|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[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," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[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, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 3 - 1; > while ((m >= 10) and ((abs(array_y_higher[1,m]) < glob_small_float) or (abs(array_y_higher[1,m-1]) < glob_small_float) or (abs(array_y_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_y_higher[1,m]/array_y_higher[1,m-1]; > rm1 := array_y_higher[1,m-1]/array_y_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 > #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 - 3 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_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_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_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_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_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 > 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 2 > 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 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > 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 2 > 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 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > 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 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > 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 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; n := glob_max_terms; m := n - 4; while 10 <= m and (abs(array_y_higher[1, m]) < glob_small_float or abs(array_y_higher[1, m - 1]) < glob_small_float or abs(array_y_higher[1, m - 2]) < glob_small_float) do m := m - 1 end do; if 10 < m then rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_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 - 4; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_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_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_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; 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; 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; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > 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_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > #emit pre sin $eq_no = 1 iii = 1 > #emit pre sin 1 $eq_no = 1 > array_tmp1[1] := sin(array_x[1]); > array_tmp1_g[1] := cos(array_x[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_y_set_initial[1,4] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (3)) * factorial_3(0,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,2] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > #emit pre sin $eq_no = 1 iii = 2 > #emit pre sin 2 $eq_no = 1 > array_tmp1[2] := att(1,array_tmp1_g,array_x,1); > array_tmp1_g[2] := -att(1,array_tmp1,array_x,1); > #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_y_set_initial[1,5] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (3)) * factorial_3(1,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,3] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > #emit pre sin $eq_no = 1 iii = 3 > #emit pre sin 3 $eq_no = 1 > array_tmp1[3] := att(2,array_tmp1_g,array_x,1); > array_tmp1_g[3] := -att(2,array_tmp1,array_x,1); > #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_y_set_initial[1,6] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (3)) * factorial_3(2,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,4] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > #emit pre sin $eq_no = 1 iii = 4 > #emit pre sin 4 $eq_no = 1 > array_tmp1[4] := att(3,array_tmp1_g,array_x,1); > array_tmp1_g[4] := -att(3,array_tmp1,array_x,1); > #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_y_set_initial[1,7] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (3)) * factorial_3(3,6); > array_y[7] := temporary; > array_y_higher[1,7] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,6] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,5] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > #emit pre sin $eq_no = 1 iii = 5 > #emit pre sin 5 $eq_no = 1 > array_tmp1[5] := att(4,array_tmp1_g,array_x,1); > array_tmp1_g[5] := -att(4,array_tmp1,array_x,1); > #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_y_set_initial[1,8] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (3)) * factorial_3(4,7); > array_y[8] := temporary; > array_y_higher[1,8] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,7] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,6] := temporary > ; > temporary := temporary / glob_h * (4.0); > array_y_higher[4,5] := 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 sin $eq_no = 1 > array_tmp1[kkk] := att(kkk-1,array_tmp1_g,array_x,1); > array_tmp1_g[kkk] := -att(kkk-1,array_tmp1,array_x,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 3; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_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_y[kkk + order_d] := temporary; > array_y_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_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; array_tmp1[1] := sin(array_x[1]); array_tmp1_g[1] := cos(array_x[1]); array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 4] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h^3*factorial_3(0, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 2] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := att(1, array_tmp1_g, array_x, 1); array_tmp1_g[2] := -att(1, array_tmp1, array_x, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 5] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h^3*factorial_3(1, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 3] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := att(2, array_tmp1_g, array_x, 1); array_tmp1_g[3] := -att(2, array_tmp1, array_x, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 6] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h^3*factorial_3(2, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 4] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := att(3, array_tmp1_g, array_x, 1); array_tmp1_g[4] := -att(3, array_tmp1, array_x, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 7] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h^3*factorial_3(3, 6); array_y[7] := temporary; array_y_higher[1, 7] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 6] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 5] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := att(4, array_tmp1_g, array_x, 1); array_tmp1_g[5] := -att(4, array_tmp1, array_x, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 8] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h^3*factorial_3(4, 7); array_y[8] := temporary; array_y_higher[1, 8] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 7] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 6] := temporary; temporary := temporary*4.0/glob_h; array_y_higher[4, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := att(kkk - 1, array_tmp1_g, array_x, 1); array_tmp1_g[kkk] := -att(kkk - 1, array_tmp1, array_x, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 3; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_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_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0 - sin(x); > end; exact_soln_y := proc(x) 1.0 - sin(x) end proc > exact_soln_yp := proc(x) > -cos(x); > end; exact_soln_yp := proc(x) -cos(x) end proc > exact_soln_ypp := proc(x) > sin(x); > end; exact_soln_ypp := proc(x) sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > ALWAYS, > DEBUGMASSIVE, > INFO, > glob_max_terms, > glob_iolevel, > DEBUGL, > #Top Generate Globals Decl > glob_current_iter, > glob_unchanged_h_cnt, > glob_dump_analytic, > glob_large_float, > glob_disp_incr, > djd_debug, > glob_optimal_expect_sec, > glob_hmax, > glob_reached_optimal_h, > glob_curr_iter_when_opt, > glob_smallish_float, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > MAX_UNCHANGED, > glob_no_eqs, > glob_relerr, > glob_last_good_h, > glob_almost_1, > sec_in_min, > glob_optimal_clock_start_sec, > glob_max_opt_iter, > glob_percent_done, > glob_log10abserr, > glob_warned, > glob_log10_abserr, > glob_not_yet_finished, > glob_log10normmin, > glob_subiter_method, > glob_max_sec, > glob_h, > glob_iter, > glob_orig_start_sec, > glob_max_rel_trunc_err, > glob_max_hours, > glob_abserr, > glob_look_poles, > glob_hmin, > hours_in_day, > djd_debug2, > glob_max_minutes, > glob_max_iter, > glob_log10_relerr, > glob_log10relerr, > glob_small_float, > glob_optimal_start, > glob_max_trunc_err, > glob_initial_pass, > centuries_in_millinium, > years_in_century, > days_in_year, > glob_dump, > glob_normmax, > glob_start, > glob_warned2, > glob_hmin_init, > glob_optimal_done, > glob_clock_start_sec, > glob_html_log, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_3, > #END CONST > array_m1, > array_pole, > array_y, > array_x, > array_1st_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_y_init, > array_tmp1_g, > array_last_rel_error, > array_norms, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher_work, > array_y_higher_work2, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > DEBUGMASSIVE := 4; > INFO := 2; > glob_max_terms := 30; > glob_iolevel := 5; > DEBUGL := 3; > glob_current_iter := 0; > glob_unchanged_h_cnt := 0; > glob_dump_analytic := false; > glob_large_float := 9.0e100; > glob_disp_incr := 0.1; > djd_debug := true; > glob_optimal_expect_sec := 0.1; > glob_hmax := 1.0; > glob_reached_optimal_h := false; > glob_curr_iter_when_opt := 0; > glob_smallish_float := 0.1e-100; > glob_not_yet_start_msg := true; > glob_clock_sec := 0.0; > min_in_hour := 60.0; > glob_display_flag := true; > MAX_UNCHANGED := 10; > glob_no_eqs := 0; > glob_relerr := 0.1e-10; > glob_last_good_h := 0.1; > glob_almost_1 := 0.9990; > sec_in_min := 60.0; > glob_optimal_clock_start_sec := 0.0; > glob_max_opt_iter := 10; > glob_percent_done := 0.0; > glob_log10abserr := 0.0; > glob_warned := false; > glob_log10_abserr := 0.1e-10; > glob_not_yet_finished := true; > glob_log10normmin := 0.1; > glob_subiter_method := 3; > glob_max_sec := 10000.0; > glob_h := 0.1; > glob_iter := 0; > glob_orig_start_sec := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_abserr := 0.1e-10; > glob_look_poles := false; > glob_hmin := 0.00000000001; > hours_in_day := 24.0; > djd_debug2 := true; > glob_max_minutes := 0.0; > glob_max_iter := 1000; > glob_log10_relerr := 0.1e-10; > glob_log10relerr := 0.0; > glob_small_float := 0.1e-50; > glob_optimal_start := 0.0; > glob_max_trunc_err := 0.1e-10; > glob_initial_pass := true; > centuries_in_millinium := 10.0; > years_in_century := 100.0; > days_in_year := 365.0; > glob_dump := false; > glob_normmax := 0.0; > glob_start := 0; > glob_warned2 := false; > glob_hmin_init := 0.001; > glob_optimal_done := false; > glob_clock_start_sec := 0.0; > glob_html_log := 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 := 1; > 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/h3sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 3 ) = sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 50;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);"); > omniout_str(ALWAYS,"array_y_init[2 + 1] := exact_soln_ypp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 20;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0 - sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_yp := proc(x)"); > omniout_str(ALWAYS,"-cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_ypp := proc(x)"); > omniout_str(ALWAYS,"sin(x);"); > omniout_str(ALWAYS,"end;"); > 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 := 50; > 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(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_tmp1_g:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(4+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(4+ 1) ,(1..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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[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_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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[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_norms[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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 <=1 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 <=1 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 <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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 <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_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 <=4 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_higher[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[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_tmp1_g := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > array_y_init[1 + 1] := exact_soln_yp(x_start); > array_y_init[2 + 1] := exact_soln_ypp(x_start); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 20; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.001 ; > glob_look_poles := true; > glob_max_iter := 1000; > glob_max_minutes := 15; > #END OVERRIDE BLOCK > #END SECOND INPUT BLOCK > #BEGIN INITS AFTER SECOND INPUT BLOCK > glob_last_good_h := glob_h; > glob_max_terms := max_terms; > glob_max_sec := convfloat(60.0) * convfloat(glob_max_minutes) + convfloat(3600.0) * convfloat(glob_max_hours); > glob_abserr := 10.0 ^ (glob_log10_abserr); > glob_relerr := 10.0 ^ (glob_log10_relerr); > chk_data(); > #AFTER INITS AFTER SECOND INPUT BLOCK > array_y_set_initial[1,1] := true; > array_y_set_initial[1,2] := true; > array_y_set_initial[1,3] := true; > array_y_set_initial[1,4] := false; > array_y_set_initial[1,5] := false; > array_y_set_initial[1,6] := false; > array_y_set_initial[1,7] := false; > array_y_set_initial[1,8] := false; > array_y_set_initial[1,9] := false; > array_y_set_initial[1,10] := false; > array_y_set_initial[1,11] := false; > array_y_set_initial[1,12] := false; > array_y_set_initial[1,13] := false; > array_y_set_initial[1,14] := false; > array_y_set_initial[1,15] := false; > array_y_set_initial[1,16] := false; > array_y_set_initial[1,17] := false; > array_y_set_initial[1,18] := false; > array_y_set_initial[1,19] := false; > array_y_set_initial[1,20] := false; > array_y_set_initial[1,21] := false; > array_y_set_initial[1,22] := false; > array_y_set_initial[1,23] := false; > array_y_set_initial[1,24] := false; > array_y_set_initial[1,25] := false; > array_y_set_initial[1,26] := false; > array_y_set_initial[1,27] := false; > array_y_set_initial[1,28] := false; > array_y_set_initial[1,29] := false; > array_y_set_initial[1,30] := false; > if glob_html_log then # if number 2 > html_log_file := fopen("html/entry.html",WRITE,TEXT); > fi;# end if 2 > ; > #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 := 3; > #Start Series array_y > term_no := 1; > while (term_no <= order_diff) do # do number 2 > array_y[term_no] := array_y_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_y_higher[r_order,term_no] := array_y_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_y(); > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 2 > tmp := abs(array_y_higher[1,1]); > log10norm := (log10(tmp)); > if (log10norm < glob_log10normmin) then # if number 3 > glob_log10normmin := log10norm; > fi;# end if 3 > fi;# end if 2 > ; > 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; > atomall(); > if (glob_look_poles) then # if number 2 > #left paren 0004C > check_for_pole(); > fi;# end if 2 > ;#was right paren 0004C > array_x[1] := array_x[1] + glob_h; > array_x[2] := glob_h; > #Jump Series array_y > order_diff := 3; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 4; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[4,iii] := array_y_higher[4,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 4; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[3,iii] := array_y_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 3; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[3,iii] := array_y_higher[3,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 3; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 3; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 3; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 4; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 4; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 3; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 3; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_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_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_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 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 3 ) = sin(x);"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-15T20:35:44-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"h3sin") > ; > logitem_str(html_log_file,"diff ( y , x , 3 ) = sin(x);") > ; > 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 3 > 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 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"h3sin diffeq.mxt") > ; > logitem_str(html_log_file,"h3sin maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; 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; global ALWAYS, DEBUGMASSIVE, INFO, glob_max_terms, glob_iolevel, DEBUGL, glob_current_iter, glob_unchanged_h_cnt, glob_dump_analytic, glob_large_float, glob_disp_incr, djd_debug, glob_optimal_expect_sec, glob_hmax, glob_reached_optimal_h, glob_curr_iter_when_opt, glob_smallish_float, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, MAX_UNCHANGED, glob_no_eqs, glob_relerr, glob_last_good_h, glob_almost_1, sec_in_min, glob_optimal_clock_start_sec, glob_max_opt_iter, glob_percent_done, glob_log10abserr, glob_warned, glob_log10_abserr, glob_not_yet_finished, glob_log10normmin, glob_subiter_method, glob_max_sec, glob_h, glob_iter, glob_orig_start_sec, glob_max_rel_trunc_err, glob_max_hours, glob_abserr, glob_look_poles, glob_hmin, hours_in_day, djd_debug2, glob_max_minutes, glob_max_iter, glob_log10_relerr, glob_log10relerr, glob_small_float, glob_optimal_start, glob_max_trunc_err, glob_initial_pass, centuries_in_millinium, years_in_century, days_in_year, glob_dump, glob_normmax, glob_start, glob_warned2, glob_hmin_init, glob_optimal_done, glob_clock_start_sec, glob_html_log, array_const_0D0, array_const_3, array_m1, array_pole, array_y, array_x, array_1st_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_y_init, array_tmp1_g, array_last_rel_error, array_norms, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher_work, array_y_higher_work2, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; DEBUGMASSIVE := 4; INFO := 2; glob_max_terms := 30; glob_iolevel := 5; DEBUGL := 3; glob_current_iter := 0; glob_unchanged_h_cnt := 0; glob_dump_analytic := false; glob_large_float := 0.90*10^101; glob_disp_incr := 0.1; djd_debug := true; glob_optimal_expect_sec := 0.1; glob_hmax := 1.0; glob_reached_optimal_h := false; glob_curr_iter_when_opt := 0; glob_smallish_float := 0.1*10^(-100); glob_not_yet_start_msg := true; glob_clock_sec := 0.; min_in_hour := 60.0; glob_display_flag := true; MAX_UNCHANGED := 10; glob_no_eqs := 0; glob_relerr := 0.1*10^(-10); glob_last_good_h := 0.1; glob_almost_1 := 0.9990; sec_in_min := 60.0; glob_optimal_clock_start_sec := 0.; glob_max_opt_iter := 10; glob_percent_done := 0.; glob_log10abserr := 0.; glob_warned := false; glob_log10_abserr := 0.1*10^(-10); glob_not_yet_finished := true; glob_log10normmin := 0.1; glob_subiter_method := 3; glob_max_sec := 10000.0; glob_h := 0.1; glob_iter := 0; glob_orig_start_sec := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_abserr := 0.1*10^(-10); glob_look_poles := false; glob_hmin := 0.1*10^(-10); hours_in_day := 24.0; djd_debug2 := true; glob_max_minutes := 0.; glob_max_iter := 1000; glob_log10_relerr := 0.1*10^(-10); glob_log10relerr := 0.; glob_small_float := 0.1*10^(-50); glob_optimal_start := 0.; glob_max_trunc_err := 0.1*10^(-10); glob_initial_pass := true; centuries_in_millinium := 10.0; years_in_century := 100.0; days_in_year := 365.0; glob_dump := false; glob_normmax := 0.; glob_start := 0; glob_warned2 := false; glob_hmin_init := 0.001; glob_optimal_done := false; glob_clock_start_sec := 0.; glob_html_log := true; glob_orig_start_sec := elapsed_time_seconds(); MAX_UNCHANGED := 10; glob_curr_iter_when_opt := 0; glob_display_flag := true; glob_no_eqs := 1; 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/h3sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 3 ) = sin(x);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 50;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);"); omniout_str(ALWAYS, "array_y_init[2 + 1] := exact_soln_ypp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 20;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0 - sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_yp := proc(x)"); omniout_str(ALWAYS, "-cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_ypp := proc(x)"); omniout_str(ALWAYS, "sin(x);"); omniout_str(ALWAYS, "end;"); 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 := 50; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_m1 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_tmp1_g := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 5, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 5, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 5, 1 .. 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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[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_norms[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 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 <= 1 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 <= 4 do term := 1; while term <= max_terms do array_y_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 4 do term := 1; while term <= max_terms do array_y_higher[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[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_tmp1_g := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1_g[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); array_y_init[2] := exact_soln_yp(x_start); array_y_init[3] := exact_soln_ypp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; glob_h := 0.001; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; glob_last_good_h := glob_h; glob_max_terms := max_terms; glob_max_sec := convfloat(60.0)*convfloat(glob_max_minutes) + convfloat(3600.0)*convfloat(glob_max_hours); glob_abserr := 10.0^glob_log10_abserr; glob_relerr := 10.0^glob_log10_relerr; chk_data(); array_y_set_initial[1, 1] := true; array_y_set_initial[1, 2] := true; array_y_set_initial[1, 3] := true; array_y_set_initial[1, 4] := false; array_y_set_initial[1, 5] := false; array_y_set_initial[1, 6] := false; array_y_set_initial[1, 7] := false; array_y_set_initial[1, 8] := false; array_y_set_initial[1, 9] := false; array_y_set_initial[1, 10] := false; array_y_set_initial[1, 11] := false; array_y_set_initial[1, 12] := false; array_y_set_initial[1, 13] := false; array_y_set_initial[1, 14] := false; array_y_set_initial[1, 15] := false; array_y_set_initial[1, 16] := false; array_y_set_initial[1, 17] := false; array_y_set_initial[1, 18] := false; array_y_set_initial[1, 19] := false; array_y_set_initial[1, 20] := false; array_y_set_initial[1, 21] := false; array_y_set_initial[1, 22] := false; array_y_set_initial[1, 23] := false; array_y_set_initial[1, 24] := false; array_y_set_initial[1, 25] := false; array_y_set_initial[1, 26] := false; array_y_set_initial[1, 27] := false; array_y_set_initial[1, 28] := false; array_y_set_initial[1, 29] := false; array_y_set_initial[1, 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 := 3; term_no := 1; while term_no <= order_diff do array_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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_y(); if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_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; atomall(); 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 := 3; ord := 4; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[4, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[3, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 3; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[3, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 4; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 3; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_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 ( y , x , 3 ) = sin(x);"); 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, "2012-06-15T20:35:44-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "h3sin"); logitem_str(html_log_file, "diff ( y , x , 3 ) = sin(x);"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "h3sin diffeq.mxt"); logitem_str(html_log_file, "h3sin maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/h3sinpostode.ode################# diff ( y , x , 3 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK Digits := 50; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); array_y_init[1 + 1] := exact_soln_yp(x_start); array_y_init[2 + 1] := exact_soln_ypp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 20; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0 - sin(x); end; exact_soln_yp := proc(x) -cos(x); end; exact_soln_ypp := proc(x) sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 0.90016658335317184769318580158938 y[1] (numeric) = 0.90016658335317184769318580158938 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 0.89917162927043200487024788047681 y[1] (numeric) = 0.89917162912128250578920005293013 absolute error = 1.4914949908104782754667892027830e-10 relative error = 1.6587433836415016344597758481299e-08 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 0.89817677601605448925135770391935 y[1] (numeric) = 0.89817677482322362141267466335016 absolute error = 1.1928308678386830405691827902844e-09 relative error = 1.3280580167409736581902396005394e-07 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 0.89718202458489247230959578949541 y[1] (numeric) = 0.89718202056032099192052280805893 absolute error = 4.0245714803890729814364824662768e-09 relative error = 4.4857914783247678103432358210238e-07 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 0.89618737597169730231102924533054 y[1] (numeric) = 0.89618736643489521701242741680904 absolute error = 9.5368020852986018285215035988518e-09 relative error = 1.0641526918361529952906784249708e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 0.89519283117111750956344639997322 y[1] (numeric) = 0.8951928125502615964102500009297 absolute error = 1.8620855913153196399043516484442e-08 relative error = 2.0800943958401506314468054662802e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 0.89419839117769781176790938198128 y[1] (numeric) = 0.89419835901073002654273954107322 absolute error = 3.2166967785225169840908058414351e-08 relative error = 3.5972965398494943843835194925487e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 0.89320405698587811947411929758354 y[1] (numeric) = 0.89320400592160489623564475095712 absolute error = 5.1064273223238474546626418920854e-08 relative error = 5.7169773047779404848022174120001e-06 % h = 0.001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.9MB, time=0.39 NO POLE x[1] = 0.108 y[1] (analytic) = 0.89220982958999254164058855096841 y[1] (numeric) = 0.89220975338918498140733402698083 absolute error = 7.6200807560233254523987587774421e-08 relative error = 8.5406823633909849669194384551780e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 0.89121570998426839130061474694456 y[1] (numeric) = 0.89121560152076333877002838808836 absolute error = 1.0846350505253058635885620044196e-07 relative error = 1.2170286479178555796032226737770e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 0.89022169916282519133505050991655 y[1] (numeric) = 0.89022155042462719853675370463503 absolute error = 1.4873819799279829680528151527235e-07 relative error = 1.6707995113203084459296886219799e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 0.88922779811967368035286344632307 y[1] (numeric) = 0.88922760021005785613411950929715 absolute error = 1.9790961582421874393702592112083e-07 relative error = 2.2256346038968943199875432040614e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 0.88823400784871481868048036989479 y[1] (numeric) = 0.88823375098733056292103267723679 absolute error = 2.5686138425575944769265800453477e-07 relative error = 2.8918210965359526696478769872527e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 0.8872403293437387944609098003048 y[1] (numeric) = 0.8872400028677144159134552567989 absolute error = 3.2647602437854745454350590396253e-07 relative error = 3.6796797167688551673023316146110e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 0.88624676359842402986363663600634 y[1] (numeric) = 0.88624635596347224651531672597369 absolute error = 4.0763495178334831991003264756513e-07 relative error = 4.5995649126912444682500306741857e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 0.8852533116063361874062827912803 y[1] (numeric) = 0.88525281038786050825569194370279 absolute error = 5.0121847567915059084757751483960e-07 relative error = 5.6618650177050987161249485336933e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 0.88425997436092717638902747574917 y[1] (numeric) = 0.88425936625512916353235705884188 absolute error = 6.0810579801285667041690728502190e-07 relative error = 6.8770024160863687810780632521528e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 0.88326675285553415944278068185407 y[1] (numeric) = 0.88326602368052156936183663321442 absolute error = 7.2917501259008094404863964262624e-07 relative error = 8.2554337093829655450382491278473e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 0.88227364808337855919210333203896 y[1] (numeric) = 0.88227278278027436213605622869985 absolute error = 8.6530310419705604710333910887668e-07 relative error = 9.8076498836479050711420872885981e-05 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.1MB, time=0.87 NO POLE x[1] = 0.119 y[1] (analytic) = 0.88128066103756506503386742263883 y[1] (numeric) = 0.88127964367161734138571570169406 absolute error = 1.0173659477236481517209447644601e-06 relative error = 0.00011544176477512450233001595288051 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 0.88028779271108064003264938572903 y[1] (numeric) = 0.8802866064727733525504994415592 absolute error = 1.1862383072874821499441698321158e-06 relative error = 0.00013475573751104118335540216083295 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 0.87929504409679352793384977345972 y[1] (numeric) = 0.87929367130295816875624078284271 absolute error = 1.3727938353591776089906170060962e-06 relative error = 0.00015612436855814455434355237695312 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 0.87830241618745226029553225167281 y[1] (numeric) = 0.87830083828238037159915881409145 absolute error = 1.5779050718886963734375813593823e-06 relative error = 0.00017965396004921509456657297399525 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 0.8773099099756846637399747708799 y[1] (numeric) = 0.87730810753224123093728679901406 absolute error = 1.8024434434328026879718658394873e-06 relative error = 0.00020545116645071965845507233186869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 0.87631752645399686732592566296706 y[1] (numeric) = 0.87631547917473458368921241855317 absolute error = 2.0472792622836367132444138913777e-06 relative error = 0.00023362299628627941292044200270432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 0.87532526661477231004255729128789 y[1] (numeric) = 0.87532295333304671164025103511716 absolute error = 2.3132817255984023062561707340094e-06 relative error = 0.00026427681386883463189418168170973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.126 y[1] (analytic) = 0.87433313145027074842610976010826 y[1] (numeric) = 0.87433053013135621825617417278788 absolute error = 2.6013189145301699355873203786005e-06 relative error = 0.00029752034104155694738960860780396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 0.87334112195262726430021706667654 y[1] (numeric) = 0.87333820969483390450461639976581 absolute error = 2.9122577933597956006669107263168e-06 relative error = 0.00033346165892755998165522948279821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 0.87234923911385127264090795551028 y[1] (numeric) = 0.87234599214964264368428479163515 absolute error = 3.2469642086289566231638751356562e-06 relative error = 0.00037220920968845961256657876141135 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 0.87135748392582552956727360981603 y[1] (numeric) = 0.87135387762293725526209614622921 absolute error = 3.6063028882743051774635868214963e-06 relative error = 0.00041387179829183545431245269659524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.2MB, time=1.33 x[1] = 0.13 y[1] (analytic) = 0.87036585738030514045879418929169 y[1] (numeric) = 0.87036186624286437771836811294823 absolute error = 3.9911374407627404260763434553806e-06 relative error = 0.00045855859428764546769035784588317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 0.86937436046891656820031609690237 y[1] (numeric) = 0.86936995813856234040019139132787 absolute error = 4.4023303542278001247055744979050e-06 relative error = 0.00050637913359364594895296382240452 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 0.86838299418315664155567172956986 y[1] (numeric) = 0.86837815344016103438311114547563 absolute error = 4.8407429956071725605840942276343e-06 relative error = 0.00055744332028986948316087623426748 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 0.86739175951439156367093333907315 y[1] (numeric) = 0.8673864522787817823412467726829 absolute error = 5.3072356097813296865663902562932e-06 relative error = 0.00061186142842221378741575710587192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 0.86640065745385592070829249982374 y[1] (numeric) = 0.86639485478653720742598015608208 absolute error = 5.8026673187132823123437416573716e-06 relative error = 0.00066974410381519471119050494276943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 0.86540968899265169061155654955344 y[1] (numeric) = 0.86540336109653110115334352264964 absolute error = 6.3278961205894582130269038059637e-06 relative error = 0.00073120236589391700525881298973287 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 0.86441885512174725200425323733583 y[1] (numeric) = 0.86441197134285829030023901915607 absolute error = 6.8837788889617040142181797536654e-06 relative error = 0.00079634760951531681747406128195179 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 0.86342815683197639322133468075391 y[1] (numeric) = 0.86342068566060450280962310983234 absolute error = 7.4711713718904117115709215666191e-06 relative error = 0.00086529160680873022287643756589638 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 0.86243759511403732147547160042766 y[1] (numeric) = 0.862429504185846232704789890557 absolute error = 8.0909281910887706817098706610834e-06 relative error = 0.00093814650902584244733685995166274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 0.86144717095849167215892866552446 y[1] (numeric) = 0.86143842705565060401288840526956 absolute error = 8.7439028410681460402602549038575e-06 relative error = 0.001015024848400072798196291763882 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 0.86045688535576351828201164829463 y[1] (numeric) = 0.8604474544080752336978100410814 absolute error = 9.4309476882845842016072132299942e-06 relative error = 0.0010960395400154506721491651499126 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 0.85946673929613838004907694910232 y[1] (numeric) = 0.85945658638216809360258306918542 absolute error = 1.0152913970286446493879916893845e-05 relative error = 0.0011813038836850383699698019444704 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.2MB, time=1.82 x[1] = 0.142 y[1] (analytic) = 0.85847673376976223457309391585971 y[1] (numeric) = 0.85846582311796737140141238915837 absolute error = 1.0910651794863171681526701338784e-05 relative error = 0.0012709315658389568096110456939156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 0.85748686976664052572975024321969 y[1] (numeric) = 0.85747516475650133056150352460452 absolute error = 1.1705010139195168246718615174026e-05 relative error = 0.001365036661422070593735077050093 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 0.85649714827663717415209059733904 y[1] (numeric) = 0.85648461143978816931481090830503 absolute error = 1.2536836849004837279689034012681e-05 relative error = 0.0014637336358013892548880288034626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 0.85550757028947358736667847149108 y[1] (numeric) = 0.855494163310835878639851485113 absolute error = 1.3406978637708726826986378083340e-05 relative error = 0.0015671373466832418713231745034765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 0.85451813679472767007227113628341 y[1] (numeric) = 0.8545038205136420992537256507687 absolute error = 1.4316281085570818545485514708684e-05 relative error = 0.0016753630460402826189329404097724 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 0.85352884878183283456199740572324 y[1] (numeric) = 0.85351358319319397761448853460216 absolute error = 1.5265588638856947508871121080246e-05 relative error = 0.0017885263820483851998887671987545 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 0.85253970724007701129002779687021 y[1] (numeric) = 0.85252345149546802093401562373983 absolute error = 1.6255744608990356012173130380978e-05 relative error = 0.001906743401033484466431088104948 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 0.85155071315860165958372651632402 y[1] (numeric) = 0.85153342556742995120150771593767 absolute error = 1.7287591171708382218800386349642e-05 relative error = 0.0020301305494284239388207382819854 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 0.85056186752640077850227456131236 y[1] (numeric) = 0.85054350555703455821778117752338 absolute error = 1.8361969366220284493383788977435e-05 relative error = 0.0021588046757398682997794936739808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 0.8495731713323199178427530766738 y[1] (numeric) = 0.84955369161322555164049047214549 absolute error = 1.9479719094366202262604528312404e-05 relative error = 0.002292883032525340333832869118451 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 0.84858462556505518929467596156972 y[1] (numeric) = 0.84856398388593541204043091509426 absolute error = 2.0641679119777254245046475456807e-05 relative error = 0.0024324832783804421688446839736244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 0.84759623121315227774396057131025 y[1] (numeric) = 0.84757438252608524096907059687934 absolute error = 2.1848687067036774889974430913244e-05 relative error = 0.0025777234799363210687223169208616 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=2.29 NO POLE x[1] = 0.154 y[1] (analytic) = 0.84660798926500545272732521024132 y[1] (numeric) = 0.84658488768558461003746140851972 absolute error = 2.3101579420842689863801721604318e-05 relative error = 0.0027287221138674404207962975630234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 0.84561990070885658003810196121268 y[1] (numeric) = 0.84559549951733140900668008962238 absolute error = 2.4401191525171031421871590296221e-05 relative error = 0.0028855980689097169587603907994244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 0.84463196653279413348445324573189 y[1] (numeric) = 0.84460621817521169288995120879595 absolute error = 2.5748357582440594502036935937768e-05 relative error = 0.0030484706478890856623212842246008 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 0.84364418772475220680098035650535 y[1] (numeric) = 0.84361704381409952806660497426362 absolute error = 2.7143910652678734375382241723192e-05 relative error = 0.0032174595697605541778732480342387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 0.84265656527250952571471205067536 y[1] (numeric) = 0.84262797658985683740802376070472 absolute error = 2.8588682652688306688289970639867e-05 relative error = 0.0033926849716578090106057575598154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 0.84166910016368846016646113768246 y[1] (numeric) = 0.84163901665933324441573222636544 absolute error = 3.0083504355215750728911317012946e-05 relative error = 0.0035742674109534361474943062386326 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 0.84068179338575403668853684031401 y[1] (numeric) = 0.84065016418036591637178688233576 absolute error = 3.1629205388120316749957978249730e-05 relative error = 0.0037623278673298191826399482760331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 0.83969464592601295093980055114447 y[1] (numeric) = 0.83966141931177940650162196358971 absolute error = 3.3226614233544438178587554760976e-05 relative error = 0.0039569877448607784314351551426362 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 0.83870765877161258039905244922922 y[1] (numeric) = 0.83867278221338549514950943893018 absolute error = 3.4876558227085249543010299038071e-05 relative error = 0.0041583688741040149380662128937871 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 0.83772083290953999721773628358307 y[1] (numeric) = 0.83768425304598302996679198436483 absolute error = 3.6579863556967250944299218239175e-05 relative error = 0.004366593514204423701939699392563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 0.8367341693266209812329494706565 y[1] (numeric) = 0.83669583197135776511304873166697 absolute error = 3.8337355263216119900738989529584e-05 relative error = 0.0045817843550083408727668418591275 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=22.8MB, alloc=4.3MB, time=2.77 x[1] = 0.165 y[1] (analytic) = 0.83574766900951903314174549271711 y[1] (numeric) = 0.83570751915228219947035459094213 absolute error = 4.0149857236833671390901774978400e-05 relative error = 0.0048040645191887900912792564180205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 0.83476133294473438783771542275181 y[1] (numeric) = 0.83471931475251541387079493292763 absolute error = 4.2018192218973966920489824182373e-05 relative error = 0.005033557564381793582907415769873 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 0.83377516211860302791083523922592 y[1] (numeric) = 0.83373121893680290733739840349681 absolute error = 4.3943181800120573436835729116706e-05 relative error = 0.0052703874853338140452540967086652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 0.83278915751729569731156543076966 y[1] (numeric) = 0.83274323187087643233865162942151 absolute error = 4.5925646419264972913801348150858e-05 relative error = 0.0055146787160603938068641605247796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 0.83180332012681691518018922661023 y[1] (numeric) = 0.83175535372145382905676056086437 absolute error = 4.7966405363086123428665745864510e-05 relative error = 0.0057665561320160581746546696503306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.17 y[1] (analytic) = 0.83081765093300398984237562332915 y[1] (numeric) = 0.83076758465623885866982418232574 absolute error = 5.0066276765131172551441003405884e-05 relative error = 0.0060261450522755503304511172342387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 0.8298321509215260329719532122995 y[1] (numeric) = 0.8297799248439210356480873098577 absolute error = 5.2226077604997323865902441802696e-05 relative error = 0.0062935712417264655834022395210653 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 0.82884682107788297392188064494727 y[1] (numeric) = 0.82879237445417545906444017827826 absolute error = 5.4446623707514857440466669017747e-05 relative error = 0.0065689609132733532346435157128022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 0.82786166238740457422439940478408 y[1] (numeric) = 0.82780493365766264291933350787229 absolute error = 5.6728729741931305065896911789474e-05 relative error = 0.0068524407300533547634742852222943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 0.82687667583524944226135438597639 y[1] (numeric) = 0.82681760262602834548027872564982 absolute error = 5.9073209221096781075660326566736e-05 relative error = 0.0071441378076634475005319058709758 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 0.82589186240640404810566760804859 y[1] (numeric) = 0.8258303815319033976361040016473 absolute error = 6.1480874500650469563606401291426e-05 relative error = 0.0074441797163993634130152479804364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 0.82490722308568173853495022516409 y[1] (numeric) = 0.82484327054890353026613774600153 absolute error = 6.3952536778208268812479162557783e-05 relative error = 0.0077526944835062530899560113290254 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=3.24 NO POLE x[1] = 0.177 y[1] (analytic) = 0.82392275885772175221823781629032 y[1] (numeric) = 0.82385626985162920062449219759838 absolute error = 6.6489006092551593745618691939893e-05 relative error = 0.0080698105954411654818870432047438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 0.82293847070698823507683376943031 y[1] (numeric) = 0.82286937961566541773962071999812 absolute error = 6.9091091322817337213049432186081e-05 relative error = 0.008395657000147414419039442869298 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 0.82195435961776925582024539899536 y[1] (numeric) = 0.82188260001758156682932340506568 absolute error = 7.1759600187688990921993929688646e-05 relative error = 0.0087303631093409034054424174652522 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 0.82097042657417582165819726030079 y[1] (numeric) = 0.82089593123493123273137656928548 absolute error = 7.4495339244588926820691015308635e-05 relative error = 0.0090740588008084806630295060590958 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 0.81998667256014089418970594908918 y[1] (numeric) = 0.81990937344625202234996271211675 absolute error = 7.7299113888871839743236972427565e-05 relative error = 0.0094268744207183968801000562276987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 0.81900309855941840547020049692454 y[1] (numeric) = 0.81892292683106538611807848994437 absolute error = 8.0171728353019352122006980171833e-05 relative error = 0.0097889407859429386022741125960563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 0.81801970555558227425767229525488 y[1] (numeric) = 0.81793659156987643847609924320261 absolute error = 8.3113985705835781573052052272098e-05 relative error = 0.010160389186393310691440799720747 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 0.81703649453202542243883830191132 y[1] (numeric) = 0.81695036784417377736667959809218 absolute error = 8.6126687851645072158703819141320e-05 relative error = 0.010541351387366841769163745224828 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 0.81605346647195879163630110379855 y[1] (numeric) = 0.81596425583642930274617064797491 absolute error = 8.9210635529488890130455823644288e-05 relative error = 0.010931959631906587055601239897519 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.186 y[1] (analytic) = 0.81507062235841035999768922853466 y[1] (numeric) = 0.81497825573009803411273520301381 absolute error = 9.2366628312325884954025520851990e-05 relative error = 0.011332346643173403513253072999173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 0.81408796317422415916776091581804 y[1] (numeric) = 0.81399236770961792705134357992805 absolute error = 9.5595464606232116417335889990580e-05 relative error = 0.011742645626830572706789975777157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.3MB, time=3.71 x[1] = 0.188 y[1] (analytic) = 0.81310548990205929144445437633573 y[1] (numeric) = 0.81300659196040968879583338685175 absolute error = 9.8897941649602648620989483972250e-05 relative error = 0.012162990273441047295885278283789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 0.81212320352438894711986738208099 y[1] (numeric) = 0.81202092866887659280821774122149 absolute error = 0.00010227485551235431164964085950014 relative error = 0.012593514760877397587381922133656 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 0.81114110502349942200714884701869 y[1] (numeric) = 0.81103537802240429237542734136876 absolute error = 0.0001057270010951296317215056499383 relative error = 0.01303435375674453508632182956213 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 0.81015919538148913515428487112495 y[1] (numeric) = 0.81004994020936063322367279505985 absolute error = 0.00010925517212850193061207606509855 relative error = 0.013485642420815290502369530890036 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 0.80917747558026764674576153393323 y[1] (numeric) = 0.80906461541909546515061459060524 absolute error = 0.0001128601611721815951469433279869 relative error = 0.013947516407478924189008893795914 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 0.80819594660155467619308653584224 y[1] (numeric) = 0.8080794038419404526755290783527 absolute error = 0.00011654275961422351755745748954305 relative error = 0.014420111868202647517612048473969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 0.8072146094268791204151515965821 y[1] (numeric) = 0.80709430566920888470765981238243 absolute error = 0.00012030375767023570749178419966638 relative error = 0.014903565454006234217104709556278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 0.80623346503757807230941733039465 y[1] (numeric) = 0.80610932109319548323294458403713 absolute error = 0.00012414394438258907647274635752269 relative error = 0.015398014317949801242513884914406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 0.80525251441479583941490212666118 y[1] (numeric) = 0.80512445030717621101930946054374 absolute error = 0.00012806410761962839559266611743886 relative error = 0.015903596117634839272214541687939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 0.80427175853948296276795637290694 y[1] (numeric) = 0.80413969350540807834072212341715 absolute error = 0.00013206503407488442723424948978976 relative error = 0.016420449017718573474223564629428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 0.80329119839239523595180316432647 y[1] (numeric) = 0.80315505088312894872019778257613 absolute error = 0.00013614750926628723160538175033714 relative error = 0.016948711692441735726454972309308 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 0.8023108349540927243408264502072 y[1] (numeric) = 0.80217052263655734369195192314953 absolute error = 0.0001403123175353806488745270576674 relative error = 0.017488523328169830024482824544232 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.3MB, time=4.18 x[1] = 0.2 y[1] (analytic) = 0.80133066920493878454058737288161 y[1] (numeric) = 0.80118610896289224658289512280374 absolute error = 0.00014456024204653795769225007786874 relative error = 0.018040023625947973363090824494456 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 0.80035070212509908402454935910971 y[1] (numeric) = 0.80020181006031290531366615808015 absolute error = 0.00014889206478617871088320102956421 relative error = 0.018603352804069394934753852179438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.202 y[1] (analytic) = 0.79937093469454062096849232708521 y[1] (numeric) = 0.79921762612797863421940059869315 absolute error = 0.00015330856656198674909172839205209 relative error = 0.019178651600657677049230422556995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.203 y[1] (analytic) = 0.79839136789303074428359617456935 y[1] (numeric) = 0.79823355736602861489043306900358 absolute error = 0.0001578105270021293931631055657752 relative error = 0.019766061276262821743680502462109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204 y[1] (analytic) = 0.79741200270013617384917351498742 y[1] (numeric) = 0.79724960397558169603313233594859 absolute error = 0.00016239872455447781604117903882526 relative error = 0.020365723616471227622194712968277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 0.79643284009522202094603142867336 y[1] (numeric) = 0.79626576615873619235106936257649 absolute error = 0.00016707393648582859496206609686514 relative error = 0.020977780934529662037363461116833 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 0.79545388105745080889144179581925 y[1] (numeric) = 0.79528204411856968244671944600135 absolute error = 0.00017183693888112644472234981790059 relative error = 0.021602376073983314304563072065004 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 0.79447512656578149387669957607767 y[1] (numeric) = 0.79429843805913880574390053805873 absolute error = 0.00017668850664268813279903801893431 relative error = 0.022239652411328016222025927746263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 0.79349657759896848600824819717701 y[1] (numeric) = 0.79331494818547905843115082620714 absolute error = 0.00018162941348942757709737096986951 relative error = 0.022889753858676716756528675970184 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.209 y[1] (analytic) = 0.79251823513556067055335101134286 y[1] (numeric) = 0.79233157470360458842624963128058 absolute error = 0.00018666043195608212710138006228032 relative error = 0.023552824866440298345712789068458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 0.79154010015390042939128757377236 y[1] (numeric) = 0.79134831782050798936208665755434 absolute error = 0.00019178233339244002920091621801355 relative error = 0.024229010426022822863681481070055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 0.79056217363212266267105329188374 y[1] (numeric) = 0.79036517774416009359408560923752 absolute error = 0.00019699588796256907696768264621566 relative error = 0.024918456072531295896632920235793 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.3MB, time=4.66 NO POLE x[1] = 0.212 y[1] (analytic) = 0.78958445654815381067654078755991 y[1] (numeric) = 0.78938215468350976422938916595143 absolute error = 0.00020230186464404644715162160847304 relative error = 0.025621307887500038579928811957317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 0.7886069498797108759001811071231 y[1] (numeric) = 0.78839924884848368617801328799161 absolute error = 0.00020770103122718972216781913149838 relative error = 0.026337712501629756857197120158966 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 0.78762965460430044532602270531804 y[1] (numeric) = 0.78741646044998615622617980020166 absolute error = 0.00021319415431428909984290511637714 relative error = 0.027067817097541398635865623564935 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 0.78665257169921771292322592014294 y[1] (numeric) = 0.78643378969989887213203718110895 absolute error = 0.00021878199931884079118873903399133 relative error = 0.027811769412544889931957185400108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.216 y[1] (analytic) = 0.78567570214154550235095044495269 y[1] (numeric) = 0.78545123681108072074398046158364 absolute error = 0.00022446533046478160696998336905147 relative error = 0.028569717741422841720086412225696 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 0.78469904690815328987561309286506 y[1] (numeric) = 0.78446880199736756514178211468369 absolute error = 0.00023024491078572473383097818137881 relative error = 0.029341810939229319832419495996272 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.218 y[1] (analytic) = 0.78372260697569622750149293613085 y[1] (numeric) = 0.78348648547357203080074679553697 absolute error = 0.00023612150212419670074614059387799 relative error = 0.030128198424103770882933528132544 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 0.78274638332061416631566068978145 y[1] (numeric) = 0.78250428745548329077910376708823 absolute error = 0.00024209586513087553655692269321444 relative error = 0.030929030180100197830677852645669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 0.78177037691913068004820899454299 y[1] (numeric) = 0.78152220815986684992885182430024 absolute error = 0.00024816875926383011935717024275171 relative error = 0.031744456760031679437937849910448 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.221 y[1] (analytic) = 0.78079458874725208884876003870549 y[1] (numeric) = 0.78054024780446432813027250594649 absolute error = 0.00025434094278776071848753275900268 relative error = 0.032574629288330328526271035397732 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 0.77981901978076648328022674235797 y[1] (numeric) = 0.77955840660799324255032835946407 absolute error = 0.00026061317277324072989838289389618 relative error = 0.033419699463922784585367002922478 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=41.9MB, alloc=4.3MB, time=5.13 x[1] = 0.223 y[1] (analytic) = 0.778843670995242748530803510147 y[1] (numeric) = 0.77857668479014678892516400045025 absolute error = 0.000266986205095959605639509696751 relative error = 0.034279819563121336946617390218507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 0.77786854336602958884516234048672 y[1] (numeric) = 0.77759508257159362186692868428354 absolute error = 0.0002734607944359669782336562031749 relative error = 0.035155142442530775395210916062699 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 0.7768936378682545521758298599428 y[1] (numeric) = 0.77661360017397763419514008302844 absolute error = 0.00028003769427691798068977691436123 relative error = 0.036045821541971065761533226179754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.226 y[1] (analytic) = 0.77591895547682305505572063133211 y[1] (numeric) = 0.77563223781991773529280993624147 absolute error = 0.0002867176569053197629106950906359 relative error = 0.03695201088741594870469376015032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.227 y[1] (analytic) = 0.77494449716641740769280186292349 y[1] (numeric) = 0.77465099573300762848755321953469 absolute error = 0.00029350143340977920524864338880686 relative error = 0.037873865093947560578164464547572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.228 y[1] (analytic) = 0.7739702639114958392878644239937 y[1] (numeric) = 0.77366987413781558745790344976861 absolute error = 0.00030038977368025182996097422508518 relative error = 0.038811539368727175949840663942059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 0.77299625668629152357637484888623 y[1] (numeric) = 0.77268887325988423166505772054095 absolute error = 0.00030738342640729191131712834527641 relative error = 0.039765189513982172036365884790136 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.23 y[1] (analytic) = 0.77202247646481160459538278763993 y[1] (numeric) = 0.77170799332573030081027603620715 absolute error = 0.00031448313908130378510675143278303 relative error = 0.04073497193000931600434342306539 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 0.77104892422083622267645813619863 y[1] (numeric) = 0.77072723456284442831816048701472 absolute error = 0.00032168965799179435829764918391035 relative error = 0.04172104361819447678913186612453 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 0.77007560092791754066563185318355 y[1] (numeric) = 0.76974659719969091384604078205332 absolute error = 0.00032900372822662681959107113023007 relative error = 0.042723562184048863785333933744108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 0.76910250755937877037131424320659 y[1] (numeric) = 0.76876608146570749481969363061606 absolute error = 0.00033642609367127555162061259052678 relative error = 0.043742685840261895471882607186908 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 0.7681296450883131992411642587249 y[1] (numeric) = 0.76778568759130511699562443623357 absolute error = 0.0003439574970080822455398224913348 relative error = 0.044778573409770801748850690837637 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=45.7MB, alloc=4.3MB, time=5.61 x[1] = 0.235 y[1] (analytic) = 0.7671570144875832172688831434866 y[1] (numeric) = 0.76680541580786770405014074108013 absolute error = 0.00035159867971551321874240240646726 relative error = 0.045831384328847064482805232302173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 0.76618461672981934413190551069257 y[1] (numeric) = 0.76582526634775192619544783165912 absolute error = 0.00035935038206741793645767903344791 relative error = 0.046901278650199801482742563504089 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 0.76521245278741925656096071810253 y[1] (numeric) = 0.76484523944428696782299788965294 absolute error = 0.00036721334313228873796282844958354 relative error = 0.047988417046096199859419486647143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 0.76424052363254681594247717044265 y[1] (numeric) = 0.76386533533177429417432504456888 absolute error = 0.00037518830077252176815212587376328 relative error = 0.04909296081149910545728810830108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 0.76326883023713109615480194662958 y[1] (numeric) = 0.76288555424548741703959965732644 absolute error = 0.00038327599164367911520228930314576 relative error = 0.050215071867221875790293243807765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 0.76229737357286541163920791551018 y[1] (numeric) = 0.76190589642167165948413613621228 absolute error = 0.00039147715119375215507177929790223 relative error = 0.051354912763100604660549826568141 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 0.76132615461120634570666026902879 y[1] (numeric) = 0.76092636209754391960308955867546 absolute error = 0.00039979251366242610357071035332775 relative error = 0.05251264668118382739243145308784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 0.76035517432337277908131416597463 y[1] (numeric) = 0.7599469515112924333045773442465 absolute error = 0.00040822281208034577673682172812179 relative error = 0.053688437438939816373918606444266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.243 y[1] (analytic) = 0.75938443368034491868171494273065 y[1] (numeric) = 0.75896766490207653612146319543897 absolute error = 0.00041676877826838256025174729168078 relative error = 0.054882449492481577362225204962003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 0.7584139336528633266406721097428 y[1] (numeric) = 0.75798850251002642405204149482976 absolute error = 0.00042543114283690258863061491304688 relative error = 0.056094847939809657781794345994754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 0.7574436752114279495647781137546 y[1] (numeric) = 0.75700946457624291342986131761367 absolute error = 0.00043421063518503613491679614092848 relative error = 0.057325798524072879019778337703155 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 0.75647365932629714803454260620757 y[1] (numeric) = 0.75603055134279719982293018978841 absolute error = 0.00044310798349994821161241641915869 relative error = 0.058575467636847105507144674240175 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.3MB, time=6.09 NO POLE x[1] = 0.247 y[1] (analytic) = 0.75550388696748672634611271759229 y[1] (numeric) = 0.75505176305273061596253869274599 absolute error = 0.00045212391475611038357402484629816 relative error = 0.059844022321432164162629314782498 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 0.75453435910476896249554959594889 y[1] (numeric) = 0.75407309995005438870194798542586 absolute error = 0.00046125915471457379360161052303033 relative error = 0.061131630276167028571942745284413 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 0.75356507670767163840663122515975 y[1] (numeric) = 0.75309456227974939500518328532199 absolute error = 0.00047051442792224340144793983775162 relative error = 0.062438459857763383075974577182125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 0.75259604074547707040315129515061 y[1] (numeric) = 0.75211615028776591696617731953007 absolute error = 0.00047989045771115343697397562053897 relative error = 0.063764680084657682749291090349043 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.251 y[1] (analytic) = 0.75162725218722113992668365162059 y[1] (numeric) = 0.7511378642210233958585087266709 absolute error = 0.000489387966197744068174924949697 relative error = 0.065110460640381826064029861272466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.252 y[1] (analytic) = 0.75065871200169232450078160745575 y[1] (numeric) = 0.75015970432741018521598135993119 absolute error = 0.00049900767428213928480024752455898 relative error = 0.0664759718769525578544196214453 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 0.74969042115743072894258115154618 y[1] (numeric) = 0.74918167085578330294429141062182 absolute error = 0.00050875030164742599828974092435716 relative error = 0.067861384818279721023645446844777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 0.7487223806227271168227768433228 y[1] (numeric) = 0.7482037640559681824640302405658 absolute error = 0.00051861656675893435874660275700199 relative error = 0.069266871163593476267693465266491 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 0.74775459136562194217493893295701 y[1] (numeric) = 0.74722598417875842288527178029227 absolute error = 0.00052860718686351928966715266473462 relative error = 0.070692603290890609930200163991446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 0.7467870543539043814551399978256 y[1] (numeric) = 0.74624833147591553821399431842854 absolute error = 0.00053872287798884324114567939705858 relative error = 0.072138754260400050948254272235184 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.257 y[1] (analytic) = 0.74581977055511136575285913553355 y[1] (numeric) = 0.74527080620016870559058747584722 absolute error = 0.00054896435494266016227165968633283 relative error = 0.073605497818067718701609779242737 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=53.4MB, alloc=4.3MB, time=6.56 x[1] = 0.258 y[1] (analytic) = 0.74485274093652661325413150250981 y[1] (numeric) = 0.74429340860521451256069612604067 absolute error = 0.00055933233131210069343537646913858 relative error = 0.07509300839906082443692314479574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 0.74388596646517966195791073494597 y[1] (numeric) = 0.74331613894571670337865399085773 absolute error = 0.00056982751946295857925674408823423 relative error = 0.076601461131291749804482901384735 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.26 y[1] (analytic) = 0.74291944810784490264661153563478 y[1] (numeric) = 0.74233899747730592434376060814797 absolute error = 0.00058045063053897830285092748680755 relative error = 0.078131031838961626917512900760615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 0.74195318683104061211179945608533 y[1] (numeric) = 0.74136198445657946816965633501529 absolute error = 0.00059120237446114394214312107004232 relative error = 0.079681897046123745223559218999444 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 0.74098718360102798663599464814456 y[1] (numeric) = 0.7403851001411010173870510172846 absolute error = 0.00060208345992696924894363085995839 relative error = 0.08125423398026691136377353853082 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 0.74002143938381017573155610324072 y[1] (numeric) = 0.73940834478940038678006292243144 absolute error = 0.00061309459440978895149318080928303 relative error = 0.082848220575918889089141551095316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 0.73905595514513131613761264028424 y[1] (numeric) = 0.73843171866097326485642549961426 absolute error = 0.00062423648415805128118714066998918 relative error = 0.0844640354782700472029329994557 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 0.73809073185047556607600664521424 y[1] (numeric) = 0.73745522201628095435182049658092 absolute error = 0.00063550983419461172418614863331642 relative error = 0.086101858046817344405930379408248 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 0.73712577046506613976721630616662 y[1] (numeric) = 0.73647885511675011176859692909483 absolute error = 0.00064691534831602799861937707179833 relative error = 0.087761868359028780835386598710485 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.267 y[1] (analytic) = 0.73616107195386434220722182826113 y[1] (numeric) = 0.73550261822477248594913636413985 absolute error = 0.00065845372909185625808546412127824 relative error = 0.08944424721402844701022914306752 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 0.73519663728156860420628085106048 y[1] (numeric) = 0.73452651160370465568412594351715 absolute error = 0.00067012567786394852215490754333231 relative error = 0.09114917613630230182383120974457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 0.73423246741261351769057802984597 y[1] (numeric) = 0.73355053551786776635600153953881 absolute error = 0.0006819318947457513345764903071586 relative error = 0.092876837379424812161771092256698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=57.2MB, alloc=4.3MB, time=7.03 x[1] = 0.27 y[1] (analytic) = 0.73326856331116887126771347897946 y[1] (numeric) = 0.7325746902325472656178243993534 absolute error = 0.00069387307862160564988907962606131 relative error = 0.094627413929806587665462673440602 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.271 y[1] (analytic) = 0.73230492594113868605699451178298 y[1] (numeric) = 0.73159897601399263810785559900459 absolute error = 0.0007059499271460479491389127783884 relative error = 0.096401089510463145113425636408722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 0.73134155626616025178549484656383 y[1] (numeric) = 0.73062339312941713920009359262643 absolute error = 0.0007181631367431125854012539373965 relative error = 0.098198048584804937850337955620528 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.273 y[1] (analytic) = 0.73037845524960316315084518264563 y[1] (numeric) = 0.72964794184699752779104110621538 absolute error = 0.00073051340260563535980407643024832 relative error = 0.10001847636044878665994000663734 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.274 y[1] (analytic) = 0.72941562385456835645171878353456 y[1] (numeric) = 0.72867262243587379812296858919014 absolute error = 0.00074300141869455832875019434442497 relative error = 0.10186255879305084945140446307207 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 0.72845306304388714648697543665472 y[1] (numeric) = 0.72769743516614891064394240045324 absolute error = 0.0007556278777382358430330362014889 relative error = 0.10373048259016126811001487594548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.276 y[1] (analytic) = 0.72749077378012026372442689042862 y[1] (numeric) = 0.72672238030888852190488686890403 absolute error = 0.00076839347123174181954002152459374 relative error = 0.10562243521510063185197491661543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.277 y[1] (analytic) = 0.72652875702555689174018659985692 y[1] (numeric) = 0.72574745813612071349395033131829 absolute error = 0.00078129888943617824623626853863699 relative error = 0.10753860489085839741996679781373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 0.72556701374221370492956634116763 y[1] (numeric) = 0.72477266892083572000844621320591 absolute error = 0.00079434482137798492112012796172342 relative error = 0.10947918060401340746075908829544 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 0.72460554489183390649048198455785 y[1] (numeric) = 0.72379801293698565606464118068297 absolute error = 0.00080753195484825042584080387488354 relative error = 0.11144435210867664943879936383474 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 0.72364435143588626668033044154215 y[1] (numeric) = 0.72282349045948424234566335354714 absolute error = 0.00082086097640202433466708799500747 relative error = 0.11343430993045639846038489442865 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 0.72268343433556416134729952995054 y[1] (numeric) = 0.72184910176420653068780453162559 absolute error = 0.000834332571357630659494998324944 relative error = 0.11544924537044588841175450979455 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.3MB, time=7.50 NO POLE x[1] = 0.282 y[1] (analytic) = 0.72172279455178461073707222518593 y[1] (numeric) = 0.72087484712798862820549134807002 absolute error = 0.00084794742379598253158087711591321 relative error = 0.11748935050923365685135722598673 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.283 y[1] (analytic) = 0.72076243304518731857588649095688 y[1] (numeric) = 0.71990072682862742045520122460485 absolute error = 0.00086170621655989812068526635202495 relative error = 0.11955481821093671014169913357147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.284 y[1] (analytic) = 0.71980235077613371143091160634557 y[1] (numeric) = 0.71892674114488029363859996478955 absolute error = 0.00087560963125341779231164155602092 relative error = 0.12164584212725665635962109239562 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 0.71884254870470597834890162875478 y[1] (numeric) = 0.71795289035646485584517878213418 absolute error = 0.00088965834824112250372284662060286 relative error = 0.12376261670155895458568827828788 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 0.71788302779070611077408635400021 y[1] (numeric) = 0.7169791747440586573346695204081 absolute error = 0.0009038530466474534394168335921119 relative error = 0.12590533717297543024365159734618 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 0.71692378899365494274625985557732 y[1] (numeric) = 0.7160055945892989098595177837032 absolute error = 0.00091819440435603288674207187412211 relative error = 0.12807419958053020723974413069135 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 0.71596483327279119138002640493412 y[1] (numeric) = 0.71503215017478220502769465375518 absolute error = 0.00093268309800898635233175117894534 relative error = 0.13026940076728920873897750331917 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 0.71500616158707049762616329342395 y[1] (numeric) = 0.71405884178406423170612863168759 absolute error = 0.00094731980300626592003466173635417 relative error = 0.1324911383845333795116784984627 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 0.71404777489516446731605979449563 y[1] (numeric) = 0.71308566970165949246504040072337 absolute error = 0.0009621051935049748510193937722559 relative error = 0.13473961089595578388833119134607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 0.71308967415545971249019122160201 y[1] (numeric) = 0.71211263421304101906346396550517 absolute error = 0.00097703994241869342672725609683477 relative error = 0.1370150175818827344744409025309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 0.71213186032605689301158675327299 y[1] (numeric) = 0.71113973560464008697623868247992 absolute error = 0.00099212472141680603534807079306403 relative error = 0.13931755854351910789969064931466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=64.8MB, alloc=4.4MB, time=7.97 x[1] = 0.293 y[1] (analytic) = 0.71117433436476975846524941180534 y[1] (numeric) = 0.71016697416384592896275765433162 absolute error = 0.0010073602009238295024917574737172 relative error = 0.14164743470721800500719651835851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.294 y[1] (analytic) = 0.71021709722912419034448629606947 y[1] (numeric) = 0.70919435017900544767775891969015 absolute error = 0.0010227470501187426667273763793214 relative error = 0.1440048478287749140292642524463 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 0.70926014987635724452510688202316 y[1] (numeric) = 0.70822186393942292732444682730102 absolute error = 0.001038285936934317200660054722142 relative error = 0.14639000049774653644578484925323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 0.70830349326341619402844691665405 y[1] (numeric) = 0.70724951573535974435023194151054 absolute error = 0.0010539775280564496782149751435056 relative error = 0.14880309614179443638036237993684 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 0.70734712834695757207417514224732 y[1] (numeric) = 0.7062773058580340771853787833025 absolute error = 0.0010698224889234948887963589448132 relative error = 0.15124433903105367555752358726829 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.298 y[1] (analytic) = 0.70639105608334621542383979809208 y[1] (numeric) = 0.70530523459962061502485166821438 absolute error = 0.0010858214837256003989881298777037 relative error = 0.1537139342825265970219979291492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.299 y[1] (analytic) = 0.70543527742865430801611155600021 y[1] (numeric) = 0.70433330225325026565364985926296 absolute error = 0.0011019751754040423624616967372482 relative error = 0.15621208786450192200816118922304 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3 y[1] (analytic) = 0.70447979333866042489467925431497 y[1] (numeric) = 0.70336150911300986231592420951993 absolute error = 0.0011182842256505625787550447950463 relative error = 0.1587390066009993255443889687771 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 0.70352460476884857642975450243418 y[1] (numeric) = 0.7023898554739418696281684251963 absolute error = 0.0011347492949067068015860772378859 relative error = 0.16129489817623965758335248970198 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 0.70256971267440725283414093426342 y[1] (numeric) = 0.70141834163204408853677903601993 absolute error = 0.001151371042363164297361898243485 relative error = 0.16387997113914097766529317125984 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 0.7016151180102284689748235944506 y[1] (numeric) = 0.70044696788426936032027911532161 absolute error = 0.0011681501259591086545444791289955 relative error = 0.16649443490784057234712020439005 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 0.70066082173090680948103364573289 y[1] (numeric) = 0.69947573452852526963650174758122 absolute error = 0.0011850872023815398445318981516695 relative error = 0.16913849977424312586587347156656 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=68.6MB, alloc=4.4MB, time=8.45 x[1] = 0.305 y[1] (analytic) = 0.69970682479073847414974328925156 y[1] (numeric) = 0.69850464186367384661503019622594 absolute error = 0.0012021829270646275347130930256217 relative error = 0.17181237690859521575077011643277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 0.69875312814372032364954549226047 y[1] (numeric) = 0.69753369018953126799519267921526 absolute error = 0.0012194379541890556543528130452097 relative error = 0.17451627836408630635379516617271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 0.69779973274354892552387281926885 y[1] (numeric) = 0.69656287980686755730991061439339 absolute error = 0.0012368529366813682139622048754616 relative error = 0.17725041708147641453469401216821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 0.69684663954361960049450936332003 y[1] (numeric) = 0.69559221101740628411570015073558 absolute error = 0.0012544285262133163788092125844502 relative error = 0.18001500689375062301236728188655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 0.6958938494970254690663494738148 y[1] (numeric) = 0.69462168412382426226912775546199 absolute error = 0.0012721653732012067972217183528021 relative error = 0.1828102625308006181811475766563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 0.69494136355655649843435667604104 y[1] (numeric) = 0.69365129942975124725002158053814 absolute error = 0.0012900641268052511843350955028964 relative error = 0.18563639962413343048734447317667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.311 y[1] (analytic) = 0.69398918267469854969367587537158 y[1] (numeric) = 0.69268105723976963253174128532558 absolute error = 0.0013081254349289171619345900459977 relative error = 0.18849363471160755676887174522243 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.312 y[1] (analytic) = 0.69303730780363242535385163593833 y[1] (numeric) = 0.69171095785941414499880994508748 absolute error = 0.0013263499442182803550416908508453 relative error = 0.19138218524219664527881250608469 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 0.69208573989523291715810501948532 y[1] (numeric) = 0.69074100159517153941221262769198 absolute error = 0.0013447383000613777458923917933375 relative error = 0.19430226958078092544252835730482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 0.69113447990106785420862116504429 y[1] (numeric) = 0.68977118875448029192266717318913 absolute error = 0.0013632911465875622859539918551592 relative error = 0.19725410701296656573747302561979 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 0.69018352877239715139879948406602 y[1] (numeric) = 0.68880151964573029263217366296524 absolute error = 0.0013820091266668587666258211007738 relative error = 0.2002379177499331444353256726607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.316 y[1] (analytic) = 0.68923288746017185815341803867781 y[1] (numeric) = 0.68783199457826253720415001689943 absolute error = 0.0014008928819093209492680217783728 relative error = 0.20325392293330941930751129995868 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.4MB, time=8.92 NO POLE x[1] = 0.317 y[1] (analytic) = 0.6882825569150332074776633628236 y[1] (numeric) = 0.68686261386236881752246210836117 absolute error = 0.0014199430526643899552012544624319 relative error = 0.20630234464007758376772361835104 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 0.68733253808731166531597667717754 y[1] (numeric) = 0.68589337780929141139965773799284 absolute error = 0.0014391602780202539163189391846978 relative error = 0.20938340588750619830880853300904 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 0.6863828319270259802216671389056 y[1] (numeric) = 0.68492428673122277133471475801759 absolute error = 0.0014585451958032088869523808880045 relative error = 0.21249733063811198748640410404363 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 0.68543343938388223333824245658285 y[1] (numeric) = 0.68395534094130521232061458929832 absolute error = 0.0014780984425770210176278672845342 relative error = 0.21564434380465069410816654309376 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 0.68448436140727288869340688885654 y[1] (numeric) = 0.68298654075363059870205332354826 absolute error = 0.0014978206536422899913535653082741 relative error = 0.21882467125513718370534354791996 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.322 y[1] (analytic) = 0.68353559894627584380667633277783 y[1] (numeric) = 0.6820178864832400300836035529561 absolute error = 0.0015177124630358137230727798217247 relative error = 0.22203853981789499379298910398502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.323 y[1] (analytic) = 0.68258715294965348061155989410811 y[1] (numeric) = 0.68104937844612352628864101903745 absolute error = 0.0015377745035299543229188750706601 relative error = 0.22528617728663552386635184368263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 0.68163902436585171669325701733906 y[1] (numeric) = 0.68008101695921971136935112175988 absolute error = 0.0015580074066320053239058955791821 relative error = 0.22856781242556706353401721546587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.325 y[1] (analytic) = 0.68069121414299905684281893765035 y[1] (numeric) = 0.67911280234041549666813127890864 absolute error = 0.0015784118025835601746876587417156 relative error = 0.2318836749745338576533481683614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.326 y[1] (analytic) = 0.67974372322890564492872290056454 y[1] (numeric) = 0.67814473490854576293070607426431 absolute error = 0.0015989883203598819980168263002281 relative error = 0.23523399565418540881075693135637 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 0.67879655257106231608680727764583 y[1] (numeric) = 0.67717681498339304147127308145075 absolute error = 0.0016197375876692746155341961950808 relative error = 0.23861900617117621897845993939852 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=76.2MB, alloc=4.4MB, time=9.39 x[1] = 0.328 y[1] (analytic) = 0.67784970311663964922951538822866 y[1] (numeric) = 0.67620904288568719438999819828086 absolute error = 0.001640660230952454839517189947806 relative error = 0.24203893922339617368072826520399 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 0.67690317581248701987539551785335 y[1] (numeric) = 0.67524141893710509384318027407834 absolute error = 0.0016617568753819260322152437750127 relative error = 0.24549402850523177351635736635396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 0.67595697160513165329980430382978 y[1] (numeric) = 0.67427394346027030036640575978395 absolute error = 0.0016830281448613529333985440458273 relative error = 0.2489845087128584194102539399523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 0.67501109144077767800776033714693 y[1] (numeric) = 0.67330661677875274025101505766489 absolute error = 0.0017044746620249377567452794820361 relative error = 0.25251061554956395950578667560045 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.332 y[1] (analytic) = 0.67406553626530517952989450779567 y[1] (numeric) = 0.67233943921706838197420319413399 absolute error = 0.0017260970482367975556913136616849 relative error = 0.25607258573110370716098529994661 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 0.67312030702426925454244329747574 y[1] (numeric) = 0.67137241110067891168307838555117 absolute error = 0.0017478959235903428593649119245766 relative error = 0.25967065699108714107591321778205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 0.67217540466289906531223089961467 y[1] (numeric) = 0.67040553275599140773300301292151 absolute error = 0.0017698719069076575792278866931614 relative error = 0.26330506808639650015569910954662 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 0.67123083012609689446758572163781 y[1] (numeric) = 0.66943880451035801428054246712181 absolute error = 0.001792025615738880187043254515998 relative error = 0.26697605880263748730390901789712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 0.67028658435843720009613649849422 y[1] (numeric) = 0.66847222669207561393134827167966 absolute error = 0.0018143576663615861647882268145607 relative error = 0.27068386995962229794429087434423 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 0.66934266830416567117043291956346 y[1] (numeric) = 0.66750579963038549944330283519452 absolute error = 0.0018368686737801717271300843689396 relative error = 0.27442874341688519068554737375035 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 0.66839908290719828330233534324402 y[1] (numeric) = 0.66653952365547304448525413022882 absolute error = 0.0018595592517252388170812130152029 relative error = 0.27821092207923081917381107023134 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.339 y[1] (analytic) = 0.66745582911112035482711784475499 y[1] (numeric) = 0.66557339909846737345166953990686 absolute error = 0.0018824300126529813754483048481348 relative error = 0.28203064990231554582102920347721 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=80.1MB, alloc=4.4MB, time=9.87 x[1] = 0.34 y[1] (analytic) = 0.66651290785918560321822851296921 y[1] (numeric) = 0.66460742629144103033353905754021 absolute error = 0.0019054815677445728846894554290036 relative error = 0.28588817189826195975463793340729 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 0.66557032009431520183365058143904 y[1] (numeric) = 0.66364160556740964664585896834881 absolute error = 0.0019287145269055551877916130902258 relative error = 0.2897837341413068230048404429298 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 0.66462806675909683699480764717492 y[1] (numeric) = 0.66267593726033160841202808576637 absolute error = 0.0019521294987652285827795614085432 relative error = 0.29371758377348267063062607174068 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 0.66368614879578376539895589819304 y[1] (numeric) = 0.66171042170510772220548955790614 absolute error = 0.0019757270906760431934663402869075 relative error = 0.29768996901033329218450481892798 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.344 y[1] (analytic) = 0.66274456714629387186600593736127 y[1] (numeric) = 0.66074505923758088024895220251734 absolute error = 0.0019995079087129916170537348439298 relative error = 0.30170113914666332362891100431444 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 0.66180332275220872742071645564298 y[1] (numeric) = 0.65977985019453572457152627118318 absolute error = 0.0020234725576730028491901844597952 relative error = 0.30575134456232218054448068242843 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.346 y[1] (analytic) = 0.66086241655477264771120167246664 y[1] (numeric) = 0.65881479491369831022410948559642 absolute error = 0.0020476216410743374870921868702265 relative error = 0.309840836728022565212059915607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.347 y[1] (analytic) = 0.65992184949489175176469412463536 y[1] (numeric) = 0.65784989373373576755336013049867 absolute error = 0.0020719557611559842113339941366931 relative error = 0.31396986821119378190648688706722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.348 y[1] (analytic) = 0.65898162251313302108150404793491 y[1] (numeric) = 0.65688514699425596353459492928204 absolute error = 0.0020964755188770575469091186528758 relative error = 0.31813869268187009651104303403018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 0.65804173654972335906811625740272 y[1] (numeric) = 0.65592055503580716216395036932702 absolute error = 0.0021211815139161969041658880756959 relative error = 0.32234756491861437834712119258919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 0.65710219254454865081036509308237 y[1] (numeric) = 0.6549561181998776839101470848871 absolute error = 0.0021460743446709669002180081952726 relative error = 0.32659674081447726391424779592965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 0.65616299143715282318762765801042 y[1] (numeric) = 0.65399183682889556422619784572715 absolute error = 0.0021711546082572589614298122832727 relative error = 0.33088647738299208405125843462714 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=10.34 NO POLE x[1] = 0.352 y[1] (analytic) = 0.65522413416673690532897523416392 y[1] (numeric) = 0.65302771126622821112140063977938 absolute error = 0.0021964229005086942075745943845379 relative error = 0.33521703276420579786029991851029 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.353 y[1] (analytic) = 0.65428562167215808941222242013895 y[1] (numeric) = 0.65206374185618206179395927779505 absolute error = 0.0022218798159760276182631423438957 relative error = 0.33958866623074617858155710272706 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 0.65334745489192879180681319143277 y[1] (numeric) = 0.6510999289440022383245748873428 absolute error = 0.0022475259479265534822383040899677 relative error = 0.34400163819392549846832028220395 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 0.65240963476421571456148274036527 y[1] (numeric) = 0.6501362728758722024313526025334 absolute error = 0.0022733618883435121301301378318655 relative error = 0.34845621020988096158936145701457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 0.65147216222683890723763360789966 y[1] (numeric) = 0.64917277399891340928636869453547 absolute error = 0.0022993882279254979512649133641811 relative error = 0.35295264498575213537871919231784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 0.65053503821727082908936427390812 y[1] (numeric) = 0.64820943266118496039424432628618 absolute error = 0.0023256055560858686951199476219432 relative error = 0.35749120638589563366204754965693 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 0.64959826367263541159108802577568 y[1] (numeric) = 0.64724624921168325553307305279421 absolute error = 0.0023520144609521560580149729814746 relative error = 0.3620721594381373058138115194842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 0.64866183952970712131367957764527 y[1] (numeric) = 0.6462832240003416437580501260786 absolute error = 0.0023786155293654775556294515666679 relative error = 0.3666957703400621886409578803606 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 0.64772576672491002315008656407927 y[1] (numeric) = 0.64532035737803007346815260108492 absolute error = 0.0024054093468799496819339629943527 relative error = 0.37136230646534247954640628157206 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.361 y[1] (analytic) = 0.64679004619431684389134268244803 y[1] (numeric) = 0.64435764969655474153622017586957 absolute error = 0.0024323964977621023551225065784644 relative error = 0.37607203637010379149994193294685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 0.64585467887364803615391890795416 y[1] (numeric) = 0.64339510130865774150278763594224 absolute error = 0.0024595775649902946511312720119144 relative error = 0.3808252297993299523350014517134 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=87.7MB, alloc=4.4MB, time=10.82 x[1] = 0.363 y[1] (analytic) = 0.64491966569827084265934885386328 y[1] (numeric) = 0.64243271256801671083402070890458 absolute error = 0.0024869531302541318253281449587046 relative error = 0.38562215769330661289758156439366 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.364 y[1] (analytic) = 0.64398500760319836086706399723811 y[1] (numeric) = 0.64147048382924447724410807141992 absolute error = 0.0025145237739538836229559258181969 relative error = 0.39046309219410393059822245166263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 0.64305070552308860796137413726246 y[1] (numeric) = 0.64050841544788870408246318609261 absolute error = 0.0025422900751999038789109511698462 relative error = 0.39534830665209859695988108907895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 0.64211676039224358619352809909695 y[1] (numeric) = 0.63954650778043153478609058102554 absolute error = 0.0025702526118120514074375180714079 relative error = 0.4002780756325354798136741006092 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.367 y[1] (analytic) = 0.64118317314460834857978934112779 y[1] (numeric) = 0.63858476118428923639747211965986 absolute error = 0.0025984119603191121823172214679371 relative error = 0.40525267492212915287109513706936 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 0.64024994471377006495646076745515 y[1] (numeric) = 0.63762317601781184214832974298106 absolute error = 0.0026267686959582228081310244740901 relative error = 0.41027238153570558749556097583642 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 0.63931707603295708839279269051843 y[1] (numeric) = 0.63666175264028279310962210029881 absolute error = 0.0026553233926742952831705902196134 relative error = 0.41533747372288428360817741279276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.37 y[1] (analytic) = 0.63838456803503802196270753087285 y[1] (numeric) = 0.63570049141191857890813341857409 absolute error = 0.0026840766231194430545741122987534 relative error = 0.42044823097480111879260624530425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.371 y[1] (analytic) = 0.63745242165252078587627448231464 y[1] (numeric) = 0.63473939269386837751001389367471 absolute error = 0.0027130289586524083662605886399255 relative error = 0.42560493403087219681202556865908 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 0.63652063781755168497186701080265 y[1] (numeric) = 0.633778456848213694071631819989 absolute error = 0.0027421809693379909002351908136495 relative error = 0.43080786488559897891757626850607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 0.63558921746191447656993569494098 y[1] (numeric) = 0.63281768423796799885809860751521 absolute error = 0.0027715332239464777118370874257684 relative error = 0.43605730679541498351254874590258 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 0.6346581615170294386893285541723 y[1] (numeric) = 0.63185707522707636422982876787168 absolute error = 0.0028010862899530744594997863006205 relative error = 0.44135354428557434194005805273237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=91.5MB, alloc=4.4MB, time=11.30 x[1] = 0.375 y[1] (analytic) = 0.63372747091395243862709064828374 y[1] (numeric) = 0.63089663018041510069749788263731 absolute error = 0.0028308407335373379295927656464275 relative error = 0.44669686315708250038425699133089 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 0.63279714658337400190267436834815 y[1] (numeric) = 0.62993634946379139204576249903417 absolute error = 0.0028607971195826098569118693139752 relative error = 0.45208755049366936011642136504731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 0.63186718945561838156749147481296 y[1] (numeric) = 0.62897623344394292952610682920194 absolute error = 0.0028909560116754520413846456110121 relative error = 0.45752589466880515057768727165199 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.378 y[1] (analytic) = 0.6309376004606426278807375731069 y[1] (numeric) = 0.62801628248853754511918206018694 absolute error = 0.0029213179721050827615555129199519 relative error = 0.46301218535275933207000673779022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 0.63000838052803565835241935086267 y[1] (numeric) = 0.62705649696617284386700501227592 absolute error = 0.0029518835618628144854143385867504 relative error = 0.46854671351970282712619656227676 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.38 y[1] (analytic) = 0.6290795305870173281545145336508 y[1] (numeric) = 0.62609687724637583527538381344528 absolute error = 0.002982653340641492879130720205518 relative error = 0.47412977145485388194896928471569 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 0.62815105156643750090119414798726 y[1] (numeric) = 0.62513742369960256378693918746942 absolute error = 0.0030136278668349371142549605178401 relative error = 0.47976165276166786164773991360305 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 0.6272229443947751197990363113152 y[1] (numeric) = 0.62417813669723773832509088263601 absolute error = 0.0030448076975373814739454286791876 relative error = 0.48544265236907128536098451943244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 0.62629521000013727916816039866944 y[1] (numeric) = 0.62321901661159436090937969705091 absolute error = 0.0030761933885429182587807016185235 relative error = 0.49117306653874040973117602387985 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 0.62536784931025829633521006481245 y[1] (numeric) = 0.62226006381591335434249648517991 absolute error = 0.0031077854943449419927135796325409 relative error = 0.49695319287242467159902943341735 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 0.6244408632524987838991132287812 y[1] (numeric) = 0.621301278684363188969390458567 absolute error = 0.0031395845681355949297227702141991 relative error = 0.50278333031931530320414627072031 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 0.62351425275384472237054675500772 y[1] (numeric) = 0.62034266159203950850883002159005 absolute error = 0.0031715911618052138617167334176674 relative error = 0.50866377918345943562035092624771 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=11.79 NO POLE x[1] = 0.387 y[1] (analytic) = 0.62258801874090653318603319147135 y[1] (numeric) = 0.61938421291496475495779031066162 absolute error = 0.0032038058259417782282428808097316 relative error = 0.51459484113122000861625696387675 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 0.62166216213991815209759655070879 y[1] (numeric) = 0.61842593303008779256904253245631 absolute error = 0.0032362291098303595285540182524724 relative error = 0.52057681919878180761508797143386 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 0.62073668387673610293890374394874 y[1] (numeric) = 0.61746782231528353090232112354385 absolute error = 0.0032688615614525720365826204048927 relative error = 0.52661001779970395093270629936571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 0.61981158487683857176881790215284 y[1] (numeric) = 0.6165098811493525469494456802294 absolute error = 0.0033017037274860248193722219234431 relative error = 0.53269474273251915299937699841819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 0.61888686606532448139328944033205 y[1] (numeric) = 0.61555210991202070633377553344766 absolute error = 0.0033347561533037750595139068843911 relative error = 0.53883130118838009181921856269045 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 0.61796252836691256626651034317064 y[1] (numeric) = 0.61459450898393878358437576922465 absolute error = 0.0033680193829737826821345739459874 relative error = 0.54502000175875321149177393666492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 0.6170385727059404477722567707261 y[1] (numeric) = 0.61363707874668208148527442050938 absolute error = 0.0034014939592583662869823502167162 relative error = 0.5512611544431602932128840224777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.394 y[1] (analytic) = 0.61611500000636370988634470278558 y[1] (numeric) = 0.61267981958275004950019148108671 absolute error = 0.0034351804236136603861532216988774 relative error = 0.55755507065696813078727315922042 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.395 y[1] (analytic) = 0.61519181119175497522112295934603 y[1] (numeric) = 0.61172273187556590127312131681039 absolute error = 0.0034690793161890739480016425356387 relative error = 0.56390206323922664932317545982221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 0.61426900718530298145292755264793 y[1] (numeric) = 0.6107658160094762312051509735421 absolute error = 0.0035031911758267502477765791058289 relative error = 0.57030244646055580844015841583484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.397 y[1] (analytic) = 0.61334658890981165813342094323165 y[1] (numeric) = 0.60980907236975063010789780494623 absolute error = 0.0035375165400610280255231382854141 relative error = 0.57675653603108163400525398622003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 0.61242455728769920388573938859978 y[1] (numeric) = 0.60885250134258129993395076667065 absolute error = 0.0035720559451179039517886219291259 relative error = 0.58326464910842172511980790527735 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=12.25 NO POLE x[1] = 0.399 y[1] (analytic) = 0.6115029132409971639863711882616 y[1] (numeric) = 0.60789610331508266758470064644021 absolute error = 0.003606809925914496401670541821393 relative error = 0.58982710430572058581032789707312 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 0.61058165769134950833368824320429 y[1] (numeric) = 0.60693987867529099779594542220042 absolute error = 0.0036417790160585105377428210038742 relative error = 0.596444221699735133631275902402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 0.60966079156001170980405296118265 y[1] (numeric) = 0.60598382781216400510165786267383 absolute error = 0.0036769637478477047023950985088172 relative error = 0.60311632283897074016643568204119 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 0.60874031576784982299642215164349 y[1] (numeric) = 0.60502795111558046487630340652902 absolute error = 0.0037123646522693581201187451144693 relative error = 0.60984373075186816121842499510785 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 0.60782023123533956336636916560423 y[1] (numeric) = 0.60407224897633982345609727781206 absolute error = 0.0037479822589997399102718877921668 relative error = 0.6166267699550417173033430942546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.404 y[1] (analytic) = 0.60690053888256538675044514638653 y[1] (numeric) = 0.60311672178616180733959071635069 absolute error = 0.0037838170964035794108544300358304 relative error = 0.62346576646156908791968408002679 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 0.60598123962921956928179986676729 y[1] (numeric) = 0.60216136993768603146797712251258 absolute error = 0.0038198696915335378138227442547051 relative error = 0.63036104778933308593774171126939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 0.60506233439460128769798223684934 y[1] (numeric) = 0.60120619382447160658550983597871 absolute error = 0.0038561405701296811124724008706236 relative error = 0.63731294296941578135802104745384 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 0.60414382409761570004184017477465 y[1] (numeric) = 0.60025119384099674568042418808151 absolute error = 0.0038926302566189543614159866931409 relative error = 0.64432178255454534661489877471517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.408 y[1] (analytic) = 0.60322570965677302675643913930379 y[1] (numeric) = 0.59929637038265836950675738675287 absolute error = 0.0039293392741146572496817525509129 relative error = 0.65138789862759599855518174313082 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 0.60230799199018763217491822926617 y[1] (numeric) = 0.5983417238457717111874607122292 absolute error = 0.0039662681444159209874575170369654 relative error = 0.65851162481014141520054918021336 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=102.9MB, alloc=4.4MB, time=12.73 x[1] = 0.41 y[1] (analytic) = 0.60139067201557710640620235994886 y[1] (numeric) = 0.59738725462756991989919942036849 absolute error = 0.0040034173880071865070029395803614 relative error = 0.66569329627106200840837789457957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 0.6004737506502613476174886306349 y[1] (numeric) = 0.5964329631262036636392366687464 absolute error = 0.0040407875240576839782519618885062 relative error = 0.67293324973520643657739381145478 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.412 y[1] (analytic) = 0.59955722881116164471442460072855 y[1] (numeric) = 0.59547884974074073107479869861428 absolute error = 0.0040783790704209136396259021142778 relative error = 0.68023182349210774460322230222382 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.413 y[1] (analytic) = 0.59864110741479976041989579421255 y[1] (numeric) = 0.59452491487116563247531942332092 absolute error = 0.0041161925436341279445763708916236 relative error = 0.6875893574047545213744815748474 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 0.59772538737729701475233935357361 y[1] (numeric) = 0.59357115891837919972796349092006 absolute error = 0.0041542284589178150243758626535529 relative error = 0.69500619291841746821283817928792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 0.5968100696143733689045003648061 y[1] (numeric) = 0.59261758228419818543682780540721 absolute error = 0.0041924873301751834676725593988884 relative error = 0.70248267306953177480068448905505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 0.59589515504134650952354697466115 y[1] (numeric) = 0.59166418537135486110622240735111 absolute error = 0.0042309696699916484173245673100396 relative error = 0.71001914249463570230807065293589 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.417 y[1] (analytic) = 0.59498064457313093339346001994986 y[1] (numeric) = 0.59071096858349661440843253060513 absolute error = 0.0042696759896343189850274893447343 relative error = 0.71761594743936577662649657724224 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 0.59406653912423703252061248643465 y[1] (numeric) = 0.58975793232518554553636456730323 absolute error = 0.0043086067990514869842479191314216 relative error = 0.72527343576750899784141443872355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.419 y[1] (analytic) = 0.59315283960877017962345371165307 y[1] (numeric) = 0.58880507700189806264147958846083 absolute error = 0.0043477626068721169819741231922464 relative error = 0.73299195697011247532808334713907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 0.59223954694042981402721284191366 y[1] (numeric) = 0.58785240302002447635741898221324 absolute error = 0.0043871439204053376697938597004167 relative error = 0.74077186217465090113703227779895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.421 y[1] (analytic) = 0.59132666203250852796453564868418 y[1] (numeric) = 0.58689991078686859340972768603241 absolute error = 0.0044267512456399345548079626517613 relative error = 0.748613504154252277646105412714 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=106.8MB, alloc=4.4MB, time=13.20 x[1] = 0.422 y[1] (analytic) = 0.59041418579789115328296840365935 y[1] (numeric) = 0.58594760071064730931208140316473 absolute error = 0.004466585087243843970887000494615 relative error = 0.75651723733698231879616866350626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 0.58950211914905384856020210494802 y[1] (numeric) = 0.58499547320049020014942510702881 absolute error = 0.0045066459485636484107769979192103 relative error = 0.76448341781518794759733349767738 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 0.58859046299806318662798993905953 y[1] (numeric) = 0.58404352866643911344843105040073 absolute error = 0.004546934331624073179558888658795 relative error = 0.77251240335490031599229338290271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 0.58767921825657524250565045469569 y[1] (numeric) = 0.58309176751944775813568540889461 absolute error = 0.0045874507371274843699650458010796 relative error = 0.7806045534052977765933614001466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 0.58676838583583468174406851476933 y[1] (numeric) = 0.58214019017138129358401360051768 absolute error = 0.0046281956644533881600549142516478 relative error = 0.7887602291082292392703401569645 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 0.58585796664667384918110568257234 y[1] (numeric) = 0.58118879703501591774735523494037 absolute error = 0.0046691696116579314337504476319725 relative error = 0.79697979330779834905774549736661 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 0.58494796159951185810933128660698 y[1] (numeric) = 0.58023758852403845438460055757199 absolute error = 0.0047103730754734037247307290349858 relative error = 0.80526361056000892537244526877093 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.429 y[1] (analytic) = 0.58403837160435367985698499627348 y[1] (numeric) = 0.5792865650530459393728011645714 absolute error = 0.004751806551307740484183831702077 relative error = 0.81361204714247210608676839582315 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.43 y[1] (analytic) = 0.58312919757078923378308132737543 y[1] (numeric) = 0.57833572703754520611016867554717 absolute error = 0.0047934705332440276729126518282645 relative error = 0.82202547106417564358789579940769 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 0.58222044040799247768756608226273 y[1] (numeric) = 0.5773850748939524700092759609143 absolute error = 0.0048353655140400076782901213484235 relative error = 0.83050425207531580357217464691507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 0.58131210102472049863743431437966 y[1] (numeric) = 0.57643460903959291208087643067148 absolute error = 0.0048774919851275865565578837081847 relative error = 0.83904876167719232097321571028406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 0.58040418032931260420971899102467 y[1] (numeric) = 0.57548432989270026160875780074491 absolute error = 0.0049198504366123426009611902797634 relative error = 0.84765937313216687110555828702708 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=13.67 NO POLE x[1] = 0.434 y[1] (analytic) = 0.57949667922968941415225911125708 y[1] (numeric) = 0.57453423787241637791604766201021 absolute error = 0.0049624413572730362362114492468712 relative error = 0.8563364614736855178216396527742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.435 y[1] (analytic) = 0.57858959863335195246315561810729 y[1] (numeric) = 0.57358433339879083122338908565198 absolute error = 0.0050052652345611212397665324553191 relative error = 0.8650804035163656042291112484615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 0.5776829394473807398898230255586 y[1] (numeric) = 0.57263461689278048259940540665032 absolute error = 0.0050483225546002572904176189082728 relative error = 0.87389157786614755529853012783497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 0.57677670257843488684854426117356 y[1] (numeric) = 0.57168508877624906300387423489486 absolute error = 0.0050916138021858238446700262786966 relative error = 0.88277036493051206550845348853876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 0.57587088893275118676543580473445 y[1] (numeric) = 0.57073574947196675142403165071681 absolute error = 0.0051351394607844353414041540176441 relative error = 0.89171714692876314852631183104444 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 0.57496549941614320983972978185704 y[1] (numeric) = 0.56978659940360975210442844849998 absolute error = 0.0051789000125334577353013333570518 relative error = 0.90073230790237752980947148499135 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 0.57406053493400039723027924922008 y[1] (numeric) = 0.56883763899575987087076119847918 absolute error = 0.0052228959382405263595180507408987 relative error = 0.90981623372542086693196260754062 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.441 y[1] (analytic) = 0.57315599639128715566619248482993 y[1] (numeric) = 0.5678888686739040905481018028596 absolute error = 0.0052671277173830651180906819703285 relative error = 0.91896931211503128639879067534262 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 0.57225188469254195248250167261022 y[1] (numeric) = 0.56694028886443414547395012799229 absolute error = 0.0053115958281078070085515446179337 relative error = 0.92819193264197072970191807269904 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.443 y[1] (analytic) = 0.57134820074187641108177094557285 y[1] (numeric) = 0.56599189999464609510653519951766 absolute error = 0.0053563007472303159752357460551934 relative error = 0.93748448674124460540025150871427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 0.57044494544297440682254832588658 y[1] (numeric) = 0.56504370249273989672879135214021 absolute error = 0.0054012429502345100937569737463699 relative error = 0.94684736772279024807065837816267 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=114.4MB, alloc=4.4MB, time=14.14 x[1] = 0.445 y[1] (analytic) = 0.56954211969909116333556567331613 y[1] (numeric) = 0.56409569678781897724843663002279 absolute error = 0.0054464229112721860871290432933398 relative error = 0.95628097078223468907852237872365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.446 y[1] (analytic) = 0.56863972441305234926859032575643 y[1] (numeric) = 0.56314788330988980409458163768624 absolute error = 0.0054918411031625451740086880701889 relative error = 0.96578569301172224825500118233857 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 0.56773776048725317546083168693519 y[1] (numeric) = 0.56220026248986145521129794476993 absolute error = 0.0055374979973917202495337421652663 relative error = 0.975361933410812459744336154496 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 0.56683622882365749254780558680187 y[1] (numeric) = 0.56125283475954518814857605104875 absolute error = 0.0055833940641123043992295357531158 relative error = 0.98501009289744884949865944487546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.449 y[1] (analytic) = 0.56593513032379688899755880966357 y[1] (numeric) = 0.56030560055165400825110382071297 absolute error = 0.0056295297721428807464549889505965 relative error = 0.99473057431899908615012470428506 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 0.5650344658887697895791557537681 y[1] (numeric) = 0.55935856029980223594529719709618 absolute error = 0.0056759055889675536338585566719206 relative error = 1.0045237824633670312812357776443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 0.56413423641924055426432875377253 y[1] (numeric) = 0.55841171443850507312501591078494 absolute error = 0.0057225219807354811393128429875957 relative error = 1.0143901240701772194443486834699 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 0.56323444281543857756319316437161 y[1] (numeric) = 0.55746506340317816863639779535791 absolute error = 0.0057693794122604089267953690136985 relative error = 1.0243300078420323026508659092812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 0.56233508597715738829492786929617 y[1] (numeric) = 0.5565186076301371828622462258843 absolute error = 0.0058164783470202054326816434118678 relative error = 1.0343438444558439984600226609569 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 0.56143616680375374979432144492579 y[1] (numeric) = 0.55557234755659735140640609575758 absolute error = 0.0058638192471563983879153491682121 relative error = 1.0444320465742380852467806226503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 0.56053768619414676055508377189468 y[1] (numeric) = 0.55462628362067304787856464745236 absolute error = 0.0059114025734737126765191244423197 relative error = 1.0545950288570339927185987721376 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.456 y[1] (analytic) = 0.55963964504681695531082245130418 y[1] (numeric) = 0.5536804162613773457799143723671 absolute error = 0.0059592287854396095309080789370814 relative error = 1.0648332079727995402821500047133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.4MB, time=14.62 x[1] = 0.457 y[1] (analytic) = 0.55874204425980540655458294449053 y[1] (numeric) = 0.55273474591862157949011609405313 absolute error = 0.0060072983411838270644668504374067 relative error = 1.0751470026104813804338083396025 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 0.55784488473071282649785091673299 y[1] (numeric) = 0.5517892730332149043560012478305 absolute error = 0.0060556116974979221418496689024902 relative error = 1.0855368334911117089623604037757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 0.55694816735669866946991482582499 y[1] (numeric) = 0.55084399804686385588245326805161 absolute error = 0.0061041693098348135874615577733842 relative error = 1.0960031233795918084093173444073 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 0.5560518930344802347584863560711 y[1] (numeric) = 0.54989892140217190802590889209449 absolute error = 0.0061529716323083267325774639766126 relative error = 1.1065462970965529959318445500902 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 0.55515606266033176989247585701442 y[1] (numeric) = 0.54895404354263903059092108754768 absolute error = 0.0062020191176927393015547694667397 relative error = 1.1171667815302955514561164556172 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.462 y[1] (analytic) = 0.55426067713008357436781950404435 y[1] (numeric) = 0.54800936491266124573022620598681 absolute error = 0.0062513122174223286375932980575416 relative error = 1.1278650056488062067952768702986 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.463 y[1] (analytic) = 0.55336573733912110381725445498295 y[1] (numeric) = 0.54706488595753018354875886323892 absolute error = 0.0063008513815909202684955917440394 relative error = 1.1386414005118547812365810773333 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 0.55247124418238407462493783279988 y[1] (numeric) = 0.54612060712343263681205894208238 absolute error = 0.0063506370589514378128788907175018 relative error = 1.149496399283170553977158597416 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.465 y[1] (analytic) = 0.55157719855436556898680491976248 y[1] (numeric) = 0.54517652885745011475951600893856 absolute error = 0.006400669696915454227288910823926 relative error = 1.1604304372426989687076140704402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 0.55068360134911114041756150258825 y[1] (numeric) = 0.54423265160755839602289733127342 absolute error = 0.0064509497415527443946641713148259 relative error = 1.1714439517989392706078322009426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.467 y[1] (analytic) = 0.54979045346021791970520486153262 y[1] (numeric) = 0.5432889758226270806506065771439 absolute error = 0.0065014776375908390545982843887136 relative error = 1.1825373825013636810303301498787 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 0.54889775578083372131396744881682 y[1] (numeric) = 0.54234550195241914123812117259301 absolute error = 0.0065522538284145800758462762238135 relative error = 1.1937111710529187202037712090377 % h = 0.001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=15.09 NO POLE x[1] = 0.469 y[1] (analytic) = 0.54800550920365615023657685337748 y[1] (numeric) = 0.54140223044759047316505718641885 absolute error = 0.0066032787560656770715196669586272 relative error = 1.2049657613226092933932862543079 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 0.54711371462093170929672519960359 y[1] (numeric) = 0.54045916175968944393931150521527 absolute error = 0.0066545528612422653574136943883198 relative error = 1.2163015993581661611055187084253 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 0.54622237292445490690264067751721 y[1] (numeric) = 0.53951629634115644164873195450434 absolute error = 0.0067060765832984652539087230128673 relative error = 1.2277191333987974191252941618881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 0.54533148500556736525265345075175 y[1] (numeric) = 0.53857363464532342252076691425292 absolute error = 0.0067578503602439427318865364988321 relative error = 1.2392188138880246194180023149271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 0.54444105175515692899364773668793 y[1] (numeric) = 0.53763117712641345759054686908607 absolute error = 0.0068098746287434714031008676018599 relative error = 1.2508010934866041682276567932153 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 0.54355107406365677433329140022077 y[1] (numeric) = 0.5366889242395402784778512250779 absolute error = 0.0068621498241164958554401751428686 relative error = 1.2624664270855346430456633659973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 0.54266155282104451860693394885391 y[1] (numeric) = 0.53574687644070782227341461611515 absolute error = 0.0069146763803366963335193327387622 relative error = 1.2742152718191506755200803643987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.476 y[1] (analytic) = 0.54177248891684133030006336214914 y[1] (numeric) = 0.53480503418680977553502781348943 absolute error = 0.0069674547300315547650355486597059 relative error = 1.2860480870783040528201034289959 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 0.54088388324011103952721173299992 y[1] (numeric) = 0.53386339793562911739388924257904 absolute error = 0.0070204853044819221333224904208761 relative error = 1.2979653345236326954661625074468 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.478 y[1] (analytic) = 0.53999573667945924896819924174937 y[1] (numeric) = 0.53292196814583766177166400023086 absolute error = 0.0070737685336215871965352415185109 relative error = 1.309967478098918175182900370006 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 0.53910805012303244526260552683451 y[1] (numeric) = 0.53198074527699559870870815574515 absolute error = 0.0071273048460368465538973710893617 relative error = 1.3220549840445324419309326732079 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.48 y[1] (analytic) = 0.53822082445851711086335705741136 y[1] (numeric) = 0.53103972978955103480391700720071 absolute error = 0.00718109466896607605944005021065 relative error = 1.334228320910974434924199474718 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.4MB, time=15.57 NO POLE x[1] = 0.481 y[1] (analytic) = 0.53733406057313883635031865429955 y[1] (numeric) = 0.53009892214483953276665685323385 absolute error = 0.007235138428299303583661801065698 relative error = 1.3464879595724972581434426851637 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.482 y[1] (analytic) = 0.5364477593536614332047768455809 y[1] (numeric) = 0.52915832280508365008124072830103 absolute error = 0.0072894365485777831235361172798787 relative error = 1.3588343732408266066134248117332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 0.53556192168638604704570228229476 y[1] (numeric) = 0.52821793223339247678440943691098 absolute error = 0.0073439894529935702612928453837763 relative error = 1.3712680374789711355224891279913 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 0.53467654845715027132867797789364 y[1] (numeric) = 0.52727775089376117235628010930684 absolute error = 0.0073987975633890989723978685867962 relative error = 1.3837894302151254701285038407139 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 0.53379164055132726150837967245725 y[1] (numeric) = 0.52633777925107050172522538761097 absolute error = 0.0074538613002567597831542848462741 relative error = 1.3963990317566665603156928592104 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 0.53290719885382484966549415911054 y[1] (numeric) = 0.52539801777108637038714723751479 absolute error = 0.0075091810827384792783469215957543 relative error = 1.4090973248042440896428996177706 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 0.53202322424908465959896094565383 y[1] (numeric) = 0.52445846692045935863961026620095 absolute error = 0.0075647573286253009593506794528799 relative error = 1.4218847944659656547560306163688 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 0.53113971762108122238442215908945 y[1] (numeric) = 0.52351912716672425493130031232583 absolute error = 0.0076205904543569674531218467636234 relative error = 1.43476192827167743712636091094 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.489 y[1] (analytic) = 0.53025667985332109239976513452147 y[1] (numeric) = 0.52257999897829958832727495856474 absolute error = 0.0076766808750215040724901759567274 relative error = 1.4477292161873410952226401864164 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.49 y[1] (analytic) = 0.52937411182884196381864166281204 y[1] (numeric) = 0.52164108282448716009047350143047 absolute error = 0.0077330290043548037281681613815748 relative error = 1.4607871506295076114291073478116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.491 y[1] (analytic) = 0.52849201443021178757284740340174 y[1] (numeric) = 0.52070237917547157437995479681612 absolute error = 0.0077896352547402131928926065856213 relative error = 1.4739362264798888342842024921963 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.4MB, time=16.04 x[1] = 0.492 y[1] (analytic) = 0.52761038853952788878444449984064 y[1] (numeric) = 0.51976388850231976806633228298529 absolute error = 0.0078465000372081207181122168553443 relative error = 1.4871769411000274629365631443529 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 0.52672923503841608466850996583417 y[1] (numeric) = 0.51882561127698053966487636553542 absolute error = 0.0079036237614355450036336002987497 relative error = 1.500509794346066227096419042078 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.494 y[1] (analytic) = 0.52584855480802980290739193898176 y[1] (numeric) = 0.51788754797228407738675523119258 absolute error = 0.0079610068357457255206367077891845 relative error = 1.5139352885836170222023757414832 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 0.52496834872904920049735542787856 y[1] (numeric) = 0.51694969906194148630888603915769 absolute error = 0.0080186496671077141884693887208739 relative error = 1.5274539287027307660264280676703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 0.52408861768168028306849870586105 y[1] (numeric) = 0.51601206502054431466286932011345 absolute error = 0.0080765526611359684056293857476019 relative error = 1.5410662221329687495045032281354 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.497 y[1] (analytic) = 0.52320936254565402467882103140682 y[1] (numeric) = 0.51507464632356407924348029391819 absolute error = 0.0081347162220899454353407374886247 relative error = 1.5547726788585762612065406649935 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 0.52233058420022548808332190104733 y[1] (numeric) = 0.51413744344735178993719169745571 absolute error = 0.0081931407528736981461302035916146 relative error = 1.5685738114337592715497191285264 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 0.52145228352417294547901156562125 y[1] (numeric) = 0.51320045686913747337120359407873 absolute error = 0.0082518266550354721078079715425201 relative error = 1.5824701349980649696115960296123 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 0.52057446139579699972671206478443 y[1] (numeric) = 0.51226368706702969568345651557637 absolute error = 0.0083107743287673040432555492080608 relative error = 1.596462167291866952217292323275 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 0.5196971186929197060505275579023 y[1] (numeric) = 0.5113271345200150844141051666128 absolute error = 0.008369984172904621636422391289501 relative error = 1.6105504286719558718571079621392 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.502 y[1] (analytic) = 0.51882025629288369421586225178126 y[1] (numeric) = 0.51039079970795784951893080012354 absolute error = 0.0084294565849258446969314516577279 relative error = 1.6247354421272363569387659229231 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.503 y[1] (analytic) = 0.51794387507255129118686374714781 y[1] (numeric) = 0.50945468311159930350517125021697 absolute error = 0.0084891919609519876816924969308439 relative error = 1.6390177332945310248925422444734 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=133.5MB, alloc=4.4MB, time=16.52 x[1] = 0.504 y[1] (analytic) = 0.51706797590830364426416914635909 y[1] (numeric) = 0.50851878521255738069024848671126 absolute error = 0.0085491906957462635739206596478384 relative error = 1.6533978304744924157285385177042 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.505 y[1] (analytic) = 0.51619255967603984470383078452566 y[1] (numeric) = 0.50758310649332615558387443253889 absolute error = 0.0086094531827136891199563519867734 relative error = 1.6678762646476236807939928299199 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.506 y[1] (analytic) = 0.51531762725117605181829796504763 y[1] (numeric) = 0.50664764743727536039401666187296 absolute error = 0.0086699798139006914242813031746743 relative error = 1.6824535694904088686955142779387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.507 y[1] (analytic) = 0.51444317950864461756033059850955 y[1] (numeric) = 0.50571240852864990165720647296924 absolute error = 0.0087307709799947159031241255403035 relative error = 1.6971302813915536576371819102022 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.508 y[1] (analytic) = 0.51356921732289321159072016094739 y[1] (numeric) = 0.5047773902525693759936727053758 absolute error = 0.0087918270703238355970474555715813 relative error = 1.7119069394683373907812966161633 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.509 y[1] (analytic) = 0.51269574156788394683069290369378 y[1] (numeric) = 0.50384259309502758498778554633583 absolute error = 0.0088531484728563618429073573579542 relative error = 1.7267840855830772786649476260405 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.51 y[1] (analytic) = 0.51182275311709250549986976232543 y[1] (numeric) = 0.50290801754289204919429544589956 absolute error = 0.0089147355742004563055743164258646 relative error = 1.7417622643597056402031958884008 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.511 y[1] (analytic) = 0.51095025284350726564065692667989 y[1] (numeric) = 0.5019736640839035212708531344659 absolute error = 0.0089765887596037443698037922139969 relative error = 1.7568420232004610613793351324757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.512 y[1] (analytic) = 0.51007824161962842812994054747852 y[1] (numeric) = 0.50103953320667549823729761019299 absolute error = 0.0090387084129529298926429372855301 relative error = 1.772023912302694358365126980206 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.513 y[1] (analytic) = 0.50920672031746714417895856778793 y[1] (numeric) = 0.50010562540069373286219983694935 absolute error = 0.0091010949167734113167587308385733 relative error = 1.7873084846757902395298868482292 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.514 y[1] (analytic) = 0.50833568980854464332222217937555 y[1] (numeric) = 0.49917194115631574417715076622089 absolute error = 0.0091637486522288991450714131546611 relative error = 1.8026962961582055685875991941056 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.515 y[1] (analytic) = 0.5074651509638913618963589149652 y[1] (numeric) = 0.4982384809647703271192831686452 absolute error = 0.0092266699991210347770757463199963 relative error = 1.8181879054346251389966494686957 % h = 0.001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.4MB, time=16.99 NO POLE x[1] = 0.516 y[1] (analytic) = 0.50659510465404607200974889747675 y[1] (numeric) = 0.49730524531815706130251763261034 absolute error = 0.009289859335889010707231264866416 relative error = 1.8337838740532358776680705366246 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.517 y[1] (analytic) = 0.50572555174905501100382527654134 y[1] (numeric) = 0.49637223470944581891802395863116 absolute error = 0.0093533170396091920858013179101809 relative error = 1.8494847664431204040562170749265 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.518 y[1] (analytic) = 0.50485649311847101140690939091887 y[1] (numeric) = 0.49543944963247627176439004900086 absolute error = 0.0094170434859947396425193419180073 relative error = 1.8652911499317708788013155830873 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.519 y[1] (analytic) = 0.50398792963135263138145070291028 y[1] (numeric) = 0.49450689058195739740799126250763 absolute error = 0.009481039049395233973459440402648 relative error = 1.8812035947627240842672125494419 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.52 y[1] (analytic) = 0.50311986215626328566554105745225 y[1] (numeric) = 0.49357455805346698447405407380612 absolute error = 0.0095453041027963011914869836461322 relative error = 1.8972226741133186875706909370431 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.521 y[1] (analytic) = 0.50225229156127037700957232430744 y[1] (numeric) = 0.49264245254345113706890874633857 absolute error = 0.0096098390178192399406635779688682 relative error = 1.9133489641125756450317870174952 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.522 y[1] (analytic) = 0.50138521871394442810890598662047 y[1] (numeric) = 0.49171057454922377833392659651192 absolute error = 0.0096746441647206497749793901085588 relative error = 1.9295830438592027153884669781473 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.523 y[1] (analytic) = 0.50051864448135821403342274309759 y[1] (numeric) = 0.49077892456896615313163829515196 absolute error = 0.0097397199123920609017844479456353 relative error = 1.9459254954397240576146768063572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.524 y[1] (analytic) = 0.49965256973008589515481969418814 y[1] (numeric) = 0.48984750310172632986453052007508 absolute error = 0.0098050666283595652902891741130554 relative error = 1.9623769039467358977590308535182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.525 y[1] (analytic) = 0.4987869953262021505725221848984 y[1] (numeric) = 0.48891631064741870142701914093921 absolute error = 0.009870684678783449145503043959191 relative error = 1.9789378574972892578831354551921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.526 y[1] (analytic) = 0.49792192213528131203907687825382 y[1] (numeric) = 0.4879853477068234852910979843593 absolute error = 0.009936574428457826747978893894519 relative error = 1.9956089472514007489246455279099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=141.1MB, alloc=4.4MB, time=17.47 x[1] = 0.527 y[1] (analytic) = 0.49705735102239649838589213394419 y[1] (numeric) = 0.4870546147815862227261630935969 absolute error = 0.010002736240810275659729040347295 relative error = 2.0123907674306924381415260446005 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.528 y[1] (analytic) = 0.49619328285211875045019126633951 y[1] (numeric) = 0.48612411237421727715351326295782 absolute error = 0.010069170477901473296678003381691 relative error = 2.029283915337161810711549077099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.529 y[1] (analytic) = 0.49532971848851616650404375485096 y[1] (numeric) = 0.48519384098809133163602849235557 absolute error = 0.010135877500424834868015262495388 relative error = 2.0462889913720828540657236873378 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.53 y[1] (analytic) = 0.49446665879515303818633897753392 y[1] (numeric) = 0.48426380112744688550352887232023 absolute error = 0.010202857667706152682810105213694 relative error = 2.0634065990550393026270641179844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.531 y[1] (analytic) = 0.49360410463508898693856653588713 y[1] (numeric) = 0.48333399329738575011431727405185 absolute error = 0.010270111337703236824249261835286 relative error = 2.0806373450430910898077961515945 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.532 y[1] (analytic) = 0.49274205687087810094526673499584 y[1] (numeric) = 0.48240441800387254375341008293385 absolute error = 0.010337638867005557191856652061991 relative error = 2.0979818391500750633897378894788 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.533 y[1] (analytic) = 0.49188051636456807258001427849642 y[1] (numeric) = 0.48147507575373418566796107723339 absolute error = 0.010405440610833886912053201263033 relative error = 2.1154406943660410297751364434215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.534 y[1] (analytic) = 0.491019483977699336357797732307 y[1] (numeric) = 0.48054596705465938924038441652278 absolute error = 0.010473516923039947117413315784218 relative error = 2.1330145268768242020496743539496 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.535 y[1] (analytic) = 0.49015896057130420739465680467269 y[1] (numeric) = 0.47961709241519815429968356665672 absolute error = 0.01054186815610605309497323801597 relative error = 2.1507039560837551363466686332519 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.536 y[1] (analytic) = 0.48929894700590602037543898281642 y[1] (numeric) = 0.47868845234476125857149384993404 absolute error = 0.010610494661144761803945132882384 relative error = 2.168509604623508250642672476163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.537 y[1] (analytic) = 0.48843944414151826903053655836697 y[1] (numeric) = 0.47776004735361974826734717035914 absolute error = 0.010679396787898520763189388007832 relative error = 2.1864320983880900298507679452577 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.538 y[1] (analytic) = 0.48758045283764374612246456475538 y[1] (numeric) = 0.47683187795290442781366832469582 absolute error = 0.010748574884739318308796240059564 relative error = 2.2044720665449680309098322812786 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.4MB, time=17.94 x[1] = 0.539 y[1] (analytic) = 0.48672197395327368394313963993034 y[1] (numeric) = 0.4759039446546053487210131702748 absolute error = 0.010818029298668335222126469655533 relative error = 2.2226301415573418114970079434055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.54 y[1] (analytic) = 0.48586400834688689532271931704176 y[1] (numeric) = 0.47497624797157129759405978027404 absolute error = 0.010887760375315597728659536767714 relative error = 2.2409069592045569160175562847921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.541 y[1] (analytic) = 0.485006556876448915150860734182 y[1] (numeric) = 0.47404878841750928328286457643814 absolute error = 0.010957768458939631867996157743868 relative error = 2.2593031586026630626522885265249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.542 y[1] (analytic) = 0.48414962039941114241125724185424 y[1] (numeric) = 0.47312156650698402317589628793787 absolute error = 0.011028053892427119235360953916377 relative error = 2.2778193822251176854689195443841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.543 y[1] (analytic) = 0.48329319977270998273031087355997 y[1] (numeric) = 0.47219458275541742863536144329317 absolute error = 0.011098617017292554094949430266799 relative error = 2.2964562759236359959310667517327 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.544 y[1] (analytic) = 0.48243729585276599144079813076171 y[1] (numeric) = 0.47126783767908808957533595999111 absolute error = 0.011169458173677901865462170770605 relative error = 2.3152144889491887385683177224681 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.545 y[1] (analytic) = 0.4815819094954830171613860184838 y[1] (numeric) = 0.47034133179513075818321825362436 absolute error = 0.011240577700352258978167764859436 relative error = 2.3340946739731488261039288384041 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.546 y[1] (analytic) = 0.48072704155624734589285475196364 y[1] (numeric) = 0.46941506562153583178502014505404 absolute error = 0.011311975934711514107834606909604 relative error = 2.3530974871085880499744190347403 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.547 y[1] (analytic) = 0.47987269288992684563188303805971 y[1] (numeric) = 0.46848903967714883485501270026288 absolute error = 0.011383653212778010776870337796823 relative error = 2.3722235879317250729187268744043 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.548 y[1] (analytic) = 0.47901886435087011150325131755937 y[1] (numeric) = 0.46756325448166990017024499320978 absolute error = 0.011455609869200211333006324349591 relative error = 2.3914736395035259211648584472447 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.549 y[1] (analytic) = 0.47816555679290561141131783611242 y[1] (numeric) = 0.46663771055565324911045463712366 absolute error = 0.011527846237252362300863198988756 relative error = 2.4108483083914582047002343985102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.55 y[1] (analytic) = 0.47731277106934083221162189224271 y[1] (numeric) = 0.46571240842050667110388978428287 absolute error = 0.011600362648834161107732107959836 relative error = 2.4303482646914003051794270490924 % h = 0.001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.4MB, time=18.41 NO POLE x[1] = 0.551 y[1] (analytic) = 0.47646050803296142640346809076379 y[1] (numeric) = 0.46478734859849100221956314841472 absolute error = 0.01167315943447042418390494234907 relative error = 2.4499741820497067822008574335642 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.552 y[1] (analytic) = 0.47560876853603035934434490894292 y[1] (numeric) = 0.46386253161271960290645945741761 absolute error = 0.011746236923310756437885451525308 relative error = 2.4697267376854312599735057377564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.553 y[1] (analytic) = 0.47475755343028705698703036092402 y[1] (numeric) = 0.46293795798715783488021859715493 absolute error = 0.011819595443129222106811763769097 relative error = 2.4896066124127080677970000663081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.554 y[1] (analytic) = 0.47390686356694655414023702323283 y[1] (numeric) = 0.46201362824662253715781755959384 absolute error = 0.011893235320324016982419463638985 relative error = 2.5096144906632939192948253134553 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.555 y[1] (analytic) = 0.47305669979669864325364816064811 y[1] (numeric) = 0.46108954291678150124077516056342 absolute error = 0.01196715687991714201287300008469 relative error = 2.5297510605092709269720885373937 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.556 y[1] (analytic) = 0.47220706296970702372819616733216 y[1] (numeric) = 0.46016570252415294544740434388367 absolute error = 0.012041360445554078280791823448485 relative error = 2.5500170136859122604175570202758 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.557 y[1] (analytic) = 0.47135795393560845175243401287092 y[1] (numeric) = 0.45924210759610498839463773956931 absolute error = 0.012115846339503463357796273301611 relative error = 2.5704130456147117683358326768898 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.558 y[1] (analytic) = 0.47050937354351189066584985678171 y[1] (numeric) = 0.45831875866085512162995299423888 absolute error = 0.012190614882656769035896862542837 relative error = 2.5909398554265788965808395708689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.559 y[1] (analytic) = 0.46966132264199766184997446810299 y[1] (numeric) = 0.45739565624746968141392524175995 absolute error = 0.01226566639452798043604922634304 relative error = 2.6115981459852002464675934937276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.56 y[1] (analytic) = 0.46881380207911659614813055888797 y[1] (numeric) = 0.45647280088586331965393493153386 absolute error = 0.01234100119325327649419562735411 relative error = 2.6323886239105691298668231174709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.561 y[1] (analytic) = 0.46796681270238918581467261178217 y[1] (numeric) = 0.45555019310679847398956008066813 absolute error = 0.012416619595590711825112531114043 relative error = 2.6533119996026844899377663818507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.562 y[1] (analytic) = 0.46712035535880473699456525237423 y[1] (numeric) = 0.45462783344188483703018286460008 absolute error = 0.012492521916919899964382387774153 relative error = 2.6743689872654205688297349438475 % h = 0.001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.4MB, time=18.88 NO POLE x[1] = 0.563 y[1] (analytic) = 0.46627443089482052273414768667114 y[1] (numeric) = 0.45370572242357882474534130852094 absolute error = 0.012568708471241697988806378150206 relative error = 2.695560304930568716284201517143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.564 y[1] (analytic) = 0.46542904015636093652393119286274 y[1] (numeric) = 0.45278386058518304400835768920429 absolute error = 0.012645179571177892515573503658453 relative error = 2.7168866744820527457976141907191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.565 y[1] (analytic) = 0.46458418398881664637427612450758 y[1] (numeric) = 0.45186224846084575929377610356626 absolute error = 0.012721935527970887080500020941316 relative error = 2.7383488216803192578622895924861 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.566 y[1] (analytic) = 0.46373986323704374942479434939252 y[1] (numeric) = 0.4509408865855603585291425064753 absolute error = 0.012798976651483390895651842917223 relative error = 2.7599474761869043627900113567716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.567 y[1] (analytic) = 0.4628960787453629270883225145933 y[1] (numeric) = 0.45001977549516481810166136598703 absolute error = 0.012876303250198108986661148606274 relative error = 2.7816833715891782487418073337821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.568 y[1] (analytic) = 0.46205283135755860073031099369233 y[1] (numeric) = 0.44909891572634116702026392930304 absolute error = 0.01295391563121743371004706438929 relative error = 2.8035572454252690538392614104231 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.569 y[1] (analytic) = 0.46121012191687808788447283669442 y[1] (numeric) = 0.44817830781661495023362393734057 absolute error = 0.013031814100263137650848899353858 relative error = 2.8255698392091675146191144854685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.57 y[1] (analytic) = 0.46036795126603075900553650692117 y[1] (numeric) = 0.44725795230435469110465746985261 absolute error = 0.013109998961676067900879037068561 relative error = 2.8477218984560138766153228054427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.571 y[1] (analytic) = 0.45952632024718719475994565206105 y[1] (numeric) = 0.44633784972877135304204444655405 absolute error = 0.013188470518415841717901205507003 relative error = 2.8700141727075685665126874610333 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.572 y[1] (analytic) = 0.45868522970197834385534861860512 y[1] (numeric) = 0.4454180006299178002893101526871 absolute error = 0.013267229072060543566038465918013 relative error = 2.8924474155578681391151817396051 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.573 y[1] (analytic) = 0.45784468047149468140971988010875 y[1] (numeric) = 0.44449840554868825787200599989997 absolute error = 0.013346274922806423537713880208782 relative error = 2.9150223846790680263117372740249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=156.4MB, alloc=4.4MB, time=19.36 x[1] = 0.574 y[1] (analytic) = 0.45700467339628536786095501008776 y[1] (numeric) = 0.44357906502681777070352957521262 absolute error = 0.013425608369467597157425434875145 relative error = 2.9377398418474736293040784883394 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.575 y[1] (analytic) = 0.45616520931635740841778028988382 y[1] (numeric) = 0.44265997960688166185012487220476 absolute error = 0.013505229709475746567655417679055 relative error = 2.9606005529697613095868098533048 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.576 y[1] (analytic) = 0.45532628907117481305281750051966 y[1] (numeric) = 0.44174114983229498995560443938067 absolute error = 0.013585139238879823097213061138985 relative error = 2.9836052881093908485409734882549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.577 y[1] (analytic) = 0.45448791349965775703864390540909 y[1] (numeric) = 0.44082257624731200582633602094328 absolute error = 0.013665337252345751212307884465811 relative error = 3.00675482151321096002033691822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.578 y[1] (analytic) = 0.45365008344018174202768688779204 y[1] (numeric) = 0.43990425939702560817703710494585 absolute error = 0.013745824043156133850649782846187 relative error = 3.0300499316382594549763934936118 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.579 y[1] (analytic) = 0.45281279973057675767679216292994 y[1] (numeric) = 0.4389861998273667985379216329812 absolute error = 0.01382659990320995913887052994874 relative error = 3.0534914011787596719851324841658 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.58 y[1] (analytic) = 0.45197606320812644381730394042354 y[1] (numeric) = 0.43806839808510413532374396421637 absolute error = 0.013907665123022308493559976207167 relative error = 3.077080017093314802507754019758 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.581 y[1] (analytic) = 0.45113987470956725317149486650297 y[1] (numeric) = 0.43715085471784318706528602468328 absolute error = 0.013989019991724066106208841819696 relative error = 3.100816570632301754840378460738 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.582 y[1] (analytic) = 0.45030423507108761461618302979055 y[1] (numeric) = 0.43623357027402598480383441029265 absolute error = 0.014070664797061629812348619497908 relative error = 3.1247018573654662159861640493678 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.583 y[1] (analytic) = 0.44946914512832709699437276684941 y[1] (numeric) = 0.43531654530293047364919504904848 absolute error = 0.014152599825396623345177717800933 relative error = 3.1487366772097205861188557281457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.584 y[1] (analytic) = 0.44863460571637557347575545580759 y[1] (numeric) = 0.4343997803546699635017938644027 absolute error = 0.014234825361705609973961591404894 relative error = 3.1729218344571464759014182962471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.585 y[1] (analytic) = 0.4478006176697723864669059374871 y[1] (numeric) = 0.4334832759801925789394127176035 absolute error = 0.014317341689579807527493219883595 relative error = 3.1972581378032034726788569650422 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=160.2MB, alloc=4.4MB, time=19.85 x[1] = 0.586 y[1] (analytic) = 0.44696718182250551307200965377196 y[1] (numeric) = 0.43256703273128070826911074225571 absolute error = 0.014400149091224804802898911516241 relative error = 3.2217464003751458974824183790206 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.587 y[1] (analytic) = 0.44613429900801073110495504241853 y[1] (numeric) = 0.43165105116055045174488201912578 absolute error = 0.014483247847460279360073023292747 relative error = 3.2463874397606492908649382547769 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.588 y[1] (analytic) = 0.44530197005917078565362517614627 y[1] (numeric) = 0.43073533182145106895160137348788 absolute error = 0.014566638237719716702023802658395 relative error = 3.2711820780366483818360236770433 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.589 y[1] (analytic) = 0.44447019580831455619722208164774 y[1] (numeric) = 0.42981987526826442535581091101913 absolute error = 0.014650320540050130841411170628605 relative error = 3.2961311417983883105829175540255 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.59 y[1] (analytic) = 0.44363897708721622427745662112423 y[1] (numeric) = 0.42890468205610443802390074141149 absolute error = 0.01473429503111178625355587971274 relative error = 3.3212354621886908922502019177903 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.591 y[1] (analytic) = 0.44280831472709444172443626508772 y[1] (numeric) = 0.4279897527409165205082381714731 absolute error = 0.014818561986177921216198093614628 relative error = 3.3464958749274377258108914817894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.592 y[1] (analytic) = 0.44197820955861149943808253047211 y[1] (numeric) = 0.42707508787947702690180048154395 absolute error = 0.014903121679134472536282048928154 relative error = 3.3719132203412719689949089561314 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.593 y[1] (analytic) = 0.44114866241187249672590930256691 y[1] (numeric) = 0.42616068802939269506186723054658 absolute error = 0.014987974382479801664042072020329 relative error = 3.3974883433935206173504032101209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.594 y[1] (analytic) = 0.44031967411642451119799270292604 y[1] (numeric) = 0.42524655374910008900332886593304 absolute error = 0.015073120367324422194663836992998 relative error = 3.4232220937143391428008792445201 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.595 y[1] (analytic) = 0.43949124550125576921996260821254 y[1] (numeric) = 0.42433268559786504046216924517333 absolute error = 0.01515855990339072875779336303921 relative error = 3.44911532563108036452868885351 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.596 y[1] (analytic) = 0.43866337739479481692484536691856 y[1] (numeric) = 0.4234190841357820896296805052559 absolute error = 0.015244293259012727295164861662668 relative error = 3.4751688981988894426651418921319 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.597 y[1] (analytic) = 0.43783607062490969178458670204891 y[1] (numeric) = 0.42250574992377392505796954593898 absolute error = 0.015330320701135766726617156109935 relative error = 3.5013836752315269031014249469224 % h = 0.001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.4MB, time=20.34 NO POLE x[1] = 0.598 y[1] (analytic) = 0.43700932601890709474208322817614 y[1] (numeric) = 0.42159268352359082273731622119952 absolute error = 0.015416642495316272004767006976614 relative error = 3.5277605253324216197547676636495 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.599 y[1] (analytic) = 0.43618314440353156290455045076672 y[1] (numeric) = 0.4206798854978100843459441614748 absolute error = 0.015503258905721478558606289291926 relative error = 3.5543003219259556988330140958893 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6 y[1] (analytic) = 0.43535752660496464279905455434134 y[1] (numeric) = 0.41976735640983547467276597687895 absolute error = 0.015590170195129168126288577462389 relative error = 3.5810039432889832280401009885017 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.601 y[1] (analytic) = 0.43453247344882406419103472386862 y[1] (numeric) = 0.41885509682389665821366541860263 absolute error = 0.015677376624927405977369305265992 relative error = 3.6078722725825848722571077565053 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.602 y[1] (analytic) = 0.43370798576016291446664218080111 y[1] (numeric) = 0.41794310730504863494187990216631 absolute error = 0.015764878455114279524762278634805 relative error = 3.6349061978840603160207423534393 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.603 y[1] (analytic) = 0.43288406436346881357972155134577 y[1] (numeric) = 0.41703138841917117525304762209803 absolute error = 0.015852675944297638326673929247741 relative error = 3.6621066122191605721056093424247 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.604 y[1] (analytic) = 0.43206071008266308956425961991864 y[1] (numeric) = 0.41611994073296825408548431294111 absolute error = 0.015940769349694835478775306977528 relative error = 3.6894744135945621947006455709009 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.605 y[1] (analytic) = 0.4312379237410999546131259552665 y[1] (numeric) = 0.41520876481396748421625553626813 absolute error = 0.016029158927132470396870418998376 relative error = 3.7170105050305854550560077571609 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.606 y[1] (analytic) = 0.43041570616156568172392933044603 y[1] (numeric) = 0.41429786123051954873361119758149 absolute error = 0.016117844931046132990318132864539 relative error = 3.7447157945941585570667868301912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.607 y[1] (analytic) = 0.42959405816627778191281329073545 y[1] (numeric) = 0.41338723055179763268634982061887 absolute error = 0.016206827614480149226463470116572 relative error = 3.7725911954320299900565671811115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.608 y[1] (analytic) = 0.42877298057688418199701365561464 y[1] (numeric) = 0.41247687334779685391068092965188 absolute error = 0.016296107229087328086332725962764 relative error = 3.8006376258042311360294359921275 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=167.8MB, alloc=4.4MB, time=20.80 x[1] = 0.609 y[1] (analytic) = 0.42795247421446240294700017218763 y[1] (numeric) = 0.41156679018933369303515471286807 absolute error = 0.016385684025128709911845459319564 relative error = 3.8288560091177912688759995708832 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.61 y[1] (analytic) = 0.42713253989951873880902396783728 y[1] (numeric) = 0.41065698164804542266422896185926 absolute error = 0.016475558251473316144795005978017 relative error = 3.8572472739607071034497317658344 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.611 y[1] (analytic) = 0.42631317845198743619889187949639 y[1] (numeric) = 0.40974744829638953574104410360153 absolute error = 0.016565730155597900457847775894865 relative error = 3.8858123541361690730770466889003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.612 y[1] (analytic) = 0.42549439069122987436778816569248 y[1] (numeric) = 0.40883819070764317308997796210424 absolute error = 0.016656199983586701277810203588246 relative error = 3.9145521886970465349303681520317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.613 y[1] (analytic) = 0.42467617743603374584096353547619 y[1] (numeric) = 0.40792920945590255013955270712573 absolute error = 0.016746967980131195701410828350452 relative error = 3.943467721980634123780707301284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.614 y[1] (analytic) = 0.42385853950461223763011085547598 y[1] (numeric) = 0.40702050511608238282626726700085 absolute error = 0.016838034388529854803843588475133 relative error = 3.9725599036436614959574360488535 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.615 y[1] (analytic) = 0.4230414777146032130202463226353 y[1] (numeric) = 0.40611207826391531267992930170003 absolute error = 0.016929399450687900340317020935271 relative error = 4.0018296886975687268806679232564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.616 y[1] (analytic) = 0.42222499288306839393191431568267 y[1] (numeric) = 0.40520392947595133109106165074022 absolute error = 0.017021063407117062840852664942449 relative error = 4.0312780375440496472985739124801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.617 y[1] (analytic) = 0.42140908582649254385953356306188 y[1] (numeric) = 0.40429605932955720276095898849302 absolute error = 0.017113026496935341098574574568862 relative error = 4.0609059160108654253607464219741 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.618 y[1] (analytic) = 0.42059375736078265138670168890796 y[1] (numeric) = 0.40338846840291588833497123678548 absolute error = 0.017205288957866763051730452122489 relative error = 4.0907142953879307238920913545854 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.619 y[1] (analytic) = 0.41977900830126711427927462169634 y[1] (numeric) = 0.40248115727502596621959110146195 absolute error = 0.017297851026241148059683520234398 relative error = 4.1207041524636747847024228470139 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.62 y[1] (analytic) = 0.41896483946269492415703677241779 y[1] (numeric) = 0.40157412652570105358392391577131 absolute error = 0.017390712936993870573112856646477 relative error = 4.1508764695616798144777387061129 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=171.6MB, alloc=4.4MB, time=21.27 x[1] = 0.621 y[1] (analytic) = 0.41815125165923485174477731054103 y[1] (numeric) = 0.40066737673556922654611878906145 absolute error = 0.017483874923665625198658521479577 relative error = 4.1812322345775990697528839363804 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.622 y[1] (analytic) = 0.41733824570447463270358728661891 y[1] (numeric) = 0.39976090848607243954534087430156 absolute error = 0.017577337218402193158246412317352 relative error = 4.2117724410163570616648178052967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.623 y[1] (analytic) = 0.41652582241142015404319177017304 y[1] (numeric) = 0.39885472235946594389986538241156 absolute error = 0.017671100051954210143326387761485 relative error = 4.2424980880296343246338760322192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.624 y[1] (analytic) = 0.41571398259249464111613059045704 y[1] (numeric) = 0.39794881893881770555187478525621 absolute error = 0.017765163653676935564255805200831 relative error = 4.2734101804536392168201903000907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.625 y[1] (analytic) = 0.41490272705953784519460068584992 y[1] (numeric) = 0.39704319880800782199954146245822 absolute error = 0.017859528251530023195059223391704 relative error = 4.3045097288471692441567562956551 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.626 y[1] (analytic) = 0.41409205662380523163077248496947 y[1] (numeric) = 0.39613786255172793841697885989896 absolute error = 0.017954194072077293213793625070503 relative error = 4.3357977495299644239725308503293 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.627 y[1] (analytic) = 0.4132819720959671686013921591217 y[1] (numeric) = 0.39523281075548066296264503990726 absolute error = 0.018049161340486505638747119214444 relative error = 4.3672752646213552286914290250132 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.628 y[1] (analytic) = 0.41247247428610811643748100141646 y[1] (numeric) = 0.39432804400557898127678331468362 absolute error = 0.018144430280529135160697686732832 relative error = 4.3989433020792076748292628169347 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.629 y[1] (analytic) = 0.4116635640037258175399426027822 y[1] (numeric) = 0.39342356288914567016848546547085 absolute error = 0.018240001114580147371457137311345 relative error = 4.4308028957391681475136338831879 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.63 y[1] (analytic) = 0.41085524205773048688188790920538 y[1] (numeric) = 0.39251936799411271049296386035864 absolute error = 0.01833587406361777638892404884674 relative error = 4.4628550853542105760247228041066 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.631 y[1] (analytic) = 0.41004750925644400309848765780185 y[1] (numeric) = 0.39161545990922069921961959340134 absolute error = 0.018432049347223303878868064400508 relative error = 4.4951009166344886014010072534971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.632 y[1] (analytic) = 0.40924036640759910016516110180038 y[1] (numeric) = 0.39071183922401826069149457693163 absolute error = 0.018528527183580839473666524868755 relative error = 4.5275414412874954029764326485777 % h = 0.001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.4MB, time=21.75 NO POLE x[1] = 0.633 y[1] (analytic) = 0.40843381431833855966490934618239 y[1] (numeric) = 0.389808506528861457076696327569 absolute error = 0.018625307789477102588213018613395 relative error = 4.5601777170585338768177349880629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.634 y[1] (analytic) = 0.40762785379521440364560102657702 y[1] (numeric) = 0.38890546241491319801238499444911 absolute error = 0.018722391380301205633216032127908 relative error = 4.5930108077714998854158027283249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.635 y[1] (analytic) = 0.40682248564418708806801747405878 y[1] (numeric) = 0.38800270747414264944191298563783 absolute error = 0.018819778170044438626104488420956 relative error = 4.6260417833699813246565318752121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.636 y[1] (analytic) = 0.40601771067062469684546391773531 y[1] (numeric) = 0.38710024229932464164570835554094 absolute error = 0.01891746837130005519975556219437 relative error = 4.6592717199586757810579888720933 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.637 y[1] (analytic) = 0.40521352967930213647575268544688 y[1] (numeric) = 0.38619806748403907646649392237703 absolute error = 0.019015462195263060009258763069851 relative error = 4.6927016998451295795153065551301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.638 y[1] (analytic) = 0.40440994347440033126636377052741 y[1] (numeric) = 0.38529618362267033372943489044482 absolute error = 0.019113759851729997536928880082597 relative error = 4.7263328115818010493461015829015 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.639 y[1] (analytic) = 0.40360695285950541915358753939926 y[1] (numeric) = 0.38439459131040667685780855698795 absolute error = 0.019212361549098742295778982411304 relative error = 4.7601661500084508642808650664034 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.64 y[1] (analytic) = 0.40280455863760794811645376079207 y[1] (numeric) = 0.38349329114323965768479048793801 absolute error = 0.01931126749436829043166327285406 relative error = 4.7942028162948623401983355852993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.641 y[1] (analytic) = 0.40200276161110207318625054258986 y[1] (numeric) = 0.38259228371796352046195235069994 absolute error = 0.019410477893138552724298191889913 relative error = 4.8284439179838946028689562084261 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.642 y[1] (analytic) = 0.40120156258178475405243616672017 y[1] (numeric) = 0.38169156963217460506506739543241 absolute error = 0.01950999294961014898736877128776 relative error = 4.8628905690348715667438329073018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.643 y[1] (analytic) = 0.40040096235085495326574621610695 y[1] (numeric) = 0.38079114948427074939782037896789 absolute error = 0.019609812866584203867925837139061 relative error = 4.8975438898673096949158874341317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.644 y[1] (analytic) = 0.3996009617189128350392977905129 y[1] (numeric) = 0.37989102387345069099401952761272 absolute error = 0.019709937845462144045278262900176 relative error = 4.9324050074049875397879187931764 % h = 0.001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.4MB, time=22.23 NO POLE x[1] = 0.645 y[1] (analytic) = 0.39880156148595896464849201010053 y[1] (numeric) = 0.37899119339971346781890893656538 absolute error = 0.019810368086245496829583073535151 relative error = 4.9674750551203600937128889108038 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.646 y[1] (analytic) = 0.3980027624513935084305154067426 y[1] (numeric) = 0.37809165866385781827018060459052 absolute error = 0.01991110378753569016033480215208 relative error = 5.0027551730793210089288153345971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.647 y[1] (analytic) = 0.39720456541401543438424020351384 y[1] (numeric) = 0.37719242026748158037928610288682 absolute error = 0.020012145146533854004954100627018 relative error = 5.0382465079863157764981230939588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.648 y[1] (analytic) = 0.39640697117202171337132288239725 y[1] (numeric) = 0.37629347881298109021364867678697 absolute error = 0.020113492359040623157674205610279 relative error = 5.0739502132298089846831672859337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.649 y[1] (analytic) = 0.39560998052300652091929983903959 y[1] (numeric) = 0.37539483490355057948037737802737 absolute error = 0.020215145619455941438922461012216 relative error = 5.1098674489281088082499280223523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.65 y[1] (analytic) = 0.39481359426396043962747832139406 y[1] (numeric) = 0.3744964891431815723320856238234 absolute error = 0.020317105120778867295392697570662 relative error = 5.1459993819755519115946938066108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.651 y[1] (analytic) = 0.39401781319126966217642024629276 y[1] (numeric) = 0.37359844213666228137541737688133 absolute error = 0.020419371054607380801002869411431 relative error = 5.1823471860890519803380358847355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.652 y[1] (analytic) = 0.39322263810071519494181588439859 y[1] (numeric) = 0.37270069448957700288288493777042 absolute error = 0.02052194361113819205893094662817 relative error = 5.2189120418550151281307370559277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.653 y[1] (analytic) = 0.39242806978747206221354379959662 y[1] (numeric) = 0.37180324680830551120862313776691 absolute error = 0.020624822979166551004920661829704 relative error = 5.2556951367766254578718317706005 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.654 y[1] (analytic) = 0.39163410904610851102071282369871 y[1] (numeric) = 0.37090609970002245240866551636543 absolute error = 0.020728009346086058612047307333273 relative error = 5.2926976653215040893538543392154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.655 y[1] (analytic) = 0.39084075667058521656348124135303 y[1] (numeric) = 0.3700092537726967370663488631309 absolute error = 0.020831502897888479497132378222135 relative error = 5.3299208289697449985291500917285 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=183.1MB, alloc=4.4MB, time=22.72 x[1] = 0.656 y[1] (analytic) = 0.39004801345425448825244775327319 y[1] (numeric) = 0.36911270963509093232345329843592 absolute error = 0.02093530381916355592899445483727 relative error = 5.3673658362623310471381096712907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.657 y[1] (analytic) = 0.38925588018985947635640817832977 y[1] (numeric) = 0.36821646789676065311768586189296 absolute error = 0.021039412293098823238722316436811 relative error = 5.4050339028499336153599273919989 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.658 y[1] (analytic) = 0.38846435766953337925927124668149 y[1] (numeric) = 0.36732052916805395262711637094679 absolute error = 0.0211438285014794266321548757347 relative error = 5.442926251542099284443508427133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.659 y[1] (analytic) = 0.38767344668479865132692622696415 y[1] (numeric) = 0.36642489406011071192217510514079 absolute error = 0.02124855262468793940475112182337 relative error = 5.4810441123568270509550646801992 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.66 y[1] (analytic) = 0.3868831480265662113848545206037 y[1] (numeric) = 0.36552956318486202882582266400834 absolute error = 0.021353584841704182559031856595363 relative error = 5.5193887225705395893444150262433 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.661 y[1] (analytic) = 0.38609346248513465180727674557586 y[1] (numeric) = 0.36463453715502960598250313836874 absolute error = 0.021458925330105045824773607207115 relative error = 5.55796132676845211498877392072 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.662 y[1] (analytic) = 0.38530439085018944821862622039934 y[1] (numeric) = 0.36373981658412513813649252602326 absolute error = 0.02156457426606431008213369437608 relative error = 5.5967631768953424357256680064626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.663 y[1] (analytic) = 0.38451593391080216980813914682333 y[1] (numeric) = 0.362845402086449698620255113452 absolute error = 0.021670531824352471187884033371326 relative error = 5.6357955323067258161404221898771 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.664 y[1] (analytic) = 0.38372809245542969025835117655314 y[1] (numeric) = 0.36195129427709312505342133510402 absolute error = 0.021776798178336565204929841449121 relative error = 5.6750596598204383155333285504693 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.665 y[1] (analytic) = 0.38294086727191339928828943345192 y[1] (numeric) = 0.36105749377193340425300141125167 absolute error = 0.021883373499979995035288022200242 relative error = 5.7145568337686322975621431399145 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.666 y[1] (analytic) = 0.38215425914747841481214844796039 y[1] (numeric) = 0.36016400118763605635544985414422 absolute error = 0.021990257959842358456698593816168 relative error = 5.7542883360501878470420038215334 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.667 y[1] (analytic) = 0.38136826886873279571423784499337 y[1] (numeric) = 0.35927081714165351815119672034497 absolute error = 0.022097451727079277563041124648402 relative error = 5.7942554561835438672923512284369 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=186.9MB, alloc=4.4MB, time=23.19 x[1] = 0.668 y[1] (analytic) = 0.38058289722166675524098901029949 y[1] (numeric) = 0.35837794225222452563226227466922 absolute error = 0.022204954969442229608726735630275 relative error = 5.8344594913599526697541579208542 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.669 y[1] (analytic) = 0.37979814499165187501080734321209 y[1] (numeric) = 0.35748537713837349575357251805696 absolute error = 0.022312767853278379257234825155128 relative error = 5.8749017464971619063659909548548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.67 y[1] (analytic) = 0.37901401296344031964255608587341 y[1] (numeric) = 0.35659312241990990740859381801323 absolute error = 0.022420890543530412233962267860177 relative error = 5.9155835342935277343894842191461 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.671 y[1] (analytic) = 0.37823050192116405200345710038291 y[1] (numeric) = 0.35570117871742768161990566592992 absolute error = 0.022529323203736370383551434452988 relative error = 5.9565061752825631430190847981086 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.672 y[1] (analytic) = 0.37744761264833404907719334590347 y[1] (numeric) = 0.35480954665230456094533137066466 absolute error = 0.022638065996029488131861975238808 relative error = 5.9976709978879254112029409312316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.673 y[1] (analytic) = 0.37666534592783951845299718755764 y[1] (numeric) = 0.35391822684670148810024728219431 absolute error = 0.02274711908113803035274990536333 relative error = 6.0390793384788467066470704892516 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.674 y[1] (analytic) = 0.37588370254194711543650804796045 y[1] (numeric) = 0.35302721992356198379669192298214 absolute error = 0.022856482618385131639816124978307 relative error = 6.0807325414260118769791159589001 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.675 y[1] (analytic) = 0.3751026832723001607831822904657 y[1] (numeric) = 0.35213652650661152379989718789761 absolute error = 0.02296615676568863698328510256809 relative error = 6.1226319591578875255167585588746 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.676 y[1] (analytic) = 0.37432228889991785905503760065086 y[1] (numeric) = 0.35124614722035691520286455610572 absolute error = 0.023076141679560943852173044545141 relative error = 6.164778952217506506025011407337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.677 y[1] (analytic) = 0.37354252020519451760151350923091 y[1] (numeric) = 0.35035608269008567191961004029774 absolute error = 0.023186437515108845681903468933172 relative error = 6.2071748893197120132619991375872 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.678 y[1] (analytic) = 0.37276337796789876616522907547561 y[1] (numeric) = 0.34946633354186538939770237996629 absolute error = 0.023297044426033376767526695509328 relative error = 6.2498211474088654890103980804565 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.679 y[1] (analytic) = 0.3719848629671727771134181253074 y[1] (numeric) = 0.34857690040254311855071976613445 absolute error = 0.023407962564629658562698359172952 relative error = 6.2927191117170226066774768912134 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.4MB, time=23.67 NO POLE x[1] = 0.68 y[1] (analytic) = 0.37120697598153148629582181257975 y[1] (numeric) = 0.3476877838997447389112511650301 absolute error = 0.023519192081786747384570647549659 relative error = 6.3358701758225816414267440002122 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.681 y[1] (analytic) = 0.37042971778886181452981764557857 y[1] (numeric) = 0.34679898466187433100506908765182 absolute error = 0.02363073312698748352474855792675 relative error = 6.3792757417094085771847603350918 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.682 y[1] (analytic) = 0.36965308916642188971356349355254 y[1] (numeric) = 0.34591050331811354794710143100138 absolute error = 0.023742585848308341766462062551157 relative error = 6.4229372198264433467539825691797 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.683 y[1] (analytic) = 0.36887709089084026956793446006375 y[1] (numeric) = 0.34502234049842098625983079495846 absolute error = 0.023854750392419283308103665105294 relative error = 6.4668560291477916466629184589267 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.684 y[1] (analytic) = 0.36810172373811516500802988115697 y[1] (numeric) = 0.34413449683353155591475045634606 absolute error = 0.02396722690458360909327942481091 relative error = 6.5110335972333068143048432630127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.685 y[1] (analytic) = 0.36732698848361366414502707677567 y[1] (numeric) = 0.34324697295495584959750695867796 absolute error = 0.024080015528657814547520118097708 relative error = 6.5554713602896663013623745504977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.686 y[1] (analytic) = 0.36655288590207095691915785350657 y[1] (numeric) = 0.34235976949497951119736005239312 absolute error = 0.024193116407091445721797801113449 relative error = 6.6001707632319473244939511172799 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.687 y[1] (analytic) = 0.36577941676758956036458312561155 y[1] (numeric) = 0.34147288708666260352159149606454 absolute error = 0.024306529680926956842991629547011 relative error = 6.6451332597457063217764202273652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.688 y[1] (analytic) = 0.36500658185363854450694038940761 y[1] (numeric) = 0.34058632636383897523549500412093 absolute error = 0.02442025548979956927144538528669 relative error = 6.6903603123495668914623080902499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.689 y[1] (analytic) = 0.36423438193305275889433815338313 y[1] (numeric) = 0.33970008796111562702858040103866 absolute error = 0.024534293971937131865757752344475 relative error = 6.7358533924583209382278269840601 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.69 y[1] (analytic) = 0.36346281777803205976257079299128 y[1] (numeric) = 0.33881417251387207700762581574689 absolute error = 0.024648645264159982754944977244391 relative error = 6.7816139804465478012652492272654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.691 y[1] (analytic) = 0.36269189016014053783532666484154 y[1] (numeric) = 0.33792858065825972531721252314083 absolute error = 0.024763309501880812518114141700711 relative error = 6.8276435657127561883180400803837 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.4MB, time=24.14 NO POLE x[1] = 0.692 y[1] (analytic) = 0.36192159985030574676016168001679 y[1] (numeric) = 0.33704331303120121798837781211541 absolute error = 0.024878286819104528771783867901381 relative error = 6.8739436467440537900762731495708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.693 y[1] (analytic) = 0.36115194761881793218100990047802 y[1] (numeric) = 0.33615837027038981001602203141336 absolute error = 0.024993577348428122164987869064662 relative error = 6.9205157311813495002506366883691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.694 y[1] (analytic) = 0.36038293423532926144800208598196 y[1] (numeric) = 0.3352737530142887276657067358277 absolute error = 0.025109181221040533782295350154268 relative error = 6.9673613358850932181331617529393 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.695 y[1] (analytic) = 0.35961456046885305396536248162878 y[1] (numeric) = 0.33438946190213053001048162590722 absolute error = 0.025225098566722523954880855721555 relative error = 7.0144819870015582625391500463563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.696 y[1] (analytic) = 0.35884682708776301217815349807899 y[1] (numeric) = 0.33350549757391646969837874428501 absolute error = 0.025341329513846542479774753793972 relative error = 7.0618792200296714787152407926825 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.697 y[1] (analytic) = 0.35807973485979245319863729763077 y[1] (numeric) = 0.33262186067041585295121316108228 absolute error = 0.025457874189376600247424136548494 relative error = 7.1095545798883961731008276883822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.698 y[1] (analytic) = 0.35731328455203354107302265973213 y[1] (numeric) = 0.33173855183316539879533014953372 absolute error = 0.025574732718868142277692510198412 relative error = 7.1575096209846730647519213184256 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.699 y[1] (analytic) = 0.35654747693093651968936485911696 y[1] (numeric) = 0.33085557170446859752493962103373 absolute error = 0.025691905226467922164425238083231 relative error = 7.2057459072819244967859602895027 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7 y[1] (analytic) = 0.35578231276230894632738564860128 y[1] (numeric) = 0.32997292092739506839867935621552 absolute error = 0.025809391834913877928706292385763 relative error = 7.2542650123691272063910267094235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.701 y[1] (analytic) = 0.35501779281131492585097979665585 y[1] (numeric) = 0.32909060014577991657004933544654 absolute error = 0.025927192665535009280930461209314 relative error = 7.3030685195304590077715512694977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.702 y[1] (analytic) = 0.35425391784247434554417398718465 y[1] (numeric) = 0.32820861000422308925236023825211 absolute error = 0.026045307838251256291813748932535 relative error = 7.3521580218155247988831462443369 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=198.3MB, alloc=4.4MB, time=24.61 x[1] = 0.703 y[1] (analytic) = 0.35349068861966211059130324548666 y[1] (numeric) = 0.32732695114808873111883994666523 absolute error = 0.026163737471573379472463298821423 relative error = 7.4015351221101673599500425429461 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.704 y[1] (analytic) = 0.35272810590610738020216941016085 y[1] (numeric) = 0.32644562422350453893854265234229 absolute error = 0.026282481682602841263626757818561 relative error = 7.4512014332078684695682077524549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.705 y[1] (analytic) = 0.35196617046439280438294552573213 y[1] (numeric) = 0.32556462987736111544870593148179 absolute error = 0.026401540587031688934239594250345 relative error = 7.501158577881745922684182801934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.706 y[1] (analytic) = 0.35120488305645376135358938503038 y[1] (numeric) = 0.32468396875731132246420191513524 absolute error = 0.026520914299142438889387469895136 relative error = 7.55140818895715209391271279197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.707 y[1] (analytic) = 0.35044424444357759561252880384534 y[1] (numeric) = 0.32380364151176963322472944540503 absolute error = 0.026640602931807962387799358440313 relative error = 7.6019519093848797495242023305363 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.708 y[1] (analytic) = 0.3496842553864028566493805631088 y[1] (numeric) = 0.32292364878991148398039487028321 absolute error = 0.026760606596491372668985692825594 relative error = 7.6527913923149808720048611806547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.709 y[1] (analytic) = 0.34892491664491853830646430582142 y[1] (numeric) = 0.32204399124167262481632989149636 absolute error = 0.026880925403245913490134414325057 relative error = 7.7039283011712043223772119910822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.71 y[1] (analytic) = 0.34816622897846331878987202714716 y[1] (numeric) = 0.32116466951774846971699564068462 absolute error = 0.027001559460714849072876386462547 relative error = 7.7553643097260582274756261349668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.711 y[1] (analytic) = 0.3474081931457248013308531465424 y[1] (numeric) = 0.32028568426959344587082291955654 absolute error = 0.027122508876131355460030226985856 relative error = 7.807101102176503042110083917533 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.712 y[1] (analytic) = 0.34665080990473875549827450047127 y[1] (numeric) = 0.31940703614942034221583929932545 absolute error = 0.027243773755318413282435201145816 relative error = 7.8591403732202812995309012167756 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.713 y[1] (analytic) = 0.34589408001288835916291394318423 y[1] (numeric) = 0.31852872581019965722693453374578 absolute error = 0.027365354202688701935979409438456 relative error = 7.9114838281328901278373394806035 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.714 y[1] (analytic) = 0.34513800422690344111434559120292 y[1] (numeric) = 0.3176507539056589459454164984297 absolute error = 0.027487250321244495168929092773227 relative error = 7.964133182845202674963569363459 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=202.1MB, alloc=4.4MB, time=25.09 x[1] = 0.715 y[1] (analytic) = 0.344382583302859724331174094563 y[1] (numeric) = 0.31677312109028216625151062683371 absolute error = 0.027609462212577558079663467729291 relative error = 8.0170901640217446506362776248154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.716 y[1] (analytic) = 0.34362781799617806990537466451765 y[1] (numeric) = 0.31589582801930902438045657036121 absolute error = 0.027731989976869045524918094156444 relative error = 8.0703565091396322602393198635283 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.717 y[1] (analytic) = 0.34287370906162372162149493329869 y[1] (numeric) = 0.31501887534873431968285656642984 absolute error = 0.027854833712889401938638366868851 relative error = 8.1239339665681778728523981624233 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.718 y[1] (analytic) = 0.3421202572533055511914740666705 y[1] (numeric) = 0.31414226373530728862993075410075 absolute error = 0.027977993517998262561543312569746 relative error = 8.177824295649169833863097194828 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.719 y[1] (analytic) = 0.34136746332467530414583389439473 y[1] (numeric) = 0.31326599383653094806433543195966 absolute error = 0.028101469488144356081498462435069 relative error = 8.2320292667778329014952059417776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.72 y[1] (analytic) = 0.34061532802852684638199616735183 y[1] (numeric) = 0.31239006631066143769720100737677 absolute error = 0.028225261717865408684795159975063 relative error = 8.2865506614844758563616950030718 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.721 y[1] (analytic) = 0.3398638521169954113704793929394 y[1] (numeric) = 0.31151448181670736185204714005289 absolute error = 0.028349370300288049518432252886514 relative error = 8.3413902725168329037487729475458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.722 y[1] (analytic) = 0.33911303634155684801972804248768 y[1] (numeric) = 0.31063924101442913045623333588161 absolute error = 0.028473795327127717563494706606076 relative error = 8.3965499039231055597790242365782 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.723 y[1] (analytic) = 0.33836288145302686920032626580041 y[1] (numeric) = 0.30976434456433829928060399962212 absolute error = 0.028598536888688569919722266178295 relative error = 8.4520313711357117848978069518898 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.724 y[1] (analytic) = 0.33761338820156030092934758854468 y[1] (numeric) = 0.30888979312769690942798770668263 absolute error = 0.028723595073863391501359881862043 relative error = 8.5078365010557492012890902433026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.725 y[1] (analytic) = 0.33686455733665033221559140807746 y[1] (numeric) = 0.30801558736651682607121120546006 absolute error = 0.028848969970133506144380202617393 relative error = 8.563967132138179304866129315391 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.726 y[1] (analytic) = 0.33611638960712776556645644240991 y[1] (numeric) = 0.30714172794355907644128941216686 absolute error = 0.028974661663568689125167030243051 relative error = 8.6204251144777396574103634721649 % h = 0.001 TOP MAIN SOLVE Loop memory used=205.9MB, alloc=4.4MB, time=25.57 NO POLE x[1] = 0.727 y[1] (analytic) = 0.33536888576116026815720062537343 y[1] (numeric) = 0.30626821552233318706645340989985 absolute error = 0.029100670238827081090747215473582 relative error = 8.6772123098955911202603996987639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.728 y[1] (analytic) = 0.33462204654625162366333627866526 y[1] (numeric) = 0.30539505076709652026267921286787 absolute error = 0.029226995779155103400657065797385 relative error = 8.7343305920267072676937984052244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.729 y[1] (analytic) = 0.33387587270924098475690872831604 y[1] (numeric) = 0.30452223434285360987638080519411 absolute error = 0.029353638366387374880527923121928 relative error = 8.7917818464080131958096683030604 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.73 y[1] (analytic) = 0.33313036499630212626740586923847 y[1] (numeric) = 0.30364976691535549627993171154472 absolute error = 0.029480598080946629987474157693752 relative error = 8.8495679705672810213220366974359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.731 y[1] (analytic) = 0.33238552415294269900804551688526 y[1] (numeric) = 0.30277764915109906062068010400685 absolute error = 0.029607875001843638387365412878414 relative error = 8.9076908741127894442249989878819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.732 y[1] (analytic) = 0.33164135092400348426818671966681 y[1] (numeric) = 0.30190588171732635832412319614538 absolute error = 0.029735469206677125944063523521429 relative error = 8.9661524788237548288033553326166 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.733 y[1] (analytic) = 0.33089784605365764897261053965515 y[1] (numeric) = 0.30103446528202395185190742100845 absolute error = 0.029863380771633697120703118646709 relative error = 9.0249547187415413389495837249105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.734 y[1] (analytic) = 0.33015501028541000150841514223148 y[1] (numeric) = 0.30016340051392224271532163502606 absolute error = 0.029991609771487758793093507205427 relative error = 9.0840995402616577462225325101822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.735 y[1] (analytic) = 0.32941284436209624822026936771989 y[1] (numeric) = 0.29929268808249480274495133425282 absolute error = 0.030120156279601445475318033467073 relative error = 9.1435889022265486125582847702389 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.736 y[1] (analytic) = 0.32867134902588225057476828969201 y[1] (numeric) = 0.29842232865795770461716261324489 absolute error = 0.030249020367924545957605676447118 relative error = 9.2034247760191876340325858696897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.737 y[1] (analytic) = 0.32793052501826328299463359552502 y[1] (numeric) = 0.29755232291126885163808534003145 absolute error = 0.030378202106994431356548255493565 relative error = 9.2636091456574810175905613728361 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.738 y[1] (analytic) = 0.32719037308006329136350095495073 y[1] (numeric) = 0.29668267151412730678576576314154 absolute error = 0.030507701565935984577735191809193 relative error = 9.3241440078894888492169098397563 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.4MB, time=26.05 NO POLE x[1] = 0.739 y[1] (analytic) = 0.32645089395143415220203587174673 y[1] (numeric) = 0.29581337513897262101115950847788 absolute error = 0.030637518812461531190876363268857 relative error = 9.3850313722894724996322579090012 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.74 y[1] (analytic) = 0.32571208837185493251611884239183 y[1] (numeric) = 0.29494443445898416079863666498862 absolute error = 0.030767653912870771717482177403212 relative error = 9.4462732613547762022830408037502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.741 y[1] (analytic) = 0.32497395708013115031783997343909 y[1] (numeric) = 0.29407585014808043498667139857592 absolute error = 0.030898106932050715331168574863172 relative error = 9.5078717106035510281574534182957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.742 y[1] (analytic) = 0.32423650081439403582004253655019 y[1] (numeric) = 0.29320762288091842084938927349564 absolute error = 0.03102887793347561497065326305455 relative error = 9.5698287686733295728232484003026 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.743 y[1] (analytic) = 0.32349972031209979330515426658597 y[1] (numeric) = 0.29233975333289288943964619964471 absolute error = 0.031159966979206903865508066941253 relative error = 9.6321464974204597630591938937096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.744 y[1] (analytic) = 0.32276361631002886366904453386027 y[1] (numeric) = 0.29147224218013573019431366260088 absolute error = 0.031291374129893133474730871259388 relative error = 9.6948269720204062835558167767539 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.745 y[1] (analytic) = 0.32202818954428518764064484663867 y[1] (numeric) = 0.29060509009951527480244563107351 absolute error = 0.031423099444769912838199215565161 relative error = 9.7578722810689282184078388561361 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.746 y[1] (analytic) = 0.32129344075029546967806946419994 y[1] (numeric) = 0.289738297768635620337003273542 absolute error = 0.031555142981659849341066190657931 relative error = 9.8212845266841415975258781948714 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.747 y[1] (analytic) = 0.32055937066280844254197222427846 y[1] (numeric) = 0.28887186586583595165081435230089 absolute error = 0.03168750479697249089115787197757 relative error = 9.8850658246094756346741768359446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.748 y[1] (analytic) = 0.31982598001589413254687501146943 y[1] (numeric) = 0.28800579507018986303744489889555 absolute error = 0.031820184945704269509430112573889 relative error = 9.949218304317531541610201168982 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.749 y[1] (analytic) = 0.3190932695429431254912026152071 y[1] (numeric) = 0.28714008606150467915766151002046 absolute error = 0.031953183481438446333541105186639 relative error = 10.013744109114852901777047531033 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=213.6MB, alloc=4.4MB, time=26.52 x[1] = 0.75 y[1] (analytic) = 0.31836123997666583326675804722011 y[1] (numeric) = 0.28627473952032077523216333736118 absolute error = 0.032086500456345058034594709858926 relative error = 10.078645396247616687197016453689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.751 y[1] (analytic) = 0.31762989204909176114837170892742 y[1] (numeric) = 0.28540975612791089650126357859116 absolute error = 0.032220135921180864647108130336266 relative error = 10.143924337008254103651078844401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.752 y[1] (analytic) = 0.3168992264915687757644571190647 y[1] (numeric) = 0.28454513656627947695220100978546 absolute error = 0.032354089925289298812256109279239 relative error = 10.209583116843010551921076220144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.753 y[1] (analytic) = 0.31616924403476237374920523092425 y[1] (numeric) = 0.28368088151816195731476283188292 absolute error = 0.032488362516600416434442399041331 relative error = 10.275623935460454096836454049946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.754 y[1] (analytic) = 0.31543994540865495107714868695348 y[1] (numeric) = 0.2828169916670241023259008355171 absolute error = 0.032622953741630848751247851436376 relative error = 10.342049006940941941122454714796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.755 y[1] (analytic) = 0.31471133134254507308082667608652 y[1] (numeric) = 0.28195346769706131726402361954301 absolute error = 0.032757863645483755816803056543508 relative error = 10.408860559847054507609584283784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.756 y[1] (analytic) = 0.31398340256504674515228037608347 y[1] (numeric) = 0.28109031029319796375364832891035 absolute error = 0.032893092271848781398632047173121 relative error = 10.476060837335006841252666416191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.757 y[1] (analytic) = 0.31325615980408868412910827932099 y[1] (numeric) = 0.28022752014108667484109610717463 absolute error = 0.033028639663002009288012172146356 relative error = 10.543652097267047151640024079687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.758 y[1] (analytic) = 0.31252960378691359036581001591817 y[1] (numeric) = 0.27936509792710766934191618789354 absolute error = 0.033164505859805921023893828024625 relative error = 10.611636612324852427267672223129 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.759 y[1] (analytic) = 0.31180373524007742049114660279324 y[1] (numeric) = 0.27850304433836806546072427742735 absolute error = 0.033300690901709355030422325365888 relative error = 10.68001667012393116482852316369 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.76 y[1] (analytic) = 0.31107855488944866085224436123027 y[1] (numeric) = 0.27764136006270119368414160924783 absolute error = 0.033437194826747467168102751982441 relative error = 10.748794573329043370141441085802 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.761 y[1] (analytic) = 0.31035406346020760164616905879138 y[1] (numeric) = 0.27678004578866590894752177675934 absolute error = 0.033574017671541692698647282032041 relative error = 10.817972639770648102138755796576 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=217.4MB, alloc=4.4MB, time=27.00 x[1] = 0.762 y[1] (analytic) = 0.30963026167684561173969614393974 y[1] (numeric) = 0.27591910220554590207615317784784 absolute error = 0.033711159471299709663542966091904 relative error = 10.887553202562388947563069668708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.763 y[1] (analytic) = 0.30890715026316441417800225354293 y[1] (numeric) = 0.2750585300033490105016256298982 absolute error = 0.033848620259815403676376623644724 relative error = 10.957538610219627931714668963221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.764 y[1] (analytic) = 0.30818472994227536238300248450447 y[1] (numeric) = 0.27419832987280652825405043885557 absolute error = 0.033986400069468834128952045648896 relative error = 11.027931226779038489759682151995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.765 y[1] (analytic) = 0.30746300143659871704205723112624 y[1] (numeric) = 0.27333850250537251523082393005332 absolute error = 0.03412449893122620181123330107292 relative error = 11.098733431919268243776716234307 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.766 y[1] (analytic) = 0.30674196546786292368777169943441 y[1] (numeric) = 0.27247904859322310574262517198644 absolute error = 0.034262916874639817945146527447972 relative error = 11.1699476210826824529067571493 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.767 y[1] (analytic) = 0.30602162275710389096961051860939 y[1] (numeric) = 0.2716199688292558163373393469751 absolute error = 0.034401653927848074632271171634292 relative error = 11.241576205598199127698664024978 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.768 y[1] (analytic) = 0.30530197402466426961804917784491 y[1] (numeric) = 0.27076126390708885290259894473724 absolute error = 0.034540710117575416715450233107667 relative error = 11.313621612805226925031958073874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.769 y[1] (analytic) = 0.30458301999019273210198332442474 y[1] (numeric) = 0.26990293452106041704763567627132 absolute error = 0.034680085469132315054347648153424 relative error = 11.386086286178717066871466629564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.77 y[1] (analytic) = 0.30386476137264325298011626554779 y[1] (numeric) = 0.26904498136622801176513672613946 absolute error = 0.034819780006415241214979539408332 relative error = 11.45897268545534065458671985679 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.771 y[1] (analytic) = 0.30314719889027438994704432245398 y[1] (numeric) = 0.26818740513836774637379968123694 absolute error = 0.034959793751906643573244641217041 relative error = 11.532283286760802880675133722674 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.772 y[1] (analytic) = 0.30243033326064856557475899070575 y[1] (numeric) = 0.2673302065339736407422811934351 absolute error = 0.035100126726674924832477797270651 relative error = 11.606020582738305771484607931016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.773 y[1] (analytic) = 0.30171416520063134975028416506311 y[1] (numeric) = 0.26647338625025692879523515209108 absolute error = 0.035240778950374420955049012972035 relative error = 11.680187082678171227961225677875 % h = 0.001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.4MB, time=27.47 NO POLE x[1] = 0.774 y[1] (analytic) = 0.30099869542639074281016599125526 y[1] (numeric) = 0.26561694498514536130213686032815 absolute error = 0.03538175044124538150802913092711 relative error = 11.754785312648636266574616859729 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.775 y[1] (analytic) = 0.30028392465339645937253221009913 y[1] (numeric) = 0.26476088343728250794959042620439 absolute error = 0.03552304121611395142294178389474 relative error = 11.829817815627832499420946679055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.776 y[1] (analytic) = 0.29956985359641921286743716184588 y[1] (numeric) = 0.26390520230602705869781729640408 absolute error = 0.035664651290392154169619865441798 relative error = 11.905287151636962031095487574792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.777 y[1] (analytic) = 0.29885648296953000076620792035069 y[1] (numeric) = 0.26304990229145212442202457590516 absolute error = 0.035806580678077876344183344445526 relative error = 11.981195897874682090287761352056 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.778 y[1] (analytic) = 0.29814381348609939051050632766018 y[1] (numeric) = 0.2621949840943445368393524921961 absolute error = 0.035948829391754853671153835464071 relative error = 12.057546648852710856207110824941 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.779 y[1] (analytic) = 0.29743184585879680614182099989582 y[1] (numeric) = 0.26134044841620414772210107703634 absolute error = 0.036091397442592658419719922859478 relative error = 12.134342016532667083920466155038 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.78 y[1] (analytic) = 0.29672058079958981563210267488208 y[1] (numeric) = 0.26048629595924312739793685247531 absolute error = 0.036234284840346688234165822406772 relative error = 12.211584630464156278502585996404 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.781 y[1] (analytic) = 0.2960100190197434189162555708243 y[1] (numeric) = 0.25963252742638526253778102086479 absolute error = 0.036377491593358156378474549959508 relative error = 12.289277137924116315588145265532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.782 y[1] (analytic) = 0.29530016122981933662719672348589 y[1] (numeric) = 0.25877914352126525323208137091804 absolute error = 0.036521017708554083395115352567846 relative error = 12.367422204057435555501076165025 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.783 y[1] (analytic) = 0.29459100813967529953419456674599 y[1] (numeric) = 0.257926144948228009356170823485 absolute error = 0.036664863191447290178023743260991 relative error = 12.446022512018856649646318554309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.784 y[1] (analytic) = 0.29388256045846433868519731813999 y[1] (numeric) = 0.25707353241232794622541625162658 absolute error = 0.036809028046136392459781066513411 relative error = 12.525080763116179391309783408859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.785 memory used=225.0MB, alloc=4.4MB, time=27.96 y[1] (analytic) = 0.29317481889463407625386102699527 y[1] (numeric) = 0.25622130661932827954086191978048 absolute error = 0.036953512275305796712999107214786 relative error = 12.604599676954776118451481314145 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.786 y[1] (analytic) = 0.292467784155926017091986438075 y[1] (numeric) = 0.25536946827570031962607259631624 absolute error = 0.037098315880225697465913841758759 relative error = 12.684581991583433333522444910099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.787 y[1] (analytic) = 0.29176145694937484098807311823418 y[1] (numeric) = 0.25451801808862276495588210257768 absolute error = 0.037243438860752076032191015656502 relative error = 12.765030463641533364816741096562 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.788 y[1] (analytic) = 0.29105583798130769563269858747478 y[1] (numeric) = 0.25366695676598099497775376960537 absolute error = 0.037388881215326700654944817869408 relative error = 12.84594786850759005541442698666 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.789 y[1] (analytic) = 0.29035092795734349029142948896187 y[1] (numeric) = 0.25281628501636636222645998111961 absolute error = 0.037534642940977128064969507842264 relative error = 12.92733700044915262940910198219 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.79 y[1] (analytic) = 0.2896467275823921901859711250308 y[1] (numeric) = 0.25196600354907548373278868802541 absolute error = 0.037680724033316706453182437005393 relative error = 13.009200672774092050874550952207 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.791 y[1] (analytic) = 0.28894323756065411158426097797705 y[1] (numeric) = 0.25111611307410953172698548567405 absolute error = 0.037827124486544579857275492302998 relative error = 13.091541717983284358939127056995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.792 y[1] (analytic) = 0.28824045859561921760021112547646 y[1] (numeric) = 0.25026661430217352363764055037983 absolute error = 0.037973844293445693962570575096626 relative error = 13.174362987924705632434724515663 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.793 y[1] (analytic) = 0.2875383913900664147038037508348 y[1] (numeric) = 0.24941750794467561138673043624604 absolute error = 0.038120883445390803317073314588763 relative error = 13.257667353948953409900657238476 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.794 y[1] (analytic) = 0.28683703664606284994224323791253 y[1] (numeric) = 0.2485687947137263699815254371991 absolute error = 0.038268241932336479960717800713437 relative error = 13.341457707066209565283190904213 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.795 y[1] (analytic) = 0.28613639506496320887286762951401 y[1] (numeric) = 0.24772047532213808540407392226418 absolute error = 0.038415919742825123468793707249832 relative error = 13.425736958104659816511070639771 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.796 y[1] (analytic) = 0.28543646734740901420852151627135 y[1] (numeric) = 0.24687255048342404179897575453875 absolute error = 0.038563916863984972409545761732604 relative error = 13.510508037870385223278843909555 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=228.8MB, alloc=4.4MB, time=28.45 x[1] = 0.797 y[1] (analytic) = 0.28473725419332792517609171059139 y[1] (numeric) = 0.24602502091179780796015760603098 absolute error = 0.038712233281530117215934104560409 relative error = 13.595773897308741211866310092314 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.798 y[1] (analytic) = 0.28403875630193303758890634707191 y[1] (numeric) = 0.24517788732217252311736368152857 absolute error = 0.038860868979760514471542665543333 relative error = 13.681537507667239848697766319752 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.799 y[1] (analytic) = 0.28334097437172218463369733692953 y[1] (numeric) = 0.24433115043016018202307606494747 absolute error = 0.039009823941562002610621271982061 relative error = 13.767801860659951270633124371483 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8 y[1] (analytic) = 0.28264390910047723837282538941861 y[1] (numeric) = 0.24348481095207091934057960118066 absolute error = 0.039159098148406319032245788237959 relative error = 13.854569968633440368719244741715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.801 y[1] (analytic) = 0.28194756118526341196246609795798 y[1] (numeric) = 0.2426388696049122933338869253226 absolute error = 0.039308691580351118628579172635385 relative error = 13.941844864734255013349317626923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.802 y[1] (analytic) = 0.28125193132242856258745487272111 y[1] (numeric) = 0.24179332710638856886023994928443 absolute error = 0.039458604216039993727214923436688 relative error = 14.029629603077982302516719301054 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.803 y[1] (analytic) = 0.28055702020760249511348778478693 y[1] (numeric) = 0.2409481841748999996659048132388 absolute error = 0.039608836032702495447582971548134 relative error = 14.117927258919889511143954967791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.804 y[1] (analytic) = 0.27986282853569626645737466959218 y[1] (numeric) = 0.24010344152954210998597800603955 absolute error = 0.039759387006154156471396663552628 relative error = 14.206740928827166618354110250564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.805 y[1] (analytic) = 0.27916935700090149067604011937443 y[1] (numeric) = 0.23925909989010497544892205475026 absolute error = 0.039910257110796515227118064624162 relative error = 14.296073730852787491069303109186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.806 y[1] (analytic) = 0.27847660629668964477496727554668 y[1] (numeric) = 0.238415159977072503286549878686 absolute error = 0.040061446319617141488417396860686 relative error = 14.385928804711007006506181860143 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.807 y[1] (analytic) = 0.27778457711581137523677861250211 y[1] (numeric) = 0.237571622511621711850177597924 absolute error = 0.040212954604189663386601014578111 relative error = 14.47630931195451160303138463506 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.808 y[1] (analytic) = 0.27709327015029580527064718421017 y[1] (numeric) = 0.23672848821562200943366628007046 absolute error = 0.040364781934673795836980904139711 relative error = 14.567218436153240958479508756161 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=232.7MB, alloc=4.4MB, time=28.94 x[1] = 0.809 y[1] (analytic) = 0.2764026860914498427832310841352 y[1] (numeric) = 0.2358857578116344724040738021814 absolute error = 0.040516928279815370379157281953797 relative error = 14.65865938307489870746260965728 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.81 y[1] (analytic) = 0.27571282562985748907182314748546 y[1] (numeric) = 0.23504343202291112264063869712591 absolute error = 0.040669393606946366431184450359544 relative error = 14.75063538086717032445427024439 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.811 y[1] (analytic) = 0.27502368945537914824040720258509 y[1] (numeric) = 0.23420151157339420428281854534735 absolute error = 0.040822177881984943957588657237738 relative error = 14.843149680241666517554213661687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.812 y[1] (analytic) = 0.27433527825715093733931145525542 y[1] (numeric) = 0.23335999718771545978810616392414 absolute error = 0.040975281069435477551205291331283 relative error = 14.93620555465961069887329577464 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.813 y[1] (analytic) = 0.27364759272358399722914886649459 y[1] (numeric) = 0.23251888959119540530034753505347 absolute error = 0.041128703132388591928801331441124 relative error = 15.029806300519289321466199943353 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.814 y[1] (analytic) = 0.27296063354236380416973365945774 y[1] (numeric) = 0.23167818950984260532928610557963 absolute error = 0.041282444032521198840447553878103 relative error = 15.123955237345284099723640273482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.815 y[1] (analytic) = 0.27227440140044948213466236676389 y[1] (numeric) = 0.23083789767035294674205877796229 absolute error = 0.041436503730096535392603588801598 relative error = 15.218655707979505360161429555273 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.816 y[1] (analytic) = 0.2715888969840731158522471034912 y[1] (numeric) = 0.2299980148001089120673696011281 absolute error = 0.041590882183964203784877502363096 relative error = 15.313911078774046002655160265891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.817 y[1] (analytic) = 0.27090412097873906457348802486997 y[1] (numeric) = 0.22915854162717885211306785697155 absolute error = 0.041745579351560212460420167898424 relative error = 15.40972473978587578841197599897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.818 y[1] (analytic) = 0.27022007406922327656777120064388 y[1] (numeric) = 0.22831947888031625789785792486618 absolute error = 0.041900595188907018669913275777699 relative error = 15.506100104973395910391202639159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.819 y[1] (analytic) = 0.26953675693957260434697741034436 y[1] (numeric) = 0.22748082728895903189786899241583 absolute error = 0.04205592965061357244910841792853 relative error = 15.603040612394874044530433858137 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.82 y[1] (analytic) = 0.26885417027310412061868663531228 y[1] (numeric) = 0.22664258758322875860881336581522 absolute error = 0.042211582689875362009873269497055 relative error = 15.700549724408780326050751591238 % h = 0.001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.4MB, time=29.42 NO POLE x[1] = 0.821 y[1] (analytic) = 0.26817231475240443496916229420547 y[1] (numeric) = 0.22580476049392997442446281760106 absolute error = 0.042367554258474460544699476604412 relative error = 15.79863092787604494435260698299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.822 y[1] (analytic) = 0.2674911910593290112767985389509 y[1] (numeric) = 0.22496734675254943683217309325624 absolute error = 0.042523844306779574444625445694662 relative error = 15.897287734364258302621772664166 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.823 y[1] (analytic) = 0.26681079987500148585671319763723 y[1] (numeric) = 0.22413034709125539292618738108184 absolute error = 0.042680452783746092930525816555387 relative error = 15.99652368035383494429278254424 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.824 y[1] (analytic) = 0.26613114187981298633716821969816 y[1] (numeric) = 0.22329376224289684723945023197254 absolute error = 0.042837379636916139097717987725622 relative error = 16.096342327446162708016291561999 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.825 y[1] (analytic) = 0.26545221775342145126849874690922 y[1] (numeric) = 0.22245759294100282889466409722035 absolute error = 0.042994624812418622373834649688867 relative error = 16.196747262573758835798531862662 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.826 y[1] (analytic) = 0.26477402817475095046523120121228 y[1] (numeric) = 0.22162183991978165807532133322929 absolute error = 0.043152188254969292389909867982992 relative error = 16.297742098212455025578070849713 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.827 y[1] (analytic) = 0.26409657382199100608207004719305 y[1] (numeric) = 0.22078650391412021181744520204758 absolute error = 0.043310069907870794264624845145467 relative error = 16.399330472595633689730802833617 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.828 y[1] (analytic) = 0.26341985537259591442443215316827 y[1] (numeric) = 0.21995158565958318912277407591554 absolute error = 0.043468269713012725301658077252737 relative error = 16.501516049930537954902812135563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.829 y[1] (analytic) = 0.26274387350328406849420694029164 y[1] (numeric) = 0.2191170858924123753941237325833 absolute error = 0.043626787610871693100083207708336 relative error = 16.604302520616678216217599658881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.83 y[1] (analytic) = 0.26206862889003728127141977386192 y[1] (numeric) = 0.21828300534952590619366330597522 absolute error = 0.043785623540511375077756467886703 relative error = 16.707693601466358340345236513367 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.831 y[1] (analytic) = 0.26139412220810010973247531511345 y[1] (numeric) = 0.21744934476851753032484113386321 absolute error = 0.043944777439582579407634181250243 relative error = 16.811693035927344897213283861647 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=240.3MB, alloc=4.4MB, time=29.90 x[1] = 0.832 y[1] (analytic) = 0.26072035413197917960565681518938 y[1] (numeric) = 0.21661610488765587223869742056219 absolute error = 0.044104249244323307366959394627187 relative error = 16.916304594307703089340717795473 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.833 y[1] (analytic) = 0.26004732533544251086455659574197 y[1] (numeric) = 0.21578328644588369376530130827314 absolute error = 0.044264038889558817099255287468832 relative error = 17.021532074002823340945491802683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.834 y[1] (analytic) = 0.25937503649151884396011222267346 y[1] (numeric) = 0.21495089018281715517105062557541 absolute error = 0.044424146308701688789061597098053 relative error = 17.127379299724662806173594210969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.835 y[1] (analytic) = 0.25870348827249696679192214092496 y[1] (numeric) = 0.21411891683874507554257325570686 absolute error = 0.044584571433751891249348885218097 relative error = 17.233850123733226357083334955834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.836 y[1] (analytic) = 0.2580326813499250424195137989418 y[1] (numeric) = 0.21328736715462819249796974066885 absolute error = 0.04474531419529684992154405827295 relative error = 17.340948426070311917454947821714 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.837 y[1] (analytic) = 0.25736261639460993751423655149115 y[1] (numeric) = 0.21245624187209842122613740985175 absolute error = 0.044906374522511516288099141639407 relative error = 17.44867811479554531814526316532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.838 y[1] (analytic) = 0.25669329407661655155245088888304 y[1] (numeric) = 0.21162554173345811285491699379517 absolute error = 0.045067752343158438697533895087865 relative error = 17.557043126224730163634071996842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.839 y[1] (analytic) = 0.25602471506526714675068479934958 y[1] (numeric) = 0.21079526748167931214880335487445 absolute error = 0.045229447583587834601881444475131 relative error = 17.666047425170538517677801412715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.84 y[1] (analytic) = 0.25535688002914067874342732937035 y[1] (numeric) = 0.20996541986040301453696263714074 absolute error = 0.045391460168737664206464692229616 relative error = 17.775695005185568538663265209547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.841 y[1] (analytic) = 0.25468978963607212800422866409446 y[1] (numeric) = 0.20913599961393842247229880723579 absolute error = 0.045553790022133705531929856858665 relative error = 17.885989888807795522406648040781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.842 y[1] (analytic) = 0.25402344455315183201077530670349 y[1] (numeric) = 0.20830700748726220112231322725278 absolute error = 0.045716437065889630888462079450712 relative error = 17.996936127808443141838746858321 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.843 y[1] (analytic) = 0.25335784544672481815460819158468 y[1] (numeric) = 0.20747844422601773339250156862163 absolute error = 0.045879401220707084762106622963054 relative error = 18.108537803442302009326183981613 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=244.1MB, alloc=4.4MB, time=30.37 x[1] = 0.844 y[1] (analytic) = 0.25269299298239013739615082154036 y[1] (numeric) = 0.20665031057651437428303304355985 absolute error = 0.046042682405875763113117777980512 relative error = 18.220799026700523028370330977322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.845 y[1] (analytic) = 0.2520288878250001986657137739502 y[1] (numeric) = 0.20582260728572670457945759734751 absolute error = 0.046206280539273494086256176602695 relative error = 18.333723938565913347172726113326 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.846 y[1] (analytic) = 0.25136553063866010401114117482621 y[1] (numeric) = 0.20499533510129378387818737065693 absolute error = 0.046370195537366320132953804169277 relative error = 18.447316710270763077130711682642 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.847 y[1] (analytic) = 0.25070292208672698449276399305858 y[1] (numeric) = 0.20416849477151840294749940639347 absolute error = 0.046534427315208581545264586665109 relative error = 18.561581543557231294803960545927 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.848 y[1] (analytic) = 0.25004106283180933682632425984381 y[1] (numeric) = 0.20334208704536633542480723998225 absolute error = 0.046698975786443001401517019861563 relative error = 18.676522670940320206346843812264 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.849 y[1] (analytic) = 0.24937995353576636077453357031556 y[1] (numeric) = 0.20251611267246558885094967576704 absolute error = 0.046863840863300771923583894548521 relative error = 18.79214435597346671890981658964 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.85 y[1] (analytic) = 0.24871959485970729728792847576453 y[1] (numeric) = 0.20169057240310565504224571517001 absolute error = 0.047029022456601642245682760594523 relative error = 18.908450893516781034153054976444 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.851 y[1] (analytic) = 0.24805998746399076739568462553681 y[1] (numeric) = 0.20086546698823675980106526449493 absolute error = 0.047194520475754007594619361041886 relative error = 19.025446610007962254866662973317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.852 y[1] (analytic) = 0.2474011320082241118470507677415 y[1] (numeric) = 0.20004079717946911196566591174067 absolute error = 0.047360334828754999881384856000821 relative error = 19.143135863735921376834413908965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.853 y[1] (analytic) = 0.24674302915126273150406296727849 y[1] (numeric) = 0.19921656372907215180004672252564 absolute error = 0.047526465422190579704016244752848 relative error = 19.26152304511714242459408584467 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.854 y[1] (analytic) = 0.24608567955120942848619864841736 y[1] (numeric) = 0.19839276738997379872457066520658 absolute error = 0.047692912161235629761627983210777 relative error = 19.38061257697481288172026500458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.855 y[1] (analytic) = 0.24542908386541374806762931721824 y[1] (numeric) = 0.19756940891575969838810793450684 absolute error = 0.047859674949654049679521382711404 relative error = 19.500408914820754963769703810403 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=247.9MB, alloc=4.4MB, time=30.85 x[1] = 0.856 y[1] (analytic) = 0.24477324275047132132773006648732 y[1] (numeric) = 0.19674648906067246908245310144788 absolute error = 0.048026753689798852245276965039439 relative error = 19.620916547140189685171042078965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.857 y[1] (analytic) = 0.24411815686222320855550321270245 y[1] (numeric) = 0.19592400857961094749976967510413 absolute error = 0.04819414828261226105573353759832 relative error = 19.742139995679366080197502415741 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.858 y[1] (analytic) = 0.24346382685575524340857266043075 y[1] (numeric) = 0.19510196822812943383381631867377 absolute error = 0.048361858627625809574756341756979 relative error = 19.864083815736088352822111206962 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.859 y[1] (analytic) = 0.24281025338539737782740483518898 y[1] (numeric) = 0.19428036876243693622570961857631 absolute error = 0.04852988462296044160169521661267 relative error = 19.986752596453174150810645966375 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.86 y[1] (analytic) = 0.24215743710472302770541127047135 y[1] (numeric) = 0.19345921093939641455497896075129 absolute error = 0.048698226165326613150432309720062 relative error = 20.11015096111487758594998078717 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.861 y[1] (analytic) = 0.24150537866654841931558717878744 y[1] (numeric) = 0.19263849551652402357666972304006 absolute error = 0.04886688315002439573891745574738 relative error = 20.234283567446311054932476939934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.862 y[1] (analytic) = 0.24085407872293193649433958001736 y[1] (numeric) = 0.19181822325198835540525164648454 absolute error = 0.049035855470943581089087933532819 relative error = 20.359155107915900354215826893619 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.863 y[1] (analytic) = 0.24020353792517346858315780320164 y[1] (numeric) = 0.19099839490460968134608990157143 absolute error = 0.049205143020563787237067901630209 relative error = 20.484770310040908027249217435495 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.864 y[1] (analytic) = 0.2395537569238137591287784200408 y[1] (numeric) = 0.19017901123385919307523701788748 absolute error = 0.049374745689954566053541402153318 relative error = 20.611133936696060333899400075215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.865 y[1] (analytic) = 0.23890473636863375534249590988562 y[1] (numeric) = 0.18936007299985824316830449733084 absolute error = 0.049544663368775512174191412554772 relative error = 20.738250786425313689824502978507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.866 y[1] (analytic) = 0.23825647690865395831926959685314 y[1] (numeric) = 0.18854158096337758497917358194354 absolute error = 0.049714895945276373340096014909603 relative error = 20.866125693756796888031167602412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.867 y[1] (analytic) = 0.23760897919213377401727663990728 y[1] (numeric) = 0.18772353588583661186930529759083 absolute error = 0.049885443306297162147971342316456 relative error = 20.994763529520965886015577190802 % h = 0.001 TOP MAIN SOLVE Loop memory used=251.7MB, alloc=4.4MB, time=31.32 NO POLE x[1] = 0.868 y[1] (analytic) = 0.23696224386657086499856009629705 y[1] (numeric) = 0.18690593852930259578841054411423 absolute error = 0.05005630533726826921014955218282 relative error = 21.124169201172008419836681059655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.869 y[1] (analytic) = 0.23631627157870050293142031765021 y[1] (numeric) = 0.18608878965648992520724165122447 absolute error = 0.050227481922210577724178666425739 relative error = 21.254347653112536191307744711581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.87 y[1] (analytic) = 0.23567106297449492185519717627715 y[1] (numeric) = 0.18527209003075934240326746727943 absolute error = 0.050398972943735579451929708997713 relative error = 21.385303867021602866329460629106 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.871 y[1] (analytic) = 0.23502661869916267220808985684866 y[1] (numeric) = 0.18445584041611718009999469520835 absolute error = 0.050570778283045492108095161640314 relative error = 21.517042862186086621335314928611 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.872 y[1] (analytic) = 0.23438293939714797561866018557423 y[1] (numeric) = 0.18364004157721459746069883619739 absolute error = 0.050742897819933378157961349376841 relative error = 21.649569695835476480990720550999 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.873 y[1] (analytic) = 0.2337400257121300804616647053235 y[1] (numeric) = 0.18282469427934681543732874734196 absolute error = 0.05091533143278326502433595798154 relative error = 21.782889463480102203796556846027 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.874 y[1] (analytic) = 0.23309787828702261817885994080533 y[1] (numeric) = 0.18200979928845235147534946429747 absolute error = 0.051088078998570266703510476507867 relative error = 21.917007299252847993212152483192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.875 y[1] (analytic) = 0.23245649776397296036542453294546 y[1] (numeric) = 0.18119535737111225357528858402195 absolute error = 0.051261140392860706790135948923513 relative error = 22.051928376254390840451401027244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.876 y[1] (analytic) = 0.231815884784361576622641155987 y[1] (numeric) = 0.18038136929454933371175214600033 absolute error = 0.05143451548981224291088900998667 relative error = 22.187657906902004841339665214471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.877 y[1] (analytic) = 0.23117603998880139317748036457849 y[1] (numeric) = 0.17956783582662740061067659287061 absolute error = 0.051608204162173992566803771707883 relative error = 22.324201143281973373671576530817 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.878 y[1] (analytic) = 0.23053696401713715226972775121205 y[1] (numeric) = 0.17875475773585049188558403313597 absolute error = 0.051782206281286660384143718076077 relative error = 22.461563377505651573506091184631 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=255.5MB, alloc=4.4MB, time=31.79 x[1] = 0.879 y[1] (analytic) = 0.22989865750844477230729502683122 y[1] (numeric) = 0.17794213579136210553360866964373 absolute error = 0.051956521717082666773686357187492 relative error = 22.599749942069222108902733218418 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.88 y[1] (analytic) = 0.22926112110103070879035486924401 y[1] (numeric) = 0.17712997076294443079206289774044 absolute error = 0.052131150338086277998291971503563 relative error = 22.738766210217187817871584238226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.881 y[1] (analytic) = 0.22862435543243131600493861515303 y[1] (numeric) = 0.17631826342101757835631221647317 absolute error = 0.052306092011413737648626398679861 relative error = 22.878617596309645353911286033194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.882 y[1] (analytic) = 0.22798836113941220948663510215197 y[1] (numeric) = 0.17550701453663880995972873489772 absolute error = 0.052481346602773399526906367254256 relative error = 23.019309556193384567578444472992 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.883 y[1] (analytic) = 0.22735313885796762925502819693626 y[1] (numeric) = 0.17469622488150176731649369347621 absolute error = 0.052656913976465861938534503460047 relative error = 23.160847587576858946205060168937 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.884 y[1] (analytic) = 0.2267186892233198038195097752374 y[1] (numeric) = 0.17388589522793570042802005769717 absolute error = 0.052832793995384103391489717540236 relative error = 23.303237230409073036297070547848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.885 y[1] (analytic) = 0.22608501286991831495710414761512 y[1] (numeric) = 0.17307602634890469525376687743124 absolute error = 0.053008986521013619703337270183875 relative error = 23.44648406726243338444832966319 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.886 y[1] (analytic) = 0.22545211043143946326293915322968 y[1] (numeric) = 0.17226661901800690074721774114384 absolute error = 0.053185491413432562515721412085841 relative error = 23.590593723719610152934436957509 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.887 y[1] (analytic) = 0.22481998254078563447399837107075 y[1] (numeric) = 0.1714576740094737552577962889218 absolute error = 0.053362308531311879216202082148947 relative error = 23.735571868764457195656363104987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.888 y[1] (analytic) = 0.22418862983008466656678812483747 y[1] (numeric) = 0.17064919209816921229949238233413 absolute error = 0.053539437731915454267295742503338 relative error = 23.881424215177039018934015766092 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.889 y[1] (analytic) = 0.22355805293068921762955218375027 y[1] (numeric) = 0.16984117405958896568697316243613 absolute error = 0.05371687887110025194257902131414 relative error = 24.028156519932813699956593143768 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.89 y[1] (analytic) = 0.22292825247317613450966628702682 y[1] (numeric) = 0.16903362066985967403995385974124 absolute error = 0.053894631803316460469712427285579 relative error = 24.175774584606021493634338892792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=259.4MB, alloc=4.4MB, time=32.26 x[1] = 0.891 y[1] (analytic) = 0.22229922908734582223684384457509 y[1] (numeric) = 0.16822653270573818465660385172519 absolute error = 0.054072696381607637580239992849903 relative error = 24.324284255777329526322438072303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.892 y[1] (analytic) = 0.22167098340222161422278339064533 y[1] (numeric) = 0.16741991094461075675676409439177 absolute error = 0.054251072457610857466019296253563 relative error = 24.473691425445783652562382951852 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.893 y[1] (analytic) = 0.22104351604604914323788759074086 y[1] (numeric) = 0.16661375616449228409575268461796 absolute error = 0.054429759881556859142134906122901 relative error = 24.624002031445119238772148838572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.894 y[1] (analytic) = 0.22041682764629571316568282501642 y[1] (numeric) = 0.16580806914402551694953593940817 absolute error = 0.054608758502270196216146885608244 relative error = 24.775222057864483335879824932465 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.895 y[1] (analytic) = 0.219790918829649671535567593692 y[1] (numeric) = 0.1650028506624802834720430068216 absolute error = 0.0547880681671693880635245868704 relative error = 24.927357535473621411404783165407 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.896 y[1] (analytic) = 0.21916579022201978283451721168161 y[1] (numeric) = 0.16419810149975271042540265119328 absolute error = 0.054967688722267072409114560488339 relative error = 25.0804145421525825306179046151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.897 y[1] (analytic) = 0.2185414424485346025983714806799 y[1] (numeric) = 0.16339382243636444328388148234702 absolute error = 0.055147620012170159314489998332885 relative error = 25.234399203325997606332768708084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.898 y[1] (analytic) = 0.21791787613354185228333124736692 y[1] (numeric) = 0.16259001425346186571230352479713 absolute error = 0.05532786188007998657102772256979 relative error = 25.389317692401986077771140060543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.899 y[1] (analytic) = 0.21729509190060779491828897618233 y[1] (numeric) = 0.16178667773281531841973164845416 absolute error = 0.055508414167792476498557327728168 relative error = 25.545176231215747130989862460142 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9 y[1] (analytic) = 0.21667309037251661153861768428645 y[1] (numeric) = 0.16098381365681831738919200708826 absolute error = 0.055689276715698294149425677198196 relative error = 25.701981090477892336736958703954 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.901 y[1] (analytic) = 0.2160518721712697784020418048673 y[1] (numeric) = 0.16018142280848677148422325476051 absolute error = 0.055870449362783006917818550106784 relative error = 25.859738590227577356510240703397 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.902 y[1] (analytic) = 0.21543143791808544498721276287073 y[1] (numeric) = 0.15937950597145819943303293360787 absolute error = 0.056051931946627245554179829262857 relative error = 26.018455100290491154213355968126 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.4MB, time=32.74 NO POLE x[1] = 0.903 y[1] (analytic) = 0.21481178823339781277561126452646 y[1] (numeric) = 0.15857806392999094619104404875997 absolute error = 0.05623372430340686658456721576649 relative error = 26.178137040741761949336697982013 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.904 y[1] (analytic) = 0.21419292373685651481739751871573 y[1] (numeric) = 0.15777709746896339868261546777603 absolute error = 0.0564158262678931161347820509397 relative error = 26.338790882373839958232284940284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.905 y[1] (analytic) = 0.2135748450473259960818298242788 y[1] (numeric) = 0.15697660737387320092272040281605 absolute error = 0.056598237673452795159109421462747 relative error = 26.500423147169417793004461265249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.906 y[1] (analytic) = 0.21295755278288489459287117279202 y[1] (numeric) = 0.15617659443083646851936785380243 absolute error = 0.056780958352048426073503318989586 relative error = 26.663040408779450223007669173371 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.907 y[1] (analytic) = 0.21234104756082542335060273115629 y[1] (numeric) = 0.15537705942658700255755251008508 absolute error = 0.056963988134238420793050221071209 relative error = 26.826649293006335852137888117626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.908 y[1] (analytic) = 0.21172532999765275303906228253193 y[1] (numeric) = 0.15457800314847550286551922659463 absolute error = 0.057147326849177250173543055937301 relative error = 26.991256478292324126238781775481 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.909 y[1] (analytic) = 0.21111040070908439552112491773005 y[1] (numeric) = 0.1537794263844687806641288081537 absolute error = 0.057330974324615614856996109576356 relative error = 27.156868696213211959234153312178 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.91 y[1] (analytic) = 0.21049626031004958812104248212845 y[1] (numeric) = 0.15298132992314897060011245251486 absolute error = 0.05751493038690061752093002961359 relative error = 27.323492731977395154265989275859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.911 y[1] (analytic) = 0.20988290941468867869525749552114 y[1] (numeric) = 0.15218371455371274216400281880514 absolute error = 0.057699194860975936531254676715999 relative error = 27.491135424930340697387220229263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.912 y[1] (analytic) = 0.20927034863635251149210647403642 y[1] (numeric) = 0.15138658106597051049353030338024 absolute error = 0.05788376757038200099857617065618 relative error = 27.659803669064546916459522292803 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.913 y[1] (analytic) = 0.2086585785876018138010267943691 y[1] (numeric) = 0.15058993025034564656327371962663 absolute error = 0.058068648337256167237753074742464 relative error = 27.829504413535059427072421180697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.914 y[1] (analytic) = 0.20804759988020658339188045106857 y[1] (numeric) = 0.1497937628978736867613551919947 absolute error = 0.05825383698233289663052525907387 relative error = 28.000244663180611730768328815754 % h = 0.001 TOP MAIN SOLVE Loop memory used=267.0MB, alloc=4.4MB, time=33.21 NO POLE x[1] = 0.915 y[1] (analytic) = 0.20743741312514547674500726750837 y[1] (numeric) = 0.14899807980020154185396968750252 absolute error = 0.058439333324943934891037580005848 relative error = 28.172031479050460288871014445922 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.916 y[1] (analytic) = 0.20682801893260519807261933043264 y[1] (numeric) = 0.14820288174958670533854022011457 absolute error = 0.058625137183018492734079110318072 relative error = 28.344871978936984868018929645867 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.917 y[1] (analytic) = 0.20621941791197988913214762663437 y[1] (numeric) = 0.14740816953889646118629037477428 absolute error = 0.058811248373083427945857251860091 relative error = 28.518773337914125941350871471793 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.918 y[1] (analytic) = 0.20561161067187051983215106836788 y[1] (numeric) = 0.14661394396160709097502640845195 absolute error = 0.058997666710263428857124659915928 relative error = 28.693742788881731932435433054035 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.919 y[1] (analytic) = 0.20500459782008427963139730153571 y[1] (numeric) = 0.14582020581180308041292179535975 absolute error = 0.059184392008281199218475506175957 relative error = 28.869787623115890107738053034995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.92 y[1] (analytic) = 0.20439837996363396973172389751838 y[1] (numeric) = 0.14502695588417632525409769248314 absolute error = 0.059371424079457644477626205035237 relative error = 29.046915190825315957945571119099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.921 y[1] (analytic) = 0.20379295770873739606528773573527 y[1] (numeric) = 0.1442341949740253366067934097822 absolute error = 0.059558762734712059458494325953065 relative error = 29.225132901713876959088300330922 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.922 y[1] (analytic) = 0.20318833166081676307680958963652 y[1] (numeric) = 0.14344192387725444563492157682601 absolute error = 0.059746407783562317441888012810505 relative error = 29.404448225549327671389047783084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.923 y[1] (analytic) = 0.20258450242449806830142013383096 y[1] (numeric) = 0.14265014339037300765380330423875 absolute error = 0.059934359034125060647616829592212 relative error = 29.584868692738334217407703643868 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.924 y[1] (analytic) = 0.20198147060361049773871279445357 y[1] (numeric) = 0.14185885431049460562087924415598 absolute error = 0.060122616293115892117833550297585 relative error = 29.766401894907867281624663718269 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.925 y[1] (analytic) = 0.20137923680118582202360806866915 y[1] (numeric) = 0.1410680574353362530221930589137 absolute error = 0.060311179365849569001415009755453 relative error = 29.949055485493043891407494324033 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=270.8MB, alloc=4.4MB, time=33.71 x[1] = 0.926 y[1] (analytic) = 0.20077780161945779339463314239777 y[1] (numeric) = 0.14027775356321759615544441142023 absolute error = 0.06050004805624019723918873097754 relative error = 30.132837180331499374629385750323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.927 y[1] (analytic) = 0.20017716565986154346021983793189 y[1] (numeric) = 0.13948794349306011581040919409157 absolute error = 0.060689222166801427649810643840317 relative error = 30.317754758264372042357137313483 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.928 y[1] (analytic) = 0.19957732952303298176362312509717 y[1] (numeric) = 0.13869862802438632834752531586332 absolute error = 0.060878701498646653416097809233856 relative error = 30.503816061743984316308418974538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.929 y[1] (analytic) = 0.19897829380880819514706163098832 y[1] (numeric) = 0.13790980795731898617544296862691 absolute error = 0.061068485851489208971618662361418 relative error = 30.691028997448305210506404896882 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.93 y[1] (analytic) = 0.19838005911622284791568078408935 y[1] (numeric) = 0.13712148409258027762833889547323 absolute error = 0.061258575023642570287341888616112 relative error = 30.879401536902280285054031940629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.931 y[1] (analytic) = 0.19778262604351158280193842876516 y[1] (numeric) = 0.13633365723149102624379478336273 absolute error = 0.061448968812020556558143645402434 relative error = 31.068941717106116417535596119691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.932 y[1] (analytic) = 0.19718599518810742273101194568898 y[1] (numeric) = 0.1355463281759698894420405022767 absolute error = 0.061639667012137533288971443412272 relative error = 31.259657641170609984561817795531 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.933 y[1] (analytic) = 0.19659016714664117338782511274851 y[1] (numeric) = 0.13475949772853255660736351154008 absolute error = 0.061830669418108616780461601208425 relative error = 31.451557478959608312743823615795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.934 y[1] (analytic) = 0.19599514251494082658629213935434 y[1] (numeric) = 0.13397316669229094657248635183912 absolute error = 0.062021975822649880013805787515212 relative error = 31.644649467739695545256067310583 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.935 y[1] (analytic) = 0.19540092188803096444137550485671 y[1] (numeric) = 0.13318733587095240450671473848992 absolute error = 0.062213586017078559934660766366792 relative error = 31.83894191283719537747894744917 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.936 y[1] (analytic) = 0.19480750586013216434455342896323 y[1] (numeric) = 0.1324020060688188982086593677425 absolute error = 0.062405499791313266135894061220733 relative error = 32.034443188302584443356365723994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.937 y[1] (analytic) = 0.19421489502466040474329199864048 y[1] (numeric) = 0.13161717809078621380433514333195 absolute error = 0.062597716933874190938956855308529 relative error = 32.2311617375824114834261123687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=274.6MB, alloc=4.4MB, time=34.19 x[1] = 0.938 y[1] (analytic) = 0.19362308997422647172511617197774 y[1] (numeric) = 0.13083285274234315085144212511004 absolute error = 0.062790237231883320873674046867705 relative error = 32.429106074198818796353135556306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.939 y[1] (analytic) = 0.19303209130063536640687307489267 y[1] (numeric) = 0.13004903082957071685063309540962 absolute error = 0.062983060471064649556239979483049 relative error = 32.62828478243676386859592435804 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.94 y[1] (analytic) = 0.19244189959488571312978020136585 y[1] (numeric) = 0.12926571315914132116457323180685 absolute error = 0.063176186435744391965206969559002 relative error = 32.828706518039040491950138407847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.941 y[1] (analytic) = 0.19185251544716916846085032210711 y[1] (numeric) = 0.12848290053831796834559796715459 absolute error = 0.063369614908851200115252354952518 relative error = 33.030380008909200116534383847768 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.942 y[1] (analytic) = 0.19126393944686983100128410017909 y[1] (numeric) = 0.12770059377495345087277570916175 absolute error = 0.063563345671916380128508391017336 relative error = 33.233314055822475647711354195777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.943 y[1] (analytic) = 0.19067617218256365200242060513652 y[1] (numeric) = 0.12691879367748954129918268238869 absolute error = 0.063757378505074110703237922747838 relative error = 33.437517533144811379881831473563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.944 y[1] (analytic) = 0.19008921424201784678983510968148 y[1] (numeric) = 0.12613750105495618381019774531644 absolute error = 0.063951713187061662979637364365039 relative error = 33.642999389560104268465558498481 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.945 y[1] (analytic) = 0.18950306621219030699617274468771 y[1] (numeric) = 0.12535671671697068519362562412766 absolute error = 0.064146349495219621802547120560051 relative error = 33.849768648805763274116069818004 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.946 y[1] (analytic) = 0.18891772867922901360330577971155 y[1] (numeric) = 0.12457644147373690522245759300852 absolute error = 0.064341287205492108380848186703035 relative error = 34.057834410416695070738737734663 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.947 y[1] (analytic) = 0.18833320222847145079440148678306 y[1] (numeric) = 0.12379667613604444645107921814347 absolute error = 0.06453652609242700434332226863959 relative error = 34.267205850477825991633464030851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.948 y[1] (analytic) = 0.18774948744444402061648673536087 y[1] (numeric) = 0.12301742151526784342573536912772 absolute error = 0.06473206592917617719075136623315 relative error = 34.477892222385271696515097606745 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.949 y[1] (analytic) = 0.18716658491086145845409465583714 y[1] (numeric) = 0.12223867842336575131006328726458 absolute error = 0.064927906487495707144031368572566 relative error = 34.689902857616267676733991028843 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.4MB, time=34.67 NO POLE x[1] = 0.95 y[1] (analytic) = 0.18658449521062624931457789789744 y[1] (numeric) = 0.12146044767288013392650508514724 absolute error = 0.065124047537746115388072812750206 relative error = 34.903247166507975377193254291055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.951 y[1] (analytic) = 0.18600321892582804492567219837358 y[1] (numeric) = 0.12068273007693545121441163604475 absolute error = 0.065320488848892593711260562328823 relative error = 35.117934639045280401714461152317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.952 y[1] (analytic) = 0.1854227566377430816458931609772 y[1] (numeric) = 0.11990552644923784610565039492055 absolute error = 0.065517230188505235540242766056643 relative error = 35.333974845657700984425353949165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.953 y[1] (analytic) = 0.18484310892683359918834833746895 y[1] (numeric) = 0.11912883760407433081853027540796 absolute error = 0.065714271322759268369818062060988 relative error = 35.551377438025526653626517947667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.954 y[1] (analytic) = 0.18426427637274726015854588640262 y[1] (numeric) = 0.11835266435631197257085728875005 absolute error = 0.065911612016435287587688597652571 relative error = 35.770152149895308787043798162324 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.955 y[1] (analytic) = 0.18368625955431657040678027158725 y[1] (numeric) = 0.1175770075213970787129352315803 absolute error = 0.066109252032919491693845040006958 relative error = 35.990308797904826558904059169708 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.956 y[1] (analytic) = 0.18310905904955830019567464783323 y[1] (numeric) = 0.11680186791535438128132628947547 absolute error = 0.066307191134203918914348358357762 relative error = 36.211857282417653610408508580295 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.957 y[1] (analytic) = 0.18253267543567290618345876639169 y[1] (numeric) = 0.11602724635478622097418700245217 absolute error = 0.066505429080886685209271763939523 relative error = 36.434807588367452636455317680136 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.958 y[1] (analytic) = 0.18195710928904395422356041676126 y[1] (numeric) = 0.1152531436568717305489956170031 absolute error = 0.066703965632172223674564799758157 relative error = 36.659169786112126973427332441083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.959 y[1] (analytic) = 0.18138236118523754298108760522243 y[1] (numeric) = 0.11447956063936601764348742687759 absolute error = 0.066902800545871525337600178344839 relative error = 36.884954032297960196067708347141 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.96 y[1] (analytic) = 0.18080843169900172836677785356957 y[1] (numeric) = 0.11370649812059934702061528160302 absolute error = 0.067101933578402381346162571966552 relative error = 37.112170570733876686483767460061 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.961 y[1] (analytic) = 0.18023532140426594878899018404309 y[1] (numeric) = 0.11293395691947632223835301771841 absolute error = 0.067301364484789626550637166324682 relative error = 37.340829733275958125725956631909 % h = 0.001 TOP MAIN SOLVE Loop memory used=282.2MB, alloc=4.4MB, time=35.13 NO POLE x[1] = 0.962 y[1] (analytic) = 0.17966303087414045122431453842204 y[1] (numeric) = 0.11216193785547506674516014284862 absolute error = 0.067501093018665384479154395573423 relative error = 37.570941940722352878774660800247 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.963 y[1] (analytic) = 0.17909156068091571810737256061982 y[1] (numeric) = 0.11139044174864640440192667708617 absolute error = 0.06770111893226931370544588353365 relative error = 37.802517703718717297734709390071 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.964 y[1] (analytic) = 0.1785209113960618950403828529345 y[1] (numeric) = 0.11061946941961303943121762966763 absolute error = 0.067901441976448855609165223266866 relative error = 38.035567623674330056199609961355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.965 y[1] (analytic) = 0.17795108359022821932306299634073 y[1] (numeric) = 0.10984902168956873579463716163164 absolute error = 0.068102061900659483528425834709083 relative error = 38.27010239368902275073100163893 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.966 y[1] (analytic) = 0.17738207783324244930343980487371 y[1] (numeric) = 0.10907909938027749599913305702616 absolute error = 0.068302978452964953304306747847543 relative error = 38.506132799491072163842203957281 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.967 y[1] (analytic) = 0.17681389469411029455013846324732 y[1] (numeric) = 0.10830970331407273933306269629194 absolute error = 0.068504191380037555217075766955374 relative error = 38.743669720386201777429490160584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.968 y[1] (analytic) = 0.1762465347410148468467203753698 y[1] (numeric) = 0.10754083431385647953284229568779 absolute error = 0.068705700427158367313878079682012 relative error = 38.982724130217842356925343900132 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.969 y[1] (analytic) = 0.17567999854131601200863872937179 y[1] (numeric) = 0.1067724932030985018810017460399 absolute error = 0.068907505338217510127636983331894 relative error = 39.223307098338803695232315274424 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.97 y[1] (analytic) = 0.17511428666154994252337996214366 y[1] (numeric) = 0.10600468080583553973646795269174 absolute error = 0.069109605855714402786912009451914 relative error = 39.465429790594511912425661800222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.971 y[1] (analytic) = 0.17454939966742847101435848319357 y[1] (numeric) = 0.1052373979466704504979001463027 absolute error = 0.069312001720758020516458336890868 relative error = 39.709103470317969052993159978809 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.972 y[1] (analytic) = 0.17398533812383854452913119388423 y[1] (numeric) = 0.1044706454507713910009012010913 absolute error = 0.069514692673067153528229992792931 relative error = 39.954339499336594107730957989879 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=286.1MB, alloc=4.4MB, time=35.61 x[1] = 0.973 y[1] (analytic) = 0.17342210259484165965249751378665 y[1] (numeric) = 0.10370442414387099234992956324311 absolute error = 0.069717678450970667302567950543536 relative error = 40.201149338991107013069312107609 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.974 y[1] (analytic) = 0.17285969364367329844504980100387 y[1] (numeric) = 0.10293873485226553418573695750261 absolute error = 0.069920958791407764259312843501252 relative error = 40.449544551166619647310577955472 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.975 y[1] (analytic) = 0.17229811183274236520773822786723 y[1] (numeric) = 0.10217357840281411838915760444248 absolute error = 0.070124533429928246818580623424747 relative error = 40.699536799336100351788175181666 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.976 y[1] (analytic) = 0.17173735772363062407301334739332 y[1] (numeric) = 0.10140895562293784222207524455221 absolute error = 0.070328402100692781850938102841108 relative error = 40.951137849616381056079200321645 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.977 y[1] (analytic) = 0.17117743187709213742310875931219 y[1] (numeric) = 0.10064486734061897090639482811018 absolute error = 0.070532564536473166516713931202008 relative error = 41.204359571836878680920586580419 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.978 y[1] (analytic) = 0.17061833485305270513602545733743 y[1] (numeric) = 0.099881314384400109641846291798537 absolute error = 0.070737020468652595494179165538891 relative error = 41.459213940621205131201079476224 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.979 y[1] (analytic) = 0.17006006721060930465977861164691 y[1] (numeric) = 0.099118297583383375063448404188019 absolute error = 0.070941769627225929596330207458887 relative error = 41.715713036481842875157270038261 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.98 y[1] (analytic) = 0.16950262950802953191546671228085 y[1] (numeric) = 0.098355817767229566139461222559958 absolute error = 0.071146811740799965776005489720896 relative error = 41.973869046928065835536903659626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.981 y[1] (analytic) = 0.16894602230275104302972217034147 y[1] (numeric) = 0.097593875766157334510656263043824 absolute error = 0.071352146536593708519065907297651 relative error = 42.233694267587288094869384437657 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.982 y[1] (analytic) = 0.168390246151380996897101644497 y[1] (numeric) = 0.096832472410942354271734044731043 absolute error = 0.07155777374043864262536759976596 relative error = 42.495201103340025740982248818754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.983 y[1] (analytic) = 0.1678353016096954985729735303534 y[1] (numeric) = 0.096071608532916491195719226278346 absolute error = 0.071763693076779007377254304075056 relative error = 42.758402069468660051421914726077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.984 y[1] (analytic) = 0.16728118923263904349745921975985 y[1] (numeric) = 0.095311284963966971402164110536276 absolute error = 0.07196990426867207209529510922357 relative error = 43.02330979282019313739425177553 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=289.9MB, alloc=4.4MB, time=36.09 x[1] = 0.985 y[1] (analytic) = 0.16672790957432396255098390606041 y[1] (numeric) = 0.094551502536535549469991848930091 absolute error = 0.07217640703778841308099205713032 relative error = 43.289937012983190140171408997919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.986 y[1] (analytic) = 0.16617546318802986794199187969491 y[1] (numeric) = 0.093792262083617675995811232680511 absolute error = 0.072383201104412191946180647014398 relative error = 43.558296583479105096571161639385 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.987 y[1] (analytic) = 0.16562385062620309992738042638742 y[1] (numeric) = 0.093033564438761664598535512480165 absolute error = 0.072590286187441435328844913907252 relative error = 43.828401472968190666078852902669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.988 y[1] (analytic) = 0.16507307244045617436620560744248 y[1] (numeric) = 0.092275410436067858371138241937491 absolute error = 0.072797662004388315995067365504986 relative error = 44.100264766470195041445080214722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.989 y[1] (analytic) = 0.16452312918156723110721236839716 y[1] (numeric) = 0.091517800910187795780379692962793 absolute error = 0.073005328271379435326832675434363 relative error = 44.373899666600052548170548953859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.99 y[1] (analytic) = 0.16397402139947948321074058845289 y[1] (numeric) = 0.090760736696323376015337943300518 absolute error = 0.073213284703156107195402645152371 relative error = 44.64931949481877767722006503512 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.991 y[1] (analytic) = 0.16342574964330066700555784873517 y[1] (numeric) = 0.090004218630226023785579287607129 absolute error = 0.073421531013074643219978561128037 relative error = 44.926537692699775590649148830874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.992 y[1] (analytic) = 0.16287831446130249298116886250245 y[1] (numeric) = 0.089248247548195853569803173834546 absolute error = 0.073630066913106639411365688667905 relative error = 45.205567823210785492660014382712 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.993 y[1] (analytic) = 0.16233171640092009751615067494915 y[1] (numeric) = 0.088492824287080833315797416204579 absolute error = 0.07383889211383926420035325874457 relative error = 45.486423572011676670032058005586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.994 y[1] (analytic) = 0.16178595600875149544306190422175 y[1] (numeric) = 0.087737949684275947592539984749456 absolute error = 0.074048006324475547850521919472289 relative error = 45.769118748768320477022040324905 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.995 y[1] (analytic) = 0.16124103383055703345047345869323 y[1] (numeric) = 0.086983624577722360195284219246906 absolute error = 0.074257409252834673255189239446327 relative error = 46.053667288482765071850964425227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.996 y[1] (analytic) = 0.16069695041125884432266732841958 y[1] (numeric) = 0.086229849805906576204464862394804 absolute error = 0.074467100605352268118202466024778 relative error = 46.340083252839943305962564563342 % h = 0.001 TOP MAIN SOLVE Loop memory used=293.7MB, alloc=4.4MB, time=36.57 NO POLE x[1] = 0.997 y[1] (analytic) = 0.16015370629494030201754921103397 y[1] (numeric) = 0.085476626207859603499262853249529 absolute error = 0.074677080087080698518286357784436 relative error = 46.628380831571147824551365731108 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.998 y[1] (analytic) = 0.15961130202484547758331989412072 y[1] (numeric) = 0.084723954623156113726667367293348 absolute error = 0.074887347401689363856652526827369 relative error = 46.918574343834511158640786135546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.999 y[1] (analytic) = 0.15906973814337859591444947735228 y[1] (numeric) = 0.083971835891913602726874133998877 absolute error = 0.075097902251464993187575343353408 relative error = 47.210678239612732376493933631973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1 y[1] (analytic) = 0.1585290151921034933474976783697 y[1] (numeric) = 0.083220270854791550415859606422339 absolute error = 0.075308744337311942931638071947362 relative error = 47.504707101128295716638256518268 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.001 y[1] (analytic) = 0.15798913371174307609732262654106 y[1] (numeric) = 0.082469260352990580125971100181439 absolute error = 0.075519873358752495971351526359617 relative error = 47.800675644276430547583781345176 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.002 y[1] (analytic) = 0.15745009424217877953421970834405 y[1] (numeric) = 0.081718805228251617405373561157651 absolute error = 0.075731289013927162128846147186398 relative error = 48.098598720076065991744729537216 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.003 y[1] (analytic) = 0.15691189732245002830253118718872 y[1] (numeric) = 0.080968906322855048277194162406065 absolute error = 0.075942990999594980025337024782653 relative error = 48.398491316139037614495603934759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.004 y[1] (analytic) = 0.15637454349075369728126647902573 y[1] (numeric) = 0.080219564479619876959206471058045 absolute error = 0.076154979011133820322060007967687 relative error = 48.700368558157807715094111958892 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.005 y[1] (analytic) = 0.15583803328444357338727212307505 y[1] (numeric) = 0.079470780541902883044896465462334 absolute error = 0.076367252742540690342375657612718 relative error = 49.004245711411964965802932683949 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.006 y[1] (analytic) = 0.15530236724002981822148964446015 y[1] (numeric) = 0.078722555353597778146753221428371 absolute error = 0.076579811886432040074736423031776 relative error = 49.310138182293773430389068505769 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.007 y[1] (analytic) = 0.1547675458931784315588386624451 y[1] (numeric) = 0.077974889759134362002627624210835 absolute error = 0.076792656134044069556211038234269 relative error = 49.618061519853045354753118879175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=297.5MB, alloc=4.4MB, time=37.03 x[1] = 1.008 y[1] (analytic) = 0.15423356977871071568226175434684 y[1] (numeric) = 0.077227784603477678046002999806395 absolute error = 0.077005785175233037636258754540449 relative error = 49.928031417361616562252808280691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.009 y[1] (analytic) = 0.15370043943060274056146674103291 y[1] (numeric) = 0.076481240732127168441022095221652 absolute error = 0.077219198698475572120444645811257 relative error = 50.240063713897707805879530880629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.01 y[1] (analytic) = 0.15316815538198480987690121521799 y[1] (numeric) = 0.075735258991115828583115372614898 absolute error = 0.077432896390868981293785842603096 relative error = 50.55417439595046003040083919522 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.011 y[1] (analytic) = 0.15263671816514092788949328854018 y[1] (numeric) = 0.074989840227009361066076116612911 absolute error = 0.077646877938131566823417171927265 relative error = 50.870379599044936181507039991616 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.012 y[1] (analytic) = 0.15210612831150826715669168763168 y[1] (numeric) = 0.074244985286905329116428387657209 absolute error = 0.077861143024602938040263299974472 relative error = 51.188695609387886967542539079666 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.013 y[1] (analytic) = 0.15157638635167663709533748309973 y[1] (numeric) = 0.073500695018432309495934386941233 absolute error = 0.078075691333244327599403096158492 relative error = 51.509138865534582834244119406766 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.014 y[1] (analytic) = 0.15104749281538795339189888850143 y[1] (numeric) = 0.072756970269749044873088330360528 absolute error = 0.078290522545638908518810558140901 relative error = 51.831725960077019355767254224816 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.015 y[1] (analytic) = 0.15051944823153570826059971903376 y[1] (numeric) = 0.072013811889543595664444459911385 absolute error = 0.078505636341992112596155259122376 relative error = 52.156473641353808277913505618132 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.016 y[1] (analytic) = 0.14999225312816444154997125176595 y[1] (numeric) = 0.071271220727032491346627351139285 absolute error = 0.078721032401131950203343900626665 relative error = 52.483398815182071573670921543446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.017 y[1] (analytic) = 0.14946590803246921269835638081839 y[1] (numeric) = 0.070529197631959881239873204556082 absolute error = 0.078936710400509331458483176262304 relative error = 52.812518546611661088778133984582 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.018 y[1] (analytic) = 0.14894041347079507353889411193989 y[1] (numeric) = 0.069787743454596684763951337413885 absolute error = 0.079152670016198388774942774526002 relative error = 53.143850061702031667894643646503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.019 y[1] (analytic) = 0.14841576996863654195451159145488 y[1] (numeric) = 0.069046859045739741167315619843335 absolute error = 0.079368910922896800787195971611545 relative error = 53.477410749322101062018623185294 % h = 0.001 TOP MAIN SOLVE Loop memory used=301.3MB, alloc=4.4MB, time=37.51 NO POLE x[1] = 1.02 y[1] (analytic) = 0.14789197805063707638345001454462 y[1] (numeric) = 0.068306545256710958730336126133973 absolute error = 0.079585432793926117653113888410652 relative error = 53.813218162973435426995528574796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.021 y[1] (analytic) = 0.14736903824058855117584990729276 y[1] (numeric) = 0.067566802939356463443461797854155 absolute error = 0.079802235301232087732388109438601 relative error = 54.15129002263710483330489924835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.022 y[1] (analytic) = 0.14684695106143073280192042586617 y[1] (numeric) = 0.066827632946045747161165440576916 absolute error = 0.080019318115384985640754985289256 relative error = 54.491644216644558920841973451949 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.023 y[1] (analytic) = 0.1463257170352507569122164646183 y[1] (numeric) = 0.06608903612967081523252290019578 absolute error = 0.080236680905579941679693564422515 relative error = 54.834298803572878651213216158589 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.024 y[1] (analytic) = 0.14580533668328260625054651279403 y[1] (numeric) = 0.065351013343645333609278788180324 absolute error = 0.080454323339637272641267724613707 relative error = 55.179272014164766036274749430723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.025 y[1] (analytic) = 0.14528581052590658942003334688506 y[1] (numeric) = 0.064613565441903775432251647634696 absolute error = 0.080672245084002813987781699250367 relative error = 55.526582253273639757441416829728 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.026 y[1] (analytic) = 0.14476713908264882050284879253134 y[1] (numeric) = 0.063876693278900567096931973682789 absolute error = 0.080890445803748253405916818848551 relative error = 55.876248101834210737911596377866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.027 y[1] (analytic) = 0.14424932287218069953414293619066 y[1] (numeric) = 0.063140397709609233799127022510912 absolute error = 0.081108925162571465735015913679749 relative error = 56.228288318858917991668219917233 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.028 y[1] (analytic) = 0.1437323624123183938306873126038 y[1] (numeric) = 0.062404679589521544561506863351919 absolute error = 0.081327682822796849269180449251883 relative error = 56.582721843460611451259799827507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.029 y[1] (analytic) = 0.14321625822002232017475073936883 y[1] (numeric) = 0.061669539774646656741906646793519 absolute error = 0.081546718445375663432844092575312 relative error = 56.939567796901874973318590279753 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.03 y[1] (analytic) = 0.14270101081139662785372561470558 y[1] (numeric) = 0.060934979121510260024240581037194 absolute error = 0.081766031689886367829485033668386 relative error = 57.298845484671389338971502517552 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=305.1MB, alloc=4.4MB, time=37.98 x[1] = 1.031 y[1] (analytic) = 0.14218662070168868255602163874092 y[1] (numeric) = 0.060200998487153719892883625122417 absolute error = 0.081985622214534962663138013618507 relative error = 57.660574398587741808232723186119 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.032 y[1] (analytic) = 0.14167308840528855112374306237812 y[1] (numeric) = 0.059467598729133220591377424663103 absolute error = 0.082205489676155330532365637715018 relative error = 58.024774218931095655680632786934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.033 y[1] (analytic) = 0.14116041443572848716266471103004 y[1] (numeric) = 0.058734780705518907566317531318935 absolute error = 0.082425633730209579596347179711101 relative error = 58.391464816603140111818236093621 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.034 y[1] (analytic) = 0.14064859930568241751002117319736 y[1] (numeric) = 0.058002545274894029397279462042885 absolute error = 0.082646054030788388112741711154474 relative error = 58.760666255315748263157105082912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.035 y[1] (analytic) = 0.14013764352696542956062268605983 y[1] (numeric) = 0.057270893296354079213641668107356 absolute error = 0.082866750230611350346981017952469 relative error = 59.13239879380877772697099273635 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.036 y[1] (analytic) = 0.13962754761053325945181039192184 y[1] (numeric) = 0.056539825629505935599163997014442 absolute error = 0.0830877219810273238526463949074 relative error = 59.506682888097456316619452309823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.037 y[1] (analytic) = 0.1391183120664817811077627805146 y[1] (numeric) = 0.05580934313446700298518074264024 absolute error = 0.083308968932014778122582037874364 relative error = 59.883539193749802453189599952711 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.038 y[1] (analytic) = 0.13860993740404649614366427280568 y[1] (numeric) = 0.055079446671864351533267890348536 absolute error = 0.083530490732182144610396382457143 relative error = 60.262988568194537761855701492385 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.039 y[1] (analytic) = 0.13810242413160202463024604210498 y[1] (numeric) = 0.054350137102833856508244674334943 absolute error = 0.083752287028768168122001367770034 relative error = 60.645052073059957119787749014382 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.04 y[1] (analytic) = 0.13759577275666159671920830788383 y[1] (numeric) = 0.053621415289019337142370074128215 absolute error = 0.083974357467642259576838233755619 relative error = 61.02975097654422939969553906777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.041 y[1] (analytic) = 0.13708998378587654513003247684256 y[1] (numeric) = 0.052893282092571694991595385980471 absolute error = 0.084196701693304850138437090862091 relative error = 61.417106755817610282287279555981 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=309.0MB, alloc=4.4MB, time=38.47 x[1] = 1.042 y[1] (analytic) = 0.13658505772503579849869064437203 y[1] (numeric) = 0.052165738376148051784734512821976 absolute error = 0.084419319348887746713956131550057 relative error = 61.807141099457056795235847747672 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.043 y[1] (analytic) = 0.13608099507906537558875910765756 y[1] (numeric) = 0.05143878500291088676641412353831 absolute error = 0.084642210076154488822344984119249 relative error = 62.199875909913741678938772980715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.044 y[1] (analytic) = 0.13557779635202788036544167926943 y[1] (numeric) = 0.050712422836527173534666338547911 absolute error = 0.084865373515500706830775340721515 relative error = 62.595333306013974283761772738105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.045 y[1] (analytic) = 0.13507546204712199793300772717468 y[1] (numeric) = 0.049986652741167516374027104015354 absolute error = 0.085088809305954481558980623159323 relative error = 62.993535625494043472978707081835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.046 y[1] (analytic) = 0.13457399266668199133614900369011 y[1] (numeric) = 0.049261475581505286085003921530027 absolute error = 0.085312517085176705251145082160079 relative error = 63.394505427569506943750046420231 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.047 y[1] (analytic) = 0.1340733887121771992257584619777 y[1] (numeric) = 0.048536892222715755310777103710461 absolute error = 0.085536496489461443914981358267235 relative error = 63.798265495539460488784676394782 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.048 y[1] (analytic) = 0.13357365068421153438963339426183 y[1] (numeric) = 0.047812903530475233361999228961003 absolute error = 0.085760747153736301027634165300826 relative error = 64.204838839426330007455799183834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.049 y[1] (analytic) = 0.13307477908252298314860436102333 y[1] (numeric) = 0.047089510370960200540557970509273 absolute error = 0.08598526871156278260804639051406 relative error = 64.614248698651738540825007629847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.05 y[1] (analytic) = 0.13257677440598310561859051499973 y[1] (numeric) = 0.046366713610846441963167975889446 absolute error = 0.086210060795136663655422539110283 relative error = 65.026518544749010254090069254214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.051 y[1] (analytic) = 0.1320796371525965368390810578947 y[1] (numeric) = 0.045644514117308180885657973207286 absolute error = 0.086435123035288355953423084687415 relative error = 65.441672084112883126321087844574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.052 y[1] (analytic) = 0.13158336781950048876854170127377 y[1] (numeric) = 0.044922912758017211528819779827619 absolute error = 0.086660455061483277239721921446147 relative error = 65.85973326078701213498703821927 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.053 y[1] (analytic) = 0.13108796690296425314724413619817 y[1] (numeric) = 0.044201910401142031406686387562951 absolute error = 0.086886056501822221740557748635222 relative error = 66.280726259289854945794020461636 % h = 0.001 TOP MAIN SOLVE Loop memory used=312.8MB, alloc=4.4MB, time=38.95 NO POLE x[1] = 1.054 y[1] (analytic) = 0.13059343489838870522801564872615 y[1] (numeric) = 0.043481507915346973158106796012865 absolute error = 0.087111926983041732069908852713289 relative error = 66.704675507479542540947436722349 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.055 y[1] (analytic) = 0.13009977230030580837540515049052 y[1] (numeric) = 0.042761706169791335882485762406986 absolute error = 0.087338066130514472492919388083536 relative error = 67.131605679458347845400221942957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.056 y[1] (analytic) = 0.12960697960237811953376102514534 y[1] (numeric) = 0.042042506034128515980557132139411 absolute error = 0.087564473568249603553203893005933 relative error = 67.561541698517376245346397216046 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.057 y[1] (analytic) = 0.12911505729739829556471532256259 y[1] (numeric) = 0.041323908378505137501059909148805 absolute error = 0.087791148918893158063655413413782 relative error = 67.994508740122112940654829477923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.058 y[1] (analytic) = 0.12862400587728860045456796325345 y[1] (numeric) = 0.040605914073560181994186719395657 absolute error = 0.088018091803728418460381243857789 relative error = 68.430532234939473337709201903773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.059 y[1] (analytic) = 0.12813382583310041339206374558905 y[1] (numeric) = 0.039888523990424117872674813915698 absolute error = 0.088245301842676295519388931673355 relative error = 68.869637871907014175932314346722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.06 y[1] (analytic) = 0.12764451765501373771705407800258 y[1] (numeric) = 0.039171739000718029281410250285927 absolute error = 0.088472778654295708435643827716654 relative error = 69.311851601344974794942666909892 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.061 y[1] (analytic) = 0.12715608183233671074053448747008 y[1] (numeric) = 0.038455559976552744476416382826481 absolute error = 0.088700521855783966264118104643601 relative error = 69.757199638111829894749644543757 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.062 y[1] (analytic) = 0.12666851885350511443654808419172 y[1] (numeric) = 0.037739987790527963714098282477213 absolute error = 0.088928531062977150722449801714504 relative error = 70.205708464804047323688347274672 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.063 y[1] (analytic) = 0.12618182920608188700644429052911 y[1] (numeric) = 0.037025023315731386651615197031882 absolute error = 0.08915680589035050035482909349723 relative error = 70.657404835000756853094060684596 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.064 y[1] (analytic) = 0.12569601337675663531598126989944 y[1] (numeric) = 0.03631066742573783925925365128479 absolute error = 0.089385345951018796056727618614651 relative error = 71.112315776554048569310522063254 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=316.6MB, alloc=4.4MB, time=39.42 x[1] = 1.065 y[1] (analytic) = 0.12521107185134514820575961848314 y[1] (numeric) = 0.035596920994608400245674274643989 absolute error = 0.089614150856736747960085343839149 relative error = 71.570468594925632437932804474598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.066 y[1] (analytic) = 0.12472700511478891067547400927103 y[1] (numeric) = 0.034883784896889526996905930891454 absolute error = 0.089843220217899383678568078379578 relative error = 72.03189087657060377775168710655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.067 y[1] (analytic) = 0.12424381365115461894246860415874 y[1] (numeric) = 0.034171260007612181029961211023237 absolute error = 0.090072553643542437912507393135502 relative error = 72.49661049236907282837161866559 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.068 y[1] (analytic) = 0.1237614979436336963750811754925 y[1] (numeric) = 0.033459347202290952961947835481235 absolute error = 0.090302150741342743413133340011269 relative error = 72.964655601106430311735019530583 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.069 y[1] (analytic) = 0.12328005847454181030126000368204 y[1] (numeric) = 0.032748047356923186995550996592264 absolute error = 0.090532011117618623305709007089775 relative error = 73.436054653003034879757864053617 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.07 y[1] (analytic) = 0.12279949572531838969293674222318 y[1] (numeric) = 0.032037361347988104921762155659108 absolute error = 0.090762134377330284771174586564071 relative error = 73.910836393294122614064993129209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.071 y[1] (analytic) = 0.1223198101765261437266375657173 y[1] (numeric) = 0.031327290052445929640730291901778 absolute error = 0.090992520124080214085907273815523 relative error = 74.389029865860753305655540567221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.072 y[1] (analytic) = 0.12184100230785058122081404023625 y[1] (numeric) = 0.03061783434773700820161208232467 absolute error = 0.091223167960113573019201957911584 relative error = 74.870664416912623098627542795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.073 y[1] (analytic) = 0.12136307259809953095037427866185 y[1] (numeric) = 0.02990899511178093436229797258637 absolute error = 0.091454077486318596588076306075483 relative error = 75.355769698723588239399754244987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.074 y[1] (analytic) = 0.12088602152520266283889406642884 y[1] (numeric) = 0.029200773222975670669891579072919 absolute error = 0.091685248302226992169002487355923 relative error = 75.844375673420760137900693585329 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.075 y[1] (analytic) = 0.12040984956621101002898676542027 y[1] (numeric) = 0.028493169560196670062820341621968 absolute error = 0.091916680006014339966166423798301 relative error = 76.336512616828047726826249037736 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=320.4MB, alloc=4.4MB, time=39.89 x[1] = 1.076 y[1] (analytic) = 0.11993455719729649183130992560556 y[1] (numeric) = 0.027786185002795996995455824713972 absolute error = 0.092148372194500494835854100891591 relative error = 76.832211122365039206341809562245 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.077 y[1] (analytic) = 0.11946014489375143755268565537494 y[1] (numeric) = 0.027079820430601448086122542436891 absolute error = 0.092380324463149989466563112938045 relative error = 77.33150210500213169173912333655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.078 y[1] (analytic) = 0.11898661312998811120381092241007 y[1] (numeric) = 0.026374076723915672289374659142285 absolute error = 0.092612536406072438914436263267784 relative error = 77.834416805272834047944969279335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.079 y[1] (analytic) = 0.11851396237953823708703307734115 y[1] (numeric) = 0.025668954763515290593420393442777 absolute error = 0.092845007616022946493612683898373 relative error = 78.340986793344185304992805846892 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.08 y[1] (analytic) = 0.11804219311505252626466501237524 y[1] (numeric) = 0.024964455430650015243574428053143 absolute error = 0.0930777376844025110210905843221 relative error = 78.851243973146248510370702039668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.081 y[1] (analytic) = 0.11757130580830020390831348654134 y[1] (numeric) = 0.024260579607041768492619101949202 absolute error = 0.093310726201258435415694384592134 relative error = 79.365220586561657695501221584818 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.082 y[1] (analytic) = 0.11710130093016853752969326818436 y[1] (numeric) = 0.023557328174883800878955634409876 absolute error = 0.093543972755284736650737633774485 relative error = 79.882949217676213822640095225484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.083 y[1] (analytic) = 0.11663217895066236609339886385476 y[1] (numeric) = 0.022854702016839809033427102717738 absolute error = 0.093777476933822557059971761137017 relative error = 80.404462797091544143550722044306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.084 y[1] (analytic) = 0.11616394033890363001210472078256 y[1] (numeric) = 0.022152702016043053015695366621534 absolute error = 0.094011238322860576996409354161024 relative error = 80.929794606300858350978118357048 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.085 y[1] (analytic) = 0.11569658556313090202466390769669 y[1] (numeric) = 0.021451329056095473181054603110207 absolute error = 0.094245256507035428843609304586484 relative error = 81.458978282128854246978867741891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.086 y[1] (analytic) = 0.11523011509069891895757439585166 y[1] (numeric) = 0.020750584021066806578564584611294 absolute error = 0.094479531069632112379009811240363 relative error = 81.992047821236845397551292625925 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.087 y[1] (analytic) = 0.11476452938807811437028117875633 y[1] (numeric) = 0.020050467795493702881387302406791 absolute error = 0.094714061592584411488893876349544 relative error = 82.529037584694203399965128548361 % h = 0.001 TOP MAIN SOLVE Loop memory used=324.2MB, alloc=4.4MB, time=40.37 NO POLE x[1] = 1.088 y[1] (analytic) = 0.11429982892085415208478158526382 y[1] (numeric) = 0.019350981264378839850211004856169 absolute error = 0.094948847656475312234570580407651 relative error = 83.069982302617227967155457250785 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.089 y[1] (analytic) = 0.11383601415372746060000025637812 y[1] (numeric) = 0.018652125313190038330646186928822 absolute error = 0.095183888840537422269354069449303 relative error = 83.614917078876579042201171159435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.09 y[1] (analytic) = 0.11337308555051276839139937136395 y[1] (numeric) = 0.017953900827859376785478533576177 absolute error = 0.095419184722653391605920837787773 relative error = 84.163877395874426605176464093316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.091 y[1] (analytic) = 0.1129110435741386400962888235106 y[1] (numeric) = 0.017256308694782305362664284616758 absolute error = 0.095654734879356334733624538893837 relative error = 84.716899119392495734717092413851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.092 y[1] (analytic) = 0.11244988868664701358530016020116 y[1] (numeric) = 0.016559349800816759499953953064993 absolute error = 0.095890538885830254085346207136168 relative error = 85.274018503512206847910219184555 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.093 y[1] (analytic) = 0.11198962134919273792048721577454 y[1] (numeric) = 0.01586302503328227306703079220619 absolute error = 0.096126596315910464853456423568354 relative error = 85.835272195608133875289818070507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.094 y[1] (analytic) = 0.11153024202204311220051547904107 y[1] (numeric) = 0.015167335279959091046050869205313 absolute error = 0.096362906742084021154464609835762 relative error = 86.400697241416026443761856781732 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.095 y[1] (analytic) = 0.11107175116457742529340135022401 y[1] (numeric) = 0.014472281429087281751472064635525 absolute error = 0.096599469735490143541929285588486 relative error = 86.970331090176665950435925966032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.096 y[1] (analytic) = 0.11061414923528649645726155454927 y[1] (numeric) = 0.013777864369365848590059778023537 absolute error = 0.096836284865920647867201776525729 relative error = 87.544211599856849726129548679825 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.097 y[1] (analytic) = 0.11015743669177221684953209169568 y[1] (numeric) = 0.01308408498995184136195757933202 absolute error = 0.097073351701820375487574512363658 relative error = 88.122377042448822320558696182943 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.098 y[1] (analytic) = 0.10970161399074709192511521184868 y[1] (numeric) = 0.012390944180459467103711505234385 absolute error = 0.09731066981028762482140370661429 relative error = 88.704866109349498304055440931551 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=328.0MB, alloc=4.4MB, time=40.85 x[1] = 1.099 y[1] (analytic) = 0.10924668158803378472391202017221 y[1] (numeric) = 0.011698442830959200474137157083529 absolute error = 0.097548238757074584249774863088679 relative error = 89.291717916820846885493743859309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.1 y[1] (analytic) = 0.1087926399385646600481974221283 y[1] (numeric) = 0.011006581831976893683919214633312 absolute error = 0.097786058106587766364278207494984 relative error = 89.882972011532835105708408686432 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 3 ) = sin(x); Iterations = 1000 Total Elapsed Time = 40 Seconds Elapsed Time(since restart) = 40 Seconds Expected Time Remaining = 2 Minutes 38 Seconds Optimized Time Remaining = 2 Minutes 38 Seconds Time to Timeout = 14 Minutes 19 Seconds Percent Done = 20.43 % > quit memory used=328.6MB, alloc=4.4MB, time=40.92