|\^/| 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 > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > 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_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[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_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[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 DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, 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_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[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_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[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 > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > 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 (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 (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 DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, glob_last; hnew := h_param; glob_normmax := glob_small_float; 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_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_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 > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > 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 DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, 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 > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > 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_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[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_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[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_y1_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_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 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := 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 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_y2_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_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 3 > array_complex_pole[2,1] := glob_large_float; > array_complex_pole[2,2] := 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 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 DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, glob_last; 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[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_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[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_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[1, 1] := glob_large_float; array_complex_pole[1, 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[1, 1] := glob_large_float; array_complex_pole[1, 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[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_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[2, 1] := glob_large_float; array_complex_pole[2, 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[2, 1] := glob_large_float; array_complex_pole[2, 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[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 > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > 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_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 > ; > 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 > #GET NORMS > ; > fi;# end if 3 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, 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_y1[iii]) then array_norms[iii] := abs(array_y1[iii]) end if; iii := iii + 1 end do; 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 end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre diff $eq_no = 1 i = 1 > array_tmp1[1] := array_y2_higher[6,1]; > #emit pre add $eq_no = 1 i = 1 > array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; > #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5 > if not array_y1_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_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; > #emit pre sub $eq_no = 2 i = 1 > array_tmp4[1] := (array_y1[1] - (array_const_2D0[1])); > #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5 > if not array_y2_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_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; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre diff $eq_no = 1 i = 2 > array_tmp1[2] := array_y2_higher[6,2]; > #emit pre add $eq_no = 1 i = 2 > array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; > #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5 > if not array_y1_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_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; > #emit pre sub $eq_no = 2 i = 2 > array_tmp4[2] := (array_y1[2] - (array_const_2D0[2])); > #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5 > if not array_y2_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_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; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre diff $eq_no = 1 i = 3 > array_tmp1[3] := array_y2_higher[6,3]; > #emit pre add $eq_no = 1 i = 3 > array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; > #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5 > if not array_y1_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_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; > #emit pre sub $eq_no = 2 i = 3 > array_tmp4[3] := (array_y1[3] - (array_const_2D0[3])); > #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5 > if not array_y2_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_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; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre diff $eq_no = 1 i = 4 > array_tmp1[4] := array_y2_higher[6,4]; > #emit pre add $eq_no = 1 i = 4 > array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; > #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5 > if not array_y1_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_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; > #emit pre sub $eq_no = 2 i = 4 > array_tmp4[4] := (array_y1[4] - (array_const_2D0[4])); > #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5 > if not array_y2_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_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; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre diff $eq_no = 1 i = 5 > array_tmp1[5] := array_y2_higher[6,5]; > #emit pre add $eq_no = 1 i = 5 > array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; > #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5 > if not array_y1_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_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; > #emit pre sub $eq_no = 2 i = 5 > array_tmp4[5] := (array_y1[5] - (array_const_2D0[5])); > #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5 > if not array_y2_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_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; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit diff $eq_no = 1 > array_tmp1[kkk] := array_y2_higher[6,kkk]; > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y1_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_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 > ; > #emit sub $eq_no = 2 > array_tmp4[kkk] := (array_y1[kkk] - (array_const_2D0[kkk])); > #emit assign $eq_no = 2 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y2_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_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 > ; > 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 DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, glob_last; array_tmp1[1] := array_y2_higher[6, 1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y1_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[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_tmp4[1] := array_y1[1] - array_const_2D0[1]; if not array_y2_set_initial[2, 2] then if 1 <= glob_max_terms then temporary := array_tmp4[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_tmp1[2] := array_y2_higher[6, 2]; array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y1_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[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_tmp4[2] := array_y1[2] - array_const_2D0[2]; if not array_y2_set_initial[2, 3] then if 2 <= glob_max_terms then temporary := array_tmp4[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_tmp1[3] := array_y2_higher[6, 3]; array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y1_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[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_tmp4[3] := array_y1[3] - array_const_2D0[3]; if not array_y2_set_initial[2, 4] then if 3 <= glob_max_terms then temporary := array_tmp4[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_tmp1[4] := array_y2_higher[6, 4]; array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y1_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[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_tmp4[4] := array_y1[4] - array_const_2D0[4]; if not array_y2_set_initial[2, 5] then if 4 <= glob_max_terms then temporary := array_tmp4[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_tmp1[5] := array_y2_higher[6, 5]; array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y1_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[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; array_tmp4[5] := array_y1[5] - array_const_2D0[5]; if not array_y2_set_initial[2, 6] then if 5 <= glob_max_terms then temporary := array_tmp4[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; while kkk <= glob_max_terms do array_tmp1[kkk] := array_y2_higher[6, kkk]; array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y1_set_initial[1, kkk + order_d] then temporary := array_tmp2[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; array_tmp4[kkk] := array_y1[kkk] - array_const_2D0[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y2_set_initial[2, kkk + order_d] then temporary := array_tmp4[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; 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) > if (nnn <= glob_max_terms) then # if number 13 > ret := array_fact_1[nnn]; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; Warning, `ret` is implicitly declared local to procedure `factorial_1` factorial_1 := proc(nnn) local ret; if nnn <= glob_max_terms then ret := array_fact_1[nnn] else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > ret := array_fact_2[mmm,nnn]; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; Warning, `ret` is implicitly declared local to procedure `factorial_3` factorial_3 := proc(mmm, nnn) local ret; if nnn <= glob_max_terms and mmm <= glob_max_terms then ret := array_fact_2[mmm, nnn] else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y1 := proc(x) > 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 > DEBUGL, > glob_max_terms, > DEBUGMASSIVE, > INFO, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_log10abserr, > glob_small_float, > glob_optimal_done, > centuries_in_millinium, > MAX_UNCHANGED, > glob_start, > glob_hmin, > min_in_hour, > glob_warned2, > glob_max_trunc_err, > glob_dump_analytic, > glob_initial_pass, > glob_clock_start_sec, > days_in_year, > hours_in_day, > glob_normmax, > glob_current_iter, > glob_curr_iter_when_opt, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_hmin_init, > glob_almost_1, > glob_dump, > glob_optimal_expect_sec, > glob_warned, > glob_no_eqs, > glob_max_iter, > glob_relerr, > glob_log10_abserr, > glob_hmax, > glob_disp_incr, > glob_reached_optimal_h, > years_in_century, > glob_percent_done, > glob_max_hours, > glob_max_opt_iter, > glob_subiter_method, > glob_large_float, > glob_not_yet_start_msg, > glob_display_flag, > djd_debug, > glob_log10relerr, > glob_unchanged_h_cnt, > glob_look_poles, > glob_h, > sec_in_min, > glob_max_sec, > glob_log10_relerr, > glob_not_yet_finished, > glob_clock_sec, > glob_html_log, > glob_log10normmin, > glob_max_minutes, > glob_smallish_float, > glob_abserr, > glob_iter, > glob_optimal_start, > glob_optimal_clock_start_sec, > glob_last_good_h, > djd_debug2, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_0D0, > array_const_5, > array_const_1, > #END CONST > array_m1, > array_type_pole, > array_y2_init, > array_last_rel_error, > array_1st_rel_error, > array_y1, > array_y2, > array_pole, > array_fact_1, > array_norms, > array_y1_init, > array_x, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_y2_set_initial, > array_y1_higher_work, > array_poles, > array_y2_higher, > array_y1_higher_work2, > array_y2_higher_work, > array_fact_2, > array_y1_set_initial, > array_y1_higher, > array_real_pole, > array_complex_pole, > array_y2_higher_work2, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > INFO := 2; > ALWAYS := 1; > glob_iolevel := 5; > glob_log10abserr := 0.0; > glob_small_float := 0.1e-50; > glob_optimal_done := false; > centuries_in_millinium := 10.0; > MAX_UNCHANGED := 10; > glob_start := 0; > glob_hmin := 0.00000000001; > min_in_hour := 60.0; > glob_warned2 := false; > glob_max_trunc_err := 0.1e-10; > glob_dump_analytic := false; > glob_initial_pass := true; > glob_clock_start_sec := 0.0; > days_in_year := 365.0; > hours_in_day := 24.0; > glob_normmax := 0.0; > glob_current_iter := 0; > glob_curr_iter_when_opt := 0; > glob_orig_start_sec := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_hmin_init := 0.001; > glob_almost_1 := 0.9990; > glob_dump := false; > glob_optimal_expect_sec := 0.1; > glob_warned := false; > glob_no_eqs := 0; > glob_max_iter := 1000; > glob_relerr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_hmax := 1.0; > glob_disp_incr := 0.1; > glob_reached_optimal_h := false; > years_in_century := 100.0; > glob_percent_done := 0.0; > glob_max_hours := 0.0; > glob_max_opt_iter := 10; > glob_subiter_method := 3; > glob_large_float := 9.0e100; > glob_not_yet_start_msg := true; > glob_display_flag := true; > djd_debug := true; > glob_log10relerr := 0.0; > glob_unchanged_h_cnt := 0; > glob_look_poles := false; > glob_h := 0.1; > sec_in_min := 60.0; > glob_max_sec := 10000.0; > glob_log10_relerr := 0.1e-10; > glob_not_yet_finished := true; > glob_clock_sec := 0.0; > glob_html_log := true; > glob_log10normmin := 0.1; > glob_max_minutes := 0.0; > glob_smallish_float := 0.1e-100; > glob_abserr := 0.1e-10; > glob_iter := 0; > glob_optimal_start := 0.0; > glob_optimal_clock_start_sec := 0.0; > glob_last_good_h := 0.1; > djd_debug2 := true; > #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/mtest9postode.ode#################"); > omniout_str(ALWAYS,"diff(y1,x,1) = diff(y2,x,5);"); > omniout_str(ALWAYS,"diff(y2,x,1) = y1 - 2.0;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms:=30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.5;"); > 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,""); > 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_m1:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_y2_init:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_y1:= Array(0..(max_terms + 1),[]); > array_y2:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y1_init:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_tmp3:= Array(0..(max_terms + 1),[]); > array_tmp4:= Array(0..(max_terms + 1),[]); > array_y2_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y2_higher := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher_work2 := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_y2_higher_work := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_y1_set_initial := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y1_higher := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_complex_pole := Array(0..(2+ 1) ,(0..3+ 1),[]); > array_y2_higher_work2 := Array(0..(6+ 1) ,(0..max_terms+ 1),[]); > 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_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_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y1[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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_x[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 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 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 <=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 <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y1_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_complex_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=6 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y2_higher_work2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_y2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_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_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_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_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_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > temp1 := iiif !; > temp2 := jjjf !; > array_fact_1[iiif] := temp1; > array_fact_2[iiif,jjjf] := temp1/temp2; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.5; > 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_y1_set_initial[1,1] := true; > array_y1_set_initial[1,2] := false; > array_y1_set_initial[1,3] := false; > array_y1_set_initial[1,4] := false; > array_y1_set_initial[1,5] := false; > array_y1_set_initial[1,6] := false; > array_y1_set_initial[1,7] := false; > array_y1_set_initial[1,8] := false; > array_y1_set_initial[1,9] := false; > array_y1_set_initial[1,10] := false; > array_y1_set_initial[1,11] := false; > array_y1_set_initial[1,12] := false; > array_y1_set_initial[1,13] := false; > array_y1_set_initial[1,14] := false; > array_y1_set_initial[1,15] := false; > array_y1_set_initial[1,16] := false; > array_y1_set_initial[1,17] := false; > array_y1_set_initial[1,18] := false; > array_y1_set_initial[1,19] := false; > array_y1_set_initial[1,20] := false; > array_y1_set_initial[1,21] := false; > array_y1_set_initial[1,22] := false; > array_y1_set_initial[1,23] := false; > array_y1_set_initial[1,24] := false; > array_y1_set_initial[1,25] := false; > array_y1_set_initial[1,26] := false; > array_y1_set_initial[1,27] := false; > array_y1_set_initial[1,28] := false; > array_y1_set_initial[1,29] := false; > array_y1_set_initial[1,30] := false; > array_y2_set_initial[2,1] := true; > array_y2_set_initial[2,2] := true; > array_y2_set_initial[2,3] := true; > array_y2_set_initial[2,4] := true; > array_y2_set_initial[2,5] := true; > array_y2_set_initial[2,6] := false; > array_y2_set_initial[2,7] := false; > array_y2_set_initial[2,8] := false; > array_y2_set_initial[2,9] := false; > array_y2_set_initial[2,10] := false; > array_y2_set_initial[2,11] := false; > array_y2_set_initial[2,12] := false; > array_y2_set_initial[2,13] := false; > array_y2_set_initial[2,14] := false; > array_y2_set_initial[2,15] := false; > array_y2_set_initial[2,16] := false; > array_y2_set_initial[2,17] := false; > array_y2_set_initial[2,18] := false; > array_y2_set_initial[2,19] := false; > array_y2_set_initial[2,20] := false; > array_y2_set_initial[2,21] := false; > array_y2_set_initial[2,22] := false; > array_y2_set_initial[2,23] := false; > array_y2_set_initial[2,24] := false; > array_y2_set_initial[2,25] := false; > array_y2_set_initial[2,26] := false; > array_y2_set_initial[2,27] := false; > array_y2_set_initial[2,28] := false; > array_y2_set_initial[2,29] := false; > array_y2_set_initial[2,30] := false; > if glob_html_log then # if number 3 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 3 > ; > #BEGIN SOLUTION CODE > omniout_str(ALWAYS,"START of Soultion"); > #Start Series -- INITIALIZE FOR SOLUTION > array_x[1] := x_start; > array_x[2] := glob_h; > order_diff := 1; > #Start Series array_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 > ; > 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 > ; > current_iter := 1; > glob_clock_start_sec := elapsed_time_seconds(); > 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) > ; > 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) > ; > 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_y1 > order_diff := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > 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 =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y1 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y1_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y1_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =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_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 > #Jump Series array_y2 > order_diff := 5; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =2 > #sum_and_adjust array_y2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 5; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 4; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > 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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 5; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =2 > #BEFORE ADJUST SUBSERIES EQ =2 > 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 =2 > #BEFORE SUM SUBSERIES EQ =2 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y2 > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y2_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y2_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =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_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 > 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(y1,x,1) = diff(y2,x,5);"); > omniout_str(INFO,"diff(y2,x,1) = y1 - 2.0;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 4 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-17T01:13:22-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"mtest9") > ; > logitem_str(html_log_file,"diff(y1,x,1) = diff(y2,x,5);") > ; > 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," 091 ") > ; > logitem_str(html_log_file,"mtest9 diffeq.mxt") > ; > logitem_str(html_log_file,"mtest9 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly for speeding factorials") > ; > logend(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logitem_str(html_log_file,"diff(y2,x,1) = y1 - 2.0;") > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > ; > logditto(html_log_file) > ; > logitem_float(html_log_file,array_1st_rel_error[2]) > ; > logitem_float(html_log_file,array_last_rel_error[2]) > ; > logditto(html_log_file) > ; > logitem_pole(html_log_file,array_type_pole[2]) > ; > if array_type_pole[2] = 1 or array_type_pole[2] = 2 then # if number 5 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 5 > ; > logditto(html_log_file) > ; > if glob_percent_done < 100.0 then # if number 5 > logditto(html_log_file) > ; > 0 > else > logditto(html_log_file) > ; > 0 > fi;# end if 5 > ; > logditto(html_log_file); > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logditto(html_log_file) > ; > logend(html_log_file) > ; > ; > fi;# end if 4 > ; > if glob_html_log then # if number 4 > fclose(html_log_file); > fi;# end if 4 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; Warning, `iiif` is implicitly declared local to procedure `mainprog` Warning, `jjjf` is implicitly declared local to procedure `mainprog` Warning, `temp1` is implicitly declared local to procedure `mainprog` Warning, `temp2` is implicitly declared local to procedure `mainprog` 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, iiif, jjjf, temp1, temp2, subiter; global DEBUGL, glob_max_terms, DEBUGMASSIVE, INFO, ALWAYS, glob_iolevel, glob_log10abserr, glob_small_float, glob_optimal_done, centuries_in_millinium, MAX_UNCHANGED, glob_start, glob_hmin, min_in_hour, glob_warned2, glob_max_trunc_err, glob_dump_analytic, glob_initial_pass, glob_clock_start_sec, days_in_year, hours_in_day, glob_normmax, glob_current_iter, glob_curr_iter_when_opt, glob_orig_start_sec, glob_max_rel_trunc_err, glob_hmin_init, glob_almost_1, glob_dump, glob_optimal_expect_sec, glob_warned, glob_no_eqs, glob_max_iter, glob_relerr, glob_log10_abserr, glob_hmax, glob_disp_incr, glob_reached_optimal_h, years_in_century, glob_percent_done, glob_max_hours, glob_max_opt_iter, glob_subiter_method, glob_large_float, glob_not_yet_start_msg, glob_display_flag, djd_debug, glob_log10relerr, glob_unchanged_h_cnt, glob_look_poles, glob_h, sec_in_min, glob_max_sec, glob_log10_relerr, glob_not_yet_finished, glob_clock_sec, glob_html_log, glob_log10normmin, glob_max_minutes, glob_smallish_float, glob_abserr, glob_iter, glob_optimal_start, glob_optimal_clock_start_sec, glob_last_good_h, djd_debug2, array_const_2D0, array_const_0D0, array_const_5, array_const_1, array_m1, array_type_pole, array_y2_init, array_last_rel_error, array_1st_rel_error, array_y1, array_y2, array_pole, array_fact_1, array_norms, array_y1_init, array_x, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_y2_set_initial, array_y1_higher_work, array_poles, array_y2_higher, array_y1_higher_work2, array_y2_higher_work, array_fact_2, array_y1_set_initial, array_y1_higher, array_real_pole, array_complex_pole, array_y2_higher_work2, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; glob_max_terms := 30; DEBUGMASSIVE := 4; INFO := 2; ALWAYS := 1; glob_iolevel := 5; glob_log10abserr := 0.; glob_small_float := 0.1*10^(-50); glob_optimal_done := false; centuries_in_millinium := 10.0; MAX_UNCHANGED := 10; glob_start := 0; glob_hmin := 0.1*10^(-10); min_in_hour := 60.0; glob_warned2 := false; glob_max_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; glob_initial_pass := true; glob_clock_start_sec := 0.; days_in_year := 365.0; hours_in_day := 24.0; glob_normmax := 0.; glob_current_iter := 0; glob_curr_iter_when_opt := 0; glob_orig_start_sec := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_hmin_init := 0.001; glob_almost_1 := 0.9990; glob_dump := false; glob_optimal_expect_sec := 0.1; glob_warned := false; glob_no_eqs := 0; glob_max_iter := 1000; glob_relerr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_hmax := 1.0; glob_disp_incr := 0.1; glob_reached_optimal_h := false; years_in_century := 100.0; glob_percent_done := 0.; glob_max_hours := 0.; glob_max_opt_iter := 10; glob_subiter_method := 3; glob_large_float := 0.90*10^101; glob_not_yet_start_msg := true; glob_display_flag := true; djd_debug := true; glob_log10relerr := 0.; glob_unchanged_h_cnt := 0; glob_look_poles := false; glob_h := 0.1; sec_in_min := 60.0; glob_max_sec := 10000.0; glob_log10_relerr := 0.1*10^(-10); glob_not_yet_finished := true; glob_clock_sec := 0.; glob_html_log := true; glob_log10normmin := 0.1; glob_max_minutes := 0.; glob_smallish_float := 0.1*10^(-100); glob_abserr := 0.1*10^(-10); glob_iter := 0; glob_optimal_start := 0.; glob_optimal_clock_start_sec := 0.; glob_last_good_h := 0.1; djd_debug2 := true; 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/mtest9postode.ode#################"); omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"); omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms:=30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.5;"); 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, ""); 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_m1 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_y2_init := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_y1 := Array(0 .. max_terms + 1, []); array_y2 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y1_init := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_tmp3 := Array(0 .. max_terms + 1, []); array_tmp4 := Array(0 .. max_terms + 1, []); array_y2_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher_work := Array(0 .. 3, 0 .. max_terms + 1, []); array_poles := Array(0 .. 3, 0 .. 4, []); array_y2_higher := Array(0 .. 7, 0 .. max_terms + 1, []); array_y1_higher_work2 := Array(0 .. 3, 0 .. max_terms + 1, []); array_y2_higher_work := Array(0 .. 7, 0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_y1_set_initial := Array(0 .. 4, 0 .. max_terms + 1, []); array_y1_higher := Array(0 .. 3, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 3, 0 .. 4, []); array_complex_pole := Array(0 .. 3, 0 .. 4, []); array_y2_higher_work2 := Array(0 .. 7, 0 .. max_terms + 1, []); term := 1; while term <= max_terms do array_m1[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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y1[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_x[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; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y2_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_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 <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y1_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y1_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= 3 do array_complex_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 6 do term := 1; while term <= max_terms do array_y2_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; 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_y1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y1[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_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_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_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_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_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do temp1 := iiif!; temp2 := jjjf!; array_fact_1[iiif] := temp1; array_fact_2[iiif, jjjf] := temp1/temp2; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; 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_y1_set_initial[1, 1] := true; array_y1_set_initial[1, 2] := false; array_y1_set_initial[1, 3] := false; array_y1_set_initial[1, 4] := false; array_y1_set_initial[1, 5] := false; array_y1_set_initial[1, 6] := false; array_y1_set_initial[1, 7] := false; array_y1_set_initial[1, 8] := false; array_y1_set_initial[1, 9] := false; array_y1_set_initial[1, 10] := false; array_y1_set_initial[1, 11] := false; array_y1_set_initial[1, 12] := false; array_y1_set_initial[1, 13] := false; array_y1_set_initial[1, 14] := false; array_y1_set_initial[1, 15] := false; array_y1_set_initial[1, 16] := false; array_y1_set_initial[1, 17] := false; array_y1_set_initial[1, 18] := false; array_y1_set_initial[1, 19] := false; array_y1_set_initial[1, 20] := false; array_y1_set_initial[1, 21] := false; array_y1_set_initial[1, 22] := false; array_y1_set_initial[1, 23] := false; array_y1_set_initial[1, 24] := false; array_y1_set_initial[1, 25] := false; array_y1_set_initial[1, 26] := false; array_y1_set_initial[1, 27] := false; array_y1_set_initial[1, 28] := false; array_y1_set_initial[1, 29] := false; array_y1_set_initial[1, 30] := false; array_y2_set_initial[2, 1] := true; array_y2_set_initial[2, 2] := true; array_y2_set_initial[2, 3] := true; array_y2_set_initial[2, 4] := true; array_y2_set_initial[2, 5] := true; array_y2_set_initial[2, 6] := false; array_y2_set_initial[2, 7] := false; array_y2_set_initial[2, 8] := false; array_y2_set_initial[2, 9] := false; array_y2_set_initial[2, 10] := false; array_y2_set_initial[2, 11] := false; array_y2_set_initial[2, 12] := false; array_y2_set_initial[2, 13] := false; array_y2_set_initial[2, 14] := false; array_y2_set_initial[2, 15] := false; array_y2_set_initial[2, 16] := false; array_y2_set_initial[2, 17] := false; array_y2_set_initial[2, 18] := false; array_y2_set_initial[2, 19] := false; array_y2_set_initial[2, 20] := false; array_y2_set_initial[2, 21] := false; array_y2_set_initial[2, 22] := false; array_y2_set_initial[2, 23] := false; array_y2_set_initial[2, 24] := false; array_y2_set_initial[2, 25] := false; array_y2_set_initial[2, 26] := false; array_y2_set_initial[2, 27] := false; array_y2_set_initial[2, 28] := false; array_y2_set_initial[2, 29] := false; array_y2_set_initial[2, 30] := false; if glob_html_log then html_log_file := fopen("html/entry.html", WRITE, TEXT) end if; omniout_str(ALWAYS, "START of Soultion"); array_x[1] := x_start; array_x[2] := glob_h; order_diff := 1; term_no := 1; while term_no <= order_diff do array_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; 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; current_iter := 1; glob_clock_start_sec := elapsed_time_seconds(); 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); 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); glob_clock_sec := elapsed_time_seconds(); glob_current_iter := 0; glob_iter := 0; omniout_str(DEBUGL, " "); glob_reached_optimal_h := true; glob_optimal_clock_start_sec := elapsed_time_seconds(); while glob_current_iter < glob_max_iter and array_x[1] <= x_end and convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < convfloat(glob_max_sec) do omniout_str(INFO, " "); omniout_str(INFO, "TOP MAIN SOLVE Loop"); glob_iter := glob_iter + 1; glob_clock_sec := elapsed_time_seconds(); glob_current_iter := glob_current_iter + 1; if glob_subiter_method = 1 then atomall() elif glob_subiter_method = 2 then subiter := 1; while subiter <= 2 do atomall(); subiter := subiter + 1 end do else subiter := 1; while subiter <= 2 + glob_max_terms do atomall(); subiter := subiter + 1 end do end if; if glob_look_poles then check_for_pole() end if; array_x[1] := array_x[1] + glob_h; array_x[2] := glob_h; order_diff := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y1_higher_work[ord, iii]; iii := iii - 1 end do; array_y1_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y1[term_no] := array_y1_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y1_higher[ord, term_no] := array_y1_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; 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)/factorial_1(calc_term - 1)!; ord := 5; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( 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)/factorial_1(calc_term - 1)!; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[5, iii] := array_y2_higher[5, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 5; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 4; calc_term := 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)/factorial_1(calc_term - 1)!; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[4, iii] := array_y2_higher[4, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 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)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 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)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 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)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 5; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y2_higher_work[ord, iii]; iii := iii - 1 end do; array_y2_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/factorial_1(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y2[term_no] := array_y2_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y2_higher[ord, term_no] := array_y2_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; 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(y1,x,1) = diff(y2,x,5);"); omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-17T01:13:22-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "mtest9") ; logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"); 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, " 091 "); logitem_str(html_log_file, "mtest9 diffeq.mxt"); logitem_str(html_log_file, "mtest9 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly for speeding factorials"); logend(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logitem_float(html_log_file, array_1st_rel_error[2]); logitem_float(html_log_file, array_last_rel_error[2]); logditto(html_log_file); logitem_pole(html_log_file, array_type_pole[2]); if array_type_pole[2] = 1 or array_type_pole[2] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logditto(html_log_file); if glob_percent_done < 100.0 then logditto(html_log_file); 0 else logditto(html_log_file); 0 end if; logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logditto(html_log_file); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/mtest9postode.ode################# diff(y1,x,1) = diff(y2,x,5); diff(y2,x,1) = y1 - 2.0; ! #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 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.001 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.001 x[1] = 0.5 y1[1] (analytic) = 2.4794255386042030002732879352156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0 relative error = 0 % h = 0.001 y2[1] (analytic) = 1.1224174381096272838837184173962 y2[1] (numeric) = 1.1224174381096272838837184173962 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.501 y1[1] (analytic) = 2.4803028813070802939494724420977 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0008773427028772936761845068821 relative error = 0.035372401874360924089566086208289 % h = 0.001 y2[1] (analytic) = 1.1228973023595716136926687557886 y2[1] (numeric) = 1.1228973023595716096962371645635 absolute error = 3.9964315912251e-18 relative error = 3.5590357041799818917528935659069e-16 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.502 y1[1] (analytic) = 2.4811797437071163057841377482187 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0017542051029133055108498130031 relative error = 0.070700444309300938093178385518425 % h = 0.001 y2[1] (analytic) = 1.1233780437121404920409717621522 y2[1] (numeric) = 1.1233780437915603625823077305536 absolute error = 7.94198705413359684014e-11 relative error = 7.0697367627817797960044662136185e-09 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=3.8MB, alloc=3.0MB, time=0.48 x[1] = 0.503 y1[1] (analytic) = 2.4820561249274487088131362528522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0026305863232457085398483176366 relative error = 0.10598415953719021627869493626097 % h = 0.001 y2[1] (analytic) = 1.1238596616865926064215271335312 y2[1] (numeric) = 1.1238596623229056785506126368749 absolute error = 6.363130721290855033437e-10 relative error = 5.6618552460025229812948425162685e-08 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.504 y1[1] (analytic) = 2.4829320240916963557358308536409 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0035064854874933554625429184253 relative error = 0.14122357976256294749295818319025 % h = 0.001 y2[1] (analytic) = 1.1243421558013100225170503558855 y2[1] (numeric) = 1.1243421579529181873517235814938 absolute error = 2.1516081648346732256083e-09 relative error = 1.9136596041809342326865845554282e-07 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.505 y1[1] (analytic) = 2.4838074403239601552961692154743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0043819017197571550228812802587 relative error = 0.17641873716207358683165415092659 % h = 0.001 y2[1] (analytic) = 1.1248255255737986658179668865485 y2[1] (numeric) = 1.1248255306815921442335619952268 absolute error = 5.1077934784155951086783e-09 relative error = 4.5409651206217029800596352562101e-07 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.506 y1[1] (analytic) = 2.4846823727488239481817020349524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0052568341446209479084140997368 relative error = 0.2115696638844533806737925932691 % h = 0.001 y2[1] (analytic) = 1.1253097705206888041164464559634 y2[1] (numeric) = 1.1253097805089275013231938899973 absolute error = 9.9882386972067474340339e-09 relative error = 8.8759903795957611013482087921445e-07 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.507 y1[1] (analytic) = 2.4855568204913553824396694014904 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0061312818871523821663814662748 relative error = 0.24667639205046716400687694163286 % h = 0.001 y2[1] (analytic) = 1.1257948901577355308760949947039 y2[1] (numeric) = 1.125794907434924258221678149238 absolute error = 1.72771887273455831545341e-08 relative error = 1.5346657618000797612418614481025e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.508 y1[1] (analytic) = 2.4864307826771067884092798390526 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.007005244072903788135991903837 relative error = 0.28173895375287042897210788637658 % h = 0.001 y2[1] (analytic) = 1.1262808839998192494768208161278 y2[1] (numeric) = 1.1262809114595824149256902636442 absolute error = 2.74597631654488694475164e-08 relative error = 2.4380919143304288125880276974964e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=7.6MB, alloc=4.3MB, time=1.12 x[1] = 0.509 y1[1] (analytic) = 2.4873042584321160531693070963062 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0078787198279130528960191610906 relative error = 0.31675738105636666356223183993781 % h = 0.001 y2[1] (analytic) = 1.126767751560946158334390809836 y2[1] (numeric) = 1.1267677925829019714352025289717 absolute error = 4.10219558131008117191357e-08 relative error = 3.6406753526866410281929477743592e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.51 y1[1] (analytic) = 2.4881772468829074945001302376746 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.008751708278704494226842302459 relative error = 0.35173170599756495940790535457244 % h = 0.001 y2[1] (analytic) = 1.1272554923542487368941915264245 y2[1] (numeric) = 1.1272555508048829277502147143518 absolute error = 5.84506341908560231879273e-08 relative error = 5.1852161810081880143523450835657e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.511 y1[1] (analytic) = 2.4890497471564927343593430733201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0096242085522897340860551381045 relative error = 0.38666196058493788759169880261458 % h = 0.001 y2[1] (analytic) = 1.1277441058919862324987091598053 y2[1] (numeric) = 1.1277441861255252838707268178606 absolute error = 8.02335390513720176580553e-08 relative error = 7.1145163723034057542905369104197e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.512 y1[1] (analytic) = 2.4899217583803715718700594525215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0104962197761685715967715173059 relative error = 0.42154817679877964143210727811901 % h = 0.001 y2[1] (analytic) = 1.1282335916855451481282415596589 y2[1] (numeric) = 1.128233698544829039796738839482 absolute error = 1.068592838916684972798231e-07 relative error = 9.4713793915694463133654912686692e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.513 y1[1] (analytic) = 2.4907932796825328558210414322121 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0113677410783298555477534969965 relative error = 0.45639038659116444518317374841848 % h = 0.001 y2[1] (analytic) = 1.1287239492454397310143545333464 y2[1] (numeric) = 1.1287240880627941955282507792159 absolute error = 1.388173544645138962458695e-07 relative error = 1.2298609820170318844252544307363e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.514 y1[1] (analytic) = 2.4916643101914553566777778206244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0122387715872523564044898854088 relative error = 0.4911886218859052275985589770279 % h = 0.001 y2[1] (analytic) = 1.1292151780813124621255938238659 y2[1] (numeric) = 1.1292153546794207510652626370623 absolute error = 1.765981082889396688131964e-07 relative error = 1.5639012981476520881994078412979e-05 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=1.76 NO POLE NO POLE x[1] = 0.515 y1[1] (analytic) = 2.4925348490361086381036410850348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0131093104319056378303531498192 relative error = 0.5259429145785125593121146588246 % h = 0.001 y2[1] (analytic) = 1.1297072777019345465249632781811 y2[1] (numeric) = 1.1297074983947087064077744130213 absolute error = 2.206927741598828111348402e-07 relative error = 1.9535394567769711539505606393565e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.516 y1[1] (analytic) = 2.4934048953459539279902511025232 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0139793567417509277169631673076 relative error = 0.5606532965361538529902305589296 % h = 0.001 y2[1] (analytic) = 1.1302002476152064045986788484863 y2[1] (numeric) = 1.1302005192086580615557861070928 absolute error = 2.715934516569571072586065e-07 relative error = 2.4030560268415828918710796357015e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.517 y1[1] (analytic) = 2.4942744482509449889961747234587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0148489096467419887228867882431 relative error = 0.59531979959761282521443323237872 % h = 0.001 y2[1] (analytic) = 1.1306940873281581641557071976931 y2[1] (numeric) = 1.1306944171212688165092977192768 absolute error = 3.297931106523535905215837e-07 relative error = 2.9167315399310004861969629273039e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.518 y1[1] (analytic) = 2.4951435068815289885930906090811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0157179682773259883198026738655 relative error = 0.62994245557324921905591312628167 % h = 0.001 y2[1] (analytic) = 1.1311887963469501533975968096429 y2[1] (numeric) = 1.1311891921325409712683092495733 absolute error = 3.957855908178707124399304e-07 relative error = 3.4988464533596581084697492600984e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.519 y1[1] (analytic) = 2.4960120703686473686185492970897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0165865317644443683452613618741 relative error = 0.6645212962449587863068485349416 % h = 0.001 y2[1] (analytic) = 1.1316843741768733947581086342535 y2[1] (numeric) = 1.1316848442424745258328206979823 absolute error = 4.700656011310747120637288e-07 relative error = 4.1536811133667481754709383019917e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.52 y1[1] (analytic) = 2.4968801378437367143344589425478 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0174545992395337140611710073322 relative error = 0.69905635336613352833657899470403 % h = 0.001 y2[1] (analytic) = 1.1321808203223500996121524280115 y2[1] (numeric) = 1.1321813734510694802028320645038 absolute error = 5.531287193805906796364923e-07 relative error = 4.8855157184442148718503232557391e-05 % h = 0.001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=2.40 NO POLE NO POLE x[1] = 0.521 y1[1] (analytic) = 2.4977477084387296229904276756926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.018322169834526622717139740477 relative error = 0.73354765866162219454385727487693 % h = 0.001 y2[1] (analytic) = 1.1326781342869341638535340809147 y2[1] (numeric) = 1.1326787797583258343783433491378 absolute error = 6.454713916705248092682231e-07 relative error = 5.6986302827932196821047929292361e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.522 y1[1] (analytic) = 2.4986147812860555718910940133795 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0191892426818525716178060781639 relative error = 0.76799524382769103737957814754559 % h = 0.001 y2[1] (analytic) = 1.1331763155733116643410183521593 y2[1] (numeric) = 1.1331770631642435883593545518843 absolute error = 7.475909319240183361997250e-07 relative error = 6.5973045999093898125275778765294e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.523 y1[1] (analytic) = 2.4994813555186417859665772569024 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0200558169144387856932893216868 relative error = 0.80239914053198482291754360789496 % h = 0.001 y2[1] (analytic) = 1.133675363683301356212210568549 y2[1] (numeric) = 1.1336762236688227421458656727433 absolute error = 8.599855213859336551041943e-07 relative error = 7.5858182062971555311992945657062e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.524 y1[1] (analytic) = 2.5003474302699141048451803058119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0209218916657111045718923705963 relative error = 0.83675938041348809595397817241225 % h = 0.001 y2[1] (analytic) = 1.134175278117855171064759971788 y2[1] (numeric) = 1.1341762612720632957378767117149 absolute error = 9.831542081246731167399269e-07 relative error = 8.6684503453134776131894945496111e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.525 y1[1] (analytic) = 2.5012130046737978494274778151016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.021787466069594849154189879886 relative error = 0.87107599508248669861965431007077 % h = 0.001 y2[1] (analytic) = 1.1346760583770587160043865334936 y2[1] (numeric) = 1.134677175973965249135387668799 absolute error = 1.1175969065331310011353054e-06 relative error = 9.8494799311412612490374380889642e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.526 y1[1] (analytic) = 2.5020780778647186879609231217462 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0226525392605156876876351865306 relative error = 0.90534901612052954149162696626603 % h = 0.001 y2[1] (analytic) = 1.135177703960131773559232189945 y2[1] (numeric) = 1.1351789677745286023383985439956 absolute error = 1.2638143968287791663540506e-06 relative error = 0.00011133185512892747957438379873943 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=3.05 NO POLE NO POLE x[1] = 0.527 y1[1] (analytic) = 2.5029426489776035016141078660558 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0235171103734005013408199308402 relative error = 0.9395784750803906261947075261474 % h = 0.001 y2[1] (analytic) = 1.1356802143654288024600365822581 y2[1] (numeric) = 1.1356816366737533553469093373047 absolute error = 1.4223083245528868727550466e-06 relative error = 0.00012523845238843172238030356970514 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.528 y1[1] (analytic) = 2.5038067171478812495498087336605 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0243811785436782492765207984449 relative error = 0.97376440348603131848593143841097 % h = 0.001 y2[1] (analytic) = 1.1361835890904394392856365218521 y2[1] (numeric) = 1.1361851826716395081609200487263 absolute error = 1.5935812000688752835268742e-06 relative error = 0.00014025736820794964907408233263827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.529 y1[1] (analytic) = 2.504670281511483833495956245149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0252447429072808332226683099334 relative error = 1.0079068328325628708183900876048 % h = 0.001 y2[1] (analytic) = 1.1366878276317890009732875357502 y2[1] (numeric) = 1.1366896057681870607804306782604 absolute error = 1.7781363980598071431425102e-06 relative error = 0.00015643137498572780281136971278195 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.53 y1[1] (analytic) = 2.5055333412048469618136610224661 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0261078026006439615403730872505 relative error = 1.042005794586209193383906368475 % h = 0.001 y2[1] (analytic) = 1.1371929294852389881933049814358 y2[1] (numeric) = 1.137194905963396013205441225907 absolute error = 1.9764781570250121362444712e-06 relative error = 0.00017380324004649619596743658685926 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.531 y1[1] (analytic) = 2.5063958953649110130614334641129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0269703567607080127881455288973 relative error = 1.0760613201842698726371347848636 % h = 0.001 y2[1] (analytic) = 1.1376988941456875895875213566629 y2[1] (numeric) = 1.1377010832572663654359516916661 absolute error = 2.1891115787758484303350032e-06 relative error = 0.00019241572528904318317585087022255 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.532 y1[1] (analytic) = 2.5072579431291218990547332650042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0278324045249188987814453297886 relative error = 1.1100734410350834363067607743614 % h = 0.001 y2[1] (analytic) = 1.138205721107170186871055565808 y2[1] (numeric) = 1.1382081376497981174719620755377 absolute error = 2.4165426279306009065097297e-06 relative error = 0.00021231158683510660215260353160642 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=3.69 NO POLE NO POLE x[1] = 0.533 y1[1] (analytic) = 2.5081194836354319274199857215036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.028693945031228927146697786288 relative error = 1.1440421885179908639025603534242 % h = 0.001 y2[1] (analytic) = 1.1387134098628598607968890410339 y2[1] (numeric) = 1.1387160691409912693134723775218 absolute error = 2.6592781314085165833364879e-06 relative error = 0.00023353357467958376399010442509823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.534 y1[1] (analytic) = 2.508980516022300663642202267693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0295549774180976633689143324774 relative error = 1.1779675939832993417301600923899 % h = 0.001 y2[1] (analytic) = 1.1392219599050678979827427537335 y2[1] (numeric) = 1.1392248777308458209604825976185 absolute error = 2.9178257779229777398438850e-06 relative error = 0.00025612443234206282744461606904872 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.535 y1[1] (analytic) = 2.5098410394286957926053431953273 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0304155008244927923320552601117 relative error = 1.211849688752246261428408871237 % h = 0.001 y2[1] (analytic) = 1.1397313707252442985997482894172 y2[1] (numeric) = 1.1397345634193617724129927358277 absolute error = 3.1926941174738132444464105e-06 relative error = 0.00028012689651967804471267898528485 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.536 y1[1] (analytic) = 2.5107010529940939796245610171836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.031275514389890979351273081968 relative error = 1.2456885041169634610473368412739 % h = 0.001 y2[1] (analytic) = 1.1402416418139782849224052974161 y2[1] (numeric) = 1.1402451262065391236710027921494 absolute error = 3.4843925608387485974947333e-06 relative error = 0.0003055836967412913192983000427848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.537 y1[1] (analytic) = 2.511560555858481730969463441633 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0321350172542787306961755064174 relative error = 1.2794840713404417076877335311725 % h = 0.001 y2[1] (analytic) = 1.1407527726609988107393167654858 y2[1] (numeric) = 1.1407565660923778747345127665836 absolute error = 3.7934313790639951960010978e-06 relative error = 0.00033253755502300246981450686778904 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.538 y1[1] (analytic) = 2.5124195471623562538775354352446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.032994008558153253604247500029 relative error = 1.3132364216564954207264260941613 % h = 0.001 y2[1] (analytic) = 1.1412647627551750716241927086173 y2[1] (numeric) = 1.1412688830768780256035226591303 absolute error = 4.1203217029539793299505130e-06 relative error = 0.00036103118552499054694168272046485 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=4.35 NO POLE NO POLE x[1] = 0.539 y1[1] (analytic) = 2.5132780260467263160568603600697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0338524874425233157835724248541 relative error = 1.346945586269727634654380302806 % h = 0.001 y2[1] (analytic) = 1.1417776115845170160666120010952 y2[1] (numeric) = 1.1417820771600395762780324697895 absolute error = 4.4655755225602114204686943e-06 relative error = 0.00039110729420968850428223696153489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.54 y1[1] (analytic) = 2.5141359916531131046772806829582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0347104530489101044039927477426 relative error = 1.3806115963554952005577810653469 % h = 0.001 y2[1] (analytic) = 1.1422913186361758574620312210822 y2[1] (numeric) = 1.1422961483418625267580421985612 absolute error = 4.8297056866692960109774790e-06 relative error = 0.00042280857850129347750797225487524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.541 y1[1] (analytic) = 2.514993443123551084849139265818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0355679045193480845758513306024 relative error = 1.414234483059874225275275969045 % h = 0.001 y2[1] (analytic) = 1.1428058833964445869605285177651 y2[1] (numeric) = 1.1428110966223468770435518454454 absolute error = 5.2132259022900830233276803e-06 relative error = 0.00045617772694661487999429955148186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.542 y1[1] (analytic) = 2.5158503796005888575887427581458 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0364248409963858573154548229302 relative error = 1.4478142774996257472675846581109 % h = 0.001 y2[1] (analytic) = 1.1433213053507584871737696523608 y2[1] (numeric) = 1.1433269220014926271345614104421 absolute error = 5.6166507341399607917580813e-06 relative error = 0.000491257418877262477075530989026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.543 y1[1] (analytic) = 2.51670680022729001726968912644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0372812616230870169964011912244 relative error = 1.4813510107621616482386887333922 % h = 0.001 y2[1] (analytic) = 1.1438375839836956467396825060591 y2[1] (numeric) = 1.1438436244792997770310708935513 absolute error = 6.0404956041302913883874922e-06 relative error = 0.00052809032407317655513913751423251 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.544 y1[1] (analytic) = 2.5175627041472340085592018692383 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0381371655430310082859139340227 relative error = 1.5148447139055107995508213241878 % h = 0.001 y2[1] (analytic) = 1.1443547187789774757443254902696 y2[1] (numeric) = 1.1443612040557683267330802947731 absolute error = 6.4852767908509887548045035e-06 relative error = 0.00056671910242750225600536633458494 % h = 0.001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.3MB, time=5.00 NO POLE NO POLE x[1] = 0.545 y1[1] (analytic) = 2.5184180905045169828386139815162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0389925519003139825653260463006 relative error = 1.548295417958285442478472536587 % h = 0.001 y2[1] (analytic) = 1.1448727092194692220004344373497 y2[1] (numeric) = 1.1448796607308982762405896141074 absolute error = 6.9515114290542401551767577e-06 relative error = 0.00060718640361281010141323105235897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.546 y1[1] (analytic) = 2.5192729584437526541071452480364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0398474198395496538338573128208 relative error = 1.5817031539196478013496166344112 % h = 0.001 y2[1] (analytic) = 1.1453915547871804881821316933069 y2[1] (numeric) = 1.1453989945046896255535988515542 absolute error = 7.4397175091373714671582473e-06 relative error = 0.00064953486674866468695585911682994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.547 y1[1] (analytic) = 2.5201273071100731543681169619403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0407017685058701540948290267247 relative error = 1.6150679527592769286253490645899 % h = 0.001 y2[1] (analytic) = 1.1459112549632657498152802778119 y2[1] (numeric) = 1.1459192053771423746721080071135 absolute error = 7.9504138766248568277293016e-06 relative error = 0.00069380712007054347947873274033127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.548 y1[1] (analytic) = 2.5209811356491298884967486824406 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.041555597044926888223460747225 relative error = 1.6483898454173357809720963064167 % h = 0.001 y2[1] (analytic) = 1.1464318092280248741229651212096 y2[1] (numeric) = 1.1464402933482565235961170807853 absolute error = 8.4841202316494731519595757e-06 relative error = 0.00074004578060010760677470575091711 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.549 y1[1] (analytic) = 2.5218344432070943885886821638876 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.042408904602891388315394228672 relative error = 1.6816688628044385253835290098796 % h = 0.001 y2[1] (analytic) = 1.1469532170609036397255825330915 y2[1] (numeric) = 1.1469622584180320723256260725696 absolute error = 9.0413571284326000435394781e-06 relative error = 0.00078829345381682648338101542348319 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.55 y1[1] (analytic) = 2.5226872289306591677883781077573 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0432616903264561675150901725417 relative error = 1.7149050358016180744122689999509 % h = 0.001 y2[1] (analytic) = 1.1474754779404942571950182023822 y2[1] (numeric) = 1.1474851005864690208606349824664 absolute error = 9.6226459747636656167800842e-06 relative error = 0.00083859273333095807140701885879948 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.3MB, time=5.64 NO POLE NO POLE x[1] = 0.551 y1[1] (analytic) = 2.5235394919670385735965319092362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0441139533628355733232439740206 relative error = 1.7480983952602938495744334681979 % h = 0.001 y2[1] (analytic) = 1.1479985913445358904623931748063 y2[1] (numeric) = 1.1480088198535673692011438104757 absolute error = 1.02285090314787387506356694e-05 relative error = 0.00089098620055788653059823404406666 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.552 y1[1] (analytic) = 2.5243912314639696406556550910571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0449656928597666403823671558415 relative error = 1.7812489720022397719930050577058 % h = 0.001 y2[1] (analytic) = 1.1485225567499151790788564000321 y2[1] (numeric) = 1.1485334162193271173471525565975 absolute error = 1.08594694119382682961565654e-05 relative error = 0.00094551642439381896727360903590691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.553 y1[1] (analytic) = 2.525242446569712943012969639076 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0458169079655099427396817038604 relative error = 1.8143567968195524793489545796575 % h = 0.001 y2[1] (analytic) = 1.1490473736326667613289015877443 y2[1] (numeric) = 1.1490588896837482652986612208319 absolute error = 1.15160510815039697596330876e-05 relative error = 0.0010022259608928429473599148419061 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.554 y1[1] (analytic) = 2.5260931364330534458597629767672 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0466675978288504455864750415516 relative error = 1.8474219004746197682119737872459 % h = 0.001 y2[1] (analytic) = 1.1495730414679737981956852593716 y2[1] (numeric) = 1.1495852402468308130556698031788 absolute error = 1.21987788570148599845438072e-05 relative error = 0.0010611573529453463944908809230672 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.555 y1[1] (analytic) = 2.5269433002033013567463518393519 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0475177615990983564730639041363 relative error = 1.8804443137000892608255989824759 % h = 0.001 y2[1] (analytic) = 1.150099559730168498177822030195 y2[1] (numeric) = 1.1501124679085747606181783036382 absolute error = 1.29081784062624403562734432e-05 relative error = 0.0011223531299578014500402730088144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=38.1MB, alloc=4.4MB, time=6.28 x[1] = 0.556 y1[1] (analytic) = 2.5277929370302929762718038326678 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0483673984260899759985158974522 relative error = 1.9134240671988372954244222515677 % h = 0.001 y2[1] (analytic) = 1.1506269278927326429571323050854 y2[1] (numeric) = 1.1506405726689801079861867222101 absolute error = 1.36447762474650290544171247e-05 relative error = 0.0011858558075339138280186425457682 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.557 y1[1] (analytic) = 2.5286420460643915482475659871291 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0492165074601885479742780519135 relative error = 1.946361191643938039163995822631 % h = 0.001 y2[1] (analytic) = 1.1511551454282981139168167201663 y2[1] (numeric) = 1.1511695545280468551596950588945 absolute error = 1.44090997487412428783387282e-05 relative error = 0.0012517078871571391539840326788971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.558 y1[1] (analytic) = 2.5294906264564881093341501432183 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0500650878522851090608622080027 relative error = 1.9792557176786328227469364228357 % h = 0.001 y2[1] (analytic) = 1.1516842118086474195095308122717 y2[1] (numeric) = 1.1516994134857750021387033136914 absolute error = 1.52016771275826291725014197e-05 relative error = 0.0013199518558745677334985680751704 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.559 y1[1] (analytic) = 2.530338677358002338150025531897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0509131387537993378767375966814 relative error = 2.0121076759162996958316305894297 % h = 0.001 y2[1] (analytic) = 1.1522141265047142234748325481675 y2[1] (numeric) = 1.1522301495421645489232114866008 absolute error = 1.60230374503254483789384333e-05 relative error = 0.0013906301859821791522066323048869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.56 y1[1] (analytic) = 2.531186197920883403851869441112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0517606593166804035785815058964 relative error = 2.0449170969404232023128286671607 % h = 0.001 y2[1] (analytic) = 1.1527448889865838739054744961337 y2[1] (numeric) = 1.1527617626972154955132195776227 absolute error = 1.68737106316216077450814890e-05 relative error = 0.0014637853347114680663172779207511 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.561 y1[1] (analytic) = 2.5320331872976108141853273882178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0526076486934078139120394530022 relative error = 2.0776840113045643745662947124054 % h = 0.001 y2[1] (analytic) = 1.153276498723493933162011573659 y2[1] (numeric) = 1.1532942529509278419087275867571 absolute error = 1.77542274339087467160130981e-05 relative error = 0.0015394597439174424991446380911993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=41.9MB, alloc=4.4MB, time=6.92 x[1] = 0.562 y1[1] (analytic) = 2.5328796446411952630054347476258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0534541060369922627321468124102 relative error = 2.1104084495323309457525517291988 % h = 0.001 y2[1] (analytic) = 1.1538089551838347086351944566842 y2[1] (numeric) = 1.153827620303301588109735514004 absolute error = 1.86651194668794745410573198e-05 relative error = 0.0016176958397679959163964161059422 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.563 y1[1] (analytic) = 2.5337255691051794772658523133289 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0543000305009764769925643781133 relative error = 2.143090442117347779277626592704 % h = 0.001 y2[1] (analytic) = 1.1543422578351497843556178880455 y2[1] (numeric) = 1.1543618647543367341162433593635 absolute error = 1.96069191869497606254713180e-05 relative error = 0.0016985360324346543101030073978997 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.564 y1[1] (analytic) = 2.5345709598436390634760688071373 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0551454212394360632027808719217 relative error = 2.1757300195232275145115566796189 % h = 0.001 y2[1] (analytic) = 1.1548764061441365534500922755128 y2[1] (numeric) = 1.1548969863040332799282511228355 absolute error = 2.05801598967264781588473227e-05 relative error = 0.001782022715784699478449430144365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.565 y1[1] (analytic) = 2.5354158160111833536257238754924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0559902774069803533524359402768 relative error = 2.2083272121835414278682706306582 % h = 0.001 y2[1] (analytic) = 1.1554113995766467514442061230971 y2[1] (numeric) = 1.15543298495239122554575880442 absolute error = 2.15853757444741015526813229e-05 relative error = 0.0018681982670746696463099622359387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.566 y1[1] (analytic) = 2.5362601367629562505752056506075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0568345981587532503019177153919 relative error = 2.2408820505017905083532988261491 % h = 0.001 y2[1] (analytic) = 1.1559472375976869904105459931083 y2[1] (numeric) = 1.155969860699410570968766404117 absolute error = 2.26231017235805582204110087e-05 relative error = 0.0019571050466452385289921472607685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.567 y1[1] (analytic) = 2.5371039212546370729116774854067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0576783826504340726383895501911 relative error = 2.2733945648513767466886050699314 % h = 0.001 y2[1] (analytic) = 1.1564839196714192939620398507875 y2[1] (numeric) = 1.1565076135450913161972739219265 absolute error = 2.36938736720222352340711390e-05 relative error = 0.0020487853976174738995735681229847 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=7.56 NO POLE NO POLE x[1] = 0.568 y1[1] (analytic) = 2.5379471686424413992696890063077 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0585216300382383989964010710921 relative error = 2.3058647855755746371266596580326 % h = 0.001 y2[1] (analytic) = 1.157021445261161633089888798216 y2[1] (numeric) = 1.1570462434894334612312813578485 absolute error = 2.47982282718281413925596325e-05 relative error = 0.0021432816455904766782624068822649 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.569 y1[1] (analytic) = 2.5387898780831219121155271633056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.05936433947891891184223922809 relative error = 2.3382927429875028910686954649239 % h = 0.001 y2[1] (analytic) = 1.1575598138293884628455513596132 y2[1] (numeric) = 1.157585750532437006070788711883 absolute error = 2.59367030485432252373522698e-05 relative error = 0.0022406360983404015204322126127198 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.57 y1[1] (analytic) = 2.5396320487339692409944634930788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0602065101297662407211755578632 relative error = 2.3706784673700963616049029207394 % h = 0.001 y2[1] (analytic) = 1.158099024837731259866243636084 y2[1] (numeric) = 1.15812613467410195071579598403 absolute error = 2.71098363706908495523479460e-05 relative error = 0.0023408910455208598383733690167487 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.571 y1[1] (analytic) = 2.540473679752812805240054347939 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0610481411486098049667664127234 relative error = 2.4030219889760781780971267856779 % h = 0.001 y2[1] (analytic) = 1.158639077746979060743417804361 y2[1] (numeric) = 1.1586673959144282951663031742895 absolute error = 2.83181674492344228853699285e-05 relative error = 0.0024440887583647061503693599436695 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.572 y1[1] (analytic) = 2.5413147702980216561446513813949 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0618892316938186558713634461793 relative error = 2.4353233380279320899274274619847 % h = 0.001 y2[1] (analytic) = 1.1591799720170790012336805911064 y2[1] (numeric) = 1.1592095342534160394223102826616 absolute error = 2.95622363370381886296915552e-05 relative error = 0.0025502714893872086094459290275335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.573 y1[1] (analytic) = 2.5421553195285053185902801198912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0627297809243023183169921846756 relative error = 2.467582544717875018538662228083 % h = 0.001 y2[1] (analytic) = 1.1597217071071368563116125119018 y2[1] (numeric) = 1.1597525496910651834838173091462 absolute error = 3.08425839283271722047972444e-05 relative error = 0.00265948147209060452305645911514 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=8.20 NO POLE NO POLE x[1] = 0.574 y1[1] (analytic) = 2.5429953266037146321390449899122 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0635697879995116318657570546966 relative error = 2.4997996392078298168960272420956 % h = 0.001 y2[1] (analytic) = 1.1602642824754175810639478221502 y2[1] (numeric) = 1.1602964422273757273508242537433 absolute error = 3.21597519581462868764315931e-05 relative error = 0.0027717609206700416340581853253748 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.575 y1[1] (analytic) = 2.5438347906836425915822197101162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0644092520794395913089317749006 relative error = 2.5319746516293982355012794525378 % h = 0.001 y2[1] (analytic) = 1.1608076975793458524245742857562 y2[1] (numeric) = 1.1608412118623476710233311164529 absolute error = 3.35142830018185987568306967e-05 relative error = 0.0028871520297209058926020126247925 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.576 y1[1] (analytic) = 2.5446737109288251869471824994803 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0652481723246221866738945642647 relative error = 2.5641076120838340940941286808358 % h = 0.001 y2[1] (analytic) = 1.1613519518755066117498110266296 y2[1] (numeric) = 1.161386858595981014501337897275 absolute error = 3.49067204744027515268706454e-05 relative error = 0.0030056969739475364080045334283472 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.577 y1[1] (analytic) = 2.5455120865003422429613560945909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0660865478961392426880681593753 relative error = 2.5961985506420166581780541127425 % h = 0.001 y2[1] (analytic) = 1.1618970448196456082334218877795 y2[1] (numeric) = 1.1619333824282757577848445962096 absolute error = 3.63376086301495514227084301e-05 relative error = 0.0031274379078733282292951151067279 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.578 y1[1] (analytic) = 2.546349916559818257972313112208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0669243779556152576990251769924 relative error = 2.628247497344424219510556262531 % h = 0.001 y2[1] (analytic) = 1.162442975866669943160820883031 y2[1] (numeric) = 1.1624807833592319008738512132567 absolute error = 3.78074925619577130303302257e-05 relative error = 0.0032524169655522235629344204543051 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.579 y1[1] (analytic) = 2.5471872002694232423232078370701 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0677616616652202420499199018545 relative error = 2.6602544822011078797006051644972 % h = 0.001 y2[1] (analytic) = 1.1629897444706486150019254872046 y2[1] (numeric) = 1.1630290613888494437683577484163 absolute error = 3.93169182008287664322612117e-05 relative error = 0.0033806762602815919961841907164048 % h = 0.001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.4MB, time=8.86 NO POLE NO POLE x[1] = 0.58 y1[1] (analytic) = 2.5480239367918735561826960595765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0685983981876705559094081243609 relative error = 2.6922195351916655360587881093964 % h = 0.001 y2[1] (analytic) = 1.16353735008481306534211267195 y2[1] (numeric) = 1.1635782165171283864683642016884 absolute error = 4.08664323153211262515297384e-05 relative error = 0.0035122578843165002547723011160222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.581 y1[1] (analytic) = 2.548860125290432746828505133497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0694345866862297465552171982814 relative error = 2.724142686265216068848395688654 % h = 0.001 y2[1] (analytic) = 1.1640857921615577256507317563242 y2[1] (numeric) = 1.164128248744068728973870573073 absolute error = 4.24565825110033231388167488e-05 relative error = 0.0036472039085853719838427190501311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.582 y1[1] (analytic) = 2.5496957649289123853838169702094 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0702702263247093851105290349938 relative error = 2.7560239653403737290884132455654 % h = 0.001 y2[1] (analytic) = 1.1646350701524405648866273036464 y2[1] (numeric) = 1.1646791580696704712848768625702 absolute error = 4.40879172299063982495589238e-05 relative error = 0.0037855563824070380017077677227385 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.583 y1[1] (analytic) = 2.5505308548716729030056272331506 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.071105316267469902732339297935 relative error = 2.7878634023052227260621060694901 % h = 0.001 y2[1] (analytic) = 1.165185183508183637940124459152 y2[1] (numeric) = 1.1652309444939336134013830701799 absolute error = 4.57609857499754612586110279e-05 relative error = 0.0039273573332091774366307208951993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.584 y1[1] (analytic) = 2.5513653942836244265242445441924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0719398556794214262509566089768 relative error = 2.8196610270172920136876008158076 % h = 0.001 y2[1] (analytic) = 1.1657361316786736349109282865074 y2[1] (numeric) = 1.1657836080168581553233891959021 absolute error = 4.74763381845204124609093947e-05 relative error = 0.004072648766248150117760911986022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.585 y1[1] (analytic) = 2.5521993823302276135330940625129 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0727738437260246132598061272973 relative error = 2.8514168693035302749095727003818 % h = 0.001 y2[1] (analytic) = 1.1662879141129624312213878253303 y2[1] (numeric) = 1.1663371486384440970508952397368 absolute error = 4.92345254816658295074144065e-05 relative error = 0.004221472664330220552421903342115 % h = 0.001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.4MB, time=9.51 NO POLE NO POLE x[1] = 0.586 y1[1] (analytic) = 2.553032818177494486927990346228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0736072795732914866547024110124 relative error = 2.8831309589602811032738480119188 % h = 0.001 y2[1] (analytic) = 1.1668405302592676385645747564984 y2[1] (numeric) = 1.166891566358691438583901201684 absolute error = 5.10360994238000193264451856e-05 relative error = 0.0043738709875341737832164852305922 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.587 y1[1] (analytic) = 2.5538657009919892688950449575815 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0744401623877862686217570223659 relative error = 2.9148033257532583808494244187152 % h = 0.001 y2[1] (analytic) = 1.1673939795649731566866257272142 y2[1] (numeric) = 1.1674468611776001799224070817437 absolute error = 5.28816126270232357813545295e-05 relative error = 0.0045298856729353233798610018973063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.588 y1[1] (analytic) = 2.5546980299408292143463748238537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0752724913366262140730868886381 relative error = 2.9464339994175218516650974269552 % h = 0.001 y2[1] (analytic) = 1.1679482614766297260027965535271 y2[1] (numeric) = 1.1680030330951703210664128799159 absolute error = 5.47716185405950636163263888e-05 relative error = 0.0046895586343309117822963628712784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.589 y1[1] (analytic) = 2.5555298041916854438027779183523 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0761042655874824435294899831367 relative error = 2.9780230096574528898305601861543 % h = 0.001 y2[1] (analytic) = 1.1685033754399554810466756843086 y2[1] (numeric) = 1.1685600821114018620159185962006 absolute error = 5.67066714463809692429118920e-05 relative error = 0.0048529317619669031734447056238532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.59 y1[1] (analytic) = 2.5563610229127837757225433788758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0769354843085807754492554436602 relative error = 3.0095703861467304615145156424937 % h = 0.001 y2[1] (analytic) = 1.1690593208998365047520034775093 y2[1] (numeric) = 1.1691180082262948027709242305978 absolute error = 5.86873264582980189207530885e-05 relative error = 0.0050200469222661690219896342103288 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.591 y1[1] (analytic) = 2.5571916852729055582755637349123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0777661466687025580022757996967 relative error = 3.0410761585283072799550048232859 % h = 0.001 y2[1] (analytic) = 1.1696160973003273835665430069271 y2[1] (numeric) = 1.1696768114398491433314297831075 absolute error = 6.07141395217597648867761804e-05 relative error = 0.0051909459575580663977548530239072 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.4MB, time=10.15 NO POLE NO POLE x[1] = 0.592 y1[1] (analytic) = 2.5580217904413885005619174695279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0785962518371855002886295343123 relative error = 3.0725403564143861526798128044012 % h = 0.001 y2[1] (analytic) = 1.1701737040846517633974472856612 y2[1] (numeric) = 1.1702364917520648836974352537298 absolute error = 6.27876674131202999879680686e-05 relative error = 0.0053656706858094091246414216515192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.593 y1[1] (analytic) = 2.5588513375881275032740906974331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0794257989839245030008027622175 relative error = 3.103963009386396520117464677924 % h = 0.001 y2[1] (analytic) = 1.1707321406952029063875669609314 y2[1] (numeric) = 1.1707970491629420238689406424646 absolute error = 6.49084677391174813736815332e-05 relative error = 0.0055442629003568317986583355384123 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.594 y1[1] (analytic) = 2.559680325883575488802007297074 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0802547872793724885287193618584 relative error = 3.1353441469949711847819676087763 % h = 0.001 y2[1] (analytic) = 1.1712914065735442485221417040005 y2[1] (numeric) = 1.1713584836724805638459459493119 absolute error = 6.70770989363153238042453114e-05 relative error = 0.0057267643696405466613452359509896 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.595 y1[1] (analytic) = 2.5605087544987442307800373917875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0810832158945412305067494565719 relative error = 3.1666837987599232302170918568458 % h = 0.001 y2[1] (analytic) = 1.1718515011604099580653176885558 y2[1] (numeric) = 1.1719207952806805036284511742717 absolute error = 6.92941202705455631334857159e-05 relative error = 0.0059132168369394932818403045834394 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.596 y1[1] (analytic) = 2.5613366226052051830751546330814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0819110840010021828018666978658 relative error = 3.1979819941702231288886134550952 % h = 0.001 y2[1] (analytic) = 1.172412423895705494825932721079 y2[1] (numeric) = 1.172483983987541843216456317344 absolute error = 7.15600918363483905235962650e-05 relative error = 0.0061036620201078809639913248062203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.597 y1[1] (analytic) = 2.5621639293750903082154132979511 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0827383907708873079421253627355 relative error = 3.2292387626839760382155640842174 % h = 0.001 y2[1] (analytic) = 1.1729741742185081702520097574644 y2[1] (numeric) = 1.1730480497930645826099613785288 absolute error = 7.38755745564123579516210644e-05 relative error = 0.0062981416113131237582439997785144 % h = 0.001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=10.80 NO POLE NO POLE x[1] = 0.598 y1[1] (analytic) = 2.5629906739810929052579167718239 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0835651353768899049846288366083 relative error = 3.2604541337283992839341495806934 % h = 0.001 y2[1] (analytic) = 1.1735367515670677083533987114403 y2[1] (numeric) = 1.1736129926972487218089663578261 absolute error = 7.62411301810134555676463858e-05 relative error = 0.0064966972767751679215694013055842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.599 y1[1] (analytic) = 2.5638168555964684370954495492333 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0843913169922654368221616140177 relative error = 3.2916281366998000299906074678557 % h = 0.001 y2[1] (analytic) = 1.1741001553788068074520056321979 y2[1] (numeric) = 1.1741788127000942608134712552359 absolute error = 7.86573212874533614656230380e-05 relative error = 0.0066993706565072116324123642757972 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.6 y1[1] (analytic) = 2.5646424733950353572009454456587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0852169347908323569276575104431 relative error = 3.3227608009635531341618759185234 % h = 0.001 y2[1] (analytic) = 1.1746643850903217027590475010446 y2[1] (numeric) = 1.1747455098016011996234760707582 absolute error = 8.11247112794968644285697136e-05 relative error = 0.0069062033640578167315552069974506 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.601 y1[1] (analytic) = 2.5654675265511759358089652761314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0860419879469729355356773409158 relative error = 3.3538521558540791886055416535691 % h = 0.001 y2[1] (analytic) = 1.1752294401373827297787700698751 y2[1] (numeric) = 1.1753130840017695382389808043931 absolute error = 8.36438643868084602107345180e-05 relative error = 0.0071172369862544122238968026662837 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.602 y1[1] (analytic) = 2.5662920142398370855333578191989 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0868664756356340852600698839833 relative error = 3.3849022306748227445431224633943 % h = 0.001 y2[1] (analytic) = 1.1757953199549348885380653377883 y2[1] (numeric) = 1.1758815353005992766599854561405 absolute error = 8.62153456643881219201183522e-05 relative error = 0.0073325130829481892404461939255756 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.603 y1[1] (analytic) = 2.5671159356365311864202784486542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0876903970323281861469905134386 relative error = 3.4159110546982307202833213189365 % h = 0.001 y2[1] (analytic) = 1.1763620239770984086414244362806 y2[1] (numeric) = 1.1764508636980904148864900260004 absolute error = 8.88397209920062450655897198e-05 relative error = 0.007552073186760387124323059481148 % h = 0.001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=11.45 NO POLE NO POLE x[1] = 0.604 y1[1] (analytic) = 2.5679392899173369104357403800814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0885137513131339101624524448658 relative error = 3.4468786571657309917944634260815 % h = 0.001 y2[1] (analytic) = 1.1769295516371693151506608681084 y2[1] (numeric) = 1.1770210691942429529184945139728 absolute error = 9.15175570736377678336458644e-05 relative error = 0.0077759588028299702692448254436475 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.605 y1[1] (analytic) = 2.5687620762589000453868740447335 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0893365376546970451135861095179 relative error = 3.4778050672877111650378950822063 % h = 0.001 y2[1] (analytic) = 1.177497902367619995288838220145 y2[1] (numeric) = 1.1775921517890568907559989200577 absolute error = 9.42494214368954671606999127e-05 relative error = 0.0080042114085626953038624675938438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.606 y1[1] (analytic) = 2.569584293838434318276070669554 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0901587552342313180027827343384 relative error = 3.5086903142434975292766838268634 % h = 0.001 y2[1] (analytic) = 1.1780670756000997659678356463513 y2[1] (numeric) = 1.1781641114825322283990032442551 absolute error = 9.70358824324624311675979038e-05 relative error = 0.0082368724533815681803844650227476 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.607 y1[1] (analytic) = 2.5704059418337222180871867092646 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.090980403229519217813898774049 relative error = 3.5395344271813341905765131501844 % h = 0.001 y2[1] (analytic) = 1.1786370707654354421389835933405 y2[1] (numeric) = 1.178736948274668965847507486565 absolute error = 9.98775092335237085238932245e-05 relative error = 0.0084739833584786906912013184314066 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.608 y1[1] (analytic) = 2.5712270194231158180029863443854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0918014808189128177296984091698 relative error = 3.5703374352183623847182119436167 % h = 0.001 y2[1] (analytic) = 1.1792078872936319059662014179512 y2[1] (numeric) = 1.1793106621654671031015116469874 absolute error = 0.0001027748718351971353102290362 relative error = 0.0087155855165684959026919025523143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.609 y1[1] (analytic) = 2.5720475257855375970529998278124 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0926219871813345967797118925968 relative error = 3.6010993674405999687438989579265 % h = 0.001 y2[1] (analytic) = 1.1797795246138726768210677237362 y2[1] (numeric) = 1.1798852531549266401610157255223 absolute error = 0.0001057285410539633399480017861 relative error = 0.008961720291642371961058035805221 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=12.09 NO POLE NO POLE x[1] = 0.61 y1[1] (analytic) = 2.5728674601004812611909760321627 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0934419214962782609176880969471 relative error = 3.6318202529029210903612557840579 % h = 0.001 y2[1] (analytic) = 1.1803519821545204820992534213452 y2[1] (numeric) = 1.1804607212430475770260197221697 absolute error = 0.0001087390885270949267663008245 relative error = 0.0092124290187246736908953601833168 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.611 y1[1] (analytic) = 2.5736868215480125638011081205036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.094261282943809563527820185288 relative error = 3.6625001206290360344329683037879 % h = 0.001 y2[1] (analytic) = 1.1809252593431178288577466964165 y2[1] (numeric) = 1.1810370664298299136965236369297 absolute error = 0.0001118070867120848387769405132 relative error = 0.0094677530036301213732672594969679 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.612 y1[1] (analytic) = 2.5745056093087701256322118343075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0950800707045671253589238990919 relative error = 3.6931389996114712457808961797835 % h = 0.001 y2[1] (analytic) = 1.1814993556063875762722982477992 y2[1] (numeric) = 1.1816142887152736501725274698022 absolute error = 0.000114933108886073900229222003 relative error = 0.0097277335227225860563044197578688 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.613 y1[1] (analytic) = 2.5753238225639662541590364645238 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0958982839597632538857485293082 relative error = 3.7237369188115495275370427794905 % h = 0.001 y2[1] (analytic) = 1.1820742703702335089145143387088 y2[1] (numeric) = 1.1821923880993787864540312207872 absolute error = 0.0001181177291452775395168820784 relative error = 0.009992411822675260717806054800188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.614 y1[1] (analytic) = 2.576141460495387762369889144524 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0967159218911847620966012093084 relative error = 3.7542939071593704142759039646728 % h = 0.001 y2[1] (analytic) = 1.1826500030597409108480243837716 y2[1] (numeric) = 1.1827713645821453225410348898847 absolute error = 0.0001213615224044116930105061131 relative error = 0.010261829120232216565970074212208 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.615 y1[1] (analytic) = 2.5769585222853967869797536773647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0975329836811937867064657421491 relative error = 3.7848099935537907191652734394429 % h = 0.001 y2[1] (analytic) = 1.1832265530991771405431489758368 y2[1] (numeric) = 1.1833512181635732584335384770947 absolute error = 0.0001246650643961178903895012579 relative error = 0.010536026601971343731228838893822 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=12.76 NO POLE NO POLE x[1] = 0.616 y1[1] (analytic) = 2.5777750071169316060680856843173 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0983494685127286057947977491017 relative error = 3.8152852068624052543750748447606 % h = 0.001 y2[1] (analytic) = 1.1838039199119922066094934379379 y2[1] (numeric) = 1.1839319488436625941315419824172 absolute error = 0.0001280289316703875220485444793 relative error = 0.010815045424068675569214897813802 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.617 y1[1] (analytic) = 2.5785909141735074561404664369381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0991653755693044558671785017225 relative error = 3.8457195759215277239862765276675 % h = 0.001 y2[1] (analytic) = 1.1843821029208193443458911678558 y2[1] (numeric) = 1.1845135566224133296350454058522 absolute error = 0.0001314537015939852891542379964 relative error = 0.011098926712064095762127483898759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.618 y1[1] (analytic) = 2.579406242639217348613298311092 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.0999807040350143483400103758764 relative error = 3.8761131295361717886444239095876 % h = 0.001 y2[1] (analytic) = 1.1849611015474755931071202253905 y2[1] (numeric) = 1.1850960414998254649440487473997 absolute error = 0.0001349399523498718369285220092 relative error = 0.011387711560628427373215809015941 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.619 y1[1] (analytic) = 2.5802209916987328857207253783037 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1007954530945298854474374430881 relative error = 3.9064658964800323012047966410118 % h = 0.001 y2[1] (analytic) = 1.1855409152129623744868157956707 y2[1] (numeric) = 1.1856794034758990000585520070597 absolute error = 0.000138488262936625571736211389 relative error = 0.011681441033331902976739570140364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.62 y1[1] (analytic) = 2.5810351605373050758429632275822 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1016096219331020755696752923666 relative error = 3.9367779054954667126186632703545 % h = 0.001 y2[1] (analytic) = 1.1861215433374660713160003456393 y2[1] (numeric) = 1.1862636425506339349785551848323 absolute error = 0.000142099213167863662554839193 relative error = 0.011980156162414014953610778748105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=80.1MB, alloc=4.4MB, time=13.41 x[1] = 0.621 y1[1] (analytic) = 2.581848748340765148255222689459 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1024232097365621479819347542434 relative error = 3.9670491852934766473125649841116 % h = 0.001 y2[1] (analytic) = 1.1867029853403586074766524752305 y2[1] (numeric) = 1.1868487587240302697040582807174 absolute error = 0.0001457733836716622274058054869 relative error = 0.012283897948554745010964262175653 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.622 y1[1] (analytic) = 2.5826617542955253672964127133811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1032362156913223670231247781655 relative error = 3.9972797645536896473150121040467 % h = 0.001 y2[1] (analytic) = 1.1872852406401980285297346497202 y2[1] (numeric) = 1.187434751996088004235061294715 absolute error = 0.0001495113558899757053266449948 relative error = 0.012592707360647171952147153593636 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.623 y1[1] (analytic) = 2.583474177588579845956808229827 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1040486389843768456835202946114 relative error = 4.0274696719243410843874224667694 % h = 0.001 y2[1] (analytic) = 1.1878683086547290831570991852689 y2[1] (numeric) = 1.1880216223668071385715642268251 absolute error = 0.0001533137120780554144650415562 relative error = 0.012906625335571456692060571561476 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.624 y1[1] (analytic) = 2.584286017407505358883869409543 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1048604788033023586105814743274 relative error = 4.0576189360222562394185695718972 % h = 0.001 y2[1] (analytic) = 1.1884521888008838054166910457999 y2[1] (numeric) = 1.1886093698361876727135670770477 absolute error = 0.0001571810353038672968760312478 relative error = 0.013225692777970203481429662935744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.625 y1[1] (analytic) = 2.5850972729404621548053993141501 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1056717343362591545321113789345 relative error = 4.0877275854328325483442404789218 % h = 0.001 y2[1] (analytic) = 1.1890368804947820978104651960589 y2[1] (numeric) = 1.1891979944042296066610698453828 absolute error = 0.0001611139094475088506046493239 relative error = 0.013549950560025196272421405522994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.626 y1[1] (analytic) = 2.5859079433761947683692275150305 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1064824047719917680959395798149 relative error = 4.1177956487100220138562288703778 % h = 0.001 y2[1] (analytic) = 1.189622383151732315164435442986 y2[1] (numeric) = 1.1897874960709329404140725318304 absolute error = 0.0001651129192006252496370888444 relative error = 0.013879439521235509127073189235608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=83.9MB, alloc=4.4MB, time=14.05 x[1] = 0.627 y1[1] (analytic) = 2.5867180279040328313986078408783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1072924892998298311253199056627 relative error = 4.1478231543763137821672074915037 % h = 0.001 y2[1] (analytic) = 1.1902086961862318493202708853993 y2[1] (numeric) = 1.1903778748362976739725751363905 absolute error = 0.0001691786500658246523042509912 relative error = 0.01421420046819698953923935495484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.628 y1[1] (analytic) = 2.5875275257138918835625189985835 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1081019871096888832892310633679 relative error = 4.1778101309227168841004363351864 % h = 0.001 y2[1] (analytic) = 1.1907958190119677146378552804441 y2[1] (numeric) = 1.1909691307003238073365776590631 absolute error = 0.000173311688356092698722378619 relative error = 0.014554274174383113510207695846738 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.629 y1[1] (analytic) = 2.5883364359962741824600573972178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1089108973920711821867694620022 relative error = 4.2077566068087431397756684770144 % h = 0.001 y2[1] (analytic) = 1.1913837510418171343082238242947 y2[1] (numeric) = 1.1915612636630113405060800998482 absolute error = 0.0001775126211942061978562755535 relative error = 0.01489970137992721118778353332548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.63 y1[1] (analytic) = 2.5891447579422695131181120907946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.109719219338066512844824155579 relative error = 4.2376626104623902261650143896036 % h = 0.001 y2[1] (analytic) = 1.1919724916878481274762910342229 y2[1] (numeric) = 1.1921542737243602734810824587459 absolute error = 0.000181782036512146004791424523 relative error = 0.015250522791406061848485472881869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.631 y1[1] (analytic) = 2.5899524907435559969015123421982 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1105269521393529966282244069826 relative error = 4.2675281702801249067949178897863 % h = 0.001 y2[1] (analytic) = 1.1925620403613200971727826093538 y2[1] (numeric) = 1.1927481608843706062615847357561 absolute error = 0.0001861205230505090888021264023 relative error = 0.015606779081624856972544418718659 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.632 y1[1] (analytic) = 2.5907596335924008998348388981996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.111334094988197899561550962984 relative error = 4.2973533146268664228727826073781 % h = 0.001 y2[1] (analytic) = 1.1931523964726844190547833382246 y2[1] (numeric) = 1.1933429251430423388475869308788 absolute error = 0.0001905286703579197928035926542 relative error = 0.015968510889403530131645963010895 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=14.71 NO POLE NO POLE x[1] = 0.633 y1[1] (analytic) = 2.5915661856816614403350906538176 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.112140647077458440061802718602 relative error = 4.3271380718359700451191670220827 % h = 0.001 y2[1] (analytic) = 1.1937435594315850309543123126502 y2[1] (numeric) = 1.193938566500375471239089044114 absolute error = 0.0001950070687904402847767314638 relative error = 0.016335758819364452379805936897142 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.634 y1[1] (analytic) = 2.592372146204785596354398973423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1129466076005825960811110382074 relative error = 4.3568824702092107855888387062452 % h = 0.001 y2[1] (analytic) = 1.1943355286468590232343358993664 y2[1] (numeric) = 1.1945350849563700034360910754617 absolute error = 0.0001995563095109802017551760953 relative error = 0.016708563441721491808419779051793 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.635 y1[1] (analytic) = 2.5931775143558129119319825259412 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1137519757516099116586945907256 relative error = 4.3865865380167672687663444477524 % h = 0.001 y2[1] (analytic) = 1.1949283035265372299516281134903 y2[1] (numeric) = 1.1951324805110259354385930249219 absolute error = 0.0002041769844887054869649114316 relative error = 0.017086965292070435897378492024559 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.636 y1[1] (analytic) = 2.5939822893293753031545360822647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1145567507251723028812481470491 relative error = 4.416250303497205761224112420087 % h = 0.001 y2[1] (analytic) = 1.1955218834778448208258872309833 y2[1] (numeric) = 1.1957307531643432672465948924946 absolute error = 0.0002088696864984464207076615113 relative error = 0.017471004871180775265197358625334 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.637 y1[1] (analytic) = 2.5947864703206978635242473145531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1153609317164948632509593793375 relative error = 4.4458737948574643591334555272216 % h = 0.001 y2[1] (analytic) = 1.1961162679072018940145166710524 y2[1] (numeric) = 1.1963299029163219988600966781798 absolute error = 0.0002136350091201048455800071274 relative error = 0.017860722644788847392358307355236 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.638 y1[1] (analytic) = 2.5955900565255996687336362294726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.116164517921396668460348294257 relative error = 4.4754570402728373329211914910751 % h = 0.001 y2[1] (analytic) = 1.1967114562202240696924773737563 y2[1] (numeric) = 1.1969299297669621302790983819775 absolute error = 0.0002184735467380605866210082212 relative error = 0.018256159043392338863522867974285 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=15.35 NO POLE NO POLE x[1] = 0.639 y1[1] (analytic) = 2.5963930471404945808464124606007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1169675085362915805731245253851 relative error = 4.505000067886959628366935179818 % h = 0.001 y2[1] (analytic) = 1.1973074478217230844366180930148 y2[1] (numeric) = 1.1975308337162636615036000038877 absolute error = 0.0002233858945405770669819108729 relative error = 0.018657354462046144645930052279476 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.64 y1[1] (analytic) = 2.5971954413623920518835462392079 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1177699027581890516102583039923 relative error = 4.5345029058117915234384521083715 % h = 0.001 y2[1] (analytic) = 1.1979042421157073864138892207397 y2[1] (numeric) = 1.1981326147642265925336015439105 absolute error = 0.0002283726485192061197123231708 relative error = 0.019064349260159582893152230060628 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.641 y1[1] (analytic) = 2.5979972383888979268137494574101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1185716997846949265404615221945 relative error = 4.5639655821276034401647889889422 % h = 0.001 y2[1] (analytic) = 1.198501838505382731372844953923 y2[1] (numeric) = 1.1987352729108509233691030020458 absolute error = 0.0002334344054681919962580481228 relative error = 0.01947718376129496373544213265429 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.642 y1[1] (analytic) = 2.5987984374182152459475638332798 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1193728988140122456742758980642 relative error = 4.5933881248829609108492176815203 % h = 0.001 y2[1] (analytic) = 1.1991002363931527794378378132311 y2[1] (numeric) = 1.1993388081561366540101043782936 absolute error = 0.0002385717629838745722665650625 relative error = 0.019895898252967510490165484314634 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.643 y1[1] (analytic) = 2.599599037649145046734253783893 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1201734990449420464609658486774 relative error = 4.6227705620947096979263429028712 % h = 0.001 y2[1] (analytic) = 1.1996994351806196927053087189588 y2[1] (numeric) = 1.1999432205000837844566056726539 absolute error = 0.0002437853194640917512969536951 relative error = 0.020320532986446631698276401729729 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.644 y1[1] (analytic) = 2.6003990382810871649607022094871 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1209734996768841646874142742715 relative error = 4.6521129217479610667700316098188 % h = 0.001 y2[1] (analytic) = 1.2002994342685847336415750281037 y2[1] (numeric) = 1.2005485099426923147086068851267 absolute error = 0.000249075674107581067031857023 relative error = 0.02075112817655854236545657131156 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=16.00 NO POLE NO POLE x[1] = 0.645 y1[1] (analytic) = 2.6011984385140410353515079898995 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1217728999098380350782200546839 relative error = 4.681415231796077210761123089686 % h = 0.001 y2[1] (analytic) = 1.2009002330570488642815181348221 y2[1] (numeric) = 1.201154676483962244766108015712 absolute error = 0.0002544434269133804845898808899 relative error = 0.021187724001490232759404259655894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.646 y1[1] (analytic) = 2.6019972375486064915694845932574 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1225716989444034912961966580418 relative error = 4.7106775201606568279261734796457 % h = 0.001 y2[1] (analytic) = 1.2015018309452133462275714356296 y2[1] (numeric) = 1.2017617201238935746291090644098 absolute error = 0.0002598891786802284015376287802 relative error = 0.021630360602594783087825371518489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.647 y1[1] (analytic) = 2.6027954345859845656157597964862 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1233698959817815653424718612706 relative error = 4.7398998147315208484607767087401 % h = 0.001 y2[1] (analytic) = 1.2021042273314803414484086604078 y2[1] (numeric) = 1.2023696408624863042976100312201 absolute error = 0.0002654135310059628492013708123 relative error = 0.022079078084198022354945969457507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.648 y1[1] (analytic) = 2.6035930288279782866286771176028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1241674902237752863553891823872 relative error = 4.769082143366698312453285723345 % h = 0.001 y2[1] (analytic) = 1.2027074216134535138767317705792 y2[1] (numeric) = 1.2029784386997404337716109161429 absolute error = 0.0002710170862869198948791455637 relative error = 0.022533916513406529667833826914789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.649 y1[1] (analytic) = 2.6043900194769934790807001609604 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1249644808727904788074122257448 relative error = 4.7982245338924123971270333305875 % h = 0.001 y2[1] (analytic) = 1.203311413187938631805556826712 y2[1] (numeric) = 1.2035881136356559630511117191783 absolute error = 0.0002767004477173312455548924663 relative error = 0.022994915919916976237485610039095 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.65 y1[1] (analytic) = 2.6051864057360395603725216786059 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1257608671318365600992337433903 relative error = 4.8273270141030665929214210861246 % h = 0.001 y2[1] (analytic) = 1.2039162014509441710823954293201 y2[1] (numeric) = 1.2041986656702328921361124403262 absolute error = 0.0002824642192887210537170110061 relative error = 0.023462116295826806293506070645065 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=16.64 NO POLE NO POLE x[1] = 0.651 y1[1] (analytic) = 2.6059821868087303378235797537072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1265566482045273375502918184916 relative error = 4.8563896117612310277345073747963 % h = 0.001 y2[1] (analytic) = 1.2045217857976819191007285387257 y2[1] (numeric) = 1.2048100948034712210266130795866 absolute error = 0.0002883090057893019258845408609 relative error = 0.023935557595446255105276072625026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.652 y1[1] (analytic) = 2.6067773618992848050581841156014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1273518232950818047848961803858 relative error = 4.8854123545976289386519821965807 % h = 0.001 y2[1] (analytic) = 1.2051281656225675795881686825627 y2[1] (numeric) = 1.2054224010353709497226136369595 absolute error = 0.0002942354128033701344449543968 relative error = 0.024415279735111702276777244669888 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.653 y1[1] (analytic) = 2.6075719302125279377864562004034 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1281463916083249375131682651878 relative error = 4.9143952703111232904896661877052 % h = 0.001 y2[1] (analytic) = 1.2057353403192213781907057628076 y2[1] (numeric) = 1.2060355843659320782241141124449 absolute error = 0.0003002440467107000334083496373 relative error = 0.024901322593000358456712424493536 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.654 y1[1] (analytic) = 2.6083658909538914889792871763013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1289403523496884887059992410857 relative error = 4.9433383865687035404789150896414 % h = 0.001 y2[1] (analytic) = 1.2063433092804686688524308781435 y2[1] (numeric) = 1.2066496447951546065311145060428 absolute error = 0.0003063355146859376786836278993 relative error = 0.025393726008946283580232692723096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.655 y1[1] (analytic) = 2.609159243329414783436518758647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1297337047252117831632308234314 relative error = 4.9722417310054725484265482387333 % h = 0.001 y2[1] (analytic) = 1.2069520718983405409901317819836 y2[1] (numeric) = 1.2072645823230385346436148177532 absolute error = 0.0003125104246979936534830357696 relative error = 0.025892529784257734733453540248345 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.656 y1[1] (analytic) = 2.6099519865457455117475522467268 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1305264479415425114742643115112 relative error = 5.0011053312246336316831506982117 % h = 0.001 y2[1] (analytic) = 1.207561627564074427462152801609 y2[1] (numeric) = 1.2078803969495838625616150475761 absolute error = 0.0003187693855094350994622459671 relative error = 0.026397773681535841707014412487613 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.4MB, time=17.29 NO POLE NO POLE x[1] = 0.657 y1[1] (analytic) = 2.6107441198101405236435918216702 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1313185812059375233703038864546 relative error = 5.029929214797477764255823404278 % h = 0.001 y2[1] (analytic) = 1.2081719756681147133309112496125 y2[1] (numeric) = 1.2084970886747905902851151955115 absolute error = 0.000325113006675876954203945899 relative error = 0.026909497424494608280207360462601 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.658 y1[1] (analytic) = 2.6115356423304666207407287533185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1321101037262636204674408181029 relative error = 5.0587134092633709194036741604268 % h = 0.001 y2[1] (analytic) = 1.2087831156001133454184615651814 y2[1] (numeric) = 1.2091146574986587178141152615594 absolute error = 0.000331541898545372395653696378 relative error = 0.027427740697782237252671625892898 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.659 y1[1] (analytic) = 2.6123265533152013486730737730358 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1329010147109983483997858378202 relative error = 5.0874579421297415550565545014021 % h = 0.001 y2[1] (analytic) = 1.2093950467489304426544976297072 y2[1] (numeric) = 1.2097331034211882451486152457199 absolute error = 0.0003380566722578024941176160127 relative error = 0.027952543146803777216321509785843 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.66 y1[1] (analytic) = 2.6131168519734337886151454793963 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1336913133692307883418575441807 relative error = 5.116162840872068241399753371776 % h = 0.001 y2[1] (analytic) = 1.2100077685026349072161829087698 y2[1] (numeric) = 1.2103524264423791722886151479929 absolute error = 0.0003446579397442650724322392231 relative error = 0.028483944377545089036044627810427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.661 y1[1] (analytic) = 2.6139065375148653481927232544241 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1344809989106623479194353192085 relative error = 5.1448281329338674299695582360836 % h = 0.001 y2[1] (analytic) = 1.2106212802485050364591972807178 y2[1] (numeric) = 1.2109726265622314992341149683784 absolute error = 0.0003513463137264627749176876606 relative error = 0.029021983956398129983776437685149 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.662 y1[1] (analytic) = 2.6146956091498105517813737796007 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1352700705456075515080858443851 relative error = 5.1734538457266813636067876698688 % h = 0.001 y2[1] (analytic) = 1.2112355813730291356393886208484 y2[1] (numeric) = 1.2115937037807452259851147068764 absolute error = 0.000358122407716090345726086028 relative error = 0.029566701409987553446824522354744 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=17.94 NO POLE NO POLE x[1] = 0.663 y1[1] (analytic) = 2.6154840660891978301918608531767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1360585274849948299185729179611 relative error = 5.2020400066300661266175866853581 % h = 0.001 y2[1] (analytic) = 1.2118506712619061314244164195866 y2[1] (numeric) = 1.2122156580979203525416143634869 absolute error = 0.0003649868360142211171979439003 relative error = 0.030118136224998622107782307686806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.664 y1[1] (analytic) = 2.6162719075445703097416488234469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1368463689403673094683608882313 relative error = 5.230586642991579834492957034435 % h = 0.001 y2[1] (analytic) = 1.2124665493000461861947739230711 y2[1] (numeric) = 1.2128384895137568789036139382099 absolute error = 0.0003719402137106927088400151388 relative error = 0.030676327848006432470036455738564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.665 y1[1] (analytic) = 2.6170591327280866007117105665481 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1376335941238836004384226313325 relative error = 5.2590937821267709625406695162698 % h = 0.001 y2[1] (analytic) = 1.2130832148715713131335744951767 y2[1] (numeric) = 1.2134621980282548050711134310454 absolute error = 0.0003789831566834919375389358687 relative error = 0.031241315685306448579734866978938 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.666 y1[1] (analytic) = 2.6178457408525215851878515520396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.138420202248318584914563616824 relative error = 5.2875614513191668127853739102098 % h = 0.001 y2[1] (analytic) = 1.213700667359815992104487111237 y2[1] (numeric) = 1.2140867836414141310441128419934 absolute error = 0.0003861162815981389396257307564 relative error = 0.03181313910274634277214280165411 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.667 y1[1] (analytic) = 2.6186317311312672042857621550066 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.139206192527064204012474219791 relative error = 5.3159896778202621184948845676121 % h = 0.001 y2[1] (analytic) = 1.2143189061473277863172051055833 y2[1] (numeric) = 1.2147122463532348568226121710539 absolute error = 0.0003933402059070705054070654706 relative error = 0.032391837425559141247572837145074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.668 y1[1] (analytic) = 2.6194171027783332447590109897005 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1399915641741302444857230544849 relative error = 5.3443784888495077856927759417571 % h = 0.001 y2[1] (analytic) = 1.2149379306158679597798315074841 y2[1] (numeric) = 1.215338586163716982406611418227 absolute error = 0.0004006555478490226267799107429 relative error = 0.032977449938197672259529952479701 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=18.60 NO POLE NO POLE x[1] = 0.669 y1[1] (analytic) = 2.6202018550083481249891926567879 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1407763164041451247159047215723 relative error = 5.3727279115942997710195724244993 % h = 0.001 y2[1] (analytic) = 1.2155577401464120955375635131482 y2[1] (numeric) = 1.2159658030728605077961105835126 absolute error = 0.0004080629264484122585470703644 relative error = 0.033570015884170314675365703036398 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.67 y1[1] (analytic) = 2.6209859870365596803574439141266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.141560448432356680084155978911 relative error = 5.4010379732099680953069608041498 % h = 0.001 y2[1] (analytic) = 1.2161783341191507146970578551619 y2[1] (numeric) = 1.2165938970806654329911096669107 absolute error = 0.0004155629615147182940518117488 relative error = 0.034169574465878044647584937929289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.671 y1[1] (analytic) = 2.6217694980788359479965428996171 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1423439594746329477232549644015 relative error = 5.4293087008197659922315914731123 % h = 0.001 y2[1] (analytic) = 1.2167997119134898962358580450436 y2[1] (numeric) = 1.2172228681871317579916086684213 absolute error = 0.0004231562736418617557506233777 relative error = 0.034776164844452778111994534375129 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.672 y1[1] (analytic) = 2.6225523873516659509228066540965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1431268487474629506495187188809 relative error = 5.4575401215148591914171662082766 % h = 0.001 y2[1] (analytic) = 1.2174218729080518975962636795423 y2[1] (numeric) = 1.2178527163922594827976075880444 absolute error = 0.0004308434842075852013439085021 relative error = 0.035389826139597006807125881348474 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.673 y1[1] (analytic) = 2.6233346540721604815470028124424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1439091154679574812737148772268 relative error = 5.4857322623543153353556359339891 % h = 0.001 y2[1] (analytic) = 1.2180448164806757760630212168607 y2[1] (numeric) = 1.21848344169604860740910642578 absolute error = 0.0004386252153728313460852089193 relative error = 0.03601059742942472548780103761197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.674 y1[1] (analytic) = 2.6241162974580528845634919520396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.144690758853849884290204016824 relative error = 5.5138851503650935295204513687649 % h = 0.001 y2[1] (analytic) = 1.2186685420084180109242148451658 y2[1] (numeric) = 1.2191150440984991318261051816281 absolute error = 0.0004465020900811209018903364623 relative error = 0.03663851775030364798434630522245 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=19.25 NO POLE NO POLE x[1] = 0.675 y1[1] (analytic) = 2.6248973167276998392168177095343 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1454717781234968389435297743187 relative error = 5.5419988125420340250469228649757 % h = 0.001 y2[1] (analytic) = 1.219293048867553126414735282546 y2[1] (numeric) = 1.2197475235996110560486038555887 absolute error = 0.0004544747320579296338685730427 relative error = 0.037273626096698709737786081846084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.676 y1[1] (analytic) = 2.6256777111000821409449623993491 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1462521724958791406716744641335 relative error = 5.5700732758478480333568530873214 % h = 0.001 y2[1] (analytic) = 1.2199183364335743154417035649992 y2[1] (numeric) = 1.2203808801993843800766024476618 absolute error = 0.0004625437658100646348988826626 relative error = 0.03791596142101685442037395663114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.677 y1[1] (analytic) = 2.6264574797948054823984864907691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1470319411906024821251985555535 relative error = 5.5981085672131076721067074535381 % h = 0.001 y2[1] (analytic) = 1.2205444040811940640912260970796 y2[1] (numeric) = 1.2210151138978191039101009578474 absolute error = 0.0004707098166250398188748607678 relative error = 0.038565562633453102230036762591889 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.678 y1[1] (analytic) = 2.6272366220321012338347709245244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1478110834278982335614829893088 relative error = 5.6261047135362360418406824912812 % h = 0.001 y2[1] (analytic) = 1.2211712511843447769158564585004 y2[1] (numeric) = 1.2216502246949152275490993861456 absolute error = 0.0004789735105704506332429276452 relative error = 0.039222468601837897426720351888826 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.679 y1[1] (analytic) = 2.6280151370328272228865818746926 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.148589598428624222613293939477 relative error = 5.6540617416834974327321214608247 % h = 0.001 y2[1] (analytic) = 1.221798877116179403002138679282 y2[1] (numeric) = 1.2222862125906727509935977325563 absolute error = 0.0004873354744933479914590532743 relative error = 0.039886718151485732658232870964581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.68 y1[1] (analytic) = 2.6287930240184685137041781874202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1493674854142655134308902522046 relative error = 5.6819796784889876607988097660643 % h = 0.001 y2[1] (analytic) = 1.2224272812490720628176059159557 y2[1] (numeric) = 1.2229230775850916742435959970795 absolute error = 0.0004957963360196114259900811238 relative error = 0.040558350065045047602981924366963 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=19.90 NO POLE NO POLE x[1] = 0.681 y1[1] (analytic) = 2.6295702822111381854701823544214 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1501447436069351851968944192058 relative error = 5.7098585507546245329797598387687 % h = 0.001 y2[1] (analytic) = 1.2230564629546186758366076818755 y2[1] (numeric) = 1.2235608196781719972990941797152 absolute error = 0.0005043567235533214624864978397 relative error = 0.041237403082349399436995866338932 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.682 y1[1] (analytic) = 2.6303469108335781102864365064475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1509213722293751100131485712319 relative error = 5.7376983852501384404631663449404 % h = 0.001 y2[1] (analytic) = 1.223686421603637588944338005864 y2[1] (numeric) = 1.2241994388699137201600922804634 absolute error = 0.0005130172662761312157542745994 relative error = 0.041923915900269902612806177603682 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.683 y1[1] (analytic) = 2.6311229091091597304320655399362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1516973705049567301587776047206 relative error = 5.7654992087130630796572777399649 % h = 0.001 y2[1] (analytic) = 1.2243171565661702056184361152149 y2[1] (numeric) = 1.2248389351603168428265902993241 absolute error = 0.0005217785941466372081541841092 relative error = 0.04261792717256893541814709411665 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.684 y1[1] (analytic) = 2.631898276261884834991970118843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1524727376576818347186821836274 relative error = 5.7932610478487263001979894029834 % h = 0.001 y2[1] (analytic) = 1.2249486672114816158875304615069 y2[1] (numeric) = 1.2254793085493813652985882362973 absolute error = 0.0005306413378997494110577747904 relative error = 0.043319475509755110762999969752959 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.685 y1[1] (analytic) = 2.6326730115163863358549729232243 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1532474729121833355816849880087 relative error = 5.8209839293302410793890168227644 % h = 0.001 y2[1] (analytic) = 1.2255809529080612270660961307334 y2[1] (numeric) = 1.226120559037107287576086091383 absolute error = 0.0005396061290460605099899606496 relative error = 0.044028599478939508624272886082434 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=122.0MB, alloc=4.4MB, time=20.55 x[1] = 0.686 y1[1] (analytic) = 2.6334471140979290430808421464934 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1540215754937260428075542112778 relative error = 5.8486678797984966224725545998463 % h = 0.001 y2[1] (analytic) = 1.2262140130236233952649949029474 y2[1] (numeric) = 1.2267626866234946096590838645812 absolute error = 0.0005486735998712143940889616338 relative error = 0.044745337603693167558360369046222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.687 y1[1] (analytic) = 2.6342205832324104396354168743884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1547950446282074393621289391728 relative error = 5.8763129258621495881303683844685 % h = 0.001 y2[1] (analytic) = 1.2268478469251080576770664509304 y2[1] (numeric) = 1.2274056913085433315475815558919 absolute error = 0.0005578443834352738705151049615 relative error = 0.045469728363905832672973331973246 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.688 y1[1] (analytic) = 2.6349934181463614554930596105924 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1555678795421584552197716753768 relative error = 5.9039190940976154386173022996708 % h = 0.001 y2[1] (analytic) = 1.2274824539786813656371383923497 y2[1] (numeric) = 1.2280495730922534532415791653152 absolute error = 0.0005671191135720876044407729655 relative error = 0.046201810195645957430965122564592 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.689 y1[1] (analytic) = 2.6357656180669472411056618466169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1563400794627442408323739114013 relative error = 5.9314864110490599139312139156503 % h = 0.001 y2[1] (analytic) = 1.2281178335497363184558221354451 y2[1] (numeric) = 1.228694331974624974741076692851 absolute error = 0.0005764984248886562852545574059 relative error = 0.046941621491021956640405391735774 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.69 y1[1] (analytic) = 2.6365371822219679402374292070087 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1571116436177649399641412717931 relative error = 5.9590149032283906294253724576355 % h = 0.001 y2[1] (analytic) = 1.2287539850028933980264606845022 y2[1] (numeric) = 1.2293399679556578960460741384993 absolute error = 0.0005859829527644980196134539971 relative error = 0.047689200598044707966868998155779 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.691 y1[1] (analytic) = 2.6373081098398594621646733351585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1578825712356564618913853999429 relative error = 5.9865045971152487962713736570507 % h = 0.001 y2[1] (analytic) = 1.2293909077020012042045937982186 y2[1] (numeric) = 1.2299864810353522171565715022601 absolute error = 0.0005955733333510129519777040415 relative error = 0.048444585820491299285811882423248 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=125.8MB, alloc=4.4MB, time=21.21 x[1] = 0.692 y1[1] (analytic) = 2.6380784001496942532398383199832 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1586528615454912529665503847676 relative error = 6.0139555191570010641826365071518 % h = 0.001 y2[1] (analytic) = 1.2300286010101370909593051215486 y2[1] (numeric) = 1.2306338712137079380725687841334 absolute error = 0.0006052702035708471132636625848 relative error = 0.049207815417770019174999351779981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.693 y1[1] (analytic) = 2.638848052381182067818990099522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1594225137769790675457021643064 relative error = 6.0413676957687314858105531718217 % h = 0.001 y2[1] (analytic) = 1.2306670642896078032958151397345 y2[1] (numeric) = 1.2312821384907250587940659841192 absolute error = 0.0006150742011172554982508443847 relative error = 0.049978927604786587829234064097549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.694 y1[1] (analytic) = 2.639617065764670738551997914018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1601915271604677382787099788024 relative error = 6.0687411533332336022273634317269 % h = 0.001 y2[1] (analytic) = 1.2313062969019501149486830319832 y2[1] (numeric) = 1.2319312828664035793210631022175 absolute error = 0.0006249859644534643723800702343 relative error = 0.050757960551811625662100739265583 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.695 y1[1] (analytic) = 2.6403854395311469460346375183712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1609599009269439457613495831556 relative error = 6.0960759182010026489118193485249 % h = 0.001 y2[1] (analytic) = 1.2319462982079314668449797316401 y2[1] (numeric) = 1.2325813043407434996535601384283 absolute error = 0.0006350061328120328085804067882 relative error = 0.051544952384349356842101798793291 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.696 y1[1] (analytic) = 2.641153172912236987821846501921 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1617276343080339875485585667054 relative error = 6.123372016690227881655694296687 % h = 0.001 y2[1] (analytic) = 1.2325870675675506063367937297397 y2[1] (numeric) = 1.2332322029137448197915570927516 absolute error = 0.0006451353461942134547633630119 relative error = 0.052339941183007544993402277943129 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.697 y1[1] (analytic) = 2.6419202651402075468013627023692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1624947265360045465280747671536 relative error = 6.1506294750867850218111731668764 % h = 0.001 y2[1] (analytic) = 1.2332286043400382272024303894814 y2[1] (numeric) = 1.2338839785854075397350539651875 absolute error = 0.0006553742453693125326235757061 relative error = 0.053142964983368658274432999174266 % h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.4MB, time=21.87 NO POLE NO POLE x[1] = 0.698 y1[1] (analytic) = 2.6426867154479664589269773402679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1632611768437634586536894050523 relative error = 6.1778483196442288203011373962789 % h = 0.001 y2[1] (analytic) = 1.2338709078838576104156647704838 y2[1] (numeric) = 1.2345366313557316594840507557359 absolute error = 0.0006657234718740490683859852521 relative error = 0.053954061775862261030817666228816 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.699 y1[1] (analytic) = 2.643452523069063480310635140883 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1640269844648604800373472056674 relative error = 6.2050285765837857398163295425691 % h = 0.001 y2[1] (analytic) = 1.234513977556705265682407193618 y2[1] (numeric) = 1.2351901612247171790385474643968 absolute error = 0.0006761836680119133561402707788 relative error = 0.054773269505638629202491753308812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.7 y1[1] (analytic) = 2.6442176872376910536726143513987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1647921486334880533993264161831 relative error = 6.2321702720943467546253474014694 % h = 0.001 y2[1] (analytic) = 1.2351578127155115737441400098081 y2[1] (numeric) = 1.2358445681923640983985440911702 absolute error = 0.0006867554768525246544040813621 relative error = 0.055600626072443586648468336078911 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.701 y1[1] (analytic) = 2.6449822071886850741490202033442 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1655566685844820738757322681286 relative error = 6.2592734323324602674253771851652 % h = 0.001 y2[1] (analytic) = 1.2358024127164414294474832694162 y2[1] (numeric) = 1.2364998522586724175640406360561 absolute error = 0.0006974395422309881165573666399 relative error = 0.056436169330494559536477848299931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.702 y1[1] (analytic) = 2.6457460821575256544558260128154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1663205435533226541825380775998 relative error = 6.2863380834223251426635290430358 % h = 0.001 y2[1] (analytic) = 1.2364477769148948855792462226979 y2[1] (numeric) = 1.2371560134236421365350370990545 absolute error = 0.0007082365087472509557908763566 relative error = 0.057279937088357845928664650835558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.703 y1[1] (analytic) = 2.6465093113803378894086967545133 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1670837727761348891354088192977 relative error = 6.313364251455783855760586228899 % h = 0.001 y2[1] (analytic) = 1.2370939046655077974663208163335 y2[1] (numeric) = 1.2378130516872732553115334801654 absolute error = 0.0007191470217654578452126638319 relative error = 0.058131967108827097678662763665764 % h = 0.001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.4MB, time=22.53 NO POLE NO POLE x[1] = 0.704 y1[1] (analytic) = 2.6472718940938926197978305898392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1678463554896896195245426546236 relative error = 6.340351962492315757670921513011 % h = 0.001 y2[1] (analytic) = 1.2377407953221524683397725861917 y2[1] (numeric) = 1.2384709670495657738935297793888 absolute error = 0.0007301717274133055537571931971 relative error = 0.058992297108803011739695627951066 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.705 y1[1] (analytic) = 2.6480338295356071956170544742679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1686082909314041953437665390523 relative error = 6.3673012425590304542142710145098 % h = 0.001 y2[1] (analytic) = 1.2383884482379382954624835822915 y2[1] (numeric) = 1.2391297595105196922810259967247 absolute error = 0.0007413112725813968185424144332 relative error = 0.059860964759174227967849816771014 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.706 y1[1] (analytic) = 2.6487951169435462386464106149696 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.169369578339343238373122679754 relative error = 6.3942121176506612996169865033523 % h = 0.001 y2[1] (analytic) = 1.2390368627652124170197011983717 y2[1] (numeric) = 1.2397894290701350104740221321731 absolute error = 0.0007525663049225934543209338014 relative error = 0.06073800768469943048935968095404 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.707 y1[1] (analytic) = 2.6495557555564224043874711961547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1701302169522194041141832609391 relative error = 6.421084613729559003702312401921 % h = 0.001 y2[1] (analytic) = 1.2396860382555603597718460155734 y2[1] (numeric) = 1.2404499757284117284725181857341 absolute error = 0.0007639374728513687006721701607 relative error = 0.061623463463890649685608472876231 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.708 y1[1] (analytic) = 2.6503157446135971433506194368912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1708902060093941430773315016756 relative error = 6.4479187567256853521711532183191 % h = 0.001 y2[1] (analytic) = 1.2403359740598066874689310074817 y2[1] (numeric) = 1.2411113994853498462765141574076 absolute error = 0.0007754254255431588075831499259 relative error = 0.062517369628897761834601005346454 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.709 y1[1] (analytic) = 2.6510750833550814616935356941786 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.171649544750878461420247758963 relative error = 6.4747145725366070394167109778115 % h = 0.001 y2[1] (analytic) = 1.2409866695280156500259436921618 y2[1] (numeric) = 1.2417737003409493638860100471936 absolute error = 0.0007870308129337138600663550318 relative error = 0.063419763665394183432892838015613 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=23.18 NO POLE NO POLE x[1] = 0.71 y1[1] (analytic) = 2.6518337710215366812101279728528 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1724082324173336809368400376372 relative error = 6.5014720870274896133182803981574 % h = 0.001 y2[1] (analytic) = 1.2416381240094918334585420558604 y2[1] (numeric) = 1.2424368782952102813010058550921 absolute error = 0.0007987542857184478424637992317 relative error = 0.064330683012463757207370798018921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.711 y1[1] (analytic) = 2.6525918068542751986691468534576 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.173166268250072198395858918242 relative error = 6.5281913260310915314613920915587 % h = 0.001 y2[1] (analytic) = 1.2422903368527808105784143127322 y2[1] (numeric) = 1.2431009333481325985215015811031 absolute error = 0.0008105964953517879430872683709 relative error = 0.065250165062488826811868787945834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.712 y1[1] (analytic) = 2.6533491900952612445017254995287 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1739236514910582442284375643131 relative error = 6.5548723153477583282333909822048 % h = 0.001 y2[1] (analytic) = 1.2429433074056697924476518052839 y2[1] (numeric) = 1.2437658654997163155474972252266 absolute error = 0.0008225580940465230998454199427 relative error = 0.066178247161039497189370761163156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.713 y1[1] (analytic) = 2.6541059199871116408370860568158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1746803813829086405637981216002 relative error = 6.5815150807454168922454284169874 % h = 0.001 y2[1] (analytic) = 1.2435970350151882805914835912195 y2[1] (numeric) = 1.2444316747499614323789927874626 absolute error = 0.0008346397347731517875091962431 relative error = 0.067114966606764077566498894179844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.714 y1[1] (analytic) = 2.6548619957730965588856544087971 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1754364571688935586123664735815 relative error = 6.6081196479595698535337321295107 % h = 0.001 y2[1] (analytic) = 1.2442515190276087199687205040045 y2[1] (numeric) = 1.2450983610988679490159882678111 absolute error = 0.0008468420712592290472677638066 relative error = 0.068060360651280704033108797707155 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.715 y1[1] (analytic) = 2.655617416697140275668825905437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1761918780929372753955379702214 relative error = 6.6346860426932900799948983070395 % h = 0.001 y2[1] (analytic) = 1.2449067587884471526992557167609 y2[1] (numeric) = 1.2457659245464358654584836662721 absolute error = 0.0008591657579887127592279495112 relative error = 0.069014466499070138646114514399276 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.4MB, time=23.83 NO POLE NO POLE x[1] = 0.716 y1[1] (analytic) = 2.6563721820038219300946253354824 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1769466433996189298213374002668 relative error = 6.6612142906172152825118245181599 % h = 0.001 y2[1] (analytic) = 1.2455627536424638725479680820458 y2[1] (numeric) = 1.2464343650926651817064789828457 absolute error = 0.0008716114502013091585109007999 relative error = 0.069977321307369741983143481873503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.717 y1[1] (analytic) = 2.6571262909383762783785050667013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1777007523341732781052171314857 relative error = 6.687704417369542728228771198571 % h = 0.001 y2[1] (analytic) = 1.2462195029336640801643737636656 y2[1] (numeric) = 1.2471036827375558977599742175318 absolute error = 0.0008841798038918175956004538662 relative error = 0.070948962186068616058275017628784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.718 y1[1] (analytic) = 2.6578797427466944488085259333295 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1784542041424914485352379981139 relative error = 6.7141564485560240614359027755712 % h = 0.001 y2[1] (analytic) = 1.2468770060052985390773709209283 y2[1] (numeric) = 1.2477738774811080136189693703304 absolute error = 0.0008968714758094745415984494021 relative error = 0.07192942619760391449894462823683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.719 y1[1] (analytic) = 2.6586325366753246958541661056053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1792069980711216955808781703897 relative error = 6.7405704097499602315255173507357 % h = 0.001 y2[1] (analytic) = 1.2475352621998642324444214506442 y2[1] (numeric) = 1.2484449493233215292834644412415 absolute error = 0.0009096871234572968390429905973 relative error = 0.072918750356858316870099972759878 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.72 y1[1] (analytic) = 2.6593846719714731536180038326482 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1799591333672701533447158974326 relative error = 6.7669463264921965274840261676881 % h = 0.001 y2[1] (analytic) = 1.248194270859105020554513037748 y2[1] (numeric) = 1.2491168982641964447534594302651 absolute error = 0.0009226274050914241989463925171 relative error = 0.073916971631058664018872031079443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.721 y1[1] (analytic) = 2.6601361478830045886295206070606 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.180710609278801588356232671845 relative error = 6.7932842242911177183855908795733 % h = 0.001 y2[1] (analytic) = 1.2488540313240122990842440116342 y2[1] (numeric) = 1.2497897243037327600289543374012 absolute error = 0.000935692979720460944710325767 relative error = 0.074924126939675751300376347333922 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.4MB, time=24.48 NO POLE NO POLE x[1] = 0.722 y1[1] (analytic) = 2.6608869636584431519802719575123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1814614250542401517069840222967 relative error = 6.819584128622643299355167911546 % h = 0.001 y2[1] (analytic) = 1.249514542934825658106372752177 y2[1] (numeric) = 1.2504634274419304751099491626498 absolute error = 0.0009488845071048170035764104728 relative error = 0.075940253154325276532783538721044 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.723 y1[1] (analytic) = 2.6616371185469731307996737341996 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.182211579942770130526385798984 relative error = 6.8458460649302228424705449994247 % h = 0.001 y2[1] (analytic) = 1.2501758050310335418501726369398 y2[1] (numeric) = 1.2511380076787895899964439060109 absolute error = 0.0009622026477560481462712690711 relative error = 0.076965387098669939517494978551235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.724 y1[1] (analytic) = 2.6623866117984396990706524114553 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1829610731942366987973644762397 relative error = 6.8720700586248314520747852889943 % h = 0.001 y2[1] (analytic) = 1.2508378169513739092129327692739 y2[1] (numeric) = 1.2518134650143101046884385674845 absolute error = 0.0009756480629361954755057982106 relative error = 0.077999565548322689948128072613603 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.725 y1[1] (analytic) = 2.6631354426633496677844085919225 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1837099040591466675111206567069 relative error = 6.898256135084965323972319213603 % h = 0.001 y2[1] (analytic) = 1.2515005780338348950219439758613 y2[1] (numeric) = 1.2524897994484920191859331470706 absolute error = 0.0009892214146571241639891712093 relative error = 0.079042825230751120520055238957468 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.726 y1[1] (analytic) = 2.6638836103928722344335435575901 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1844580717886692341602556223745 relative error = 6.9244043196566374079837437428849 % h = 0.001 y2[1] (analytic) = 1.2521640876156554720463088117698 y2[1] (numeric) = 1.2531670109813353334889276447693 absolute error = 0.0010029233656798614426188329995 relative error = 0.080095202825183002040450958621938 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.727 y1[1] (analytic) = 2.6646311142388397318427993746266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.185205575634636731569511439411 relative error = 6.9505146376533731733362025251764 % h = 0.001 y2[1] (analytic) = 1.2528283450333261137579135612673 y2[1] (numeric) = 1.2538450996128400475974220605805 absolute error = 0.0010167545795139338395084993132 relative error = 0.081156734962512957327181469320831 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=25.14 NO POLE NO POLE x[1] = 0.728 y1[1] (analytic) = 2.6653779534537483763366637213347 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1859524148495453760633757861191 relative error = 6.9765871143562064763680289425739 % h = 0.001 y2[1] (analytic) = 1.2534933496225894578408994734763 y2[1] (numeric) = 1.2545240653430061615114163945042 absolute error = 0.0010307157204167036705169210279 relative error = 0.082227458225210270673421204035234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.729 y1[1] (analytic) = 2.666124127290759015243091271684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1866985886865560149698033364684 relative error = 7.0026217750136755300281371729956 % h = 0.001 y2[1] (analytic) = 1.2541591007184409704489697234547 y2[1] (numeric) = 1.2552039081718336752309106465404 absolute error = 0.0010448074533927047819409230857 relative error = 0.083307409147227829643598303742563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.73 y1[1] (analytic) = 2.6668696350036978737325941307615 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1874440963994948734593061955459 relative error = 7.028618644841818974652444020332 % h = 0.001 y2[1] (analytic) = 1.2548255976551296112098678414497 y2[1] (numeric) = 1.2558846280993225887559048166891 absolute error = 0.0010590304441929775460369752394 relative error = 0.08439662421391219595515782968709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.731 y1[1] (analytic) = 2.6676144758470573009919544831147 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1881889372428543007186665478991 relative error = 7.0545777490241720495013965443032 % h = 0.001 y2[1] (analytic) = 1.2554928397661584989763626059028 y2[1] (numeric) = 1.2565662251254729020863989049503 absolute error = 0.0010733853593144031100362990475 relative error = 0.085495139861914802189685030097396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.732 y1[1] (analytic) = 2.6683586490759965157318132803332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1889331104717935154585253451176 relative error = 7.0804991127117628645444674077163 % h = 0.001 y2[1] (analytic) = 1.2561608263842855783230736492765 y2[1] (numeric) = 1.257248699250284615222392911324 absolute error = 0.0010878728659990368993192620475 relative error = 0.086602992479104271066151542447946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.733 y1[1] (analytic) = 2.6691021539463423510273894603448 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1896766153421393507541015251292 relative error = 7.1063827610231087719792613735486 % h = 0.001 y2[1] (analytic) = 1.2568295568415242867884712799312 y2[1] (numeric) = 1.2579320504737577281638868358102 absolute error = 0.001102493632233441375415555879 relative error = 0.087720218404479853998434093700895 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=25.79 NO POLE NO POLE x[1] = 0.734 y1[1] (analytic) = 2.6698449897145899984915848577685 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1904194511103869982182969225529 relative error = 7.1322287190442128369746525391931 % h = 0.001 y2[1] (analytic) = 1.2574990304691442228613832781104 y2[1] (numeric) = 1.2586162787958922409108806784089 absolute error = 0.0011172483267480180494974002985 relative error = 0.088846853928085985648807452262859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.735 y1[1] (analytic) = 2.6705871556379037517797306322801 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1911616170337007515064426970645 relative error = 7.1580370118285604071291427029629 % h = 0.001 y2[1] (analytic) = 1.2581692465976718147113406795812 y2[1] (numeric) = 1.2593013842166881534633744391201 absolute error = 0.0011321376190163387520337595389 relative error = 0.08998293529092795117883043949803 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.736 y1[1] (analytic) = 2.671328650974117749425231710308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1919031123699147491519437750924 relative error = 7.1838076643971157801373967309282 % h = 0.001 y2[1] (analytic) = 1.2588402045568909896620938166407 y2[1] (numeric) = 1.2599873667361454658213681179439 absolute error = 0.0011471621792544761592743013032 relative error = 0.091128498684888662888925072804462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.737 y1[1] (analytic) = 2.672069474981736717005366404475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1926439363775337167320784692594 relative error = 7.2095407017383189691596709422136 % h = 0.001 y2[1] (analytic) = 1.2595119036758438444076291430284 y2[1] (numeric) = 1.2606742263542641779848617148802 absolute error = 0.0011623226784203335772325718518 relative error = 0.092283580252646542927993732267455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.738 y1[1] (analytic) = 2.6728096269199367086364990450493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1933840883157337083632111098337 relative error = 7.2352361488080825653906053707657 % h = 0.001 y2[1] (analytic) = 1.2601843432828313159700166267826 y2[1] (numeric) = 1.261361963071044289953855229929 absolute error = 0.0011776197882129739838386031464 relative error = 0.09344821608759450874462696065796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.739 y1[1] (analytic) = 2.6735491060485658477979641282533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1941235674443628475246761930377 relative error = 7.2608940305297886973256003032031 % h = 0.001 y2[1] (analytic) = 1.2608575227054138533984167532507 y2[1] (numeric) = 1.2620505768864858017283486630903 absolute error = 0.0011930541810719483299319098396 relative error = 0.094622442233760057941824459837999 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.4MB, time=26.46 NO POLE NO POLE x[1] = 0.74 y1[1] (analytic) = 2.6742879116281450674838811576082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1948623730239420672105932223926 relative error = 7.2865143717942860862247417481814 % h = 0.001 y2[1] (analytic) = 1.2615314412704120902085754393012 y2[1] (numeric) = 1.2627400678005887133083420143641 absolute error = 0.0012086265301766230997665750629 relative error = 0.095806294685726449187683372209337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.741 y1[1] (analytic) = 2.6750260429198688496821600265609 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1956005043156658494088720913453 relative error = 7.3120971974598871972759794748446 % h = 0.001 y2[1] (analytic) = 1.2622060983039075175621344192991 y2[1] (numeric) = 1.2634304358133530246938352837504 absolute error = 0.0012243375094455071317008644513 relative error = 0.096999809388554975825200364929793 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.742 y1[1] (analytic) = 2.6757634991856059641799574634498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1963379605814029639066695282342 relative error = 7.3376425323523654859609949787623 % h = 0.001 y2[1] (analytic) = 1.2628814931312431581850839235906 y2[1] (numeric) = 1.2641216809247787358848284712492 absolute error = 0.0012401877935355776997445476586 relative error = 0.098203022237708328815186697362729 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.743 y1[1] (analytic) = 2.676500279687900206694845733414 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1970747410836972064215577981984 relative error = 7.3631504012649527391289252053945 % h = 0.001 y2[1] (analytic) = 1.2635576250770242410246837310994 y2[1] (numeric) = 1.2648138031348658468813215768605 absolute error = 0.0012561780578416058566378457611 relative error = 0.099415969078975045637307674918359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.744 y1[1] (analytic) = 2.6772363836899711363309554661397 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1978108450857681360576675309241 relative error = 7.3886208289583365102848310959776 % h = 0.001 y2[1] (analytic) = 1.2642344934651188766441779391716 y2[1] (numeric) = 1.2655068024436143576833146005843 absolute error = 0.0012723089784954810391366614127 relative error = 0.10063868570839504176542899824164 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.745 y1[1] (analytic) = 2.6779718104557148123593551533613 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1985462718515118120860672181457 relative error = 7.4140538401606576486015180307971 % h = 0.001 memory used=160.2MB, alloc=4.4MB, time=27.11 y2[1] (analytic) = 1.2649120976186587333546280560096 y2[1] (numeric) = 1.2662006788510242682908075424207 absolute error = 0.0012885812323655349361794864111 relative error = 0.10187120787218622132478182717079 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.746 y1[1] (analytic) = 2.6787065592497045303219305358001 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.1992810206455015300486426005845 relative error = 7.4394494595675079211650280426061 % h = 0.001 y2[1] (analytic) = 1.2655904368600397140831882839174 y2[1] (numeric) = 1.2668954323570955787038004023696 absolute error = 0.0013049954970558646206121184522 relative error = 0.10311357126667216352994521121972 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.747 y1[1] (analytic) = 2.6794406293371915574580277757215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2000150907329885571847398405059 relative error = 7.4648077118419277279658312704014 % h = 0.001 y2[1] (analytic) = 1.266269510510922633977146125141 y2[1] (numeric) = 1.267591062961828288922293180431 absolute error = 0.00132155245090565494514705529 relative error = 0.10436581153821088149428820802605 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.748 y1[1] (analytic) = 2.6801740199841058674531249885306 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.200748481379902867179837053315 relative error = 7.4901286216144039091494465333956 % h = 0.001 y2[1] (analytic) = 1.2669493178922338987430507063167 y2[1] (numeric) = 1.2682875706652223989462858766049 absolute error = 0.0013382527729885002032351702882 relative error = 0.10562796428312464999331383140815 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.749 y1[1] (analytic) = 2.6809067304570568745087973847929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2014811918528538742355094495773 relative error = 7.5154122134828676440419181386171 % h = 0.001 y2[1] (analytic) = 1.2676298583241661837202504824584 y2[1] (numeric) = 1.2689849554672779087757784908913 absolute error = 0.0013550971431117250555280084329 relative error = 0.10690006504763089875630225035447 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.75 y1[1] (analytic) = 2.6816387600233341667332419527799 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2022132214191311664599540175643 relative error = 7.5406585120126924414672681059768 % h = 0.001 y2[1] (analytic) = 1.2683111311261791136881612469999 y2[1] (numeric) = 1.2696832173679948184107710232902 absolute error = 0.0013720862418157047226097762903 relative error = 0.10818214932777416785276070835138 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=164.0MB, alloc=4.4MB, time=27.77 x[1] = 0.751 y1[1] (analytic) = 2.6823701079509082388516282910726 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.202944569346705238578340355857 relative error = 7.5658675417366922208757299131905 % h = 0.001 y2[1] (analytic) = 1.2689931356169999434065846406836 y2[1] (numeric) = 1.2703823563673731278512634738016 absolute error = 0.001389220750373184444678833118 relative error = 0.10947425256935912173245175238834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.752 y1[1] (analytic) = 2.6831007735084312242355428809353 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2036752349042282239622549457197 relative error = 7.5910393271551194838032516427375 % h = 0.001 y2[1] (analytic) = 1.2696758711146242388883966190315 y2[1] (numeric) = 1.2710823724654128370972558424255 absolute error = 0.001406501350788598208859223394 relative error = 0.1107764101678846184701888571011 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.753 y1[1] (analytic) = 2.6838307559652376262507947690758 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2044052173610346259775068338602 relative error = 7.6161738927356635751844330655286 % h = 0.001 y2[1] (analytic) = 1.270359336936316559403924605769 y2[1] (numeric) = 1.2717832656621139461487481291619 absolute error = 0.0014239287257973867448235233929 relative error = 0.11208865746847883075915870053488 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.754 y1[1] (analytic) = 2.6845600545913450489228513130465 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2051345159871420486495633778309 relative error = 7.6412712629134490340427327336982 % h = 0.001 y2[1] (analytic) = 1.2710435323986111402163313278786 y2[1] (numeric) = 1.2724850359574764550057403340108 absolute error = 0.0014415035588653147894090061322 relative error = 0.11341102976583541518925149343643 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.755 y1[1] (analytic) = 2.6852886686574549269191733239135 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2058631300532519266458853886979 relative error = 7.666331462091034033083447590102 % h = 0.001 y2[1] (analytic) = 1.2717284568173125760473225969591 y2[1] (numeric) = 1.2731876833515003636682324569723 absolute error = 0.0014592265341877876209098600132 relative error = 0.11474356230415072633975417809666 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.756 y1[1] (analytic) = 2.6860165974349532548477196239165 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2065910588307502545744316887009 relative error = 7.6913545146384089067166289464939 % h = 0.001 y2[1] (analytic) = 1.2724141095074965052724955712377 y2[1] (numeric) = 1.2738912078441856721362244980463 absolute error = 0.0014770983366891668637289268086 relative error = 0.11608629027706207220878529064163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=167.8MB, alloc=4.4MB, time=28.41 x[1] = 0.757 y1[1] (analytic) = 2.686743840195911315870891720679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2073183015917083155976037854634 relative error = 7.7163404448929947670387549487574 % h = 0.001 y2[1] (analytic) = 1.2731004897835102948456433029448 y2[1] (numeric) = 1.2745956094355323804097164572328 absolute error = 0.001495119652022085564073154288 relative error = 0.11743924882758700749502411272193 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.758 y1[1] (analytic) = 2.6874703962130864096341899840818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2080448576088834093609020488662 relative error = 7.7412892771596422073036308473205 % h = 0.001 y2[1] (analytic) = 1.2737875969589737259513306468032 y2[1] (numeric) = 1.2753008881255404884887083345318 absolute error = 0.0015132911665667625373776877286 relative error = 0.11880247304806366124060971471127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.759 y1[1] (analytic) = 2.6881962647599225795088533972068 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2087707261557195792355654619912 relative error = 7.7662010357106300924146345369539 % h = 0.001 y2[1] (analytic) = 1.274475430346779680385055877114 y2[1] (numeric) = 1.2760070439142099963732001299433 absolute error = 0.0015316135674303159881442528293 relative error = 0.12017599798009209533755690011854 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.76 y1[1] (analytic) = 2.6889214451105513391477556387697 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2094959065063483388744677035541 relative error = 7.7910757447856644359720659339063 % h = 0.001 y2[1] (analytic) = 1.275163989259094827660311633333 y2[1] (numeric) = 1.2767140768015409040631918434673 absolute error = 0.0015500875424460764028802101343 relative error = 0.12155985861447669039365518566841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.761 y1[1] (analytic) = 2.6896459365397923983538309412086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.210220397935589398080543005993 relative error = 7.81591342859187736341099483257 % h = 0.001 y2[1] (analytic) = 1.2758532730073603128418580871366 y2[1] (numeric) = 1.2774219867875332115586834751038 absolute error = 0.0015687137801728987168253879672 relative error = 0.12295408989116955544758307629125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.762 y1[1] (analytic) = 2.6903697383231543882603038560603 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2109441997189513879870159208447 relative error = 7.8407141113038261607666329400224 % h = 0.001 y2[1] (analytic) = 1.2765432809022924451045204977583 y2[1] (numeric) = 1.2781307738721869188596750248528 absolute error = 0.0015874929698944737551545270945 relative error = 0.12435872669921495801688230216933 % h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.4MB, time=29.06 NO POLE NO POLE x[1] = 0.763 y1[1] (analytic) = 2.6910928497368355858219977464571 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2116673111326325855487098112415 relative error = 7.8654778170634924086058818376643 % h = 0.001 y2[1] (analytic) = 1.2772340122538833870168225968583 y2[1] (numeric) = 1.2788404380555020259661664927143 absolute error = 0.001606425801618638949343895856 relative error = 0.12577380387669477095649465431431 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.764 y1[1] (analytic) = 2.6918152700577246376169975154955 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2123897314535216373437095802799 relative error = 7.8902045699802812006653296762428 % h = 0.001 y2[1] (analytic) = 1.277925466371401844548766519348 y2[1] (numeric) = 1.2795509793374785328781578786884 absolute error = 0.0016255129660766883293913593404 relative error = 0.12719935621067493259976686591582 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.765 y1[1] (analytic) = 2.6925369985634012829579427688738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2131114599591982826846548336582 relative error = 7.9148943941310204467375854862449 % h = 0.001 y2[1] (analytic) = 1.2786176425633937578030692724491 y2[1] (numeric) = 1.280262397718116439595649182775 absolute error = 0.0016447551547226817925799103259 relative error = 0.12863541843715291664817591387541 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.766 y1[1] (analytic) = 2.6932580345321370763122283005656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.21383249592793407603894036535 relative error = 7.9395473135599602593494510919709 % h = 0.001 y2[1] (analytic) = 1.2793105401376829924691650118068 y2[1] (numeric) = 1.2809746931974157461186404049741 absolute error = 0.0016641530597327536494753931673 relative error = 0.13008202524100620827051743509961 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.767 y1[1] (analytic) = 2.6939783772428961090303894813906 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.214552838638693108757101546175 relative error = 7.9641633522787724237770367666475 % h = 0.001 y2[1] (analytic) = 1.2800041584013720319992816707128 y2[1] (numeric) = 1.2816878657753764524471315452857 absolute error = 0.0016837073740044204478498745729 relative error = 0.13153921125594178286693293717789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.768 y1[1] (analytic) = 2.6946980259753357303819508221551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2152724873711327301086628869395 relative error = 7.9887425342665499509445279695173 % h = 0.001 y2[1] (analytic) = 1.2806984966608426705058997664195 y2[1] (numeric) = 1.2824019154519985585811226037098 absolute error = 0.0017034187911558880752228372903 relative error = 0.13300701106444658394792640608505 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=29.71 NO POLE NO POLE x[1] = 0.769 y1[1] (analytic) = 2.6954169800098072678980166755753 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2159914414056042676247287403597 relative error = 8.0132848834698067127549067764678 % h = 0.001 y2[1] (analytic) = 1.2813935542217567063799004861449 y2[1] (numeric) = 1.2831168422272820645206135802464 absolute error = 0.0017232880055253581407130941015 relative error = 0.13448545919773899657343704438011 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.77 y1[1] (analytic) = 2.6961352386273567470198837344522 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2167097000231537467465957992366 relative error = 8.0377904238024771594025229649946 % h = 0.001 y2[1] (analytic) = 1.2820893303890566366287094346757 y2[1] (numeric) = 1.2838326461012269702656044748955 absolute error = 0.0017433157121703336368950402198 relative error = 0.13597459013572131279209148156402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.771 y1[1] (analytic) = 2.696852801109725610052955677546 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2174272625055226097796677423304 relative error = 8.0622591791459161182189961544647 % h = 0.001 y2[1] (analytic) = 1.2827858244669663519337417054856 y2[1] (numeric) = 1.2845493270738332758160952876571 absolute error = 0.0017635026068669238823535821715 relative error = 0.13747443830693318551595515061088 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.772 y1[1] (analytic) = 2.6975696667393514344252410092942 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2181441281351484341519530740786 relative error = 8.0866911733488986736055119455824 % h = 0.001 y2[1] (analytic) = 1.2834830357589918324264532179796 y2[1] (numeric) = 1.2852668851451009811720860185312 absolute error = 0.0017838493861091487456328005516 relative error = 0.13898503808850606726143788903471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.773 y1[1] (analytic) = 2.6982858347993686502497158349369 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2188602961951656499764278997213 relative error = 8.1110864302276201276061516608929 % h = 0.001 y2[1] (analytic) = 1.2841809635679218441823025448716 y2[1] (numeric) = 1.2859853203150300863335766675178 absolute error = 0.0018043567471082421512741226462 relative error = 0.14050642380611863018248246299018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.774 y1[1] (analytic) = 2.6990013045736092571898340087447 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2195757659694062569165460735291 relative error = 8.1354449735656960406784670727505 % h = 0.001 y2[1] (analytic) = 1.2848796071958286364319267357915 y2[1] (numeric) = 1.286704632583620591300567234617 absolute error = 0.0018250253877919548686404988255 relative error = 0.14203862973395316381777589368682 % h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=30.35 NO POLE NO POLE x[1] = 0.775 y1[1] (analytic) = 2.6997160753466035406274677899009 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2202905367424005403541798546853 relative error = 8.1597668271141623522190784288308 % h = 0.001 y2[1] (analytic) = 1.2855789659440686394888339260045 y2[1] (numeric) = 1.2874248219508724960730577198287 absolute error = 0.0018458560068038565842237938242 relative error = 0.14358169009465294696947144925155 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.776 y1[1] (analytic) = 2.7004301464035807871325628381541 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2210046077993777868592749029385 relative error = 8.1840520145914755804036361594389 % h = 0.001 y2[1] (analytic) = 1.2862790391132831633929148026071 y2[1] (numeric) = 1.2881458884167858006510481231529 absolute error = 0.0018668493035026372581333205458 relative error = 0.14513563905928059012679321430946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.777 y1[1] (analytic) = 2.7011435170304699992337920796493 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2217179784262669989605041444337 relative error = 8.2083005596835131009020438881901 % h = 0.001 y2[1] (analytic) = 1.2869798260033990972690742847478 y2[1] (numeric) = 1.2888678319813605050345384445896 absolute error = 0.0018880059779614077654641598418 relative error = 0.14670051074727734484391452379885 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.778 y1[1] (analytic) = 2.7018561865139006094894936723398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2224306479096976092162057371242 relative error = 8.23251248604357350403139277924 % h = 0.001 y2[1] (analytic) = 1.2876813259136296094002840592981 y2[1] (numeric) = 1.2895906526445966092235286841388 absolute error = 0.0019093267309669998232446248407 relative error = 0.14827633922642337647765550780729 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.779 y1[1] (analytic) = 2.7025681541412031938581790001042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2231426155370001935848910648886 relative error = 8.2566878172923770299106048529499 % h = 0.001 y2[1] (analytic) = 1.28838353814247484801435589898 y2[1] (numeric) = 1.2903143504064941132180188418005 absolute error = 0.0019308122640192652036629428205 relative error = 0.14986315851279899668683279821452 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.78 y1[1] (analytic) = 2.7032794192004101843678973251179 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2238538805962071840946093899023 relative error = 8.2808265770180660811823256988019 % h = 0.001 y2[1] (analytic) = 1.2890864619877226427837349762354 y2[1] (numeric) = 1.2910389252670530170180089175747 absolute error = 0.0019524632793303742342739413393 relative error = 0.15146100257074685209151535415793 % h = 0.001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.4MB, time=31.01 NO POLE NO POLE x[1] = 0.781 y1[1] (analytic) = 2.7039899809802565810837444291757 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2245644423760535808104564939601 relative error = 8.3049287887762058128691450221179 % h = 0.001 y2[1] (analytic) = 1.289790096746449207037611673102 y2[1] (numeric) = 1.2917643772262733206234989114614 absolute error = 0.0019742804798241135858872383594 relative error = 0.15306990531283506548699362872535 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.782 y1[1] (analytic) = 2.7046998387701806633728032765141 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2252743001659776630995153412985 relative error = 8.3289944760897847989327566910316 % h = 0.001 y2[1] (analytic) = 1.2904944417150198406856496750424 y2[1] (numeric) = 1.2924907062841550240344888234606 absolute error = 0.0019962645691351833488391484182 relative error = 0.15468990059982132600395417991069 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.783 y1[1] (analytic) = 2.705408991860324700465805433254 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2259834532561217001925174980384 relative error = 8.3530236624492157751061984146479 % h = 0.001 y2[1] (analytic) = 1.2911994961890896338526274250576 y2[1] (numeric) = 1.2932179124406981272509786535723 absolute error = 0.0020184162516084933983512285147 relative error = 0.15632102224061792460316758033971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.784 y1[1] (analytic) = 2.70611743954153566131480268186 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2266919009373326610415147466444 relative error = 8.3770163713123364575708348937478 % h = 0.001 y2[1] (analytic) = 1.2919052594636041712232893035015 y2[1] (numeric) = 1.2939459956959026302729684017966 absolute error = 0.0020407362322984590496790982951 relative error = 0.15796330399225773128994335756455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.785 y1[1] (analytic) = 2.7068251811053659237461389730047 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2273996425011629234728510377891 relative error = 8.4009726261044104370512672540994 % h = 0.001 y2[1] (analytic) = 1.2926117308328002370967021888034 y2[1] (numeric) = 1.2946749560497685331004580681334 absolute error = 0.00206322521696829600375587933 relative error = 0.15961677955986111043068095366352 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.786 y1[1] (analytic) = 2.707532215844073982908013561925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2281066772398709826347256267094 relative error = 8.4248924502181281479028658109598 % h = 0.001 y2[1] (analytic) = 1.293318909590206521149412344802 y2[1] (numeric) = 1.2954047935022958357334476525827 absolute error = 0.0020858839120893145840353077807 relative error = 0.16128148259660377055104958320043 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.4MB, time=31.68 NO POLE NO POLE x[1] = 0.787 y1[1] (analytic) = 2.7082385430506251590119268817658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2288130044464221587386389465502 relative error = 8.4487758670136079117681327336798 % h = 0.001 y2[1] (analytic) = 1.2940267950286443249066968715924 y2[1] (numeric) = 1.2961355080534845381719371551445 absolute error = 0.0021087130248402132652402835521 relative error = 0.16295744670368554499266164526075 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.788 y1[1] (analytic) = 2.7089441620186923043673014125252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2295186234144893040940134773096 relative error = 8.4726228998183970553796059933374 % h = 0.001 y2[1] (analytic) = 1.2947353864402282689212032486917 y2[1] (numeric) = 1.2968670997033346404159265758188 absolute error = 0.0021317132631063714947233271271 relative error = 0.16464470543030009980256326100862 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.789 y1[1] (analytic) = 2.7096490720426565097085705110381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2302235334384535094352825758225 relative error = 8.4964335719274731020885160956598 % h = 0.001 y2[1] (analytic) = 1.2954446831163670006582697919461 y2[1] (numeric) = 1.2975995684518461424654159146056 absolute error = 0.0021548853354791418071461226595 relative error = 0.1663432922736055652274508140805 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.79 y1[1] (analytic) = 2.7103532724176078098140288749692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2309277338134048095407409397536 relative error = 8.5202079066032450366999025382318 % h = 0.001 y2[1] (analytic) = 1.296154684347763903087219138915 y2[1] (numeric) = 1.2983329142990190443204051715049 absolute error = 0.0021782299512551412331860325899 relative error = 0.16805324067869608718223332039959 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.791 y1[1] (analytic) = 2.711056762439345888415739022023 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2316312238351428881424510868074 relative error = 8.5439459270755546431963876966559 % h = 0.001 y2[1] (analytic) = 1.2968653894244178039779161714986 y2[1] (numeric) = 1.2990671372448533459808943465167 absolute error = 0.0022017478204355420029781750181 relative error = 0.16977458403857429506039629607805 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.792 y1[1] (analytic) = 2.7117595414043807823997888745235 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2323340028001777821265009393079 relative error = 8.5676476565416779149342919509374 % h = 0.001 y2[1] (analytic) = 1.2975767976356236859018810793109 y2[1] (numeric) = 1.299802237289349047446883439641 absolute error = 0.0022254396537253615450023603301 relative error = 0.17150735569412468225158277900728 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.4MB, time=32.35 NO POLE NO POLE x[1] = 0.793 y1[1] (analytic) = 2.7124616086099335852961962491652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2330360700057305850229083139496 relative error = 8.5913131181663265368972553225627 % h = 0.001 y2[1] (analytic) = 1.2982889082699733969372475627432 y2[1] (numeric) = 1.3005382144325061487183724508779 absolute error = 0.0022493061625327517811248881347 relative error = 0.17325158893408789572989054191892 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.794 y1[1] (analytic) = 2.7131629633539371500577567620875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2337374247497341497844688268719 relative error = 8.6149423350816494395940077162244 % h = 0.001 y2[1] (analytic) = 1.2990017206153563620768554708199 y2[1] (numeric) = 1.3012750686743246497953613802273 absolute error = 0.0022733480589682877185059094074 relative error = 0.17500731699503593107459056204335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.795 y1[1] (analytic) = 2.713863604935036791127132370486 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2344380663308337908538444352704 relative error = 8.6385353303872344241884020600185 % h = 0.001 y2[1] (analytic) = 1.2997152339589602953387664658126 y2[1] (numeric) = 1.3020128000148045506778502276892 absolute error = 0.0022975660558442553390837618766 relative error = 0.17677457306134822928329973589471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.796 y1[1] (analytic) = 2.7145635326525909857914784837286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.235137994048387985518190548513 relative error = 8.6620921271501098584512922253465 % h = 0.001 y2[1] (analytic) = 1.3004294475872719125784906041565 y2[1] (numeric) = 1.3027514084539458513658389932636 absolute error = 0.0023219608666739387873483891071 relative error = 0.17855339026518867173608989631723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.797 y1[1] (analytic) = 2.7152627458066720748239082894086 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.235837207202469074550620354193 relative error = 8.6856127484047464431253005950171 % h = 0.001 y2[1] (analytic) = 1.3011443607860776450022110215024 y2[1] (numeric) = 1.3034908939917485518593276769505 absolute error = 0.0023465332056709068571166554481 relative error = 0.18034380168648346966758465341918 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.798 y1[1] (analytic) = 2.7159612436980669624110936529281 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2365357050938639621378057177125 relative error = 8.7090972171530590482949785464574 % h = 0.001 y2[1] (analytic) = 1.3018599728404643533802932087375 y2[1] (numeric) = 1.3042312566282126521583162787499 absolute error = 0.0023712837877482987780230700124 relative error = 0.1821458403528999445027846909051 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=32.99 NO POLE NO POLE x[1] = 0.799 y1[1] (analytic) = 2.7166590256282778153663026630705 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2372334870240748150930147278549 relative error = 8.7325455563644086193563169384766 % h = 0.001 y2[1] (analytic) = 1.3025762830348200429603646655274 y2[1] (numeric) = 1.3049724963633381522628047986618 absolute error = 0.0023962133285181093024401331344 relative error = 0.18395953923982619541117015399432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.8 y1[1] (analytic) = 2.7173560908995227616271746105814 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2379305522953197613538866753658 relative error = 8.7559577889756041521810129460799 % h = 0.001 y2[1] (analytic) = 1.3032932906528345790792500183577 y2[1] (numeric) = 1.3057146131971250521727932366862 absolute error = 0.0024213225442904730935432183285 relative error = 0.18578493127035165043255491535919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.801 y1[1] (analytic) = 2.718052438814736588037533902042 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2386269002105335877642459668264 relative error = 8.7793339378909047370723442904032 % h = 0.001 y2[1] (analytic) = 1.3040109949775004034730459911998 y2[1] (numeric) = 1.3064576071295733518882815928231 absolute error = 0.0024466121520729484152356016233 relative error = 0.18762204931524849752721105023347 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.802 y1[1] (analytic) = 2.7187480686775714374125451272789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2393225300733684371392571920633 relative error = 8.8026740259820216711109420713074 % h = 0.001 y2[1] (analytic) = 1.3047293952911132512846199187868 y2[1] (numeric) = 1.3072014781606830514092698670725 absolute error = 0.0024720828695698001246499482857 relative error = 0.18947092619295399190194204145182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.803 y1[1] (analytic) = 2.7194429797923975048865122152131 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2400174411881945046132242799975 relative error = 8.8259780760881206384901890403286 % h = 0.001 y2[1] (analytic) = 1.3054484908752728687678147950589 y2[1] (numeric) = 1.3079462262904541507357580594345 absolute error = 0.0024977354151812819679432643756 relative error = 0.19133159466955363596305932008186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.804 y1[1] (analytic) = 2.7201371714643037335426253304078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2407116328601007332693373951922 relative error = 8.849246111015823958442401263151 % h = 0.001 y2[1] (analytic) = 1.3061682810108837316876431526351 y2[1] (numeric) = 1.308691851518886649867746169909 absolute error = 0.0025235705080029181801030172739 relative error = 0.19320408745876522824660797688707 % h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.4MB, time=33.65 NO POLE NO POLE x[1] = 0.805 y1[1] (analytic) = 2.7208306429990985093239598806256 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.24140510439489550905067194541 relative error = 8.8724781535392129003583777250567 % h = 0.001 y2[1] (analytic) = 1.3068887649781557644157513731752 y2[1] (numeric) = 1.309438353845980548805234198496 absolute error = 0.0025495888678247843894828253208 relative error = 0.19508843722192377767569310597596 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.806 y1[1] (analytic) = 2.7215233937033103552250327244533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2420978550991073549517447892377 relative error = 8.8956742263998300657043245416278 % h = 0.001 y2[1] (analytic) = 1.3076099420566050597204353332294 y2[1] (numeric) = 1.3101857332717358475482221451955 absolute error = 0.0025757912151307878277868119661 relative error = 0.19698467656796727949437751379518 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.807 y1[1] (analytic) = 2.7222154228841886247632213874979 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2427898842799856244899334522823 relative error = 8.9188343523066818363415780619723 % h = 0.001 y2[1] (analytic) = 1.3083318115250545992504875956188 y2[1] (numeric) = 1.3109339897961525460967100100075 absolute error = 0.0026021782710979468462224143887 relative error = 0.19889283805342334922735369680191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.808 y1[1] (analytic) = 2.7229067298497041947293528157898 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2434811912455011944560648805742 relative error = 8.941958553936240888855964304158 % h = 0.001 y2[1] (analytic) = 1.3090543726616349747121556625597 y2[1] (numeric) = 1.311683123419230644450697792932 absolute error = 0.0026287507575956697385421303723 relative error = 0.20081295418239671101443730989956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.809 y1[1] (analytic) = 2.7235973139085501572167689158648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2441717753043471569434809806492 relative error = 8.9650468539324487745050408544903 % h = 0.001 y2[1] (analytic) = 1.3097776247437851097384901136346 y2[1] (numeric) = 1.312433134140970142610185493969 absolute error = 0.0026555093971850328716953803344 relative error = 0.20274505740655753666888506734097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.81 y1[1] (analytic) = 2.7242871743701425109281768525145 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2448616357659395106548889172989 relative error = 8.9880992749067185643928716046333 % memory used=202.1MB, alloc=4.4MB, time=34.30 h = 0.001 y2[1] (analytic) = 1.3105015670482529824503607593199 y2[1] (numeric) = 1.3131840219613710405751731131185 absolute error = 0.0026824549131180581248123537986 relative error = 0.20468918012513063180860639073923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.811 y1[1] (analytic) = 2.7249763105446208517595927974149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2455507719404178514863048621993 relative error = 9.0111158394379375594833845055669 % h = 0.001 y2[1] (analytic) = 1.311226198851096348708418249117 y2[1] (numeric) = 1.3139357868804333383456606503805 absolute error = 0.0027095880293369896372424012635 relative error = 0.20664535468488546540951439683457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.812 y1[1] (analytic) = 2.7256647217428490626606885447446 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.246239183138646062387400609529 relative error = 9.0340965700724700650647578958337 % h = 0.001 y2[1] (analytic) = 1.3119515194276834660552778823829 y2[1] (numeric) = 1.3146884288981570359216481057551 absolute error = 0.0027369094704735698663702233722 relative error = 0.20861361338012703913054725524536 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.813 y1[1] (analytic) = 2.7263524072764160027708511335054 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2469268686722130024975631982898 relative error = 9.0570414893241602292786719256079 % h = 0.001 y2[1] (analytic) = 1.3126775280526938183472016797382 y2[1] (numeric) = 1.3154419480145421333031354792422 absolute error = 0.002764419961848314955933799504 relative error = 0.21059398845268759276028479573598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.814 y1[1] (analytic) = 2.7270393664576361958302663405423 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2476138278534331955569784053267 relative error = 9.0799506196743349453296481587468 % h = 0.001 y2[1] (analytic) = 1.3134042240001188410745540834314 y2[1] (numeric) = 1.3161963442295886304901227708418 absolute error = 0.0027921202294697894155686874104 relative error = 0.21258651209191914213558676107801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.815 y1[1] (analytic) = 2.7277255985995505178653376332361 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2483000599953475175920496980205 relative error = 9.1028239835718068169910826039731 % h = 0.001 y2[1] (analytic) = 1.3141316065432626473703059662622 y2[1] (numeric) = 1.3169516175432965274826099805539 absolute error = 0.0028200110000338801123040142917 relative error = 0.2145912164346868458832875395481 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=205.9MB, alloc=4.4MB, time=34.95 x[1] = 0.816 y1[1] (analytic) = 2.7284111030159268841477528965088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2489855644117238838744649612932 relative error = 9.1256616034328771870259552151183 % h = 0.001 y2[1] (analytic) = 1.314859674954742754705860940622 y2[1] (numeric) = 1.3177077679556658242805971083785 absolute error = 0.0028480930009230695747361677565 relative error = 0.21660813356536319733669682587717 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.817 y1[1] (analytic) = 2.72909587902126093542651197513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2496703404170579351532240399144 relative error = 9.1484635016413392281415723200789 % h = 0.001 y2[1] (analytic) = 1.315588428506490812273477271886 y2[1] (numeric) = 1.3184647954666965208840841543156 absolute error = 0.0028763669602057086106068824296 relative error = 0.2186372955158230379794757076529 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.818 y1[1] (analytic) = 2.7297799259307767234322287993561 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2503543873265737231589408641405 relative error = 9.1712297005484810960990675007284 % h = 0.001 y2[1] (analytic) = 1.316317866469753329054558013794 y2[1] (numeric) = 1.3192227000763886172930711183652 absolute error = 0.0029048336066352882385131045712 relative error = 0.22067873426543938877038241245697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.819 y1[1] (analytic) = 2.7304632430604273956530225896556 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.25103770445622439537973465444 relative error = 9.1939602224730891445997511623412 % h = 0.001 y2[1] (analytic) = 1.3170479881150924025730812975917 y2[1] (numeric) = 1.3199814817847421135075580005273 absolute error = 0.0029334936696497109344767029356 relative error = 0.22273248174108009570341063655997 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.82 y1[1] (analytic) = 2.7311458297268958793813133646877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2517202911226928791080254294721 relative error = 9.2166550897014512015717594130151 % h = 0.001 y2[1] (analytic) = 1.3177787927123864483334420215631 y2[1] (numeric) = 1.3207411405917570095275448008019 absolute error = 0.0029623478793705611941027792388 relative error = 0.22479856981710528595897526783794 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.821 y1[1] (analytic) = 2.7318276852475955650308377057945 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2524021466433925647575497705789 relative error = 9.239314324487359906481808932105 % h = 0.001 y2[1] (analytic) = 1.3185102795308309299419755031717 y2[1] (numeric) = 1.321501676497433305353031519189 absolute error = 0.0029913969666023754110560160173 relative error = 0.22687703031536563100303467263342 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=209.8MB, alloc=4.4MB, time=35.60 x[1] = 0.822 y1[1] (analytic) = 2.7325088089406709887232014610491 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2530832703364679884499135258335 relative error = 9.2619379490521161082982162534957 % h = 0.001 y2[1] (analytic) = 1.3192424478389390899114329723498 y2[1] (numeric) = 1.3222630895017710009840181556887 absolute error = 0.0030206416628319110725851833389 relative error = 0.22896789500520141299237479818249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.823 y1[1] (analytic) = 2.7331892001249985141432868023628 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2537636615207955138699988671472 relative error = 9.2845259855845323237326873357101 % h = 0.001 y2[1] (analytic) = 1.3199752969045426811476781015192 y2[1] (numeric) = 1.3230253796047700964205047103009 absolute error = 0.0030500827002274152728266087817 relative error = 0.23107119560344239084571741079227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.824 y1[1] (analytic) = 2.7338688581201870136628317803018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2544433195159840133895438450862 relative error = 9.3070784562409362553897264479548 % h = 0.001 y2[1] (analytic) = 1.3207088259947926991178730857087 y2[1] (numeric) = 1.3237885468064305916624911830256 absolute error = 0.0030797208116378925446180973169 relative error = 0.23318696377440846234185210607749 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.825 y1[1] (analytic) = 2.7345477822465785487315012530908 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2551222436423755484582133178752 relative error = 9.3295953831451743694538522803886 % h = 0.001 y2[1] (analytic) = 1.3214430343761601146994221046441 y2[1] (numeric) = 1.3245525911067524867099775738628 absolute error = 0.0031095567305923720105554692187 relative error = 0.23531523112991111860762855440123 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.826 y1[1] (analytic) = 2.7352259718252490495347687987877 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2558004332210460492614808635721 relative error = 9.3520767883886155325461437994853 % h = 0.001 y2[1] (analytic) = 1.3221779213144366077089393179268 y2[1] (numeric) = 1.3253175125057357815629638828125 absolute error = 0.0031395911912991738540245648857 relative error = 0.23745602922925568736038104640348 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.827 y1[1] (analytic) = 2.735903426178008993917929952807 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2564778875738059936446420175914 relative error = 9.3745226940301547073829687268813 % h = 0.001 y2[1] (analytic) = 1.3229134860747353011105078643946 y2[1] (numeric) = 1.3260833110033804762214501098747 absolute error = 0.0031698249286451751109422454801 relative error = 0.23960938957924436127119104399738 % h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.4MB, time=36.25 NO POLE NO POLE x[1] = 0.828 y1[1] (analytic) = 2.7365801446274040855755678468317 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2571546060232010853022799116161 relative error = 9.3969331220962167068710736332696 % h = 0.001 y2[1] (analytic) = 1.3236497279214914959024956574681 y2[1] (numeric) = 1.3268499865996865706854362550494 absolute error = 0.0032002586781950747829405975813 relative error = 0.24177534363418000781732438790024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.829 y1[1] (analytic) = 2.7372561264967159315057930597084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2578305878925129312325051244928 relative error = 9.4193080945807600062745365197812 % h = 0.001 y2[1] (analytic) = 1.3243866461184634066821930897261 y2[1] (numeric) = 1.3276175392946540649549223183366 absolute error = 0.0032308931761906582727292286105 relative error = 0.24395392279587075699420733067234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.83 y1[1] (analytic) = 2.7379313711099627187285802261381 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2585058325057597184552922909225 relative error = 9.441647633445280613090400418174 % h = 0.001 y2[1] (analytic) = 1.3251242399287328978875370821356 y2[1] (numeric) = 1.3283859690882829590299082997363 absolute error = 0.0032617291595500611423712176007 relative error = 0.24614515841363536325942892149313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.831 y1[1] (analytic) = 2.7386058777918998902675246848866 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.259180339187696889994236749671 relative error = 9.4639517606188159942711199902844 % h = 0.001 y2[1] (analytic) = 1.3258625086147062207151852362717 y2[1] (numeric) = 1.3291552759805732529103941992485 absolute error = 0.0032927673658670321952089629768 relative error = 0.24834908178430933808347573579796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.832 y1[1] (analytic) = 2.7392796458680208203943431848106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.259854107263817820121055249595 relative error = 9.4862204979979490604332623567348 % h = 0.001 y2[1] (analytic) = 1.3266014514381147507142031715169 y2[1] (numeric) = 1.3299254599715249465963800168733 absolute error = 0.0033240085334101958821768453564 relative error = 0.25056572415225184948421778848425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.833 y1[1] (analytic) = 2.739952674664557489135443404258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2605271360603544888621554690424 relative error = 9.508453867446812206693208447026 % h = 0.001 y2[1] (analytic) = 1.3273410676600157260546274536119 y2[1] (numeric) = 1.3306965210611380400878657526106 absolute error = 0.0033554534011223140332382989987 relative error = 0.25279511670935338492457096636873 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.4MB, time=36.90 NO POLE NO POLE x[1] = 0.834 y1[1] (analytic) = 2.7406249635084811560398877773265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2611994249042781557665998421109 relative error = 9.5306518907970914097719020481735 % h = 0.001 y2[1] (analytic) = 1.3280813565407929864701658460576 y2[1] (numeric) = 1.3314684592494125333848514064604 absolute error = 0.0033871027086195469146855604028 relative error = 0.25503729059504417395526073565027 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.835 y1[1] (analytic) = 2.741296511727503033208077859075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2618709731233000329347899238594 relative error = 9.5528145898480303810119904488806 % h = 0.001 y2[1] (analytic) = 1.3288223173401577128742959417292 y2[1] (numeric) = 1.3322412745363484264873369784227 absolute error = 0.0034189571961907136130410366935 relative error = 0.25729227689630336698720349776383 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.836 y1[1] (analytic) = 2.7419673186500749575804862010582 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2625417800458719573071982658426 relative error = 9.5749419863664347749519931413972 % h = 0.001 y2[1] (analytic) = 1.3295639493171491676490225586661 y2[1] (numeric) = 1.3330149669219457193953224684975 absolute error = 0.0034510176047965517462999098314 relative error = 0.2595601066476689665807050574241 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.837 y1[1] (analytic) = 2.7426373836053900624857634485088 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2632118450011870622124755132932 relative error = 9.5970341020866764531034234652651 % h = 0.001 y2[1] (analytic) = 1.3303062517301354356055536113409 y2[1] (numeric) = 1.3337895364062044121088078766848 absolute error = 0.0034832846760689765032542653439 relative error = 0.26184081083124850764144950640754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.838 y1[1] (analytic) = 2.743306705923383448447549111117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2638811673191804481742611759014 relative error = 9.6190909587106978025780723670068 % h = 0.001 y2[1] (analytic) = 1.3310492238368141656161534967937 y2[1] (numeric) = 1.3345649829891245046277932029846 absolute error = 0.0035157591523103390116397061909 relative error = 0.2641344203767304829161156933862 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.839 y1[1] (analytic) = 2.7439752849347328532493152006504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2645497463305298529760272654348 relative error = 9.6411125779080161092139436184842 % h = 0.001 y2[1] (analytic) = 1.3317928648942133129164323638407 y2[1] (numeric) = 1.3353413066707059969522784473969 absolute error = 0.0035484417764926840358460835562 relative error = 0.26644096616139651018341162343123 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=37.55 NO POLE NO POLE x[1] = 0.84 y1[1] (analytic) = 2.7446431199708593212565726706296 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.265217581366656320983284735414 relative error = 9.6630989813157279848496058955976 % h = 0.001 y2[1] (analytic) = 1.3325371741586918820773289631291 y2[1] (numeric) = 1.3361185074509488890822636099217 absolute error = 0.0035813332922570070049346467926 relative error = 0.26876047901013423753935889135676 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.841 y1[1] (analytic) = 2.7453102103639278719957713359055 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2658846717597248717224834006899 relative error = 9.6850501905385138483979990786157 % h = 0.001 y2[1] (analytic) = 1.3332821508859406706460441061175 y2[1] (numeric) = 1.3368965853298531810177486905591 absolute error = 0.0036144344439125103717045844416 relative error = 0.27109298969545098317878888273417 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.842 y1[1] (analytic) = 2.7459765554468481679892246932965 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2665510168426451677159367580809 relative error = 9.7069662271486424603720000075688 % h = 0.001 y2[1] (analytic) = 1.3340277943309830134551810921098 y2[1] (numeric) = 1.337675540307418872758733689309 absolute error = 0.0036477459764358593035525971992 relative error = 0.27343852893748810607822925891145 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.843 y1[1] (analytic) = 2.7466421545532751818453918084153 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2672166159490721815721038731997 relative error = 9.7288471126859755105153167211015 % h = 0.001 y2[1] (analytic) = 1.334774103748175527599348794266 y2[1] (numeric) = 1.3384553723836459643052186061714 absolute error = 0.0036812686354704367058698119054 relative error = 0.27579712740403610398866246263966 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.844 y1[1] (analytic) = 2.7473070070176098626038491784596 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.267881468413406862330561243244 relative error = 9.7506928686579722581935399364642 % h = 0.001 y2[1] (analytic) = 1.3355210783912088580784824280462 y2[1] (numeric) = 1.3392360815585344556572034411463 absolute error = 0.0037150031673255975787210131001 relative error = 0.27816881571055043515002692578983 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.845 y1[1] (analytic) = 2.7479711121749998013342862260498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2685455735707968010609982908342 relative error = 9.7725035165396942252014362026548 % h = 0.001 y2[1] (analytic) = 1.3362687175131084241071363588314 y2[1] (numeric) = 1.3400176678320843468146881942337 absolute error = 0.0037489503189759227075518354023 relative error = 0.28055362442016806014280561751537 % h = 0.001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.4MB, time=38.21 NO POLE NO POLE x[1] = 0.846 y1[1] (analytic) = 2.7486344693613398959888588251738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2692089307571368957155708899582 relative error = 9.7942790777738099406438187892222 % h = 0.001 y2[1] (analytic) = 1.3370170203662351660890026394896 y2[1] (numeric) = 1.3408001312042956377776728654336 absolute error = 0.003783110838060471688670225944 relative error = 0.28295158404372470029560483059616 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.847 y1[1] (analytic) = 2.7492970779132730155072360069414 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2698715393090700152339480717258 relative error = 9.8160195737705997375485799708115 % h = 0.001 y2[1] (analytic) = 1.3377659862022862932559083034306 y2[1] (numeric) = 1.341583471675168328546157454746 absolute error = 0.0038174854728820352902491513154 relative error = 0.28536272503977280907126795613079 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.848 y1[1] (analytic) = 2.7499589371681906631736757401562 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2705333985639876629003878049406 relative error = 9.837725025907960600871711943055 % h = 0.001 y2[1] (analytic) = 1.3385156142722960319705437742155 y2[1] (numeric) = 1.3423676892447024191201419621709 absolute error = 0.0038520749724063871495981879554 relative error = 0.28778707781460025285779373520449 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.849 y1[1] (analytic) = 2.7506200464642336392254664296844 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2711945078600306389521784944688 relative error = 9.8593954555314110665553831699381 % h = 0.001 y2[1] (analytic) = 1.3392659038266363746921740890535 y2[1] (numeric) = 1.3431527839128979094996263877083 absolute error = 0.0038868800862615348074522986548 relative error = 0.29022467272224969759413539543821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.85 y1[1] (analytic) = 2.7512804051402927027120715242355 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2718548665360897024387835890199 relative error = 9.8810308839540961713013725271652 % h = 0.001 y2[1] (analytic) = 1.3400168541150178296045839705385 y2[1] (numeric) = 1.3439387556797547996846107313582 absolute error = 0.0039219015647369700800267608197 relative error = 0.29267554006453869766484547588114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.851 y1[1] (analytic) = 2.7519400125360092326043153744632 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2725144739318062323310274392476 relative error = 9.9026313324567924527233951810239 % h = 0.001 y2[1] (analytic) = 1.3407684643864901709055071187424 y2[1] (numeric) = 1.3447256045452730896750949931207 absolute error = 0.0039571401587829187695878743783 relative error = 0.29513971009108048350150031405182 % h = 0.001 TOP MAIN SOLVE Loop memory used=228.8MB, alloc=4.4MB, time=38.86 NO POLE NO POLE x[1] = 0.852 y1[1] (analytic) = 2.7525988679917758881529492322585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2731733293875728878796612970429 relative error = 9.9241968222879129995430817391055 % h = 0.001 y2[1] (analytic) = 1.3415207338894431897567894342973 y2[1] (numeric) = 1.3455133305094527794710791729957 absolute error = 0.0039925966200095897142897386984 relative error = 0.29761721299930544433288741306737 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.853 y1[1] (analytic) = 2.7532569708487372684959370327215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2738314322445342682226490975059 relative error = 9.9457273746635125514955958382273 % h = 0.001 y2[1] (analytic) = 1.3422736618716074458945352223685 y2[1] (numeric) = 1.3463019335722938690725632709832 absolute error = 0.0040282717006864231780280486147 relative error = 0.30010807893448330253006752594869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.854 y1[1] (analytic) = 2.7539143204487905715138013515826 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.274488781844587571240513416367 relative error = 9.9672230107672926486120950074975 % h = 0.001 y2[1] (analytic) = 1.3430272475800550198984847674316 y2[1] (numeric) = 1.3470914137337963584795472870832 absolute error = 0.0040641661537413385810625196516 relative error = 0.30261233798974597599663059190895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.855 y1[1] (analytic) = 2.7545709161345862519323706827818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2751453775303832516590827475662 relative error = 9.9886837517506068295474553709929 % h = 0.001 y2[1] (analytic) = 1.3437814902612002661198710095412 y2[1] (numeric) = 1.3478817709939602476920312212957 absolute error = 0.0041002807327599815721602117545 relative error = 0.30513002020611112505874993946796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.856 y1[1] (analytic) = 2.7552267572495286786722699335127 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2758012186453256783989819982971 relative error = 10.010109618732465878622892546008 % h = 0.001 y2[1] (analytic) = 1.3445363891608005662670023942965 y2[1] (numeric) = 1.3486730053527855367100150736207 absolute error = 0.0041366161919849704430126793242 relative error = 0.30766115557250638031400174120316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.857 y1[1] (analytic) = 2.7558818431377767914444967872976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.276456304533573791171208852082 relative error = 10.03150063279954312125431896016 % h = 0.001 y2[1] (analytic) = 1.3452919435239570836478183109831 y2[1] (numeric) = 1.3494651168102722255334988440582 absolute error = 0.0041731732863151418856805330751 relative error = 0.31020577402579424790235587253072 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.4MB, time=39.51 NO POLE NO POLE x[1] = 0.858 y1[1] (analytic) = 2.7565361731442447565914273395692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2771106345400417563181394043536 relative error = 10.052856815006179767438481764173 % h = 0.001 y2[1] (analytic) = 1.3460481525951155180686628763995 y2[1] (numeric) = 1.3502581053664203141624825326082 absolute error = 0.0042099527713047960938196562087 relative error = 0.31276390545079768866725940238384 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.859 y1[1] (analytic) = 2.757189746614602622172595164811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2777642080103996218993072295954 relative error = 10.074178186374390302970125568308 % h = 0.001 y2[1] (analytic) = 1.3468050156180668613885221656564 y2[1] (numeric) = 1.3510519710212298025969661392707 absolute error = 0.0042469554031629412084439736143 relative error = 0.31533557968032636767932423950544 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.86 y1[1] (analytic) = 2.7578425628952769722945887295286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.278417024291073972021300794313 relative error = 10.095464767893867928064620389059 % h = 0.001 y2[1] (analytic) = 1.3475625318359481537279693357761 y2[1] (numeric) = 1.3518467137747006908369496640458 absolute error = 0.0042841819387525371089803282697 relative error = 0.31792082649520357059979528762587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.861 y1[1] (analytic) = 2.7584946213334515806844128212126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.279069082729248580411124885997 relative error = 10.116716580521990043061687470593 % h = 0.001 y2[1] (analytic) = 1.3483207004912432403320614332074 y2[1] (numeric) = 1.3526423336268329788824331069334 absolute error = 0.004321633135589738550371673726 relative error = 0.32051967562429378336571414270254 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.862 y1[1] (analytic) = 2.7591459212770680635056604199826 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.279720382672865063232372484767 relative error = 10.13793364518382378088704405207 % h = 0.001 y2[1] (analytic) = 1.3490795208257835290864310224247 y2[1] (numeric) = 1.3534388305776266667334164679335 absolute error = 0.0043593097518431376469854455088 relative error = 0.32313215674453093168350521248667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.863 y1[1] (analytic) = 2.7597964620748265314168421967984 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2803709234706235311435542615828 relative error = 10.159115982772131585949972699269 % h = 0.001 y2[1] (analytic) = 1.3498389920807487486858151195816 y2[1] (numeric) = 1.3542362046270817543898997470461 absolute error = 0.0043972125463330057040846274645 relative error = 0.32575829948094727682259547357878 % h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=40.17 NO POLE NO POLE x[1] = 0.864 y1[1] (analytic) = 2.7604462430761862408712215799592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2810207044719832405979336447436 relative error = 10.180263614147376839156001516383 % h = 0.001 y2[1] (analytic) = 1.3505991134966677074542632627533 y2[1] (numeric) = 1.3550344557751982418518829442712 absolute error = 0.0044353422785305343976196815179 relative error = 0.32839813340670296420563522505768 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.865 y1[1] (analytic) = 2.7610952636313662446575040901144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2816697250271632443842161548988 relative error = 10.201376560137729528715058413238 % h = 0.001 y2[1] (analytic) = 1.3513598843134190528162658986232 y2[1] (numeric) = 1.3558335840219761291193660596088 absolute error = 0.0044736997085570763031001609856 relative error = 0.3310516880431162212969144744303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.866 y1[1] (analytic) = 2.7617435230913460416807304031469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2823179844871430414074424679313 relative error = 10.222454841539071966426635633953 % h = 0.001 y2[1] (analytic) = 1.3521213037702320314180436145485 y2[1] (numeric) = 1.3566335893674154161923490930589 absolute error = 0.0045122855971833847743054785104 relative error = 0.33371899285969420129566732691184 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.867 y1[1] (analytic) = 2.7623910208078662259827233600927 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2829654822036632257094354248771 relative error = 10.24349847911500454912466996698 % h = 0.001 y2[1] (analytic) = 1.3528833711056872498982370947791 y2[1] (numeric) = 1.3574344718115161030708320446215 absolute error = 0.0045511007058288531725949498424 relative error = 0.33640007727416446914612427047726 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.868 y1[1] (analytic) = 2.763037756133429135001439903703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2836122175292261347281519684874 relative error = 10.264507493596851564966009463156 % h = 0.001 y2[1] (analytic) = 1.3536460855577174363072370302028 y2[1] (numeric) = 1.3582362313542781897548149142966 absolute error = 0.0045901457965607534475778840938 relative error = 0.33909497065250712638140888660927 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.869 y1[1] (analytic) = 2.7636837284212994970685796823498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2842581898170964967952917471342 relative error = 10.28548190568366704424749909902 % h = 0.001 y2[1] (analytic) = 1.3544094463636082021743925623504 y2[1] (numeric) = 1.3590388679957016762442977020842 absolute error = 0.0046294216320934740699051397338 relative error = 0.34180370230898757132368060187328 % h = 0.001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.4MB, time=40.84 NO POLE NO POLE x[1] = 0.87 y1[1] (analytic) = 2.7643289370255050781448028237228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2849033984213020778715148885072 relative error = 10.306421736042240654437875647675 % h = 0.001 y2[1] (analytic) = 1.3551734527599988052223361945172 y2[1] (numeric) = 1.3598423817357865625392804079844 absolute error = 0.0046689289757877573169442134672 relative error = 0.34452630150618989116829796230471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.871 y1[1] (analytic) = 2.7649733813008373277919101431513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2855478426966343275186222079357 relative error = 10.327327005307103639111816069062 % h = 0.001 y2[1] (analytic) = 1.3559381039828829127276624557362 y2[1] (numeric) = 1.3606467725745328486397630319971 absolute error = 0.0047086685916499359121005762609 relative error = 0.34726279745505088248521689756129 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.872 y1[1] (analytic) = 2.7656170606028520243813398144258 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2861915219986490241080518792102 relative error = 10.348197734080534800474634016756 % h = 0.001 y2[1] (analytic) = 1.3567033992676093655271969569926 y2[1] (numeric) = 1.3614520405119405345457455741223 absolute error = 0.0047486412443311690185486171297 relative error = 0.35001321931489469667634488178988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.873 y1[1] (analytic) = 2.7662599742878699195383352946765 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2868344356836669192650473594609 relative error = 10.369033942932566525167265589351 % h = 0.001 y2[1] (analytic) = 1.3574693378488829426690918334692 y2[1] (numeric) = 1.36225818554800962025722803436 absolute error = 0.0047888476991266775881362008908 relative error = 0.35277759619346810693314413527668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.874 y1[1] (analytic) = 2.7669021217129773818211400591947 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2874765831087743815478521239791 relative error = 10.389835652400990853042328241819 % h = 0.001 y2[1] (analytic) = 1.3582359189607651267079829217956 y2[1] (numeric) = 1.3630652076827401057742104127102 absolute error = 0.0048292887219749790662274909146 relative error = 0.35555595714697639324441438536803 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.875 y1[1] (analytic) = 2.7675435022360270396345754670545 y1[1] (numeric) = 2.4794255386042030002732879352156 memory used=244.1MB, alloc=4.4MB, time=41.49 absolute error = 0.2881179636318240393612875318389 relative error = 10.410602882991365588603175826304 % h = 0.001 y2[1] (analytic) = 1.359003141836674869643443377204 y2[1] (numeric) = 1.3638731069161319910966927091729 absolute error = 0.0048699650794571214532493319689 relative error = 0.35834833118011984200988756378608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.876 y1[1] (analytic) = 2.768184115215638423377358844013 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2887585766114354231040709087974 relative error = 10.431335655177020454799008063334 % h = 0.001 y2[1] (analytic) = 1.3597710057093893595009677922045 y2[1] (numeric) = 1.3646818832481852762246749237481 absolute error = 0.0049108775387959167237071315436 relative error = 0.36115474724613085682103250483528 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.877 y1[1] (analytic) = 2.7688239600111986068225196354215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2893984214069956065492317002059 relative error = 10.452033989399063288870224363298 % h = 0.001 y2[1] (analytic) = 1.3605395098110447875547202358586 y2[1] (numeric) = 1.3654915366788999611581570564358 absolute error = 0.0049520268678551736034368205772 relative error = 0.36397523424681167697629657585311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.878 y1[1] (analytic) = 2.769463035982862847730272248788 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2900374973786598474569843135724 relative error = 10.472697906066386279939339835383 % h = 0.001 y2[1] (analytic) = 1.3613086533731371161912789909656 y2[1] (numeric) = 1.366302067208276045897139107236 absolute error = 0.0049934138351389297058601162704 relative error = 0.36680982103257270030390256774845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.879 y1[1] (analytic) = 2.7701013424915552276927049731688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2906758038873522274194170379532 relative error = 10.493327425555672248043905546588 % h = 0.001 y2[1] (analytic) = 1.3620784356265228474136101254846 y2[1] (numeric) = 1.3671134748363135304416210761487 absolute error = 0.0050350392097906830280109506641 relative error = 0.36965853640247140687127245290616 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.88 y1[1] (analytic) = 2.770738878898969291209645130756 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2913133402947662909363571955404 relative error = 10.513922568211400964308995638046 % h = 0.001 y2[1] (analytic) = 1.3628488558014197919845013942779 y2[1] (numeric) = 1.367925759563012414791602963174 absolute error = 0.0050769037615926228071015688961 relative error = 0.37252140910425188016616413706006 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=247.9MB, alloc=4.4MB, time=42.14 x[1] = 0.881 y1[1] (analytic) = 2.771375644567568683995061384847 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2919501059633656837217734496314 relative error = 10.534483354345855511957940779423 % h = 0.001 y2[1] (analytic) = 1.3636199131274078392086873278103 y2[1] (numeric) = 1.3687389213883726989470847683118 absolute error = 0.0051190082609648597383974405015 relative error = 0.37539846783438492234068244659313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.882 y1[1] (analytic) = 2.772011638860587790513364897848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2925861002563847902400769626324 relative error = 10.555009804239128687861100655412 % h = 0.001 y2[1] (analytic) = 1.3643916068334297273528957257406 y2[1] (numeric) = 1.3695529603123943829080664915621 absolute error = 0.0051613534789646555551707658215 relative error = 0.37828974123810876011546066594331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.883 y1[1] (analytic) = 2.7726468611420323707449718030637 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2932213225378293704716838678481 relative error = 10.575501938139129444323577741384 % h = 0.001 y2[1] (analytic) = 1.3651639361477918147030451354242 y2[1] (numeric) = 1.3703678763350774666745481329249 absolute error = 0.0052039401872856519715029975007 relative error = 0.38119525790947033794750333144277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.884 y1[1] (analytic) = 2.7732813107766801961804902247626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.293855772172477195907202289547 relative error = 10.59595977626158937081388054835 % h = 0.001 y2[1] (analytic) = 1.3659369002981648512578222581931 y2[1] (numeric) = 1.3711836694564219502465296924002 absolute error = 0.0052467691582570989887074342071 relative error = 0.38411504639136719507143406451548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.885 y1[1] (analytic) = 2.7739149871300816850428958523849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2944894485258786847696079171693 relative error = 10.616383338790069215336646811076 % h = 0.001 y2[1] (analytic) = 1.3667104985115847510578675899006 y2[1] (numeric) = 1.372000339676427833624011169988 absolute error = 0.0052898411648430825661435800874 relative error = 0.3870491351755899230302033547874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.886 y1[1] (analytic) = 2.7745478895685605367370608467703 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2951223509643575364637729115547 relative error = 10.636772645875965445153635767425 % h = 0.001 y2[1] (analytic) = 1.3674847300144533651497969666091 y2[1] (numeric) = 1.3728178869950951168069925656883 absolute error = 0.0053331569806417516571955990792 relative error = 0.38999755270286520031767975226615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=251.7MB, alloc=4.4MB, time=42.80 x[1] = 0.887 y1[1] (analytic) = 2.7751800174592143655260016289292 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2957544788550113652527136937136 relative error = 10.65712771763851684655829374219 % h = 0.001 y2[1] (analytic) = 1.3682595940325392551842860514642 y2[1] (numeric) = 1.3736363114124237997954738795011 absolute error = 0.0053767173798845446111878280369 relative error = 0.39296032736289940076197326882217 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.888 y1[1] (analytic) = 2.7758113701699153334332118751625 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2963858315657123331599239399469 relative error = 10.677448574164811163410288715048 % h = 0.001 y2[1] (analytic) = 1.3690350897909784676474441647341 y2[1] (numeric) = 1.3744556129284138825894551114264 absolute error = 0.0054205231374354149420109466923 relative error = 0.39593748749442277228482129714099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.889 y1[1] (analytic) = 2.7764419470693107823704478162497 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2970164084651077820971598810341 relative error = 10.697735235509791774137497429935 % h = 0.001 y2[1] (analytic) = 1.369811216514275308724703225707 y2[1] (numeric) = 1.3752757915430653651889362614643 absolute error = 0.0054645750287900564642330357573 relative error = 0.39892906138523418267890440617222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.89 y1[1] (analytic) = 2.7770717475268238654903337129732 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2976462089226208652170457777576 relative error = 10.717987721696264406914012902407 % h = 0.001 y2[1] (analytic) = 1.3705879734263031197964469426198 y2[1] (numeric) = 1.3760968472563782475939173296147 absolute error = 0.0055088738300751277974703869949 relative error = 0.40193507727224642905155134556516 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.891 y1[1] (analytic) = 2.7777007709126541777631561554249 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2982752323084511774898682202093 relative error = 10.738206052714903892723820912406 % h = 0.001 y2[1] (analytic) = 1.3713653597503050535646047550548 y2[1] (numeric) = 1.3769187800683525298043983158776 absolute error = 0.0055534203180474762397935608228 relative error = 0.40495556334153210758993886803072 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.892 y1[1] (analytic) = 2.7783290165977783857772166093547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2989034779935753855039286741391 relative error = 10.758390248524260956020871242713 % h = 0.001 y2[1] (analytic) = 1.3721433747088948508094344022757 y2[1] (numeric) = 1.377741589978988211820379220253 absolute error = 0.0055982152700933610109448179773 relative error = 0.40799054772837004030959194219422 % h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.4MB, time=43.46 NO POLE NO POLE x[1] = 0.893 y1[1] (analytic) = 2.7789564839539508567621124092591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.2995309453497478564888244740435 relative error = 10.77854032905076904269734304801 % h = 0.001 y2[1] (analytic) = 1.3729220175240576177757163607833 y2[1] (numeric) = 1.3785652769882852936418600427409 absolute error = 0.0056432594642276758661436819576 relative error = 0.41104005851729225545474296574315 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.894 y1[1] (analytic) = 2.7795831723537042868343171749836 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.300157633749501286561029239768 relative error = 10.798656314188751185072973826444 % h = 0.001 y2[1] (analytic) = 1.373701287417150604187582764963 y2[1] (numeric) = 1.3793898410962437752688407833413 absolute error = 0.0056885536790931710812580183783 relative error = 0.41410412374213151822591408712897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.895 y1[1] (analytic) = 2.780209081170350328464432406308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3007835425661473281911444710924 relative error = 10.818738223800426903619388024426 % h = 0.001 y2[1] (analytic) = 1.3744811836089039818912027960585 y2[1] (numeric) = 1.3802152823028636567013214420542 absolute error = 0.0057340986939596748101186459957 relative error = 0.41718277138606940851694409588365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.896 y1[1] (analytic) = 2.7808342097779802171654827883184 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3014086711737772168921948531028 relative error = 10.838786077715919145134424346859 % h = 0.001 y2[1] (analytic) = 1.3752617053194216241245458968532 y2[1] (numeric) = 1.3810416006081449379393020188796 absolute error = 0.0057798952887233138147561220264 relative error = 0.42027602938168494235058993916564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.897 y1[1] (analytic) = 2.7814585575514653974016285193201 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3020330189472623971283405841045 relative error = 10.858799895733261257082520378351 % h = 0.001 y2[1] (analytic) = 1.3760428517681818854134435423582 y2[1] (numeric) = 1.3818687960120876189827825138175 absolute error = 0.0058259442439057335693389714593 relative error = 0.42338392561100373370879216249452 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.898 y1[1] (analytic) = 2.7820821238664581477166687526331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3026565852622551474433808174175 relative error = 10.878779697618403997818269157053 % h = 0.001 y2[1] (analytic) = 1.3768246221740383820931696705131 y2[1] (numeric) = 1.3826968685146916998317629268679 absolute error = 0.0058722463406533177385932563548 relative error = 0.42650648790554769346070285278237 % h = 0.001 TOP MAIN SOLVE Loop memory used=259.4MB, alloc=4.4MB, time=44.11 NO POLE NO POLE x[1] = 0.899 y1[1] (analytic) = 2.7827049080993922050817110238177 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3032793694951892048084230886021 relative error = 10.898725503105222582411314890871 % h = 0.001 y2[1] (analytic) = 1.3776070157552207734547592513822 y2[1] (numeric) = 1.3835258181159571804862432580309 absolute error = 0.0059188023607364070314840066487 relative error = 0.42964374404638526209863338418648 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.9 y1[1] (analytic) = 2.7833269096274833884613823157136 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.303901371023280388188094380498 relative error = 10.91863733189552376379180407652 % h = 0.001 y2[1] (analytic) = 1.3783900317293355435152838485929 y2[1] (numeric) = 1.3843556448158840609462235073064 absolute error = 0.0059656130865485174309396587135 relative error = 0.43279572176418217299918683399817 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.901 y1[1] (analytic) = 2.7839481278287302215979581951327 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3045225892245272213246702599171 relative error = 10.938515203659052948936653884742 % h = 0.001 y2[1] (analytic) = 1.3791736693133667834113024028072 y2[1] (numeric) = 1.3851863486144723412117036746944 absolute error = 0.0060126793011055578004012718872 relative error = 0.43596244873925274293399575346931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.902 y1[1] (analytic) = 2.7845685620819145550127872371293 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3051430234777115547394993019137 relative error = 10.958359138033501349817941820303 % h = 0.001 y2[1] (analytic) = 1.3799579277236769744147048438388 y2[1] (numeric) = 1.3860179295117220212826837601949 absolute error = 0.0060600017880450468679789163561 relative error = 0.4391439526016116865616894553841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.903 y1[1] (analytic) = 2.7851882117666021872243887354735 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3057626731623991869511008002579 relative error = 10.978169154624513168835759362738 % h = 0.001 y2[1] (analytic) = 1.380742806176007771570165515639 y2[1] (numeric) = 1.3868503875076331011591637638079 absolute error = 0.0061075813316253295889982481689 relative error = 0.4423402609310264516399655269565 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.904 y1[1] (analytic) = 2.7858070762631434851826024812843 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3063815376589404849093145460687 relative error = 10.997945273005692818458907553547 % h = 0.001 y2[1] (analytic) = 1.3815283038854807879534227767624 y2[1] (numeric) = 1.3876837226022055808411436855334 absolute error = 0.006155418716724792887720908771 relative error = 0.44555140125707007170393730725946 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=44.77 NO POLE NO POLE x[1] = 0.905 y1[1] (analytic) = 2.7864251549526740039181701757212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3069996163484710036448822405056 relative error = 11.017687512718612174797844327024 % h = 0.001 y2[1] (analytic) = 1.3823144200665983795496005180982 y2[1] (numeric) = 1.3885179347954394603286235253714 absolute error = 0.0062035147288410807790230072732 relative error = 0.44877740105917453296427199841669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.906 y1[1] (analytic) = 2.787042447217115105407128827208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3076169086129121051338408919924 relative error = 11.037395893272817864835321795661 % h = 0.001 y2[1] (analytic) = 1.3831011539332444307507867196122 y2[1] (numeric) = 1.3893530240873347396216032833219 absolute error = 0.0062518701540903088708165637097 relative error = 0.45201828776668465218602232795177 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.907 y1[1] (analytic) = 2.7876589524391745766493972688437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3082334138349715763761093336281 relative error = 11.057070434145838587041176706266 % h = 0.001 y2[1] (analytic) = 1.3838885046986851404720835485838 y2[1] (numeric) = 1.3901889904778914187200829593849 absolute error = 0.0063004857792062782479994108011 relative error = 0.45527408875891246231648766751306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.908 y1[1] (analytic) = 2.7882746700023472469609377174681 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3088491313981442466876497822525 relative error = 11.076711154783192465098758890113 % h = 0.001 y2[1] (analytic) = 1.3846764715755698088853428833566 y2[1] (numeric) = 1.3910258339671094976240625535605 absolute error = 0.0063493623915396887387196702039 relative error = 0.45854483136519210263791766332574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.909 y1[1] (analytic) = 2.78888959929091560447887508227 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3094640606867126042055871470544 relative error = 11.096318074598394434471500748796 % h = 0.001 y2[1] (analytic) = 1.3854650537759316247698005289301 y2[1] (numeric) = 1.3918635545549889763335420658486 absolute error = 0.0063985007790573515637415369185 relative error = 0.46183054286493521022839217392313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.91 y1[1] (analytic) = 2.7895037396899504118789575178716 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.310078201085747411605669582656 relative error = 11.115891212972963661539145657316 % h = 0.001 y2[1] (analytic) = 1.3862542505111884534788217738253 y2[1] (numeric) = 1.3927021522415298548485214962492 absolute error = 0.0064479017303414013696997224239 relative error = 0.46513125048768680952177506850707 % h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=45.42 NO POLE NO POLE x[1] = 0.911 y1[1] (analytic) = 2.7901170905853113213047425044789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3106915519811083210314545692633 relative error = 11.135430589256430995034164636675 % h = 0.001 y2[1] (analytic) = 1.3870440609921436255219703215436 y2[1] (numeric) = 1.3935416270267321331690008447623 absolute error = 0.0064975660345885076470305232187 relative error = 0.46844698141318169676524564687823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.912 y1[1] (analytic) = 2.7907296513636474885078935259636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.311304112759444488234605590748 relative error = 11.154936222766346449509898759956 % h = 0.001 y2[1] (analytic) = 1.387834484428986725761612014616 y2[1] (numeric) = 1.3943819789105958112949801113879 absolute error = 0.0065474944816090855333680967719 relative error = 0.47177776277140131618055953316812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.913 y1[1] (analytic) = 2.7913414214123981861989732056309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3119158828081951859256852704153 relative error = 11.174408132788286720572969518052 % h = 0.001 y2[1] (analytic) = 1.3886255200312943832232641547054 y2[1] (numeric) = 1.395223207893120889226459296126 absolute error = 0.0065976878618265060031951414206 relative error = 0.47512362164263112464288030710475 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.914 y1[1] (analytic) = 2.7919524001197934166081195489314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3125268615155904163348316137158 relative error = 11.193846338575862731613500793778 % h = 0.001 y2[1] (analytic) = 1.3894171670080310615189006084766 y2[1] (numeric) = 1.3960653139743073669634383989766 absolute error = 0.0066481469662763054445377905 relative error = 0.4784845850575184416987533079423 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.915 y1[1] (analytic) = 2.7925625868748545232549927324916 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.313137048270651522981704797276 relative error = 11.213250859350727211767694185639 % h = 0.001 y2[1] (analytic) = 1.390209424567549849882422275997 y2[1] (numeric) = 1.3969082971541552445059174199397 absolute error = 0.0066988725866053946234951439427 relative error = 0.48186067999713078175256341860084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.916 y1[1] (analytic) = 2.7931719810673948019273806695674 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3137464424631918016540927343518 relative error = 11.232621714302582304848294194797 % h = 0.001 y2[1] (analytic) = 1.3910022919175932548165018862618 y2[1] (numeric) = 1.3977521574326645218538963590153 absolute error = 0.0067498655150712670373944727535 relative error = 0.4852519333930146652586286566066 % h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.4MB, time=46.07 NO POLE NO POLE x[1] = 0.917 y1[1] (analytic) = 2.7937805820880201108678523733656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.31435504348381711059456443815 relative error = 11.251958922589187208979471250428 % h = 0.001 y2[1] (analytic) = 1.3917957682652939923500114730661 y2[1] (numeric) = 1.3985968948098351990073752162034 absolute error = 0.0068011265445412066573637431373 relative error = 0.48865837212725490576393051018672 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.918 y1[1] (analytic) = 2.7943883893281294801678489316321 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3149628507239264798945609964165 relative error = 11.271262503336365846673638709412 % h = 0.001 y2[1] (analytic) = 1.3925898528171757809052402738607 y2[1] (numeric) = 1.3994425092856672759663539915041 absolute error = 0.0068526564684914950611137176434 relative error = 0.49208002303253436965436961307796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.919 y1[1] (analytic) = 2.7949954021799157203686026984643 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3155698635757127200953147632487 relative error = 11.290532475638014565088704835516 % h = 0.001 y2[1] (analytic) = 1.3933845447791541347741101844421 y2[1] (numeric) = 1.4002890008601607527308326849173 absolute error = 0.0069044560810066179567225004752 relative error = 0.49551691289219420546536100171329 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.92 y1[1] (analytic) = 2.7956016200363660302682761024816 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.316176081432163029994988167266 relative error = 11.309768858556109866205242351083 % h = 0.001 y2[1] (analytic) = 1.3941798433565371582025952933256 y2[1] (numeric) = 1.401136369533315629300811296443 absolute error = 0.0069565261767784710982160031174 relative error = 0.49896906844029453962554629985274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.921 y1[1] (analytic) = 2.7962070422912626039347122642647 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3167815036870596036614243290491 relative error = 11.328971671120716166664036469614 % h = 0.001 y2[1] (analytic) = 1.3949757477540263400825514114488 y2[1] (numeric) = 1.4019846153051319056762898260812 absolute error = 0.0070088675511055655937384146324 relative error = 0.50243651636167563551040018471364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.922 y1[1] (analytic) = 2.7968116683391832369231904103635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3173861297349802366499024751479 relative error = 11.348140932329993587005447370691 % h = 0.001 y2[1] (analytic) = 1.3957722571757173492501609054418 y2[1] (numeric) = 1.4028337381756095818572682738319 absolute error = 0.0070614809998922326071073683901 relative error = 0.5059192832920195126905448668729 % h = 0.001 TOP MAIN SOLVE Loop memory used=274.6MB, alloc=4.4MB, time=46.73 NO POLE NO POLE x[1] = 0.923 y1[1] (analytic) = 2.797415497575501931698579866169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3179899589712989314252919309534 relative error = 11.367276661150205770052994878714 % h = 0.001 y2[1] (analytic) = 1.3965693708251008303901975360864 y2[1] (numeric) = 1.4036837381447486578437466396951 absolute error = 0.0071143673196478274535491036087 relative error = 0.50941739581791202326765852591853 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.924 y1[1] (analytic) = 2.7980185293963895022612872055464 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3185929907921865019879992703308 relative error = 11.386378876515727728184541663484 % h = 0.001 y2[1] (analytic) = 1.3973670879050632005453153977649 y2[1] (numeric) = 1.4045346152125491336357249236708 absolute error = 0.0071675273074859330904095259059 relative error = 0.51293088047690538219897115135546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.925 y1[1] (analytic) = 2.7986207631988141779763919313308 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3191952245946111777031039961152 relative error = 11.40544759732905371923541660328 % h = 0.001 y2[1] (analytic) = 1.3981654076178874462295654496762 y2[1] (numeric) = 1.405386369379011009233203125759 absolute error = 0.0072209617611235630036376760828 relative error = 0.51645976375758114851948351156486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.926 y1[1] (analytic) = 2.7992221983805422066053668576022 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3197966597763392063320789223866 relative error = 11.424482842460805150778782049361 % h = 0.001 y2[1] (analytic) = 1.3989643291652539211453425253694 y2[1] (numeric) = 1.4062390006441342846361812459597 absolute error = 0.0072746714788803634908387205903 relative error = 0.52000407209961365437922148407929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.927 y1[1] (analytic) = 2.7998228343401384565397801620681 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3203972957359354562664922268525 relative error = 11.443484630749738512529507614047 % h = 0.001 y2[1] (analytic) = 1.3997638517482411445029651037137 y2[1] (numeric) = 1.4070925090079189598446592842729 absolute error = 0.0073286572596778153416941805592 relative error = 0.52356383189383387882104820184827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.928 y1[1] (analytic) = 2.8004226704769670182363768749028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3209971318727640179630889396872 relative error = 11.462452981002753336618768782354 % h = 0.001 y2[1] (analytic) = 1.4005639745673265999420895217925 y2[1] (numeric) = 1.4079468944703650348586372406987 absolute error = 0.0073829199030384349165477189062 relative error = 0.52713906948229376323279987874335 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=47.38 NO POLE NO POLE x[1] = 0.929 y1[1] (analytic) = 2.8010217061911918048529383690117 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3215961675869888045796504337961 relative error = 11.481387911994900185487541128929 % h = 0.001 y2[1] (analytic) = 1.4013646968223875350541597083728 y2[1] (numeric) = 1.408802157031472509678115115237 absolute error = 0.0074374602090849746239554068642 relative error = 0.53072981115833096541578725289969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.93 y1[1] (analytic) = 2.8016199408837771520843192159106 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.322194402279574151811031280695 relative error = 11.500289442469388667148110217096 % h = 0.001 y2[1] (analytic) = 1.402166017712701761505092915567 y2[1] (numeric) = 1.4096582966912413843030929078878 absolute error = 0.0074922789785396227979999923208 relative error = 0.53433608316663404922001281009441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.931 y1[1] (analytic) = 2.8022173739564884171980615712348 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3227918353522854169247736360192 relative error = 11.519157591137595477563663374874 % h = 0.001 y2[1] (analytic) = 1.4029679364369484557574013260696 y2[1] (numeric) = 1.4105153134496716587335706186511 absolute error = 0.0075473770127232029761692925815 relative error = 0.53795791170330810670479380566731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.932 y1[1] (analytic) = 2.802814004811892577268988054311 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3233884662076895769957001190954 relative error = 11.537992376679072469896972492766 % h = 0.001 y2[1] (analytic) = 1.4037704521932089603909488139114 y2[1] (numeric) = 1.4113732073067633329695482475269 absolute error = 0.0076027551135543725785994336155 relative error = 0.54159532291594080979185208063819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.933 y1[1] (analytic) = 2.8034098328533588266121748872515 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3239842942491558263388869520359 relative error = 11.556793817741554750380116779881 % h = 0.001 y2[1] (analytic) = 1.4045735641789675860215415380431 y2[1] (numeric) = 1.4122319782625164070110257945152 absolute error = 0.0076584140835488209894842564721 relative error = 0.54524834290366888838633325423359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.934 y1[1] (analytic) = 2.8040048574850591734137078606457 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3245793188808561731404199254301 relative error = 11.575561932940968800558131057383 % h = 0.001 y2[1] (analytic) = 1.4053772715911124138165504502244 y2[1] (numeric) = 1.413091626316930880858003259616 absolute error = 0.0077143547258184670414528093916 relative error = 0.54891699771724503194964956494599 % h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=48.02 NO POLE NO POLE x[1] = 0.935 y1[1] (analytic) = 2.8045990781119690355586244951433 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3251735395077660352853365599277 relative error = 11.594296740861440625660398671 % h = 0.001 y2[1] (analytic) = 1.4061815736259360986067632016613 y2[1] (numeric) = 1.4139521514700067545104806428293 absolute error = 0.007770577844070655903717441168 relative error = 0.55260131335910521151650192033621 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.936 y1[1] (analytic) = 2.8051924941398678356554465710368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3257669555356648353821586358212 relative error = 11.612998260055303928854538476572 % h = 0.001 y2[1] (analytic) = 1.4069864694791366725936623366093 y2[1] (numeric) = 1.4148135537217440279684579441551 absolute error = 0.0078270842426073553747956075458 relative error = 0.55630131578343641915692709976924 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.937 y1[1] (analytic) = 2.8057851049753395952567080013595 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3263595663711365949834200661439 relative error = 11.631666509043108311138462603602 % h = 0.001 y2[1] (analytic) = 1.4077919583458183496513260657285 y2[1] (numeric) = 1.4156758330721427012319351635935 absolute error = 0.007883874726324351580609097865 relative error = 0.56001703089624482189273503608027 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.938 y1[1] (analytic) = 2.8063769100257735282748838280223 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3269513714215705280015958928067 relative error = 11.650301506313627496627205840977 % h = 0.001 y2[1] (analytic) = 1.4085980394204923302221473173594 y2[1] (numeric) = 1.4165389895212027743009123011444 absolute error = 0.007940950100710444078764983785 relative error = 0.56374848455542432708624818379107 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.939 y1[1] (analytic) = 2.8069679086993646335931269251073 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3275423700951616333198389898917 relative error = 11.668903270323867582992048525319 % h = 0.001 y2[1] (analytic) = 1.409404711897077606805566171065 y2[1] (numeric) = 1.4174030230689242471753893568078 absolute error = 0.0079983111718466403698231857428 relative error = 0.56749570257082555632782967088436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.94 y1[1] (analytic) = 2.8075581004051142868702197986342 y1[1] (numeric) = 2.4794255386042030002732879352156 memory used=286.1MB, alloc=4.4MB, time=48.68 absolute error = 0.3281325618009112865969318634186 relative error = 11.687471819499075316810372755571 % h = 0.001 y2[1] (analytic) = 1.410211974968901770039010184776 y2[1] (numeric) = 1.4182679337153071198553663305837 absolute error = 0.0080559587464053498163561458077 relative error = 0.57125871070432522485728873543847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.941 y1[1] (analytic) = 2.8081474845528308315391496778929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3287219459486278312658617426773 relative error = 11.706007172232746393585606615963 % h = 0.001 y2[1] (analytic) = 1.4110198278287018153702365346646 y2[1] (numeric) = 1.4191337214603513923408432224721 absolute error = 0.0081138936316495769706066878075 relative error = 0.57503753466989592356288038105228 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.942 y1[1] (analytic) = 2.8087360605531301689987158998209 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3293105219489271687254279646053 relative error = 11.724509346886633782197522873436 % h = 0.001 y2[1] (analytic) = 1.4118282696686249503202692954725 y2[1] (numeric) = 1.420000386304057064631820032473 absolute error = 0.0081721166354321143115507370005 relative error = 0.5788322001336763006102707590031 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.943 y1[1] (analytic) = 2.8093238278174363479975793948635 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3298982892132333477242914596479 relative error = 11.742978361790756073544067333187 % h = 0.001 y2[1] (analytic) = 1.4126372996802294023361245984231 y2[1] (numeric) = 1.4208679282464241367282967605864 absolute error = 0.0082306285661947343921721621633 relative error = 0.58264273271404163976252001834874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.944 y1[1] (analytic) = 2.8099107857579821532101648903185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3304852471537791529368769551029 relative error = 11.761414235243405853136797697275 % h = 0.001 y2[1] (analytic) = 1.41344691705448522723251581406 y2[1] (numeric) = 1.4217363472874526086302734068123 absolute error = 0.0082894302329673813977575927523 relative error = 0.58646915798167483246083977729883 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.945 y1[1] (analytic) = 2.8104969337878096930038272553123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3310713951836066927305393200967 relative error = 11.779816985511158097412916384683 % h = 0.001 y2[1] (analytic) = 1.4142571209817751182217303183736 y2[1] (numeric) = 1.4226056434271424803377499711507 absolute error = 0.0083485224453673621160196527771 relative error = 0.5903115014596377407446124827676 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=289.9MB, alloc=4.4MB, time=49.35 x[1] = 0.946 y1[1] (analytic) = 2.8110822713207709863966942202884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3316567327165679861234062850728 relative error = 11.798186630828878593527780346215 % h = 0.001 y2[1] (analytic) = 1.4150679106518952155308688124071 y2[1] (numeric) = 1.4234758166654937518507264536016 absolute error = 0.0084079060135985363198576411945 relative error = 0.59416978862344294809791426526291 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.947 y1[1] (analytic) = 2.8116667977715285492055985132169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3322412591673255489323105780013 relative error = 11.816523189399732382392667453412 % h = 0.001 y2[1] (analytic) = 1.4158792852540559166056375781701 y2[1] (numeric) = 1.4243468670025064231692028541651 absolute error = 0.008467581748450506563565275995 relative error = 0.59804404490112589531856099140581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.948 y1[1] (analytic) = 2.8122505125555559793835132646391 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3328249739513529791102253294235 relative error = 11.834826679395192224723472565874 % h = 0.001 y2[1] (analytic) = 1.4166912439768826868998834671338 y2[1] (numeric) = 1.4252187944381804942931791728411 absolute error = 0.0085275504612978073932957057073 relative error = 0.60193429567331739851449859703931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.949 y1[1] (analytic) = 2.8128334150891385415459053441629 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3334078764849355412726174089473 relative error = 11.853097118955047089866896895646 % h = 0.001 y2[1] (analytic) = 1.4175037860084168712500608318425 y2[1] (numeric) = 1.4260915989725159652226554096296 absolute error = 0.0085878129640990939725945777871 relative error = 0.60584056627331654634118298335963 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.95 y1[1] (analytic) = 2.8134155047893737506854221021026 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.333989966185170750412134166887 relative error = 11.871334526187410667171581799125 % h = 0.001 y2[1] (analytic) = 1.4183169105361165058338190262395 y2[1] (numeric) = 1.4269652806055128359576315645306 absolute error = 0.0086483700693963301238125382911 relative error = 0.60976288198716397360244131350364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.951 y1[1] (analytic) = 2.8139967810741719550743278016264 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3345712424699689548010398664108 relative error = 11.889538919168729899672522645768 % h = 0.001 y2[1] (analytic) = 1.4191306167468571307118985161905 y2[1] (numeric) = 1.4278398393371711064981076375441 absolute error = 0.0087092225903139757862091213536 relative error = 0.61370126805371550834617499566961 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=293.7MB, alloc=4.4MB, time=50.02 x[1] = 0.952 y1[1] (analytic) = 2.8145772433622569183541068390228 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3351517047580539180808189038072 relative error = 11.907710315943793539857979947351 % h = 0.001 y2[1] (analytic) = 1.419944903826932602952523058373 y2[1] (numeric) = 1.4287152751674907768440836286701 absolute error = 0.0087703713405581738915605702971 relative error = 0.61765574966471618959515452393877 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.953 y1[1] (analytic) = 2.815156891073166400811651662531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3357313524689634005383637273154 relative error = 11.925848734525740727288983490874 % h = 0.001 y2[1] (analytic) = 1.4207597709620559103374748232099 y2[1] (numeric) = 1.4295915880964718469955595379086 absolute error = 0.0088318171344159366580847146987 relative error = 0.62162635196487465286206721242036 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.954 y1[1] (analytic) = 2.8157357236272527398414541135974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3363101850230497395681661783818 relative error = 11.943954192896069587842400811363 % h = 0.001 y2[1] (analytic) = 1.4215752173373599856490387558386 y2[1] (numeric) = 1.4304687781241143169525353652596 absolute error = 0.008893560786754331303496609421 relative error = 0.62561310005193788060691025073173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.955 y1[1] (analytic) = 2.8163137404456834295932197284128 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3368882018414804293199317931972 relative error = 11.962026709004645854349413976456 % h = 0.001 y2[1] (analytic) = 1.4223912421373985215370018882395 y2[1] (numeric) = 1.4313468452504181867150111107231 absolute error = 0.0089556031130196651780092224836 relative error = 0.62961601897676631480377297787593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.956 y1[1] (analytic) = 2.8168909409504416998043253521668 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3374654023462386995310374169512 relative error = 11.980066300769711508402118342213 % h = 0.001 y2[1] (analytic) = 1.4232078445461467859648927355918 y2[1] (numeric) = 1.4322257894753834562829867742992 absolute error = 0.0090179449292366703180940387074 relative error = 0.63363513374340932879302337046136 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.957 y1[1] (analytic) = 2.8174673245643270938165412336083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3380417859601240935432532983927 relative error = 11.998072986077893443101823687374 % h = 0.001 y2[1] (analytic) = 1.4240250237470024382346453306867 y2[1] (numeric) = 1.4331056107990101256564623559878 absolute error = 0.0090805870520076874218170253011 relative error = 0.63767046930918105560390402469092 % h = 0.001 TOP MAIN SOLVE Loop memory used=297.5MB, alloc=4.4MB, time=50.69 NO POLE NO POLE x[1] = 0.958 y1[1] (analytic) = 2.8180428907109560457764395832387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3386173521067530455031516480231 relative error = 12.016046782784212146523501950666 % h = 0.001 y2[1] (analytic) = 1.4248427789227863455888718718004 y2[1] (numeric) = 1.4339863092212981948354378557889 absolute error = 0.0091435302985118492465659839885 relative error = 0.64172205058473656994155193842894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.959 y1[1] (analytic) = 2.8186176388147624570189123947776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.339192100210559456745624459562 relative error = 12.033987708712090405671686691323 % h = 0.001 y2[1] (analytic) = 1.4256611092557434003899273818234 y2[1] (numeric) = 1.4348678847422476638199132737025 absolute error = 0.0092067754865042634299858918791 relative error = 0.64578990243414842104148372945767 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.96 y1[1] (analytic) = 2.8191915683009982716332221464304 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3397660296967952713599342112148 relative error = 12.051895781653362030703987375677 % h = 0.001 y2[1] (analytic) = 1.4264800139275433378749491996481 y2[1] (numeric) = 1.4357503373618585326098886097286 absolute error = 0.0092703234343151947349394100805 relative error = 0.6498740496749835136036331234505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.961 y1[1] (analytic) = 2.8197646785957340512110098159569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3403391399915310509377218807413 relative error = 12.069771019368280599199236671347 % h = 0.001 y2[1] (analytic) = 1.4272994921192815544860535488458 y2[1] (numeric) = 1.4366336670801308012053638638672 absolute error = 0.0093341749608492467193103150214 relative error = 0.65397451707838033402709017513862 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.962 y1[1] (analytic) = 2.820336969125859548775685461578 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3409114305216565485023975263624 relative error = 12.087613439585528220248141113821 % h = 0.001 y2[1] (analytic) = 1.4281195430114799267748708535018 y2[1] (numeric) = 1.4375178738970644696063390361183 absolute error = 0.0093983308855845428314681826165 relative error = 0.65809132936912651917577131878437 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.963 y1[1] (analytic) = 2.8209084393190842818926274393802 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3414829007148812816193395041646 relative error = 12.105423060002224318145154807288 % h = 0.001 y2[1] (analytic) = 1.4289401657840876308806008967442 y2[1] (numeric) = 1.4384029578126595378128141264819 absolute error = 0.0094627920285719069322132297377 relative error = 0.66222451122573676491434554947447 % h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.4MB, time=51.34 NO POLE NO POLE x[1] = 0.964 y1[1] (analytic) = 2.8214790886039381049596171470655 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3420535499997351046863292118499 relative error = 12.123199898283934435461142240683 % h = 0.001 y2[1] (analytic) = 1.4297613596164819625807683439772 y2[1] (numeric) = 1.439288918826916005824789134958 absolute error = 0.0095275592104340432440207909808 relative error = 0.66637408728053107166285439070961 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.965 y1[1] (analytic) = 2.8220489164097717806769370036593 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3426233778055687804036490684437 relative error = 12.140943972064679055277239850195 % h = 0.001 y2[1] (analytic) = 1.4305831236874691579138585801337 y2[1] (numeric) = 1.4401757569398338736422640615466 absolute error = 0.0095926332523647157284054814129 relative error = 0.67054008211971332422759138186264 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.966 y1[1] (analytic) = 2.8226179221667575506965601951263 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3431923835625545504232722599107 relative error = 12.158655298946942442361166649562 % h = 0.001 y2[1] (analytic) = 1.4314054571752852143730132383785 y2[1] (numeric) = 1.4410634721514131412652389062478 absolute error = 0.0096580149761279268922256678693 relative error = 0.67472252028345020317495020218461 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.967 y1[1] (analytic) = 2.8231861053058897054498615367527 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3437605667016867051765736015371 relative error = 12.176333896501681503068072088021 % h = 0.001 y2[1] (analytic) = 1.4322283592575967126699642266353 y2[1] (numeric) = 1.4419520644616538086937136690615 absolute error = 0.0097237052040570960237494424262 relative error = 0.67892142626595042502410881761097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.968 y1[1] (analytic) = 2.8237534652589851531532796246302 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3443279266547821528799916894146 relative error = 12.193979782268334663748844291454 % h = 0.001 y2[1] (analytic) = 1.4330518291115016390683844880724 y2[1] (numeric) = 1.4428415338705558759276883499877 absolute error = 0.0097897047590542368593038619153 relative error = 0.68313682451554430854358977837247 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.969 y1[1] (analytic) = 2.8243200014586839879913612706282 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3448944628544809877180733354126 relative error = 12.211592973754830767449634003948 % h = 0.001 y2[1] (analytic) = 1.4338758659135302082858331622636 y2[1] (numeric) = 1.4437318803781193429671629490264 absolute error = 0.0098560144645891346813297867628 relative error = 0.68736873943476366444592359676414 % h = 0.001 TOP MAIN SOLVE Loop memory used=305.1MB, alloc=4.4MB, time=52.00 NO POLE NO POLE x[1] = 0.97 y1[1] (analytic) = 2.8248857133384500574766200378563 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3454601747342470572033321026407 relative error = 12.229173488437597988687178882994 % h = 0.001 y2[1] (analytic) = 1.4347004688396456869634722451501 y2[1] (numeric) = 1.4446231039843442098121374661776 absolute error = 0.0099226351446985228486652210275 relative error = 0.69161719538042200578384258582157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.971 y1[1] (analytic) = 2.8254506003325715289856415168064 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3460250617283685287123535815908 relative error = 12.246721343761572766085339320889 % h = 0.001 y2[1] (analytic) = 1.4355256370652452177027312781524 y2[1] (numeric) = 1.4455152046892304764626119014413 absolute error = 0.0099895676239852587598806232889 relative error = 0.69588221666369507636064623487558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.972 y1[1] (analytic) = 2.8260146618761614554708688061158 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3465891232719584551975808709002 relative error = 12.264236557140208752659080675839 % h = 0.001 y2[1] (analytic) = 1.4363513697651606436680960298383 y2[1] (numeric) = 1.4464081824927781429185862548175 absolute error = 0.0100568127276174992504902249792 relative error = 0.70016382755020169447660573168007 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.973 y1[1] (analytic) = 2.8265778974051583403475024862134 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3471523588009553400742145509978 relative error = 12.281719145955485783532957707705 % h = 0.001 y2[1] (analytic) = 1.4371776661136593337551965674268 y2[1] (numeric) = 1.4473020373949872091800605263062 absolute error = 0.0101243712813278754248639588794 relative error = 0.70446205226008490934251421276366 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.974 y1[1] (analytic) = 2.8271403063563267015549501989961 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3477147677521237012816622637805 relative error = 12.299169127557918860881975133604 % h = 0.001 y2[1] (analytic) = 1.4380045252844450083233695501071 y2[1] (numeric) = 1.4481967693958576752470347159074 absolute error = 0.0101922441114126669236651658003 relative error = 0.70877691496809346750074033445929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.975 y1[1] (analytic) = 2.8277018881672576347922617721328 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3482763495630546345189738369172 relative error = 12.316586519266567155883513556413 % h = 0.001 y2[1] (analytic) = 1.4388319464506585654918690116816 y2[1] (numeric) = 1.4490923784953895411195088236211 absolute error = 0.0102604320447309756276398119395 relative error = 0.71310843980366358660340541032199 % h = 0.001 TOP MAIN SOLVE Loop memory used=308.9MB, alloc=4.4MB, time=52.66 NO POLE NO POLE x[1] = 0.976 y1[1] (analytic) = 2.8282626422763693759269866526067 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3488371036721663756536987173911 relative error = 12.333971338369043027469822583032 % h = 0.001 y2[1] (analytic) = 1.4396599287848789079988993363884 y2[1] (numeric) = 1.4499888646935828067974828494474 absolute error = 0.010328935908703898798583513059 relative error = 0.71745665085100103390657826389749 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.977 y1[1] (analytic) = 2.8288225681229078625768912406878 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3493970295187048623036033054722 relative error = 12.351323602121521057671392747765 % h = 0.001 y2[1] (analytic) = 1.4404884714591237706226435689417 y2[1] (numeric) = 1.4508862279904374722809567933862 absolute error = 0.0103977565313137016583132244445 relative error = 0.72182157214916350684866670690428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.978 y1[1] (analytic) = 2.8293816651469472948639745426626 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.349956126542744294590686607447 relative error = 12.368643327748747103342324897523 % h = 0.001 y2[1] (analytic) = 1.4413175736448505481634596378282 y2[1] (numeric) = 1.4517844683859535375699306554375 absolute error = 0.0104668947411029894064710176093 relative error = 0.72620322769214331309047978533239 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.979 y1[1] (analytic) = 2.8299399327893906953402213883531 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3505143941851876950669334531375 relative error = 12.385930532444047364059619988651 % h = 0.001 y2[1] (analytic) = 1.4421472345129571239864165097351 y2[1] (numeric) = 1.4526835858801310026644044356013 absolute error = 0.0105363513671738786779879258662 relative error = 0.7306016414289503474037402524747 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.98 y1[1] (analytic) = 2.8304973704919704680845332877192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3510718318877674678112453525036 relative error = 12.403185233369337465989113798188 % h = 0.001 y2[1] (analytic) = 1.4429774532337826991233417326401 y2[1] (numeric) = 1.4535835804729698675643781338776 absolute error = 0.0106061272391871684410364012375 relative error = 0.73501683726369536280414174766188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.981 y1[1] (analytic) = 2.8310539776972489569702778296585 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3516284390930459566969898944429 relative error = 12.420407447655131561511579873773 % h = 0.001 y2[1] (analytic) = 1.4438082289771086219335512655861 y2[1] (numeric) = 1.4544844521644701322698517502664 absolute error = 0.0106762231873615103363004846803 relative error = 0.73944883905567353333436950056698 % h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.4MB, time=53.32 NO POLE NO POLE x[1] = 0.982 y1[1] (analytic) = 2.831609753848619003102898355503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3521842152444160028296104202874 relative error = 12.437597192400551444403320144884 % h = 0.001 y2[1] (analytic) = 1.4446395609121592183224319344801 y2[1] (numeric) = 1.4553862009546317967808252847677 absolute error = 0.0107466400424725784583933502876 relative error = 0.74389767061944830591183666703338 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.983 y1[1] (analytic) = 2.8321646983903045014270264696466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.352739159786101501153738534431 relative error = 12.454754484673335680366356001541 % h = 0.001 y2[1] (analytic) = 1.4454714482076026225170462954026 y2[1] (numeric) = 1.4562888268434548610972987373815 absolute error = 0.0108173786358522385802524419789 relative error = 0.74836335572493553866523025821087 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.984 y1[1] (analytic) = 2.8327188107673609565025407802402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3532932721631579562292528450246 relative error = 12.471879341509848752704123324131 % h = 0.001 y2[1] (analytic) = 1.4463038900315516083979291298914 y2[1] (numeric) = 1.4571923298309393252192721081078 absolute error = 0.0108884397993877168213429782164 relative error = 0.7528459180974879231933106781396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.985 y1[1] (analytic) = 2.8332720904256760374490160939396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.353846551821473037175728158724 relative error = 12.488971779915090222939362927146 % h = 0.001 y2[1] (analytic) = 1.4471368855515644213862442404742 y2[1] (numeric) = 1.4580967099170851891467453969467 absolute error = 0.0109598243655207677605011564725 relative error = 0.75734538141797968818876676612522 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.986 y1[1] (analytic) = 2.8338245368119701320580081203051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3543989982077671317847201850895 relative error = 12.506031816862703906171683169521 % h = 0.001 y2[1] (analytic) = 1.4479704339346456108854696593607 y2[1] (numeric) = 1.4590019671018924528797186038981 absolute error = 0.0110315331672468419942489445374 relative error = 0.76186176932289158187929358283263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.987 y1[1] (analytic) = 2.8343761493737969000726195736126 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.354950610769593899799331638397 relative error = 12.523059469294987060973054092611 % h = 0.001 y2[1] (analytic) = 1.4488045343472468632767788286789 y2[1] (numeric) = 1.459908101385361116418191728962 absolute error = 0.0111035670381142531414129002831 relative error = 0.76639510540439613074743261807016 % h = 0.001 TOP MAIN SOLVE Loop memory used=316.6MB, alloc=4.4MB, time=53.97 NO POLE NO POLE x[1] = 0.988 y1[1] (analytic) = 2.8349269275595438256337943925575 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3555013889553408253605064573419 relative error = 12.540054754122899593620272382406 % h = 0.001 y2[1] (analytic) = 1.4496391859552678354672847569453 y2[1] (numeric) = 1.4608151127674911797621647721384 absolute error = 0.0111759268122233442948800151931 relative error = 0.77094541321044317200009327215641 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.989 y1[1] (analytic) = 2.8354768708184327688927876316028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3560513322142297686194996963872 relative error = 12.557017688226073276464213723396 % h = 0.001 y2[1] (analytic) = 1.4504743879240569889903136035916 y2[1] (numeric) = 1.4617230012482826429116377334273 absolute error = 0.0112486133242256539213241298357 relative error = 0.77551271624484565726806001320618 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.99 y1[1] (analytic) = 2.8360259786005205167892594115471 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3566004399963175165159714763315 relative error = 12.573948288452820980236463725889 % h = 0.001 y2[1] (analytic) = 1.4513101394184124246568735913464 y2[1] (numeric) = 1.4626317668277355058666106128287 absolute error = 0.0113216274093230812097370214823 relative error = 0.78009703796736572502518118175938 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.991 y1[1] (analytic) = 2.8365742503566993329944421512648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3571487117524963327211542160492 relative error = 12.590846571620145920094690574926 % h = 0.001 y2[1] (analytic) = 1.4521464396025827177574845950707 y2[1] (numeric) = 1.4635414095058497686270834103426 absolute error = 0.0113949699032670508695988152719 relative error = 0.78469840179380103922633264955462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.992 y1[1] (analytic) = 2.8371216855386975070188311374976 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.357696146934494506745543202282 relative error = 12.607712554513750915208891875328 % h = 0.001 y2[1] (analytic) = 1.4529832876402677538135332052885 y2[1] (numeric) = 1.464451929282625431193056125969 absolute error = 0.0114686416423576773795229206805 relative error = 0.78931683109607139167265208838319 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.993 y1[1] (analytic) = 2.8376682835990799024838493250508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3582427449948769022105613898352 relative error = 12.624546253888047661691414862026 % h = 0.001 y2[1] (analytic) = 1.4538206826946195648773175151265 y2[1] (numeric) = 1.4653633261580624935645287597079 absolute error = 0.0115426434634429286872112445814 relative error = 0.79395234920230556562194712003822 % h = 0.001 TOP MAIN SOLVE Loop memory used=320.4MB, alloc=4.4MB, time=54.62 NO POLE NO POLE x[1] = 0.994 y1[1] (analytic) = 2.8382140439912485045569380957782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3587885053870455042836501605626 relative error = 12.641347686466166018674413216221 % h = 0.001 y2[1] (analytic) = 1.4546586239282431663799453306873 y2[1] (numeric) = 1.4662756001321609557415013115593 absolute error = 0.011616976203917789361555980872 relative error = 0.79860497939692845817159275281443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.995 y1[1] (analytic) = 2.8387589661694429665495265413068 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3593334275652399662762386060912 relative error = 12.658116868939963307339165183617 % h = 0.001 y2[1] (analytic) = 1.4554971105031973945262489570286 y2[1] (numeric) = 1.4671887512049208177239737815233 absolute error = 0.0116916407017234231977248244947 relative error = 0.8032747449207484589506499203386 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.996 y1[1] (analytic) = 2.8393030495887411556773326715804 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3598775109845381554040447363648 relative error = 12.674853817970033622702436539963 % h = 0.001 y2[1] (analytic) = 1.4563361415809957442358791649033 y2[1] (numeric) = 1.4681027793763420795119461695998 absolute error = 0.0117666377953463352760670046965 relative error = 0.80796166897104508266735728399215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.997 y1[1] (analytic) = 2.839846293705059697982450788966 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3604207551008566977091628537504 relative error = 12.691558550185717157965828198815 % h = 0.001 y2[1] (analytic) = 1.4571757163226072076297403972349 y2[1] (numeric) = 1.4690176846464247411054184757888 absolute error = 0.0118419683238175334756780785539 relative error = 0.81266577470165685306757240248274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.998 y1[1] (analytic) = 2.8403886979751545224166801058793 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3609631593709515221433921706637 relative error = 12.708231082185109541234801915319 % h = 0.001 y2[1] (analytic) = 1.4580158338884571130609287289657 y2[1] (numeric) = 1.4699334670151688025043907000903 absolute error = 0.0119176331267116894434619711246 relative error = 0.81738708522306943586916557461933 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 0.999 y1[1] (analytic) = 2.8409302618566214040855505226477 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3615047232524184038122625874321 relative error = 12.724871430535071184414828616052 % h = 0.001 y2[1] (analytic) = 1.4588564934384279646893335494061 y2[1] (numeric) = 1.4708501264825742637088628425043 absolute error = 0.0119936330441462990195292930982 relative error = 0.82212562360250401824679979240605 % h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.4MB, time=55.28 NO POLE NO POLE x[1] = 1 y1[1] (analytic) = 2.8414709848078965066525023216303 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3620454462036935063792143864147 relative error = 12.74147961177123664409285238639 % h = 0.001 y2[1] (analytic) = 1.459697694131860282599063392557 y2[1] (numeric) = 1.4717676630486411247188349030308 absolute error = 0.0120699689167808421197715104738 relative error = 0.8268814128640059324509629683944 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.001 y1[1] (analytic) = 2.8420108662882569239026773734589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3625853276840539236293894382433 relative error = 12.758055642398023994213009081703 % h = 0.001 y2[1] (analytic) = 1.4605394351275534434578557980464 y2[1] (numeric) = 1.4726860767133693855343068816698 absolute error = 0.0121466415858159420764510836234 relative error = 0.83165447598853352115455359778987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.002 y1[1] (analytic) = 2.842549905757821220465780291656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3631243671536182201924923564404 relative error = 12.774599538888644210356281905063 % h = 0.001 y2[1] (analytic) = 1.4613817155837665217176305433427 y2[1] (numeric) = 1.4736053674767590461552787784213 absolute error = 0.0122236518929925244376482350786 relative error = 0.83644483591404724212975795459373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.003 y1[1] (analytic) = 2.8430881026775499716974688128113 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3636625640733469714241808775957 relative error = 12.791111317685110565434517119844 % h = 0.001 y2[1] (analytic) = 1.4622245346582191313553450467597 y2[1] (numeric) = 1.4745255353388101065817505932853 absolute error = 0.0123010006805909752264055465256 relative error = 0.84125251553559900986739548048844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.004 y1[1] (analytic) = 2.8436254565092463027187335209743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3641999179050433024454455857587 relative error = 12.807590995198248036609961348992 % h = 0.001 y2[1] (analytic) = 1.4630678915080922681533102004696 y2[1] (numeric) = 1.4754465802995225668137223262619 absolute error = 0.0123786887914302986604121257923 relative error = 0.84607753770542177176034888349639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=328.0MB, alloc=4.4MB, time=55.93 x[1] = 1.005 y1[1] (analytic) = 2.844161966715556426612727876925 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3647364281113534263394399417094 relative error = 12.82403858780770272325221766133 % h = 0.001 y2[1] (analytic) = 1.4639117852900291525181243532775 y2[1] (numeric) = 1.476368502358896426851193977351 absolute error = 0.0124567170688672743330696240735 relative error = 0.85091992523301931648213630347868 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.006 y1[1] (analytic) = 2.8446976327599701817785103555398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3652720941557671815052224203242 relative error = 12.840454111861951275745250867654 % h = 0.001 y2[1] (analytic) = 1.4647562151601360728373826242936 y2[1] (numeric) = 1.4772913015169316866941655465526 absolute error = 0.012535086356795613856782922259 relative error = 0.85577970088525631220112440731744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.007 y1[1] (analytic) = 2.8452324541068215684411613375549 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3658069155026185681678734023393 relative error = 12.856837583678310334957803152915 % h = 0.001 y2[1] (analytic) = 1.4656011802739832293733181908644 y2[1] (numeric) = 1.4782149777736283463426370338667 absolute error = 0.0126137974996451169693188430023 relative error = 0.86065688738644857228032313497462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.008 y1[1] (analytic) = 2.8457664302212892843177382456532 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3663408916170862840444503104376 relative error = 12.873189019542945982191309363741 % h = 0.001 y2[1] (analytic) = 1.4664466797866055786925316571923 y2[1] (numeric) = 1.4791395311289864057966084392933 absolute error = 0.012692851342380827104076782101 relative error = 0.86555150741845354612214471847745 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.009 y1[1] (analytic) = 2.8462995605693972594385332589671 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3668740219651942591652453237515 relative error = 12.889508435710883199420126960964 % h = 0.001 y2[1] (analytic) = 1.467292712852503678630964073983 y2[1] (numeric) = 1.4800649615830058650560797628324 absolute error = 0.0127722487305021864251156888494 relative error = 0.87046358362076103282695123092845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.01 y1[1] (analytic) = 2.846831844618015190123098784782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3674063060138121898498108495664 relative error = 12.905795848406015339639618842126 % h = 0.001 y2[1] (analytic) = 1.4681392786256445337932686442208 y2[1] (numeric) = 1.480991269135686724121051004484 absolute error = 0.0128519905100421903277823602632 relative error = 0.87539313859058411534365598593341 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=331.8MB, alloc=4.4MB, time=56.58 NO POLE x[1] = 1.011 y1[1] (analytic) = 2.8473632818348590721105067114598 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3679377432306560718372187762442 relative error = 12.922051273821113607138347947521 % h = 0.001 y2[1] (analytic) = 1.4689863762594624415857356157674 y2[1] (numeric) = 1.4819184537870289829915221642481 absolute error = 0.0129320775275665414057865484807 relative error = 0.88034019488295031280008429737446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.012 y1[1] (analytic) = 2.8478938716884917328433083123683 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3684683330842887325700203771527 relative error = 12.938274728117836547511360792789 % h = 0.001 y2[1] (analytic) = 1.4698340049068598387819243279326 y2[1] (numeric) = 1.4828465155370326416674932421247 absolute error = 0.0130125106301728028855689141921 relative error = 0.8853047750107929487102381231039 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.013 y1[1] (analytic) = 2.8484236136483233629046625169003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3689980750441203626313745816847 relative error = 12.95446622742673954723225282928 % h = 0.001 y2[1] (analytic) = 1.4706821637202081486201558464534 y2[1] (numeric) = 1.4837754543856977001489642381138 absolute error = 0.0130932906654895515288083916604 relative error = 0.89028690144504273276504665729219 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.014 y1[1] (analytic) = 2.8489525071846120466081011114986 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.369526968580409046334813176283 relative error = 12.970625787847284342602421828244 % h = 0.001 y2[1] (analytic) = 1.4715308518513486284320190894609 y2[1] (numeric) = 1.4847052703330241584359351522155 absolute error = 0.0131744184816755300039160627546 relative error = 0.89528659661471955392262070783263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.015 y1[1] (analytic) = 2.8494805517684642917394002809662 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3700550131642612914661123457506 relative error = 12.98675342544784853789662632419 % h = 0.001 y2[1] (analytic) = 1.472380068451593217801042815998 y2[1] (numeric) = 1.4856359633790120165284059844297 absolute error = 0.0132558949274187987273631684317 relative error = 0.9003038829070244825234624050831 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.016 y1[1] (analytic) = 2.850007746871835558450028748234 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3705822082676325581767408130184 relative error = 13.002849156265735132524674544174 % h = 0.001 y2[1] (analytic) = 1.4732298126717253872506853184886 y2[1] (numeric) = 1.4865675335236612744263767347564 absolute error = 0.0133377208519358871756914162678 relative error = 0.90533878266743197916551314480582 % h = 0.001 TOP MAIN SOLVE Loop memory used=335.6MB, alloc=4.4MB, time=57.23 NO POLE NO POLE x[1] = 1.017 y1[1] (analytic) = 2.8505340919675307873016436191816 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.371108553363327787028355683966 relative error = 13.018912996307182057029775201237 % h = 0.001 y2[1] (analytic) = 1.4740800836620009874607931312371 y2[1] (numeric) = 1.4874999807669719321298474031956 absolute error = 0.0134198971049709446690542719585 relative error = 0.91039131819978230808335138366382 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.018 y1[1] (analytic) = 2.8510595865292049264611058880601 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3716340479250019261878179528445 relative error = 13.034944961547371717744785049455 % h = 0.001 y2[1] (analytic) = 1.4749308805721490990116795385718 y2[1] (numeric) = 1.4884333051089439896388179897473 absolute error = 0.0135024245367948906271384511755 relative error = 0.91546151176637415278527769348713 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.019 y1[1] (analytic) = 2.8515842300313634580454884085451 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3721586914271604577722004733295 relative error = 13.050945067930440549928289192668 % h = 0.001 y2[1] (analytic) = 1.4757822025513728826549731386242 y2[1] (numeric) = 1.4893675065495774469532884944115 absolute error = 0.0135853039982045642983153557873 relative error = 0.92054938558805743171144705774718 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.02 y1[1] (analytic) = 2.8521080219493629236165499854554 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3726824833451599233432620502398 relative error = 13.066913331369488579203148816855 % h = 0.001 y2[1] (analytic) = 1.4766340487483504301103861919662 y2[1] (numeric) = 1.4903025850888723040732589171882 absolute error = 0.013668536340521873962872725222 relative error = 0.92565496184432631168562747882482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.021 y1[1] (analytic) = 2.8526309617594114488241500927072 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3732054231552084485508621574916 relative error = 13.082849767746588991120847284876 % h = 0.001 y2[1] (analytic) = 1.4774864183112356153875519584076 y2[1] (numeric) = 1.4912385407268285609987292580774 absolute error = 0.0137521224155929456111772996698 relative error = 0.93077826267341241694257927906173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.022 y1[1] (analytic) = 2.8531530489385692671980795741338 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3737275103343662669247916389182 relative error = 13.098754392912797708675659399691 % h = 0.001 y2[1] (analytic) = 1.4783393103876589466320797001881 y2[1] (numeric) = 1.4921753734634462177296995170791 absolute error = 0.013836063075787271097619816891 relative error = 0.93591931017237823152246074588969 % h = 0.001 TOP MAIN SOLVE Loop memory used=339.5MB, alloc=4.4MB, time=57.89 NO POLE NO POLE x[1] = 1.023 y1[1] (analytic) = 2.8536742829647492430877835353817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3742487443605462428144956001661 relative error = 13.114627222688162977593360115685 % h = 0.001 y2[1] (analytic) = 1.4791927241247284184949755055798 y2[1] (numeric) = 1.4931130832987252742661696941933 absolute error = 0.0139203591739968557711941886135 relative error = 0.9410781263972106928330727177216 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.024 y1[1] (analytic) = 2.854194663316717393749453487206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3747691247125143934761655519904 relative error = 13.130468272861734959219878065323 % h = 0.001 y2[1] (analytic) = 1.4800466586690303650245765635492 y2[1] (numeric) = 1.4940516702326657306081397894201 absolute error = 0.0140050115636353655835632258709 relative error = 0.94625473336291497419015706115352 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.025 y1[1] (analytic) = 2.8547141894740934105799666531149 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3752886508698904103066787178993 relative error = 13.146277559191575330835985977277 % h = 0.001 y2[1] (analytic) = 1.4809011131666303130801459976169 y2[1] (numeric) = 1.4949911342652675867556098027594 absolute error = 0.0140900210986372736754638051425 relative error = 0.95144915304360845415536148181166 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.026 y1[1] (analytic) = 2.8552328609173511794971512074687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3758073223131481792238632722531 relative error = 13.162055097404766893224804400418 % h = 0.001 y2[1] (analytic) = 1.4817560867630738362662748453913 y2[1] (numeric) = 1.4959314753965308427085797342112 absolute error = 0.0141753886334570064423048888199 relative error = 0.95666140737261487050087547476845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.027 y1[1] (analytic) = 2.8557506771278193004658570638093 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3763251385236163001925691285937 relative error = 13.177800903197423185319577122801 % h = 0.001 y2[1] (analytic) = 1.4826115786033874093872372494439 y2[1] (numeric) = 1.4968726936264554984670495837755 absolute error = 0.0142611150230680890798123343316 relative error = 0.96189151824255865663912919072883 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.028 y1[1] (analytic) = 2.8562676375876816061693126873962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3768420989834786058960247521806 relative error = 13.193514992234698105759856294169 % h = 0.001 y2[1] (analytic) = 1.4834675878320792634204444052437 y2[1] (numeric) = 1.4978147889550415540310193514523 absolute error = 0.0143472011229622906105749462086 relative error = 0.96713950750545945836532830915582 % h = 0.001 TOP MAIN SOLVE Loop memory used=343.3MB, alloc=4.4MB, time=58.54 NO POLE NO POLE x[1] = 1.029 y1[1] (analytic) = 2.8567837417799776798252492606312 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3773582031757746795519613254156 relative error = 13.209197380150795541184912531271 % h = 0.001 y2[1] (analytic) = 1.4843241135931402410081422927682 y2[1] (numeric) = 1.4987577613822890094004890372416 absolute error = 0.0144336477891487683923467444734 relative error = 0.97240539697282682876997340960167 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.03 y1[1] (analytic) = 2.8572989891886033721462743852944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3778734505844003718729864500788 relative error = 13.224848082548979001093860215981 % h = 0.001 y2[1] (analytic) = 1.4851811550300446524664977001626 y2[1] (numeric) = 1.4997016109081978645754586411434 absolute error = 0.0145204558781532121089609409808 relative error = 0.97768920841575509918788156021811 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.031 y1[1] (analytic) = 2.8578133792983113174439783612591 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3783878406941083171706904260435 relative error = 13.240467115001581259102660793387 % h = 0.001 y2[1] (analytic) = 1.4860387112857511323112165304354 y2[1] (numeric) = 1.5006463375327681195559281631577 absolute error = 0.0146076262470169872447116327223 relative error = 0.98299096356501842405959064199914 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.032 y1[1] (analytic) = 2.8583269115947114488762569376219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3789013729905084486029690024063 relative error = 13.256054493050014000428837148847 % h = 0.001 y2[1] (analytic) = 1.4868967815027034962988378656402 y2[1] (numeric) = 1.5015919412559997743418976032845 absolute error = 0.0146951597532962780430597376443 relative error = 0.98831068411116599759038304715773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.033 y1[1] (analytic) = 2.85883958556427151283733528897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3794140469600685125640473537544 relative error = 13.27161023220477747543540009674 % h = 0.001 y2[1] (analytic) = 1.4877553648228315989828467473245 y2[1] (numeric) = 1.5025384220778928289333669615239 absolute error = 0.0147830572550612299505202141994 relative error = 0.99364839170461744010151457800524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.034 y1[1] (analytic) = 2.8593514006943175824899788268026 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.379925862090114582216690891587 relative error = 13.287134347945470159066153656605 % h = 0.001 y2[1] (analytic) = 1.4886144603875521917837481172009 y2[1] (numeric) = 1.5034857799984472833303362378758 absolute error = 0.0148713196108950915465881206749 relative error = 0.9990041079557583519775763822879 % h = 0.001 TOP MAIN SOLVE Loop memory used=347.1MB, alloc=4.4MB, time=59.20 NO POLE NO POLE x[1] = 1.035 y1[1] (analytic) = 2.8598623564730345704393773139402 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3804368178688315701660893787246 relative error = 13.302626855720798416005209132335 % h = 0.001 y2[1] (analytic) = 1.489474067337769781572243848041 y2[1] (numeric) = 1.5044340150176631375328054323402 absolute error = 0.0149599476798933559605615842992 relative error = 1.0043778544350360331232523445981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.036 y1[1] (analytic) = 2.8603724523894667405481896080782 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3809469137852637402749016728626 relative error = 13.318087770948586171394199054106 % h = 0.001 y2[1] (analytic) = 1.4903341848138774897646542816844 y2[1] (numeric) = 1.5053831271355403915407745449171 absolute error = 0.0150489423216629017761202632327 relative error = 1.0097696526730553658520612687771 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.037 y1[1] (analytic) = 2.8608816879335182188922372194854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3814561493293152186189492842698 relative error = 13.33351710901578458694134079869 % h = 0.001 y2[1] (analytic) = 1.4911948119557579119297251788145 y2[1] (numeric) = 1.5063331163520790453542435756065 absolute error = 0.015138304396321133424518396792 relative error = 1.015179524160674859138992190907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.038 y1[1] (analytic) = 2.8613900625959535038563357271943 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3819645239917505035830477919787 relative error = 13.348914885278481742257156178489 % h = 0.001 y2[1] (analytic) = 1.4920559479027839779059604737648 y2[1] (numeric) = 1.5072839826672790989732125244084 absolute error = 0.0152280347644951210672520506436 relative error = 1.0206074903491028521782520180551 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.039 y1[1] (analytic) = 2.861897575868397975369753957895 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3824720372641949750964660226794 relative error = 13.364281115061912321252307491061 % h = 0.001 y2[1] (analytic) = 1.4929175917938198124286207170946 y2[1] (numeric) = 1.5082357260811405523976813913228 absolute error = 0.0153181342873207399690606742282 relative error = 1.0260535726499938751966471570121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.04 y1[1] (analytic) = 2.8624042272433384032807916921162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3829786886391354030075037569006 relative error = 13.379615813660467303433662455958 % h = 0.001 y2[1] (analytic) = 1.4937797427672215962655265790078 y2[1] (numeric) = 1.5091883465936634056276501763497 absolute error = 0.0154086038264418093621235973419 relative error = 1.03151779243554516548241464543 % h = 0.001 TOP MAIN SOLVE Loop memory used=350.9MB, alloc=4.4MB, time=59.87 NO POLE NO POLE x[1] = 1.041 y1[1] (analytic) = 2.8629100162141234548699675231574 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3834844776099204545966795879418 relative error = 13.394918996337703659935350141982 % h = 0.001 y2[1] (analytic) = 1.4946423999608384278608062778836 y2[1] (numeric) = 1.5101418442048476586631188794891 absolute error = 0.0154994442440092308023126016055 relative error = 1.0370001710385933365986032926151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.042 y1[1] (analytic) = 2.863414942274964201501309355628 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3839894036707612012280214204124 relative error = 13.410190678326354054122217412702 % h = 0.001 y2[1] (analytic) = 1.4955055625120131854857252902416 y2[1] (numeric) = 1.511096218914693311504087500741 absolute error = 0.0155906564026801260183622104994 relative error = 1.0425007297527111987593812487217 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.043 y1[1] (analytic) = 2.8639190049209346244112408923424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3844934663167316241379529571268 relative error = 13.425430874828336546603740598504 % h = 0.001 y2[1] (analytic) = 1.4963692295575833898957361913855 y2[1] (numeric) = 1.5120514707232003641505560401055 absolute error = 0.01568224116561697425481984872 relative error = 1.0480194898323047283569130206712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.044 y1[1] (analytic) = 2.8644222036479721196345583207306 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.384996665043769119361270385515 relative error = 13.440639601014764304497090047191 % h = 0.001 y2[1] (analytic) = 1.4972334002338820674928859697464 y2[1] (numeric) = 1.5130075996303688166025244975825 absolute error = 0.0157741993964867491096385278361 relative error = 1.0535564724927101846357060158879 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.045 y1[1] (analytic) = 2.8649245379528780020669922728253 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3854989993486750017937043376097 relative error = 13.455816872025955314778685918841 % h = 0.001 y2[1] (analytic) = 1.4980980736767386139927176525903 y2[1] (numeric) = 1.513964605636198668859992873172 absolute error = 0.0158665319594600548672752205817 relative error = 1.0591116989102913715205739967654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=354.7MB, alloc=4.4MB, time=60.54 x[1] = 1.046 y1[1] (analytic) = 2.8654260073333180086638509963099 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3860004687291150083905630610943 relative error = 13.470962702971442101564222082398 % h = 0.001 y2[1] (analytic) = 1.4989632490214796585948025762604 y2[1] (numeric) = 1.514922488740689920922961166874 absolute error = 0.0159592397192102623281585906136 relative error = 1.064685190222537042613602148255 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.047 y1[1] (analytic) = 2.8659266112878228007742415380223 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3865010726836198005009536028067 relative error = 13.486077108929981447157771247582 % h = 0.001 y2[1] (analytic) = 1.499828925402929928656039130494 y2[1] (numeric) = 1.5158812489438425727914293786885 absolute error = 0.0160523235409126441353902481945 relative error = 1.0702769675281584473847255793575 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.048 y1[1] (analytic) = 2.8664263493157884656103666057382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3870008107115854653370786705226 relative error = 13.501160104949564116711218534308 % h = 0.001 y2[1] (analytic) = 1.5006951019554131148658533035871 y2[1] (numeric) = 1.5168408862456566244653975086155 absolute error = 0.0161457842902435095995442050284 relative error = 1.0758870518871870165897497791968 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.049 y1[1] (analytic) = 2.8669252209174770168513956389767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3874996823132740165781077037611 relative error = 13.516211706047424586335902549331 % h = 0.001 y2[1] (analytic) = 1.5015617778127527369224358532785 y2[1] (numeric) = 1.517801400646132075944865556655 absolute error = 0.0162396228333793390224297033765 relative error = 1.0815154643210721849588476150364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.05 y1[1] (analytic) = 2.8674232255940168943814094850003 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3879976869898138941081215497847 relative error = 13.531231927210050774508972714008 % h = 0.001 y2[1] (analytic) = 1.5024289521082730097091504271879 y2[1] (numeric) = 1.518762792145268927229833522807 absolute error = 0.0163338400369959175206830956191 relative error = 1.0871622258127793492077626804549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.051 y1[1] (analytic) = 2.8679203628474034631609189421053 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3884948242432004628876310068897 relative error = 13.546220783393193776617599074756 % h = 0.001 y2[1] (analytic) = 1.5032966239747997099702464564727 y2[1] (numeric) = 1.5197250607430671783203014070715 absolute error = 0.0164284367682674683500549505988 relative error = 1.0928273573068879594331329661781 % h = 0.001 TOP MAIN SOLVE Loop memory used=358.5MB, alloc=4.4MB, time=61.19 NO POLE NO POLE x[1] = 1.052 y1[1] (analytic) = 2.8684166321804995112314582987262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3889910935762965109581703635106 relative error = 13.561178289521877602484796136266 % h = 0.001 y2[1] (analytic) = 1.5041647925446610434850101470624 y2[1] (numeric) = 1.5206882064395268292162692094486 absolute error = 0.0165234138948657857312590623862 relative error = 1.0985108797096897419625217256373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.053 y1[1] (analytic) = 2.8689120330970357468527558638018 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3894864944928327465794679285862 relative error = 13.576104460490408916721245393888 % h = 0.001 y2[1] (analytic) = 1.5050334569496885127394863943916 y2[1] (numeric) = 1.5216522292346478799177369299382 absolute error = 0.0166187722849593671782505355466 relative error = 1.1042128138892870517389038356163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.054 y1[1] (analytic) = 2.8694065651016112947719843512738 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3899810264974082944986964160582 relative error = 13.590999311162386781748122213001 % h = 0.001 y2[1] (analytic) = 1.5059026163212177850949039499833 y2[1] (numeric) = 1.5226171291284303304247045685403 absolute error = 0.016714512807212545329800618557 relative error = 1.1099331806756913523285057053767 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.055 y1[1] (analytic) = 2.8699002276996941916245948495095 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3904746890954911913513069142939 relative error = 13.605862856370712403336551516647 % h = 0.001 y2[1] (analytic) = 1.5067722697900895614519356715277 y2[1] (numeric) = 1.5235829061208741807371721252549 absolute error = 0.0168106363307846192852364537272 relative error = 1.1156720008609218216500346633891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.056 y1[1] (analytic) = 2.8703930203976218804662389748547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3909674817934188801929510396391 relative error = 13.620695110917598878509933405366 % h = 0.001 y2[1] (analytic) = 1.5076424164866504454099251922705 y2[1] (numeric) = 1.524549560211979430855139600082 absolute error = 0.0169071437253289854452144078115 relative error = 1.1214292951991040815324595489615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.057 y1[1] (analytic) = 2.8708849427026017044352846774374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3914594040983987041619967422218 relative error = 13.635496089574580945655994352151 % h = 0.001 y2[1] (analytic) = 1.508513055540753812920210850555 y2[1] (numeric) = 1.5255170914017460807786069930216 absolute error = 0.0170040358609922678583961424666 relative error = 1.1272050844065690492176177593522 % h = 0.001 TOP MAIN SOLVE Loop memory used=362.4MB, alloc=4.4MB, time=61.85 NO POLE NO POLE x[1] = 1.058 y1[1] (analytic) = 2.8713759941227113995454320367466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.391950455518508399272144101531 relative error = 13.650265807082524736696031997584 % h = 0.001 y2[1] (analytic) = 1.5093841860817606824326772262677 y2[1] (numeric) = 1.5264854996901741305075743040737 absolute error = 0.017101313608413448074897077806 relative error = 1.1329993891619519089330250549007 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.059 y1[1] (analytic) = 2.871866174166899586607936254411 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3924406355626965863346483191954 relative error = 13.665004278151637531159431822814 % h = 0.001 y2[1] (analytic) = 1.5102558072385405855346641377078 y2[1] (numeric) = 1.5274547850772635800420415332383 absolute error = 0.0171989778387229945073773955305 relative error = 1.1388122301062912016693528122303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.06 y1[1] (analytic) = 2.8723554823449862622829459219974 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3929299437407832620096579867818 relative error = 13.679711517461477512012142107955 % h = 0.001 y2[1] (analytic) = 1.5111279181394724380813624600436 y2[1] (numeric) = 1.5284249475630144293820086805154 absolute error = 0.0172970294235419913006462204718 relative error = 1.144643627843128031306112946603 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.061 y1[1] (analytic) = 2.8728439181676632892594655125299 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3934183795634602889861775773143 relative error = 13.694387539660963523088399597656 % h = 0.001 y2[1] (analytic) = 1.5120005179124454118168256350344 y2[1] (numeric) = 1.529395987147426678527475745905 absolute error = 0.0173954692349812667106501108706 relative error = 1.1504936029386053852381532093988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.062 y1[1] (analytic) = 2.8733314811464948855634519158083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3939059425422918852901639805927 relative error = 13.70903235936838482797560220115 % h = 0.001 y2[1] (analytic) = 1.5128736056848598064847252510766 y2[1] (numeric) = 1.5303679038305003274784427294072 absolute error = 0.0174942981456405209937174783306 relative error = 1.1563621759215675676646148184959 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.063 y1[1] (analytic) = 2.8738181707939181129935557094709 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3943926321897151127202677742553 relative error = 13.723645991171410870202826857969 % h = 0.001 y2[1] (analytic) = 1.513747180583627922427978582893 y2[1] (numeric) = 1.5313406976122353762349096310219 absolute error = 0.0175935170286074538069310481289 relative error = 1.1622493672836597437110402114404 % h = 0.001 TOP MAIN SOLVE Loop memory used=366.2MB, alloc=4.4MB, time=62.51 NO POLE NO POLE x[1] = 1.064 y1[1] (analytic) = 2.8743039866232433646840187301006 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.394878448019040364410730794885 relative error = 13.738228449627101034584090409494 % h = 0.001 y2[1] (analytic) = 1.5146212417351749336763754913097 y2[1] (numeric) = 1.5323143684926318247968764507491 absolute error = 0.0176931267574568911205009594394 relative error = 1.168155197479427592564340941444 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.065 y1[1] (analytic) = 2.8747889281486548517942403815169 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3953633895444518515209524463013 relative error = 13.752779749261914409568048937689 % h = 0.001 y2[1] (analytic) = 1.5154957882654397615213315955666 y2[1] (numeric) = 1.5332889164716896731643431885888 absolute error = 0.0177931282062499116430115930222 relative error = 1.1740796869264170678093441818571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.066 y1[1] (analytic) = 2.875272994885211089324525990729 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3958474562810080890512380555134 relative error = 13.767299904571719550446426572701 % h = 0.001 y2[1] (analytic) = 1.5163708192998759485768941434805 y2[1] (numeric) = 1.534264341549408921337309844541 absolute error = 0.0178935222495329727604157010605 relative error = 1.1800228560052742631646307871748 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.067 y1[1] (analytic) = 2.8757561863488453810575313958413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3963306477446423807842434606257 relative error = 13.781788930021804243274058237107 % h = 0.001 y2[1] (analytic) = 1.5172463339634525333261265185295 y2[1] (numeric) = 1.5352406437257895693157764186057 absolute error = 0.0179943097623370359896499000762 relative error = 1.1859847250598453818243581996517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.068 y1[1] (analytic) = 2.8762385020563663036249188245075 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3968129634521633033516308892919 relative error = 13.796246840046885269354022193669 % h = 0.001 y2[1] (analytic) = 1.5181223313806549251519968375448 y2[1] (numeric) = 1.5362178230008316170997429107829 absolute error = 0.0180954916201766919477460732381 relative error = 1.191965314397276807621727515547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.069 y1[1] (analytic) = 2.876719941525458189698739996318 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3972944029212551894254520611024 relative error = 13.810673649051118170141927602206 % h = 0.001 y2[1] (analytic) = 1.5189988106754857798518956081959 y2[1] (numeric) = 1.5371958793745350646892093210726 absolute error = 0.0181970686990492848373137128767 relative error = 1.1979646442881152762387055593645 % h = 0.001 TOP MAIN SOLVE Loop memory used=370.0MB, alloc=4.4MB, time=63.16 NO POLE NO POLE x[1] = 1.07 y1[1] (analytic) = 2.8772005042746816103070632577768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3977749656704786100337753225612 relative error = 13.825069371408107012424009576331 % h = 0.001 y2[1] (analytic) = 1.5198757709714658756349069318241 y2[1] (numeric) = 1.5381748128468999120841756494748 absolute error = 0.0182990418754340364492687176507 relative error = 1.2039827349664081446955496875574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.071 y1[1] (analytic) = 2.8776801898234738562733624342827 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3982546512192708560000744990671 relative error = 13.839434021460914153624269469556 % h = 0.001 y2[1] (analytic) = 1.5207532113916349896009572544251 y2[1] (numeric) = 1.5391546234179261592846418959895 absolute error = 0.0184014120262911696836846415644 relative error = 1.2100196066298037573626050849432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.072 y1[1] (analytic) = 2.8781589976921494187791859597638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3987334590879464185058980245482 relative error = 13.853767613522070007096481318876 % h = 0.001 y2[1] (analytic) = 1.521631131058552774700965186707 y2[1] (numeric) = 1.5401353110876138062906080606168 absolute error = 0.0185041800290610315896428739098 relative error = 1.2160752794396519067457513597252 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.073 y1[1] (analytic) = 2.8786369274019004690496257213382 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3992113887976974687763377861226 relative error = 13.868070161873582807257466539809 % h = 0.001 y2[1] (analytic) = 1.5225095290942996371771154331449 y2[1] (numeric) = 1.5411168758559628531020741433566 absolute error = 0.0186073467616632159249587102117 relative error = 1.2221497735211043873057671214765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.074 y1[1] (analytic) = 2.8791139784747973371611059335712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.3996884398705943368878179983556 relative error = 13.882341680766948374418618106245 % h = 0.001 y2[1] (analytic) = 1.5233884046204776144823793898327 y2[1] (numeric) = 1.5420993177229732997190401442089 absolute error = 0.0187109131024956852366607543762 relative error = 1.2282431089632156405807577761483 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.075 y1[1] (analytic) = 2.8795901504337889899710132345797 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4001646118295859896977252993641 relative error = 13.89658218442315987917323256844 % h = 0.001 y2[1] (analytic) = 1.5242677567582112536784044916836 y2[1] (numeric) = 1.5430826366886451461415060631737 absolute error = 0.0188148799304338924631015714901 relative error = 1.2343553058190434898896528317549 % h = 0.001 TOP MAIN SOLVE Loop memory used=373.8MB, alloc=4.4MB, time=63.82 NO POLE NO POLE x[1] = 1.076 y1[1] (analytic) = 2.8800654428027035081686900743944 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4006399041985005078954021391788 relative error = 13.910791687032717606197783369688 % h = 0.001 y2[1] (analytic) = 1.5251475846281484903108939111643 y2[1] (numeric) = 1.544066832752978392369471900251 absolute error = 0.0189192481248299020585779890867 relative error = 1.2404863841057499629036244176707 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.077 y1[1] (analytic) = 2.8805398551062485624473143446251 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4011143165020455621740264094095 relative error = 13.924970202755638717325842023343 % h = 0.001 y2[1] (analytic) = 1.5260278873504615277615977332555 y2[1] (numeric) = 1.5450519059159730384029376554408 absolute error = 0.0190240185655115106413399221853 relative error = 1.2466363638047022003811083216048 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.078 y1[1] (analytic) = 2.8810133868700118887961890775899 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4015878482658088885229011423743 relative error = 13.939117745721467013753924813691 % h = 0.001 y2[1] (analytic) = 1.5269086640448477170760362547213 y2[1] (numeric) = 1.5460378561776290842419033287431 absolute error = 0.0191291921327813671658670740218 relative error = 1.2528052648615734493709224847995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.079 y1[1] (analytic) = 2.8814860376204617629129669226588 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4020604990162587626396789874432 relative error = 13.953234330029282697239111793402 % h = 0.001 y2[1] (analytic) = 1.527789913830530437266075580037 y2[1] (numeric) = 1.5470246835379465298863689201579 absolute error = 0.0192347697074160926202933401209 relative error = 1.2589931071864441391967754138652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.08 y1[1] (analytic) = 2.8819578068849474737353349876248 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4025322682807444734620470524092 relative error = 13.96731996974771213014885197341 % h = 0.001 y2[1] (analytic) = 1.528671635826259976086475211474 y2[1] (numeric) = 1.5480123879969253753363344296852 absolute error = 0.0193407521706653992498592182112 relative error = 1.2651999106539030385452382141928 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.081 y1[1] (analytic) = 2.8824286941916997960916865134587 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4030031555874967958183985782431 relative error = 13.981374678914937594223933745115 % h = 0.001 y2[1] (analytic) = 1.5295538291503144112845268568664 y2[1] (numeric) = 1.5490009695545656205917998573251 absolute error = 0.0194471404042512093072730004587 relative error = 1.271425695103148491988018774908 % h = 0.001 TOP MAIN SOLVE Loop memory used=377.6MB, alloc=4.4MB, time=64.47 NO POLE NO POLE x[1] = 1.082 y1[1] (analytic) = 2.8828986990698314624703067318156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4034731604656284621970187966 relative error = 13.995398471538707047916162746046 % h = 0.001 y2[1] (analytic) = 1.5304364929205004923219032054952 y2[1] (numeric) = 1.5499904282108672656527652030775 absolute error = 0.0195539352903667733308619975823 relative error = 1.2776704803380897342781248895491 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.083 y1[1] (analytic) = 2.8833678210493376339066011361452 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4039422824451346336333132009296 relative error = 14.009391361596343882162850585282 % h = 0.001 y2[1] (analytic) = 1.5313196262541545225678349503138 y2[1] (numeric) = 1.5509807639658303105192304669424 absolute error = 0.0196611377116757879513955166286 relative error = 1.2839342861274482807682346339968 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.084 y1[1] (analytic) = 2.8838360596610963699878952792174 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4044105210568933697146073440018 relative error = 14.023353363034756674460777090851 % h = 0.001 y2[1] (analytic) = 1.5322032282681432419627338634115 y2[1] (numeric) = 1.5519719768194547551911956489198 absolute error = 0.0197687485513115132284617855083 relative error = 1.2902171322048593923083069977058 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.085 y1[1] (analytic) = 2.8843034144368690979753360923033 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4048778758326660977020481570877 relative error = 14.037284489770448941102846034278 % h = 0.001 y2[1] (analytic) = 1.533087298078864710151379261166 y2[1] (numeric) = 1.5529640667717405996686607490097 absolute error = 0.0198767686928758895172814878437 relative error = 1.2965190382689736129881634335237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.086 y1[1] (analytic) = 2.8847698849093010810424256041483 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4053443463050980807691376689327 relative error = 14.051184755689528887441209634203 % h = 0.001 y2[1] (analytic) = 1.5339718348022491900847847259714 y2[1] (numeric) = 1.5539570338226878439516257672121 absolute error = 0.0199851990204386538668410412407 relative error = 1.3028400239835583790994515135939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=381.4MB, alloc=4.4MB, time=65.12 x[1] = 1.087 y1[1] (analytic) = 2.8852354706119218856297188212437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4058099320077188853564308860281 relative error = 14.065054174647719156041190548065 % h = 0.001 y2[1] (analytic) = 1.5348568375537600320898614827493 y2[1] (numeric) = 1.554950877972296488040090703527 absolute error = 0.0200940404185364559502292207777 relative error = 1.3091801089775996977000651143529 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.088 y1[1] (analytic) = 2.8857001710791458479152184147362 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4062746324749428476419304795206 relative error = 14.078892760470366572590881534724 % h = 0.001 y2[1] (analytic) = 1.5357423054483945584059943606521 y2[1] (numeric) = 1.5559455992205665319340555579544 absolute error = 0.0202032937721719735280611973023 relative error = 1.315539312845403893172741364957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.089 y1[1] (analytic) = 2.8861639858462725393999997436219 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4067384472420695391267118084063 relative error = 14.092700526952451889431852518305 % h = 0.001 y2[1] (analytic) = 1.5366282376006849481876458034578 y2[1] (numeric) = 1.5569411975674979756335203304943 absolute error = 0.0203129599668130274458745270365 relative error = 1.3219176551466994201781828440808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.09 y1[1] (analytic) = 2.886626914449487231608600628636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4072013758452842313353126934204 relative error = 14.106477487858599526576942410629 % h = 0.001 y2[1] (analytic) = 1.5375146331246991229721029261249 y2[1] (numeric) = 1.5579376730130908191384850211467 absolute error = 0.0204230398883916961663820950218 relative error = 1.3283151554067387414116640663254 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.091 y1[1] (analytic) = 2.8870889564258613599037111764894 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4076634178216583596304232412738 relative error = 14.12022365692308731008165876332 % h = 0.001 y2[1] (analytic) = 1.5384014911340416326114821498343 y2[1] (numeric) = 1.5589350255573450624489496299117 absolute error = 0.0205335344233034298374674800774 relative error = 1.334731833116400268580674028356 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.092 y1[1] (analytic) = 2.8875501113133529864146998397988 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4081245727091499861414119045832 relative error = 14.13393904784985620763625212706 % h = 0.001 y2[1] (analytic) = 1.5392888107418545416681054835882 y2[1] (numeric) = 1.5599332552002607055649141567892 absolute error = 0.020644444458406163896808673201 relative error = 1.3411677077322903650297213558804 % h = 0.001 TOP MAIN SOLVE Loop memory used=385.2MB, alloc=4.4MB, time=65.78 NO POLE NO POLE x[1] = 1.093 y1[1] (analytic) = 2.8880103786508072620795127842255 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4085848400466042618062248490099 relative error = 14.147623674312520061246073901432 % h = 0.001 y2[1] (analytic) = 1.5401765910608183162723620570624 y2[1] (numeric) = 1.5609323619418377484863786017792 absolute error = 0.0207557708810194322140165447168 relative error = 1.3476227986768454084469852769981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.094 y1[1] (analytic) = 2.8884697579779568877994845209589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4090442193737538875261965857433 relative error = 14.16127754995437531686836647022 % h = 0.001 y2[1] (analytic) = 1.5410648312031527114421680469252 y2[1] (numeric) = 1.5619323457820761912133429648817 absolute error = 0.0208675145789234797711749179565 relative error = 1.3540971253384339120960341172405 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.095 y1[1] (analytic) = 2.888928248835422574706598649776 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4095027102312195744333107145604 relative error = 14.174900688388410750874172541114 % h = 0.001 y2[1] (analytic) = 1.5419535302806176588631376772364 y2[1] (numeric) = 1.5629332067209760337458072460967 absolute error = 0.0209796764403583748826695688603 relative error = 1.3605907070714587030243531421939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.096 y1[1] (analytic) = 2.8893858507647135035427384454507 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4099603121605105032694505102351 relative error = 14.188493103197317193204586851 % h = 0.001 y2[1] (analytic) = 1.5428426874045141551285775138303 y2[1] (numeric) = 1.5639349447585372760837714454242 absolute error = 0.0210922573540231209551939315939 relative error = 1.3671035631964591557089252403619 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.097 y1[1] (analytic) = 2.8898425633082277831504679083043 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4104170247040247828771799730887 relative error = 14.202054807933497247091107765787 % h = 0.001 y2[1] (analytic) = 1.5437323016856851504384158127608 y2[1] (numeric) = 1.5649375598947599182272355628642 absolute error = 0.0212052582090747677888197501034 relative error = 1.3736357130002134796075910204013 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.098 y1[1] (analytic) = 2.8902983860092529080748847881513 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4108728474050499078015968529357 relative error = 14.215585816119075005210378802466 % h = 0.001 y2[1] (analytic) = 1.5446223722345164377561782239551 y2[1] (numeric) = 1.5659410521296439601761995984167 absolute error = 0.0213186798951275224200213744616 relative error = 1.3801871757358410590933792719335 % h = 0.001 TOP MAIN SOLVE Loop memory used=389.1MB, alloc=4.4MB, time=66.42 NO POLE NO POLE x[1] = 1.099 y1[1] (analytic) = 2.8907533184119662152760879798278 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4113277798077632150028000446122 relative error = 14.229086141245905762144140737992 % h = 0.001 y2[1] (analytic) = 1.5455128981609375424231206931733 y2[1] (numeric) = 1.5669454214631894019306635520817 absolute error = 0.0214325233022518595075428589084 relative error = 1.3867579706229048442574442898708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.1 y1[1] (analytic) = 2.8912073600614353399518025778717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4117818214572323396785146426561 relative error = 14.242555796775585723015743750369 % h = 0.001 y2[1] (analytic) = 1.5464038785744226122286299482153 y2[1] (numeric) = 1.5679506678953962434906274238593 absolute error = 0.021546789320973631261997475644 relative error = 1.3933481168475137910746731708753 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.101 y1[1] (analytic) = 2.8916605105036186704697067677687 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4122349718994156701964188325531 relative error = 14.255994796139461708175095968752 % h = 0.001 y2[1] (analytic) = 1.5472953125839913079360014990487 y2[1] (numeric) = 1.5689567914262644848560912137494 absolute error = 0.0216614788422731769200897147007 relative error = 1.3999576335624253494344337421122 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.102 y1[1] (analytic) = 2.8921127692853658024090056214744 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4126872306811628021357176862588 relative error = 14.269403152738640853804449897538 % h = 0.001 y2[1] (analytic) = 1.5481871992982096942627046261544 y2[1] (numeric) = 1.569963792055794126027054921752 absolute error = 0.0217765927575844317643502955976 relative error = 1.4065865398871479975473221631797 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.103 y1[1] (analytic) = 2.8925641359544179917107977556764 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4131385973502149914375098204608 relative error = 14.282780879944000308317951430671 % h = 0.001 y2[1] (analytic) = 1.5490795378251911313142433768984 y2[1] (numeric) = 1.5709716697839851670035185478671 absolute error = 0.0218921319587940356892751709687 relative error = 1.413234854908043821247138339715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.104 y1[1] (analytic) = 2.8930146100594086069367817024688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4135890714552056066634937672532 relative error = 14.296127991096196924428397593169 % h = 0.001 y2[1] (analytic) = 1.5499723272725971664707221361436 y2[1] (numeric) = 1.5719804246108376077854820920947 absolute error = 0.0220080973382404413147599559511 relative error = 1.4199025976784311367156669914018 % h = 0.001 TOP MAIN SOLVE Loop memory used=392.9MB, alloc=4.4MB, time=67.08 NO POLE NO POLE x[1] = 1.105 y1[1] (analytic) = 2.8934641911498635806358497337686 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.414038652545660580362561798553 relative error = 14.309444499505676946755168743109 % h = 0.001 y2[1] (analytic) = 1.5508655667476384267252238846103 y2[1] (numeric) = 1.5729900565363514483729455544348 absolute error = 0.0221244897887130216477216698245 relative error = 1.4265897872186871551661724190625 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.106 y1[1] (analytic) = 2.8939128787762018598181177729194 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4144873401719988595448298377038 relative error = 14.322730418452685694847818745712 % h = 0.001 y2[1] (analytic) = 1.551759255357075511473108806681 y2[1] (numeric) = 1.5740005655605266887659089348874 absolute error = 0.0222413102034511772928001282064 relative error = 1.4332964425163506880298256080435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.107 y1[1] (analytic) = 2.8943606724897358555359409194884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4149351338855328552626529842728 relative error = 14.335985761187277241500322597552 % h = 0.001 y2[1] (analytic) = 1.5526533922072198857513404584262 y2[1] (numeric) = 1.5750119516833633289643722334525 absolute error = 0.0223585594761434432130317750263 relative error = 1.4400225825262248911975731824457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.108 y1[1] (analytic) = 2.8948075718426718915714650062808 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4153820332384688912981770710652 relative error = 14.349210540929324086231495139864 % h = 0.001 y2[1] (analytic) = 1.5535479764039347739269462565986 y2[1] (numeric) = 1.5760242149048613689683354501301 absolute error = 0.0224762385009265950413891935315 relative error = 1.4467682261704800468782287832601 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.109 y1[1] (analytic) = 2.8952535763881106522302655010551 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4158280377839076519569775658395 relative error = 14.362404770868526823807606861294 % h = 0.001 y2[1] (analytic) = 1.5544430070526360538337186002104 y2[1] (numeric) = 1.5770373552250208087777985849202 absolute error = 0.0225943481723847549440799847098 relative error = 1.4535333923387563816418185802949 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.11 y1[1] (analytic) = 2.8956986856800476292406259593394 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4162731470758446289673380241238 relative error = 14.375568464164423807683733358837 % h = 0.001 y2[1] (analytic) = 1.5553384832582931513562624880664 y2[1] (numeric) = 1.5780513726438416483927616378229 absolute error = 0.0227128893855484970364991497565 relative error = 1.4603180998882669192254437425372 % h = 0.001 TOP MAIN SOLVE Loop memory used=396.7MB, alloc=4.4MB, time=67.72 NO POLE NO POLE x[1] = 1.111 y1[1] (analytic) = 2.8961428992733735677580091291065 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4167173606691705674847211938909 relative error = 14.38870163394640080824088380689 % h = 0.001 y2[1] (analytic) = 1.5562344041254299354604950482804 y2[1] (numeric) = 1.5790662671613238878132246088381 absolute error = 0.0228318630358939523527295605577 relative error = 1.4671223676439003666871336845915 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.112 y1[1] (analytic) = 2.896586216723874911474274702875 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4171606781196719112009867676594 relative error = 14.401804293313700665696460784858 % h = 0.001 y2[1] (analytic) = 1.5571307687581256136697019493493 y2[1] (numeric) = 1.5800820387774675270391874979658 absolute error = 0.0229512700193419133694855486165 relative error = 1.4739462143983240325013546809055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.113 y1[1] (analytic) = 2.8970286375882342468311986080539 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4176030989840312465579106728383 relative error = 14.414876455335432937566109039389 % h = 0.001 y2[1] (analytic) = 1.5580275762600156279852552168044 y2[1] (numeric) = 1.581098687492272566070650305206 absolute error = 0.0230711112322569380853950884016 relative error = 1.4807896589120867751980088977548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.114 y1[1] (analytic) = 2.8974701614240307463378496220504 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4180446228198277460645616868348 relative error = 14.427918133050583540555514214601 % h = 0.001 y2[1] (analytic) = 1.5589248257342925512510965347952 y2[1] (numeric) = 1.5821162133057390049076130305587 absolute error = 0.0231913875714464536565164957635 relative error = 1.4876527199137219811549089417792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.115 y1[1] (analytic) = 2.8979107877897406109913799948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4184852491855376107180920595844 relative error = 14.44092933946802438676121427829 % h = 0.001 y2[1] (analytic) = 1.5598225162837069839610896681975 y2[1] (numeric) = 1.5831346162178668435500756740239 absolute error = 0.0233120999341598595889860058264 relative error = 1.4945354160998505701618425691835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.116 y1[1] (analytic) = 2.8983505162447375118007876579656 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.41892497764053451152749972275 relative error = 14.453910087566523014059986310554 % h = 0.001 y2[1] (analytic) = 1.5607206470105684515083451979695 y2[1] (numeric) = 1.5841538962286560819980382356016 absolute error = 0.0234332492180876304896930376321 relative error = 1.5014377661352840273824511505489 % h = 0.001 TOP MAIN SOLVE Loop memory used=400.5MB, alloc=4.4MB, time=68.38 NO POLE NO POLE x[1] = 1.117 y1[1] (analytic) = 2.8987893463492930304132084970801 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4193638077450900301399205618645 relative error = 14.466860390294752210566869509386 % h = 0.001 y2[1] (analytic) = 1.5616192170167463018756203205038 y2[1] (numeric) = 1.5851740533381067202515007152918 absolute error = 0.023554836321360418375880394788 relative error = 1.508359788653127460348233752673 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.118 y1[1] (analytic) = 2.8992272776645770988422980603767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4198017390603740985690101251611 relative error = 14.479780260571299633042381711744 % h = 0.001 y2[1] (analytic) = 1.5625182254036706037658960206517 y2[1] (numeric) = 1.5861950875462187583104631130945 absolute error = 0.0236768621425481545445670924428 relative error = 1.5153015022548826796270561917037 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.119 y1[1] (analytic) = 2.8996643097526584382982629759624 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4202387711484554380249750407468 relative error = 14.49266971128467741912998143446 % h = 0.001 y2[1] (analytic) = 1.5634176712723330451722334879172 y2[1] (numeric) = 1.5872169988529921961749254290097 absolute error = 0.0237993275806591510026919410925 relative error = 1.5222629255105513018165910447931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.12 y1[1] (analytic) = 2.9001004421765049971191032473392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4206749035723019968458153121236 relative error = 14.505528755293331793305320413083 % h = 0.001 y2[1] (analytic) = 1.5643175537232878323860112060389 y2[1] (numeric) = 1.5882397872584270338448876630375 absolute error = 0.0239222335351392014588764569986 relative error = 1.5292440769587378735211402945818 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.121 y1[1] (analytic) = 2.9005356744999843878026274960677 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4211101358957813875293395608521 relative error = 14.518357405425652666419322864492 % h = 0.001 y2[1] (analytic) = 1.5652178718566525894426437077979 y2[1] (numeric) = 1.5892634527625232713203498151778 absolute error = 0.0240455809058706818777061073799 relative error = 1.5362449751067530149782969379719 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.122 y1[1] (analytic) = 2.9009700062878643231388041195943 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4215444676836613228655161843787 relative error = 14.531155674479983228717617226753 % h = 0.001 memory used=404.3MB, alloc=4.4MB, time=69.05 y2[1] (analytic) = 1.5661186247721092580038825494078 y2[1] (numeric) = 1.5902879953652809086013118854306 absolute error = 0.0241693705931716505974293360228 relative error = 1.5432656384307165820098854355016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.123 y1[1] (analytic) = 2.9014034371058130514420122319265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4219778985016100511687242967109 relative error = 14.543923575224629536219333943342 % h = 0.001 y2[1] (analytic) = 1.5670198115689049976757996222608 y2[1] (numeric) = 1.5913134150666999456877738737959 absolute error = 0.0242936034977949480119742515351 relative error = 1.5503060853756608449795832285993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.124 y1[1] (analytic) = 2.9018359665203997908827571549424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4224104279161967906094692197268 relative error = 14.55666112039787009033876896442 % h = 0.001 y2[1] (analytic) = 1.5679214313458530867615524841214 y2[1] (numeric) = 1.5923397118667803825797357802737 absolute error = 0.0244182805209272958181832961523 relative error = 1.5573663343556336834475666298285 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.125 y1[1] (analytic) = 2.9022675940990951629184161286548 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4228420554948921626451281934392 relative error = 14.569368322707965410633897041327 % h = 0.001 y2[1] (analytic) = 1.5688234832013338234480309570783 y2[1] (numeric) = 1.593366885765522219277197604864 absolute error = 0.0245434025641883958291666477857 relative error = 1.5644464037538017952204441172191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.126 y1[1] (analytic) = 2.9026983194102716248225808097203 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4232727808060686245492928745047 relative error = 14.58204519483316760056620159781 % h = 0.001 y2[1] (analytic) = 1.5697259662332954274254838056815 y2[1] (numeric) = 1.5943949367629254557801593475668 absolute error = 0.0246689705296300283546755418853 relative error = 1.571546311922553918502638361517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.127 y1[1] (analytic) = 2.9031281420232039013125640288867 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4237026034190009010392760936711 relative error = 14.594691749421729906156768978598 % h = 0.001 y2[1] (analytic) = 1.5706288795392549419392238757145 y2[1] (numeric) = 1.5954238648589900920886210083821 absolute error = 0.0247949853197351501493971326676 relative error = 1.5786660771836040658632551086463 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=408.1MB, alloc=4.4MB, time=69.71 x[1] = 1.128 y1[1] (analytic) = 2.903557061508069415274639179909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4241315229038664150013512446934 relative error = 14.607307999091916267424074208877 % h = 0.001 y2[1] (analytic) = 1.571532222216299136272509641971 y2[1] (numeric) = 1.5964536700537161282025825873099 absolute error = 0.0249214478374169919300729453389 relative error = 1.5858057178280947687403322554874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.129 y1[1] (analytic) = 2.9039850774359487175865815147284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4245595388317457173132935795128 relative error = 14.619893956432010862489363052576 % h = 0.001 y2[1] (analytic) = 1.5724359933610854086597006822295 y2[1] (numeric) = 1.5974843523471035641220440843503 absolute error = 0.0250483589860181554623434021208 relative error = 1.592965252116700331212196022138 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.13 y1[1] (analytic) = 2.9044121893788259160370815224114 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4249866507746229157637935871958 relative error = 14.632449634000327644236011139538 % h = 0.001 y2[1] (analytic) = 1.5733401920698426896287841643465 y2[1] (numeric) = 1.5985159117391523998470054995032 absolute error = 0.0251757196693097102182213351567 relative error = 1.6001446982797300917734629669494 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.131 y1[1] (analytic) = 2.9048383969095891033416014724691 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4254128583053861030683135372535 relative error = 14.644975044325219869409715246907 % h = 0.001 y2[1] (analytic) = 1.5742448174383723457723690040154 y2[1] (numeric) = 1.5995483482298626353774668327686 absolute error = 0.0253035307914902896050978287532 relative error = 1.607344074517231691861016642436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.132 y1[1] (analytic) = 2.9052636996020307842542471067375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4258381609978277839809591715219 relative error = 14.657470199905089620046844474831 % h = 0.001 y2[1] (analytic) = 1.5751498685620490839462439222745 y2[1] (numeric) = 1.6005816618192342707134280841465 absolute error = 0.025431793257185186767184161872 relative error = 1.6145633989990943498830558811233 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.133 y1[1] (analytic) = 2.9056880970308483017752273679812 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4262625584266453015019394327656 relative error = 14.669935113208397317118750056306 % h = 0.001 y2[1] (analytic) = 1.5760553445358218558945952042796 y2[1] (numeric) = 1.6016158525072673058548892536369 absolute error = 0.0255605079714454499602940493573 relative error = 1.6218026898651521395120579647857 % h = 0.001 TOP MAIN SOLVE Loop memory used=411.9MB, alloc=4.4MB, time=70.36 NO POLE NO POLE x[1] = 1.134 y1[1] (analytic) = 2.9061115887716442624534759577981 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4266860501674412621801880225825 relative error = 14.68236979667367122628030189174 % h = 0.001 y2[1] (analytic) = 1.5769612444542147633009795341995 y2[1] (numeric) = 1.6026509202939617408018503412398 absolute error = 0.0256896758397469775008708070403 relative error = 1.6290619652252872710102242012649 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.135 y1[1] (analytic) = 2.906534174400926960784009421237 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4271086357967239605107214860214 relative error = 14.694774262709516955611387606256 % h = 0.001 y2[1] (analytic) = 1.5778675674113279632641468553367 y2[1] (numeric) = 1.6036868651793175755543113469552 absolute error = 0.0258192977679896122901644916185 relative error = 1.636341243159533374363677646531 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.136 y1[1] (analytic) = 2.9069558534961108026995973608071 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4275303148919078024263094255915 relative error = 14.707148523694626945240575997864 % h = 0.001 y2[1] (analytic) = 1.578774312500838574197807779727 y2[1] (numeric) = 1.6047236871633348101122722707831 absolute error = 0.0259493746624962359144644910561 relative error = 1.6436405417181787830093628023408 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.137 y1[1] (analytic) = 2.9073766256355167281563212882432 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4279510870313137278830333530276 relative error = 14.719492591977789948740611182977 % h = 0.001 y2[1] (analytic) = 1.5796814788160015821534396475239 y2[1] (numeric) = 1.6057613862460134444757331127235 absolute error = 0.0260799074300118623222934651996 relative error = 1.6509598789218698169462550304308 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.138 y1[1] (analytic) = 2.9077964903983726328125995285035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4283709517941696325393115932879 relative error = 14.731806479877900506185866558341 % h = 0.001 y2[1] (analytic) = 1.5805890654496507475652249134399 y2[1] (numeric) = 1.6067999624273534786446938727764 absolute error = 0.0262108969777027310794689593365 relative error = 1.6582992727617140640301230913895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.139 y1[1] (analytic) = 2.9082154473648137888012564970109 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4287899087606107885279685617953 relative error = 14.744090199683968408762348890875 % h = 0.001 y2[1] (analytic) = 1.5814970714941995124162151153795 y2[1] (numeric) = 1.6078394157073549126191545509419 absolute error = 0.0263423442131554002029394355624 relative error = 1.6656587411993836582587015821774 % h = 0.001 TOP MAIN SOLVE Loop memory used=415.8MB, alloc=4.4MB, time=71.02 NO POLE NO POLE x[1] = 1.14 y1[1] (analytic) = 2.9086334961158832645942155781022 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4292079575116802643209276428866 relative error = 14.756343763655128154821302424947 % h = 0.001 y2[1] (analytic) = 1.5824054960416419078248132591774 y2[1] (numeric) = 1.6088797460860177463991151472199 absolute error = 0.0264742500443758385743018880425 relative error = 1.673038302167218553861721051582 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.141 y1[1] (analytic) = 2.909050636233532343959395740028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4296250976293293436861078048124 relative error = 14.768567184020648397267920866119 % h = 0.001 y2[1] (analytic) = 1.5833143381835534620506670330335 y2[1] (numeric) = 1.6099209535633419799845756616104 absolute error = 0.0266066153797885179339086285769 relative error = 1.6804379735683297940178121624026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.142 y1[1] (analytic) = 2.9094668673006209440093929296424 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4300413286964179437361049944268 relative error = 14.780760472979941382177131466925 % h = 0.001 y2[1] (analytic) = 1.5842235970110921089190648458288 y2[1] (numeric) = 1.6109630381393276133755360941134 absolute error = 0.0267394411282355044564712482846 relative error = 1.6878577732767027730278463862827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.143 y1[1] (analytic) = 2.9098821889009180323415281981339 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4304566502967150320682402629183 relative error = 14.792923642702572378528870209505 % h = 0.001 y2[1] (analytic) = 1.5851332716149990966629262650005 y2[1] (numeric) = 1.6120059998139746465719964447289 absolute error = 0.0268727281989755499090701797284 relative error = 1.6952977191373004907817993091114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.144 y1[1] (analytic) = 2.910296600619102043268845417787 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4308710620148990429955574825714 relative error = 14.805056705328269098955720257866 % h = 0.001 y2[1] (analytic) = 1.5860433610855998971814780120622 y2[1] (numeric) = 1.6130498385872830795739567134569 absolute error = 0.0270064775016831823924787013947 relative error = 1.7027578289661667983637236379574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.145 y1[1] (analytic) = 2.9107101020407612931416423588084 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4312845634365582928683544235928 relative error = 14.817159672966931111396237444335 % h = 0.001 y2[1] (analytic) = 1.5869538645128051157147062571694 y2[1] (numeric) = 1.6140945544592529123814169002974 absolute error = 0.027140689946447796666710643128 relative error = 1.7102381205505296336468973837161 % h = 0.001 TOP MAIN SOLVE Loop memory used=419.6MB, alloc=4.4MB, time=71.68 NO POLE NO POLE x[1] = 1.146 y1[1] (analytic) = 2.9111226927523943947591198047236 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.431697154148191394485831869508 relative error = 14.829232557698639241547736566725 % h = 0.001 y2[1] (analytic) = 1.5878647809861114009326755383524 y2[1] (numeric) = 1.6151401474298841449943770052504 absolute error = 0.027275366443772744061701466898 relative error = 1.7177386116489042457386683966883 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.147 y1[1] (analytic) = 2.9115343723414106708707342947284 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4321088337372076705974463595128 relative error = 14.841275371573664966012760709851 % h = 0.001 y2[1] (analytic) = 1.5887761095946023554388042161757 y2[1] (numeric) = 1.6161866174991767774128370283159 absolute error = 0.0274105079045744219740328121402 relative error = 1.7252593199911964071419494056965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.148 y1[1] (analytic) = 2.9119451403961305667668409916768 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4325196017919275664935530564612 relative error = 14.853288126612479796033902673448 % h = 0.001 y2[1] (analytic) = 1.5896878494269494466861859606218 y2[1] (numeric) = 1.617233964667130809636796969494 absolute error = 0.0275461152401813629506110088722 relative error = 1.7328002632788056125077279081564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.149 y1[1] (analytic) = 2.9123549965057860619582140850978 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4329294579015830616849261498822 relative error = 14.86527083480576465171209289358 % h = 0.001 y2[1] (analytic) = 1.590599999571412918306046353956 y2[1] (numeric) = 1.6182821889337462416662568287846 absolute error = 0.0276821893623333233602104748286 relative error = 1.7403614591847282628603426309903 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.15 y1[1] (analytic) = 2.9127639402605210809440330497537 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4333384016563180806707451145381 relative error = 14.877223508114419226603911991951 % h = 0.001 y2[1] (analytic) = 1.5915125591158427018474232811901 y2[1] (numeric) = 1.6193312902990230735012166061877 absolute error = 0.0278187311831803716537933249976 relative error = 1.747942925353660834184642786318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.151 y1[1] (analytic) = 2.913171971251391903067923991789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4337464326471889027946360565734 relative error = 14.889146158469571342593928282896 % h = 0.001 y2[1] (analytic) = 1.5924255271476793289271593685416 y2[1] (numeric) = 1.6203812687629613051416763017033 absolute error = 0.0279557416152819762145169331617 relative error = 1.755544679402103029271487936038 % h = 0.001 TOP MAIN SOLVE Loop memory used=423.4MB, alloc=4.4MB, time=72.34 NO POLE NO POLE x[1] = 1.152 y1[1] (analytic) = 2.9135790890703675714616462264618 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4341535504661645711883582912462 relative error = 14.901038797772586294938501216469 % h = 0.001 y2[1] (analytic) = 1.5933389027539548437892943199711 y2[1] (numeric) = 1.6214321243255609365876359153314 absolute error = 0.0280932215716060927983415953603 relative error = 1.7631667389184609117253649138218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.153 y1[1] (analytic) = 2.9139852933103303010760151438061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4345597547061273008027272085905 relative error = 14.912901437895076187377930843948 % h = 0.001 y2[1] (analytic) = 1.594252685021293716272944592482 y2[1] (numeric) = 1.622483856986821967839095447072 absolute error = 0.02823117196552825156615085459 relative error = 1.7708091214631500210451938890511 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.154 y1[1] (analytic) = 2.9143905835650758857986533313354 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4349650449608728855253653961198 relative error = 14.924734090678909257214270964383 % h = 0.001 y2[1] (analytic) = 1.5951668730359137551877574423796 y2[1] (numeric) = 1.6235364667467443988960548969251 absolute error = 0.0283695937108306437082974545455 relative error = 1.7784718445686984676966682546146 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.155 y1[1] (analytic) = 2.9147949594293141046581628360706 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.435369420825111104384874900855 relative error = 14.93653676793621919025255965335 % h = 0.001 y2[1] (analytic) = 1.5960814658836270220960259671097 y2[1] (numeric) = 1.6245899536053282297585142648907 absolute error = 0.028508487721701207662488297781 relative error = 1.7861549257398500071017225398618 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.156 y1[1] (analytic) = 2.9151984204986691271143123617542 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4357728818944661268410244265386 relative error = 14.948309481449414425503655393232 % h = 0.001 y2[1] (analytic) = 1.5969964626498407455005513606404 y2[1] (numeric) = 1.6256443175625734604264735509688 absolute error = 0.0286478549127327149259221903284 relative error = 1.7938583824536670914779489523995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.157 y1[1] (analytic) = 2.9156009663696799174338341110968 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4361754277654769171605461758812 relative error = 14.96005224297118744954730002363 % h = 0.001 y2[1] (analytic) = 1.5979118624195582354373381945989 y2[1] (numeric) = 1.6266995586184800908999327551594 absolute error = 0.0287876961989218554625945605605 relative error = 1.8015822321596338984679864016983 % h = 0.001 TOP MAIN SOLVE Loop memory used=427.2MB, alloc=4.4MB, time=73.00 NO POLE NO POLE x[1] = 1.158 y1[1] (analytic) = 2.9160025966398006381514258972928 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4365770580355976378781379620772 relative error = 14.97176506422452408045446121643 % h = 0.001 y2[1] (analytic) = 1.5988276642773797984722081325456 y2[1] (numeric) = 1.6277556767730481211788918774626 absolute error = 0.028928012495668322706683744917 relative error = 1.8093264922797593355060859164894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.159 y1[1] (analytic) = 2.9164033109074010526155550638374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4369777723031980523422671286218 relative error = 14.983447956902712741168437158156 % h = 0.001 y2[1] (analytic) = 1.5997438673075036531004170808466 y2[1] (numeric) = 1.6288126720262775512633509178783 absolute error = 0.0290688047187738981629338370317 relative error = 1.8170911802086800188762132026406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.16 y1[1] (analytic) = 2.9168031087717669266186616668743 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4373775701675639263453737316587 relative error = 14.995100932669353722244634597836 % h = 0.001 y2[1] (analytic) = 1.600660470593726845548360376606 y2[1] (numeric) = 1.6298705443781683811533098764065 absolute error = 0.0292100737844415356049494998005 relative error = 1.8248763133137632264231826641665 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.161 y1[1] (analytic) = 2.9172019898331004291113592899035 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4377764512288974288380713546879 relative error = 15.006724003158368433849358397253 % h = 0.001 y2[1] (analytic) = 1.6015774732194461659764502110262 y2[1] (numeric) = 1.6309292938287206108487687530472 absolute error = 0.029351820609274444872318542021 relative error = 1.8326819089352098228854274951917 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.162 y1[1] (analytic) = 2.9175999536925205320002327766828 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4381744150883175317269448414672 relative error = 15.018317179974008646918376207668 % h = 0.001 y2[1] (analytic) = 1.602494874267659065082249085398 y2[1] (numeric) = 1.6319889203779342403497275478004 absolute error = 0.0294940461102751752674784624024 relative error = 1.8405079843861571568250974126471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.163 memory used=431.0MB, alloc=4.4MB, time=73.66 y1[1] (analytic) = 2.917996999952063409028833084559 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4385714613478604087555451493434 relative error = 15.0298804746908657233764458981 % h = 0.001 y2[1] (analytic) = 1.6034126728209645711029426966612 y2[1] (numeric) = 1.6330494240258092696561862606661 absolute error = 0.0296367512048446985532435640049 relative error = 1.8483545569527819281382392087773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.164 y1[1] (analytic) = 2.9183931282146828337414703772652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4389675896104798334681824420496 relative error = 15.041413898853879835319415880521 % h = 0.001 y2[1] (analytic) = 1.6043308679615642072162352501407 y2[1] (numeric) = 1.6341108047723456987681448916443 absolute error = 0.0297799368107814915519096415036 relative error = 1.8562216438944030251348555286967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.165 y1[1] (analytic) = 2.9187883380842505765294073934265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4393627994800475762561194582109 relative error = 15.052917463978349173060929522482 % h = 0.001 y2[1] (analytic) = 1.6052494587712629093387497986382 y2[1] (numeric) = 1.635173062617543527685603440735 absolute error = 0.0299236038462806183468536420968 relative error = 1.8641092624435843301856540938336 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.166 y1[1] (analytic) = 2.9191826291655568007590560446127 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4397570905613538004857681093971 relative error = 15.064391181549939141946184412708 % h = 0.001 y2[1] (analytic) = 1.6061684443314699443210158095567 y2[1] (numeric) = 1.6362361975614027564085619079382 absolute error = 0.0300677532299328120875460983815 relative error = 1.8720174298062374929392929691882 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.167 y1[1] (analytic) = 2.9195760010643104579817811147742 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4401504624601074577084931795586 relative error = 15.075835063024691547835615355781 % h = 0.001 y2[1] (analytic) = 1.6070878237231998285381257651454 y2[1] (numeric) = 1.6373002096039233849370202932539 absolute error = 0.0302123858807235563988945281085 relative error = 1.8799461631617246701208973853022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.168 y1[1] (analytic) = 2.9199684533871396822249158512909 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4405429147829366819516279160753 relative error = 15.087249119829033771161786623443 % h = 0.001 y2[1] (analytic) = 1.6080075960270732468751422052864 y2[1] (numeric) = 1.6383650987451054132709785966822 absolute error = 0.0303575027180321663958363913958 relative error = 1.8878954796629612309295700489117 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=434.8MB, alloc=4.4MB, time=74.32 x[1] = 1.169 y1[1] (analytic) = 2.9203599857415921833635951566516 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.440934447137389183090307221436 relative error = 15.098633363359787929463194187547 % h = 0.001 y2[1] (analytic) = 1.6089277603233179721063362274918 y2[1] (numeric) = 1.639430864984948841410436818223 absolute error = 0.0305031046616308693041005907312 relative error = 1.8958653964365184270595397859586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.17 y1[1] (analytic) = 2.920750597736135639573013008962 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4413250591319326392997250737464 relative error = 15.109987804984180028299092408644 % h = 0.001 y2[1] (analytic) = 1.6098483156917697846673380649495 y2[1] (numeric) = 1.6404975083234536693553949578763 absolute error = 0.0306491926316838846880568929268 relative error = 1.9038559305827260263764927334937 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.171 y1[1] (analytic) = 2.9211402889801580888607116590592 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4417147503759550885874237238436 relative error = 15.121312456039849100449871960091 % h = 0.001 y2[1] (analytic) = 1.6107692612118733928192799705438 y2[1] (numeric) = 1.6415650287606198971058530156421 absolute error = 0.0307957675487465042865730450983 relative error = 1.911867099175774909287506110954 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.172 y1[1] (analytic) = 2.9215290590839683196785110719728 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4421035204797653194052231367572 relative error = 15.132607327834856333307926635294 % h = 0.001 y2[1] (analytic) = 1.6116905959626833532040112427848 y2[1] (numeric) = 1.6426334262964475246618109915204 absolute error = 0.0309428303337641714577997487356 relative error = 1.9198989192638196268498568356148 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.173 y1[1] (analytic) = 2.9219169076587962606136880008392 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4424913690545932603404000656236 relative error = 15.143872431647694184364356121143 % h = 0.001 y2[1] (analytic) = 1.6126123190228649917894648385082 y2[1] (numeric) = 1.6437027009309365520232688855112 absolute error = 0.031090381908071560233804047003 relative error = 1.9279514078690809196708058814156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.174 y1[1] (analytic) = 2.9223038343167933691590150021193 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4428782957125903688857270669037 relative error = 15.155107778727295484697259828446 % h = 0.001 y2[1] (analytic) = 1.6135344294706953252042546270552 y2[1] (numeric) = 1.6447728526640869791902266976145 absolute error = 0.0312384231933916539859720705593 relative error = 1.9360245819879481966572642959437 % h = 0.001 TOP MAIN SOLVE Loop memory used=438.6MB, alloc=4.4MB, time=74.98 NO POLE NO POLE x[1] = 1.175 y1[1] (analytic) = 2.9226898386710330195612706221156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4432643000668300192879826869 relative error = 15.166313380293042530367783456191 % h = 0.001 y2[1] (analytic) = 1.6144569263840639824605819514124 y2[1] (numeric) = 1.6458438814958988061626844278303 absolute error = 0.0313869551118348237021024764179 relative error = 1.9441184585910819726810281689974 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.176 y1[1] (analytic) = 2.923074920335510889747832906309 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4436493817313078894745449710934 relative error = 15.177489247534776161630485135317 % h = 0.001 y2[1] (analytic) = 1.6153798088404741270645297734828 y2[1] (numeric) = 1.6469157874263720329406420761586 absolute error = 0.0315359785858979058761123026758 relative error = 1.9522330546235162642320275708985 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.177 y1[1] (analytic) = 2.9234590789251453473309693049552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4440335403209423470576813697396 relative error = 15.188635391612804829864991755226 % h = 0.001 y2[1] (analytic) = 1.6163030759170433795128222932681 y2[1] (numeric) = 1.6479885704555066595240996425995 absolute error = 0.0316854945384632800112773493314 relative error = 1.9603683870047609421387685337416 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.178 y1[1] (analytic) = 2.923842314055777834689436970682 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4444167754515748344161490354664 relative error = 15.199751823657913652136318427241 % h = 0.001 y2[1] (analytic) = 1.6172267266905047401751275452828 y2[1] (numeric) = 1.6490622305833026859130571271529 absolute error = 0.0318355038927979457379295818701 relative error = 1.9685244726289040404418575181023 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.179 y1[1] (analytic) = 2.9242246253441732531270083665204 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4447990867399702528537204313048 relative error = 15.210838554771373453291624989149 % h = 0.001 y2[1] (analytic) = 1.6181507602372075125609800899718 y2[1] (numeric) = 1.6501367678097601121075145298188 absolute error = 0.031986007572552599546534439847 relative error = 1.976701328364714020513184478725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.18 y1[1] (analytic) = 2.9246060124080203461075380258748 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4451804738038173458342500906592 relative error = 15.22189559602494979550158300887 % h = 0.001 y2[1] (analytic) = 1.6190751756331182269704005332872 y2[1] (numeric) = 1.6512121821348789381074718505972 absolute error = 0.03213700650176071113707131731 relative error = 1.9848989710557419895200036004799 % h = 0.001 TOP MAIN SOLVE Loop memory used=442.5MB, alloc=4.4MB, time=75.62 NO POLE NO POLE x[1] = 1.181 y1[1] (analytic) = 2.924986474865932081566187229398 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4455609362617290812928992941824 relative error = 15.232922958460911995154924908427 % h = 0.001 y2[1] (analytic) = 1.6199999719538215645272882238809 y2[1] (numeric) = 1.6522884735586591639129290894881 absolute error = 0.0322885016048375993856408656072 relative error = 1.9931174175204238723397900096577 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.182 y1[1] (analytic) = 2.9253660123374460332964242875787 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4459404737332430330231363523631 relative error = 15.243920653092042127015143606988 % h = 0.001 y2[1] (analytic) = 1.620925148274521281594663094598 y2[1] (numeric) = 1.6533656420811007895238862464915 absolute error = 0.0324404938065795079292231518935 relative error = 2.0013566845521825360383662631538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.183 y1[1] (analytic) = 2.9257446244430247614124190420718 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4463190858388217611391311068562 relative error = 15.254888690901644015548706478734 % h = 0.001 y2[1] (analytic) = 1.621850703670041134570832233106 y2[1] (numeric) = 1.6544436877022038149403433216074 absolute error = 0.0325929840321626803695110885014 relative error = 2.0096167889195298660303841694928 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.184 y1[1] (analytic) = 2.9261223108040561918864511234096 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.446696772199853191613163188194 relative error = 15.265827082843552213334541443168 % h = 0.001 y2[1] (analytic) = 1.6227766372148258050655563855695 y2[1] (numeric) = 1.6555226104219682401623003148358 absolute error = 0.0327459732071424350967439292663 relative error = 2.0178977473661687930478154912773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.185 y1[1] (analytic) = 2.926499071042853995160952427717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4470735324386509948876644925014 relative error = 15.276735839842140966464945657029 % h = 0.001 y2[1] (analytic) = 1.6237029479829418254552912172827 y2[1] (numeric) = 1.6566024102403940651897572261767 absolute error = 0.032899462257452239734466008894 relative error = 2.0261995766110952700486493098153 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.186 y1[1] (analytic) = 2.9268749047826579638348052004202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4474493661784549635615172652046 relative error = 15.28761497279233316684845856356 % h = 0.001 y2[1] (analytic) = 1.6246296350480785048165777750938 y2[1] (numeric) = 1.6576830871574812900227140556301 absolute error = 0.0330534521094027852061362805363 relative error = 2.034522293348700198204514292314 % h = 0.001 TOP MAIN SOLVE Loop memory used=446.3MB, alloc=4.4MB, time=76.28 NO POLE NO POLE x[1] = 1.187 y1[1] (analytic) = 2.9272498116476343894235180406812 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4478242730434313891502301054656 relative error = 15.298464492559609291325630981405 % h = 0.001 y2[1] (analytic) = 1.6255566974835488552366562183088 y2[1] (numeric) = 1.6587646411732299146611708031961 absolute error = 0.0332079436896810594245145848873 relative error = 2.0428659142488713011124407826525 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.188 y1[1] (analytic) = 2.9276237912628764381929030664147 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4481982526586734379196151311991 relative error = 15.30928440998001632750901048722 % h = 0.001 y2[1] (analytic) = 1.6264841343622905185003765075383 y2[1] (numeric) = 1.6598470722876399391051274688746 absolute error = 0.0333629379253494206047509613363 relative error = 2.0512304559570949463824505330354 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.189 y1[1] (analytic) = 2.9279968432544045260658784062408 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4485713046502015257925904710252 relative error = 15.320074735860176686259050568002 % h = 0.001 y2[1] (analytic) = 1.6274119447568666931524793646539 y2[1] (numeric) = 1.6609303805007113633545840526656 absolute error = 0.0335184357438446702021046880117 relative error = 2.0596159350945579137591110007682 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.19 y1[1] (analytic) = 2.9283689672491666926020211116027 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4489434286449636923287331763871 relative error = 15.330835480977297100708036896421 % h = 0.001 y2[1] (analytic) = 1.6283401277394670619343204416495 y2[1] (numeric) = 1.6620145658124441874095405545691 absolute error = 0.0336744380729771254752201129196 relative error = 2.0680223682582491089416164476262 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.191 y1[1] (analytic) = 2.9287401628750389740494965095271 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4493146242708359737762085743115 relative error = 15.341566656079177511744508620002 % h = 0.001 y2[1] (analytic) = 1.6292686823819087195941102617622 y2[1] (numeric) = 1.6630996282228384112699969745851 absolute error = 0.0338309458409296916758867128229 relative error = 2.0764497720210612222733595957499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.192 y1[1] (analytic) = 2.9291104297608257754689909441298 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4496848911566227751957030089142 relative error = 15.352268271884219939871035758083 % h = 0.001 y2[1] (analytic) = 1.6301976077556371010697421226884 y2[1] (numeric) = 1.6641855677318940349359533127136 absolute error = 0.0339879599762569338662111900252 relative error = 2.0848981629318923314783353115581 % h = 0.001 TOP MAIN SOLVE Loop memory used=450.1MB, alloc=4.4MB, time=76.93 NO POLE NO POLE x[1] = 1.193 y1[1] (analytic) = 2.929479767536260241929275782964 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4500542289320572416559878477484 relative error = 15.362940339081437343348595673793 % h = 0.001 y2[1] (analytic) = 1.6311269029317269100432797791466 y2[1] (numeric) = 1.6652723843396110584074095689546 absolute error = 0.034145481407884148364129789808 relative error = 2.0933675575157474476280717056797 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.194 y1[1] (analytic) = 2.9298481758320046287740314926789 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4504226372278016285007435574633 relative error = 15.373582868330462462541172137262 % h = 0.001 y2[1] (analytic) = 1.6320565669808830478661763503744 y2[1] (numeric) = 1.6663600780459894816843657433081 absolute error = 0.0343035110651064338181893929337 relative error = 2.1018579722738400035291141525841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.195 y1[1] (analytic) = 2.9302156542796506709595615171946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.450790115675447670686273581979 relative error = 15.384195870261556650374579725487 % h = 0.001 y2[1] (analytic) = 1.63298659897344154285429552742 y2[1] (numeric) = 1.6674486488510293047668218357741 absolute error = 0.0344620498775877619125263083541 relative error = 2.1103694236836932837273940475943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.196 y1[1] (analytic) = 2.9305822025117199514630266207112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4511566639075169511897386854956 relative error = 15.394779355475618688823894219112 % h = 0.001 y2[1] (analytic) = 1.6339169979793704799518057852832 y2[1] (numeric) = 1.6685380967547305276547778463527 absolute error = 0.0346210987753600477029720610695 relative error = 2.1189019281992417953320966332484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.197 y1[1] (analytic) = 2.9309478201616642687608312873475 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4515222815574612684875433521319 relative error = 15.40533333454419359134424626149 % h = 0.001 y2[1] (analytic) = 1.6348477630682709307630179360904 y2[1] (numeric) = 1.6696284217570931503482337750438 absolute error = 0.0347806586888222195852158389534 relative error = 2.1274555022509325788679009425061 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.198 y1[1] (analytic) = 2.9313125068638660033767946990539 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4518869682596630031035067638383 relative error = 15.415857818009481391160110845974 % h = 0.001 y2[1] (analytic) = 1.6357788933093778839512359915417 y2[1] (numeric) = 1.6707196238581171728471896218474 absolute error = 0.0349407305487392888959536303057 relative error = 2.1360301622458264583706998265731 % h = 0.001 TOP MAIN SOLVE Loop memory used=453.9MB, alloc=4.4MB, time=77.60 NO POLE NO POLE x[1] = 1.199 y1[1] (analytic) = 2.9316762622536384834997397436597 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4522507236494354832264518084441 relative error = 15.426352816384345915328599198323 % h = 0.001 y2[1] (analytic) = 1.6367103877715611760036909358589 y2[1] (numeric) = 1.6718117030578025951516453867635 absolute error = 0.0351013152862414191479544509046 relative error = 2.144625924567699229948119162427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.2 y1[1] (analytic) = 2.9320390859672263496701344354948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4526135473630233493968465002792 relative error = 15.436818340152323544492632327205 % h = 0.001 y2[1] (analytic) = 1.6376422455233264223616266443769 y2[1] (numeric) = 1.6729046593561494172616010697921 absolute error = 0.0352624138328229948999744254152 relative error = 2.1532428055771427880323426750428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.201 y1[1] (analytic) = 2.9324009776418059185354210619766 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.452975439037602918262133126761 relative error = 15.447254399767631958240246932338 % h = 0.001 y2[1] (analytic) = 1.6385744656328159489146068177702 y2[1] (numeric) = 1.6739984927531576391770566709332 absolute error = 0.035424027120341690262449853163 relative error = 2.1618808216116661885589123657403 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.202 y1[1] (analytic) = 2.9327619369154855456736693008611 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4533363983112825454003813656455 relative error = 15.457661005655178865986654491182 % h = 0.001 y2[1] (analytic) = 1.6395070471678097238581114376854 y2[1] (numeric) = 1.6750932032488272608980121901868 absolute error = 0.0355861560810175370399007525014 relative error = 2.170539988985796648311314317364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.203 y1[1] (analytic) = 2.9331219634273059874851904845377 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4536964248231029872119025493221 relative error = 15.468038168210570723296043196884 % h = 0.001 y2[1] (analytic) = 1.6404399891957262899134908862618 y2[1] (numeric) = 1.6761887908431582824244676275529 absolute error = 0.0357488016474319925109767412911 relative error = 2.1792203239911804796772756555687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=457.7MB, alloc=4.4MB, time=78.25 x[1] = 1.204 y1[1] (analytic) = 2.9334810568172407621517511197817 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4540555182130377618784631845661 relative error = 15.478385897800121433560479996551 % h = 0.001 y2[1] (analytic) = 1.6413732907836236969093455096614 y2[1] (numeric) = 1.6772852555361507037564229830315 absolute error = 0.0359119647525270068470774733701 relative error = 2.1879218428966839600687906909639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.205 y1[1] (analytic) = 2.9338392167261965096630247037822 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4544136781219935093897367685666 relative error = 15.488704204760861034953636285401 % h = 0.001 y2[1] (analytic) = 1.6423069509982004347233980443092 y2[1] (numeric) = 1.6783825973278045248938782566226 absolute error = 0.0360756463296040901704802123134 relative error = 2.1966445619484941352639627566071 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.206 y1[1] (analytic) = 2.9341964427960133509099218100225 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4547709041918103506366338748069 relative error = 15.498993099400544372577425853316 % h = 0.001 y2[1] (analytic) = 1.6432409689057963665839259640468 y2[1] (numeric) = 1.6794808162181197458368334483263 absolute error = 0.0362398473123233792529074842795 relative error = 2.2053884973702195559347929993536 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.207 y1[1] (analytic) = 2.9345527346694652458444393507144 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4551271960652622455711514154988 relative error = 15.509252591997659755720007461021 % h = 0.001 y2[1] (analytic) = 1.6441753435723936627298204468466 y2[1] (numeric) = 1.6805799122070963665852885581425 absolute error = 0.0364045686347027038554681112959 relative error = 2.2141536653629909466310683902117 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.208 y1[1] (analytic) = 2.9349080919902603507056708559653 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4554825533860573504323829207497 relative error = 15.51948269280143760014396694802 % h = 0.001 y2[1] (analytic) = 1.6451100740636177344283383011036 y2[1] (numeric) = 1.6816798852947343871392435860712 absolute error = 0.0365698112311166527109052849676 relative error = 2.2229400821055618064964984997165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.209 y1[1] (analytic) = 2.9352625144030413743116205436987 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4558369757988383740383326084831 relative error = 15.529683412031859055323855048745 % h = 0.001 y2[1] (analytic) = 1.6460451594447381683496128338324 y2[1] (numeric) = 1.6827807354810338074986985321124 absolute error = 0.03673557603629563914908569828 relative error = 2.2317477637544089409992241492154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=461.5MB, alloc=4.4MB, time=78.92 x[1] = 1.21 y1[1] (analytic) = 2.9356160015533859334164648885436 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.456190462949182933143176953328 relative error = 15.53985475987966461655261712163 % h = 0.001 y2[1] (analytic) = 1.6469805987806696612969892863352 y2[1] (numeric) = 1.6838824627659946276636533962661 absolute error = 0.0369018639853249663666641099309 relative error = 2.2405767264438329239647709109394 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.211 y1[1] (analytic) = 2.9359685530878069071329063324602 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4565430144836039068596183972446 relative error = 15.549996746506362721836809782986 % h = 0.001 y2[1] (analytic) = 1.6479163911359729552922501070842 y2[1] (numeric) = 1.6849850671496168476341081785323 absolute error = 0.0370686760136438923418580714481 relative error = 2.2494269862860584892054466003001 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.212 y1[1] (analytic) = 2.9363201686537527904192647147783 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4568946300495497901459767795627 relative error = 15.560109382044238333500856988405 % h = 0.001 y2[1] (analytic) = 1.6488525355748557730147949766699 y2[1] (numeric) = 1.686088548631900467410062878911 absolute error = 0.0372360130570446943952679022411 relative error = 2.2582985593713348510460843969716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.213 y1[1] (analytic) = 2.9366708478996080466309529345866 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.457245309295405046357664999371 relative error = 15.570192676596361504420954423709 % h = 0.001 y2[1] (analytic) = 1.6497890311611737535938401457143 y2[1] (numeric) = 1.6871929072128454869915174974022 absolute error = 0.0374038760516717333976773516879 relative error = 2.2671914617680359530519120603725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.214 y1[1] (analytic) = 2.9370205904746934591359842940259 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4575950518704904588626963588103 relative error = 15.580246640236595928809586159924 % h = 0.001 y2[1] (analytic) = 1.6507258769584313887527012936274 y2[1] (numeric) = 1.6882981428924519063784720340059 absolute error = 0.0375722659340205176257707403785 relative error = 2.2761057095227606442701828852775 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.215 y1[1] (analytic) = 2.9373693960292664819941599070089 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4579438574250634817208719717933 relative error = 15.590271283009607477471971397333 % h = 0.001 y2[1] (analytic) = 1.6516630720297829593042237640016 y2[1] (numeric) = 1.6894042556707197255709264887221 absolute error = 0.0377411836409367662667027247205 relative error = 2.285041318660432782303035589519 % h = 0.001 TOP MAIN SOLVE Loop memory used=465.4MB, alloc=4.4MB, time=79.57 NO POLE NO POLE x[1] = 1.216 y1[1] (analytic) = 2.9377172642145215896995854942074 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4582917256103185894262975589918 relative error = 15.600266614930872717456111776828 % h = 0.001 y2[1] (analytic) = 1.6526006154380334719964236812925 y2[1] (numeric) = 1.6905112455476489445688808615509 absolute error = 0.0379106301096154725724571802584 relative error = 2.2939983051844012625348582540764 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.217 y1[1] (analytic) = 2.938064194682590625986167821821 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4586386560783876257128798866054 relative error = 15.610232645986687416018461177621 % h = 0.001 y2[1] (analytic) = 1.6535385062456395967074031032222 y2[1] (numeric) = 1.6916191125232395633723351524922 absolute error = 0.03808060627759996666493204927 relative error = 2.3029766850765399728432157632024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.218 y1[1] (analytic) = 2.938410187086543151695741978658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4589846484823401514224540434424 relative error = 15.620169386134175028827590153184 % h = 0.001 y2[1] (analytic) = 1.6544767435147106039886020140696 y2[1] (numeric) = 1.692727856597491581981289361546 absolute error = 0.0382511130827809779926873474764 relative error = 2.3119764742973476731281609357332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.219 y1[1] (analytic) = 2.9387552410803867917084816234314 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4593297024761837914351936882158 relative error = 15.630076845301295172328566187257 % h = 0.001 y2[1] (analytic) = 1.6554153263070093029554496156717 y2[1] (numeric) = 1.6938374777704050003957434887123 absolute error = 0.0384221514633956974402938730406 relative error = 2.3209976887860477990004867166638 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.22 y1[1] (analytic) = 2.9390993563190675809352452718884 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4596738177148645806619573366728 relative error = 15.639955033386852080191118783231 % h = 0.001 y2[1] (analytic) = 1.6563542536839529795244770255648 y2[1] (numeric) = 1.6949479760419798186156975339911 absolute error = 0.0385937223580268390912205084263 relative error = 2.3300403444606881889751904287117 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.221 y1[1] (analytic) = 2.9394425324584703093715126314552 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4600169938542673090982246962396 relative error = 15.649803960260503043765005038022 % h = 0.001 y2[1] (analytic) = 1.6572935247066143349959531452297 y2[1] (numeric) = 1.6960593514122160366411514973824 absolute error = 0.0387658267056017016451983521527 relative error = 2.3391044572182407345221111868694 % h = 0.001 TOP MAIN SOLVE Loop memory used=469.2MB, alloc=4.4MB, time=80.21 NO POLE NO POLE x[1] = 1.222 y1[1] (analytic) = 2.9397847691554188662125659294917 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4603592305512158659392779942761 relative error = 15.659623635762766836466336800467 % h = 0.001 y2[1] (analytic) = 1.6582331384357224249811051158837 y2[1] (numeric) = 1.6971716038811136544721053788862 absolute error = 0.0389384654453912294910002630025 relative error = 2.3481900429347009523313681742348 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.223 y1[1] (analytic) = 2.94012606606767658302957212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4607005274634735827562841847844 relative error = 15.669414069705032122018974778654 % h = 0.001 y2[1] (analytic) = 1.6591730939316635986729844346777 y2[1] (numeric) = 1.6982847334486726721085591785025 absolute error = 0.0391116395170090734355747438248 relative error = 2.3572971174651874781568705856967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.224 y1[1] (analytic) = 2.9404664228539465760062227927368 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4610408842497435757329348575212 relative error = 15.67917527186956584647543804563 % h = 0.001 y2[1] (analytic) = 1.6601133902544824384600394605093 y2[1] (numeric) = 1.6993987401148930895505128962313 absolute error = 0.039285349860410651090473435722 relative error = 2.3664256966440414816067896886056 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.225 y1[1] (analytic) = 2.9408058391738720872355895481154 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4613803005696690869623016128998 relative error = 15.688907252009521613942119302616 % h = 0.001 y2[1] (analytic) = 1.6610540264638826998814546959592 y2[1] (numeric) = 1.7005136238797749067979665320727 absolute error = 0.0394595974158922069165118361135 relative error = 2.3755757962849260012554796478546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.226 y1[1] (analytic) = 2.9411443146880368250768535410717 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4617187760838338248035656058561 relative error = 15.69861001984894804593393699843 % h = 0.001 y2[1] (analytic) = 1.6619950016192282519233168900892 y2[1] (numeric) = 1.7016293847433181238509200860266 absolute error = 0.0396343831240898719276031959374 relative error = 2.3847474321809251994569065398705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.227 y1[1] (analytic) = 2.9414818490579653035715688371935 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4620563104537623032982809019779 relative error = 15.708283585082797124283894977508 % h = 0.001 y2[1] (analytic) = 1.6629363147795440176546676660131 y2[1] (numeric) = 1.702746022705522740709373558093 absolute error = 0.0398097079259787230547058920799 relative error = 2.3939406201046435362451943586906 % h = 0.001 TOP MAIN SOLVE Loop memory used=473.0MB, alloc=4.4MB, time=80.86 NO POLE NO POLE x[1] = 1.228 y1[1] (analytic) = 2.9418184419461231809191201648767 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4623929033419201806458322296611 relative error = 15.717927957376932517533358741452 % h = 0.001 y2[1] (analytic) = 1.6638779650035169152025020372686 y2[1] (numeric) = 1.7038635377663887573733269482719 absolute error = 0.0399855727628718421708249110033 relative error = 2.4031553758083048617134228208636 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.229 y1[1] (analytic) = 2.9421540930159175970110365880794 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4627285544117145967377486528638 relative error = 15.727543146368137890729194665124 % h = 0.001 y2[1] (analytic) = 1.6648199513494967990647718380677 y2[1] (numeric) = 1.7049819299259161738427802565633 absolute error = 0.0401619785764193747780084184956 relative error = 2.4123917150238514262673144297912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.23 y1[1] (analytic) = 2.9424888019316975100238235653892 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4630632633274945097505356301736 relative error = 15.73712916166412519855425461241 % h = 0.001 y2[1] (analytic) = 1.6657622728754974017604527545023 y2[1] (numeric) = 1.7061011991841049901177334829672 absolute error = 0.0403389263086075883572807284649 relative error = 2.4216496534630428081559275878366 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.231 y1[1] (analytic) = 2.9428225683587540320699768025983 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4633970297545510317966888673827 relative error = 15.746686012843542961718023353452 % h = 0.001 y2[1] (analytic) = 1.6667049286391972758157333067154 y2[1] (numeric) = 1.7072213455409552061981866274836 absolute error = 0.0405164169017579303824533207682 relative error = 2.4309292068175547576869285726831 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.232 y1[1] (analytic) = 2.9431553919633207639068422478012 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4637298533591177636335543125856 relative error = 15.756213709455984526534579999151 % h = 0.001 y2[1] (analytic) = 1.6676479176979407360853837959275 y2[1] (numeric) = 1.7083423689964668220841396901125 absolute error = 0.040694451298526085998755894185 relative error = 2.4402303907590779575394479483722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.233 y1[1] (analytic) = 2.9434872724125741287029875201834 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4640617338083711284296995849678 relative error = 15.765712261021996307615357344425 % h = 0.001 y2[1] (analytic) = 1.6685912391087388024083628950293 y2[1] (numeric) = 1.7094642695506398377755926708539 absolute error = 0.0408730304419010353672297758246 relative error = 2.4495532209394166985929364880508 % h = 0.001 TOP MAIN SOLVE Loop memory used=476.8MB, alloc=4.4MB, time=81.52 NO POLE NO POLE x[1] = 1.234 y1[1] (analytic) = 2.9438182093746337048617510061568 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4643926707704307045884630709412 relative error = 15.775181677033086013604514553705 % h = 0.001 y2[1] (analytic) = 1.6695348919282701425967192272101 y2[1] (numeric) = 1.7105870472034742532725455697078 absolute error = 0.0410521552752041106758263424977 relative error = 2.4588977129905874706958219722521 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.235 y1[1] (analytic) = 2.9441482025185625579016357993198 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4647226639143595576283478641042 relative error = 15.784621966951730855885069035014 % h = 0.001 y2[1] (analytic) = 1.6704788752128820157568449438006 y2[1] (numeric) = 1.7117107019549700685749983866743 absolute error = 0.0412318267420880528181534428737 relative error = 2.4682638825249174678031313204489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.236 y1[1] (analytic) = 2.9444772515143675713932166038778 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4650517129101645711199286686622 relative error = 15.794033140211385740184262637243 % h = 0.001 y2[1] (analytic) = 1.6714231880185912159421379801556 y2[1] (numeric) = 1.7128352338051272836829511217533 absolute error = 0.0414120457865360677408131415977 relative error = 2.4776517451351430069175824437479 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.237 y1[1] (analytic) = 2.9448053560329997769522286646428 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4653798174287967766789407294272 relative error = 15.803415206216491441006965473289 % h = 0.001 y2[1] (analytic) = 1.6723678294010850161361293369909 y2[1] (numeric) = 1.7139606427539458985964037749448 absolute error = 0.0415928133528608824602744379539 relative error = 2.4870613163945078602739670017196 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.238 y1[1] (analytic) = 2.9451325157463546832885087305517 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4657069771421516830152207953361 relative error = 15.812768174342482758826247724281 % h = 0.001 y2[1] (analytic) = 1.673312798415722112565131404128 y2[1] (numeric) = 1.7150869288014259133153563462488 absolute error = 0.0417741303857038007502249421208 relative error = 2.4964926118568615002119389350338 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.239 y1[1] (analytic) = 2.9454587303272726043104590027897 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4660331917230696040371710675741 relative error = 15.822092053935796659960575721453 % h = 0.001 y2[1] (analytic) = 1.6742580941175335693394630140758 y2[1] (numeric) = 1.7162140919475673278398088356653 absolute error = 0.0419559978300337585003458215895 relative error = 2.5059456470567572561875942590507 % h = 0.001 TOP MAIN SOLVE Loop memory used=480.6MB, alloc=4.4MB, time=82.17 NO POLE NO POLE x[1] = 1.24 y1[1] (analytic) = 2.9457839994495389862847059630818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4663584608453359860114180278662 relative error = 15.831386854313880399067413436996 % h = 0.001 y2[1] (analytic) = 1.6752037155612237634223065843026 y2[1] (numeric) = 1.7173421321923701421697612431943 absolute error = 0.0421384166311463787474546588917 relative error = 2.5154204375095503833794751711866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.241 y1[1] (analytic) = 2.9461083227878847340506269225208 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4666827841836817337773389873052 relative error = 15.840652584765199624183334247774 % h = 0.001 y2[1] (analytic) = 1.6761496618011713299252523794216 y2[1] (numeric) = 1.7184710495358343563052135688358 absolute error = 0.0423213877346630263799611894142 relative error = 2.5249169987114960423498560780919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.242 y1[1] (analytic) = 2.9464317000179865362894180764331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4670061614137835360161301412175 relative error = 15.849889254549246464241070470671 % h = 0.001 y2[1] (analytic) = 1.6770959318914301077295845978224 y2[1] (numeric) = 1.7196008439779599702461658125898 absolute error = 0.0425049120865298625165812147674 relative error = 2.5344353461398471892273707192979 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.243 y1[1] (analytic) = 2.9467541308164671898473787962413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4673285922122641895740908610257 relative error = 15.859096872896547598994249709929 % h = 0.001 y2[1] (analytic) = 1.678042524885730085432363661543 y2[1] (numeric) = 1.7207315155187469839926179744563 absolute error = 0.0426889906330168985602543129133 relative error = 2.5439754952529523758822181832477 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.244 y1[1] (analytic) = 2.9470756148608959231130878350644 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4676500762566929228397998998488 relative error = 15.868275449008672311280887509567 % h = 0.001 y2[1] (analytic) = 1.6789894398374783476163587633775 y2[1] (numeric) = 1.7218630641581953975445700544353 absolute error = 0.0428736243207170499282112910578 relative error = 2.5535374614903534595703413129158 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=484.4MB, alloc=4.5MB, time=82.83 x[1] = 1.245 y1[1] (analytic) = 2.9473961518297887184481480699102 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4679706132255857181748601346946 relative error = 15.87742499205824052155702517249 % h = 0.001 y2[1] (analytic) = 1.6799366757997600214428844013667 y2[1] (numeric) = 1.7229954898963052109020220525269 absolute error = 0.0430588140965451894591376511602 relative error = 2.5631212602728832215281038138261 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.246 y1[1] (analytic) = 2.9477157414026086336711773497374 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4682902027984056333978894145218 relative error = 15.886545511188930804632219896102 % h = 0.001 y2[1] (analytic) = 1.6808842318253392235665943079135 y2[1] (numeric) = 1.724128792733076424064973968731 absolute error = 0.0432445609077372004983796608175 relative error = 2.5727269070027628940041023412015 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.247 y1[1] (analytic) = 2.9480343832597661225947239654277 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4686088446555631223214360302121 relative error = 15.895637015515488388538911587286 % h = 0.001 y2[1] (analytic) = 1.6818321069666600073712858588082 y2[1] (numeric) = 1.7252629726685090370334258030476 absolute error = 0.0434308657018490296621399442394 relative error = 2.5823544170636995952198369890628 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.248 y1[1] (analytic) = 2.9483520770826193546147862047755 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4689265384784163543414982695599 relative error = 15.90469951412373313546800686107 % h = 0.001 y2[1] (analytic) = 1.6827803002758473105257677264381 y2[1] (numeric) = 1.7263980297026030498073775554767 absolute error = 0.0436177294267557392816098290386 relative error = 2.5920038058209836717560279666613 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.249 y1[1] (analytic) = 2.9486688225534745333526164030051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4692432839492715330793284677895 relative error = 15.913733016070567504703335802331 % h = 0.001 y2[1] (analytic) = 1.683728810804707902858843221393 y2[1] (numeric) = 1.7275339638353584623868292260183 absolute error = 0.0438051530306505595279860046253 relative error = 2.6016750886215859478664078619526 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.25 y1[1] (analytic) = 2.948984619355586214348490847036 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4695590807513832140752029118204 relative error = 15.922737530383984497487951082205 % h = 0.001 y2[1] (analytic) = 1.684677637604731334552461447562 y2[1] (numeric) = 1.7286707750667752747717808146724 absolute error = 0.0439931374620439402193193671104 relative error = 2.6113682807942548812258377931179 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=488.2MB, alloc=4.5MB, time=83.50 x[1] = 1.251 y1[1] (analytic) = 2.949299467173157621807127839754 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4698739285689546215338399045384 relative error = 15.931713066063075583755551975361 % h = 0.001 y2[1] (analytic) = 1.6856267797270908846520880776495 y2[1] (numeric) = 1.729808463396853486962232321439 absolute error = 0.0441816836697626023101442437895 relative error = 2.6210833976496136246245919733522 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.252 y1[1] (analytic) = 2.9496133656913409643944371788953 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4701878270871379641211492436797 relative error = 15.940659632078038610660627724895 % h = 0.001 y2[1] (analytic) = 1.6865762362226445098933472388189 y2[1] (numeric) = 1.7309470288255930989581837463181 absolute error = 0.0443707926029485890648365074992 relative error = 2.630820454480256993125628797638 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.253 y1[1] (analytic) = 2.9499263145962377500852852538222 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4705007759920347498119973186066 relative error = 15.949577237370185692841225553077 % h = 0.001 y2[1] (analytic) = 1.6875260061419357938439856819008 y2[1] (numeric) = 1.7320864713529941107596350893097 absolute error = 0.0445604652110583169156494074089 relative error = 2.6405794665608483362066175398776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.254 y1[1] (analytic) = 2.9502383135748991000619609124496 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.470812774970696099788672977234 relative error = 15.958465890851951084348558422328 % h = 0.001 y2[1] (analytic) = 1.6884760885351948963602100922806 y2[1] (numeric) = 1.7332267909790565223665863504139 absolute error = 0.0447507024438616260063762581333 relative error = 2.6503604491482163144134181617072 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.255 y1[1] (analytic) = 2.9505493623153260616630281998839 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4711238237111230613897402646683 relative error = 15.967325601406899032177976416558 % h = 0.001 y2[1] (analytic) = 1.689426482452339503356448086208 y2[1] (numeric) = 1.7343679877037803337790375296306 absolute error = 0.0449415052514408304225894434226 relative error = 2.6601634174814515800566176182722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.256 y1[1] (analytic) = 2.9508594605064699203822530199469 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4714339219022669201089650847313 relative error = 15.976156377889731611336133342156 % h = 0.001 y2[1] (analytic) = 1.690377186942975776887583122846 y2[1] (numeric) = 1.7355100615271655449969886269598 absolute error = 0.0451328745841897681094055041138 relative error = 2.669988386782003361487609439639 % h = 0.001 TOP MAIN SOLVE Loop memory used=492.1MB, alloc=4.5MB, time=84.15 NO POLE NO POLE x[1] = 1.257 y1[1] (analytic) = 2.9511686078382325109172917206849 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4717430692340295106440037854693 relative error = 15.984958229126296541379486845081 % h = 0.001 y2[1] (analytic) = 1.6913282010563993055427132499031 y2[1] (numeric) = 1.7366530124492121560204396424015 absolute error = 0.0453248113928128504777263924984 relative error = 2.6798353722537759504955643074062 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.258 y1[1] (analytic) = 2.9514768040014665272678305551992 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4720512653972635269945426199836 relative error = 15.993731163913594984359576009838 % h = 0.001 y2[1] (analytic) = 1.6922795238415960551494832891709 y2[1] (numeric) = 1.7377968404699201668493905759557 absolute error = 0.0455173166283241116999072867848 relative error = 2.6897043890832250923714778738037 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.259 y1[1] (analytic) = 2.9517840486879758318828659196852 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4723585100837728316095779844696 relative error = 16.002475191019789324110825051962 % h = 0.001 y2[1] (analytic) = 1.6932311543472433197880397577119 y2[1] (numeric) = 1.7389415455892895774838414276224 absolute error = 0.0457103912420462576958016699105 relative error = 2.6995954524394542781902982247407 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.26 y1[1] (analytic) = 2.9520903415905157638568162214254 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4726648029863127635835282862098 relative error = 16.011190319184210926816925342249 % h = 0.001 y2[1] (analytic) = 1.6941830916217106731136575108235 y2[1] (numeric) = 1.7400871278073203879237921974016 absolute error = 0.0459040361856097148101346865781 relative error = 2.7095085774743109388669292080221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.261 y1[1] (analytic) = 2.9523956824027934461741571806503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4729701437985904459008692454347 relative error = 16.01987655711736788279215061254 % h = 0.001 y2[1] (analytic) = 1.6951353347130609199870867842308 y2[1] (numeric) = 1.7412335871240125981692428852933 absolute error = 0.0460982524109516781821561010625 relative error = 2.7194437793224825405466773743143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.262 y1[1] (analytic) = 2.9527000708194680920022733216569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4732745322152650917289853864413 relative error = 16.028533913500952729414261793783 % h = 0.001 y2[1] (analytic) = 1.6960878826690510484116690052385 y2[1] (numeric) = 1.7423809235393662082201934912975 absolute error = 0.046293040870315159808524486059 relative error = 2.729401073101592580895459551737 % h = 0.001 TOP MAIN SOLVE Loop memory used=495.9MB, alloc=4.5MB, time=84.82 NO POLE NO POLE x[1] = 1.263 y1[1] (analytic) = 2.9530035065361513100322193603595 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4735779679319483097589314251439 relative error = 16.037162396987850155145958531487 % h = 0.001 y2[1] (analytic) = 1.6970407345371331817762694358089 y2[1] (numeric) = 1.7435291370533812180766440154142 absolute error = 0.0464884025162480363003745796053 relative error = 2.7393804739122964858598151357722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.264 y1[1] (analytic) = 2.9533059892494074088670861475366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.473880450645204408593798212321 relative error = 16.045762016202144684582134015833 % h = 0.001 y2[1] (analytic) = 1.6979938893644555314030744047084 y2[1] (numeric) = 1.7446782276660576277385944576435 absolute error = 0.0466843383016020963355200529351 relative error = 2.7493819968383774064714720672145 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.265 y1[1] (analytic) = 2.9536075186567537004576667794332 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4741819800525507001843788442176 relative error = 16.054332779739128344460488357786 % h = 0.001 y2[1] (analytic) = 1.698947346197863349399300581009 y2[1] (numeric) = 1.7458281953773954372060448179853 absolute error = 0.0468808491795320878067442369763 relative error = 2.7594056569468419152758982321289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.266 y1[1] (analytic) = 2.953908094456660802585119440078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4744825558524578023118315048624 relative error = 16.062874696165308310573353342893 % h = 0.001 y2[1] (analytic) = 1.6999011040838998818118634373116 y2[1] (numeric) = 1.7469790401873946464789950964396 absolute error = 0.047077936103494764667131659128 relative error = 2.7694514692880156019689306935969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.267 y1[1] (analytic) = 2.9542077163485529403903244926773 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4747821777443499401170365574617 relative error = 16.071387774018414535518878005044 % h = 0.001 y2[1] (analytic) = 1.7008551620688073220840517481035 y2[1] (numeric) = 1.7481307620960552555574452930064 absolute error = 0.0472756000272479334733935449029 relative error = 2.7795194488956385678302137959413 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.268 y1[1] (analytic) = 2.9545063840328082469496342907547 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4750808454286052466763463555391 relative error = 16.079872021807407357230020087801 % h = 0.001 y2[1] (analytic) = 1.7018095191985277648132546666555 y2[1] (numeric) = 1.7492833611033772644413954076857 absolute error = 0.0474738419048494996281407410302 relative error = 2.7896096107869608185467938126152 % h = 0.001 TOP MAIN SOLVE Loop memory used=499.7MB, alloc=4.5MB, time=85.48 NO POLE NO POLE x[1] = 1.269 y1[1] (analytic) = 2.9548040972107590628967151333101 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4753785586065560626234271980945 relative error = 16.088327448012485088220083104781 % h = 0.001 y2[1] (analytic) = 1.7027641745187041598087876228096 y2[1] (numeric) = 1.7504368372093606731308454404775 absolute error = 0.0476726626906565133220578176679 relative error = 2.7997219699628375550248124817214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.27 y1[1] (analytic) = 2.9551008555846922350901817421829 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4756753169804892348168938069673 relative error = 16.096754061085091585483832377598 % h = 0.001 y2[1] (analytic) = 1.703719127074681266448862983912 y2[1] (numeric) = 1.7515911904140054816257953913818 absolute error = 0.0478720633393242151769324074698 relative error = 2.8098565414078243617918145317592 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.271 y1[1] (analytic) = 2.9553966588578494143267255940087 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4759711202536464140534376587931 relative error = 16.105151869447923800993516123806 % h = 0.001 y2[1] (analytic) = 1.7046743759115066083357511220005 y2[1] (numeric) = 1.7527464207173116899262452603986 absolute error = 0.0480720448058050815904941383981 relative error = 2.8200133400902722925967351891455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.272 y1[1] (analytic) = 2.9556915067344273520994393936663 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4762659681302243518261514584507 relative error = 16.113520881494939312729409392543 % h = 0.001 y2[1] (analytic) = 1.705629920073931428248177232163 y2[1] (numeric) = 1.7539025281192792980321950475279 absolute error = 0.0482726080453478697840178153649 relative error = 2.8301923809624228528191627226176 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.273 y1[1] (analytic) = 2.9559853989195781964010409309148 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4765598603153751961277529956992 relative error = 16.121861105591363836184789406188 % h = 0.001 y2[1] (analytic) = 1.7065857586064116433899989497525 y2[1] (numeric) = 1.7550595126199083059436447527698 absolute error = 0.0484737540134966625536458030173 relative error = 2.8403936789605028783039783621077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.274 y1[1] (analytic) = 2.9562783351194097865717005170224 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4768527965152067862984125818068 relative error = 16.130172550073698716285540666523 % h = 0.001 y2[1] (analytic) = 1.7075418905531088009342095178582 y2[1] (numeric) = 1.7562173742191987136605943761242 absolute error = 0.048675483666089912726384858266 relative error = 2.8506172490048193102419614770939 % h = 0.001 TOP MAIN SOLVE Loop memory used=503.5MB, alloc=4.5MB, time=86.13 NO POLE NO POLE x[1] = 1.275 y1[1] (analytic) = 2.9565703150409859471911771535838 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4771447764367829469178892183682 relative error = 16.13845522324972839966487702764 % h = 0.001 y2[1] (analytic) = 1.7084983149578910338613109611106 y2[1] (numeric) = 1.7573761129171505211830439175911 absolute error = 0.0488777979592594873217329564805 relative error = 2.8608631059998538657214117562954 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.276 y1[1] (analytic) = 2.9568613383923267810149695414138 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4774357997881237807416816061982 relative error = 16.146709133398527887233955829353 % h = 0.001 y2[1] (analytic) = 1.7094550308643340170911014275266 y2[1] (numeric) = 1.7585357287137637285109933771705 absolute error = 0.0490806978494297114198919496439 relative error = 2.8711312648343576035802823432157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.277 y1[1] (analytic) = 2.9571514048824089609541889933913 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4777258662782059606809010581757 relative error = 16.154934288770470166989446128306 % h = 0.001 y2[1] (analytic) = 1.710412037315721923906920566687 y2[1] (numeric) = 1.7596962216090383356444427548624 absolute error = 0.0492841842933164117375221881754 relative error = 2.8814217403814453851927384964705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.278 y1[1] (analytic) = 2.9574405142211660210988622714049 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4780149756169630208255743361893 relative error = 16.163130697587233626999399063305 % h = 0.001 y2[1] (analytic) = 1.7113693333550483826713965200802 y2[1] (numeric) = 1.7608575916029743425833920506668 absolute error = 0.0494882582479259599119955305866 relative error = 2.89173454749869022982845540639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.279 y1[1] (analytic) = 2.9577286661194886467843733241215 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4783031275152856465110853889059 relative error = 16.171298368041809448509053450779 % h = 0.001 y2[1] (analytic) = 1.7123269180250174338327378079462 y2[1] (numeric) = 1.7620198386955717493278412645837 absolute error = 0.0496929206705543154951034566375 relative error = 2.9020697010282175642273463567581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.28 y1[1] (analytic) = 2.9580158602892249637007538591603 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4785903216850219634274659239447 relative error = 16.179437308298508979108493829779 % h = 0.001 y2[1] (analytic) = 1.7132847903680444872206131064074 y2[1] (numeric) = 1.7631829628868305558777903966131 absolute error = 0.0498981725187860686571772902057 relative error = 2.9124272157967993660367685201902 % h = 0.001 TOP MAIN SOLVE Loop memory used=507.3MB, alloc=4.5MB, time=86.79 NO POLE NO POLE x[1] = 1.281 y1[1] (analytic) = 2.9583020964431808260445336404056 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.47887655783897782577124570519 relative error = 16.187547526492971085904361367617 % h = 0.001 y2[1] (analytic) = 1.7142429494262572796306616190864 y2[1] (numeric) = 1.764346964176750762233239446755 absolute error = 0.0501040147504934826025778276686 relative error = 2.9228071066159482007625883644001 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.282 y1[1] (analytic) = 2.9585873742951201037128623586324 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4791618356909171034395744234168 relative error = 16.195629030732169488638100301173 % h = 0.001 y2[1] (analytic) = 1.7152013942414968326966764587811 y2[1] (numeric) = 1.7655118425653323683941884150094 absolute error = 0.0503104483238355356975119562283 relative error = 2.9332093882820111518898019724721 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.283 y1[1] (analytic) = 2.9588716935597649685396158813466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.479446154955561968266327946131 relative error = 16.203681829094420072693503929122 % h = 0.001 y2[1] (analytic) = 1.7161601238553184110495031670929 y2[1] (numeric) = 1.7666775980525753743606373013764 absolute error = 0.0505174741972569633111341342835 relative error = 2.9436340755762636438326975912878 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.284 y1[1] (analytic) = 2.9591550539527961795732006457579 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4797295153485931792999127105423 relative error = 16.211705929629388181936604590848 % h = 0.001 y2[1] (analytic) = 1.7171191373089924807616952131887 y2[1] (numeric) = 1.7678442306384797801325861058559 absolute error = 0.0507250933294872993708908926672 relative error = 2.9540811832650031573788184664847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.285 y1[1] (analytic) = 2.9594374551908533673957709171033 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4800119165866503671224829818877 relative error = 16.21970134035809589133123157272 % h = 0.001 y2[1] (analytic) = 1.7180784336435056680769680271228 y2[1] (numeric) = 1.7690117403230455857100348284479 absolute error = 0.0509333066795399176330668013251 relative error = 2.9645507260996428372952335484218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=511.1MB, alloc=4.5MB, time=87.44 x[1] = 1.286 y1[1] (analytic) = 2.9597188969915353174835745931305 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4802933583873323172102866579149 relative error = 16.227668069272929259273839475741 % h = 0.001 y2[1] (analytic) = 1.7190380118995617184234928383428 y2[1] (numeric) = 1.7701801271062727910929834691524 absolute error = 0.0511421152067110726694906308096 relative error = 2.9750427188168049917698520106253 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.287 y1[1] (analytic) = 2.9599993790734002526081441944156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4805738404691972523348562592 relative error = 16.235606124337645559591487264128 % h = 0.001 y2[1] (analytic) = 1.719997871117582455710071306166 y2[1] (numeric) = 1.7713493909881613962814320279694 absolute error = 0.0513515198705789405713607218034 relative error = 2.9855571761384144833647247589439 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.288 y1[1] (analytic) = 2.9602789011559661142780506393499 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4808533625517631140047627041343 relative error = 16.243515513487380493147124996537 % h = 0.001 y2[1] (analytic) = 1.7209580103377087419042316461334 y2[1] (numeric) = 1.7725195319687114012753805048989 absolute error = 0.0515615216310026593711488587655 relative error = 2.9960941127717920111624622756393 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.289 y1[1] (analytic) = 2.9605574629597108432209383620653 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4811319243555078429476504268497 relative error = 16.251396244628655378996621124077 % h = 0.001 y2[1] (analytic) = 1.7219184285998014368912866742218 y2[1] (numeric) = 1.7736905500479228060748288999409 absolute error = 0.0517721214481213691835422257191 relative error = 3.0066535434097472837910632880759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.29 y1[1] (analytic) = 2.9608350642060726589055612912854 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4814095256018696586322733560698 relative error = 16.259248325639384325042238225986 % h = 0.001 y2[1] (analytic) = 1.7228791249434423586133939099388 y2[1] (numeric) = 1.7748624452257956106797772130954 absolute error = 0.0519833202823532520663833031566 relative error = 3.0172354827306720830165929253989 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.291 y1[1] (analytic) = 2.9611117046174503381035401680906 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.481686166013247337830252232875 relative error = 16.267071764368881378127539149083 % h = 0.001 y2[1] (analytic) = 1.7238400984079352434876575993199 y2[1] (numeric) = 1.7760352175023298150902254443624 absolute error = 0.0521951190943945716025678450425 relative error = 3.0278399453986332175972722801019 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=514.9MB, alloc=4.5MB, time=88.10 x[1] = 1.292 y1[1] (analytic) = 2.9613873839172034924905626408631 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4819618453130004922172747056475 relative error = 16.274866568637867653518978724542 % h = 0.001 y2[1] (analytic) = 1.7248013480323067071023122398045 y2[1] (numeric) = 1.7772088668775254193061735937419 absolute error = 0.0524075188452187122038613539374 relative error = 3.0384669460634653670966436744093 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.293 y1[1] (analytic) = 2.9616621018296528452867485362342 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4822365632254498450134606010186 relative error = 16.282632746238478443719708559195 % h = 0.001 y2[1] (analytic) = 1.7257628728553072051900269108886 y2[1] (numeric) = 1.778383393351382423327621661234 absolute error = 0.0526205204960752181375947503454 relative error = 3.0491164993608638153575574946822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.294 y1[1] (analytic) = 2.961935858080080506935903665692 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4825103194758775066626157304764 relative error = 16.290370304934270306561393842608 % h = 0.001 y2[1] (analytic) = 1.7267246719154119948773694373303 y2[1] (numeric) = 1.7795587969239008271545696468386 absolute error = 0.0528341250084888322772002095083 relative error = 3.0597886199124770733427872519462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.295 y1[1] (analytic) = 2.9622086523947302498233864886192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4827831137905272495500985534036 relative error = 16.298079252460228132520111679187 % h = 0.001 y2[1] (analytic) = 1.7276867442508220962094691355221 y2[1] (numeric) = 1.7807350775950806307870175505557 absolute error = 0.0530483333442585345775484150336 relative error = 3.0704833223259993910521196044084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.296 y1[1] (analytic) = 2.9624804845008077820323129139162 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4830549458966047817590249787006 relative error = 16.305759596522772191202670150759 % h = 0.001 y2[1] (analytic) = 1.7286490888994652539489166184497 y2[1] (numeric) = 1.7819122353649218342249653723853 absolute error = 0.0532631464654565802760487539356 relative error = 3.0812006211952631582297854891828 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.297 y1[1] (analytic) = 2.9627513541264810201378254840286 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.483325815522278019864537548813 relative error = 16.313411344799765156949956143277 % h = 0.001 y2[1] (analytic) = 1.729611704898996899647938860416 y2[1] (numeric) = 1.7830902702334244374684131123274 absolute error = 0.0534785653344275378204742519114 relative error = 3.091940531100331193580097308386 % h = 0.001 TOP MAIN SOLVE Loop memory used=518.8MB, alloc=4.5MB, time=88.77 NO POLE NO POLE x[1] = 1.298 y1[1] (analytic) = 2.9630212610008803610391541471312 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4835957223966773607658662119156 relative error = 16.321034504940519113504187935313 % h = 0.001 y2[1] (analytic) = 1.7305745912868011139928874494357 y2[1] (numeric) = 1.784269182200588440517360770382 absolute error = 0.0536945909137873265244733209463 relative error = 3.1027030666075889222131353501032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.299 y1[1] (analytic) = 2.9632902048540989528291967854324 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4838646662498959525559088502168 relative error = 16.328629084565802537687215650028 % h = 0.001 y2[1] (analytic) = 1.7315377470999915894200776828939 y2[1] (numeric) = 1.7854489712664138433718083465491 absolute error = 0.0539112241664222539517306636552 relative error = 3.1134882422698364410462843502074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.3 y1[1] (analytic) = 2.9635581854171929647013486300396 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.484132646812989964428060694824 relative error = 16.33619509126784726203727891981 % h = 0.001 y2[1] (analytic) = 1.7325011713754125930020158907071 y2[1] (numeric) = 1.7866296374309006460317558408287 absolute error = 0.0541284660554880530297399501216 relative error = 3.1242960726263804718913583692947 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.301 y1[1] (analytic) = 2.9638252024221818558933106555778 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4843996638179788556200227203622 relative error = 16.343732532610355416351896508045 % h = 0.001 y2[1] (analytic) = 1.7334648631496399296030520998424 y2[1] (numeric) = 1.7878111806940488484972032532208 absolute error = 0.0543463175444089188941511533784 relative error = 3.135126572203126201960969021823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.302 y1[1] (analytic) = 2.964091255602048643667608010779 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4846657169978456433943200755634 relative error = 16.351241416128506348084827179273 % h = 0.001 y2[1] (analytic) = 1.7344288214589819053034948846199 y2[1] (numeric) = 1.7889936010558584507681505837255 absolute error = 0.0545647795968765454646556991056 relative error = 3.1459797555126690115316886060306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.303 y1[1] (analytic) = 2.9643563446907401703285505045413 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4849308060865371700552625693257 relative error = 16.358721749328963521545304810824 % h = 0.001 y2[1] (analytic) = 1.7353930453394802910912249787663 y2[1] (numeric) = 1.7901768985163294528445978323427 absolute error = 0.0547838531768491617533728535764 relative error = 3.1568556370543860885054358950881 % h = 0.001 TOP MAIN SOLVE Loop memory used=522.6MB, alloc=4.5MB, time=89.43 NO POLE NO POLE x[1] = 1.304 y1[1] (analytic) = 2.9646204694231673692753681305244 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4851949308189643690020801953088 relative error = 16.366173539689881395848013600561 % h = 0.001 y2[1] (analytic) = 1.736357533826911286819843957684 y2[1] (numeric) = 1.7913610730754618547265449990724 absolute error = 0.0550035392485505679067010413884 relative error = 3.1677542313145279296143683169131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.305 y1[1] (analytic) = 2.964883629535205530091255577164 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4854580909310025298179676419484 relative error = 16.373596794660912281562531249403 % h = 0.001 y2[1] (analytic) = 1.7373222859567864854323940328691 y2[1] (numeric) = 1.7925461247332556564139920839146 absolute error = 0.0552238387764691709815980510455 relative error = 3.1786755527663097280184000241584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.306 y1[1] (analytic) = 2.9651458247636945626680606340859 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4857202861594915623947726988703 relative error = 16.380991521663213176011229188756 % h = 0.001 y2[1] (analytic) = 1.7382873007643538374496847348377 y2[1] (numeric) = 1.7937320534897108579069390868693 absolute error = 0.0554447527253570204572543520316 relative error = 3.1896196158700026470482809921541 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.307 y1[1] (analytic) = 2.9654070548464392603663523702508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4859815162422362600930644350352 relative error = 16.388357728089452577164879284763 % h = 0.001 y2[1] (analytic) = 1.7392525772845986157222619963152 y2[1] (numeric) = 1.7949188593448274592053860079365 absolute error = 0.0556662820602288434831240116213 relative error = 3.2005864350730249798509678338851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.308 y1[1] (analytic) = 2.9656673195222095622106059237861 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4862417809180065619373179885705 relative error = 16.395695421303817276085475987962 % h = 0.001 y2[1] (analytic) = 1.7402181145522443804450548837987 y2[1] (numeric) = 1.7961065422986054603093328471162 absolute error = 0.0558884277463610798642779633175 relative error = 3.2115760248100331946977925422469 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.309 y1[1] (analytic) = 2.9659266185307408141192417083394 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4865010799265378138459537731238 relative error = 16.403004608642019127866041611694 % h = 0.001 y2[1] (analytic) = 1.741183911601753944433734962928 y2[1] (numeric) = 1.7972951023510448612187796044084 absolute error = 0.0561111907492909167850446414804 relative error = 3.2225883995030128657196909144997 % h = 0.001 TOP MAIN SOLVE Loop memory used=526.4MB, alloc=4.5MB, time=90.09 NO POLE NO POLE x[1] = 1.31 y1[1] (analytic) = 2.9661849516127340291692578059375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4867594130085310288959698707219 relative error = 16.410285297411301801017440319847 % h = 0.001 y2[1] (analytic) = 1.7421499674673303386618230213838 y2[1] (numeric) = 1.7984845395021456619337262798131 absolute error = 0.0563345720348153232719032584293 relative error = 3.2336235735613694888374880372721 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.311 y1[1] (analytic) = 2.9664423185098561468951952817403 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4870167799056531466219073465247 relative error = 16.41753749489044750525248348753 % h = 0.001 y2[1] (analytic) = 1.743116281182917778057577612289 y2[1] (numeric) = 1.7996748537519078624541728733303 absolute error = 0.0565585725689900843965952610413 relative error = 3.2446815613820191826589539663316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.312 y1[1] (analytic) = 2.9666987189647402916221771217455 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4872731803605372913488891865299 relative error = 16.424761208329783697617865371197 % h = 0.001 y2[1] (analytic) = 1.7440828517822026275596996213043 y2[1] (numeric) = 1.8008660451003314627801193849601 absolute error = 0.0567831933181288352204197636558 relative error = 3.255762377349479274118038679473 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.313 y1[1] (analytic) = 2.9669541527209860298327624604265 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4875286141167830295594745252109 relative error = 16.43195644495118976692472349114 % h = 0.001 y2[1] (analytic) = 1.7450496782986143684308868017935 y2[1] (numeric) = 1.8020581135474164629115658147024 absolute error = 0.0570084352488020944806790129089 relative error = 3.2668660358359587686353715676 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.314 y1[1] (analytic) = 2.9672086195231596265673587314712 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4877830809189566262940707962556 relative error = 16.439123211948103696428872793153 % h = 0.001 y2[1] (analytic) = 1.7460167597653265648282719645854 y2[1] (numeric) = 1.8032510590931628628485121625572 absolute error = 0.0572342993278362980202401979718 relative error = 3.2779925512014487045827672138624 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.315 y1[1] (analytic) = 2.967462119116794300857935341231 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4880365805125913005846474060154 relative error = 16.446261516485528704712016521018 % h = 0.001 y2[1] (analytic) = 1.7469840952152578306297782519737 y2[1] (numeric) = 1.8044448817375706625909584285245 absolute error = 0.0574607865223128319611801765508 relative error = 3.289141937793812391838116048852 % h = 0.001 TOP MAIN SOLVE Loop memory used=530.2MB, alloc=4.5MB, time=90.75 NO POLE NO POLE x[1] = 1.316 y1[1] (analytic) = 2.9677146512483904801947834311864 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4882891126441874799214954959708 relative error = 16.45337136570003986471548980127 % h = 0.001 y2[1] (analytic) = 1.7479516836810727965154246696816 y2[1] (numeric) = 1.8056395814806398621389046126043 absolute error = 0.0576878977995670656234799429227 relative error = 3.3003142099488755342206557168399 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.317 y1[1] (analytic) = 2.967966215665416054026067262693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4885406770612130537527793274774 relative error = 16.460452766699790700878344220175 % h = 0.001 y2[1] (analytic) = 1.7489195241951830773026147955639 y2[1] (numeric) = 1.8068351583223704614923507147966 absolute error = 0.0579156341271873841897359192327 relative error = 3.3115093819905162356002166998212 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.318 y1[1] (analytic) = 2.9682168121163066262899137244747 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4887912735121036260166257892591 relative error = 16.467505726564519764331833163545 % h = 0.001 y2[1] (analytic) = 1.7498876157897482395344413298416 y2[1] (numeric) = 1.8080316122627624606512967351014 absolute error = 0.0581439964730142211168554052598 relative error = 3.3227274682307548894776139778279 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.319 y1[1] (analytic) = 2.9684664403504657669787874307981 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4890409017462627667054994955825 relative error = 16.474530252345557186102608397024 % h = 0.001 y2[1] (analytic) = 1.7508559574966767693200388986417 y2[1] (numeric) = 1.8092289433018158596157426735187 absolute error = 0.058372985805139090295703774877 relative error = 3.3339684829698439518369153127722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.32 y1[1] (analytic) = 2.9687151001182652627358998459728 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4892895615140622624626119107572 relative error = 16.48152635106583120827718829115 % h = 0.001 y2[1] (analytic) = 1.7518245483476270404260172705726 y2[1] (numeric) = 1.8104271514395306583856885300485 absolute error = 0.0586026030919036179596712594759 relative error = 3.3452324404963575970738561836882 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.321 y1[1] (analytic) = 2.9689627911710453664834018387895 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4895372525668423662101139035739 relative error = 16.488494029719874693080507245805 % h = 0.001 y2[1] (analytic) = 1.752793387374008282618006894982 y2[1] (numeric) = 1.8116262366759068569611343046909 absolute error = 0.0588328493018985743431274097089 relative error = 3.3565193550872812568081915312451 % h = 0.001 TOP MAIN SOLVE Loop memory used=534.0MB, alloc=4.5MB, time=91.41 NO POLE NO POLE x[1] = 1.322 y1[1] (analytic) = 2.9692095132611150460821100387242 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4897839746569120458088221035086 relative error = 16.495433295273831609821604246227 % h = 0.001 y2[1] (analytic) = 1.7537624736069815502513484204308 y2[1] (numeric) = 1.8128261990109444553420799974458 absolute error = 0.059063725403962905090731577015 relative error = 3.3678292410081010413912753445213 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.323 y1[1] (analytic) = 2.9694552661417522320225183342027 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4900297275375492317492303989871 relative error = 16.502344154665463499659756091276 % h = 0.001 y2[1] (analytic) = 1.754731806077460691109957602777 y2[1] (numeric) = 1.8140270384446434535285256083132 absolute error = 0.0592952323671827624185680055362 relative error = 3.3791621125128930439236407998077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.324 y1[1] (analytic) = 2.9697000495672040641468468219356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.49027451096300106387355888672 relative error = 16.509226614804155918144607677898 % h = 0.001 y2[1] (analytic) = 1.7557013838161133154923967640831 y2[1] (numeric) = 1.8152287549770038515204711372931 absolute error = 0.05952737116089053602807437321 relative error = 3.3905179838444125266008161969294 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.325 y1[1] (analytic) = 2.9699438632926871374018814852929 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4905183246884841371285935500773 relative error = 16.51608068257092485548409780714 % h = 0.001 y2[1] (analytic) = 1.7566712058533617655441837163571 y2[1] (numeric) = 1.8164313486080256493179165843855 absolute error = 0.0597601427546638837737328680284 relative error = 3.4018968692341829892090553894359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.326 y1[1] (analytic) = 2.9701867070743877466223588489025 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4907611684701847463490709136869 relative error = 16.522906364818423134494224300866 % h = 0.001 y2[1] (analytic) = 1.7576412712193840848353688178995 y2[1] (numeric) = 1.8176348193377088469208619495904 absolute error = 0.0599935481183247620854931316909 relative error = 3.4132987829025851195960858283603 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=537.8MB, alloc=4.5MB, time=92.06 x[1] = 1.327 y1[1] (analytic) = 2.9704285806694621303446508261051 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4910030420652591300713628908895 relative error = 16.529703668370946786184936787397 % h = 0.001 y2[1] (analytic) = 1.7586115789441149881824105847592 y2[1] (numeric) = 1.8188391671660534443293072329078 absolute error = 0.0602275882219384561468966481486 relative error = 3.4247237390589456259453827922242 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.328 y1[1] (analytic) = 2.9706694838360367136505059456028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4912439452318337133772180103872 relative error = 16.536472600024441402936689333114 % h = 0.001 y2[1] (analytic) = 1.7595821280572468317133800355038 y2[1] (numeric) = 1.8200443920930594415432524343377 absolute error = 0.0604622640358126098298723988339 relative error = 3.4361717519016259506858649155347 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.329 y1[1] (analytic) = 2.9709094163332083500406041135805 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4914838777290053497673161783649 relative error = 16.543213166546508469222428168708 % h = 0.001 y2[1] (analytic) = 1.7605529175882305831755237041812 y2[1] (numeric) = 1.8212504941187268385626975538801 absolute error = 0.0606975765304962553871738496989 relative error = 3.4476428356181108658722738117492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.33 y1[1] (analytic) = 2.9711483779210445623376830377638 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4917228393168415620643951025482 relative error = 16.549925374676411669830032087073 % h = 0.001 y2[1] (analytic) = 1.7615239465662767924842150139894 y2[1] (numeric) = 1.822457473243055635387642591535 absolute error = 0.0609335266767788429034275775456 relative error = 3.4591370043850969498748494720754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.331 y1[1] (analytic) = 2.9713863683605837826189954103093 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4919608297563807823457074750937 relative error = 16.556609231125083175540464678647 % h = 0.001 y2[1] (analytic) = 1.7624952140203565625123234627852 y2[1] (numeric) = 1.8236653294660458320180875473025 absolute error = 0.0611701154456892695057640845173 relative error = 3.470654272368580945220243265816 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.332 y1[1] (analytic) = 2.9716233874138355911778569170885 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4921978488096325909045689818729 relative error = 16.563264742575129906217138422532 % h = 0.001 y2[1] (analytic) = 1.7634667189792025201190308311427 y2[1] (numeric) = 1.8248740627876974284540324211825 absolute error = 0.0614073438084949083350015900398 relative error = 3.4821946537239479974289218293686 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=541.6MB, alloc=4.5MB, time=92.73 x[1] = 1.333 y1[1] (analytic) = 2.9718594348437809545140461118376 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.492433896239577954240758176622 relative error = 16.569891915680839771262230772002 % h = 0.001 y2[1] (analytic) = 1.7644384604713097874171233842259 y2[1] (numeric) = 1.826083673208010424695477213175 absolute error = 0.0616452127367006372783538289491 relative error = 3.4937581625960597746976079670181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.334 y1[1] (analytic) = 2.9720945104143724623528181647938 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4926689718101694620795302295782 relative error = 16.576490757068187887395931764435 % h = 0.001 y2[1] (analytic) = 1.7654104375249369532777888002662 y2[1] (numeric) = 1.82729416072698482074242192328 absolute error = 0.0618837232020478674646331230138 relative error = 3.5053448131193424682785789549303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.335 y1[1] (analytic) = 2.9723286138905345636922954668229 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4929030752863315634190075316073 relative error = 16.583061273334842773714841351894 % h = 0.001 y2[1] (analytic) = 1.7663826491681070450719463209256 y2[1] (numeric) = 1.8285055253446206165948665514975 absolute error = 0.0621228761765135715229202305719 relative error = 3.5169546194178746734108983992478 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.336 y1[1] (analytic) = 2.9725617450381638018789990416688 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4931362064339608016057111064532 relative error = 16.589603471050172523985972593273 % h = 0.001 y2[1] (analytic) = 1.7673550944286085006471383822999 y2[1] (numeric) = 1.8297177670609178122528110978275 absolute error = 0.0623626726323093116056727155276 relative error = 3.5285875956054751506618951065325 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.337 y1[1] (analytic) = 2.9727939036241290487112856908112 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4933683650199260484379977555956 relative error = 16.596117356755250956133054075503 % h = 0.001 y2[1] (analytic) = 1.7683277723339961405390117497482 y2[1] (numeric) = 1.83093088587587640771625556227 absolute error = 0.0626031135418802671772438125218 relative error = 3.5402437557857904675404213398462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.338 y1[1] (analytic) = 2.9730250894162717375704567675156 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4935995508120687372971688323 relative error = 16.602602936962863738872061443663 % h = 0.001 y2[1] (analytic) = 1.7693006819115921404164159451506 y2[1] (numeric) = 1.832144881789496402985199944825 absolute error = 0.0628441998779042625687839996744 relative error = 3.5519231140523825202466234132814 % h = 0.001 TOP MAIN SOLVE Loop memory used=545.5MB, alloc=4.5MB, time=93.37 NO POLE NO POLE x[1] = 1.339 y1[1] (analytic) = 2.9732553021834060955793054489858 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4938297635792030953060175137702 relative error = 16.609060218157514495453143721188 % h = 0.001 y2[1] (analytic) = 1.7702738221884870037591465215765 y2[1] (numeric) = 1.8333597548017777980596442454925 absolute error = 0.063085932613290794300497723916 relative error = 3.5636256844888159354261398812757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.34 y1[1] (analytic) = 2.9734845416953193747878703480896 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.494059003091116374514582412874 relative error = 16.615489206795430884466345195543 % h = 0.001 y2[1] (analytic) = 1.7712471921915405347673605076999 y2[1] (numeric) = 1.8345755049127205929395884642725 absolute error = 0.0633283127211800581722279565726 relative error = 3.5753514811687453517998066645183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.341 y1[1] (analytic) = 2.9737128077227720823861642789256 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.49428726911856908211287634371 relative error = 16.621889909304570657668758035326 % h = 0.001 y2[1] (analytic) = 1.7722207909473828115016911126287 y2[1] (numeric) = 1.8357921321223247876250326011651 absolute error = 0.0635713411749419761233414885364 relative error = 3.5871005181560025815430943801025 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.342 y1[1] (analytic) = 2.9739401000374982099436479635199 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4945145614332952096703600283043 relative error = 16.628262332084627694790974495047 % h = 0.001 y2[1] (analytic) = 1.7731946174824151592530885511146 y2[1] (numeric) = 1.8370096364305903821159766561702 absolute error = 0.0638150189481752228628881050556 relative error = 3.5988728095046836512926309688169 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.343 y1[1] (analytic) = 2.9741664184122054616752194401986 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.494740879808002461401931504983 relative error = 16.634606481507038015280940557678 % h = 0.001 y2[1] (analytic) = 1.774168670822811124141413619382 y2[1] (numeric) = 1.8382280178375173764124206292878 absolute error = 0.0640593470147062522710070099058 relative error = 3.610668369259235722660272495823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.344 y1[1] (analytic) = 2.9743917626205754817334909076658 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4949662240163724814602029724502 relative error = 16.640922363914985766943545165886 % h = 0.001 y2[1] (analytic) = 1.775142949994517446941810423066 y2[1] (numeric) = 1.8394472763431057705143645205179 absolute error = 0.0643043263485883235725540974519 relative error = 3.6224872114545438921382768004418 % h = 0.001 TOP MAIN SOLVE Loop memory used=549.3MB, alloc=4.5MB, time=94.03 NO POLE NO POLE x[1] = 1.345 y1[1] (analytic) = 2.9746161324372640805271257125288 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4951905938330610802538377773132 relative error = 16.647209985623409191434510804124 % h = 0.001 y2[1] (analytic) = 1.7761174540232550371378844309657 y2[1] (numeric) = 1.8406674119473555644218083298605 absolute error = 0.0645499579241005272839238988948 relative error = 3.6343293501160178702822085465702 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.346 y1[1] (analytic) = 2.9748395276379014600650091619533 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4954139890336984597917212267377 relative error = 16.653469352919006566567382119149 % h = 0.001 y2[1] (analytic) = 1.7770921819345199472007118015173 y2[1] (numeric) = 1.8418884246502667581347520573156 absolute error = 0.0647962427157468109340402557983 relative error = 3.6461947992596785400612602349256 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.347 y1[1] (analytic) = 2.9750619479990924383260278172952 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4956364093948894380527398820796 relative error = 16.65970047206024212539263950941 % h = 0.001 y2[1] (analytic) = 1.7780671327535843470927057030585 y2[1] (numeric) = 1.8431103144518393516531957028832 absolute error = 0.0650431816982550045604899998247 relative error = 3.6580835728922443942687119418497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.348 y1[1] (analytic) = 2.9752833932984166726542328989498 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4958578546942136723809449637342 relative error = 16.665903349277351952008194177795 % h = 0.001 y2[1] (analytic) = 1.7790423055054974989953651240988 y2[1] (numeric) = 1.8443330813520733449771392665633 absolute error = 0.0652907758465758459817741424645 relative error = 3.6699956850112178518882730053653 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.349 y1[1] (analytic) = 2.9755038633144288821791644072722 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4960783247102258819058764720566 relative error = 16.6720779907723498540607500308 % h = 0.001 y2[1] (analytic) = 1.7800176992150867322599314459281 y2[1] (numeric) = 1.8455567253509687381065827483559 absolute error = 0.0655390261358820058466513024278 relative error = 3.6819311496049714533150516468031 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.35 y1[1] (analytic) = 2.9757233578266590692611135392652 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4962978192224560689878256040496 relative error = 16.678224402719033211897746023902 % h = 0.001 y2[1] (analytic) = 1.7809933129069584185799778269894 y2[1] (numeric) = 1.8467812464485255310415261482611 absolute error = 0.0657879335415671124615483212717 relative error = 3.6938899806528339343328836547331 % h = 0.001 TOP MAIN SOLVE Loop memory used=553.1MB, alloc=4.5MB, time=94.70 NO POLE NO POLE x[1] = 1.351 y1[1] (analytic) = 2.9759418766156127399611019557882 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4965163380114097396878140205726 relative error = 16.684342591262988804329820101163 % h = 0.001 y2[1] (analytic) = 1.7819691456054989473849562265054 y2[1] (numeric) = 1.8480066446447437237819694662788 absolute error = 0.0660374990392447763970132397734 relative error = 3.7058721921251761787527188266349 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.352 y1[1] (analytic) = 2.9761594194627711235353574293287 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4967338808585681232620694941131 relative error = 16.690432562521598610963962760526 % h = 0.001 y2[1] (analytic) = 1.7829451963348757014537266738956 y2[1] (numeric) = 1.849232919939623316327912702409 absolute error = 0.0662877236047476148741860285134 relative error = 3.7178777979834970496197139214748 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.353 y1[1] (analytic) = 2.9763759861505913909540663778775 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4969504475463883906807784426619 relative error = 16.69649432258404559106775449814 % h = 0.001 y2[1] (analytic) = 1.7839214641190380327470931705336 y2[1] (numeric) = 1.8504600723331643086793558566517 absolute error = 0.0665386082141262759322626861181 relative error = 3.7299068121805090988996134831035 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.354 y1[1] (analytic) = 2.9765915764625068724441847661739 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4971660378583038721708968309583 relative error = 16.702527877511319438925306949049 % h = 0.001 y2[1] (analytic) = 1.7848979479817182384583703913924 y2[1] (numeric) = 1.8516881018253667008362989290069 absolute error = 0.0667901538436484623779285376145 relative error = 3.7419592486602241555579151088507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.355 y1[1] (analytic) = 2.9768061901829272740560898315276 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.497380651578724273782801896312 relative error = 16.708533233336222315645752451022 % h = 0.001 y2[1] (analytic) = 1.78587464694643253728100513609 y2[1] (numeric) = 1.8529170084162304927987419194746 absolute error = 0.0670423614697979555177367833846 relative error = 3.7540351213580387919482136200774 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.356 y1[1] (analytic) = 2.9770198270972388932538560675845 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4975942884930358929805681323689 relative error = 16.714510396063374557385351016791 % h = 0.001 y2[1] (analytic) = 1.7868515600364820458922762617974 y2[1] (numeric) = 1.8541467921057556845666848280548 absolute error = 0.0672952320692736386744085662574 relative error = 3.7661344442008196684289992002814 % h = 0.001 TOP MAIN SOLVE Loop memory used=556.9MB, alloc=4.5MB, time=95.35 NO POLE NO POLE x[1] = 1.357 y1[1] (analytic) = 2.9772324869918048335289398757774 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4978069483876018332556519405618 relative error = 16.720459371669220359944507310758 % h = 0.001 y2[1] (analytic) = 1.7878286862749537556520966143883 y2[1] (numeric) = 1.8553774528939422761401276547475 absolute error = 0.0675487666189885204880310403592 relative error = 3.7782572311069887561310479621569 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.358 y1[1] (analytic) = 2.9774441696539652180370582707955 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4980186310497622177637703355799 relative error = 16.726380166102033439701213193002 % h = 0.001 y2[1] (analytic) = 1.7888060246847215095159402591121 y2[1] (numeric) = 1.8566089907807902675190703995527 absolute error = 0.0678029660960687580031301404406 relative error = 3.7904034959866084378003896463166 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.359 y1[1] (analytic) = 2.977654874872037402258048003212 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4982293362678344019847600679964 relative error = 16.732272785281922670842653719429 % h = 0.001 y2[1] (analytic) = 1.7897835742884469791609180979423 y2[1] (numeric) = 1.8578414057662996587035130624704 absolute error = 0.0680578314778526795425949645281 relative error = 3.8025732527414664866446663017537 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.36 y1[1] (analytic) = 2.9778646024353161856784924394266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.498439063831113185405204504211 relative error = 16.738137235100837698856936175646 % h = 0.001 y2[1] (analytic) = 1.7907613341085806423240247476081 y2[1] (numeric) = 1.8590746978504704496934556435007 absolute error = 0.0683133637418898073694308958926 relative error = 3.8147665152651609231135079102073 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.361 y1[1] (analytic) = 2.9780733521340740224969045163172 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4986478135298710222236165811016 relative error = 16.743973521422574530247122777184 % h = 0.001 y2[1] (analytic) = 1.7917393031673627603515793401421 y2[1] (numeric) = 1.8603088670333026404888981426435 absolute error = 0.0685695638659398801373188025014 relative error = 3.8269832974431847495463460539025 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.362 y1[1] (analytic) = 2.978281123759561231351255065431 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4988555851553582310779671302154 relative error = 16.749781650082781098429968093062 % h = 0.001 y2[1] (analytic) = 1.7927174804868243559588826965854 y2[1] (numeric) = 1.8615439133147962310898405598988 absolute error = 0.0688264328279718751309578633134 relative error = 3.8392236131530105626238649477038 % h = 0.001 TOP MAIN SOLVE Loop memory used=560.7MB, alloc=4.5MB, time=96.01 NO POLE NO POLE x[1] = 1.363 y1[1] (analytic) = 2.9784879171040062040686367792083 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4990623784998032037953488439927 relative error = 16.755561626888962805781982047385 % h = 0.001 y2[1] (analytic) = 1.7936958650887881911991131142751 y2[1] (numeric) = 1.8627798366949512214962828952666 absolute error = 0.0690839716061630302971697809915 relative error = 3.8514874762641750435620505223912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.364 y1[1] (analytic) = 2.978693731960615613436855069589 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4992681933564126131635671343734 relative error = 16.761313457620488041795658527466 % h = 0.001 y2[1] (analytic) = 1.7946744559948697456404827988988 y2[1] (numeric) = 1.8640166371737676117082251487469 absolute error = 0.0693421811788978660677423498481 relative error = 3.8637749006383633259905428156265 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.365 y1[1] (analytic) = 2.9788985681235746199977380474311 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4994730295193716197244501122155 relative error = 16.767037148028593677308928180831 % h = 0.001 y2[1] (analytic) = 1.7956532522264781947506767642417 y2[1] (numeric) = 1.8652543147512454017256673203397 absolute error = 0.069601062524767206974990556098 relative error = 3.8760859001294932414597247603275 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.366 y1[1] (analytic) = 2.9791024253880470778619588294461 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4996768867838440775886708942305 relative error = 16.772732703836390534771111920326 % h = 0.001 y2[1] (analytic) = 1.7966322528048173884875958152689 y2[1] (numeric) = 1.866492869427384591548609410045 absolute error = 0.0698606166225672030610135947761 relative error = 3.8884204885837994425236916168434 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.367 y1[1] (analytic) = 2.979305303550175739545164357848 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.4998797649459727392718764226324 relative error = 16.778400130738868834508868980186 % h = 0.001 y2[1] (analytic) = 1.7976114567508868300954250238814 y2[1] (numeric) = 1.8677323012021851811770514178628 absolute error = 0.0701208444512983510816263939814 relative error = 3.9007786798399174033489398350817 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=564.5MB, alloc=4.5MB, time=96.66 x[1] = 1.368 y1[1] (analytic) = 2.9795072024070824598252058966025 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5000816638028794595519179613869 relative error = 16.784039434402903616955850079359 % h = 0.001 y2[1] (analytic) = 1.7985908630854826551050489013592 y2[1] (numeric) = 1.8689726100756471706109933437931 absolute error = 0.0703817469901645155059444424339 relative error = 3.913160487728967297801292115364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.369 y1[1] (analytic) = 2.9797081217568683986202673470646 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.500282583152665398346979411849 relative error = 16.789650620467260140809982355375 % h = 0.001 y2[1] (analytic) = 1.7995704708291986105378342671576 y2[1] (numeric) = 1.8702137960477705598504351878359 absolute error = 0.0706433252185719493126009206783 relative error = 3.9255659260746377549662369221525 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.37 y1[1] (analytic) = 2.9799080613986142228876885048919 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5004825227944112226144005696763 relative error = 16.795233694542599257082528235522 % h = 0.001 y2[1] (analytic) = 1.8005502790024270343118016103547 y2[1] (numeric) = 1.8714558591185553488953769499913 absolute error = 0.0709055801161283145835753396366 relative error = 3.9379950086932694920605057526151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.371 y1[1] (analytic) = 2.9801070211323803075432813594274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5006814825281773072699934242118 relative error = 16.80078866221148275900327531585 % h = 0.001 y2[1] (analytic) = 1.8015302866253598348492055376626 y2[1] (numeric) = 1.8726987992880015377458186302592 absolute error = 0.0711685126626417028966130925966 relative error = 3.9504477493939388246953401318563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.372 y1[1] (analytic) = 2.9803050007592069354009385162525 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5008794621550039351276505810369 relative error = 16.806315529028378707746428625621 % h = 0.001 y2[1] (analytic) = 1.8025104927179894708845447005008 y2[1] (numeric) = 1.8739426165561091264017602286396 absolute error = 0.0714321238381196555172155281388 relative error = 3.9629241619785410544545126591442 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.373 y1[1] (analytic) = 2.9805020000811144961323338033192 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5010764614769114958590458681036 relative error = 16.811814300519666733941990368758 % h = 0.001 y2[1] (analytic) = 1.803490896300109931472021393205 y2[1] (numeric) = 1.8751873109228781148632017451325 absolute error = 0.0716964146227681833911803519275 relative error = 3.9754242602418737337527625231231 % h = 0.001 TOP MAIN SOLVE Loop memory used=568.3MB, alloc=4.5MB, time=97.32 NO POLE NO POLE x[1] = 1.374 y1[1] (analytic) = 2.9806980189011036842465161009752 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5012724802969006839732281657596 relative error = 16.81728498218364331493762535777 % h = 0.001 y2[1] (analytic) = 1.8044714963913177161914708149938 y2[1] (numeric) = 1.8764328823883085031301431797379 absolute error = 0.0719613859969907869386723647441 relative error = 3.9879480579717198079428857998215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.375 y1[1] (analytic) = 2.9808930570231556960891984163071 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5014675184189526958159104810915 relative error = 16.822727579490527027776222893312 % h = 0.001 y2[1] (analytic) = 1.805452292011012815551779789844 y2[1] (numeric) = 1.8776793309524002912025845324558 absolute error = 0.0722270389413874756508047426118 relative error = 4.0004955689489306346422846045197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.376 y1[1] (analytic) = 2.9810871142522324258615452025277 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5016615756480294255882572673121 relative error = 16.828142097882463777854577796703 % h = 0.001 y2[1] (analytic) = 1.8064332821783996915908145409393 y2[1] (numeric) = 1.8789266566151534790805258032862 absolute error = 0.0724933744367537874897112623469 relative error = 4.0130668069475088802523268467591 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.377 y1[1] (analytic) = 2.9812801903942766606582619046366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.501854651790073660384973969421 relative error = 16.833528542773532003228824677208 % h = 0.001 y2[1] (analytic) = 1.8074144659124882586708769198454 y2[1] (numeric) = 1.8801748593765680667639669922291 absolute error = 0.0727603934640798080930900723837 relative error = 4.0256617857346912936463999974183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.378 y1[1] (analytic) = 2.9814722852562122745247916932807 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5020467466520092742515037580651 relative error = 16.838886919549747854532470313773 % h = 0.001 y2[1] (analytic) = 1.8083958422320948644687082950369 y2[1] (numeric) = 1.8814239392366440542529080992845 absolute error = 0.0730280970045491897841998042476 relative error = 4.0382805190710313570050579770365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.379 y1[1] (analytic) = 2.9816633986459444215334253296345 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5022378600417414212601373944189 relative error = 16.844217233569070350473079255539 % h = 0.001 y2[1] (analytic) = 1.8093774101558432711590601098542 y2[1] (numeric) = 1.8826738961953814415473491244525 absolute error = 0.0732964860395381703882890145983 relative error = 4.0509230207104818137791600754535 % h = 0.001 TOP MAIN SOLVE Loop memory used=572.2MB, alloc=4.5MB, time=97.98 NO POLE NO POLE x[1] = 1.38 y1[1] (analytic) = 2.981853530372359727878131085206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5024279917681567276048431499904 relative error = 16.84951949016140650887387740013 % h = 0.001 y2[1] (analytic) = 1.8103591687021656367908499264018 y2[1] (numeric) = 1.883924730252780228647290067733 absolute error = 0.0735655615506145918564401413312 relative error = 4.063589304400477073764384774063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.381 y1[1] (analytic) = 2.9820426802453264829879126217549 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5026171416411234827146246865393 relative error = 16.854793694628616453226747396833 % h = 0.001 y2[1] (analytic) = 1.8113411168893034968549215793134 y2[1] (numeric) = 1.885176441408840415552730929126 absolute error = 0.0738353245195369186978093498126 relative error = 4.076279383882015495272969523426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.382 y1[1] (analytic) = 2.9822308480756948296585037179794 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5028053094714918293852157827638 relative error = 16.860039852244518494723298246411 % h = 0.001 y2[1] (analytic) = 1.8123232537353087460424278717053 y2[1] (numeric) = 1.8864290296635620022636717086315 absolute error = 0.0741057759282532562212438369262 relative error = 4.088993272889741544390979990016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.383 y1[1] (analytic) = 2.9824180336752969532022097112956 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.50299249507109395292892177608 relative error = 16.865257968254894189730899434127 % h = 0.001 y2[1] (analytic) = 1.8133055782580446201928540550173 y2[1] (numeric) = 1.8876824950169449887801124062495 absolute error = 0.0743769167589003685872583512322 relative error = 4.1017309851520278313118490865763 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.384 y1[1] (analytic) = 2.9826042368569472696157065048811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5031786982527442693424185696655 relative error = 16.870448047877493372680777340292 % h = 0.001 y2[1] (analytic) = 1.8142880894751866784307001448004 y2[1] (numeric) = 1.88893683746898937510205302198 absolute error = 0.0746487479938026966713528771796 relative error = 4.1144925343910570237393473003164 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.385 y1[1] (analytic) = 2.9827894574344426127656089722012 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5033639188302396124923210369856 relative error = 16.8756100963020391643354785272 % h = 0.001 y2[1] (analytic) = 1.8152707864042237854898399358487 y2[1] (numeric) = 1.890192057019695161229493555823 absolute error = 0.0749212706154713757396536199743 relative error = 4.1272779343229036373555514920127 % h = 0.001 TOP MAIN SOLVE Loop memory used=576.0MB, alloc=4.5MB, time=98.64 NO POLE NO POLE x[1] = 1.386 y1[1] (analytic) = 2.9829736952225624205916215734637 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5035481566183594203183336382481 relative error = 16.880744118690232955403210805436 % h = 0.001 y2[1] (analytic) = 1.8162536680624590942245743924011 y2[1] (numeric) = 1.8914481536690623471624340077785 absolute error = 0.0751944856066032529378596153774 relative error = 4.1400871986576157033517695159211 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.387 y1[1] (analytic) = 2.9831569500370689203270849808684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5037314114328659200537970456528 relative error = 16.885850120175759365466778739857 % h = 0.001 y2[1] (analytic) = 1.8172367334670110283063969024388 y2[1] (numeric) = 1.8927051274170909329008743778465 absolute error = 0.0754683939500799045944774754077 relative error = 4.1529203410992963130227527658944 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.388 y1[1] (analytic) = 2.983339221694707312736733492119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5039136830905043124634455569034 relative error = 16.890928105864291177195035469043 % h = 0.001 y2[1] (analytic) = 1.8182199816348142651054876993967 y2[1] (numeric) = 1.893962978263780918444814666027 absolute error = 0.0757429966289666533393269666303 relative error = 4.1657773753461850394268881456914 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.389 y1[1] (analytic) = 2.9835205100132059553714789944563 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5040949714090029550981910592407 relative error = 16.895978080833494245804977385171 % h = 0.001 y2[1] (analytic) = 1.8192034115826207187559545698753 y2[1] (numeric) = 1.8952217062091323037942548723201 absolute error = 0.0760182946265115850383003024448 relative error = 4.1786583150907392361174050516016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.39 y1[1] (analytic) = 2.9837008148112765448400382244429 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5042752762070735445667502892273 relative error = 16.901000050133032383742812357186 % h = 0.001 y2[1] (analytic) = 1.820187022327000523403836782196 y2[1] (numeric) = 1.8964813112531450889491949967257 absolute error = 0.0762942889261445655453582145297 relative error = 4.1915631740197152129519618020089 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.391 y1[1] (analytic) = 2.9838801359086142980972210518888 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5044545973044112978239331166732 relative error = 16.905994018784572220552535782132 % h = 0.001 y2[1] (analytic) = 1.8211708128843430166368889878747 y2[1] (numeric) = 1.8977417933958192739096350392438 absolute error = 0.0765709805114762572727460513691 relative error = 4.2044919658142492889902896117104 % h = 0.001 TOP MAIN SOLVE Loop memory used=579.8MB, alloc=4.5MB, time=99.29 NO POLE NO POLE x[1] = 1.392 y1[1] (analytic) = 2.9840584731258981327486984996431 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5046329345216951324754105644275 relative error = 16.910959991781788037900751820753 % h = 0.001 y2[1] (analytic) = 1.8221547822708577230951616663156 y2[1] (numeric) = 1.8990031526371548586755749998744 absolute error = 0.0768483703662971355804133335588 relative error = 4.2174447041499387224918707467275 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.393 y1[1] (analytic) = 2.9842358262847908463720701945001 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5048102876805878460987822592845 relative error = 16.915897974090366579726679717301 % h = 0.001 y2[1] (analytic) = 1.8231389295025753382613945022233 y2[1] (numeric) = 1.9002653889771518432470148786175 absolute error = 0.0771264594745765049856203763942 relative error = 4.230421402696922518027910969263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.394 y1[1] (analytic) = 2.9844121952079392948540519281666 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.504986656603736294580763992951 relative error = 16.920807970648011837486487123016 % h = 0.001 y2[1] (analytic) = 1.824123253595348712430238905424 y2[1] (numeric) = 1.9015285024158102276239546754731 absolute error = 0.0774052488204615151937157700491 relative error = 4.2434220751199621107241348498669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.395 y1[1] (analytic) = 2.9845875797189745697436049911178 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5051620411147715694703170559022 relative error = 16.925689986364449810461293841245 % h = 0.001 y2[1] (analytic) = 1.8251077535648538348553257039542 y2[1] (numeric) = 1.9027924929531300118063943904412 absolute error = 0.077684739388276176951068686487 relative error = 4.2564467350785219276531860454967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.396 y1[1] (analytic) = 2.9847619796425121746208299262279 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5053364410383091743475419910123 relative error = 16.930544026121433241098390392878 % h = 0.001 y2[1] (analytic) = 1.8260924284265908180731938634319 y2[1] (numeric) = 1.9040573605891111957943340235218 absolute error = 0.0779649321625203777211401600899 relative error = 4.2694953962268498263976532764142 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.397 y1[1] (analytic) = 2.9849353948041522004814483332946 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.505509856199949200208160398079 relative error = 16.935370094772746325355416266831 % h = 0.001 y2[1] (analytic) = 1.827077277195884882403095908863 y2[1] (numeric) = 1.9053231053237537795877735747149 absolute error = 0.0782458281278688971846776658519 relative error = 4.2825680722140574108069665414574 % h = 0.001 TOP MAIN SOLVE Loop memory used=583.6MB, alloc=4.5MB, time=99.95 NO POLE NO POLE x[1] = 1.398 y1[1] (analytic) = 2.985107825030479500136697339993 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5056822864262764998634094047774 relative error = 16.94016819714420939801744267506 % h = 0.001 y2[1] (analytic) = 1.8280622988878873406216955491598 y2[1] (numeric) = 1.9065897271570577631867130440206 absolute error = 0.0785274282691704225650174948608 relative error = 4.2956647766842002239736171490374 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.399 y1[1] (analytic) = 2.9852792701490638616284623393761 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5058537315448608613551744041605 relative error = 16.944938338033683592957104077947 % h = 0.001 y2[1] (analytic) = 1.8290474925175765828116728297563 y2[1] (numeric) = 1.9078572260890231465911524314388 absolute error = 0.0788097335714465637794796016825 relative error = 4.308785523276357818456349469505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.4 y1[1] (analytic) = 2.9854497299884601806594745788061 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5060241913842571803861866435905 relative error = 16.949680522211075478308121687513 % h = 0.001 y2[1] (analytic) = 1.8300328570997590613832519647964 y2[1] (numeric) = 1.9091256021196499298010917369695 absolute error = 0.0790927450198908684178397721731 relative error = 4.3219303256247137037801519925488 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.401 y1[1] (analytic) = 2.985619204378208632038401170131 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5061936657740056317651132349154 relative error = 16.954394754418341666522760595394 % h = 0.001 y2[1] (analytic) = 1.8310183916490702762676668274503 y2[1] (numeric) = 1.9103948552489381128165309606127 absolute error = 0.0793764635998678365488641331624 relative error = 4.3350991973586351712450403595194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.402 y1[1] (analytic) = 2.9857876931488348401396560760331 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5063621545446318398663681408175 relative error = 16.959081039369493399283960113671 % h = 0.001 y2[1] (analytic) = 1.8320040951799757602815789049752 y2[1] (numeric) = 1.9116649854768876956374701023684 absolute error = 0.0796608902969119353558911973932 relative error = 4.3482921521027529960777755947414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.403 y1[1] (analytic) = 2.9859551961318500483777616127503 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5065296575276470481044736775347 relative error = 16.963739381750601107243074362032 % h = 0.001 y2[1] (analytic) = 1.8329899667067720646614623541841 y2[1] (numeric) = 1.9129359928034986782639091622366 absolute error = 0.0799460260967266136024468080525 relative error = 4.3615092034770410169627968402916 % h = 0.001 TOP MAIN SOLVE Loop memory used=587.4MB, alloc=4.5MB, time=100.60 NO POLE NO POLE x[1] = 1.404 y1[1] (analytic) = 2.9861217131597512876960909948252 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5066961745555482874228030596096 relative error = 16.968369786219798944554357088135 % h = 0.001 y2[1] (analytic) = 1.8339760052435877447669706230202 y2[1] (numeric) = 1.9142078772287710606958481402173 absolute error = 0.0802318719851833159288775171971 relative error = 4.3747503650968955929907695644762 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.405 y1[1] (analytic) = 2.9862872440660215440698234331509 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5068617054618185437965354979353 relative error = 16.97297225740728929817752117198 % h = 0.001 y2[1] (analytic) = 1.8349622098043843459522989349528 y2[1] (numeric) = 1.9154806387527048429332870363105 absolute error = 0.0805184289483204969809881013577 relative error = 4.3880156505732149380652575241527 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.406 y1[1] (analytic) = 2.9864517886851299250229442833751 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5070262500809269247496563481595 relative error = 16.977546799915347271919899243456 % h = 0.001 y2[1] (analytic) = 1.8359485794029573896045567649132 y2[1] (numeric) = 1.9167542773753000249762258505162 absolute error = 0.080805697972342635371669085603 relative error = 4.4013050735124783328101197739226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.407 y1[1] (analytic) = 2.9866153468525318251591237276735 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5071898082483288248858357924579 relative error = 16.982093418318325145189927337364 % h = 0.001 y2[1] (analytic) = 1.8369351130529373593481642684816 y2[1] (numeric) = 1.9180287930965566068246645828344 absolute error = 0.0810936800436192474765003143528 relative error = 4.4146186475168252140223127894159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.408 y1[1] (analytic) = 2.9867779184046690907063084590303 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5073523798004660904330205238147 relative error = 16.98661211716265680643386852608 % h = 0.001 y2[1] (analytic) = 1.8379218097677906874142864600103 y2[1] (numeric) = 1.9193041859164745884786032332652 absolute error = 0.0813823761486839010643167732549 relative error = 4.4279563861841341417168423665018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=591.2MB, alloc=4.5MB, time=101.25 x[1] = 1.409 y1[1] (analytic) = 2.986939503178970183074861823445 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5075139645747671828015738882294 relative error = 16.991102900966862161227888009053 % h = 0.001 y2[1] (analytic) = 1.8389086685608207411743187703302 y2[1] (numeric) = 1.9205804558350539699380418018085 absolute error = 0.0816717872742332287637230314783 relative error = 4.4413183031081016438126604314863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.41 y1[1] (analytic) = 2.9871001010138503414290888619422 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5076745624096473411558009267266 relative error = 16.995565774221551514997785204288 % h = 0.001 y2[1] (analytic) = 1.8398956884451688098364374506391 y2[1] (numeric) = 1.9218576028522947512029802884643 absolute error = 0.0819619144071259413665428378252 relative error = 4.4547044118783209385103383077124 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.411 y1[1] (analytic) = 2.9872597117487117442719836808696 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.507834173144508743998695745654 relative error = 17.000000741389429930338881982351 % h = 0.001 y2[1] (analytic) = 1.8408828684338150913042281261022 y2[1] (numeric) = 1.9231356269681969322734186932326 absolute error = 0.0822527585343818409691905671304 relative error = 4.4681147260803605344143703901128 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.412 y1[1] (analytic) = 2.9874183352239436700430375657528 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5079927966197406697697496305372 relative error = 17.004407806905301558908759312105 % h = 0.001 y2[1] (analytic) = 1.841870207539579679196405640619 y2[1] (numeric) = 1.9244145281827605131493570161134 absolute error = 0.0825443206431808339529513754944 relative error = 4.4815492592958427084549706392747 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.413 y1[1] (analytic) = 2.987575971280922656728947240911 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5081504326767196564556593056954 relative error = 17.008786975176073947865727251712 % h = 0.001 y2[1] (analytic) = 1.8428577047751235500266381731191 y2[1] (numeric) = 1.9256943064959854938307952571067 absolute error = 0.0828366017208619438041570839876 relative error = 4.495008025102521861666218878855 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.414 y1[1] (analytic) = 2.9877326197620126604870636641387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5083070811578096602137757289231 relative error = 17.013138250580762320826105422174 % h = 0.001 y2[1] (analytic) = 1.8438453591529495505424884456446 y2[1] (numeric) = 1.9269749619078718743177334162125 absolute error = 0.0831296027549223237752449705679 relative error = 4.5084910370743627528793946229713 % h = 0.001 TOP MAIN SOLVE Loop memory used=595.1MB, alloc=4.5MB, time=101.90 NO POLE NO POLE x[1] = 1.415 y1[1] (analytic) = 2.9878882805105652132814227330185 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5084627419063622130081347978029 relative error = 17.01746163747049383331358284655 % h = 0.001 y2[1] (analytic) = 1.8448331696854033852224846843611 y2[1] (numeric) = 1.9282564944184196546101714934308 absolute error = 0.0834233247330162693876868090697 relative error = 4.5219983087816186103923031314586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.416 y1[1] (analytic) = 2.9880429533709195795312002668466 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.508617414766716579257912331631 relative error = 17.021757140168511802674117329243 % h = 0.001 y2[1] (analytic) = 1.8458211353846746039303338365071 y2[1] (numeric) = 1.9295389040276288347081094887616 absolute error = 0.0837177686429542307777756522545 relative error = 4.5355298537909091216773516490209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.417 y1[1] (analytic) = 2.988196638188402911771434615729 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5087710995841999114981466805134 relative error = 17.026024762970179912430025389524 % h = 0.001 y2[1] (analytic) = 1.8468092552627975897252893891526 y2[1] (numeric) = 1.9308221907354994146115474022049 absolute error = 0.0840129354727018248862580130523 relative error = 4.5490856856652983011930733867541 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.418 y1[1] (analytic) = 2.9883493348093304053258612361401 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5089237962051274050525733009245 relative error = 17.030264510142986391047104154794 % h = 0.001 y2[1] (analytic) = 1.84779752833165254682768597948 y2[1] (numeric) = 1.9321063545420313943204852337608 absolute error = 0.0843088262103788474927992542808 relative error = 4.5626658179643722363657228098726 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.419 y1[1] (analytic) = 2.9885010430810054519917045601206 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.509075504476802451718416624905 relative error = 17.034476385926548165088816565062 % h = 0.001 y2[1] (analytic) = 1.8487859536029664887386528311363 y2[1] (numeric) = 1.9333913954472247738349229834292 absolute error = 0.0846054418442582850962701522929 relative error = 4.5762702642443167118094782608301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.42 y1[1] (analytic) = 2.9886517628517197927362734733357 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5092262242475167924629855381201 relative error = 17.038660394532614986731760743902 % h = 0.001 y2[1] (analytic) = 1.8497745300883142265130178970241 y2[1] (numeric) = 1.9346773134510795531548606512101 absolute error = 0.084902783362765326641842754186 relative error = 4.5898990380579947118556869309109 % h = 0.001 TOP MAIN SOLVE Loop memory used=598.9MB, alloc=4.5MB, time=102.55 NO POLE NO POLE x[1] = 1.421 y1[1] (analytic) = 2.9888014939707536694052077054123 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5093759553665506691319197701967 relative error = 17.042816540145073535616833455824 % h = 0.001 y2[1] (analytic) = 1.8507632567991193571844144357107 y2[1] (numeric) = 1.9359641085535957322802982371035 absolute error = 0.0852008517544763750958838013928 relative error = 4.6035521529550238014634727525533 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.422 y1[1] (analytic) = 2.9889502362883759754422234243195 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5095246976841729751689354891039 relative error = 17.046944826919951495010686198496 % h = 0.001 y2[1] (analytic) = 1.8517521327466552523416015964309 y2[1] (numeric) = 1.9372517807547733112112357411094 absolute error = 0.0854996480081180588696341446785 relative error = 4.6172296224818533855858999776113 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.423 y1[1] (analytic) = 2.9890979896558444056202073150606 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.509672451051641405346919379845 relative error = 17.051045258985421602252260673895 % h = 0.001 y2[1] (analytic) = 1.8527411569420460468550104364443 y2[1] (numeric) = 1.9385403300546122899476731632278 absolute error = 0.0857991731125662430926627267835 relative error = 4.6309314601818418470677440904264 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.424 y1[1] (analytic) = 2.9892447539254056047835094115948 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5098192153212026045102214763792 relative error = 17.055117840441805673459378148142 % h = 0.001 y2[1] (analytic) = 1.8537303283962676277525266442858 y2[1] (numeric) = 1.9398297564531126684896105034587 absolute error = 0.0860994280568450407370838591729 relative error = 4.6446576795953335631527673363198 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.425 y1[1] (analytic) = 2.9893905289502953156012859397082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5099649903460923153279980044926 relative error = 17.059162575361578602470544548593 % h = 0.001 y2[1] (analytic) = 1.8547196461201486232435210932057 y2[1] (numeric) = 1.9411200599502744468370477618021 absolute error = 0.0864004138301258235935266685964 relative error = 4.6584082942597358006802285839527 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.426 y1[1] (analytic) = 2.9895353145847385253317444175028 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5101097759805355250584564822872 relative error = 17.063179467789372333997320061821 % h = 0.001 y2[1] (analytic) = 1.8557091091243713918901392008544 y2[1] (numeric) = 1.942411240546097624989984938258 absolute error = 0.0867021314217262330998457374036 relative error = 4.6721833177095954900521765399943 % h = 0.001 TOP MAIN SOLVE Loop memory used=602.7MB, alloc=4.5MB, time=103.21 NO POLE NO POLE x[1] = 1.427 y1[1] (analytic) = 2.989679110683949611597144249272 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5102535720797466113238563140564 relative error = 17.067168521741979810962788490517 % h = 0.001 y2[1] (analytic) = 1.856698716419473011924859924003 y2[1] (numeric) = 1.9437032982405822029484220328265 absolute error = 0.0870045818211091910235621088235 relative error = 4.6859827634766758780548815551628 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.428 y1[1] (analytic) = 2.989821917104132487169407037773 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5103963784999294868961191025574 relative error = 17.071129741208358896001847703966 % h = 0.001 y2[1] (analytic) = 1.8576884670158462707133350708233 y2[1] (numeric) = 1.9449962330337281807123590455075 absolute error = 0.0873077660178819099990239746842 relative error = 4.6998066450900330596195544579527 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.429 y1[1] (analytic) = 2.9899637337024807437661918292979 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5105381950982777434929038940823 relative error = 17.075063130149636267099228178856 % h = 0.001 y2[1] (analytic) = 1.8586783599237406543615194679712 y2[1] (numeric) = 1.946290044925535558281795976301 absolute error = 0.0876116850017949039202765083298 relative error = 4.713654976076092388609281083802 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.43 y1[1] (analytic) = 2.9901045603371777948572914954818 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5106790217329747945840035602662 relative error = 17.078968692499111287341331877744 % h = 0.001 y2[1] (analytic) = 1.8596683941532633374661023754251 y2[1] (numeric) = 1.947584733916004335656732825207 absolute error = 0.0879163397627409981906304497819 relative error = 4.7275277699587247677208684897178 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.431 y1[1] (analytic) = 2.9902443968673970174812074454609 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5108188582631940172079195102453 relative error = 17.082846432162259848758168554366 % h = 0.001 y2[1] (analytic) = 1.8606585687143801730072503987307 y2[1] (numeric) = 1.9488803000051345128371695922255 absolute error = 0.0882217312907543398299191934948 relative error = 4.7414250402593228175920533143683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.432 y1[1] (analytic) = 2.9903832431533018930717608518196 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.510957704549098892798472916604 relative error = 17.086696353016738190231851011639 % h = 0.001 y2[1] (analytic) = 1.8616488826169166823826720059914 y2[1] (numeric) = 1.9501767431929260898231062773565 absolute error = 0.0885278605760094074404342713651 relative error = 4.7553468004968769252062644179744 % h = 0.001 TOP MAIN SOLVE Loop memory used=606.5MB, alloc=4.5MB, time=103.86 NO POLE NO POLE x[1] = 1.433 y1[1] (analytic) = 2.9905210990560461472945995637266 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.511095560451843147021311628511 relative error = 17.090518458912386689448294872146 % h = 0.001 y2[1] (analytic) = 1.8626393348705590455820136156229 y2[1] (numeric) = 1.9514740634793790666145428806 absolute error = 0.0888347286088200210325292649771 relative error = 4.7692930641880511716888608715594 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.434 y1[1] (analytic) = 2.9906579644377738888934608707648 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5112324258335708886201729355492 relative error = 17.094312753671233628868952055606 % h = 0.001 y2[1] (analytic) = 1.8636299244848550915005970805575 y2[1] (numeric) = 1.952772260864493443211479401956 absolute error = 0.0891423363796383517108823213985 relative error = 4.7832638448472591395904826179194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.435 y1[1] (analytic) = 2.990793839161619747546051271203 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5113683005574167472727633359874 relative error = 17.098079241087498935699590395995 % h = 0.001 y2[1] (analytic) = 1.8646206504692152883915082552446 y2[1] (numeric) = 1.9540713353482692196139158414245 absolute error = 0.0894506848790539312224075861799 relative error = 4.7972591559867395997548547531067 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.436 y1[1] (analytic) = 2.9909287230917090107294053888426 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.511503184487506010456117453627 relative error = 17.101817924927597895833314675934 % h = 0.001 y2[1] (analytic) = 1.8656115118329137344550461934394 y2[1] (numeric) = 1.9553712869307063958218521990055 absolute error = 0.0897597750977926613668060055661 relative error = 4.8112790111166320778700774341135 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.437 y1[1] (analytic) = 2.9910626160931577595945871730905 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5116370774889547593212992378749 relative error = 17.105528808930144841745206810397 % h = 0.001 y2[1] (analytic) = 1.8666025075850891485645423874153 y2[1] (numeric) = 1.9566721156118049718352884746991 absolute error = 0.0900696080267158232707460872838 relative error = 4.8253234237450523008041119612592 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.438 y1[1] (analytic) = 2.991195518032073003850597507569 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5117699794278700035773095723534 relative error = 17.109211896805956814316144978967 % h = 0.001 y2[1] (analytic) = 1.8675936367347458611275593228612 y2[1] (numeric) = 1.9579738213915649476542246685052 absolute error = 0.090380184656819086526665345644 relative error = 4.8393924073781675228268396694695 % h = 0.001 TOP MAIN SOLVE Loop memory used=610.3MB, alloc=4.5MB, time=104.51 NO POLE NO POLE x[1] = 1.439 y1[1] (analytic) = 2.991327428775552815657353343366 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5119018901713498153840654081504 relative error = 17.112867192238057198563543188682 % h = 0.001 y2[1] (analytic) = 1.8685848982907548050814774883499 y2[1] (numeric) = 1.9592764042699863232786607804238 absolute error = 0.0906915059792315181971832920739 relative error = 4.8534859755202717318227239463807 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.44 y1[1] (analytic) = 2.991458348191686462527604463958 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5120328095874834622543165287424 relative error = 17.116494698881679333256934051012 % h = 0.001 y2[1] (analytic) = 1.8695762912618545070224798438708 y2[1] (numeric) = 1.9605798642470690987085968104549 absolute error = 0.0910035729852145916861169665841 relative error = 4.867604141673860735599747033577 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.441 y1[1] (analytic) = 2.9915882761495545392376549798994 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5121627375453515389643670446838 relative error = 17.12009442036427009439649847959 % h = 0.001 y2[1] (analytic) = 1.8705678146566520784669426195275 y2[1] (numeric) = 1.9618842013228132739440327585985 absolute error = 0.091316386666161195477090139071 relative error = 4.8817469193397071284019223154113 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.442 y1[1] (analytic) = 2.9917172125192290987467576425684 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5122916739150260984734697073528 relative error = 17.123666360285493452532826563189 % h = 0.001 y2[1] (analytic) = 1.8715594674836242072442411830899 y2[1] (numeric) = 1.9631894154972188489849686248546 absolute error = 0.0916299480135946417407274417647 relative error = 4.895914322016935137734299614214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.443 y1[1] (analytic) = 2.9918451571717737821250500575858 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5124196185675707818517621223702 relative error = 17.127210522217234003906374043843 % h = 0.001 y2[1] (analytic) = 1.872551248751118149019979583679 y2[1] (numeric) = 1.9644955067702858238314044092232 absolute error = 0.0919442580191676748114248255442 relative error = 4.9101063632030953516109856459806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.444 y1[1] (analytic) = 2.9919721099792439474899028699808 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5125465713750409472166149347652 relative error = 17.130726909703600475385258636103 % h = 0.001 y2[1] (analytic) = 1.873543157467352718948652248437 y2[1] (numeric) = 1.9658024751420141984833401117043 absolute error = 0.0922593176746614795346878632673 relative error = 4.9243230563942393263382943030571 % h = 0.001 TOP MAIN SOLVE Loop memory used=614.1MB, alloc=4.5MB, time=105.16 NO POLE NO POLE x[1] = 1.445 y1[1] (analytic) = 2.9920980708146867979505509847679 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5126725322104837976772630495523 relative error = 17.134215526260929203180219863159 % h = 0.001 y2[1] (analytic) = 1.8745351926404192834547461796033 y2[1] (numeric) = 1.9671103206124039729407757322979 absolute error = 0.0925751279719846894860295526946 relative error = 4.9385644150849940749467218748479 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.446 y1[1] (analytic) = 2.9922230395521415085608798783119 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5127975009479385082875919430963 relative error = 17.137676375377787585315745161803 % h = 0.001 y2[1] (analytic) = 1.875527353278282752141291870978 y2[1] (numeric) = 1.9684190431814551472037112710041 absolute error = 0.0928916899031723950624194000261 relative error = 4.9528304527686364363870107494488 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.447 y1[1] (analytic) = 2.9923470160666393522802400477078 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5129214774624363520069521124922 relative error = 17.141109460514977507836543724187 % h = 0.001 y2[1] (analytic) = 1.8765196383887825698248710353027 y2[1] (numeric) = 1.9697286428491677212721467278228 absolute error = 0.0932090044603851514472756925201 relative error = 4.9671211829371673256071216137916 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.448 y1[1] (analytic) = 2.9924700002342038249421636373698 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5130444616300008246688757021542 relative error = 17.144514785105538744728727902685 % h = 0.001 y2[1] (analytic) = 1.8775120469796337086960891076355 y2[1] (numeric) = 1.971039119615541695146082102754 absolute error = 0.0935270726359079864499929951185 relative error = 4.9814366190813858646284787419074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.449 y1[1] (analytic) = 2.9925919919318507692308582741243 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5131664533276477689575703389087 relative error = 17.147892352554752331535240008181 % h = 0.001 y2[1] (analytic) = 1.8785045780584276606045203643295 y2[1] (numeric) = 1.9723504734805770688255173957977 absolute error = 0.0938458954221494082209970314682 relative error = 4.9957767746909633947413856856592 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=617.9MB, alloc=4.5MB, time=105.83 x[1] = 1.45 y1[1] (analytic) = 2.992712991037588497665354134323 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5132874524333854973920661991074 relative error = 17.151242166240143912645239984497 % h = 0.001 y2[1] (analytic) = 1.879497230632633429467133372752 y2[1] (numeric) = 1.9736627044442738423104526069539 absolute error = 0.0941654738116404128433192342019 relative error = 5.010141663254517369941029614384 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.451 y1[1] (analytic) = 2.9928329974304179145911812588387 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5134074588262149143178933236231 relative error = 17.154564229511487062237346745583 % h = 0.001 y2[1] (analytic) = 1.8804900037095985237992043634025 y2[1] (numeric) = 1.9749758125066320156008877362226 absolute error = 0.0944858087970334918016833728201 relative error = 5.0245312982596851317270017438481 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.452 y1[1] (analytic) = 2.992952010990332637179455124278 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5135264723861296369061671890624 relative error = 17.157858545690806578856802920366 % h = 0.001 y2[1] (analytic) = 1.8814828962965499493667259935982 y2[1] (numeric) = 1.9762897976676515886968227836038 absolute error = 0.0948069013711016393300967900056 relative error = 5.038945693193197565390758805693 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.453 y1[1] (analytic) = 2.993070031598319115433249471334 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5136444929941161151599615361184 relative error = 17.161125118072381753606809365757 % h = 0.001 y2[1] (analytic) = 1.8824759074005952019593188504015 y2[1] (numeric) = 1.9776046599273325615982577490975 absolute error = 0.095128752526737359638938898696 relative error = 5.0533848615409526379169363902368 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.454 y1[1] (analytic) = 2.9931870591363567512011363839172 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5137615205321537509278484487016 relative error = 17.164363949922749611934452084294 % h = 0.001 y2[1] (analytic) = 1.8834690360287232602826529199597 y2[1] (numeric) = 1.9789203992856749343051926327037 absolute error = 0.095451363256951674022539712744 relative error = 5.0678488167880888176258993027634 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.455 y1[1] (analytic) = 2.9933030934874180161977746055338 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5138775548832150159244866703182 relative error = 17.167575044480708128991820122012 % h = 0.001 y2[1] (analytic) = 1.8844622811878055789693861309197 y2[1] (numeric) = 1.9802370157426787068176274344224 absolute error = 0.0957747345548731278482413035027 relative error = 5.0823375724190583756863768601232 % h = 0.001 TOP MAIN SOLVE Loop memory used=621.8MB, alloc=4.5MB, time=106.49 NO POLE NO POLE x[1] = 1.456 y1[1] (analytic) = 2.9934181345354685690314280723334 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5139925959312655687581401371178 relative error = 17.170758404957319418553088627571 % h = 0.001 y2[1] (analytic) = 1.8854556418845970817076269610606 y2[1] (numeric) = 1.9815545092983438791355621542537 absolute error = 0.0960988674137467974279351931931 relative error = 5.0968511419177005696284823752325 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.457 y1[1] (analytic) = 2.9935321821654673712382976353168 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5141066435612643709650097001012 relative error = 17.173914034535912895468516528097 % h = 0.001 y2[1] (analytic) = 1.8864491171257371544859279787649 y2[1] (numeric) = 1.9828728799526704512589967921975 absolute error = 0.0964237628269332967730688134326 relative error = 5.1113895387673147089888559852824 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.458 y1[1] (analytic) = 2.9936452362633668023235499373824 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5142196976591638020502620021668 relative error = 17.177041936372088411636483223798 % h = 0.001 y2[1] (analytic) = 1.8874427059177506389538170744175 y2[1] (numeric) = 1.9841921277056584231879313482538 absolute error = 0.0967494217879077842341142738363 relative error = 5.1259527764507331032210985295814 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.459 y1[1] (analytic) = 2.9937572967161127738089284041912 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5143317581119097735356404689756 relative error = 17.180142113593719365474863324939 % h = 0.001 y2[1] (analytic) = 1.8884364072670488258968730212842 y2[1] (numeric) = 1.9855122525573077949223658224226 absolute error = 0.0970758452902589690254928011384 relative error = 5.1405408684503938920060814282271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.46 y1[1] (analytic) = 2.99386836341164484228683230125 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5144428248074418420135443660344 relative error = 17.183214569300955784873212754258 % h = 0.001 y2[1] (analytic) = 1.8894302201799304488253518908766 y2[1] (numeric) = 1.9868332545076185664623002147039 absolute error = 0.0974030343276881176369483238273 relative error = 5.1551538282484137580981235073299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.461 y1[1] (analytic) = 2.9939784362388963214807508031421 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5145528976346933212074628679265 relative error = 17.186259306566227383607413518197 % h = 0.001 y2[1] (analytic) = 1.8904241436625826776753707342597 y2[1] (numeric) = 1.9881551335565907378077345250977 absolute error = 0.097730989894008060132363790838 relative error = 5.1697916693266605228444205134237 % h = 0.001 TOP MAIN SOLVE Loop memory used=625.6MB, alloc=4.5MB, time=107.16 NO POLE NO POLE x[1] = 1.462 y1[1] (analytic) = 2.9940875150877943933119400144811 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5146619764835913930386520792655 relative error = 17.189276328434246591198598114408 % h = 0.001 y2[1] (analytic) = 1.8914181767210821126216548282017 y2[1] (numeric) = 1.989477889704224308958668753604 absolute error = 0.0980597129831421963370139254023 relative error = 5.1844544051668256245164967125728 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.463 y1[1] (analytic) = 2.9941955998492602179722318759202 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5147700612450572176989439407046 relative error = 17.192265637922011556198347893801 % h = 0.001 y2[1] (analytic) = 1.892412318361395778000854673502 y2[1] (numeric) = 1.9908015229505192799151029002228 absolute error = 0.0983892045891235019142482267208 relative error = 5.1991420492504964795938205317729 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.464 y1[1] (analytic) = 2.9943026904152090430028648824176 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.514877151811006042729576947202 relative error = 17.195227238018809122882332735742 % h = 0.001 y2[1] (analytic) = 1.8934065675893821163444388222618 y2[1] (numeric) = 1.9921260332954756506770369649541 absolute error = 0.0987194657060935343325981426923 relative error = 5.213854615059228727141087724792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.465 y1[1] (analytic) = 2.9944087866785503113792275349352 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5149832480743473111059395997196 relative error = 17.198161131686217781334732127864 % h = 0.001 y2[1] (analytic) = 1.8944009234107919825201685012882 y2[1] (numeric) = 1.9934514207390934212444709477979 absolute error = 0.0990504973283014387243024465097 relative error = 5.2285921160746183564220260842725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.466 y1[1] (analytic) = 2.9945138885331877686014064408375 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5150883499289847683281185056219 relative error = 17.201067321858110590905950170328 % h = 0.001 y2[1] (analytic) = 1.8953953848312696379811598902411 y2[1] (numeric) = 1.9947776852813725916174048487543 absolute error = 0.0993823004501029536362449585132 relative error = 5.2433545657783737178939153299857 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.467 y1[1] (analytic) = 2.9946179958740195687904319724508 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5151924572698165685171440372352 relative error = 17.203945811440658077026309150903 % h = 0.001 y2[1] (analytic) = 1.8963899508563537451215398055408 y2[1] (numeric) = 1.9961048269223131617958386678232 absolute error = 0.0997148760659594166742988622824 relative error = 5.2581419776523874177283445324142 % h = 0.001 TOP MAIN SOLVE Loop memory used=629.4MB, alloc=4.5MB, time=107.82 NO POLE NO POLE x[1] = 1.468 y1[1] (analytic) = 2.9947211085969383797901153875459 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5152955699927353795168274523303 relative error = 17.206796603312331101358578165144 % h = 0.001 y2[1] (analytic) = 1.8973846204914783617377004344665 y2[1] (numeric) = 1.9974328456619151317797724050046 absolute error = 0.1000482251704367700420719705381 relative error = 5.2729543651788080960050473333854 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.469 y1[1] (analytic) = 2.9948232265988314872743723099161 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5153976879946284870010843747005 relative error = 17.209619700323903705272364787858 % h = 0.001 y2[1] (analytic) = 1.8983793927419739355941586582709 y2[1] (numeric) = 1.9987617415001785015692060602985 absolute error = 0.1003823487582045659750474020276 relative error = 5.2877917418401120887269623546875 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.47 y1[1] (analytic) = 2.9949243497775808978599284627356 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.51549881117337789758664052752 relative error = 17.212415105298455926623569041074 % h = 0.001 y2[1] (analytic) = 1.8993742666130682990930253985376 y2[1] (numeric) = 2.0000915144371032711641396337049 absolute error = 0.1007172478240349720711142351673 relative error = 5.3026541211191749738059625929097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.471 y1[1] (analytic) = 2.9950244780320634412243045420014 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5155989394278604409510166067858 relative error = 17.215182821031376589822269852581 % h = 0.001 y2[1] (analytic) = 1.9003692411098876640460903173915 y2[1] (numeric) = 2.0014221644726894405645731252238 absolute error = 0.1010529233628017765184828078323 relative error = 5.3175415164993430011699833374954 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.472 y1[1] (analytic) = 2.995123611262150871228978112082 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5156980726579478709556901768664 relative error = 17.217922850290366069172584860794 % h = 0.001 y2[1] (analytic) = 1.9013643152374576165485270995636 y2[1] (numeric) = 2.0027536916069370097705065348552 absolute error = 0.1013893763694793932219794352916 relative error = 5.3324539414645044071435532700371 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.473 y1[1] (analytic) = 2.9952217493687099660476214002196 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.515796210764506965774333465004 relative error = 17.22063519581543902546821479906 % h = 0.001 y2[1] (analytic) = 1.9023594880007041119532244426849 y2[1] (numeric) = 2.0040860958398459787819398625991 absolute error = 0.1017266078391418668287154199142 relative error = 5.3473914094991606132549979595673 % h = 0.001 TOP MAIN SOLVE Loop memory used=633.2MB, alloc=4.5MB, time=108.47 NO POLE NO POLE x[1] = 1.474 y1[1] (analytic) = 2.9953188922536026272993148617564 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5158933536493996270260269265408 relative error = 17.223319860318927115827553788456 % h = 0.001 y2[1] (analytic) = 1.903354758404454469944747781564 y2[1] (numeric) = 2.0054193771714163475988731084555 absolute error = 0.1020646187669618776541253268915 relative error = 5.3623539340884973096248390115337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.475 y1[1] (analytic) = 2.9954150398196859781866373828792 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5159895012154829779133494476636 relative error = 17.225976846485481676752416685448 % h = 0.001 y2[1] (analytic) = 1.9043501254534383697119366725675 y2[1] (numeric) = 2.0067535356016481162213062724245 absolute error = 0.102403410148209746509369599857 relative error = 5.377341528718455423091155710266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.476 y1[1] (analytic) = 2.9955101919708124606385349828016 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.516084653366609460365247047586 relative error = 17.228606156972076380394604172556 % h = 0.001 y2[1] (analytic) = 1.9053455881522888452181426655897 y2[1] (numeric) = 2.008088571130541284649239354506 absolute error = 0.1027429829782524394310966889163 relative error = 5.3923542068758019702289091666049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.477 y1[1] (analytic) = 2.9956043486118299314578708725214 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5161788100076269311845829373058 relative error = 17.231207794408009864014695548909 % h = 0.001 y2[1] (analytic) = 1.9063411455055432805681123934568 y2[1] (numeric) = 2.0094244837580958528826723547 absolute error = 0.1030833382525525723145599612432 relative error = 5.4073919820482007954214517962489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.478 y1[1] (analytic) = 2.9956975096485817574735607226122 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5162719710443787572002727873966 relative error = 17.233781761394908332617628176614 % h = 0.001 y2[1] (analytic) = 1.9073367965176444054705205119649 y2[1] (numeric) = 2.0107612734843118209216052730065 absolute error = 0.1034244769666674154510847610416 relative error = 5.4224548677242831941436574611167 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.479 y1[1] (analytic) = 2.9957896749879069096971979879224 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5163641363837039094239100527068 relative error = 17.236328060506728134749791270701 % h = 0.001 y2[1] (analytic) = 1.9083325401929412907951570281025 y2[1] (numeric) = 2.0120989403091891887660381094255 absolute error = 0.103766400116247897970881081323 relative error = 5.4375428773937184216173098571007 % h = 0.001 TOP MAIN SOLVE Loop memory used=637.0MB, alloc=4.5MB, time=109.12 NO POLE NO POLE x[1] = 1.48 y1[1] (analytic) = 2.9958808445376400564840751325627 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5164553059334370562107871973471 relative error = 17.238846694289758311442530188011 % h = 0.001 y2[1] (analytic) = 1.9093283755356903442237734593522 y2[1] (numeric) = 2.013437484232727956415970863957 absolute error = 0.1041091086970376121921974046048 relative error = 5.4526560245472840870005787780629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.481 y1[1] (analytic) = 2.9959710182066116556985075941693 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5165454796024086554252196589537 relative error = 17.241337665262623118287125576739 % h = 0.001 y2[1] (analytic) = 1.9103243015500563059935921733094 y2[1] (numeric) = 2.014776905254928123871403536601 absolute error = 0.1044526037048718178778113632916 relative error = 5.4677943226769364332745957785289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.482 y1[1] (analytic) = 2.9960601959046480458833683221274 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5166346573004450456100803869118 relative error = 17.243800975916284520626479696192 % h = 0.001 y2[1] (analytic) = 1.9113203172401132447324831641913 y2[1] (numeric) = 2.0161172033757896911323361273575 absolute error = 0.1047968861356764463998529631662 relative error = 5.4829577852758805029913125474322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.483 y1[1] (analytic) = 2.9961483775425715364337417202262 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5167228389383685361604537850106 relative error = 17.246236628714044661848909908423 % h = 0.001 y2[1] (analytic) = 1.9123164216098455533848124311414 y2[1] (numeric) = 2.0174583785953126581987686362265 absolute error = 0.1051419569854671048139562050851 relative error = 5.4981464258386401900479870429057 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.484 y1[1] (analytic) = 2.9962355630322004967746068201009 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5168100244279974965013188848853 relative error = 17.248644626091548304769616782912 % h = 0.001 y2[1] (analytic) = 1.9133126136631489452269660325664 y2[1] (numeric) = 2.018800430913497025070701063208 absolute error = 0.1054878172503480798437350306416 relative error = 5.5133602578611281776547941738794 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.485 y1[1] (analytic) = 2.9963217522863494445424605077845 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5168962136821464442691725725689 relative error = 17.251024970456785246085561444861 % h = 0.001 y2[1] (analytic) = 1.9143088924038314499715538010618 y2[1] (numeric) = 2.0201433603303427917481334083021 absolute error = 0.1058344679265113417765796072403 relative error = 5.5285992948407157626631995992142 % h = 0.001 memory used=640.8MB, alloc=4.5MB, time=109.77 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.486 y1[1] (analytic) = 2.9964069452188291327707926217544 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5169814066146261324975046865388 relative error = 17.253377664190092703889653740136 % h = 0.001 y2[1] (analytic) = 1.9153052568356144099592966148078 y2[1] (numeric) = 2.0214871668458499582310656715087 absolute error = 0.1061819100102355482717690567009 relative error = 5.5438635502763025664238670985019 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.487 y1[1] (analytic) = 2.9964911417444466360793257370054 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5170656031402436358060378017898 relative error = 17.255702709644157678230319487996 % h = 0.001 y2[1] (analytic) = 1.9163017059621334764376010336293 y2[1] (numeric) = 2.0228318504600185245194978528278 absolute error = 0.1065301444978850480818968191985 relative error = 5.5591530376683861323439920018443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.488 y1[1] (analytic) = 2.9965743417790054358669334459171 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5171488031748024355936455107015 relative error = 17.258000109144019284702681549579 % h = 0.001 y2[1] (analytic) = 1.9172982387869396059248250212299 y2[1] (numeric) = 2.0241774111728484906134299522594 absolute error = 0.1068791723859088846886049310295 relative error = 5.5744677705191314103150653976441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.489 y1[1] (analytic) = 2.996656545239305504508151943004 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5172310066351025042348640077884 relative error = 17.260269864987071061057755658289 % h = 0.001 y2[1] (analytic) = 1.9182948543135000566592383894163 y2[1] (numeric) = 2.0255238489843398565128619698035 absolute error = 0.1072289946708397998536235803872 relative error = 5.589807762332440128183176318697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.49 y1[1] (analytic) = 2.9967377520431433885532007170437 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5173122134389403882799127818281 relative error = 17.262511979443063246816227940736 % h = 0.001 y2[1] (analytic) = 1.9192915515451993851316815154363 y2[1] (numeric) = 2.0268711638944926222177939054601 absolute error = 0.1075796123492932370861123900238 relative error = 5.6051730266140200504350518865374 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE memory used=644.6MB, alloc=4.5MB, time=110.42 x[1] = 1.491 y1[1] (analytic) = 2.9968179621093122909314291505699 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5173924235051092906581412153543 relative error = 17.264726454754105035873546806539 % h = 0.001 y2[1] (analytic) = 1.9202883294853404427009257998542 y2[1] (numeric) = 2.0282193559033067877282257592292 absolute error = 0.107931026417966345027299959375 relative error = 5.6205635768714541242741185221733 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.492 y1[1] (analytic) = 2.9968971753576021521581068232903 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5174716367533991518848188880747 relative error = 17.266913293134666802083227404836 % h = 0.001 y2[1] (analytic) = 1.9212851871371453722907392496861 y2[1] (numeric) = 2.0295684250107823530441575311108 absolute error = 0.1082832378736369807534182814247 relative error = 5.6359794266142695132619408572088 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.493 y1[1] (analytic) = 2.9969753917087997305444763126456 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.51754985310459673027118837743 relative error = 17.269072496771582297805432137695 % h = 0.001 y2[1] (analytic) = 1.922282123503756605167660489814 y2[1] (numeric) = 2.0309183712169193181655892211049 absolute error = 0.1086362477131627129979287312909 relative error = 5.6514205893540065187014589522482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.494 y1[1] (analytic) = 2.9970526110846886814109882814636 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.517627072480485681137700346248 relative error = 17.271204067824050825408055788607 % h = 0.001 y2[1] (analytic) = 1.9232791375882378577984844249848 y2[1] (numeric) = 2.0322691945217176830925208292115 absolute error = 0.1089900569334798252940364042267 relative error = 5.6668870786042873889394988989448 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.495 y1[1] (analytic) = 2.9971288334080496353036396394798 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5177032948038466350303517042642 relative error = 17.273308008423639381707708670607 % h = 0.001 y2[1] (analytic) = 1.9242762283935751287864626949956 y2[1] (numeric) = 2.0336208949251774478249523554307 absolute error = 0.1093446665316023190384896604351 relative error = 5.6823789078808850167670768961994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.496 y1[1] (analytic) = 2.9972040586026602752133365623937 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5177785199984572749400486271781 relative error = 17.27538432067428477533815582625 % h = 0.001 y2[1] (analytic) = 1.925273394922677695885221986944 y2[1] (numeric) = 2.0349734724272986123628837997624 absolute error = 0.1097000775046209164776618128184 relative error = 5.6978960907017915250970525001092 % h = 0.001 TOP MAIN SOLVE Loop memory used=648.5MB, alloc=4.5MB, time=111.08 NO POLE NO POLE x[1] = 1.497 y1[1] (analytic) = 2.9972782865932954127982051491029 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5178527479890924125249172138873 relative error = 17.277433006652295717033934723323 % h = 0.001 y2[1] (analytic) = 1.926270636178379113089403190711 y2[1] (numeric) = 2.0363269270280811767063151622066 absolute error = 0.1100562908497020636169119714956 relative error = 5.7134386405872867410997129985872 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.498 y1[1] (analytic) = 2.9973515173057270636087734948114 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5179259787015240633354855595958 relative error = 17.279454068406354882817038088851 % h = 0.001 y2[1] (analytic) = 1.927267951163438207801024307119 y2[1] (numeric) = 2.0376812587275251408552464427633 absolute error = 0.1104133075640869330542221356443 relative error = 5.7290065710600065589778878048488 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.499 y1[1] (analytic) = 2.9974237506667245213159499548364 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5179982120625215210426620196208 relative error = 17.281447507957520950074712512252 % h = 0.001 y2[1] (analytic) = 1.9282653388805400780705699424854 y2[1] (numeric) = 2.0390364675256305048096776414325 absolute error = 0.1107711286450904267391076989471 relative error = 5.7445998956450111915641994470897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE NO POLE x[1] = 1.5 y1[1] (analytic) = 2.9974949866040544309417233711415 y1[1] (numeric) = 2.4794255386042030002732879352156 absolute error = 0.5180694479998514306684354359259 relative error = 17.283413327299230606516587229319 % h = 0.001 y2[1] (analytic) = 1.9292627983322970899118101485657 y2[1] (numeric) = 2.0403925534223972685696087582142 absolute error = 0.1111297550901001786577986096485 relative error = 5.7602186278698533109240562031114 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff(y1,x,1) = diff(y2,x,5); diff(y2,x,1) = y1 - 2.0; Iterations = 1000 Total Elapsed Time = 1 Minutes 51 Seconds Elapsed Time(since restart) = 1 Minutes 51 Seconds Expected Time Remaining = 15 Minutes 45 Seconds Optimized Time Remaining = 15 Minutes 44 Seconds Time to Timeout = 13 Minutes 8 Seconds Percent Done = 10.54 % > quit memory used=650.7MB, alloc=4.5MB, time=111.46