073712858588082 y2[1] (numeric) = 1.6807054059092720842201859157569 absolute error = 0.0011267010573879231510999430513 relative error = 0.066992481159135014621301398132167 % h = 0.001 y1[1] (analytic) = 2.9480343832597661225947239654277 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4686088446555631223214360302121 relative error = 15.895637015515488388538911587286 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.248 y2[1] (analytic) = 1.6827803002758473105257677264381 y2[1] (numeric) = 1.6816457933293350333181105920345 absolute error = 0.0011345069465122772076571344036 relative error = 0.067418601603923269623410136250731 % h = 0.001 y1[1] (analytic) = 2.9483520770826193546147862047755 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4689265384784163543414982695599 relative error = 15.90469951412373313546800686107 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.249 y2[1] (analytic) = 1.683728810804707902858843221393 y2[1] (numeric) = 1.6825864542161070110092015701526 absolute error = 0.0011423565886008918496416512404 relative error = 0.067846827901871148933791506288129 % h = 0.001 y1[1] (analytic) = 2.9486688225534745333526164030051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4692432839492715330793284677895 relative error = 15.913733016070567504703335802331 % h = 0.001 TOP MAIN SOLVE Loop memory used=682.8MB, alloc=4.1MB, time=95.30 NO POLE NO POLE x[1] = 1.25 y2[1] (analytic) = 1.684677637604731334552461447562 y2[1] (numeric) = 1.6835273874332919311143118718249 absolute error = 0.0011502501714394034381495757371 relative error = 0.068277167439274912883492492688853 % h = 0.001 y1[1] (analytic) = 2.948984619355586214348490847036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4695590807513832140752029118204 relative error = 15.922737530383984497487951082205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.251 y2[1] (analytic) = 1.6856267797270908846520880776495 y2[1] (numeric) = 1.684468591843716124892404146049 absolute error = 0.0011581878833747597596839316005 relative error = 0.068709627617702810617083866605977 % h = 0.001 y1[1] (analytic) = 2.949299467173157621807127839754 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4698739285689546215338399045384 relative error = 15.931713066063075583755551975361 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.252 y2[1] (analytic) = 1.6865762362226445098933472388189 y2[1] (numeric) = 1.6854100663093283410405506691063 absolute error = 0.0011661699133161688527965697126 relative error = 0.069144215854006794643869166000971 % h = 0.001 y1[1] (analytic) = 2.9496133656913409643944371788953 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4701878270871379641211492436797 relative error = 15.940659632078038610660627724895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.253 y2[1] (analytic) = 1.6875260061419357938439856819008 y2[1] (numeric) = 1.6863518096911997456939333445621 absolute error = 0.0011741964507360481500523373387 relative error = 0.069580939580334259518065517030751 % h = 0.001 y1[1] (analytic) = 2.9499263145962377500852852538222 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4705007759920347498119973186066 relative error = 15.949577237370185692841225553077 % h = 0.001 TOP MAIN SOLVE Loop memory used=686.6MB, alloc=4.1MB, time=95.83 NO POLE NO POLE x[1] = 1.254 y2[1] (analytic) = 1.6884760885351948963602100922806 y2[1] (numeric) = 1.6872938208495239224258437032656 absolute error = 0.001182267685670973934366389015 relative error = 0.07001980624413980477444848908373 % h = 0.001 y1[1] (analytic) = 2.9502383135748991000619609124496 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.470812774970696099788672977234 relative error = 15.958465890851951084348558422328 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.255 y2[1] (analytic) = 1.689426482452339503356448086208 y2[1] (numeric) = 1.68823609864361687224768290335 absolute error = 0.001190383808722631108765182858 relative error = 0.070460823308197022245565819957659 % h = 0.001 y1[1] (analytic) = 2.9505493623153260616630281998839 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4711238237111230613897402646683 relative error = 15.967325601406899032177976416558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.256 y2[1] (analytic) = 1.690377186942975776887583122846 y2[1] (numeric) = 1.6891786419319170136089617302322 absolute error = 0.0011985450110587632786213926138 relative error = 0.070903998250610307886238930603877 % h = 0.001 y1[1] (analytic) = 2.9508594605064699203822530199469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4714339219022669201089650847313 relative error = 15.976156377889731611336133342156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.257 y2[1] (analytic) = 1.6913282010563993055427132499031 y2[1] (numeric) = 1.6901214495719851823973005966131 absolute error = 0.00120675148441412314541265329 relative error = 0.071349338564826698230686673427845 % h = 0.001 y1[1] (analytic) = 2.9511686078382325109172917206849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4717430692340295106440037854693 relative error = 15.984958229126296541379486845081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=690.4MB, alloc=4.1MB, time=96.37 x[1] = 1.258 y2[1] (analytic) = 1.6922795238415960551494832891709 y2[1] (numeric) = 1.6910645204205046319384295424774 absolute error = 0.0012150034210914232110537466935 relative error = 0.071796851759647731607222727522488 % h = 0.001 y1[1] (analytic) = 2.9514768040014665272678305551992 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4720512653972635269945426199836 relative error = 15.993731163913594984359576009838 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.259 y2[1] (analytic) = 1.6932311543472433197880397577119 y2[1] (numeric) = 1.6920078533332810329961882350937 absolute error = 0.0012233010139622867918515226182 relative error = 0.072246545359241334235096470176215 % h = 0.001 y1[1] (analytic) = 2.9517840486879758318828659196852 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4723585100837728316095779844696 relative error = 16.002475191019789324110825051962 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.26 y2[1] (analytic) = 1.6941830916217106731136575108235 y2[1] (numeric) = 1.6929514471652424737725259690146 absolute error = 0.0012316444564681993411315418089 relative error = 0.072698426903153731327667020447921 % h = 0.001 y1[1] (analytic) = 2.9520903415905157638568162214254 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4726648029863127635835282862098 relative error = 16.011190319184210926816925342249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.261 y2[1] (analytic) = 1.6951353347130609199870867842308 y2[1] (numeric) = 1.6938953007704394599075016660764 absolute error = 0.0012400339426214600795851181544 relative error = 0.073152503946321383325721469090446 % h = 0.001 y1[1] (analytic) = 2.9523956824027934461741571806503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4729701437985904459008692454347 relative error = 16.01987655711736788279215061254 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=694.2MB, alloc=4.1MB, time=96.90 x[1] = 1.262 y2[1] (analytic) = 1.6960878826690510484116690052385 y2[1] (numeric) = 1.6948394130020449144792838753995 absolute error = 0.001248469667006133932385129839 relative error = 0.073608784059082947384371082443203 % h = 0.001 y1[1] (analytic) = 2.9527000708194680920022733216569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4732745322152650917289853864413 relative error = 16.028533913500952729414261793783 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.263 y2[1] (analytic) = 1.6970407345371331817762694358089 y2[1] (numeric) = 1.695783782712354178004150773388 absolute error = 0.0012569518247790037721186624209 relative error = 0.074067274827191264236583499352341 % h = 0.001 y1[1] (analytic) = 2.9530035065361513100322193603595 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4735779679319483097589314251439 relative error = 16.037162396987850155145958531487 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.264 y2[1] (analytic) = 1.6979938893644555314030744047084 y2[1] (numeric) = 1.6967284087527850084364901637299 absolute error = 0.0012654806116705229665842409785 relative error = 0.074527983851825370556034630334018 % h = 0.001 y1[1] (analytic) = 2.9533059892494074088670861475366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.473880450645204408593798212321 relative error = 16.045762016202144684582134015833 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.265 y2[1] (analytic) = 1.698947346197863349399300581009 y2[1] (numeric) = 1.6976732899738775811687994773972 absolute error = 0.0012740562239857682305011036118 relative error = 0.074990918749602536941591121785552 % h = 0.001 y1[1] (analytic) = 2.9536075186567537004576667794332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4741819800525507001843788442176 relative error = 16.054332779739128344460488357786 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.266 y2[1] (analytic) = 1.6999011040838998818118634373116 y2[1] (numeric) = 1.6986184252252944890316857726457 absolute error = 0.0012826788586053927801776646659 relative error = 0.075456087152590331645362864969007 % h = 0.001 y1[1] (analytic) = 2.953908094456660802585119440078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4744825558524578023118315048624 relative error = 16.062874696165308310573353342893 % h = 0.001 TOP MAIN SOLVE Loop memory used=698.1MB, alloc=4.1MB, time=97.43 NO POLE NO POLE x[1] = 1.267 y2[1] (analytic) = 1.7008551620688073220840517481035 y2[1] (numeric) = 1.6995638133558207422938657350151 absolute error = 0.0012913487129865797901860130884 relative error = 0.075923496708318710165895113796013 % h = 0.001 y1[1] (analytic) = 2.9542077163485529403903244926773 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4747821777443499401170365574617 relative error = 16.071387774018414535518878005044 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.268 y2[1] (analytic) = 1.7018095191985277648132546666555 y2[1] (numeric) = 1.7005094532133637686621656773289 absolute error = 0.0013000659851639961510889893266 relative error = 0.076393155079792130827701328348724 % h = 0.001 y1[1] (analytic) = 2.9545063840328082469496342907547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4750808454286052466763463555391 relative error = 16.079872021807407357230020087801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.269 y2[1] (analytic) = 1.7027641745187041598087876228096 y2[1] (numeric) = 1.7014553436449534132815215396947 absolute error = 0.0013088308737507465272660831149 relative error = 0.076865069945501696467970884729333 % h = 0.001 y1[1] (analytic) = 2.9548040972107590628967151333101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4753785586065560626234271980945 relative error = 16.088327448012485088220083104781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.27 y2[1] (analytic) = 1.703719127074681266448862983912 y2[1] (numeric) = 1.7024014834967419387349788895038 absolute error = 0.0013176435779393277138840944082 relative error = 0.077339248999437322350920288881503 % h = 0.001 y1[1] (analytic) = 2.9551008555846922350901817421829 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4756753169804892348168938069673 relative error = 16.096754061085091585483832377598 % h = 0.001 TOP MAIN SOLVE Loop memory used=701.9MB, alloc=4.1MB, time=97.97 NO POLE NO POLE x[1] = 1.271 y2[1] (analytic) = 1.7046743759115066083357511220005 y2[1] (numeric) = 1.7033478716140040250436929214314 absolute error = 0.0013265042975025832920582005691 relative error = 0.077815699951099930429892503597338 % h = 0.001 y1[1] (analytic) = 2.9553966588578494143267255940087 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4759711202536464140534376587931 relative error = 16.105151869447923800993516123806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.272 y2[1] (analytic) = 1.705629920073931428248177232163 y2[1] (numeric) = 1.7042945068411367696669284574366 absolute error = 0.0013354132327946585812487747264 relative error = 0.078294430525513670076946446575052 % h = 0.001 y1[1] (analytic) = 2.9556915067344273520994393936663 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4762659681302243518261514584507 relative error = 16.113520881494939312729409392543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.273 y2[1] (analytic) = 1.7065857586064116433899989497525 y2[1] (numeric) = 1.7052413880216596875020599467625 absolute error = 0.00134437058475195588793900299 relative error = 0.07877544846323816539931764498702 % h = 0.001 y1[1] (analytic) = 2.9559853989195781964010409309148 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4765598603153751961277529956992 relative error = 16.121861105591363836184789406188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.274 y2[1] (analytic) = 1.7075418905531088009342095178582 y2[1] (numeric) = 1.7061885139982147108845714659359 absolute error = 0.0013533765548940900496380519223 relative error = 0.079258761520380789261771439734562 % h = 0.001 y1[1] (analytic) = 2.9562783351194097865717005170224 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4768527965152067862984125818068 relative error = 16.130172550073698716285540666523 % h = 0.001 TOP MAIN SOLVE Loop memory used=705.7MB, alloc=4.1MB, time=98.50 NO POLE NO POLE x[1] = 1.275 y2[1] (analytic) = 1.7084983149578910338613109611106 y2[1] (numeric) = 1.7071358836125661895880567187676 absolute error = 0.001362431345324844273254242343 relative error = 0.079744377468608964133512022987244 % h = 0.001 y1[1] (analytic) = 2.9565703150409859471911771535838 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4771447764367829469178892183682 relative error = 16.13845522324972839966487702764 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.276 y2[1] (analytic) = 1.7094550308643340170911014275266 y2[1] (numeric) = 1.7080834957056008908242190363522 absolute error = 0.0013715351587331262668823911744 relative error = 0.08023230409516248987795396691965 % h = 0.001 y1[1] (analytic) = 2.9568613383923267810149695414138 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4774357997881237807416816061982 relative error = 16.146709133398527887233955829353 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.277 y2[1] (analytic) = 1.710412037315721923906920566687 y2[1] (numeric) = 1.7090313491173279992428713770683 absolute error = 0.0013806881983939246640491896187 relative error = 0.080722549202865898603307761441086 % h = 0.001 y1[1] (analytic) = 2.9571514048824089609541889933913 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4777258662782059606809010581757 relative error = 16.154934288770470166989446128306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.278 y2[1] (analytic) = 1.7113693333550483826713965200802 y2[1] (numeric) = 1.7099794426868791169319363265783 absolute error = 0.0013898906681692657394601935019 relative error = 0.081215120610140836691577225998467 % h = 0.001 y1[1] (analytic) = 2.9574405142211660210988622714049 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4780149756169630208255743361893 relative error = 16.163130697587233626999399063305 % h = 0.001 TOP MAIN SOLVE Loop memory used=709.5MB, alloc=4.1MB, time=99.05 NO POLE NO POLE x[1] = 1.279 y2[1] (analytic) = 1.7123269180250174338327378079462 y2[1] (numeric) = 1.7109277752525082634174460978285 absolute error = 0.0013991427725091704152917101177 relative error = 0.081710026151018474123214496560075 % h = 0.001 y1[1] (analytic) = 2.9577286661194886467843733241215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4783031275152856465110853889059 relative error = 16.171298368041809448509053450779 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.28 y2[1] (analytic) = 1.7132847903680444872206131064074 y2[1] (numeric) = 1.7118763456515918756635425310491 absolute error = 0.0014084447164526115570705753583 relative error = 0.082207273675151941214327615062736 % h = 0.001 y1[1] (analytic) = 2.9580158602892249637007538591603 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4785903216850219634274659239447 relative error = 16.179437308298508979108493829779 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.281 y2[1] (analytic) = 1.7142429494262572796306616190864 y2[1] (numeric) = 1.7128251527206288080724770937542 absolute error = 0.0014177967056284715581845253322 relative error = 0.082706871047828792882986566627698 % h = 0.001 y1[1] (analytic) = 2.9583020964431808260445336404056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.47887655783897782577124570519 relative error = 16.187547526492971085904361367617 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.282 y2[1] (analytic) = 1.7152013942414968326966764587811 y2[1] (numeric) = 1.7137741952952403324846108807417 absolute error = 0.0014271989462565002120655780394 relative error = 0.083208826149983500560825920924355 % h = 0.001 y1[1] (analytic) = 2.9585873742951201037128623586324 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4791618356909171034395744234168 relative error = 16.195629030732169488638100301173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=713.3MB, alloc=4.1MB, time=99.59 x[1] = 1.283 y2[1] (analytic) = 1.7161601238553184110495031670929 y2[1] (numeric) = 1.7147234722101701381784146140934 absolute error = 0.0014366516451482728710885529995 relative error = 0.083713146878209971865796039354545 % h = 0.001 y1[1] (analytic) = 2.9588716935597649685396158813466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.479446154955561968266327946131 relative error = 16.203681829094420072693503929122 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.284 y2[1] (analytic) = 1.7171191373089924807616952131887 y2[1] (numeric) = 1.7156729822992843318704686431751 absolute error = 0.0014461550097081488912265700136 relative error = 0.084219841144774098151570110814562 % h = 0.001 y1[1] (analytic) = 2.9591550539527961795732006457579 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4797295153485931792999127105423 relative error = 16.211705929629388181936604590848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.285 y2[1] (analytic) = 1.7180784336435056680769680271228 y2[1] (numeric) = 1.7166227243955714377154629446364 absolute error = 0.0014557092479342303615050824864 relative error = 0.084728916877626330048771076852959 % h = 0.001 y1[1] (analytic) = 2.9594374551908533673957709171033 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4800119165866503671224829818877 relative error = 16.21970134035809589133123157272 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.286 y2[1] (analytic) = 1.7190380118995617184234928383428 y2[1] (numeric) = 1.7175726973311423973061971224107 absolute error = 0.0014653145684193211172957159321 relative error = 0.085240382020414281112840802737286 % h = 0.001 y1[1] (analytic) = 2.9597188969915353174835745931305 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4802933583873323172102866579149 relative error = 16.227668069272929259273839475741 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.287 y2[1] (analytic) = 1.719997871117582455710071306166 y2[1] (numeric) = 1.7185228999372305696735804077155 absolute error = 0.0014749711803518860364908984505 relative error = 0.085754244532495359693033646177529 % h = 0.001 y1[1] (analytic) = 2.9599993790734002526081441944156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4805738404691972523348562592 relative error = 16.235606124337645559591487264128 % h = 0.001 TOP MAIN SOLVE Loop memory used=717.1MB, alloc=4.1MB, time=100.14 NO POLE NO POLE x[1] = 1.288 y2[1] (analytic) = 1.7209580103377087419042316461334 y2[1] (numeric) = 1.719473331044191731286631659052 absolute error = 0.0014846792935170106175999870814 relative error = 0.086270512388949429136677870881552 % h = 0.001 y1[1] (analytic) = 2.9602789011559661142780506393499 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4808533625517631140047627041343 relative error = 16.243515513487380493147124996537 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.289 y2[1] (analytic) = 1.7219184285998014368912866742218 y2[1] (numeric) = 1.7204239894815040760524793622053 absolute error = 0.0014944391182973608388073120165 relative error = 0.086789193580591496442511148181728 % h = 0.001 y1[1] (analytic) = 2.9605574629597108432209383620653 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4811319243555078429476504268497 relative error = 16.251396244628655378996621124077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.29 y2[1] (analytic) = 1.7228791249434423586133939099388 y2[1] (numeric) = 1.7213748740777682153163616302445 absolute error = 0.0015042508656741432970322796943 relative error = 0.087310296113984429476560689116619 % h = 0.001 y1[1] (analytic) = 2.9608350642060726589055612912854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4814095256018696586322733560698 relative error = 16.259248325639384325042238225986 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.291 y2[1] (analytic) = 1.7238400984079352434876575993199 y2[1] (numeric) = 1.7223259836607071778616262035224 absolute error = 0.0015141147472280656260313957975 relative error = 0.087833828011451702863704350873261 % h = 0.001 y1[1] (analytic) = 2.9611117046174503381035401680906 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.481686166013247337830252232875 relative error = 16.267071764368881378127539149083 % h = 0.001 TOP MAIN SOLVE Loop memory used=720.9MB, alloc=4.1MB, time=100.68 NO POLE NO POLE x[1] = 1.292 y2[1] (analytic) = 1.7248013480323067071023122398045 y2[1] (numeric) = 1.7232773170571664099097304496759 absolute error = 0.0015240309751402971925817901286 relative error = 0.088359797311090172667716367084771 % h = 0.001 y1[1] (analytic) = 2.9613873839172034924905626408631 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4819618453130004922172747056475 relative error = 16.274866568637867653518978724542 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.293 y2[1] (analytic) = 1.7257628728553072051900269108886 y2[1] (numeric) = 1.7242288730931137751202413636256 absolute error = 0.001533999762193430069785547263 relative error = 0.088888212066782879972270162233277 % h = 0.001 y1[1] (analytic) = 2.9616621018296528452867485362342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4822365632254498450134606010186 relative error = 16.282632746238478443719708559195 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.294 y2[1] (analytic) = 1.7267246719154119948773694373303 y2[1] (numeric) = 1.7251806505936395545908355675761 absolute error = 0.0015440213217724402865338697542 relative error = 0.089419080348211883475041026168273 % h = 0.001 y1[1] (analytic) = 2.961935858080080506935903665692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4825103194758775066626157304764 relative error = 16.290370304934270306561393842608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.295 y2[1] (analytic) = 1.7276867442508220962094691355221 y2[1] (numeric) = 1.7261326483829564468572993110159 absolute error = 0.0015540958678656493521698245062 relative error = 0.089952410240871121206723247001874 % h = 0.001 y1[1] (analytic) = 2.9622086523947302498233864886192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4827831137905272495500985534036 relative error = 16.298079252460228132520111679187 % h = 0.001 TOP MAIN SOLVE Loop memory used=724.8MB, alloc=4.1MB, time=101.21 NO POLE NO POLE x[1] = 1.296 y2[1] (analytic) = 1.7286490888994652539489166184497 y2[1] (numeric) = 1.7270848652843995678935284707172 absolute error = 0.0015642236150656860553881477325 relative error = 0.090488209846079301486449629957355 % h = 0.001 y1[1] (analytic) = 2.9624804845008077820323129139162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4830549458966047817590249787006 relative error = 16.305759596522772191202670150759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.297 y2[1] (analytic) = 1.729611704898996899647938860416 y2[1] (numeric) = 1.7280373001204264511115285507363 absolute error = 0.0015744047785704485364103096797 relative error = 0.091026487280992823224776166184611 % h = 0.001 y1[1] (analytic) = 2.9627513541264810201378254840286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.483325815522278019864537548813 relative error = 16.313411344799765156949956143277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.298 y2[1] (analytic) = 1.7305745912868011139928874494357 y2[1] (numeric) = 1.7289899517126170473614146824133 absolute error = 0.0015846395741840666314727670224 relative error = 0.091567250678618725685070960592156 % h = 0.001 y1[1] (analytic) = 2.9630212610008803610391541471312 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4835957223966773607658662119156 relative error = 16.321034504940519113504187935313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.299 y2[1] (analytic) = 1.7315377470999915894200776828939 y2[1] (numeric) = 1.7299428188816737249314116243721 absolute error = 0.0015949282183178644886660585218 relative error = 0.092110508187827667813824381136872 % h = 0.001 y1[1] (analytic) = 2.9632902048540989528291967854324 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4838646662498959525559088502168 relative error = 16.328629084565802537687215650028 % h = 0.001 TOP MAIN SOLVE Loop memory used=728.6MB, alloc=4.1MB, time=101.74 NO POLE NO POLE x[1] = 1.3 y2[1] (analytic) = 1.7325011713754125930020158907071 y2[1] (numeric) = 1.7308959004474212695478537625206 absolute error = 0.0016052709279913234541621281865 relative error = 0.092656267973366937250076754428305 % h = 0.001 y1[1] (analytic) = 2.9635581854171929647013486300396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.484132646812989964428060694824 relative error = 16.33619509126784726203727891981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.301 y2[1] (analytic) = 1.7334648631496399296030520998424 y2[1] (numeric) = 1.7318491952288068843751851100506 absolute error = 0.0016156679208330452278669897918 relative error = 0.093204538215873489123840805020461 % h = 0.001 y1[1] (analytic) = 2.9638252024221818558933106555778 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4843996638179788556200227203622 relative error = 16.343732532610355416351896508045 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.302 y2[1] (analytic) = 1.7344288214589819053034948846199 y2[1] (numeric) = 1.7328027020439001900159593074377 absolute error = 0.0016261194150817152875355771822 relative error = 0.093755327111887014753078417542939 % h = 0.001 y1[1] (analytic) = 2.964091255602048643667608010779 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4846657169978456433943200755634 relative error = 16.351241416128506348084827179273 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.303 y2[1] (analytic) = 1.7353930453394802910912249787663 y2[1] (numeric) = 1.7337564197098932245108396224414 absolute error = 0.0016366256295870665803853563249 relative error = 0.094308642873863040348475193592071 % h = 0.001 y1[1] (analytic) = 2.9643563446907401703285505045413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4849308060865371700552625693257 relative error = 16.358721749328963521545304810824 % h = 0.001 TOP MAIN SOLVE Loop memory used=732.4MB, alloc=4.1MB, time=102.27 NO POLE NO POLE x[1] = 1.304 y2[1] (analytic) = 1.736357533826911286819843957684 y2[1] (numeric) = 1.734710347043100443338598950105 absolute error = 0.001647186783810843481245007579 relative error = 0.094864493730186055834941678147352 % h = 0.001 y1[1] (analytic) = 2.9646204694231673692753681305244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4851949308189643690020801953088 relative error = 16.366173539689881395848013600561 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.305 y2[1] (analytic) = 1.7373222859567864854323940328691 y2[1] (numeric) = 1.7356644828589587194161198127559 absolute error = 0.0016578030978277660162742201132 relative error = 0.095422887925182673898457044450914 % h = 0.001 y1[1] (analytic) = 2.964883629535205530091255577164 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4854580909310025298179676419484 relative error = 16.373596794660912281562531249403 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.306 y2[1] (analytic) = 1.7382873007643538374496847348377 y2[1] (numeric) = 1.7366188259720273430983943600053 absolute error = 0.0016684747923264943512903748324 relative error = 0.095983833719134819366559451318648 % h = 0.001 y1[1] (analytic) = 2.9651458247636945626680606340859 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4857202861594915623947726988703 relative error = 16.380991521663213176011229188756 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.307 y2[1] (analytic) = 1.7392525772845986157222619963152 y2[1] (numeric) = 1.7375733751959880221785243687481 absolute error = 0.0016792020886105935437376275671 relative error = 0.096547339388292949030477223272299 % h = 0.001 y1[1] (analytic) = 2.9654070548464392603663523702508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4859815162422362600930644350352 relative error = 16.388357728089452577164879284763 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=736.2MB, alloc=4.1MB, time=102.80 x[1] = 1.308 y2[1] (analytic) = 1.7402181145522443804450548837987 y2[1] (numeric) = 1.7385281293436448818877212431633 absolute error = 0.0016899852085994985573336406354 relative error = 0.097113413224889302016586451611386 % h = 0.001 y1[1] (analytic) = 2.9656673195222095622106059237861 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4862417809180065619373179885705 relative error = 16.395695421303817276085475987962 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.309 y2[1] (analytic) = 1.741183911601753944433734962928 y2[1] (numeric) = 1.7394830872269244648953060147138 absolute error = 0.0017008243748294795384289482142 relative error = 0.097682063537151180814573574148743 % h = 0.001 y1[1] (analytic) = 2.9659266185307408141192417083394 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4865010799265378138459537731238 relative error = 16.403004608642019127866041611694 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.31 y2[1] (analytic) = 1.7421499674673303386618230213838 y2[1] (numeric) = 1.7404382476568757313087093421462 absolute error = 0.0017117198104546073531136792376 relative error = 0.098253298649314263069375961913705 % h = 0.001 y1[1] (analytic) = 2.9661849516127340291692578059375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4867594130085310288959698707219 relative error = 16.410285297411301801017440319847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.311 y2[1] (analytic) = 1.743116281182917778057577612289 y2[1] (numeric) = 1.7413936094436700586734715114911 absolute error = 0.0017226717392477193841061007979 relative error = 0.098827126901635944243669523908048 % h = 0.001 y1[1] (analytic) = 2.9664423185098561468951952817403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4870167799056531466219073465247 relative error = 16.41753749489044750525248348753 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.312 y2[1] (analytic) = 1.7440828517822026275596996213043 y2[1] (numeric) = 1.742349171396601241973242436063 absolute error = 0.0017336803856013855864571852413 relative error = 0.09940355665040871125736983497653 % h = 0.001 y1[1] (analytic) = 2.9666987189647402916221771217455 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4872731803605372913488891865299 relative error = 16.424761208329783697617865371197 % h = 0.001 TOP MAIN SOLVE Loop memory used=740.0MB, alloc=4.1MB, time=103.34 NO POLE NO POLE x[1] = 1.313 y2[1] (analytic) = 1.7450496782986143684308868017935 y2[1] (numeric) = 1.7433049323240854936297816564602 absolute error = 0.0017447459745288748011051453333 relative error = 0.09998259626797354721031229733745 % h = 0.001 y1[1] (analytic) = 2.9669541527209860298327624604265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4875286141167830295594745252109 relative error = 16.43195644495118976692472349114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.314 y2[1] (analytic) = 1.7460167597653265648282719645854 y2[1] (numeric) = 1.7442608910336614435029583405649 absolute error = 0.0017558687316651213253136240205 relative error = 0.10056425414273336729397736333233 % h = 0.001 y1[1] (analytic) = 2.9672086195231596265673587314712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4877830809189566262940707962556 relative error = 16.439123211948103696428872793153 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.315 y2[1] (analytic) = 1.7469840952152578306297782519737 y2[1] (numeric) = 1.7452170463319901388907512835433 absolute error = 0.0017670488832676917390269684304 relative error = 0.10114853867916648599782887501121 % h = 0.001 y1[1] (analytic) = 2.967462119116794300857935341231 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4880365805125913005846474060154 relative error = 16.446261516485528704712016521018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.316 y2[1] (analytic) = 1.7479516836810727965154246696816 y2[1] (numeric) = 1.7461733970248550445292489078454 absolute error = 0.0017782866562177519861757618362 relative error = 0.10173545829784011571553711548478 % h = 0.001 y1[1] (analytic) = 2.9677146512483904801947834311864 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4882891126441874799214954959708 relative error = 16.45337136570003986471548980127 % h = 0.001 TOP MAIN SOLVE Loop memory used=743.8MB, alloc=4.1MB, time=103.87 NO POLE NO POLE x[1] = 1.317 y2[1] (analytic) = 1.7489195241951830773026147955639 y2[1] (numeric) = 1.747129941917162042592649263205 absolute error = 0.0017895822780210347099655323589 relative error = 0.10232502143542389685606321669696 % h = 0.001 y1[1] (analytic) = 2.967966215665416054026067262693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4885406770612130537527793274774 relative error = 16.460452766699790700878344220175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.318 y2[1] (analytic) = 1.7498876157897482395344413298416 y2[1] (numeric) = 1.74808667981293943269326002664 absolute error = 0.0018009359768088068411813032016 relative error = 0.10291723654470345956428812911469 % h = 0.001 y1[1] (analytic) = 2.9682168121163066262899137244747 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4887912735121036260166257892591 relative error = 16.467505726564519764331833163545 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.319 y2[1] (analytic) = 1.7508559574966767693200388986417 y2[1] (numeric) = 1.7490436095153379318814985024519 absolute error = 0.0018123479813388374385403961898 relative error = 0.10351211209459401715557742927542 % h = 0.001 y1[1] (analytic) = 2.9684664403504657669787874307981 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4890409017462627667054994955825 relative error = 16.474530252345557186102608397024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.32 y2[1] (analytic) = 1.7518245483476270404260172705726 y2[1] (numeric) = 1.7500007298266306746458916222264 absolute error = 0.0018238185209963657801256483462 relative error = 0.10410965657015399136838282193324 % h = 0.001 y1[1] (analytic) = 2.9687151001182652627358998459728 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4892895615140622624626119107572 relative error = 16.48152635106583120827718829115 % h = 0.001 TOP MAIN SOLVE Loop memory used=747.6MB, alloc=4.1MB, time=104.42 NO POLE NO POLE x[1] = 1.321 y2[1] (analytic) = 1.752793387374008282618006894982 y2[1] (numeric) = 1.7509580395482132129130759448328 absolute error = 0.0018353478257950697049309501492 relative error = 0.10470987847259866953869228374808 % h = 0.001 y1[1] (analytic) = 2.9689627911710453664834018387895 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4895372525668423662101139035739 relative error = 16.488494029719874693080507245805 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.322 y2[1] (analytic) = 1.7537624736069815502513484204308 y2[1] (numeric) = 1.7519155374806035160477976564244 absolute error = 0.0018469361263780342035507640064 relative error = 0.10531278631931389379985339437258 % h = 0.001 y1[1] (analytic) = 2.9692095132611150460821100387242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4897839746569120458088221035086 relative error = 16.495433295273831609821604246227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.323 y2[1] (analytic) = 1.754731806077460691109957602777 y2[1] (numeric) = 1.7528732224234419708529125704384 absolute error = 0.0018585836540187202570450323386 relative error = 0.10591838864386978241100850912321 % h = 0.001 y1[1] (analytic) = 2.9694552661417522320225183342027 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4900297275375492317492303989871 relative error = 16.502344154665463499659756091276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.324 y2[1] (analytic) = 1.7557013838161133154923967640831 y2[1] (numeric) = 1.7538310931754913815693861275959 absolute error = 0.0018702906406219339230106364872 relative error = 0.10652669399603448331709604301978 % h = 0.001 y1[1] (analytic) = 2.9697000495672040641468468219356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.49027451096300106387355888672 relative error = 16.509226614804155918144607677898 % h = 0.001 TOP MAIN SOLVE Loop memory used=751.5MB, alloc=4.1MB, time=104.96 NO POLE NO POLE x[1] = 1.325 y2[1] (analytic) = 1.7566712058533617655441837163571 y2[1] (numeric) = 1.7547891485346369698762933959019 absolute error = 0.0018820573187247956678903204552 relative error = 0.10713771094178796004308925982514 % h = 0.001 y1[1] (analytic) = 2.9699438632926871374018814852929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4905183246884841371285935500773 relative error = 16.51608068257092485548409780714 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.326 y2[1] (analytic) = 1.7576412712193840848353688178995 y2[1] (numeric) = 1.7557473872978863748908190706452 absolute error = 0.0018938839214977099445497472543 relative error = 0.10775144806333581002486259038672 % h = 0.001 y1[1] (analytic) = 2.9701867070743877466223588489025 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4907611684701847463490709136869 relative error = 16.522906364818423134494224300866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.327 y2[1] (analytic) = 1.7586115789441149881824105847592 y2[1] (numeric) = 1.7567058082613696531682574743985 absolute error = 0.0019057706827453350141531103607 relative error = 0.10836791395912311547879564162337 % h = 0.001 y1[1] (analytic) = 2.9704285806694621303446508261051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4910030420652591300713628908895 relative error = 16.529703668370946786184936787397 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.328 y2[1] (analytic) = 1.7595821280572468317133800355038 y2[1] (numeric) = 1.7576644102203392787020125570184 absolute error = 0.0019177178369075530113674784854 relative error = 0.10898711724384832691194670056956 % h = 0.001 y1[1] (analytic) = 2.9706694838360367136505059456028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4912439452318337133772180103872 relative error = 16.536472600024441402936689333114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=755.3MB, alloc=4.1MB, time=105.49 x[1] = 1.329 y2[1] (analytic) = 1.7605529175882305831755237041812 y2[1] (numeric) = 1.7586231919691701429235978956454 absolute error = 0.0019297256190604402519258085358 relative error = 0.10960906654847717937435068600213 % h = 0.001 y1[1] (analytic) = 2.9709094163332083500406041135805 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4914838777290053497673161783649 relative error = 16.543213166546508469222428168708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.33 y2[1] (analytic) = 1.7615239465662767924842150139894 y2[1] (numeric) = 1.7595821523013595547026366947038 absolute error = 0.0019417942649172377815783192856 relative error = 0.11023377052025664155472115269736 % h = 0.001 y1[1] (analytic) = 2.9711483779210445623376830377638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4917228393168415620643951025482 relative error = 16.549925374676411669830032087073 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.331 y2[1] (analytic) = 1.7624952140203565625123234627852 y2[1] (numeric) = 1.760541290009527240346861785902 absolute error = 0.0019539240108293221654616768832 relative error = 0.11086123782272889782056210976601 % h = 0.001 y1[1] (analytic) = 2.9713863683605837826189954103093 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4919608297563807823457074750937 relative error = 16.556609231125083175540464678647 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.332 y2[1] (analytic) = 1.7634667189792025201190308311427 y2[1] (numeric) = 1.761500603885415343602115628232 absolute error = 0.0019661150937871765169152029107 relative error = 0.11149147713574536330342307376406 % h = 0.001 y1[1] (analytic) = 2.9716233874138355911778569170885 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4921978488096325909045689818729 relative error = 16.563264742575129906217138422532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.333 y2[1] (analytic) = 1.7644384604713097874171233842259 y2[1] (numeric) = 1.7624600927198884256523503079699 absolute error = 0.001978367751421361764773076256 relative error = 0.11212449715548073212975993855246 % h = 0.001 y1[1] (analytic) = 2.9718594348437809545140461118376 memory used=759.1MB, alloc=4.1MB, time=106.03 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.492433896239577954240758176622 relative error = 16.569891915680839771262230772002 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.334 y2[1] (analytic) = 1.7654104375249369532777888002662 y2[1] (numeric) = 1.7634197553029334651196275386756 absolute error = 0.0019906822220034881581612615906 relative error = 0.11276030659444705889759490696608 % h = 0.001 y1[1] (analytic) = 2.9720945104143724623528181647938 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4926689718101694620795302295782 relative error = 16.576490757068187887395931764435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.335 y2[1] (analytic) = 1.7663826491681070450719463209256 y2[1] (numeric) = 1.7643795904236598580641186611929 absolute error = 0.0020030587444471870078276597327 relative error = 0.11339891418150787349890089207933 % h = 0.001 y1[1] (analytic) = 2.9723286138905345636922954668229 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4929030752863315634190075316073 relative error = 16.583061273334842773714841351894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.336 y2[1] (analytic) = 1.7673550944286085006471383822999 y2[1] (numeric) = 1.7653395968702994179841046436495 absolute error = 0.0020154975583090826630337386504 relative error = 0.11404032866189232938736945908425 % h = 0.001 y1[1] (analytic) = 2.9725617450381638018789990416688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4931362064339608016057111064532 relative error = 16.589603471050172523985972593273 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.337 y2[1] (analytic) = 1.7683277723339961405390117497482 y2[1] (numeric) = 1.7662997734302063758159760814569 absolute error = 0.0020279989037897647230356682913 relative error = 0.11468455879720938539095653977619 % h = 0.001 y1[1] (analytic) = 2.9727939036241290487112856908112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4933683650199260484379977555956 relative error = 16.596117356755250956133054075503 % h = 0.001 TOP MAIN SOLVE Loop memory used=762.9MB, alloc=4.1MB, time=106.56 NO POLE NO POLE x[1] = 1.338 y2[1] (analytic) = 1.7693006819115921404164159451506 y2[1] (numeric) = 1.7672601188898573799342331973106 absolute error = 0.00204056302173476048218274784 relative error = 0.11533161336546202116833681094882 % h = 0.001 y1[1] (analytic) = 2.9730250894162717375704567675156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4935995508120687372971688323 relative error = 16.602602936962863738872061443663 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.339 y2[1] (analytic) = 1.7702738221884870037591465215765 y2[1] (numeric) = 1.7682206320348514961514858411899 absolute error = 0.0020531901536355076076606803866 relative error = 0.1159815011610614864081357836486 % h = 0.001 y1[1] (analytic) = 2.9732553021834060955793054489858 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4938297635792030953060175137702 relative error = 16.609060218157514495453143721188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.34 y2[1] (analytic) = 1.7712471921915405347673605076999 y2[1] (numeric) = 1.769181311649910207718453490358 absolute error = 0.0020658805416303270489070173419 relative error = 0.11663423099484158386954830145404 % h = 0.001 y1[1] (analytic) = 2.9734845416953193747878703480896 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.494059003091116374514582412874 relative error = 16.615489206795430884466345195543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.341 y2[1] (analytic) = 1.7722207909473828115016911126287 y2[1] (numeric) = 1.770142156518877415323965249362 absolute error = 0.0020786344285053961777258632667 relative error = 0.11728981169407298636269329211612 % h = 0.001 y1[1] (analytic) = 2.9737128077227720823861642789256 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.49428726911856908211287634371 relative error = 16.621889909304570657668758035326 % h = 0.001 TOP MAIN SOLVE Loop memory used=766.7MB, alloc=4.1MB, time=107.09 NO POLE NO POLE x[1] = 1.342 y2[1] (analytic) = 1.7731946174824151592530885511146 y2[1] (numeric) = 1.7711031654247194370949598500329 absolute error = 0.0020914520576957221581287010817 relative error = 0.11794825210247758776679725626667 % h = 0.001 y1[1] (analytic) = 2.9739401000374982099436479635199 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4945145614332952096703600283043 relative error = 16.628262332084627694790974495047 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.343 y2[1] (analytic) = 1.774168670822811124141413619382 y2[1] (numeric) = 1.7720643371495250085964856514855 absolute error = 0.0021043336732861155449279678965 relative error = 0.11860956108024288818404310865472 % h = 0.001 y1[1] (analytic) = 2.9741664184122054616752194401986 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.494740879808002461401931504983 relative error = 16.634606481507038015280940557678 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.344 y2[1] (analytic) = 1.775142949994517446941810423066 y2[1] (numeric) = 1.7730256704745052828317006401186 absolute error = 0.0021172795200121641101097829474 relative error = 0.11927374750403641332666661070681 % h = 0.001 y1[1] (analytic) = 2.9743917626205754817334909076658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4949662240163724814602029724502 relative error = 16.640922363914985766943545165886 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.345 y2[1] (analytic) = 1.7761174540232550371378844309657 y2[1] (numeric) = 1.7739871641799938302418724296148 absolute error = 0.0021302898432612068960120013509 relative error = 0.11994082026702016823462974619576 % h = 0.001 y1[1] (analytic) = 2.9746161324372640805271257125288 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4951905938330610802538377773132 relative error = 16.647209985623409191434510804124 % h = 0.001 TOP MAIN SOLVE Loop memory used=770.5MB, alloc=4.1MB, time=107.63 NO POLE NO POLE x[1] = 1.346 y2[1] (analytic) = 1.7770921819345199472007118015173 y2[1] (numeric) = 1.7749488170454466387063782609406 absolute error = 0.0021433648890733084943335405767 relative error = 0.12061078827886512542094899400359 % h = 0.001 y1[1] (analytic) = 2.9748395276379014600650091619533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4954139890336984597917212267377 relative error = 16.653469352919006566567382119149 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.347 y2[1] (analytic) = 1.7780671327535843470927057030585 y2[1] (numeric) = 1.7759106278494421135427050023464 absolute error = 0.0021565049041422335500007007121 relative error = 0.12128366046576574754150654165569 % h = 0.001 y1[1] (analytic) = 2.9750619479990924383260278172952 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4956364093948894380527398820796 relative error = 16.65970047206024212539263950941 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.348 y2[1] (analytic) = 1.7790423055054974989953651240988 y2[1] (numeric) = 1.7768725953696810775064491493665 absolute error = 0.0021697101358164214889159747323 relative error = 0.1219594457704545446859240594024 % h = 0.001 y1[1] (analytic) = 2.9752833932984166726542328989498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4958578546942136723809449637342 relative error = 16.665903349277351952008194177795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.349 y2[1] (analytic) = 1.7800176992150867322599314459281 y2[1] (numeric) = 1.7778347183829867707913168248191 absolute error = 0.002182980832099961468614621109 relative error = 0.12263815315221666638583171587685 % h = 0.001 y1[1] (analytic) = 2.9755038633144288821791644072722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4960783247102258819058764720566 relative error = 16.6720779907723498540607500308 % h = 0.001 TOP MAIN SOLVE Loop memory used=774.4MB, alloc=4.1MB, time=108.17 NO POLE NO POLE x[1] = 1.35 y2[1] (analytic) = 1.7809933129069584185799778269894 y2[1] (numeric) = 1.7787969956653048510291237788062 absolute error = 0.0021963172416535675508540481832 relative error = 0.12331979158690452843661966145706 % h = 0.001 y1[1] (analytic) = 2.9757233578266590692611135392652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4962978192224560689878256040496 relative error = 16.678224402719033211897746023902 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.351 y2[1] (analytic) = 1.7819691456054989473849562265054 y2[1] (numeric) = 1.7797594259917033932897953887137 absolute error = 0.0022097196137955540951608377917 relative error = 0.12400437006695247462851523274396 % h = 0.001 y1[1] (analytic) = 2.9759418766156127399611019557882 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4965163380114097396878140205726 relative error = 16.684342591262988804329820101163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.352 y2[1] (analytic) = 1.7829451963348757014537266738956 y2[1] (numeric) = 1.7807220081363728900813666592115 absolute error = 0.0022231881985028113723600146841 relative error = 0.1246918976013914734825866404206 % h = 0.001 y1[1] (analytic) = 2.9761594194627711235353574293287 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4967338808585681232620694941131 relative error = 16.690432562521598610963962760526 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.353 y2[1] (analytic) = 1.7839214641190380327470931705336 y2[1] (numeric) = 1.7816847408726262513499822222533 absolute error = 0.0022367232464117813971109482803 relative error = 0.12538238321586385008703289077635 % h = 0.001 y1[1] (analytic) = 2.9763759861505913909540663778775 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4969504475463883906807784426619 relative error = 16.69649432258404559106775449814 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=778.2MB, alloc=4.1MB, time=108.70 x[1] = 1.354 y2[1] (analytic) = 1.7848979479817182384583703913924 y2[1] (numeric) = 1.7826476229728988044798963370766 absolute error = 0.0022503250088194339784740543158 relative error = 0.12607583595263805312888015795327 % h = 0.001 y1[1] (analytic) = 2.9765915764625068724441847661739 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4971660378583038721708968309583 relative error = 16.702527877511319438925306949049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.355 y2[1] (analytic) = 1.78587464694643253728100513609 y2[1] (numeric) = 1.7836106532087482942934728902029 absolute error = 0.0022639937376842429875322458871 relative error = 0.12677226487062345721596676712268 % h = 0.001 y1[1] (analytic) = 2.9768061901829272740560898315276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.497380651578724273782801896312 relative error = 16.708533233336222315645752451022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.356 y2[1] (analytic) = 1.7868515600364820458922762617974 y2[1] (numeric) = 1.7845738303508548830511853954375 absolute error = 0.0022777296856271628410908663599 relative error = 0.12747167904538520058386236783782 % h = 0.001 y1[1] (analytic) = 2.9770198270972388932538560675845 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4975942884930358929805681323689 relative error = 16.714510396063374557385351016791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.357 y2[1] (analytic) = 1.7878286862749537556520966143883 y2[1] (numeric) = 1.7855371531690211504516169938697 absolute error = 0.0022915331059326052004796205186 relative error = 0.12817408756915905828213176910447 % h = 0.001 y1[1] (analytic) = 2.9772324869918048335289398757774 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4978069483876018332556519405618 relative error = 16.720459371669220359944507310758 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.358 y2[1] (analytic) = 1.7888060246847215095159402591121 y2[1] (numeric) = 1.7865006204321720936314604538726 absolute error = 0.0023054042525494158844798052395 relative error = 0.12887949955086635093412027300315 % h = 0.001 y1[1] (analytic) = 2.9774441696539652180370582707955 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4980186310497622177637703355799 relative error = 16.726380166102033439701213193002 % h = 0.001 TOP MAIN SOLVE Loop memory used=782.0MB, alloc=4.1MB, time=109.24 NO POLE NO POLE x[1] = 1.359 y2[1] (analytic) = 1.7897835742884469791609180979423 y2[1] (numeric) = 1.7874642309083551271655181711032 absolute error = 0.0023193433800918519953999268391 relative error = 0.12958792411612888916420517914022 % h = 0.001 y1[1] (analytic) = 2.977654874872037402258048003212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4982293362678344019847600679964 relative error = 16.732272785281922670842653719429 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.36 y2[1] (analytic) = 1.7907613341085806423240247476081 y2[1] (numeric) = 1.7884279833647400830667021685024 absolute error = 0.0023333507438405592573225791057 relative error = 0.13029937040728395378622743748714 % h = 0.001 y1[1] (analytic) = 2.9778646024353161856784924394266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.498439063831113185405204504211 relative error = 16.738137235100837698856936175646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.361 y2[1] (analytic) = 1.7917393031673627603515793401421 y2[1] (numeric) = 1.789391876567619210786034096295 absolute error = 0.0023474265997435495655452438471 relative error = 0.13101384758339931184658819956376 % h = 0.001 y1[1] (analytic) = 2.9780733521340740224969045163172 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4986478135298710222236165811016 relative error = 16.743973521422574530247122777184 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.362 y2[1] (analytic) = 1.7927174804868243559588826965854 y2[1] (numeric) = 1.7903559092824071772126452319896 absolute error = 0.0023615712044171787462374645958 relative error = 0.13173136482028826861526725670882 % h = 0.001 y1[1] (analytic) = 2.978281123759561231351255065431 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4988555851553582310779671302154 relative error = 16.749781650082781098429968093062 % h = 0.001 TOP MAIN SOLVE Loop memory used=785.8MB, alloc=4.1MB, time=109.79 NO POLE NO POLE x[1] = 1.363 y2[1] (analytic) = 1.7936958650887881911991131142751 y2[1] (numeric) = 1.7913200802736410666737764803787 absolute error = 0.0023757848151471245253366338964 relative error = 0.13245193131052475561779405718426 % h = 0.001 y1[1] (analytic) = 2.9784879171040062040686367792083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4990623784998032037953488439927 relative error = 16.755561626888962805781982047385 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.364 y2[1] (analytic) = 1.7946744559948697456404827988988 y2[1] (numeric) = 1.7922843883049803809347783735388 absolute error = 0.00239006768988936470570442536 relative error = 0.13317555626345845480097715952252 % h = 0.001 y1[1] (analytic) = 2.978693731960615613436855069589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4992681933564126131635671343734 relative error = 16.761313457620488041795658527466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.365 y2[1] (analytic) = 1.7956532522264781947506767642417 y2[1] (numeric) = 1.7932488321392070391991110708301 absolute error = 0.0024044200872711555515656934116 relative error = 0.13390224890522995892497460638637 % h = 0.001 y1[1] (analytic) = 2.9788985681235746199977380474311 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4994730295193716197244501122155 relative error = 16.767037148028593677308928180831 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.366 y2[1] (analytic) = 1.7966322528048173884875958152689 y2[1] (numeric) = 1.7942134105382253781083443588969 absolute error = 0.002418842266592010379251456372 relative error = 0.13463201847878596827406578916917 % h = 0.001 y1[1] (analytic) = 2.9791024253880470778619588294461 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4996768867838440775886708942305 relative error = 16.772732703836390534771111920326 % h = 0.001 TOP MAIN SOLVE Loop memory used=789.6MB, alloc=4.1MB, time=110.32 NO POLE NO POLE x[1] = 1.367 y2[1] (analytic) = 1.7976114567508868300954250238814 y2[1] (numeric) = 1.7951781222630621517421576516672 absolute error = 0.0024333344878246783532673722142 relative error = 0.13536487424389452377826491735951 % h = 0.001 y1[1] (analytic) = 2.979305303550175739545164357848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4998797649459727392718764226324 relative error = 16.778400130738868834508868980186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.368 y2[1] (analytic) = 1.7985908630854826551050489013592 y2[1] (numeric) = 1.796142966073866531618339990353 absolute error = 0.0024478970116161234867089110062 relative error = 0.13610082547716027663769720602768 % h = 0.001 y1[1] (analytic) = 2.9795072024070824598252058966025 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5000816638028794595519179613869 relative error = 16.784039434402903616955850079359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.369 y2[1] (analytic) = 1.7995704708291986105378342671576 y2[1] (numeric) = 1.7971079407299101066927900434501 absolute error = 0.0024625300992885038450442237075 relative error = 0.13683988147203979454144134843583 % h = 0.001 y1[1] (analytic) = 2.9797081217568683986202673470646 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.500282583152665398346979411849 relative error = 16.789650620467260140809982355375 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.37 y2[1] (analytic) = 1.8005502790024270343118016103547 y2[1] (numeric) = 1.7980730449895868833595161067382 absolute error = 0.0024772340128401509522855036165 relative error = 0.13758205153885690457232574642019 % h = 0.001 y1[1] (analytic) = 2.9799080613986142228876885048919 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5004825227944112226144005696763 relative error = 16.795233694542599257082528235522 % h = 0.001 TOP MAIN SOLVE Loop memory used=793.4MB, alloc=4.1MB, time=110.85 NO POLE NO POLE x[1] = 1.371 y2[1] (analytic) = 1.8015302866253598348492055376626 y2[1] (numeric) = 1.7990382776104132854506361032809 absolute error = 0.0024920090149465493985694343817 relative error = 0.13832734500481807288895132763797 % h = 0.001 y1[1] (analytic) = 2.9801070211323803075432813594274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5006814825281773072699934242118 relative error = 16.80078866221148275900327531585 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.372 y2[1] (analytic) = 1.8025104927179894708845447005008 y2[1] (numeric) = 1.8000036373490281542363775834258 absolute error = 0.002506855368961316648167117075 relative error = 0.13907577121402782127600058326948 % h = 0.001 y1[1] (analytic) = 2.9803050007592069354009385162525 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5008794621550039351276505810369 relative error = 16.806315529028378707746428625621 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.373 y2[1] (analytic) = 1.803490896300109931472021393205 y2[1] (numeric) = 1.8009691229611927484250777248042 absolute error = 0.0025217733389171830469436684008 relative error = 0.13982733952750418065368071157144 % h = 0.001 y1[1] (analytic) = 2.9805020000811144961323338033192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5010764614769114958590458681036 relative error = 16.811814300519666733941990368758 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.374 y2[1] (analytic) = 1.8044714963913177161914708149938 y2[1] (numeric) = 1.8019347332017907441631833323313 absolute error = 0.0025367631895269720282874826625 relative error = 0.140582059323194181636938448927 % h = 0.001 y1[1] (analytic) = 2.9806980189011036842465161009752 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5012724802969006839732281657596 relative error = 16.81728498218364331493762535777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=797.2MB, alloc=4.1MB, time=111.39 x[1] = 1.375 y2[1] (analytic) = 1.805452292011012815551779789844 y2[1] (numeric) = 1.8029004668248282350352508382063 absolute error = 0.0025518251861845805165289516377 relative error = 0.14133993999598938223487530933547 % h = 0.001 y1[1] (analytic) = 2.9808930570231556960891984163071 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5014675184189526958159104810915 relative error = 16.822727579490527027776222893312 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.376 y2[1] (analytic) = 1.8064332821783996915908145409393 y2[1] (numeric) = 1.8038663225834337320639463019122 absolute error = 0.0025669595949659595268682390271 relative error = 0.14210099095774143278058453381858 % h = 0.001 y1[1] (analytic) = 2.9810871142522324258615452025277 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5016615756480294255882572673121 relative error = 16.828142097882463777854577796703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.377 y2[1] (analytic) = 1.8074144659124882586708769198454 y2[1] (numeric) = 1.804832299229858163710045410216 absolute error = 0.0025821666826300949608315096294 relative error = 0.14286522163727767818142507046324 % h = 0.001 y1[1] (analytic) = 2.9812801903942766606582619046366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.501854651790073660384973969421 relative error = 16.833528542773532003228824677208 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.378 y2[1] (analytic) = 1.8083958422320948644687082950369 y2[1] (numeric) = 1.8057983955154748758724334771684 absolute error = 0.0025974467166199885962748178685 relative error = 0.143632641480416797579543362527 % h = 0.001 y1[1] (analytic) = 2.9814722852562122745247916932807 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5020467466520092742515037580651 relative error = 16.838886919549747854532470313773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=801.1MB, alloc=4.1MB, time=111.91 x[1] = 1.379 y2[1] (analytic) = 1.8093774101558432711590601098542 y2[1] (numeric) = 1.8067646101907796318881054441041 absolute error = 0.0026127999650636392709546657501 relative error = 0.14440325994998448151225061366326 % h = 0.001 y1[1] (analytic) = 2.9816633986459444215334253296345 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5022378600417414212601373944189 relative error = 16.844217233569070350473079255539 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.38 y2[1] (analytic) = 1.8103591687021656367908499264018 y2[1] (numeric) = 1.8077309420053906125321658796416 absolute error = 0.0026282266967750242586840467602 relative error = 0.1451770865258291466616615243019 % h = 0.001 y1[1] (analytic) = 2.981853530372359727878131085206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5024279917681567276048431499904 relative error = 16.84951949016140650887387740013 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.381 y2[1] (analytic) = 1.8113411168893034968549215793134 y2[1] (numeric) = 1.8086973897080484160178289796834 absolute error = 0.00264372718125508083709259963 relative error = 0.14595413070483768828280024907691 % h = 0.001 y1[1] (analytic) = 2.9820426802453264829879126217549 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5026171416411234827146246865393 relative error = 16.854793694628616453226747396833 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.382 y2[1] (analytic) = 1.8123232537353087460424278717053 y2[1] (numeric) = 1.8096639520466160579964185674158 absolute error = 0.0026593016886926880460093042895 relative error = 0.14673440200095127039918051038924 % h = 0.001 y1[1] (analytic) = 2.9822308480756948296585037179794 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5028053094714918293852157827638 relative error = 16.860039852244518494723298246411 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.383 y2[1] (analytic) = 1.8133055782580446201928540550173 y2[1] (numeric) = 1.8106306277680789715573680933091 absolute error = 0.0026749504899656486354859617082 relative error = 0.14751790994518115385466941525164 % h = 0.001 y1[1] (analytic) = 2.9824180336752969532022097112956 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.50299249507109395292892177608 relative error = 16.865257968254894189730899434127 % h = 0.001 TOP MAIN SOLVE Loop memory used=804.9MB, alloc=4.1MB, time=112.45 NO POLE NO POLE x[1] = 1.384 y2[1] (analytic) = 1.8142880894751866784307001448004 y2[1] (numeric) = 1.8115974156185450072282206351173 absolute error = 0.0026906738566416712024795096831 relative error = 0.14830466408562456231024855981091 % h = 0.001 y1[1] (analytic) = 2.9826042368569472696157065048811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5031786982527442693424185696655 relative error = 16.870448047877493372680777340292 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.385 y2[1] (analytic) = 1.8152707864042237854898399358487 y2[1] (numeric) = 1.8125643143432444329746288978784 absolute error = 0.0027064720609793525152110379703 relative error = 0.14909467398748058627409146565247 % h = 0.001 y1[1] (analytic) = 2.9827894574344426127656089722012 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5033639188302396124923210369856 relative error = 16.8756100963020391643354785272 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.386 y2[1] (analytic) = 1.8162536680624590942245743924011 y2[1] (numeric) = 1.8135313226865299342003552139143 absolute error = 0.0027223453759291600242191784868 relative error = 0.14988794923306612525318327314582 % h = 0.001 y1[1] (analytic) = 2.9829736952225624205916215734637 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5035481566183594203183336382481 relative error = 16.880744118690232955403210805436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.387 y2[1] (analytic) = 1.8172367334670110283063969024388 y2[1] (numeric) = 1.8144984393918766137472715428307 absolute error = 0.0027382940751344145591253596081 relative error = 0.15068449942183186811451691614594 % h = 0.001 y1[1] (analytic) = 2.9831569500370689203270849808684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5037314114328659200537970456528 relative error = 16.885850120175759365466778739857 % h = 0.001 TOP MAIN SOLVE Loop memory used=808.7MB, alloc=4.1MB, time=112.99 NO POLE NO POLE x[1] = 1.388 y2[1] (analytic) = 1.8182199816348142651054876993967 y2[1] (numeric) = 1.8154656632018819918953594715172 absolute error = 0.0027543184329322732101282278795 relative error = 0.15148433417037831174370971853389 % h = 0.001 y1[1] (analytic) = 2.983339221694707312736733492119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5039136830905043124634455569034 relative error = 16.890928105864291177195035469043 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.389 y2[1] (analytic) = 1.8192034115826207187559545698753 y2[1] (numeric) = 1.8164329928582660063627102141474 absolute error = 0.0027704187243547123932443557279 relative error = 0.1522874631124718180886954832704 % h = 0.001 y1[1] (analytic) = 2.9835205100132059553714789944563 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5040949714090029550981910592407 relative error = 16.895978080833494245804977385171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.39 y2[1] (analytic) = 1.820187022327000523403836782196 y2[1] (numeric) = 1.8174004271018710123055246121786 absolute error = 0.0027865952251295110983121700174 relative error = 0.15309389589906070967595968727519 % h = 0.001 y1[1] (analytic) = 2.9837008148112765448400382244429 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5042752762070735445667502892273 relative error = 16.901000050133032383742812357186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.391 y2[1] (analytic) = 1.8211708128843430166368889878747 y2[1] (numeric) = 1.8183679646726617823181131343521 absolute error = 0.0028028482116812343187758535226 relative error = 0.15390364219829140368659934758883 % h = 0.001 y1[1] (analytic) = 2.9838801359086142980972210518888 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5044545973044112978239331166732 relative error = 16.905994018784572220552535782132 % h = 0.001 TOP MAIN SOLVE Loop memory used=812.5MB, alloc=4.1MB, time=113.52 NO POLE NO POLE x[1] = 1.392 y2[1] (analytic) = 1.8221547822708577230951616663156 y2[1] (numeric) = 1.8193356043097255064328958766931 absolute error = 0.0028191779611322166622657896225 relative error = 0.15471671169552458467930448504644 % h = 0.001 y1[1] (analytic) = 2.9840584731258981327486984996431 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5046329345216951324754105644275 relative error = 16.910959991781788037900751820753 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.393 y2[1] (analytic) = 1.8231389295025753382613945022233 y2[1] (numeric) = 1.8203033447512717921204025625106 absolute error = 0.0028355847513035461409919397127 relative error = 0.15553311409335141604717487707139 % h = 0.001 y1[1] (analytic) = 2.9842358262847908463720701945001 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5048102876805878460987822592845 relative error = 16.915897974090366579726679717301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.394 y2[1] (analytic) = 1.824123253595348712430238905424 y2[1] (numeric) = 1.8212711847346326642892725423976 absolute error = 0.0028520688607160481409663630264 relative error = 0.1563528591116097902951039607065 % h = 0.001 y1[1] (analytic) = 2.9844121952079392948540519281666 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.504986656603736294580763992951 relative error = 16.920807970648011837486487123016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.395 y2[1] (analytic) = 1.8251077535648538348553257039542 y2[1] (numeric) = 1.8222391229962625652862547942309 absolute error = 0.0028686305685912695690709097233 relative error = 0.15717595648740061822428131716165 % h = 0.001 y1[1] (analytic) = 2.9845875797189745697436049911178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5051620411147715694703170559022 relative error = 16.925689986364449810461293841245 % h = 0.001 TOP MAIN SOLVE Loop memory used=816.3MB, alloc=4.1MB, time=114.06 NO POLE NO POLE x[1] = 1.396 y2[1] (analytic) = 1.8260924284265908180731938634319 y2[1] (numeric) = 1.8232071582717383548962079231712 absolute error = 0.0028852701548524631769859402607 relative error = 0.15800241597510415711018613828696 % h = 0.001 y1[1] (analytic) = 2.9847619796425121746208299262279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5053364410383091743475419910123 relative error = 16.930544026121433241098390392878 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.397 y2[1] (analytic) = 1.827077277195884882403095908863 y2[1] (numeric) = 1.824175289295759310342100161663 absolute error = 0.0029019879001255720609957472 relative error = 0.15883224734639637796026644103307 % h = 0.001 y1[1] (analytic) = 2.9849353948041522004814483332946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.505509856199949200208160398079 relative error = 16.935370094772746325355416266831 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.398 y2[1] (analytic) = 1.8280622988878873406216955491598 y2[1] (numeric) = 1.8251435148021471262850093694348 absolute error = 0.002918784085740214336686179725 relative error = 0.15966546039026537193732255586253 % h = 0.001 y1[1] (analytic) = 2.985107825030479500136697339993 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5056822864262764998634094047774 relative error = 16.94016819714420939801744267506 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.399 y2[1] (analytic) = 1.8290474925175765828116728297563 y2[1] (numeric) = 1.826111833523845914824123033499 absolute error = 0.0029356589937306679875497962573 relative error = 0.16050206491302779603443856698819 % h = 0.001 y1[1] (analytic) = 2.9852792701490638616284623393761 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5058537315448608613551744041605 relative error = 16.944938338033683592957104077947 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=820.1MB, alloc=4.1MB, time=114.59 x[1] = 1.4 y2[1] (analytic) = 1.8300328570997590613832519647964 y2[1] (numeric) = 1.8270802441929222054967382681518 absolute error = 0.0029526129068368558865136966446 relative error = 0.16134207073834535808713192368039 % h = 0.001 y1[1] (analytic) = 2.9854497299884601806594745788061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5060241913842571803861866435905 relative error = 16.949680522211075478308121687513 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.401 y2[1] (analytic) = 1.8310183916490702762676668274503 y2[1] (numeric) = 1.8280487455405649452782618149733 absolute error = 0.002969646108505330989405012477 relative error = 0.16218548770724134120821937075251 % h = 0.001 y1[1] (analytic) = 2.985619204378208632038401170131 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5061936657740056317651132349154 relative error = 16.954394754418341666522760595394 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.402 y2[1] (analytic) = 1.8320040951799757602815789049752 y2[1] (numeric) = 1.8290173362970854985822100428276 absolute error = 0.0029867588828902616993688621476 relative error = 0.16303232567811716773072665996885 % h = 0.001 y1[1] (analytic) = 2.9857876931488348401396560760331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5063621545446318398663681408175 relative error = 16.959081039369493399283960113671 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.403 y2[1] (analytic) = 1.8329899667067720646614623541841 y2[1] (numeric) = 1.8299860151919176472602089478625 absolute error = 0.0030039515148544174012534063216 relative error = 0.16388259452676900274400020041022 % h = 0.001 y1[1] (analytic) = 2.9859551961318500483777616127503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5065296575276470481044736775347 relative error = 16.963739381750601107243074362032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.404 y2[1] (analytic) = 1.8339760052435877447669706230202 y2[1] (numeric) = 1.8309547809536175906019941535098 absolute error = 0.0030212242899701541649764695104 relative error = 0.16473630414640439730801088227043 % h = 0.001 y1[1] (analytic) = 2.9861217131597512876960909948252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5066961745555482874228030596096 relative error = 16.968369786219798944554357088135 % h = 0.001 TOP MAIN SOLVE Loop memory used=823.9MB, alloc=4.1MB, time=115.12 NO POLE NO POLE x[1] = 1.405 y2[1] (analytic) = 1.8349622098043843459522989349528 y2[1] (numeric) = 1.8319236323098639453354109104851 absolute error = 0.0030385774945204006168880244677 relative error = 0.16559346444765897143067376295144 % h = 0.001 y1[1] (analytic) = 2.9862872440660215440698234331509 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5068617054618185437965354979353 relative error = 16.97297225740728929817752117198 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.406 y2[1] (analytic) = 1.8359485794029573896045567649132 y2[1] (numeric) = 1.8328925679874577456264140967879 absolute error = 0.0030560114154996439781426681253 relative error = 0.16645408535861313689284213382949 % h = 0.001 y1[1] (analytic) = 2.9864517886851299250229442833751 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5070262500809269247496563481595 relative error = 16.977546799915347271919899243456 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.407 y2[1] (analytic) = 1.8369351130529373593481642684816 y2[1] (numeric) = 1.8338615867123224430790682177017 absolute error = 0.0030735263406149162690960507799 relative error = 0.16731817682480886000547068894949 % h = 0.001 y1[1] (analytic) = 2.9866153468525318251591237276735 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5071898082483288248858357924579 relative error = 16.982093418318325145189927337364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.408 y2[1] (analytic) = 1.8379218097677906874142864600103 y2[1] (numeric) = 1.8348306872095039067355474057938 absolute error = 0.0030911225582867806787390542165 relative error = 0.16818574880926646438328009007087 % h = 0.001 y1[1] (analytic) = 2.9867779184046690907063084590303 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5073523798004660904330205238147 relative error = 16.98661211716265680643386852608 % h = 0.001 TOP MAIN SOLVE Loop memory used=827.8MB, alloc=4.1MB, time=115.66 NO POLE NO POLE x[1] = 1.409 y2[1] (analytic) = 1.8389086685608207411743187703302 y2[1] (numeric) = 1.8357998682031704230761354209154 absolute error = 0.0031088003576503180981833494148 relative error = 0.16905681129250147381909416380473 % h = 0.001 y1[1] (analytic) = 2.986939503178970183074861823445 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5075139645747671828015738882294 relative error = 16.991102900966862161227888009053 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.41 y2[1] (analytic) = 1.8398956884451688098364374506391 y2[1] (numeric) = 1.8367691284166126960192256502015 absolute error = 0.0031265600285561138172118004376 relative error = 0.16993137427254149534286127388055 % h = 0.001 y1[1] (analytic) = 2.9871001010138503414290888619422 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5076745624096473411558009267266 relative error = 16.995565774221551514997785204288 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.411 y2[1] (analytic) = 1.8408828684338150913042281261022 y2[1] (numeric) = 1.8377384665722438469213211080711 absolute error = 0.0031444018615712443829070180311 relative error = 0.17080944776494314254921308165551 % h = 0.001 y1[1] (analytic) = 2.9872597117487117442719836808696 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.507834173144508743998695745654 relative error = 17.000000741389429930338881982351 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.412 y2[1] (analytic) = 1.841870207539579679196405640619 y2[1] (numeric) = 1.8387078813915994145770344362271 absolute error = 0.0031623261479802646193712043919 relative error = 0.17169104180280899927725693920616 % h = 0.001 y1[1] (analytic) = 2.9874183352239436700430375657528 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5079927966197406697697496305372 relative error = 17.004407806905301558908759312105 % h = 0.001 TOP MAIN SOLVE Loop memory used=831.6MB, alloc=4.1MB, time=116.21 NO POLE NO POLE x[1] = 1.413 y2[1] (analytic) = 1.8428577047751235500266381731191 y2[1] (numeric) = 1.8396773715953373552190879036561 absolute error = 0.003180333179786194807550269463 relative error = 0.17257616643680462372614254860733 % h = 0.001 y1[1] (analytic) = 2.987575971280922656728947240911 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5081504326767196564556593056954 relative error = 17.008786975176073947865727251712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.414 y2[1] (analytic) = 1.8438453591529495505424884456446 y2[1] (numeric) = 1.8406469359032380425183134066288 absolute error = 0.0031984232497115080241750390158 relative error = 0.17346483173517559308978926605521 % h = 0.001 y1[1] (analytic) = 2.9877326197620126604870636641387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5083070811578096602137757289231 relative error = 17.013138250580762320826105422174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.415 y2[1] (analytic) = 1.8448331696854033852224846843611 y2[1] (numeric) = 1.8416165730342042675836524686996 absolute error = 0.0032165966511991176388322156615 relative error = 0.17435704778376458879400752806237 % h = 0.001 y1[1] (analytic) = 2.9878882805105652132814227330185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5084627419063622130081347978029 relative error = 17.01746163747049383331358284655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.416 y2[1] (analytic) = 1.8458211353846746039303338365071 y2[1] (numeric) = 1.8425862817062612389621562407069 absolute error = 0.0032348536784133649681775958002 relative error = 0.17525282468602852241909632580022 % h = 0.001 y1[1] (analytic) = 2.9880429533709195795312002668466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.508617414766716579257912331631 relative error = 17.021757140168511802674117329243 % h = 0.001 TOP MAIN SOLVE Loop memory used=835.4MB, alloc=4.1MB, time=116.74 NO POLE NO POLE x[1] = 1.417 y2[1] (analytic) = 1.8468092552627975897252893891526 y2[1] (numeric) = 1.843556060636556582638985500773 absolute error = 0.0032531946262410070863038883796 relative error = 0.17615217256305570239084845135391 % h = 0.001 y1[1] (analytic) = 2.988196638188402911771434615729 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5087710995841999114981466805134 relative error = 17.026024762970179912430025389524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.418 y2[1] (analytic) = 1.84779752833165254682768597948 y2[1] (numeric) = 1.844525908541360342037410654304 absolute error = 0.003271619790292204790275325176 relative error = 0.17705510155358304152274638247338 % h = 0.001 y1[1] (analytic) = 2.9883493348093304053258612361401 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5089237962051274050525733009245 relative error = 17.030264510142986391047104154794 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.419 y2[1] (analytic) = 1.8487859536029664887386528311363 y2[1] (numeric) = 1.84549582413606497801881173399 absolute error = 0.0032901294669015107198410971463 relative error = 0.17796162181401330549198415877714 % h = 0.001 y1[1] (analytic) = 2.9885010430810054519917045601206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.509075504476802451718416624905 relative error = 17.034476385926548165088816565062 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.42 y2[1] (analytic) = 1.8497745300883142265130178970241 y2[1] (numeric) = 1.8464658061351853688826783998048 absolute error = 0.0033087239531288576303394972193 relative error = 0.17887174351843240233180442909866 % h = 0.001 y1[1] (analytic) = 2.9886517628517197927362734733357 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5092262242475167924629855381201 relative error = 17.038660394532614986731760743902 % h = 0.001 TOP MAIN SOLVE Loop memory used=839.2MB, alloc=4.1MB, time=117.27 NO POLE NO POLE x[1] = 1.421 y2[1] (analytic) = 1.8507632567991193571844144357107 y2[1] (numeric) = 1.8474358532523588103666099390063 absolute error = 0.0033274035467605468178044967044 relative error = 0.17978547685862671302249501454473 % h = 0.001 y1[1] (analytic) = 2.9888014939707536694052077054123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5093759553665506691319197701967 relative error = 17.042816540145073535616833455824 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.422 y2[1] (analytic) = 1.8517521327466552523416015964309 y2[1] (numeric) = 1.8484059642003450156463152661361 absolute error = 0.0033461685463102366952863302948 relative error = 0.18070283204410046326324583222514 % h = 0.001 y1[1] (analytic) = 2.9889502362883759754422234243195 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5095246976841729751689354891039 relative error = 17.046944826919951495010686198496 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.423 y2[1] (analytic) = 1.8527411569420460468550104364443 y2[1] (numeric) = 1.8493761376910261153356129230198 absolute error = 0.0033650192510199315193975134245 relative error = 0.18162381930209313650692485759719 % h = 0.001 y1[1] (analytic) = 2.9890979896558444056202073150606 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.509672451051641405346919379845 relative error = 17.051045258985421602252260673895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.424 y2[1] (analytic) = 1.8537303283962676277525266442858 y2[1] (numeric) = 1.8503463724354066574864310787668 absolute error = 0.003383955960860970266095565519 relative error = 0.18254844887759692833969096717012 % h = 0.001 y1[1] (analytic) = 2.9892447539254056047835094115948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5098192153212026045102214763792 relative error = 17.055117840441805673459378148142 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=843.0MB, alloc=4.1MB, time=117.80 x[1] = 1.425 y2[1] (analytic) = 1.8547196461201486232435210932057 y2[1] (numeric) = 1.8513166671436136075888075297704 absolute error = 0.0034029789765350156547135634353 relative error = 0.18347673103337424228722199406544 % h = 0.001 y1[1] (analytic) = 2.9893905289502953156012859397082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5099649903460923153279980044926 relative error = 17.059162575361578602470544548593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.426 y2[1] (analytic) = 1.8557091091243713918901392008544 y2[1] (numeric) = 1.8522870205248963485708896997079 absolute error = 0.0034220885994750433192495011465 relative error = 0.1844086760499752271291981455735 % h = 0.001 y1[1] (analytic) = 2.9895353145847385253317444175028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5101097759805355250584564822872 relative error = 17.063179467789372333997320061821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.427 y2[1] (analytic) = 1.856698716419473011924859924003 y2[1] (numeric) = 1.8532574312876266807989346395403 absolute error = 0.0034412851318463311259252844627 relative error = 0.18534429422575535580354407028614 % h = 0.001 y1[1] (analytic) = 2.989679110683949611597144249272 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5102535720797466113238563140564 relative error = 17.067168521741979810962788490517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.428 y2[1] (analytic) = 1.8576884670158462707133350708233 y2[1] (numeric) = 1.8542278981392988220773090275126 absolute error = 0.0034605688765474486360260433107 relative error = 0.18628359587689304598179732094132 % h = 0.001 y1[1] (analytic) = 2.989821917104132487169407037773 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5103963784999294868961191025574 relative error = 17.071129741208358896001847703966 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.429 y2[1] (analytic) = 1.8586783599237406543615194679712 y2[1] (numeric) = 1.8551984197865294076484891691537 absolute error = 0.0034799401372112467130302988175 relative error = 0.18722659133740732239683673500198 % h = 0.001 y1[1] (analytic) = 2.9899637337024807437661918292979 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5105381950982777434929038940823 relative error = 17.075063130149636267099228178856 % h = 0.001 TOP MAIN SOLVE Loop memory used=846.8MB, alloc=4.1MB, time=118.34 NO POLE NO POLE x[1] = 1.43 y2[1] (analytic) = 1.8596683941532633374661023754251 y2[1] (numeric) = 1.8561689949350574901930609972763 absolute error = 0.0034993992182058472730413781488 relative error = 0.18817329095917552100407134512744 % h = 0.001 y1[1] (analytic) = 2.9901045603371777948572914954818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5106790217329747945840035602662 relative error = 17.078968692499111287341331877744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.431 y2[1] (analytic) = 1.8606585687143801730072503987307 y2[1] (numeric) = 1.8571396222897445398297200719771 absolute error = 0.0035189464246356331775303267536 relative error = 0.18912370511195103505705883396492 % h = 0.001 y1[1] (analytic) = 2.9902443968673970174812074454609 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5108188582631940172079195102453 relative error = 17.082846432162259848758168554366 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.432 y2[1] (analytic) = 1.8616488826169166823826720059914 y2[1] (numeric) = 1.8581103005545744441152715806366 absolute error = 0.0035385820623422382674004253548 relative error = 0.19007784418338110317839225916797 % h = 0.001 y1[1] (analytic) = 2.9903832431533018930717608518196 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.510957704549098892798472916604 relative error = 17.086696353016738190231851011639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.433 y2[1] (analytic) = 1.8626393348705590455820136156229 y2[1] (numeric) = 1.8590810284326535080446303379191 absolute error = 0.0035583064379055375373832777038 relative error = 0.19103571857902463950656479258931 % h = 0.001 y1[1] (analytic) = 2.9905210990560461472945995637266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.511095560451843147021311628511 relative error = 17.090518458912386689448294872146 % h = 0.001 TOP MAIN SOLVE Loop memory used=850.6MB, alloc=4.1MB, time=118.88 NO POLE NO POLE x[1] = 1.434 y2[1] (analytic) = 1.8636299244848550915005970805575 y2[1] (numeric) = 1.860051804626210454050820785773 absolute error = 0.0035781198586446374497762947845 relative error = 0.19199733872237010599939453951951 % h = 0.001 y1[1] (analytic) = 2.9906579644377738888934608707648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5112324258335708886201729355492 relative error = 17.094312753671233628868952055606 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.435 y2[1] (analytic) = 1.8646206504692152883915082552446 y2[1] (numeric) = 1.8610226278365964220049769934304 absolute error = 0.0035980226326188663865312618142 relative error = 0.19296271505485342697446512725578 % h = 0.001 y1[1] (analytic) = 2.990793839161619747546051271203 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5113683005574167472727633359874 relative error = 17.098079241087498935699590395995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.436 y2[1] (analytic) = 1.8656115118329137344550461934394 y2[1] (numeric) = 1.8619934967642849692163426574073 absolute error = 0.0036180150686287652387035360321 relative error = 0.19393185803587594596691267376516 % h = 0.001 y1[1] (analytic) = 2.9909287230917090107294053888426 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.511503184487506010456117453627 relative error = 17.101817924927597895833314675934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.437 y2[1] (analytic) = 1.8666025075850891485645423874153 y2[1] (numeric) = 1.8629644101088720704322711015037 absolute error = 0.0036380974762170781322712859116 relative error = 0.19490477814282242498476596519377 % h = 0.001 y1[1] (analytic) = 2.9910626160931577595945871730905 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5116370774889547593212992378749 relative error = 17.105528808930144841745206810397 % h = 0.001 TOP MAIN SOLVE Loop memory used=854.5MB, alloc=4.1MB, time=119.43 NO POLE NO POLE x[1] = 1.438 y2[1] (analytic) = 1.8675936367347458611275593228612 y2[1] (numeric) = 1.8639353665690761178382252768034 absolute error = 0.0036582701656697432893340460578 relative error = 0.19588148587107908624192418155216 % h = 0.001 y1[1] (analytic) = 2.991195518032073003850597507569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5117699794278700035773095723534 relative error = 17.109211896805956814316144978967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.439 y2[1] (analytic) = 1.8685848982907548050814774883499 y2[1] (numeric) = 1.8649063648427379210577777616741 absolute error = 0.0036785334480168840236997266758 relative error = 0.19686199173405169644873531139985 % h = 0.001 y1[1] (analytic) = 2.991327428775552815657353343366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5119018901713498153840654081504 relative error = 17.112867192238057198563543188682 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.44 y2[1] (analytic) = 1.8695762912618545070224798438708 y2[1] (numeric) = 1.8658774036268207071526107617674 absolute error = 0.0036988876350337998698690821034 relative error = 0.19784630626318369374001848523124 % h = 0.001 y1[1] (analytic) = 2.991458348191686462527604463958 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5120328095874834622543165287424 relative error = 17.116494698881679333256934051012 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.441 y2[1] (analytic) = 1.8705678146566520784669426195275 y2[1] (numeric) = 1.8668484816174101206225161100187 absolute error = 0.0037193330392419578444265095088 relative error = 0.19883444000797435732025483161945 % h = 0.001 y1[1] (analytic) = 2.9915882761495545392376549798994 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5121627375453515389643670446838 relative error = 17.12009442036427009439649847959 % h = 0.001 TOP MAIN SOLVE Loop memory used=858.3MB, alloc=4.1MB, time=119.96 NO POLE NO POLE x[1] = 1.442 y2[1] (analytic) = 1.8715594674836242072442411830899 y2[1] (numeric) = 1.8678195975097142234053952666474 absolute error = 0.0037398699739099838388459164425 relative error = 0.19982640353599701990555411634782 % h = 0.001 y1[1] (analytic) = 2.9917172125192290987467576425684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5122916739150260984734697073528 relative error = 17.123666360285493452532826563189 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.443 y2[1] (analytic) = 1.872551248751118149019979583679 y2[1] (numeric) = 1.8687907499980634948772593191568 absolute error = 0.0037604987530546541427202645222 relative error = 0.20082220743291732304188836105421 % h = 0.001 y1[1] (analytic) = 2.9918451571717737821250500575858 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5124196185675707818517621223702 relative error = 17.127210522217234003906374043843 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.444 y2[1] (analytic) = 1.873543157467352718948652248437 y2[1] (numeric) = 1.8697619377759108318522289823339 absolute error = 0.0037812196914418870964232661031 relative error = 0.20182186230251151537896885068355 % h = 0.001 y1[1] (analytic) = 2.9919721099792439474899028699808 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5125465713750409472166149347652 relative error = 17.130726909703600475385258636103 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.445 y2[1] (analytic) = 1.8745351926404192834547461796033 y2[1] (numeric) = 1.8707331595358315485825345982497 absolute error = 0.0038020331045877348722115813536 relative error = 0.2028253787666847939790294260809 % h = 0.001 y1[1] (analytic) = 2.9920980708146867979505509847679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5126725322104837976772630495523 relative error = 17.134215526260929203180219863159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=862.1MB, alloc=4.1MB, time=120.50 x[1] = 1.446 y2[1] (analytic) = 1.875527353278282752141291870978 y2[1] (numeric) = 1.8717044139695233767585161362592 absolute error = 0.0038229393087593753827757347188 relative error = 0.20383276746548968873966671665389 % h = 0.001 y1[1] (analytic) = 2.9922230395521415085608798783119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5127975009479385082875919430963 relative error = 17.137676375377787585315745161803 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.447 y2[1] (analytic) = 1.8765196383887825698248710353027 y2[1] (numeric) = 1.8726756997678064655086231930011 absolute error = 0.0038439386209761043162478423016 relative error = 0.20484403905714449000977699491422 % h = 0.001 y1[1] (analytic) = 2.9923470160666393522802400477078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5129214774624363520069521124922 relative error = 17.141109460514977507836543724187 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.448 y2[1] (analytic) = 1.8775120469796337086960891076355 y2[1] (numeric) = 1.873647015620623381399414992398 absolute error = 0.0038650313590103272966741152375 relative error = 0.2058592042180517194775196278553 % h = 0.001 y1[1] (analytic) = 2.9924700002342038249421636373698 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5130444616300008246688757021542 relative error = 17.144514785105538744728727902685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.449 y2[1] (analytic) = 1.8785045780584276606045203643295 y2[1] (numeric) = 1.8746183602170391084355603856565 absolute error = 0.003886217841388552168959978673 relative error = 0.2068782736428166444091286561686 % h = 0.001 y1[1] (analytic) = 2.9925919919318507692308582741243 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5131664533276477689575703389087 relative error = 17.147892352554752331535240008181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.45 memory used=865.9MB, alloc=4.1MB, time=121.04 y2[1] (analytic) = 1.879497230632633429467133372752 y2[1] (numeric) = 1.875589732245241048059837851267 absolute error = 0.003907498387392381407295521485 relative error = 0.20790125804426583531728684880588 % h = 0.001 y1[1] (analytic) = 2.992712991037588497665354134323 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5132874524333854973920661991074 relative error = 17.151242166240143912645239984497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.451 y2[1] (analytic) = 1.8804900037095985237992043634025 y2[1] (numeric) = 1.8765611303925390191531354950038 absolute error = 0.0039288733170595046460688683987 relative error = 0.20892816815346576713767065453105 % h = 0.001 y1[1] (analytic) = 2.9928329974304179145911812588387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5134074588262149143178933236231 relative error = 17.154564229511487062237346745583 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.452 y2[1] (analytic) = 1.8814828962965499493667259935982 y2[1] (numeric) = 1.8775325533453652580344510499251 absolute error = 0.0039503429511846913322749436731 relative error = 0.20995901471974146399216980103865 % h = 0.001 y1[1] (analytic) = 2.992952010990332637179455124278 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5135264723861296369061671890624 relative error = 17.157858545690806578856802920366 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.453 y2[1] (analytic) = 1.8824759074005952019593188504015 y2[1] (numeric) = 1.878503999789274418460891876373 absolute error = 0.0039719076113207834984269740285 relative error = 0.2109938085106951876171818732841 % h = 0.001 y1[1] (analytic) = 2.993070031598319115433249471334 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5136444929941161151599615361184 relative error = 17.161125118072381753606809365757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.454 y2[1] (analytic) = 1.8834690360287232602826529199597 y2[1] (numeric) = 1.8794754684089435716276749619734 absolute error = 0.0039935676197796886549779579863 relative error = 0.21203256031222516953528003292756 % h = 0.001 y1[1] (analytic) = 2.9931870591363567512011363839172 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5137615205321537509278484487016 relative error = 17.164363949922749611934452084294 % h = 0.001 TOP MAIN SOLVE Loop memory used=869.7MB, alloc=4.1MB, time=121.57 NO POLE NO POLE x[1] = 1.455 y2[1] (analytic) = 1.8844622811878055789693861309197 y2[1] (numeric) = 1.8804469578881722061681269216361 absolute error = 0.0040153232996333728012592092836 relative error = 0.21307528092854438704845111775297 % h = 0.001 y1[1] (analytic) = 2.9933030934874180161977746055338 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5138775548832150159244866703182 relative error = 17.167575044480708128991820122012 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.456 y2[1] (analytic) = 1.8854556418845970817076269610606 y2[1] (numeric) = 1.8814184669098822281536839975549 absolute error = 0.0040371749747148535539429635057 relative error = 0.21412198118219938313100168037954 % h = 0.001 y1[1] (analytic) = 2.9934181345354685690314280723334 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5139925959312655687581401371178 relative error = 17.170758404957319418553088627571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.457 y2[1] (analytic) = 1.8864491171257371544859279787649 y2[1] (numeric) = 1.8823899941561179610938920592074 absolute error = 0.0040591229696191933920359195575 relative error = 0.21517267191408913030013108721186 % h = 0.001 y1[1] (analytic) = 2.9935321821654673712382976353168 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5141066435612643709650097001012 relative error = 17.173914034535912895468516528097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.458 y2[1] (analytic) = 1.8874427059177506389538170744175 y2[1] (numeric) = 1.883361538308046145936406603355 absolute error = 0.0040811676097044930174104710625 relative error = 0.21622736398348393854207359818455 % h = 0.001 y1[1] (analytic) = 2.9936452362633668023235499373824 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5142196976591638020502620021668 relative error = 17.177041936372088411636483223798 % h = 0.001 TOP MAIN SOLVE Loop memory used=873.5MB, alloc=4.1MB, time=122.10 NO POLE NO POLE x[1] = 1.459 y2[1] (analytic) = 1.8884364072670488258968730212842 y2[1] (numeric) = 1.8843330980459559410669927540432 absolute error = 0.004103309221092884829880267241 relative error = 0.2172860682680444073716153829336 % h = 0.001 y1[1] (analytic) = 2.9937572967161127738089284041912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5143317581119097735356404689756 relative error = 17.180142113593719365474863324939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.46 y2[1] (analytic) = 1.8894302201799304488253518908766 y2[1] (numeric) = 1.8853046720492589223095252626012 absolute error = 0.0041255481306715265158266282754 relative error = 0.21834879566384042210269769667322 % h = 0.001 y1[1] (analytic) = 2.99386836341164484228683230125 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5144428248074418420135443660344 relative error = 17.183214569300955784873212754258 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.461 y2[1] (analytic) = 1.8904241436625826776753707342597 y2[1] (numeric) = 1.8862762589964890829259885076421 absolute error = 0.0041478846660935947493822266176 relative error = 0.21941555708537019440772393632965 % h = 0.001 y1[1] (analytic) = 2.9939784362388963214807508031421 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5145528976346933212074628679265 relative error = 17.186259306566227383607413518197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.462 y2[1] (analytic) = 1.8914181767210821126216548282017 y2[1] (numeric) = 1.887247857565302833616476495063 absolute error = 0.0041703191557792790051783331387 relative error = 0.22048636346557934724309602196366 % h = 0.001 y1[1] (analytic) = 2.9940875150877943933119400144811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5146619764835913930386520792655 relative error = 17.189276328434246591198598114408 % h = 0.001 TOP MAIN SOLVE Loop memory used=877.4MB, alloc=4.1MB, time=122.64 NO POLE NO POLE x[1] = 1.463 y2[1] (analytic) = 1.892412318361395778000854673502 y2[1] (numeric) = 1.8882194664324790025191928580447 absolute error = 0.0041928519289167754816618154573 relative error = 0.22156122575588004421841449700725 % h = 0.001 y1[1] (analytic) = 2.9941955998492602179722318759202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5147700612450572176989439407046 relative error = 17.192265637922011556198347893801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.464 y2[1] (analytic) = 1.8934065675893821163444388222618 y2[1] (numeric) = 1.8891910842739188352104508570521 absolute error = 0.0042154833154632811339879652097 relative error = 0.22264015492617016348668691053885 % h = 0.001 y1[1] (analytic) = 2.9943026904152090430028648824176 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.514877151811006042729576947202 relative error = 17.195227238018809122882332735742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.465 y2[1] (analytic) = 1.8944009234107919825201685012882 y2[1] (numeric) = 1.8901627097646459947046733798338 absolute error = 0.0042382136461459878154951214544 relative error = 0.22372316196485251623280043349954 % h = 0.001 y1[1] (analytic) = 2.9944087866785503113792275349352 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5149832480743473111059395997196 relative error = 17.198161131686217781334732127864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.466 y2[1] (analytic) = 1.8953953848312696379811598902411 y2[1] (numeric) = 1.8911343415788065614543929414224 absolute error = 0.0042610432524630765267669488187 relative error = 0.22481025787885410983742726476113 % h = 0.001 y1[1] (analytic) = 2.9945138885331877686014064408375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5150883499289847683281185056219 relative error = 17.201067321858110590905950170328 % h = 0.001 TOP MAIN SOLVE Loop memory used=881.2MB, alloc=4.1MB, time=123.17 NO POLE NO POLE x[1] = 1.467 y2[1] (analytic) = 1.8963899508563537451215398055408 y2[1] (numeric) = 1.8921059783896690333502516841343 absolute error = 0.0042839724666847117712881214065 relative error = 0.22590145369364545579344519998418 % h = 0.001 y1[1] (analytic) = 2.9946179958740195687904319724508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5151924572698165685171440372352 relative error = 17.203945811440658077026309150903 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.468 y2[1] (analytic) = 1.8973846204914783617377004344665 y2[1] (numeric) = 1.8930776188696243257210013775699 absolute error = 0.0043070016218540360166990568966 relative error = 0.22699676045325992245187076358694 % h = 0.001 y1[1] (analytic) = 2.9947211085969383797901153875459 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5152955699927353795168274523303 relative error = 17.206796603312331101358578165144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.469 y2[1] (analytic) = 1.8983793927419739355941586582709 y2[1] (numeric) = 1.8940492616901857713335034186134 absolute error = 0.0043301310517881642606552396575 relative error = 0.22809618922031313267421853841094 % h = 0.001 y1[1] (analytic) = 2.9948232265988314872743723099161 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5153976879946284870010843747005 relative error = 17.209619700323903705272364787858 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.47 y2[1] (analytic) = 1.8993742666130682990930253985376 y2[1] (numeric) = 1.8950209055219891203927288314328 absolute error = 0.0043533610910791787002965671048 relative error = 0.22919975107602240646811776688152 % h = 0.001 y1[1] (analytic) = 2.9949243497775808978599284627356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.51549881117337789758664052752 relative error = 17.212415105298455926623569041074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=885.0MB, alloc=4.1MB, time=123.70 x[1] = 1.471 y2[1] (analytic) = 1.9003692411098876640460903173915 y2[1] (numeric) = 1.8959925490347925405417582674802 absolute error = 0.0043766920750951235043320499113 relative error = 0.2303074571202262486829359377715 % h = 0.001 y1[1] (analytic) = 2.9950244780320634412243045420014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5155989394278604409510166067858 relative error = 17.215182821031376589822269852581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.472 y2[1] (analytic) = 1.9013643152374576165485270995636 y2[1] (numeric) = 1.8969641908974766168617820054914 absolute error = 0.0044001243399809996867450940722 relative error = 0.23141931847140388184207891254156 % h = 0.001 y1[1] (analytic) = 2.995123611262150871228978112082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5156980726579478709556901768664 relative error = 17.217922850290366069172584860794 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.473 y2[1] (analytic) = 1.9023594880007041119532244426849 y2[1] (numeric) = 1.8979358297780443518720999514861 absolute error = 0.0044236582226597600811244911988 relative error = 0.23253534626669482418855818026705 % h = 0.001 y1[1] (analytic) = 2.9952217493687099660476214002196 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.515796210764506965774333465004 relative error = 17.22063519581543902546821479906 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.474 y2[1] (analytic) = 1.903354758404454469944747781564 y2[1] (numeric) = 1.898907464343621165530121638768 absolute error = 0.004447294060833304414626142796 relative error = 0.23365555166191851302033805923445 % h = 0.001 y1[1] (analytic) = 2.9953188922536026272993148617564 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5158933536493996270260269265408 relative error = 17.223319860318927115827553788456 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.475 y2[1] (analytic) = 1.9043501254534383697119366725675 y2[1] (numeric) = 1.8998790932604548952313662279246 absolute error = 0.0044710321929834744805704446429 relative error = 0.23477994583159397339189908205773 % h = 0.001 y1[1] (analytic) = 2.9954150398196859781866373828792 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5159895012154829779133494476636 relative error = 17.225976846485481676752416685448 % h = 0.001 TOP MAIN SOLVE Loop memory used=888.8MB, alloc=4.1MB, time=124.23 NO POLE NO POLE x[1] = 1.476 y2[1] (analytic) = 1.9053455881522888452181426655897 y2[1] (numeric) = 1.9008507151939157958094625068272 absolute error = 0.0044948729583730494086801587625 relative error = 0.23590853996895953225837840787885 % h = 0.001 y1[1] (analytic) = 2.9955101919708124606385349828016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.516084653366609460365247047586 relative error = 17.228606156972076380394604172556 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.477 y2[1] (analytic) = 1.9063411455055432805681123934568 y2[1] (numeric) = 1.9018223288084965395361488906312 absolute error = 0.0045188166970467410319635028256 relative error = 0.23704134528599257813857389650661 % h = 0.001 y1[1] (analytic) = 2.9956043486118299314578708725214 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5161788100076269311845829373058 relative error = 17.231207794408009864014695548909 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.478 y2[1] (analytic) = 1.9073367965176444054705205119649 y2[1] (numeric) = 1.9027939327678122161212734217757 absolute error = 0.0045428637498321893492470901892 relative error = 0.23817837301342936637302545257721 % h = 0.001 y1[1] (analytic) = 2.9956975096485817574735607226122 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5162719710443787572002727873966 relative error = 17.233781761394908332617628176614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.479 y2[1] (analytic) = 1.9083325401929412907951570281025 y2[1] (numeric) = 1.9037655257346003327127937699838 absolute error = 0.0045670144583409580823632581187 relative error = 0.23931963440078487005331540003648 % h = 0.001 y1[1] (analytic) = 2.9957896749879069096971979879224 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5163641363837039094239100527068 relative error = 17.236328060506728134749791270701 % h = 0.001 TOP MAIN SOLVE Loop memory used=892.6MB, alloc=4.1MB, time=124.77 NO POLE NO POLE x[1] = 1.48 y2[1] (analytic) = 1.9093283755356903442237734593522 y2[1] (numeric) = 1.9047371063707208138967772322624 absolute error = 0.0045912691649695303269962270898 relative error = 0.24046514071637267669865897581676 % h = 0.001 y1[1] (analytic) = 2.9958808445376400564840751325627 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5164553059334370562107871973471 relative error = 17.238846694289758311442530188011 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.481 y2[1] (analytic) = 1.9103243015500563059935921733094 y2[1] (numeric) = 1.9057086733371560016974007329023 absolute error = 0.0046156282129003042961914404071 relative error = 0.2416149032473249307557865335152 % h = 0.001 y1[1] (analytic) = 2.9959710182066116556985075941693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5165454796024086554252196589537 relative error = 17.241337665262623118287125576739 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.482 y2[1] (analytic) = 1.9113203172401132447324831641913 y2[1] (numeric) = 1.9066802252940106555769508234782 absolute error = 0.0046400919461025891555323407131 relative error = 0.24276893329961232199805072040263 % h = 0.001 y1[1] (analytic) = 2.9960601959046480458833683221274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5166346573004450456100803869118 relative error = 17.243800975916284520626479696192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.483 y2[1] (analytic) = 1.9123164216098455533848124311414 y2[1] (numeric) = 1.9076517609005119524358236828487 absolute error = 0.0046646607093336009489887482927 relative error = 0.24392724219806411989962473132395 % h = 0.001 y1[1] (analytic) = 2.9961483775425715364337417202262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5167228389383685361604537850106 relative error = 17.246236628714044661848909908423 % h = 0.001 TOP MAIN SOLVE Loop memory used=896.4MB, alloc=4.1MB, time=125.31 NO POLE NO POLE x[1] = 1.484 y2[1] (analytic) = 1.9133126136631489452269660325664 y2[1] (numeric) = 1.9086232788150094866125251171563 absolute error = 0.0046893348481394586144409154101 relative error = 0.24508984128638825406059174845895 % h = 0.001 y1[1] (analytic) = 2.9962355630322004967746068201009 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5168100244279974965013188848853 relative error = 17.248644626091548304769616782912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.485 y2[1] (analytic) = 1.9143088924038314499715538010618 y2[1] (numeric) = 1.9095947776949752698836705598273 absolute error = 0.0047141147088561800878832412345 relative error = 0.24625674192719144075866084300233 % h = 0.001 y1[1] (analytic) = 2.9963217522863494445424605077845 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5168962136821464442691725725689 relative error = 17.251024970456785246085561444861 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.486 y2[1] (analytic) = 1.9153052568356144099592966148078 y2[1] (numeric) = 1.9105662561970037314639850715719 absolute error = 0.0047390006386106784953115432359 relative error = 0.24742795550199935570318094168788 % h = 0.001 y1[1] (analytic) = 2.9964069452188291327707926217544 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5169814066146261324975046865388 relative error = 17.253377664190092703889653740136 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.487 y2[1] (analytic) = 1.9163017059621334764376010336293 y2[1] (numeric) = 1.9115377129768117180063033403843 absolute error = 0.004763992985321758431297693245 relative error = 0.24860349341127685306706194397485 % h = 0.001 y1[1] (analytic) = 2.9964911417444466360793257370054 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5170656031402436358060378017898 relative error = 17.255702709644157678230319487996 % h = 0.001 TOP MAIN SOLVE Loop memory used=900.2MB, alloc=4.1MB, time=125.84 NO POLE NO POLE x[1] = 1.488 y2[1] (analytic) = 1.9172982387869396059248250212299 y2[1] (numeric) = 1.9125091466892384936015696815424 absolute error = 0.0047890920977011123232553396875 relative error = 0.24978336707444823087215071263056 % h = 0.001 y1[1] (analytic) = 2.9965743417790054358669334459171 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5171488031748024355936455107015 relative error = 17.258000109144019284702681549579 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.489 y2[1] (analytic) = 1.9182948543135000566592383894163 y2[1] (numeric) = 1.9134805559882457397788380376082 absolute error = 0.0048142983252543168804003518081 relative error = 0.25096758792991754280354944777592 % h = 0.001 y1[1] (analytic) = 2.996656545239305504508151943004 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5172310066351025042348640077884 relative error = 17.260269864987071061057755658289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.49 y2[1] (analytic) = 1.9192915515451993851316815154363 y2[1] (numeric) = 1.9144519395269175555052719784274 absolute error = 0.0048396120182818296264095370089 relative error = 0.25215616743508895652830489020165 % h = 0.001 y1[1] (analytic) = 2.9967377520431433885532007170437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5173122134389403882799127818281 relative error = 17.262511979443063246816227940736 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.491 y2[1] (analytic) = 1.9202883294853404427009257998542 y2[1] (numeric) = 1.9154232959574604571861447011297 absolute error = 0.0048650335278799855147810987245 relative error = 0.2533491170663871585938388802408 % h = 0.001 y1[1] (analytic) = 2.9968179621093122909314291505699 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5173924235051092906581412153543 relative error = 17.264726454754105035873546806539 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=904.1MB, alloc=4.1MB, time=126.38 x[1] = 1.492 y2[1] (analytic) = 1.9212851871371453722907392496861 y2[1] (numeric) = 1.9163946239312033786648390301285 absolute error = 0.0048905632059419936259002195576 relative error = 0.25454644831927780598143402169098 % h = 0.001 y1[1] (analytic) = 2.9968971753576021521581068232903 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5174716367533991518848188880747 relative error = 17.266913293134666802083227404836 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.493 y2[1] (analytic) = 1.922282123503756605167660489814 y2[1] (numeric) = 1.9173659220985976712228474171214 absolute error = 0.0049162014051589339448130726926 relative error = 0.25574817270828802439003256278309 % h = 0.001 y1[1] (analytic) = 2.9969753917087997305444763126456 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.51754985310459673027118837743 relative error = 17.269072496771582297805432137695 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.494 y2[1] (analytic) = 1.9232791375882378577984844249848 y2[1] (numeric) = 1.9183371891092171035797719410896 absolute error = 0.0049419484790207542187124838952 relative error = 0.25695430176702695332555210540961 % h = 0.001 y1[1] (analytic) = 2.9970526110846886814109882814636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.517627072480485681137700346248 relative error = 17.271204067824050825408055788607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.495 y2[1] (analytic) = 1.9242762283935751287864626949956 y2[1] (numeric) = 1.9193084236117578618933243082983 absolute error = 0.0049678047818172668931383866973 relative error = 0.25816484704820633807086838714025 % h = 0.001 y1[1] (analytic) = 2.9971288334080496353036396394798 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5177032948038466350303517042642 relative error = 17.273308008423639381707708670607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=907.9MB, alloc=4.1MB, time=126.90 x[1] = 1.496 y2[1] (analytic) = 1.925273394922677695885221986944 y2[1] (numeric) = 1.9202796242540385497593258522966 absolute error = 0.0049937706686391461258961346474 relative error = 0.25937982012366116861156314456472 % h = 0.001 y1[1] (analytic) = 2.9972040586026602752133365623937 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5177785199984572749400486271781 relative error = 17.27538432067428477533815582625 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.497 y2[1] (analytic) = 1.926270636178379113089403190711 y2[1] (numeric) = 1.9212507896830001882117075339174 absolute error = 0.0050198464953789248776956567936 relative error = 0.26059923258437036559248395924374 % h = 0.001 y1[1] (analytic) = 2.9972782865932954127982051491029 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5178527479890924125249172138873 relative error = 17.277433006652295717033934723323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.498 y2[1] (analytic) = 1.927267951163438207801024307119 y2[1] (numeric) = 1.9222219185447062157225099412775 absolute error = 0.0050460326187319920785143658415 relative error = 0.26182309604047751338011300528588 % h = 0.001 y1[1] (analytic) = 2.9973515173057270636087734948114 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5179259787015240633354855595958 relative error = 17.279454068406354882817038088851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.499 y2[1] (analytic) = 1.9282653388805400780705699424854 y2[1] (numeric) = 1.9231930094843424882018832897777 absolute error = 0.0050723293961975898686866527077 relative error = 0.26305142212131164030569275825624 % h = 0.001 y1[1] (analytic) = 2.9974237506667245213159499548364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5179982120625215210426620196208 relative error = 17.281447507957520950074712512252 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.5 y2[1] (analytic) = 1.9292627983322970899118101485657 y2[1] (numeric) = 1.9241640611462172789980874221026 absolute error = 0.0050987371860798109137227264631 relative error = 0.2642842224754080461640089855315 % h = 0.001 y1[1] (analytic) = 2.9974949866040544309417233711415 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5180694479998514306684354359259 relative error = 17.283413327299230606516587229319 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff(y2,x,1) = y1 - 2.0; diff(y1,x,1) = diff(y2,x,5); Iterations = 1000 Total Elapsed Time = 2 Minutes 7 Seconds Elapsed Time(since restart) = 2 Minutes 7 Seconds Expected Time Remaining = 18 Minutes 0 Seconds Optimized Time Remaining = 18 Minutes 0 Seconds Time to Timeout = 12 Minutes 52 Seconds Percent Done = 10.54 % > quit memory used=911.7MB, alloc=4.1MB, time=127.41