|\^/| 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 > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_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 INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_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 > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > 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 INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, 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 > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 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 INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, 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 > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > 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 INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_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 > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > 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 INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, 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) > global glob_max_terms,array_fact_1; > local ret; > if (nnn <= glob_max_terms) then # if number 13 > if array_fact_1[nnn] = 0 then # if number 14 > ret := nnn!; > array_fact_1[nnn] := ret; > else > ret := array_fact_1[nnn]; > fi;# end if 14 > ; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; factorial_1 := proc(nnn) local ret; global glob_max_terms, array_fact_1; if nnn <= glob_max_terms then if array_fact_1[nnn] = 0 then ret := nnn!; array_fact_1[nnn] := ret else ret := array_fact_1[nnn] end if else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > global glob_max_terms,array_fact_2; > local ret; > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > if array_fact_2[mmm,nnn] = 0 then # if number 14 > ret := factorial_1(mmm)/factorial_1(nnn); > array_fact_2[mmm,nnn] := ret; > else > ret := array_fact_2[mmm,nnn]; > fi;# end if 14 > ; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; factorial_3 := proc(mmm, nnn) local ret; global glob_max_terms, array_fact_2; if nnn <= glob_max_terms and mmm <= glob_max_terms then if array_fact_2[mmm, nnn] = 0 then ret := factorial_1(mmm)/factorial_1(nnn); array_fact_2[mmm, nnn] := ret else ret := array_fact_2[mmm, nnn] end if else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_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,iiif,jjjf, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > INFO, > glob_iolevel, > glob_max_terms, > DEBUGMASSIVE, > DEBUGL, > ALWAYS, > #Top Generate Globals Decl > glob_curr_iter_when_opt, > glob_small_float, > glob_optimal_clock_start_sec, > glob_abserr, > glob_log10_abserr, > glob_last_good_h, > MAX_UNCHANGED, > glob_warned, > glob_unchanged_h_cnt, > glob_initial_pass, > glob_not_yet_finished, > glob_clock_start_sec, > hours_in_day, > djd_debug2, > glob_optimal_start, > glob_relerr, > glob_reached_optimal_h, > glob_percent_done, > glob_orig_start_sec, > glob_dump_analytic, > glob_log10normmin, > glob_iter, > glob_no_eqs, > glob_max_trunc_err, > glob_max_rel_trunc_err, > glob_display_flag, > glob_dump, > glob_max_opt_iter, > glob_smallish_float, > glob_look_poles, > glob_hmin, > sec_in_min, > glob_optimal_expect_sec, > glob_warned2, > glob_large_float, > glob_hmin_init, > glob_disp_incr, > djd_debug, > glob_log10relerr, > glob_current_iter, > glob_max_hours, > centuries_in_millinium, > glob_max_sec, > glob_max_iter, > glob_hmax, > glob_optimal_done, > glob_html_log, > glob_start, > glob_log10_relerr, > glob_h, > glob_not_yet_start_msg, > years_in_century, > days_in_year, > min_in_hour, > glob_subiter_method, > glob_max_minutes, > glob_log10abserr, > glob_normmax, > glob_clock_sec, > glob_almost_1, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_3, > array_const_0D0, > #END CONST > array_tmp0, > array_tmp1, > array_tmp2, > array_type_pole, > array_1st_rel_error, > array_tmp1_g, > array_fact_1, > array_y_init, > array_last_rel_error, > array_m1, > array_pole, > array_norms, > array_y, > array_x, > array_fact_2, > array_real_pole, > array_y_set_initial, > array_complex_pole, > array_poles, > array_y_higher, > array_y_higher_work2, > array_y_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > INFO := 2; > glob_iolevel := 5; > glob_max_terms := 30; > DEBUGMASSIVE := 4; > DEBUGL := 3; > ALWAYS := 1; > glob_curr_iter_when_opt := 0; > glob_small_float := 0.1e-50; > glob_optimal_clock_start_sec := 0.0; > glob_abserr := 0.1e-10; > glob_log10_abserr := 0.1e-10; > glob_last_good_h := 0.1; > MAX_UNCHANGED := 10; > glob_warned := false; > glob_unchanged_h_cnt := 0; > glob_initial_pass := true; > glob_not_yet_finished := true; > glob_clock_start_sec := 0.0; > hours_in_day := 24.0; > djd_debug2 := true; > glob_optimal_start := 0.0; > glob_relerr := 0.1e-10; > glob_reached_optimal_h := false; > glob_percent_done := 0.0; > glob_orig_start_sec := 0.0; > glob_dump_analytic := false; > glob_log10normmin := 0.1; > glob_iter := 0; > glob_no_eqs := 0; > glob_max_trunc_err := 0.1e-10; > glob_max_rel_trunc_err := 0.1e-10; > glob_display_flag := true; > glob_dump := false; > glob_max_opt_iter := 10; > glob_smallish_float := 0.1e-100; > glob_look_poles := false; > glob_hmin := 0.00000000001; > sec_in_min := 60.0; > glob_optimal_expect_sec := 0.1; > glob_warned2 := false; > glob_large_float := 9.0e100; > glob_hmin_init := 0.001; > glob_disp_incr := 0.1; > djd_debug := true; > glob_log10relerr := 0.0; > glob_current_iter := 0; > glob_max_hours := 0.0; > centuries_in_millinium := 10.0; > glob_max_sec := 10000.0; > glob_max_iter := 1000; > glob_hmax := 1.0; > glob_optimal_done := false; > glob_html_log := true; > glob_start := 0; > glob_log10_relerr := 0.1e-10; > glob_h := 0.1; > glob_not_yet_start_msg := true; > years_in_century := 100.0; > days_in_year := 365.0; > min_in_hour := 60.0; > glob_subiter_method := 3; > glob_max_minutes := 0.0; > glob_log10abserr := 0.0; > glob_normmax := 0.0; > glob_clock_sec := 0.0; > glob_almost_1 := 0.9990; > #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 := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > 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 := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_m1:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_real_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_set_initial := Array(0..(2+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work2 := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(4+ 1) ,(0..max_terms+ 1),[]); > 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_type_pole[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_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_norms[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 > ; > ord := 1; > while ord <=max_terms do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_fact_2[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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[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_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_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_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_const_3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_3[1] := 3; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > array_fact_1[iiif] := 0; > array_fact_2[iiif,jjjf] := 0; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > 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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(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)) / (factorial_1(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_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,"2012-06-17T21:02:40-05:00") > ; > 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," 092 ") > ; > logitem_str(html_log_file,"h3sin diffeq.mxt") > ; > logitem_str(html_log_file,"h3sin maple results") > ; > logitem_str(html_log_file,"Mostly affecting speed of factorials") > ; > 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, iiif, jjjf, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global INFO, glob_iolevel, glob_max_terms, DEBUGMASSIVE, DEBUGL, ALWAYS, glob_curr_iter_when_opt, glob_small_float, glob_optimal_clock_start_sec, glob_abserr, glob_log10_abserr, glob_last_good_h, MAX_UNCHANGED, glob_warned, glob_unchanged_h_cnt, glob_initial_pass, glob_not_yet_finished, glob_clock_start_sec, hours_in_day, djd_debug2, glob_optimal_start, glob_relerr, glob_reached_optimal_h, glob_percent_done, glob_orig_start_sec, glob_dump_analytic, glob_log10normmin, glob_iter, glob_no_eqs, glob_max_trunc_err, glob_max_rel_trunc_err, glob_display_flag, glob_dump, glob_max_opt_iter, glob_smallish_float, glob_look_poles, glob_hmin, sec_in_min, glob_optimal_expect_sec, glob_warned2, glob_large_float, glob_hmin_init, glob_disp_incr, djd_debug, glob_log10relerr, glob_current_iter, glob_max_hours, centuries_in_millinium, glob_max_sec, glob_max_iter, glob_hmax, glob_optimal_done, glob_html_log, glob_start, glob_log10_relerr, glob_h, glob_not_yet_start_msg, years_in_century, days_in_year, min_in_hour, glob_subiter_method, glob_max_minutes, glob_log10abserr, glob_normmax, glob_clock_sec, glob_almost_1, array_const_3, array_const_0D0, array_tmp0, array_tmp1, array_tmp2, array_type_pole, array_1st_rel_error, array_tmp1_g, array_fact_1, array_y_init, array_last_rel_error, array_m1, array_pole, array_norms, array_y, array_x, array_fact_2, array_real_pole, array_y_set_initial, array_complex_pole, array_poles, array_y_higher, array_y_higher_work2, array_y_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; INFO := 2; glob_iolevel := 5; glob_max_terms := 30; DEBUGMASSIVE := 4; DEBUGL := 3; ALWAYS := 1; glob_curr_iter_when_opt := 0; glob_small_float := 0.1*10^(-50); glob_optimal_clock_start_sec := 0.; glob_abserr := 0.1*10^(-10); glob_log10_abserr := 0.1*10^(-10); glob_last_good_h := 0.1; MAX_UNCHANGED := 10; glob_warned := false; glob_unchanged_h_cnt := 0; glob_initial_pass := true; glob_not_yet_finished := true; glob_clock_start_sec := 0.; hours_in_day := 24.0; djd_debug2 := true; glob_optimal_start := 0.; glob_relerr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_percent_done := 0.; glob_orig_start_sec := 0.; glob_dump_analytic := false; glob_log10normmin := 0.1; glob_iter := 0; glob_no_eqs := 0; glob_max_trunc_err := 0.1*10^(-10); glob_max_rel_trunc_err := 0.1*10^(-10); glob_display_flag := true; glob_dump := false; glob_max_opt_iter := 10; glob_smallish_float := 0.1*10^(-100); glob_look_poles := false; glob_hmin := 0.1*10^(-10); sec_in_min := 60.0; glob_optimal_expect_sec := 0.1; glob_warned2 := false; glob_large_float := 0.90*10^101; glob_hmin_init := 0.001; glob_disp_incr := 0.1; djd_debug := true; glob_log10relerr := 0.; glob_current_iter := 0; glob_max_hours := 0.; centuries_in_millinium := 10.0; glob_max_sec := 10000.0; glob_max_iter := 1000; glob_hmax := 1.0; glob_optimal_done := false; glob_html_log := true; glob_start := 0; glob_log10_relerr := 0.1*10^(-10); glob_h := 0.1; glob_not_yet_start_msg := true; years_in_century := 100.0; days_in_year := 365.0; min_in_hour := 60.0; glob_subiter_method := 3; glob_max_minutes := 0.; glob_log10abserr := 0.; glob_normmax := 0.; glob_clock_sec := 0.; glob_almost_1 := 0.9990; 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 := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); 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 := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_last_rel_error := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_y_higher := Array(0 .. 5, 0 .. max_terms + 1, []); array_y_higher_work2 := Array(0 .. 5, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 5, 0 .. max_terms + 1, []); 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_type_pole[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_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_norms[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 ; ord := 1; while ord <= max_terms do term := 1; while term <= max_terms do array_fact_2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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[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_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 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_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_const_3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_3[term] := 0.; term := term + 1 end do; array_const_3[1] := 3; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; iiif := 0; while iiif <= glob_max_terms do jjjf := 0; while jjjf <= glob_max_terms do array_fact_1[iiif] := 0; array_fact_2[iiif, jjjf] := 0; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; 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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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)/factorial_1(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, "2012-06-17T21:02:40-05:00"); 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, " 092 "); logitem_str(html_log_file, "h3sin diffeq.mxt"); logitem_str(html_log_file, "h3sin maple results"); logitem_str(html_log_file, "Mostly affecting speed of factorials"); 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 := 32; 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 = 1.4914949908104782754668e-10 relative error = 1.6587433836415016344597878560899e-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 = 1.19283086783868304056919e-09 relative error = 1.3280580167409736581902476275957e-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 = 4.02457148038907298143648e-09 relative error = 4.4857914783247678103432330721091e-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 = 9.53680208529860182852150e-09 relative error = 1.0641526918361529952906780233972e-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 = 1.862085591315319639904352e-08 relative error = 2.0800943958401506314468058589954e-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 = 3.216696778522516984090806e-08 relative error = 3.5972965398494943843835196698750e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 0.89320405698587811947411929758354 y[1] (numeric) = 0.89320400592160489623564475095711 absolute error = 5.106427322323847454662643e-08 relative error = 5.7169773047779404848022186523825e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=3.1MB, time=0.17 x[1] = 0.108 y[1] (analytic) = 0.89220982958999254164058855096841 y[1] (numeric) = 0.89220975338918498140733402698082 absolute error = 7.620080756023325452398759e-08 relative error = 8.5406823633909849669194387046237e-06 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.109 y[1] (analytic) = 0.89121570998426839130061474694456 y[1] (numeric) = 0.89121560152076333877002838808835 absolute error = 1.0846350505253058635885621e-07 relative error = 1.2170286479178555796032227810242e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 0.89022169916282519133505050991655 y[1] (numeric) = 0.89022155042462719853675370463502 absolute error = 1.4873819799279829680528153e-07 relative error = 1.6707995113203084459296887874179e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 0.88922779811967368035286344632307 y[1] (numeric) = 0.88922760021005785613411950929714 absolute error = 1.9790961582421874393702593e-07 relative error = 2.2256346038968943199875433039140e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 0.88823400784871481868048036989479 y[1] (numeric) = 0.88823375098733056292103267723678 absolute error = 2.5686138425575944769265801e-07 relative error = 2.8918210965359526696478770487819e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 0.8872403293437387944609098003048 y[1] (numeric) = 0.88724000286771441591345525679889 absolute error = 3.2647602437854745454350591e-07 relative error = 3.6796797167688551673023316826587e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 0.88624676359842402986363663600634 y[1] (numeric) = 0.88624635596347224651531672597368 absolute error = 4.0763495178334831991003266e-07 relative error = 4.5995649126912444682500308144949e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 0.8852533116063361874062827912803 y[1] (numeric) = 0.88525281038786050825569194370278 absolute error = 5.0121847567915059084757752e-07 relative error = 5.6618650177050987161249485919863e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 0.88425997436092717638902747574917 y[1] (numeric) = 0.88425936625512916353235705884187 absolute error = 6.0810579801285667041690730e-07 relative error = 6.8770024160863687810780634215384e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 0.88326675285553415944278068185407 y[1] (numeric) = 0.88326602368052156936183663321441 absolute error = 7.2917501259008094404863966e-07 relative error = 8.2554337093829655450382493245461e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 0.88227364808337855919210333203896 y[1] (numeric) = 0.88227278278027436213605622869984 absolute error = 8.6530310419705604710333912e-07 relative error = 9.8076498836479050711420874146738e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 0.88128066103756506503386742263883 y[1] (numeric) = 0.88127964367161734138571570169405 absolute error = 1.01736594772364815172094478e-06 relative error = 0.00011544176477512450233001595464384 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 0.88028779271108064003264938572903 y[1] (numeric) = 0.88028660647277335255049944155919 absolute error = 1.18623830728748214994416984e-06 relative error = 0.00013475573751104118335540216172859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=7.6MB, alloc=4.2MB, time=0.38 x[1] = 0.121 y[1] (analytic) = 0.87929504409679352793384977345972 y[1] (numeric) = 0.8792936713029581687562407828427 absolute error = 1.37279383535917760899061702e-06 relative error = 0.00015612436855814455434355237853437 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 0.87830241618745226029553225167281 y[1] (numeric) = 0.87830083828238037159915881409144 absolute error = 1.57790507188869637343758137e-06 relative error = 0.00017965396004921509456657297520414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 0.8773099099756846637399747708799 y[1] (numeric) = 0.87730810753224123093728679901405 absolute error = 1.80244344343280268797186585e-06 relative error = 0.00020545116645071965845507233306698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 0.87631752645399686732592566296706 y[1] (numeric) = 0.87631547917473458368921241855316 absolute error = 2.04727926228363671324441390e-06 relative error = 0.00023362299628627941292044200368824 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 0.87532526661477231004255729128789 y[1] (numeric) = 0.87532295333304671164025103511715 absolute error = 2.31328172559840230625617074e-06 relative error = 0.00026427681386883463189418168239412 % 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 = 2.60131891453016993558732038e-06 relative error = 0.00029752034104155694738960860796403 % 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 = 2.91225779335979560066691073e-06 relative error = 0.00033346165892755998165522948321995 % 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 = 3.24696420862895662316387513e-06 relative error = 0.00037220920968845961256657876076297 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 0.87135748392582552956727360981603 y[1] (numeric) = 0.87135387762293725526209614622922 absolute error = 3.60630288827430517746358681e-06 relative error = 0.00041387179829183545431245269527588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 0.87036585738030514045879418929169 y[1] (numeric) = 0.87036186624286437771836811294824 absolute error = 3.99113744076274042607634345e-06 relative error = 0.00045855859428764546769035784526497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 0.86937436046891656820031609690237 y[1] (numeric) = 0.86936995813856234040019139132788 absolute error = 4.40233035422780012470557449e-06 relative error = 0.00050637913359364594895296382149525 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 0.86838299418315664155567172956986 y[1] (numeric) = 0.86837815344016103438311114547564 absolute error = 4.84074299560717256058409422e-06 relative error = 0.00055744332028986948316087623338834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 0.86739175951439156367093333907315 y[1] (numeric) = 0.86738645227878178234124677268291 absolute error = 5.30723560978132968656639024e-06 relative error = 0.00061186142842221378741575710399351 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 0.86640065745385592070829249982374 y[1] (numeric) = 0.8663948547865372074259801560821 absolute error = 5.80266731871328231234374164e-06 relative error = 0.0006697441038151947111905049407644 % h = 0.001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.58 NO POLE x[1] = 0.135 y[1] (analytic) = 0.86540968899265169061155654955344 y[1] (numeric) = 0.86540336109653110115334352264966 absolute error = 6.32789612058945821302690378e-06 relative error = 0.00073120236589391700525881298673271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 0.86441885512174725200425323733583 y[1] (numeric) = 0.8644119713428582903002390191561 absolute error = 6.88377888896170401421817973e-06 relative error = 0.00079634760951531681747406127921407 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 0.86342815683197639322133468075391 y[1] (numeric) = 0.86342068566060450280962310983237 absolute error = 7.47117137189041171157092154e-06 relative error = 0.00086529160680873022287643756281342 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 0.86243759511403732147547160042766 y[1] (numeric) = 0.86242950418584623270478989055703 absolute error = 8.09092819108877068170987063e-06 relative error = 0.0009381465090258424473368599480586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 0.86144717095849167215892866552446 y[1] (numeric) = 0.86143842705565060401288840526959 absolute error = 8.74390284106814604026025487e-06 relative error = 0.0010150248484000727981962917599517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 0.86045688535576351828201164829463 y[1] (numeric) = 0.86044745440807523369781004108143 absolute error = 9.43094768828458420160721320e-06 relative error = 0.0010960395400154506721491651464267 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 0.85946673929613838004907694910232 y[1] (numeric) = 0.85945658638216809360258306918546 absolute error = 1.015291397028644649387991686e-05 relative error = 0.0011813038836850383699698019405325 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.142 y[1] (analytic) = 0.85847673376976223457309391585971 y[1] (numeric) = 0.85846582311796737140141238915841 absolute error = 1.091065179486317168152670130e-05 relative error = 0.0012709315658389568096110456893978 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 0.85748686976664052572975024321969 y[1] (numeric) = 0.85747516475650133056150352460455 absolute error = 1.170501013919516824671861514e-05 relative error = 0.0013650366614220705937350770461248 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 0.85649714827663717415209059733904 y[1] (numeric) = 0.85648461143978816931481090830506 absolute error = 1.253683684900483727968903398e-05 relative error = 0.001463733635801389254888028799647 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 0.85550757028947358736667847149108 y[1] (numeric) = 0.85549416331083587863985148511303 absolute error = 1.340697863770872682698637805e-05 relative error = 0.0015671373466832418713231744995793 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 0.85451813679472767007227113628341 y[1] (numeric) = 0.85450382051364209925372565076873 absolute error = 1.431628108557081854548551468e-05 relative error = 0.0016753630460402826189329404064156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 0.85352884878183283456199740572324 y[1] (numeric) = 0.85351358319319397761448853460219 absolute error = 1.526558863885694750887112105e-05 relative error = 0.0017885263820483851998887671952109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.3MB, time=0.79 x[1] = 0.148 y[1] (analytic) = 0.85253970724007701129002779687021 y[1] (numeric) = 0.85252345149546802093401562373987 absolute error = 1.625574460899035601217313034e-05 relative error = 0.0019067434010334844664310881001414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 0.85155071315860165958372651632402 y[1] (numeric) = 0.85153342556742995120150771593771 absolute error = 1.728759117170838221880038631e-05 relative error = 0.0020301305494284239388207382773302 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 0.85056186752640077850227456131236 y[1] (numeric) = 0.85054350555703455821778117752342 absolute error = 1.836196936622028449338378894e-05 relative error = 0.0021588046757398682997794936695795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 0.8495731713323199178427530766738 y[1] (numeric) = 0.84955369161322555164049047214553 absolute error = 1.947971909436620226260452827e-05 relative error = 0.0022928830325253403338328691134598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 0.84858462556505518929467596156972 y[1] (numeric) = 0.8485639838859354120404309150943 absolute error = 2.064167911977725424504647542e-05 relative error = 0.0024324832783804421688446839692869 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 0.84759623121315227774396057131025 y[1] (numeric) = 0.84757438252608524096907059687938 absolute error = 2.184868706703677488997443087e-05 relative error = 0.0025777234799363210687223169157597 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.154 y[1] (analytic) = 0.84660798926500545272732521024132 y[1] (numeric) = 0.84658488768558461003746140851976 absolute error = 2.310157942084268986380172156e-05 relative error = 0.0027287221138674404207962975577886 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 0.84561990070885658003810196121268 y[1] (numeric) = 0.84559549951733140900668008962242 absolute error = 2.440119152517103142187159026e-05 relative error = 0.0028855980689097169587603907951411 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 0.84463196653279413348445324573189 y[1] (numeric) = 0.84460621817521169288995120879599 absolute error = 2.574835758244059450203693590e-05 relative error = 0.0030484706478890856623212842201292 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 0.84364418772475220680098035650535 y[1] (numeric) = 0.84361704381409952806660497426366 absolute error = 2.714391065267873437538224169e-05 relative error = 0.0032174595697605541778732480303044 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 0.84265656527250952571471205067536 y[1] (numeric) = 0.84262797658985683740802376070475 absolute error = 2.858868265268830668828997061e-05 relative error = 0.003392684971657809010605757556271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.159 y[1] (analytic) = 0.84166910016368846016646113768246 y[1] (numeric) = 0.84163901665933324441573222636547 absolute error = 3.008350435521575072891131699e-05 relative error = 0.0035742674109534361474943062359063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 0.84068179338575403668853684031401 y[1] (numeric) = 0.84065016418036591637178688233579 absolute error = 3.162920538812031674995797822e-05 relative error = 0.0037623278673298191826399482724967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 0.83969464592601295093980055114447 y[1] (numeric) = 0.83966141931177940650162196358974 absolute error = 3.322661423354443817858755473e-05 relative error = 0.0039569877448607784314351551389473 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.4MB, time=1.00 NO POLE x[1] = 0.162 y[1] (analytic) = 0.83870765877161258039905244922922 y[1] (numeric) = 0.83867278221338549514950943893021 absolute error = 3.487655822708524954301029901e-05 relative error = 0.0041583688741040149380662128904401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 0.83772083290953999721773628358307 y[1] (numeric) = 0.83768425304598302996679198436486 absolute error = 3.657986355696725094429921821e-05 relative error = 0.0043665935142044237019396993890803 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 0.8367341693266209812329494706565 y[1] (numeric) = 0.836695831971357765113048731667 absolute error = 3.833735526321611990073898950e-05 relative error = 0.0045817843550083408727668418555919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 0.83574766900951903314174549271711 y[1] (numeric) = 0.83570751915228219947035459094216 absolute error = 4.014985723683367139090177495e-05 relative error = 0.0048040645191887900912792564146222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 0.83476133294473438783771542275181 y[1] (numeric) = 0.83471931475251541387079493292766 absolute error = 4.201819221897396692048982415e-05 relative error = 0.005033557564381793582907415765995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 0.83377516211860302791083523922592 y[1] (numeric) = 0.83373121893680290733739840349684 absolute error = 4.394318180012057343683572908e-05 relative error = 0.0052703874853338140452540967042629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 0.83278915751729569731156543076966 y[1] (numeric) = 0.83274323187087643233865162942154 absolute error = 4.592564641926497291380134812e-05 relative error = 0.0055146787160603938068641605210742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 0.83180332012681691518018922661023 y[1] (numeric) = 0.8317553537214538290567605608644 absolute error = 4.796640536308612342866574583e-05 relative error = 0.0057665561320160581746546696461819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.17 y[1] (analytic) = 0.83081765093300398984237562332915 y[1] (numeric) = 0.83076758465623885866982418232577 absolute error = 5.006627676513117255144100338e-05 relative error = 0.0060261450522755503304511172311233 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 0.8298321509215260329719532122995 y[1] (numeric) = 0.82977992484392103564808730985772 absolute error = 5.222607760499732386590244178e-05 relative error = 0.0062935712417264655834022395183303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 0.82884682107788297392188064494727 y[1] (numeric) = 0.82879237445417545906444017827828 absolute error = 5.444662370751485744046666899e-05 relative error = 0.0065689609132733532346435157094545 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 0.82786166238740457422439940478408 y[1] (numeric) = 0.82780493365766264291933350787231 absolute error = 5.672872974193130506589691177e-05 relative error = 0.006852440730053354763474285219942 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 0.82687667583524944226135438597639 y[1] (numeric) = 0.82681760262602834548027872564984 absolute error = 5.907320922109678107566032655e-05 relative error = 0.0071441378076634475005319058689518 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=22.8MB, alloc=4.4MB, time=1.21 x[1] = 0.175 y[1] (analytic) = 0.82589186240640404810566760804859 y[1] (numeric) = 0.82583038153190339763610400164732 absolute error = 6.148087450065046956360640127e-05 relative error = 0.0074441797163993634130152479778421 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.176 y[1] (analytic) = 0.82490722308568173853495022516409 y[1] (numeric) = 0.82484327054890353026613774600156 absolute error = 6.395253677820826881247916253e-05 relative error = 0.0077526944835062530899560113256574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 0.82392275885772175221823781629032 y[1] (numeric) = 0.82385626985162920062449219759841 absolute error = 6.648900609255159374561869191e-05 relative error = 0.0080698105954411654818870432011156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 0.82293847070698823507683376943031 y[1] (numeric) = 0.82286937961566541773962071999815 absolute error = 6.909109132281733721304943216e-05 relative error = 0.0083956570001474144190394428661288 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 0.82195435961776925582024539899536 y[1] (numeric) = 0.82188260001758156682932340506571 absolute error = 7.175960018768899092199392965e-05 relative error = 0.0087303631093409034054424174605505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 0.82097042657417582165819726030079 y[1] (numeric) = 0.82089593123493123273137656928552 absolute error = 7.449533924458892682069101527e-05 relative error = 0.0090740588008084806630295060543898 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 0.81998667256014089418970594908918 y[1] (numeric) = 0.81990937344625202234996271211679 absolute error = 7.729911388887183974323697239e-05 relative error = 0.0094268744207183968801000562231175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 0.81900309855941840547020049692454 y[1] (numeric) = 0.8189229268310653861180784899444 absolute error = 8.017172835301935212200698014e-05 relative error = 0.0097889407859429386022741125921695 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 0.81801970555558227425767229525488 y[1] (numeric) = 0.81793659156987643847609924320264 absolute error = 8.311398570583578157305205224e-05 relative error = 0.010160389186393310691440799716823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 0.81703649453202542243883830191132 y[1] (numeric) = 0.81695036784417377736667959809221 absolute error = 8.612668785164507215870381911e-05 relative error = 0.010541351387366841769163745220995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 0.81605346647195879163630110379855 y[1] (numeric) = 0.81596425583642930274617064797494 absolute error = 8.921063552948889013045582361e-05 relative error = 0.010931959631906587055601239893317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.186 y[1] (analytic) = 0.81507062235841035999768922853466 y[1] (numeric) = 0.81497825573009803411273520301384 absolute error = 9.236662831232588495402552082e-05 relative error = 0.011332346643173403513253072995248 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 0.81408796317422415916776091581804 y[1] (numeric) = 0.81399236770961792705134357992808 absolute error = 9.559546460623211641733588996e-05 relative error = 0.011742645626830572706789975773401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 0.81310548990205929144445437633573 y[1] (numeric) = 0.81300659196040968879583338685179 absolute error = 9.889794164960264862098948394e-05 relative error = 0.012162990273441047295885278279823 % h = 0.001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.4MB, time=1.41 NO POLE x[1] = 0.189 y[1] (analytic) = 0.81212320352438894711986738208099 y[1] (numeric) = 0.81202092866887659280821774122153 absolute error = 0.00010227485551235431164964085946 relative error = 0.012593514760877397587381922128714 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 0.81114110502349942200714884701869 y[1] (numeric) = 0.81103537802240429237542734136879 absolute error = 0.0001057270010951296317215056499 relative error = 0.013034353756744535086321829557409 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 0.81015919538148913515428487112495 y[1] (numeric) = 0.81004994020936063322367279505988 absolute error = 0.00010925517212850193061207606507 relative error = 0.013485642420815290502369530886513 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 0.80917747558026764674576153393323 y[1] (numeric) = 0.80906461541909546515061459060527 absolute error = 0.00011286016117218159514694332796 relative error = 0.01394751640747892418900889379259 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.193 y[1] (analytic) = 0.80819594660155467619308653584224 y[1] (numeric) = 0.80807940384194045267552907835272 absolute error = 0.00011654275961422351755745748952 relative error = 0.014420111868202647517612048471116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 0.8072146094268791204151515965821 y[1] (numeric) = 0.80709430566920888470765981238246 absolute error = 0.00012030375767023570749178419964 relative error = 0.01490356545400623421710470955301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 0.80623346503757807230941733039465 y[1] (numeric) = 0.80610932109319548323294458403715 absolute error = 0.0001241439443825890764727463575 relative error = 0.015398014317949801242513884911593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 0.80525251441479583941490212666118 y[1] (numeric) = 0.80512445030717621101930946054376 absolute error = 0.00012806410761962839559266611742 relative error = 0.015903596117634839272214541685597 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 0.80427175853948296276795637290694 y[1] (numeric) = 0.80413969350540807834072212341717 absolute error = 0.00013206503407488442723424948977 relative error = 0.016420449017718573474223564626971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 0.80329119839239523595180316432647 y[1] (numeric) = 0.80315505088312894872019778257615 absolute error = 0.00013614750926628723160538175032 relative error = 0.016948711692441735726454972307174 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 0.8023108349540927243408264502072 y[1] (numeric) = 0.80217052263655734369195192314955 absolute error = 0.00014031231753538064887452705765 relative error = 0.017488523328169830024482824542063 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 0.80133066920493878454058737288161 y[1] (numeric) = 0.80118610896289224658289512280376 absolute error = 0.00014456024204653795769225007785 relative error = 0.018040023625947973363090824492118 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 0.80035070212509908402454935910971 y[1] (numeric) = 0.80020181006031290531366615808017 absolute error = 0.00014889206478617871088320102954 relative error = 0.018603352804069394934753852176413 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.4MB, time=1.62 x[1] = 0.202 y[1] (analytic) = 0.79937093469454062096849232708521 y[1] (numeric) = 0.79921762612797863421940059869318 absolute error = 0.00015330856656198674909172839203 relative error = 0.019178651600657677049230422554231 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.203 y[1] (analytic) = 0.79839136789303074428359617456935 y[1] (numeric) = 0.7982335573660286148904330690036 absolute error = 0.00015781052700212939316310556575 relative error = 0.019766061276262821743680502458953 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204 y[1] (analytic) = 0.79741200270013617384917351498742 y[1] (numeric) = 0.79724960397558169603313233594862 absolute error = 0.0001623987245544778160411790388 relative error = 0.02036572361647122762219471296511 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 0.79643284009522202094603142867336 y[1] (numeric) = 0.79626576615873619235106936257652 absolute error = 0.00016707393648582859496206609684 relative error = 0.020977780934529662037363461113677 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 0.79545388105745080889144179581925 y[1] (numeric) = 0.79528204411856968244671944600138 absolute error = 0.00017183693888112644472234981787 relative error = 0.021602376073983314304563072061158 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 0.79447512656578149387669957607767 y[1] (numeric) = 0.79429843805913880574390053805877 absolute error = 0.0001766885066426881327990380189 relative error = 0.022239652411328016222025927741944 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 0.79349657759896848600824819717701 y[1] (numeric) = 0.79331494818547905843115082620718 absolute error = 0.00018162941348942757709737096983 relative error = 0.022889753858676716756528675965204 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.209 y[1] (analytic) = 0.79251823513556067055335101134286 y[1] (numeric) = 0.79233157470360458842624963128062 absolute error = 0.00018666043195608212710138006224 relative error = 0.02355282486644029834571278906337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 0.79154010015390042939128757377236 y[1] (numeric) = 0.79134831782050798936208665755438 absolute error = 0.00019178233339244002920091621798 relative error = 0.024229010426022822863681481065817 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 0.79056217363212266267105329188374 y[1] (numeric) = 0.79036517774416009359408560923756 absolute error = 0.00019699588796256907696768264618 relative error = 0.024918456072531295896632920231282 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.212 y[1] (analytic) = 0.78958445654815381067654078755991 y[1] (numeric) = 0.78938215468350976422938916595147 absolute error = 0.00020230186464404644715162160844 relative error = 0.025621307887500038579928811953133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 0.7886069498797108759001811071231 y[1] (numeric) = 0.78839924884848368617801328799164 absolute error = 0.00020770103122718972216781913146 relative error = 0.0263377125016297568571971201541 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 0.78762965460430044532602270531804 y[1] (numeric) = 0.78741646044998615622617980020169 absolute error = 0.00021319415431428909984290511635 relative error = 0.027067817097541398635865623561489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 0.78665257169921771292322592014294 y[1] (numeric) = 0.78643378969989887213203718110898 absolute error = 0.00021878199931884079118873903396 relative error = 0.027811769412544889931957185396125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=34.3MB, alloc=4.4MB, time=1.83 x[1] = 0.216 y[1] (analytic) = 0.78567570214154550235095044495269 y[1] (numeric) = 0.78545123681108072074398046158368 absolute error = 0.00022446533046478160696998336901 relative error = 0.028569717741422841720086412220419 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 0.78469904690815328987561309286506 y[1] (numeric) = 0.78446880199736756514178211468372 absolute error = 0.00023024491078572473383097818134 relative error = 0.029341810939229319832419495991327 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.218 y[1] (analytic) = 0.78372260697569622750149293613085 y[1] (numeric) = 0.78348648547357203080074679553701 absolute error = 0.00023612150212419670074614059384 relative error = 0.030128198424103770882933528127697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 0.78274638332061416631566068978145 y[1] (numeric) = 0.78250428745548329077910376708827 absolute error = 0.00024209586513087553655692269318 relative error = 0.030929030180100197830677852641269 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 0.78177037691913068004820899454299 y[1] (numeric) = 0.78152220815986684992885182430027 absolute error = 0.00024816875926383011935717024272 relative error = 0.031744456760031679437937849906392 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.221 y[1] (analytic) = 0.78079458874725208884876003870549 y[1] (numeric) = 0.78054024780446432813027250594653 absolute error = 0.00025434094278776071848753275896 relative error = 0.032574629288330328526271035392266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 0.77981901978076648328022674235797 y[1] (numeric) = 0.77955840660799324255032835946411 absolute error = 0.00026061317277324072989838289386 relative error = 0.033419699463922784585367002917838 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.223 y[1] (analytic) = 0.778843670995242748530803510147 y[1] (numeric) = 0.77857668479014678892516400045028 absolute error = 0.00026698620509595960563950969672 relative error = 0.034279819563121336946617390214527 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 0.77786854336602958884516234048672 y[1] (numeric) = 0.77759508257159362186692868428357 absolute error = 0.00027346079443596697823365620315 relative error = 0.035155142442530775395210916059498 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 0.7768936378682545521758298599428 y[1] (numeric) = 0.77661360017397763419514008302846 absolute error = 0.00028003769427691798068977691434 relative error = 0.036045821541971065761533226177021 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.226 y[1] (analytic) = 0.77591895547682305505572063133211 y[1] (numeric) = 0.7756322378199177352928099362415 absolute error = 0.00028671765690531976291069509061 relative error = 0.036952010887415948704693760146982 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.227 y[1] (analytic) = 0.77494449716641740769280186292349 y[1] (numeric) = 0.77465099573300762848755321953471 absolute error = 0.00029350143340977920524864338878 relative error = 0.037873865093947560578164464544106 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.228 y[1] (analytic) = 0.7739702639114958392878644239937 y[1] (numeric) = 0.77366987413781558745790344976863 absolute error = 0.00030038977368025182996097422507 relative error = 0.038811539368727175949840663940098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 0.77299625668629152357637484888623 y[1] (numeric) = 0.77268887325988423166505772054097 absolute error = 0.00030738342640729191131712834526 relative error = 0.039765189513982172036365884788012 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.04 NO POLE x[1] = 0.23 y[1] (analytic) = 0.77202247646481160459538278763993 y[1] (numeric) = 0.77170799332573030081027603620717 absolute error = 0.00031448313908130378510675143276 relative error = 0.040734971930009316004343423062407 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 0.77104892422083622267645813619863 y[1] (numeric) = 0.77072723456284442831816048701474 absolute error = 0.00032168965799179435829764918389 relative error = 0.041721043618194476789131866121891 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 0.77007560092791754066563185318355 y[1] (numeric) = 0.76974659719969091384604078205335 absolute error = 0.0003290037282266268195910711302 relative error = 0.042723562184048863785333933740203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 0.76910250755937877037131424320659 y[1] (numeric) = 0.76876608146570749481969363061609 absolute error = 0.0003364260936712755516206125905 relative error = 0.043742685840261895471882607183426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 0.7681296450883131992411642587249 y[1] (numeric) = 0.7677856875913051169956244362336 absolute error = 0.0003439574970080822455398224913 relative error = 0.044778573409770801748850690833106 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.235 y[1] (analytic) = 0.7671570144875832172688831434866 y[1] (numeric) = 0.76680541580786770405014074108016 absolute error = 0.00035159867971551321874240240644 relative error = 0.045831384328847064482805232298618 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 0.76618461672981934413190551069257 y[1] (numeric) = 0.76582526634775192619544783165915 absolute error = 0.00035935038206741793645767903342 relative error = 0.046901278650199801482742563500447 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 0.76521245278741925656096071810253 y[1] (numeric) = 0.76484523944428696782299788965297 absolute error = 0.00036721334313228873796282844956 relative error = 0.047988417046096199859419486644066 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 0.76424052363254681594247717044265 y[1] (numeric) = 0.76386533533177429417432504456891 absolute error = 0.00037518830077252176815212587374 relative error = 0.049092960811499105457288108298033 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 0.76326883023713109615480194662958 y[1] (numeric) = 0.76288555424548741703959965732646 absolute error = 0.00038327599164367911520228930312 relative error = 0.05021507186722187579029324380439 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 0.76229737357286541163920791551018 y[1] (numeric) = 0.76190589642167165948413613621231 absolute error = 0.00039147715119375215507177929787 relative error = 0.051354912763100604660549826563914 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 0.76132615461120634570666026902879 y[1] (numeric) = 0.76092636209754391960308955867549 absolute error = 0.0003997925136624261035707103533 relative error = 0.052512646681183827392431453084195 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 0.76035517432337277908131416597463 y[1] (numeric) = 0.75994695151129243330457734424653 absolute error = 0.0004082228120803457767368217281 relative error = 0.053688437438939816373918606441399 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=41.9MB, alloc=4.4MB, time=2.25 x[1] = 0.243 y[1] (analytic) = 0.75938443368034491868171494273065 y[1] (numeric) = 0.758967664902076536121463195439 absolute error = 0.00041676877826838256025174729165 relative error = 0.05488244949248157736222520495795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 0.7584139336528633266406721097428 y[1] (numeric) = 0.75798850251002642405204149482978 absolute error = 0.00042543114283690258863061491302 relative error = 0.05609484793980965778179434599121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 0.7574436752114279495647781137546 y[1] (numeric) = 0.75700946457624291342986131761369 absolute error = 0.00043421063518503613491679614091 relative error = 0.057325798524072879019778337700716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 0.75647365932629714803454260620757 y[1] (numeric) = 0.75603055134279719982293018978843 absolute error = 0.00044310798349994821161241641914 relative error = 0.058575467636847105507144674237705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.247 y[1] (analytic) = 0.75550388696748672634611271759229 y[1] (numeric) = 0.75505176305273061596253869274601 absolute error = 0.00045212391475611038357402484628 relative error = 0.059844022321432164162629314780095 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 0.75453435910476896249554959594889 y[1] (numeric) = 0.75407309995005438870194798542588 absolute error = 0.00046125915471457379360161052301 relative error = 0.061131630276167028571942745281718 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 0.75356507670767163840663122515975 y[1] (numeric) = 0.75309456227974939500518328532202 absolute error = 0.00047051442792224340144793983773 relative error = 0.062438459857763383075974577179255 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 0.75259604074547707040315129515061 y[1] (numeric) = 0.7521161502877659169661773195301 absolute error = 0.00047989045771115343697397562051 relative error = 0.063764680084657682749291090345194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.251 y[1] (analytic) = 0.75162725218722113992668365162059 y[1] (numeric) = 0.75113786422102339585850872667092 absolute error = 0.00048938796619774406817492494967 relative error = 0.065110460640381826064029861268874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.252 y[1] (analytic) = 0.75065871200169232450078160745575 y[1] (numeric) = 0.75015970432741018521598135993121 absolute error = 0.00049900767428213928480024752454 relative error = 0.066475971876952557854419621442771 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 0.74969042115743072894258115154618 y[1] (numeric) = 0.74918167085578330294429141062185 absolute error = 0.00050875030164742599828974092433 relative error = 0.067861384818279721023645446841154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 0.7487223806227271168227768433228 y[1] (numeric) = 0.74820376405596818246403024056583 absolute error = 0.00051861656675893435874660275697 relative error = 0.069266871163593476267693465262219 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 0.74775459136562194217493893295701 y[1] (numeric) = 0.7472259841787584228852717802923 absolute error = 0.00052860718686351928966715266471 relative error = 0.070692603290890609930200163988153 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 0.7467870543539043814551399978256 y[1] (numeric) = 0.74624833147591553821399431842857 absolute error = 0.00053872287798884324114567939703 relative error = 0.072138754260400050948254272231358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=45.7MB, alloc=4.4MB, time=2.46 x[1] = 0.257 y[1] (analytic) = 0.74581977055511136575285913553355 y[1] (numeric) = 0.74527080620016870559058747584725 absolute error = 0.0005489643549426601622716596863 relative error = 0.073605497818067718701609779238336 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.258 y[1] (analytic) = 0.74485274093652661325413150250981 y[1] (numeric) = 0.7442934086052145125606961260407 absolute error = 0.00055933233131210069343537646911 relative error = 0.075093008399060824436923144791903 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 0.74388596646517966195791073494597 y[1] (numeric) = 0.74331613894571670337865399085776 absolute error = 0.00056982751946295857925674408821 relative error = 0.076601461131291749804482901381477 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.26 y[1] (analytic) = 0.74291944810784490264661153563478 y[1] (numeric) = 0.742338997477305924343760608148 absolute error = 0.00058045063053897830285092748678 relative error = 0.078131031838961626917512900756906 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 0.74195318683104061211179945608533 y[1] (numeric) = 0.74136198445657946816965633501532 absolute error = 0.00059120237446114394214312107001 relative error = 0.079681897046123745223559218995088 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 0.74098718360102798663599464814456 y[1] (numeric) = 0.74038510014110101738705101728463 absolute error = 0.00060208345992696924894363085993 relative error = 0.081254233980266911363773538526988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 0.74002143938381017573155610324072 y[1] (numeric) = 0.73940834478940038678006292243147 absolute error = 0.00061309459440978895149318080925 relative error = 0.082848220575918889089141551090852 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 0.73905595514513131613761264028424 y[1] (numeric) = 0.73843171866097326485642549961429 absolute error = 0.00062423648415805128118714066995 relative error = 0.0844640354782700472029329994504 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 0.73809073185047556607600664521424 y[1] (numeric) = 0.73745522201628095435182049658095 absolute error = 0.00063550983419461172418614863329 relative error = 0.086101858046817344405930379404667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 0.73712577046506613976721630616662 y[1] (numeric) = 0.73647885511675011176859692909486 absolute error = 0.00064691534831602799861937707176 relative error = 0.087761868359028780835386598705285 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.267 y[1] (analytic) = 0.73616107195386434220722182826113 y[1] (numeric) = 0.73550261822477248594913636413989 absolute error = 0.00065845372909185625808546412124 relative error = 0.089444247214028447010229143062326 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 0.73519663728156860420628085106048 y[1] (numeric) = 0.73452651160370465568412594351719 absolute error = 0.00067012567786394852215490754329 relative error = 0.091149176136302301823831209738816 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 0.73423246741261351769057802984597 y[1] (numeric) = 0.73355053551786776635600153953885 absolute error = 0.00068193189474575133457649030712 relative error = 0.09287683737942481216177109225144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.27 y[1] (analytic) = 0.73326856331116887126771347897946 y[1] (numeric) = 0.73257469023254726561782439935344 absolute error = 0.00069387307862160564988907962602 relative error = 0.094627413929806587665462673434968 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=2.67 NO POLE x[1] = 0.271 y[1] (analytic) = 0.73230492594113868605699451178298 y[1] (numeric) = 0.73159897601399263810785559900464 absolute error = 0.00070594992714604794913891277834 relative error = 0.096401089510463145113425636402114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 0.73134155626616025178549484656383 y[1] (numeric) = 0.73062339312941713920009359262648 absolute error = 0.00071816313674311258540125393735 relative error = 0.09819804858480493785033795561417 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.273 y[1] (analytic) = 0.73037845524960316315084518264563 y[1] (numeric) = 0.72964794184699752779104110621543 absolute error = 0.0007305134026056353598040764302 relative error = 0.10001847636044878665994000663072 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.274 y[1] (analytic) = 0.72941562385456835645171878353456 y[1] (numeric) = 0.72867262243587379812296858919018 absolute error = 0.00074300141869455832875019434438 relative error = 0.1018625587930508494514044630659 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 0.72845306304388714648697543665472 y[1] (numeric) = 0.72769743516614891064394240045328 absolute error = 0.00075562787773823584303303620144 relative error = 0.10373048259016126811001487593877 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.276 y[1] (analytic) = 0.72749077378012026372442689042862 y[1] (numeric) = 0.72672238030888852190488686890407 absolute error = 0.00076839347123174181954002152455 relative error = 0.10562243521510063185197491660942 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.277 y[1] (analytic) = 0.72652875702555689174018659985692 y[1] (numeric) = 0.72574745813612071349395033131833 absolute error = 0.00078129888943617824623626853859 relative error = 0.10753860489085839741996679780726 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 0.72556701374221370492956634116763 y[1] (numeric) = 0.72477266892083572000844621320595 absolute error = 0.00079434482137798492112012796168 relative error = 0.10947918060401340746075908828946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 0.72460554489183390649048198455785 y[1] (numeric) = 0.72379801293698565606464118068301 absolute error = 0.00080753195484825042584080387484 relative error = 0.11144435210867664943879936382874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 0.72364435143588626668033044154215 y[1] (numeric) = 0.72282349045948424234566335354719 absolute error = 0.00082086097640202433466708799496 relative error = 0.11343430993045639846038489442209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 0.72268343433556416134729952995054 y[1] (numeric) = 0.72184910176420653068780453162564 absolute error = 0.0008343325713576306594949983249 relative error = 0.11544924537044588841175450978846 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.282 y[1] (analytic) = 0.72172279455178461073707222518593 y[1] (numeric) = 0.72087484712798862820549134807006 absolute error = 0.00084794742379598253158087711587 relative error = 0.11748935050923365685135722598074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.283 y[1] (analytic) = 0.72076243304518731857588649095688 y[1] (numeric) = 0.7199007268286274204552012246049 absolute error = 0.00086170621655989812068526635198 relative error = 0.11955481821093671014169913356523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=53.4MB, alloc=4.4MB, time=2.88 x[1] = 0.284 y[1] (analytic) = 0.71980235077613371143091160634557 y[1] (numeric) = 0.7189267411448802936385999647896 absolute error = 0.00087560963125341779231164155597 relative error = 0.12164584212725665635962109238854 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 0.71884254870470597834890162875478 y[1] (numeric) = 0.71795289035646485584517878213423 absolute error = 0.00088965834824112250372284662055 relative error = 0.12376261670155895458568827828053 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 0.71788302779070611077408635400021 y[1] (numeric) = 0.71697917474405865733466952040815 absolute error = 0.00090385304664745343941683359206 relative error = 0.12590533717297543024365159733895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 0.71692378899365494274625985557732 y[1] (numeric) = 0.71600559458929890985951778370325 absolute error = 0.00091819440435603288674207187407 relative error = 0.12807419958053020723974413068408 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 0.71596483327279119138002640493412 y[1] (numeric) = 0.71503215017478220502769465375522 absolute error = 0.0009326830980089863523317511789 relative error = 0.13026940076728920873897750331284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 0.71500616158707049762616329342395 y[1] (numeric) = 0.71405884178406423170612863168764 absolute error = 0.00094731980300626592003466173631 relative error = 0.13249113838453337951167849845652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 0.71404777489516446731605979449563 y[1] (numeric) = 0.71308566970165949246504040072342 absolute error = 0.00096210519350497485101939377221 relative error = 0.13473961089595578388833119133964 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 0.71308967415545971249019122160201 y[1] (numeric) = 0.71211263421304101906346396550522 absolute error = 0.00097703994241869342672725609679 relative error = 0.13701501758188273447444090252462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 0.71213186032605689301158675327299 y[1] (numeric) = 0.71113973560464008697623868247997 absolute error = 0.00099212472141680603534807079302 relative error = 0.13931755854351910789969064930848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.293 y[1] (analytic) = 0.71117433436476975846524941180534 y[1] (numeric) = 0.71016697416384592896275765433167 absolute error = 0.00100736020092382950249175747367 relative error = 0.14164743470721800500719651835188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.294 y[1] (analytic) = 0.71021709722912419034448629606947 y[1] (numeric) = 0.7091943501790054476777589196902 absolute error = 0.00102274705011874266672737637927 relative error = 0.14400484782877491402926425243906 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 0.70926014987635724452510688202316 y[1] (numeric) = 0.70822186393942292732444682730107 absolute error = 0.00103828593693431720066005472209 relative error = 0.14639000049774653644578484924589 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 0.70830349326341619402844691665405 y[1] (numeric) = 0.70724951573535974435023194151059 absolute error = 0.00105397752805644967821497514346 relative error = 0.14880309614179443638036237993041 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 0.70734712834695757207417514224732 y[1] (numeric) = 0.70627730585803407718537878330255 absolute error = 0.00106982248892349488879635894477 relative error = 0.15124433903105367555752358726217 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=57.2MB, alloc=4.4MB, time=3.09 x[1] = 0.298 y[1] (analytic) = 0.70639105608334621542383979809208 y[1] (numeric) = 0.70530523459962061502485166821442 absolute error = 0.00108582148372560039898812987766 relative error = 0.15371393428252659702199792914301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.299 y[1] (analytic) = 0.70543527742865430801611155600021 y[1] (numeric) = 0.704333302253250265653649859263 absolute error = 0.00110197517540404236246169673721 relative error = 0.15621208786450192200816118921762 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3 y[1] (analytic) = 0.70447979333866042489467925431497 y[1] (numeric) = 0.70336150911300986231592420951997 absolute error = 0.001118284225650562578755044795 relative error = 0.15873900660099932554438896877052 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 0.70352460476884857642975450243418 y[1] (numeric) = 0.70238985547394186962816842519634 absolute error = 0.00113474929490670680158607723784 relative error = 0.16129489817623965758335248969546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 0.70256971267440725283414093426342 y[1] (numeric) = 0.70141834163204408853677903601998 absolute error = 0.00115137104236316429736189824344 relative error = 0.16387997113914097766529317125343 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 0.7016151180102284689748235944506 y[1] (numeric) = 0.70044696788426936032027911532166 absolute error = 0.00116815012595910865454447912894 relative error = 0.16649443490784057234712020438215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 0.70066082173090680948103364573289 y[1] (numeric) = 0.69947573452852526963650174758128 absolute error = 0.00118508720238153984453189815161 relative error = 0.16913849977424312586587347155806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.305 y[1] (analytic) = 0.69970682479073847414974328925156 y[1] (numeric) = 0.69850464186367384661503019622599 absolute error = 0.00120218292706462753471309302557 relative error = 0.17181237690859521575077011642538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 0.69875312814372032364954549226047 y[1] (numeric) = 0.69753369018953126799519267921531 absolute error = 0.00121943795418905565435281304516 relative error = 0.1745162783640863063537951661656 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 0.69779973274354892552387281926885 y[1] (numeric) = 0.69656287980686755730991061439344 absolute error = 0.00123685293668136821396220487541 relative error = 0.17725041708147641453469401216081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 0.69684663954361960049450936332003 y[1] (numeric) = 0.69559221101740628411570015073564 absolute error = 0.00125442852621331637880921258439 relative error = 0.18001500689375062301236728187791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 0.6958938494970254690663494738148 y[1] (numeric) = 0.69462168412382426226912775546205 absolute error = 0.00127216537320120679722171835275 relative error = 0.18281026253080061818114757664881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 0.69494136355655649843435667604104 y[1] (numeric) = 0.6936512994297512472500215805382 absolute error = 0.00129006412680525118433509550284 relative error = 0.18563639962413343048734447316855 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.311 y[1] (analytic) = 0.69398918267469854969367587537158 y[1] (numeric) = 0.69268105723976963253174128532564 absolute error = 0.00130812543492891716193459004594 relative error = 0.18849363471160755676887174521412 % h = 0.001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.5MB, time=3.30 NO POLE x[1] = 0.312 y[1] (analytic) = 0.69303730780363242535385163593833 y[1] (numeric) = 0.69171095785941414499880994508754 absolute error = 0.00132634994421828035504169085079 relative error = 0.1913821852421966452788125060767 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 0.69208573989523291715810501948532 y[1] (numeric) = 0.69074100159517153941221262769204 absolute error = 0.00134473830006137774589239179328 relative error = 0.19430226958078092544252835729651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 0.69113447990106785420862116504429 y[1] (numeric) = 0.68977118875448029192266717318919 absolute error = 0.0013632911465875622859539918551 relative error = 0.19725410701296656573747302561123 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 0.69018352877239715139879948406602 y[1] (numeric) = 0.6888015196457302926321736629653 absolute error = 0.00138200912666685876662582110072 relative error = 0.20023791774993314443532567265291 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.316 y[1] (analytic) = 0.68923288746017185815341803867781 y[1] (numeric) = 0.68783199457826253720415001689949 absolute error = 0.00140089288190932094926802177832 relative error = 0.20325392293330941930751129995102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.317 y[1] (analytic) = 0.6882825569150332074776633628236 y[1] (numeric) = 0.68686261386236881752246210836122 absolute error = 0.00141994305266438995520125446238 relative error = 0.2063023446400775837677236183435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 0.68733253808731166531597667717754 y[1] (numeric) = 0.68589337780929141139965773799289 absolute error = 0.00143916027802025391631893918465 relative error = 0.2093834058875061983088085330021 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 0.6863828319270259802216671389056 y[1] (numeric) = 0.68492428673122277133471475801765 absolute error = 0.00145854519580320888695238088795 relative error = 0.2124973306381119874864041040357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 0.68543343938388223333824245658285 y[1] (numeric) = 0.68395534094130521232061458929837 absolute error = 0.00147809844257702101762786728448 relative error = 0.21564434380465069410816654308585 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 0.68448436140727288869340688885654 y[1] (numeric) = 0.68298654075363059870205332354831 absolute error = 0.00149782065364228999135356530823 relative error = 0.21882467125513718370534354791352 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.322 y[1] (analytic) = 0.68353559894627584380667633277783 y[1] (numeric) = 0.68201788648324003008360355295615 absolute error = 0.00151771246303581372307277982168 relative error = 0.22203853981789499379298910397848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.323 y[1] (analytic) = 0.68258715294965348061155989410811 y[1] (numeric) = 0.6810493784461235262886410190375 absolute error = 0.00153777450352995432291887507061 relative error = 0.22528617728663552386635184367528 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 0.68163902436585171669325701733906 y[1] (numeric) = 0.68008101695921971136935112175993 absolute error = 0.00155800740663200532390589557913 relative error = 0.22856781242556706353401721545822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=64.8MB, alloc=4.5MB, time=3.51 x[1] = 0.325 y[1] (analytic) = 0.68069121414299905684281893765035 y[1] (numeric) = 0.67911280234041549666813127890869 absolute error = 0.00157841180258356017468765874166 relative error = 0.23188367497453385765334816835323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.326 y[1] (analytic) = 0.67974372322890564492872290056454 y[1] (numeric) = 0.67814473490854576293070607426437 absolute error = 0.00159898832035988199801682630017 relative error = 0.23523399565418540881075693134783 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 0.67879655257106231608680727764583 y[1] (numeric) = 0.67717681498339304147127308145081 absolute error = 0.00161973758766927461553419619502 relative error = 0.23861900617117621897845993938956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.328 y[1] (analytic) = 0.67784970311663964922951538822866 y[1] (numeric) = 0.67620904288568719438999819828092 absolute error = 0.00164066023095245483951718994774 relative error = 0.24203893922339617368072826519425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 0.67690317581248701987539551785335 y[1] (numeric) = 0.6752414189371050938431802740784 absolute error = 0.00166175687538192603221524377495 relative error = 0.24549402850523177351635736634471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 0.67595697160513165329980430382978 y[1] (numeric) = 0.67427394346027030036640575978402 absolute error = 0.00168302814486135293339854404576 relative error = 0.24898450871285841941025393994235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 0.67501109144077767800776033714693 y[1] (numeric) = 0.67330661677875274025101505766496 absolute error = 0.00170447466202493775674527948197 relative error = 0.25251061554956395950578667559065 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.332 y[1] (analytic) = 0.67406553626530517952989450779567 y[1] (numeric) = 0.67233943921706838197420319413406 absolute error = 0.00172609704823679755569131366161 relative error = 0.2560725857311037071609852999355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 0.67312030702426925454244329747574 y[1] (numeric) = 0.67137241110067891168307838555124 absolute error = 0.0017478959235903428593649119245 relative error = 0.25967065699108714107591321777068 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 0.67217540466289906531223089961467 y[1] (numeric) = 0.67040553275599140773300301292158 absolute error = 0.00176987190690765757922788669309 relative error = 0.26330506808639650015569910953599 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 0.67123083012609689446758572163781 y[1] (numeric) = 0.66943880451035801428054246712189 absolute error = 0.00179202561573888018704325451592 relative error = 0.26697605880263748730390901788549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 0.67028658435843720009613649849422 y[1] (numeric) = 0.66847222669207561393134827167974 absolute error = 0.00181435766636158616478822681448 relative error = 0.27068386995962229794429087433219 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 0.66934266830416567117043291956346 y[1] (numeric) = 0.6675057996303854994433028351946 absolute error = 0.00183686867378017172713008436886 relative error = 0.27442874341688519068554737373846 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 0.66839908290719828330233534324402 y[1] (numeric) = 0.6665395236554730444852541302289 absolute error = 0.00185955925172523881708121301512 relative error = 0.27821092207923081917381107021894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=68.6MB, alloc=4.5MB, time=3.72 x[1] = 0.339 y[1] (analytic) = 0.66745582911112035482711784475499 y[1] (numeric) = 0.66557339909846737345166953990694 absolute error = 0.00188243001265298137544830484805 relative error = 0.28203064990231554582102920346451 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.34 y[1] (analytic) = 0.66651290785918560321822851296921 y[1] (numeric) = 0.66460742629144103033353905754029 absolute error = 0.00190548156774457288468945542892 relative error = 0.28588817189826195975463793339475 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 0.66557032009431520183365058143904 y[1] (numeric) = 0.66364160556740964664585896834889 absolute error = 0.00192871452690555518779161309015 relative error = 0.28978373414130682300484044291841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 0.66462806675909683699480764717492 y[1] (numeric) = 0.66267593726033160841202808576645 absolute error = 0.00195212949876522858277956140847 relative error = 0.29371758377348267063062607172966 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 0.66368614879578376539895589819304 y[1] (numeric) = 0.66171042170510772220548955790621 absolute error = 0.00197572709067604319346634028683 relative error = 0.2976899690103332921845048189163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.344 y[1] (analytic) = 0.66274456714629387186600593736127 y[1] (numeric) = 0.66074505923758088024895220251742 absolute error = 0.00199950790871299161705373484385 relative error = 0.3017011391466633236289110043024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 0.66180332275220872742071645564298 y[1] (numeric) = 0.65977985019453572457152627118326 absolute error = 0.00202347255767300284919018445972 relative error = 0.30575134456232218054448068241706 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.346 y[1] (analytic) = 0.66086241655477264771120167246664 y[1] (numeric) = 0.65881479491369831022410948559649 absolute error = 0.00204762164107433748709218687015 relative error = 0.30984083672802256521205991559542 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.347 y[1] (analytic) = 0.65992184949489175176469412463536 y[1] (numeric) = 0.65784989373373576755336013049874 absolute error = 0.00207195576115598421133399413662 relative error = 0.31396986821119378190648688705615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.348 y[1] (analytic) = 0.65898162251313302108150404793491 y[1] (numeric) = 0.65688514699425596353459492928211 absolute error = 0.0020964755188770575469091186528 relative error = 0.31813869268187009651104303401868 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 0.65804173654972335906811625740272 y[1] (numeric) = 0.6559205550358071621639503693271 absolute error = 0.00212118151391619690416588807562 relative error = 0.32234756491861437834712119257765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 0.65710219254454865081036509308237 y[1] (numeric) = 0.65495611819987768391014708488717 absolute error = 0.0021460743446709669002180081952 relative error = 0.3265967408144772639142477959186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 0.65616299143715282318762765801042 y[1] (numeric) = 0.65399183682889556422619784572722 absolute error = 0.0021711546082572589614298122832 relative error = 0.33088647738299208405125843461606 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.352 y[1] (analytic) = 0.65522413416673690532897523416392 y[1] (numeric) = 0.65302771126622821112140063977945 absolute error = 0.00219642290050869420757459438447 relative error = 0.33521703276420579786029991849992 % h = 0.001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.5MB, time=3.93 NO POLE x[1] = 0.353 y[1] (analytic) = 0.65428562167215808941222242013895 y[1] (numeric) = 0.65206374185618206179395927779512 absolute error = 0.00222187981597602761826314234383 relative error = 0.33958866623074617858155710271703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 0.65334745489192879180681319143277 y[1] (numeric) = 0.65109992894400223832457488734287 absolute error = 0.0022475259479265534822383040899 relative error = 0.34400163819392549846832028219358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 0.65240963476421571456148274036527 y[1] (numeric) = 0.65013627287587220243135260253347 absolute error = 0.0022733618883435121301301378318 relative error = 0.34845621020988096158936145700454 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 0.65147216222683890723763360789966 y[1] (numeric) = 0.64917277399891340928636869453554 absolute error = 0.00229938822792549795126491336412 relative error = 0.35295264498575213537871919230846 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 0.65053503821727082908936427390812 y[1] (numeric) = 0.64820943266118496039424432628624 absolute error = 0.00232560555608586869511994762188 relative error = 0.35749120638589563366204754964721 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 0.64959826367263541159108802577568 y[1] (numeric) = 0.64724624921168325553307305279427 absolute error = 0.00235201446095215605801497298141 relative error = 0.36207215943813730581381151947426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 0.64866183952970712131367957764527 y[1] (numeric) = 0.64628322400034164375805012607866 absolute error = 0.00237861552936547755562945156661 relative error = 0.36669577034006218864095788035168 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 0.64772576672491002315008656407927 y[1] (numeric) = 0.64532035737803007346815260108497 absolute error = 0.0024054093468799496819339629943 relative error = 0.37136230646534247954640628156392 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.361 y[1] (analytic) = 0.64679004619431684389134268244803 y[1] (numeric) = 0.64435764969655474153622017586962 absolute error = 0.00243239649776210235512250657841 relative error = 0.37607203637010379149994193293844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 0.64585467887364803615391890795416 y[1] (numeric) = 0.64339510130865774150278763594229 absolute error = 0.00245957756499029465113127201187 relative error = 0.38082522979932995233500145170652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.363 y[1] (analytic) = 0.64491966569827084265934885386328 y[1] (numeric) = 0.64243271256801671083402070890462 absolute error = 0.00248695313025413182532814495866 relative error = 0.38562215769330661289758156438674 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.364 y[1] (analytic) = 0.64398500760319836086706399723811 y[1] (numeric) = 0.64147048382924447724410807141996 absolute error = 0.00251452377395388362295592581815 relative error = 0.39046309219410393059822245165535 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 0.64305070552308860796137413726246 y[1] (numeric) = 0.64050841544788870408246318609266 absolute error = 0.0025422900751999038789109511698 relative error = 0.39534830665209859695988108907176 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 0.64211676039224358619352809909695 y[1] (numeric) = 0.63954650778043153478609058102559 absolute error = 0.00257025261181205140743751807136 relative error = 0.40027807563253547981367410060174 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.5MB, time=4.14 NO POLE x[1] = 0.367 y[1] (analytic) = 0.64118317314460834857978934112779 y[1] (numeric) = 0.63858476118428923639747211965991 absolute error = 0.00259841196031911218231722146788 relative error = 0.40525267492212915287109513706046 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 0.64024994471377006495646076745515 y[1] (numeric) = 0.63762317601781184214832974298111 absolute error = 0.00262676869595822280813102447404 relative error = 0.41027238153570558749556097582859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 0.63931707603295708839279269051843 y[1] (numeric) = 0.63666175264028279310962210029887 absolute error = 0.00265532339267429528317059021956 relative error = 0.4153374737228842836081774127844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.37 y[1] (analytic) = 0.63838456803503802196270753087285 y[1] (numeric) = 0.63570049141191857890813341857415 absolute error = 0.0026840766231194430545741122987 relative error = 0.42044823097480111879260624529588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.371 y[1] (analytic) = 0.63745242165252078587627448231464 y[1] (numeric) = 0.63473939269386837751001389367477 absolute error = 0.00271302895865240836626058863987 relative error = 0.42560493403087219681202556865038 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 0.63652063781755168497186701080265 y[1] (numeric) = 0.63377845684821369407163181998905 absolute error = 0.0027421809693379909002351908136 relative error = 0.43080786488559897891757626849829 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 0.63558921746191447656993569494098 y[1] (numeric) = 0.63281768423796799885809860751526 absolute error = 0.00277153322394647771183708742572 relative error = 0.43605730679541498351254874589497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 0.6346581615170294386893285541723 y[1] (numeric) = 0.63185707522707636422982876787173 absolute error = 0.00280108628995307445949978630057 relative error = 0.44135354428557434194005805272441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.375 y[1] (analytic) = 0.63372747091395243862709064828374 y[1] (numeric) = 0.63089663018041510069749788263736 absolute error = 0.00283084073353733792959276564638 relative error = 0.44669686315708250038425699132339 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 0.63279714658337400190267436834815 y[1] (numeric) = 0.62993634946379139204576249903422 absolute error = 0.00286079711958260985691186931393 relative error = 0.45208755049366936011642136504016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 0.63186718945561838156749147481296 y[1] (numeric) = 0.62897623344394292952610682920199 absolute error = 0.00289095601167545204138464561097 relative error = 0.45752589466880515057768727164533 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.378 y[1] (analytic) = 0.6309376004606426278807375731069 y[1] (numeric) = 0.62801628248853754511918206018699 absolute error = 0.00292131797210508276155551291991 relative error = 0.46301218535275933207000673778357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 0.63000838052803565835241935086267 y[1] (numeric) = 0.62705649696617284386700501227596 absolute error = 0.00295188356186281448541433858671 relative error = 0.46854671351970282712619656227034 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=80.1MB, alloc=4.5MB, time=4.36 x[1] = 0.38 y[1] (analytic) = 0.6290795305870173281545145336508 y[1] (numeric) = 0.62609687724637583527538381344532 absolute error = 0.00298265334064149287913072020548 relative error = 0.47412977145485388194896928470965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 0.62815105156643750090119414798726 y[1] (numeric) = 0.62513742369960256378693918746947 absolute error = 0.00301362786683493711425496051779 relative error = 0.47976165276166786164773991359508 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 0.6272229443947751197990363113152 y[1] (numeric) = 0.62417813669723773832509088263606 absolute error = 0.00304480769753738147394542867914 relative error = 0.48544265236907128536098451942486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 0.62629521000013727916816039866944 y[1] (numeric) = 0.62321901661159436090937969705096 absolute error = 0.00307619338854291825878070161848 relative error = 0.49117306653874040973117602387291 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 0.62536784931025829633521006481245 y[1] (numeric) = 0.62226006381591335434249648517995 absolute error = 0.0031077854943449419927135796325 relative error = 0.49695319287242467159902943341081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 0.6244408632524987838991132287812 y[1] (numeric) = 0.62130127868436318896939045856704 absolute error = 0.00313958456813559492972277021416 relative error = 0.50278333031931530320414627071405 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 0.62351425275384472237054675500772 y[1] (numeric) = 0.62034266159203950850883002159009 absolute error = 0.00317159116180521386171673341763 relative error = 0.50866377918345943562035092624171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.387 y[1] (analytic) = 0.62258801874090653318603319147135 y[1] (numeric) = 0.61938421291496475495779031066166 absolute error = 0.00320380582594177822824288080969 relative error = 0.51459484113122000861625696387007 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 0.62166216213991815209759655070879 y[1] (numeric) = 0.61842593303008779256904253245635 absolute error = 0.00323622910983035952855401825244 relative error = 0.52057681919878180761508797142864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 0.62073668387673610293890374394874 y[1] (numeric) = 0.61746782231528353090232112354389 absolute error = 0.00326886156145257203658262040485 relative error = 0.52661001779970395093270629935883 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 0.61981158487683857176881790215284 y[1] (numeric) = 0.61650988114935254694944568022944 absolute error = 0.0033017037274860248193722219234 relative error = 0.53269474273251915299937699841124 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 0.61888686606532448139328944033205 y[1] (numeric) = 0.61555210991202070633377553344771 absolute error = 0.00333475615330377505951390688434 relative error = 0.5388313011883800918192185626822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 0.61796252836691256626651034317064 y[1] (numeric) = 0.6145945089839387835843757692247 absolute error = 0.00336801938297378268213457394594 relative error = 0.54502000175875321149177393665725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 0.6170385727059404477722567707261 y[1] (numeric) = 0.61363707874668208148527442050943 absolute error = 0.00340149395925836628698235021667 relative error = 0.5512611544431602932128840224702 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=83.9MB, alloc=4.5MB, time=4.57 x[1] = 0.394 y[1] (analytic) = 0.61611500000636370988634470278558 y[1] (numeric) = 0.61267981958275004950019148108676 absolute error = 0.00343518042361366038615322169882 relative error = 0.55755507065696813078727315921111 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.395 y[1] (analytic) = 0.61519181119175497522112295934603 y[1] (numeric) = 0.61172273187556590127312131681044 absolute error = 0.00346907931618907394800164253559 relative error = 0.56390206323922664932317545981429 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 0.61426900718530298145292755264793 y[1] (numeric) = 0.61076581600947623120515097354216 absolute error = 0.00350319117582675024777657910577 relative error = 0.57030244646055580844015841582525 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.397 y[1] (analytic) = 0.61334658890981165813342094323165 y[1] (numeric) = 0.60980907236975063010789780494629 absolute error = 0.00353751654006102802552313828536 relative error = 0.57675653603108163400525398621121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 0.61242455728769920388573938859978 y[1] (numeric) = 0.60885250134258129993395076667071 absolute error = 0.00357205594511790395178862192907 relative error = 0.58326464910842172511980790526822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.399 y[1] (analytic) = 0.6115029132409971639863711882616 y[1] (numeric) = 0.60789610331508266758470064644026 absolute error = 0.00360680992591449640167054182134 relative error = 0.58982710430572058581032789706446 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 0.61058165769134950833368824320429 y[1] (numeric) = 0.60693987867529099779594542220047 absolute error = 0.00364177901605851053774282100382 relative error = 0.59644422169973513363127590239313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 0.60966079156001170980405296118265 y[1] (numeric) = 0.60598382781216400510165786267388 absolute error = 0.00367696374784770470239509850877 relative error = 0.60311632283897074016643568203344 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 0.60874031576784982299642215164349 y[1] (numeric) = 0.60502795111558046487630340652907 absolute error = 0.00371236465226935812011874511442 relative error = 0.60984373075186816121842499509975 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 0.60782023123533956336636916560423 y[1] (numeric) = 0.60407224897633982345609727781211 absolute error = 0.00374798225899973991027188779212 relative error = 0.61662676995504171730334309424689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.404 y[1] (analytic) = 0.60690053888256538675044514638653 y[1] (numeric) = 0.60311672178616180733959071635075 absolute error = 0.00378381709640357941085443003578 relative error = 0.62346576646156908791968408001849 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 0.60598123962921956928179986676729 y[1] (numeric) = 0.60216136993768603146797712251264 absolute error = 0.00381986969153353781382274425465 relative error = 0.63036104778933308593774171126029 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 0.60506233439460128769798223684934 y[1] (numeric) = 0.60120619382447160658550983597877 absolute error = 0.00385614057012968111247240087057 relative error = 0.63731294296941578135802104744498 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 0.60414382409761570004184017477465 y[1] (numeric) = 0.60025119384099674568042418808157 absolute error = 0.00389263025661895436141598669308 relative error = 0.64432178255454534661489877470509 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.5MB, time=4.78 NO POLE x[1] = 0.408 y[1] (analytic) = 0.60322570965677302675643913930379 y[1] (numeric) = 0.59929637038265836950675738675293 absolute error = 0.00392933927411465724968175255086 relative error = 0.65138789862759599855518174312206 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 0.60230799199018763217491822926617 y[1] (numeric) = 0.59834172384577171118746071222926 absolute error = 0.00396626814441592098745751703691 relative error = 0.65851162481014141520054918020415 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.41 y[1] (analytic) = 0.60139067201557710640620235994886 y[1] (numeric) = 0.59738725462756991989919942036855 absolute error = 0.00400341738800718650700293958031 relative error = 0.66569329627106200840837789457102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 0.6004737506502613476174886306349 y[1] (numeric) = 0.59643296312620366363923666874645 absolute error = 0.00404078752405768397825196188845 relative error = 0.67293324973520643657739381144543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.412 y[1] (analytic) = 0.59955722881116164471442460072855 y[1] (numeric) = 0.59547884974074073107479869861433 absolute error = 0.00407837907042091363962590211422 relative error = 0.68023182349210774460322230221419 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.413 y[1] (analytic) = 0.59864110741479976041989579421255 y[1] (numeric) = 0.59452491487116563247531942332098 absolute error = 0.00411619254363412794457637089157 relative error = 0.68758935740475452137448157483843 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 0.59772538737729701475233935357361 y[1] (numeric) = 0.59357115891837919972796349092011 absolute error = 0.0041542284589178150243758626535 relative error = 0.69500619291841746821283817927907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 0.5968100696143733689045003648061 y[1] (numeric) = 0.59261758228419818543682780540727 absolute error = 0.00419248733017518346767255939883 relative error = 0.70248267306953177480068448904526 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 0.59589515504134650952354697466115 y[1] (numeric) = 0.59166418537135486110622240735117 absolute error = 0.00423096966999164841732456730998 relative error = 0.7100191424946357023080706529259 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.417 y[1] (analytic) = 0.59498064457313093339346001994986 y[1] (numeric) = 0.59071096858349661440843253060519 absolute error = 0.00426967598963431898502748934467 relative error = 0.71761594743936577662649657723144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 0.59406653912423703252061248643465 y[1] (numeric) = 0.58975793232518554553636456730329 absolute error = 0.00430860679905148698424791913136 relative error = 0.72527343576750899784141443871318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.419 y[1] (analytic) = 0.59315283960877017962345371165307 y[1] (numeric) = 0.58880507700189806264147958846089 absolute error = 0.00434776260687211698197412319218 relative error = 0.73299195697011247532808334712788 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 0.59223954694042981402721284191366 y[1] (numeric) = 0.5878524030200244763574189822133 absolute error = 0.00438714392040533766979385970036 relative error = 0.74077186217465090113703227778937 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=91.5MB, alloc=4.5MB, time=5.00 x[1] = 0.421 y[1] (analytic) = 0.59132666203250852796453564868418 y[1] (numeric) = 0.58689991078686859340972768603247 absolute error = 0.00442675124563993455480796265171 relative error = 0.74861350415425227764610541270532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.422 y[1] (analytic) = 0.59041418579789115328296840365935 y[1] (numeric) = 0.58594760071064730931208140316479 absolute error = 0.00446658508724384397088700049456 relative error = 0.75651723733698231879616866349694 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 0.58950211914905384856020210494802 y[1] (numeric) = 0.58499547320049020014942510702887 absolute error = 0.00450664594856364841077699791915 relative error = 0.76448341781518794759733349766716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 0.58859046299806318662798993905953 y[1] (numeric) = 0.58404352866643911344843105040079 absolute error = 0.00454693433162407317955888865874 relative error = 0.77251240335490031599229338289337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 0.58767921825657524250565045469569 y[1] (numeric) = 0.58309176751944775813568540889467 absolute error = 0.00458745073712748436996504580102 relative error = 0.78060455340529777659336140013646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 0.58676838583583468174406851476933 y[1] (numeric) = 0.58214019017138129358401360051774 absolute error = 0.00462819566445338816005491425159 relative error = 0.78876022910822923927034015695465 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 0.58585796664667384918110568257234 y[1] (numeric) = 0.58118879703501591774735523494042 absolute error = 0.00466916961165793143375044763192 relative error = 0.79697979330779834905774549735765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 0.58494796159951185810933128660698 y[1] (numeric) = 0.58023758852403845438460055757205 absolute error = 0.00471037307547340372473072903493 relative error = 0.80526361056000892537244526876139 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.429 y[1] (analytic) = 0.58403837160435367985698499627348 y[1] (numeric) = 0.57928656505304593937280116457146 absolute error = 0.00475180655130774048418383170202 relative error = 0.81361204714247210608676839581339 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.43 y[1] (analytic) = 0.58312919757078923378308132737543 y[1] (numeric) = 0.57833572703754520611016867554723 absolute error = 0.0047934705332440276729126518282 relative error = 0.82202547106417564358789579939664 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 0.58222044040799247768756608226273 y[1] (numeric) = 0.57738507489395247000927596091436 absolute error = 0.00483536551404000767829012134837 relative error = 0.83050425207531580357217464690587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 0.58131210102472049863743431437966 y[1] (numeric) = 0.57643460903959291208087643067154 absolute error = 0.00487749198512758655655788370812 relative error = 0.83904876167719232097321571027293 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 0.58040418032931260420971899102467 y[1] (numeric) = 0.57548432989270026160875780074497 absolute error = 0.0049198504366123426009611902797 relative error = 0.84765937313216687110555828701615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.434 y[1] (analytic) = 0.57949667922968941415225911125708 y[1] (numeric) = 0.57453423787241637791604766201028 absolute error = 0.0049624413572730362362114492468 relative error = 0.85633646147368551782163965276192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=95.3MB, alloc=4.5MB, time=5.20 x[1] = 0.435 y[1] (analytic) = 0.57858959863335195246315561810729 y[1] (numeric) = 0.57358433339879083122338908565204 absolute error = 0.00500526523456112123976653245525 relative error = 0.86508040351636560422911124844956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 0.5776829394473807398898230255586 y[1] (numeric) = 0.57263461689278048259940540665039 absolute error = 0.00504832255460025729041761890821 relative error = 0.87389157786614755529853012782409 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 0.57677670257843488684854426117356 y[1] (numeric) = 0.57168508877624906300387423489493 absolute error = 0.00509161380218582384467002627863 relative error = 0.88277036493051206550845348852721 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 0.57587088893275118676543580473445 y[1] (numeric) = 0.57073574947196675142403165071688 absolute error = 0.00513513946078443534140415401757 relative error = 0.89171714692876314852631183103158 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 0.57496549941614320983972978185704 y[1] (numeric) = 0.56978659940360975210442844850005 absolute error = 0.00517890001253345773530133335699 relative error = 0.9007323079023775298094714849806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 0.57406053493400039723027924922008 y[1] (numeric) = 0.56883763899575987087076119847925 absolute error = 0.00522289593824052635951805074083 relative error = 0.90981623372542086693196260752865 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.441 y[1] (analytic) = 0.57315599639128715566619248482993 y[1] (numeric) = 0.56788886867390409054810180285966 absolute error = 0.00526712771738306511809068197027 relative error = 0.91896931211503128639879067533241 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 0.57225188469254195248250167261022 y[1] (numeric) = 0.56694028886443414547395012799235 absolute error = 0.00531159582810780700855154461787 relative error = 0.92819193264197072970191807268791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.443 y[1] (analytic) = 0.57134820074187641108177094557285 y[1] (numeric) = 0.56599189999464609510653519951772 absolute error = 0.00535630074723031597523574605513 relative error = 0.93748448674124460540025150870317 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 0.57044494544297440682254832588658 y[1] (numeric) = 0.56504370249273989672879135214027 absolute error = 0.00540124295023451009375697374631 relative error = 0.94684736772279024807065837815218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.445 y[1] (analytic) = 0.56954211969909116333556567331613 y[1] (numeric) = 0.56409569678781897724843663002285 absolute error = 0.00544642291127218608712904329328 relative error = 0.95628097078223468907852237871315 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.446 y[1] (analytic) = 0.56863972441305234926859032575643 y[1] (numeric) = 0.5631478833098898040945816376863 absolute error = 0.00549184110316254517400868807013 relative error = 0.96578569301172224825500118232822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 0.56773776048725317546083168693519 y[1] (numeric) = 0.56220026248986145521129794476998 absolute error = 0.00553749799739172024953374216521 relative error = 0.97536193341081245974433615448608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 0.56683622882365749254780558680187 y[1] (numeric) = 0.56125283475954518814857605104881 absolute error = 0.00558339406411230439922953575306 relative error = 0.98501009289744884949865944486561 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.5MB, time=5.42 NO POLE x[1] = 0.449 y[1] (analytic) = 0.56593513032379688899755880966357 y[1] (numeric) = 0.56030560055165400825110382071302 absolute error = 0.00562952977214288074645498895055 relative error = 0.99473057431899908615012470427684 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 0.5650344658887697895791557537681 y[1] (numeric) = 0.55935856029980223594529719709623 absolute error = 0.00567590558896755363385855667187 relative error = 1.0045237824633670312812357776354 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 0.56413423641924055426432875377253 y[1] (numeric) = 0.55841171443850507312501591078498 absolute error = 0.00572252198073548113931284298755 relative error = 1.0143901240701772194443486834618 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 0.56323444281543857756319316437161 y[1] (numeric) = 0.55746506340317816863639779535795 absolute error = 0.00576937941226040892679536901366 relative error = 1.0243300078420323026508659092744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 0.56233508597715738829492786929617 y[1] (numeric) = 0.55651860763013718286224622588434 absolute error = 0.00581647834702020543268164341183 relative error = 1.0343438444558439984600226609502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 0.56143616680375374979432144492579 y[1] (numeric) = 0.55557234755659735140640609575762 absolute error = 0.00586381924715639838791534916817 relative error = 1.0444320465742380852467806226428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 0.56053768619414676055508377189468 y[1] (numeric) = 0.55462628362067304787856464745241 absolute error = 0.00591140257347371267651912444227 relative error = 1.0545950288570339927185987721287 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.456 y[1] (analytic) = 0.55963964504681695531082245130418 y[1] (numeric) = 0.55368041626137734577991437236715 absolute error = 0.00595922878543960953090807893703 relative error = 1.0648332079727995402821500047042 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.457 y[1] (analytic) = 0.55874204425980540655458294449053 y[1] (numeric) = 0.55273474591862157949011609405317 absolute error = 0.00600729834118382706446685043736 relative error = 1.0751470026104813804338083395941 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 0.55784488473071282649785091673299 y[1] (numeric) = 0.55178927303321490435600124783054 absolute error = 0.00605561169749792214184966890245 relative error = 1.0855368334911117089623604037685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 0.55694816735669866946991482582499 y[1] (numeric) = 0.55084399804686385588245326805165 absolute error = 0.00610416930983481358746155777334 relative error = 1.0960031233795918084093173443994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 0.5560518930344802347584863560711 y[1] (numeric) = 0.54989892140217190802590889209453 absolute error = 0.00615297163230832673257746397657 relative error = 1.1065462970965529959318445500826 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 0.55515606266033176989247585701442 y[1] (numeric) = 0.54895404354263903059092108754772 absolute error = 0.0062020191176927393015547694667 relative error = 1.11716678153029555145611645561 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.462 y[1] (analytic) = 0.55426067713008357436781950404435 y[1] (numeric) = 0.54800936491266124573022620598685 absolute error = 0.0062513122174223286375932980575 relative error = 1.1278650056488062067952768702911 % h = 0.001 TOP MAIN SOLVE Loop memory used=102.9MB, alloc=4.5MB, time=5.63 NO POLE x[1] = 0.463 y[1] (analytic) = 0.55336573733912110381725445498295 y[1] (numeric) = 0.54706488595753018354875886323895 absolute error = 0.006300851381590920268495591744 relative error = 1.1386414005118547812365810773262 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 0.55247124418238407462493783279988 y[1] (numeric) = 0.54612060712343263681205894208241 absolute error = 0.00635063705895143781287889071747 relative error = 1.1494963992831705539771585974102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.465 y[1] (analytic) = 0.55157719855436556898680491976248 y[1] (numeric) = 0.54517652885745011475951600893859 absolute error = 0.00640066969691545422728891082389 relative error = 1.1604304372426989687076140704337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 0.55068360134911114041756150258825 y[1] (numeric) = 0.54423265160755839602289733127345 absolute error = 0.0064509497415527443946641713148 relative error = 1.1714439517989392706078322009379 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.467 y[1] (analytic) = 0.54979045346021791970520486153262 y[1] (numeric) = 0.54328897582262708065060657714393 absolute error = 0.00650147763759083905459828438869 relative error = 1.1825373825013636810303301498744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 0.54889775578083372131396744881682 y[1] (numeric) = 0.54234550195241914123812117259304 absolute error = 0.00655225382841458007584627622378 relative error = 1.1937111710529187202037712090316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.469 y[1] (analytic) = 0.54800550920365615023657685337748 y[1] (numeric) = 0.54140223044759047316505718641888 absolute error = 0.0066032787560656770715196669586 relative error = 1.204965761322609293393286254303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 0.54711371462093170929672519960359 y[1] (numeric) = 0.5404591617596894439393115052153 absolute error = 0.00665455286124226535741369438829 relative error = 1.2163015993581661611055187084198 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 0.54622237292445490690264067751721 y[1] (numeric) = 0.53951629634115644164873195450436 absolute error = 0.00670607658329846525390872301285 relative error = 1.227719133398797419125294161885 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 0.54533148500556736525265345075175 y[1] (numeric) = 0.53857363464532342252076691425294 absolute error = 0.00675785036024394273188653649881 relative error = 1.239218813888024619418002314923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 0.54444105175515692899364773668793 y[1] (numeric) = 0.5376311771264134575905468690861 absolute error = 0.00680987462874347140310086760183 relative error = 1.2508010934866041682276567932098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 0.54355107406365677433329140022077 y[1] (numeric) = 0.53668892423954027847785122507793 absolute error = 0.00686214982411649585544017514284 relative error = 1.262466427085534643045663365992 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 0.54266155282104451860693394885391 y[1] (numeric) = 0.53574687644070782227341461611518 absolute error = 0.00691467638033669633351933273873 relative error = 1.2742152718191506755200803643927 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=106.8MB, alloc=4.5MB, time=5.84 x[1] = 0.476 y[1] (analytic) = 0.54177248891684133030006336214914 y[1] (numeric) = 0.53480503418680977553502781348946 absolute error = 0.00696745473003155476503554865968 relative error = 1.2860480870783040528201034289911 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 0.54088388324011103952721173299992 y[1] (numeric) = 0.53386339793562911739388924257907 absolute error = 0.00702048530448192213332249042085 relative error = 1.297965334523632695466162507442 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.478 y[1] (analytic) = 0.53999573667945924896819924174937 y[1] (numeric) = 0.53292196814583766177166400023089 absolute error = 0.00707376853362158719653524151848 relative error = 1.3099674780989181751829003700003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 0.53910805012303244526260552683451 y[1] (numeric) = 0.53198074527699559870870815574518 absolute error = 0.00712730484603684655389737108933 relative error = 1.322054984044532441930932673202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.48 y[1] (analytic) = 0.53822082445851711086335705741136 y[1] (numeric) = 0.53103972978955103480391700720074 absolute error = 0.00718109466896607605944005021062 relative error = 1.3342283209109744349241994747124 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.481 y[1] (analytic) = 0.53733406057313883635031865429955 y[1] (numeric) = 0.53009892214483953276665685323388 absolute error = 0.00723513842829930358366180106567 relative error = 1.3464879595724972581434426851584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.482 y[1] (analytic) = 0.5364477593536614332047768455809 y[1] (numeric) = 0.52915832280508365008124072830105 absolute error = 0.00728943654857778312353611727985 relative error = 1.3588343732408266066134248117279 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 0.53556192168638604704570228229476 y[1] (numeric) = 0.52821793223339247678440943691101 absolute error = 0.00734398945299357026129284538375 relative error = 1.3712680374789711355224891279863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 0.53467654845715027132867797789364 y[1] (numeric) = 0.52727775089376117235628010930687 absolute error = 0.00739879756338909897239786858677 relative error = 1.383789430215125470128503840709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 0.53379164055132726150837967245725 y[1] (numeric) = 0.526337779251070501725225387611 absolute error = 0.00745386130025675978315428484625 relative error = 1.3963990317566665603156928592059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 0.53290719885382484966549415911054 y[1] (numeric) = 0.52539801777108637038714723751481 absolute error = 0.00750918108273847927834692159573 relative error = 1.4090973248042440896428996177661 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 0.53202322424908465959896094565383 y[1] (numeric) = 0.52445846692045935863961026620097 absolute error = 0.00756475732862530095935067945286 relative error = 1.4218847944659656547560306163651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 0.53113971762108122238442215908945 y[1] (numeric) = 0.52351912716672425493130031232585 absolute error = 0.0076205904543569674531218467636 relative error = 1.4347619282716774371263609109356 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.489 y[1] (analytic) = 0.53025667985332109239976513452147 y[1] (numeric) = 0.52257999897829958832727495856476 absolute error = 0.00767668087502150407249017595671 relative error = 1.4477292161873410952226401864131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=110.6MB, alloc=4.5MB, time=6.05 x[1] = 0.49 y[1] (analytic) = 0.52937411182884196381864166281204 y[1] (numeric) = 0.52164108282448716009047350143049 absolute error = 0.00773302900435480372816816138155 relative error = 1.4607871506295076114291073478069 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.491 y[1] (analytic) = 0.52849201443021178757284740340174 y[1] (numeric) = 0.52070237917547157437995479681614 absolute error = 0.0077896352547402131928926065856 relative error = 1.4739362264798888342842024921922 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.492 y[1] (analytic) = 0.52761038853952788878444449984064 y[1] (numeric) = 0.51976388850231976806633228298531 absolute error = 0.00784650003720812071811221685533 relative error = 1.4871769411000274629365631443502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 0.52672923503841608466850996583417 y[1] (numeric) = 0.51882561127698053966487636553544 absolute error = 0.00790362376143554500363360029873 relative error = 1.5005097943460662270964190420742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.494 y[1] (analytic) = 0.52584855480802980290739193898176 y[1] (numeric) = 0.5178875479722840773867552311926 absolute error = 0.00796100683574572552063670778916 relative error = 1.5139352885836170222023757414786 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 0.52496834872904920049735542787856 y[1] (numeric) = 0.51694969906194148630888603915771 absolute error = 0.00801864966710771418846938872085 relative error = 1.5274539287027307660264280676657 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 0.52408861768168028306849870586105 y[1] (numeric) = 0.51601206502054431466286932011347 absolute error = 0.00807655266113596840562938574758 relative error = 1.5410662221329687495045032281312 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.497 y[1] (analytic) = 0.52320936254565402467882103140682 y[1] (numeric) = 0.51507464632356407924348029391821 absolute error = 0.00813471622208994543534073748861 relative error = 1.5547726788585762612065406649907 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 0.52233058420022548808332190104733 y[1] (numeric) = 0.51413744344735178993719169745573 absolute error = 0.0081931407528736981461302035916 relative error = 1.5685738114337592715497191285236 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 0.52145228352417294547901156562125 y[1] (numeric) = 0.51320045686913747337120359407875 absolute error = 0.0082518266550354721078079715425 relative error = 1.5824701349980649696115960296084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 0.52057446139579699972671206478443 y[1] (numeric) = 0.51226368706702969568345651557639 absolute error = 0.00831077432876730404325554920804 relative error = 1.596462167291866952217292323271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 0.5196971186929197060505275579023 y[1] (numeric) = 0.51132713452001508441410516661282 absolute error = 0.00836998417290462163642239128948 relative error = 1.6105504286719558718571079621352 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.502 y[1] (analytic) = 0.51882025629288369421586225178126 y[1] (numeric) = 0.51039079970795784951893080012355 absolute error = 0.00842945658492584469693145165771 relative error = 1.6247354421272363569387659229197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.503 y[1] (analytic) = 0.51794387507255129118686374714781 y[1] (numeric) = 0.50945468311159930350517125021698 absolute error = 0.00848919196095198768169249693083 relative error = 1.6390177332945310248925422444707 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.5MB, time=6.26 NO POLE x[1] = 0.504 y[1] (analytic) = 0.51706797590830364426416914635909 y[1] (numeric) = 0.50851878521255738069024848671127 absolute error = 0.00854919069574626357392065964782 relative error = 1.6533978304744924157285385177007 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.505 y[1] (analytic) = 0.51619255967603984470383078452566 y[1] (numeric) = 0.50758310649332615558387443253891 absolute error = 0.00860945318271368911995635198675 relative error = 1.6678762646476236807939928299154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.506 y[1] (analytic) = 0.51531762725117605181829796504763 y[1] (numeric) = 0.50664764743727536039401666187298 absolute error = 0.00866997981390069142428130317465 relative error = 1.682453569490408868695514277934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.507 y[1] (analytic) = 0.51444317950864461756033059850955 y[1] (numeric) = 0.50571240852864990165720647296927 absolute error = 0.00873077097999471590312412554028 relative error = 1.6971302813915536576371819101977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.508 y[1] (analytic) = 0.51356921732289321159072016094739 y[1] (numeric) = 0.50477739025256937599367270537583 absolute error = 0.00879182707032383559704745557156 relative error = 1.7119069394683373907812966161591 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.509 y[1] (analytic) = 0.51269574156788394683069290369378 y[1] (numeric) = 0.50384259309502758498778554633585 absolute error = 0.00885314847285636184290735735793 relative error = 1.7267840855830772786649476260358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.51 y[1] (analytic) = 0.51182275311709250549986976232543 y[1] (numeric) = 0.50290801754289204919429544589958 absolute error = 0.00891473557420045630557431642585 relative error = 1.7417622643597056402031958883979 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.511 y[1] (analytic) = 0.51095025284350726564065692667989 y[1] (numeric) = 0.50197366408390352127085313446591 absolute error = 0.00897658875960374436980379221398 relative error = 1.7568420232004610613793351324724 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.512 y[1] (analytic) = 0.51007824161962842812994054747852 y[1] (numeric) = 0.50103953320667549823729761019301 absolute error = 0.00903870841295292989264293728551 relative error = 1.7720239123026943583651269802021 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.513 y[1] (analytic) = 0.50920672031746714417895856778793 y[1] (numeric) = 0.50010562540069373286219983694937 absolute error = 0.00910109491677341131675873083856 relative error = 1.7873084846757902395298868482265 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.514 y[1] (analytic) = 0.50833568980854464332222217937555 y[1] (numeric) = 0.49917194115631574417715076622091 absolute error = 0.00916374865222889914507141315464 relative error = 1.8026962961582055685875991941014 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.515 y[1] (analytic) = 0.5074651509638913618963589149652 y[1] (numeric) = 0.49823848096477032711928316864522 absolute error = 0.00922666999912103477707574631998 relative error = 1.8181879054346251389966494686925 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.516 y[1] (analytic) = 0.50659510465404607200974889747675 y[1] (numeric) = 0.49730524531815706130251763261036 absolute error = 0.00928985933588901070723126486639 relative error = 1.8337838740532358776680705366194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=118.2MB, alloc=4.5MB, time=6.47 x[1] = 0.517 y[1] (analytic) = 0.50572555174905501100382527654134 y[1] (numeric) = 0.49637223470944581891802395863119 absolute error = 0.00935331703960919208580131791015 relative error = 1.8494847664431204040562170749204 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.518 y[1] (analytic) = 0.50485649311847101140690939091887 y[1] (numeric) = 0.49543944963247627176439004900089 absolute error = 0.00941704348599473964251934191798 relative error = 1.8652911499317708788013155830819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.519 y[1] (analytic) = 0.50398792963135263138145070291028 y[1] (numeric) = 0.49450689058195739740799126250766 absolute error = 0.00948103904939523397345944040262 relative error = 1.8812035947627240842672125494364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.52 y[1] (analytic) = 0.50311986215626328566554105745225 y[1] (numeric) = 0.49357455805346698447405407380614 absolute error = 0.00954530410279630119148698364611 relative error = 1.8972226741133186875706909370387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.521 y[1] (analytic) = 0.50225229156127037700957232430744 y[1] (numeric) = 0.49264245254345113706890874633859 absolute error = 0.00960983901781923994066357796885 relative error = 1.9133489641125756450317870174916 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.522 y[1] (analytic) = 0.50138521871394442810890598662047 y[1] (numeric) = 0.49171057454922377833392659651193 absolute error = 0.00967464416472064977497939010854 relative error = 1.9295830438592027153884669781436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.523 y[1] (analytic) = 0.50051864448135821403342274309759 y[1] (numeric) = 0.49077892456896615313163829515197 absolute error = 0.00973971991239206090178444794562 relative error = 1.9459254954397240576146768063542 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.524 y[1] (analytic) = 0.49965256973008589515481969418814 y[1] (numeric) = 0.48984750310172632986453052007509 absolute error = 0.00980506662835956529028917411305 relative error = 1.9623769039467358977590308535171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.525 y[1] (analytic) = 0.4987869953262021505725221848984 y[1] (numeric) = 0.48891631064741870142701914093922 absolute error = 0.00987068467878344914550304395918 relative error = 1.9789378574972892578831354551899 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.526 y[1] (analytic) = 0.49792192213528131203907687825382 y[1] (numeric) = 0.48798534770682348529109798435931 absolute error = 0.00993657442845782674797889389451 relative error = 1.9956089472514007489246455279081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.527 y[1] (analytic) = 0.49705735102239649838589213394419 y[1] (numeric) = 0.48705461478158622272616309359691 absolute error = 0.01000273624081027565972904034728 relative error = 2.0123907674306924381415260445975 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.528 y[1] (analytic) = 0.49619328285211875045019126633951 y[1] (numeric) = 0.48612411237421727715351326295783 absolute error = 0.01006917047790147329667800338168 relative error = 2.0292839153371618107115490770967 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.529 y[1] (analytic) = 0.49532971848851616650404375485096 y[1] (numeric) = 0.48519384098809133163602849235558 absolute error = 0.01013587750042483486801526249538 relative error = 2.0462889913720828540657236873361 % 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 = 0.01020285766770615268281010521369 relative error = 2.0634065990550393026270641179835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=122.0MB, alloc=4.5MB, time=6.68 x[1] = 0.531 y[1] (analytic) = 0.49360410463508898693856653588713 y[1] (numeric) = 0.48333399329738575011431727405185 absolute error = 0.01027011133770323682424926183528 relative error = 2.0806373450430910898077961515933 % 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 = 0.01033763886700555719185665206199 relative error = 2.0979818391500750633897378894786 % 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 = 0.01040544061083388691205320126303 relative error = 2.1154406943660410297751364434209 % 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 = 0.01047351692303994711741331578422 relative error = 2.13301452687682420204967435395 % 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 = 0.01061049466114476180394513288238 relative error = 2.1685096046235082506426724761622 % 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 = 0.01067939678789852076318938800783 relative error = 2.1864320983880900298507679452573 % 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 = 0.01074857488473931830879624005956 relative error = 2.2044720665449680309098322812778 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.539 y[1] (analytic) = 0.48672197395327368394313963993034 y[1] (numeric) = 0.4759039446546053487210131702748 absolute error = 0.01081802929866833522212646965554 relative error = 2.2226301415573418114970079434068 % 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 = 0.01088776037531559772865953676772 relative error = 2.2409069592045569160175562847933 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.541 y[1] (analytic) = 0.485006556876448915150860734182 y[1] (numeric) = 0.47404878841750928328286457643813 absolute error = 0.01095776845893963186799615774387 relative error = 2.2593031586026630626522885265252 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.542 y[1] (analytic) = 0.48414962039941114241125724185424 y[1] (numeric) = 0.47312156650698402317589628793786 absolute error = 0.01102805389242711923536095391638 relative error = 2.2778193822251176854689195443847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.543 y[1] (analytic) = 0.48329319977270998273031087355997 y[1] (numeric) = 0.47219458275541742863536144329316 absolute error = 0.01109861701729255409494943026681 relative error = 2.2964562759236359959310667517349 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.544 y[1] (analytic) = 0.48243729585276599144079813076171 y[1] (numeric) = 0.4712678376790880895753359599911 absolute error = 0.01116945817367790186546217077061 relative error = 2.315214488949188738568317722469 % h = 0.001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=6.90 NO POLE x[1] = 0.545 y[1] (analytic) = 0.4815819094954830171613860184838 y[1] (numeric) = 0.47034133179513075818321825362435 absolute error = 0.01124057770035225897816776485945 relative error = 2.3340946739731488261039288384071 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.546 y[1] (analytic) = 0.48072704155624734589285475196364 y[1] (numeric) = 0.46941506562153583178502014505403 absolute error = 0.01131197593471151410783460690961 relative error = 2.3530974871085880499744190347416 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.547 y[1] (analytic) = 0.47987269288992684563188303805971 y[1] (numeric) = 0.46848903967714883485501270026287 absolute error = 0.01138365321277801077687033779684 relative error = 2.3722235879317250729187268744078 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.548 y[1] (analytic) = 0.47901886435087011150325131755937 y[1] (numeric) = 0.46756325448166990017024499320977 absolute error = 0.0114556098692002113330063243496 relative error = 2.3914736395035259211648584472466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.549 y[1] (analytic) = 0.47816555679290561141131783611242 y[1] (numeric) = 0.46663771055565324911045463712365 absolute error = 0.01152784623725236230086319898877 relative error = 2.4108483083914582047002343985131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.55 y[1] (analytic) = 0.47731277106934083221162189224271 y[1] (numeric) = 0.46571240842050667110388978428286 absolute error = 0.01160036264883416110773210795985 relative error = 2.4303482646914003051794270490953 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.551 y[1] (analytic) = 0.47646050803296142640346809076379 y[1] (numeric) = 0.4647873485984910022195631484147 absolute error = 0.01167315943447042418390494234909 relative error = 2.4499741820497067822008574335685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.552 y[1] (analytic) = 0.47560876853603035934434490894292 y[1] (numeric) = 0.46386253161271960290645945741759 absolute error = 0.01174623692331075643788545152533 relative error = 2.4697267376854312599735057377609 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.553 y[1] (analytic) = 0.47475755343028705698703036092402 y[1] (numeric) = 0.46293795798715783488021859715491 absolute error = 0.01181959544312922210681176376911 relative error = 2.489606612412708067797000066311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.554 y[1] (analytic) = 0.47390686356694655414023702323283 y[1] (numeric) = 0.46201362824662253715781755959382 absolute error = 0.01189323532032401698241946363901 relative error = 2.5096144906632939192948253134605 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.555 y[1] (analytic) = 0.47305669979669864325364816064811 y[1] (numeric) = 0.4610895429167815012407751605634 absolute error = 0.01196715687991714201287300008471 relative error = 2.5297510605092709269720885373979 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.556 y[1] (analytic) = 0.47220706296970702372819616733216 y[1] (numeric) = 0.46016570252415294544740434388365 absolute error = 0.01204136044555407828079182344851 relative error = 2.5500170136859122604175570202811 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.557 y[1] (analytic) = 0.47135795393560845175243401287092 y[1] (numeric) = 0.45924210759610498839463773956928 absolute error = 0.01211584633950346335779627330164 relative error = 2.570413045614711768335832676896 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.558 y[1] (analytic) = 0.47050937354351189066584985678171 y[1] (numeric) = 0.45831875866085512162995299423885 absolute error = 0.01219061488265676903589686254286 relative error = 2.5909398554265788965808395708738 % h = 0.001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=7.10 NO POLE x[1] = 0.559 y[1] (analytic) = 0.46966132264199766184997446810299 y[1] (numeric) = 0.45739565624746968141392524175992 absolute error = 0.01226566639452798043604922634307 relative error = 2.6115981459852002464675934937339 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.56 y[1] (analytic) = 0.46881380207911659614813055888797 y[1] (numeric) = 0.45647280088586331965393493153383 absolute error = 0.01234100119325327649419562735414 relative error = 2.6323886239105691298668231174773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.561 y[1] (analytic) = 0.46796681270238918581467261178217 y[1] (numeric) = 0.4555501931067984739895600806681 absolute error = 0.01241661959559071182511253111407 relative error = 2.6533119996026844899377663818565 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.562 y[1] (analytic) = 0.46712035535880473699456525237423 y[1] (numeric) = 0.45462783344188483703018286460005 absolute error = 0.01249252191691989996438238777418 relative error = 2.6743689872654205688297349438532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.563 y[1] (analytic) = 0.46627443089482052273414768667114 y[1] (numeric) = 0.45370572242357882474534130852091 absolute error = 0.01256870847124169798880637815023 relative error = 2.6955603049305687162842015171481 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.564 y[1] (analytic) = 0.46542904015636093652393119286274 y[1] (numeric) = 0.45278386058518304400835768920427 absolute error = 0.01264517957117789251557350365847 relative error = 2.7168866744820527457976141907227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.565 y[1] (analytic) = 0.46458418398881664637427612450758 y[1] (numeric) = 0.45186224846084575929377610356624 absolute error = 0.01272193552797088708050002094134 relative error = 2.7383488216803192578622895924913 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.566 y[1] (analytic) = 0.46373986323704374942479434939252 y[1] (numeric) = 0.45094088658556035852914250647527 absolute error = 0.01279897665148339089565184291725 relative error = 2.7599474761869043627900113567775 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.567 y[1] (analytic) = 0.4628960787453629270883225145933 y[1] (numeric) = 0.450019775495164818101661365987 absolute error = 0.0128763032501981089866611486063 relative error = 2.7816833715891782487418073337877 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.568 y[1] (analytic) = 0.46205283135755860073031099369233 y[1] (numeric) = 0.44909891572634116702026392930302 absolute error = 0.01295391563121743371004706438931 relative error = 2.8035572454252690538392614104274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.569 y[1] (analytic) = 0.46121012191687808788447283669442 y[1] (numeric) = 0.44817830781661495023362393734054 absolute error = 0.01303181410026313765084889935388 relative error = 2.8255698392091675146191144854732 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.57 y[1] (analytic) = 0.46036795126603075900553650692117 y[1] (numeric) = 0.44725795230435469110465746985259 absolute error = 0.01310999896167606790087903706858 relative error = 2.8477218984560138766153228054468 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.571 y[1] (analytic) = 0.45952632024718719475994565206105 y[1] (numeric) = 0.44633784972877135304204444655402 absolute error = 0.01318847051841584171790120550703 relative error = 2.870014172707568566512687461039 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=133.5MB, alloc=4.5MB, time=7.31 x[1] = 0.572 y[1] (analytic) = 0.45868522970197834385534861860512 y[1] (numeric) = 0.44541800062991780028931015268708 absolute error = 0.01326722907206054356603846591804 relative error = 2.8924474155578681391151817396109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.573 y[1] (analytic) = 0.45784468047149468140971988010875 y[1] (numeric) = 0.44449840554868825787200599989995 absolute error = 0.0133462749228064235377138802088 relative error = 2.9150223846790680263117372740289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.574 y[1] (analytic) = 0.45700467339628536786095501008776 y[1] (numeric) = 0.44357906502681777070352957521259 absolute error = 0.01342560836946759715742543487517 relative error = 2.9377398418474736293040784883449 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.575 y[1] (analytic) = 0.45616520931635740841778028988382 y[1] (numeric) = 0.44265997960688166185012487220474 absolute error = 0.01350522970947574656765541767908 relative error = 2.9606005529697613095868098533102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.576 y[1] (analytic) = 0.45532628907117481305281750051966 y[1] (numeric) = 0.44174114983229498995560443938065 absolute error = 0.01358513923887982309721306113901 relative error = 2.9836052881093908485409734882604 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.577 y[1] (analytic) = 0.45448791349965775703864390540909 y[1] (numeric) = 0.44082257624731200582633602094326 absolute error = 0.01366533725234575121230788446583 relative error = 3.0067548215132109600203369182241 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.578 y[1] (analytic) = 0.45365008344018174202768688779204 y[1] (numeric) = 0.43990425939702560817703710494583 absolute error = 0.01374582404315613385064978284621 relative error = 3.0300499316382594549763934936169 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.579 y[1] (analytic) = 0.45281279973057675767679216292994 y[1] (numeric) = 0.43898619982736679853792163298118 absolute error = 0.01382659990320995913887052994876 relative error = 3.0534914011787596719851324841703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.58 y[1] (analytic) = 0.45197606320812644381730394042354 y[1] (numeric) = 0.43806839808510413532374396421635 absolute error = 0.01390766512302230849355997620719 relative error = 3.077080017093314802507754019763 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.581 y[1] (analytic) = 0.45113987470956725317149486650297 y[1] (numeric) = 0.43715085471784318706528602468326 absolute error = 0.01398901999172406610620884181971 relative error = 3.1008165706323017548403784607411 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.582 y[1] (analytic) = 0.45030423507108761461618302979055 y[1] (numeric) = 0.43623357027402598480383441029263 absolute error = 0.01407066479706162981234861949792 relative error = 3.1247018573654662159861640493706 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.583 y[1] (analytic) = 0.44946914512832709699437276684941 y[1] (numeric) = 0.43531654530293047364919504904846 absolute error = 0.01415259982539662334517771780095 relative error = 3.1487366772097205861188557281495 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.584 y[1] (analytic) = 0.44863460571637557347575545580759 y[1] (numeric) = 0.43439978035466996350179386440268 absolute error = 0.01423482536170560997396159140491 relative error = 3.1729218344571464759014182962506 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.585 y[1] (analytic) = 0.4478006176697723864669059374871 y[1] (numeric) = 0.43348327598019257893941271760349 absolute error = 0.01431734168957980752749321988361 relative error = 3.1972581378032034726788569650455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=137.3MB, alloc=4.5MB, time=7.52 x[1] = 0.586 y[1] (analytic) = 0.44696718182250551307200965377196 y[1] (numeric) = 0.4325670327312807082691107422557 absolute error = 0.01440014909122480480289891151626 relative error = 3.2217464003751458974824183790248 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.587 y[1] (analytic) = 0.44613429900801073110495504241853 y[1] (numeric) = 0.43165105116055045174488201912577 absolute error = 0.01448324784746027936007302329276 relative error = 3.2463874397606492908649382547798 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.588 y[1] (analytic) = 0.44530197005917078565362517614627 y[1] (numeric) = 0.43073533182145106895160137348786 absolute error = 0.01456663823771971670202380265841 relative error = 3.2711820780366483818360236770467 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.589 y[1] (analytic) = 0.44447019580831455619722208164774 y[1] (numeric) = 0.42981987526826442535581091101912 absolute error = 0.01465032054005013084141117062862 relative error = 3.2961311417983883105829175540289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.59 y[1] (analytic) = 0.44363897708721622427745662112423 y[1] (numeric) = 0.42890468205610443802390074141147 absolute error = 0.01473429503111178625355587971276 relative error = 3.3212354621886908922502019177948 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.591 y[1] (analytic) = 0.44280831472709444172443626508772 y[1] (numeric) = 0.42798975274091652050823817147308 absolute error = 0.01481856198617792121619809361464 relative error = 3.3464958749274377258108914817921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.592 y[1] (analytic) = 0.44197820955861149943808253047211 y[1] (numeric) = 0.42707508787947702690180048154394 absolute error = 0.01490312167913447253628204892817 relative error = 3.371913220341271968994908956135 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.593 y[1] (analytic) = 0.44114866241187249672590930256691 y[1] (numeric) = 0.42616068802939269506186723054656 absolute error = 0.01498797438247980166404207202035 relative error = 3.3974883433935206173504032101256 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.594 y[1] (analytic) = 0.44031967411642451119799270292604 y[1] (numeric) = 0.42524655374910008900332886593303 absolute error = 0.01507312036732442219466383699301 relative error = 3.4232220937143391428008792445227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.595 y[1] (analytic) = 0.43949124550125576921996260821254 y[1] (numeric) = 0.42433268559786504046216924517332 absolute error = 0.01515855990339072875779336303922 relative error = 3.4491153256310803645286888535122 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.596 y[1] (analytic) = 0.43866337739479481692484536691856 y[1] (numeric) = 0.42341908413578208962968050525588 absolute error = 0.01524429325901272729516486166268 relative error = 3.4751688981988894426651418921346 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.597 y[1] (analytic) = 0.43783607062490969178458670204891 y[1] (numeric) = 0.42250574992377392505796954593896 absolute error = 0.01533032070113576672661715610995 relative error = 3.5013836752315269031014249469257 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.598 y[1] (analytic) = 0.43700932601890709474208322817614 y[1] (numeric) = 0.42159268352359082273731622119951 absolute error = 0.01541664249531627200476700697663 relative error = 3.5277605253324216197547676636531 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.599 y[1] (analytic) = 0.43618314440353156290455045076672 y[1] (numeric) = 0.42067988549781008434594416147478 absolute error = 0.01550325890572147855860628929194 relative error = 3.5543003219259556988330140958925 % h = 0.001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=7.74 NO POLE x[1] = 0.6 y[1] (analytic) = 0.43535752660496464279905455434134 y[1] (numeric) = 0.41976735640983547467276597687894 absolute error = 0.0155901701951291681262885774624 relative error = 3.5810039432889832280401009885042 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.601 y[1] (analytic) = 0.43453247344882406419103472386862 y[1] (numeric) = 0.41885509682389665821366541860261 absolute error = 0.01567737662492740597736930526601 relative error = 3.6078722725825848722571077565096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.602 y[1] (analytic) = 0.43370798576016291446664218080111 y[1] (numeric) = 0.41794310730504863494187990216629 absolute error = 0.01576487845511427952476227863482 relative error = 3.6349061978840603160207423534428 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.603 y[1] (analytic) = 0.43288406436346881357972155134577 y[1] (numeric) = 0.41703138841917117525304762209801 absolute error = 0.01585267594429763832667392924776 relative error = 3.6621066122191605721056093424291 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.604 y[1] (analytic) = 0.43206071008266308956425961991864 y[1] (numeric) = 0.41611994073296825408548431294109 absolute error = 0.01594076934969483547877530697755 relative error = 3.689474413594562194700645570906 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.605 y[1] (analytic) = 0.4312379237410999546131259552665 y[1] (numeric) = 0.41520876481396748421625553626811 absolute error = 0.01602915892713247039687041899839 relative error = 3.7170105050305854550560077571643 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.606 y[1] (analytic) = 0.43041570616156568172392933044603 y[1] (numeric) = 0.41429786123051954873361119758147 absolute error = 0.01611784493104613299031813286456 relative error = 3.744715794594158557066786830196 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.607 y[1] (analytic) = 0.42959405816627778191281329073545 y[1] (numeric) = 0.41338723055179763268634982061885 absolute error = 0.0162068276144801492264634701166 relative error = 3.7725911954320299900565671811179 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.608 y[1] (analytic) = 0.42877298057688418199701365561464 y[1] (numeric) = 0.41247687334779685391068092965185 absolute error = 0.01629610722908732808633272596279 relative error = 3.8006376258042311360294359921335 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.609 y[1] (analytic) = 0.42795247421446240294700017218763 y[1] (numeric) = 0.41156679018933369303515471286804 absolute error = 0.01638568402512870991184545931959 relative error = 3.8288560091177912688759995708893 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.61 y[1] (analytic) = 0.42713253989951873880902396783728 y[1] (numeric) = 0.41065698164804542266422896185923 absolute error = 0.01647555825147331614479500597805 relative error = 3.857247273960707103449731765842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.611 y[1] (analytic) = 0.42631317845198743619889187949639 y[1] (numeric) = 0.40974744829638953574104410360149 absolute error = 0.0165657301555979004578477758949 relative error = 3.8858123541361690730770466889085 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.612 y[1] (analytic) = 0.42549439069122987436778816569248 y[1] (numeric) = 0.4088381907076431730899779621042 absolute error = 0.01665619998358670127781020358828 relative error = 3.9145521886970465349303681520397 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.613 y[1] (analytic) = 0.42467617743603374584096353547619 y[1] (numeric) = 0.4079292094559025501395527071257 absolute error = 0.01674696798013119570141082835049 relative error = 3.9434677219806341237807073012928 % h = 0.001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=7.94 NO POLE x[1] = 0.614 y[1] (analytic) = 0.42385853950461223763011085547598 y[1] (numeric) = 0.40702050511608238282626726700082 absolute error = 0.01683803438852985480384358847516 relative error = 3.9725599036436614959574360488598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.615 y[1] (analytic) = 0.4230414777146032130202463226353 y[1] (numeric) = 0.4061120782639153126799293017 absolute error = 0.0169293994506879003403170209353 relative error = 4.0018296886975687268806679232634 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.616 y[1] (analytic) = 0.42222499288306839393191431568267 y[1] (numeric) = 0.40520392947595133109106165074019 absolute error = 0.01702106340711706284085266494248 relative error = 4.0312780375440496472985739124874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.617 y[1] (analytic) = 0.42140908582649254385953356306188 y[1] (numeric) = 0.40429605932955720276095898849299 absolute error = 0.01711302649693534109857457456889 relative error = 4.0609059160108654253607464219808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.618 y[1] (analytic) = 0.42059375736078265138670168890796 y[1] (numeric) = 0.40338846840291588833497123678545 absolute error = 0.01720528895786676305173045212251 relative error = 4.0907142953879307238920913545904 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.619 y[1] (analytic) = 0.41977900830126711427927462169634 y[1] (numeric) = 0.40248115727502596621959110146192 absolute error = 0.01729785102624114805968352023442 relative error = 4.1207041524636747847024228470193 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.62 y[1] (analytic) = 0.41896483946269492415703677241779 y[1] (numeric) = 0.40157412652570105358392391577128 absolute error = 0.01739071293699387057311285664651 relative error = 4.1508764695616798144777387061208 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.621 y[1] (analytic) = 0.41815125165923485174477731054103 y[1] (numeric) = 0.40066737673556922654611878906142 absolute error = 0.01748387492366562519865852147961 relative error = 4.1812322345775990697528839363883 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.622 y[1] (analytic) = 0.41733824570447463270358728661891 y[1] (numeric) = 0.39976090848607243954534087430153 absolute error = 0.01757733721840219315824641231738 relative error = 4.2117724410163570616648178053034 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.623 y[1] (analytic) = 0.41652582241142015404319177017304 y[1] (numeric) = 0.39885472235946594389986538241153 absolute error = 0.01767110005195421014332638776151 relative error = 4.2424980880296343246338760322252 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.624 y[1] (analytic) = 0.41571398259249464111613059045704 y[1] (numeric) = 0.39794881893881770555187478525619 absolute error = 0.01776516365367693556425580520085 relative error = 4.2734101804536392168201903000953 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.625 y[1] (analytic) = 0.41490272705953784519460068584992 y[1] (numeric) = 0.39704319880800782199954146245819 absolute error = 0.01785952825153002319505922339173 relative error = 4.3045097288471692441567562956614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.626 y[1] (analytic) = 0.41409205662380523163077248496947 y[1] (numeric) = 0.39613786255172793841697885989894 absolute error = 0.01795419407207729321379362507053 relative error = 4.3357977495299644239725308503358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=148.7MB, alloc=4.5MB, time=8.15 x[1] = 0.627 y[1] (analytic) = 0.4132819720959671686013921591217 y[1] (numeric) = 0.39523281075548066296264503990723 absolute error = 0.01804916134048650563874711921447 relative error = 4.3672752646213552286914290250194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.628 y[1] (analytic) = 0.41247247428610811643748100141646 y[1] (numeric) = 0.3943280440055789812767833146836 absolute error = 0.01814443028052913516069768673286 relative error = 4.3989433020792076748292628169414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.629 y[1] (analytic) = 0.4116635640037258175399426027822 y[1] (numeric) = 0.39342356288914567016848546547083 absolute error = 0.01824000111458014737145713731137 relative error = 4.430802895739168147513633883194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.63 y[1] (analytic) = 0.41085524205773048688188790920538 y[1] (numeric) = 0.39251936799411271049296386035862 absolute error = 0.01833587406361777638892404884676 relative error = 4.4628550853542105760247228041115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.631 y[1] (analytic) = 0.41004750925644400309848765780185 y[1] (numeric) = 0.39161545990922069921961959340132 absolute error = 0.01843204934722330387886806440053 relative error = 4.4951009166344886014010072535024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.632 y[1] (analytic) = 0.40924036640759910016516110180038 y[1] (numeric) = 0.39071183922401826069149457693161 absolute error = 0.01852852718358083947366652486877 relative error = 4.5275414412874954029764326485813 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.633 y[1] (analytic) = 0.40843381431833855966490934618239 y[1] (numeric) = 0.38980850652886145707669632756898 absolute error = 0.01862530778947710258821301861341 relative error = 4.5601777170585338768177349880665 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.634 y[1] (analytic) = 0.40762785379521440364560102657702 y[1] (numeric) = 0.3889054624149131980123849944491 absolute error = 0.01872239138030120563321603212792 relative error = 4.593010807771499885415802728328 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.635 y[1] (analytic) = 0.40682248564418708806801747405878 y[1] (numeric) = 0.38800270747414264944191298563781 absolute error = 0.01881977817004443862610448842097 relative error = 4.6260417833699813246565318752156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.636 y[1] (analytic) = 0.40601771067062469684546391773531 y[1] (numeric) = 0.38710024229932464164570835554092 absolute error = 0.01891746837130005519975556219439 relative error = 4.6592717199586757810579888720983 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.637 y[1] (analytic) = 0.40521352967930213647575268544688 y[1] (numeric) = 0.38619806748403907646649392237701 absolute error = 0.01901546219526306000925876306987 relative error = 4.6927016998451295795153065551348 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.638 y[1] (analytic) = 0.40440994347440033126636377052741 y[1] (numeric) = 0.3852961836226703337294348904448 absolute error = 0.01911375985172999753692888008261 relative error = 4.7263328115818010493461015829047 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.639 y[1] (analytic) = 0.40360695285950541915358753939926 y[1] (numeric) = 0.38439459131040667685780855698794 absolute error = 0.01921236154909874229577898241132 relative error = 4.7601661500084508642808650664073 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.64 y[1] (analytic) = 0.40280455863760794811645376079207 y[1] (numeric) = 0.383493291143239657684790487938 absolute error = 0.01931126749436829043166327285407 relative error = 4.7942028162948623401983355853019 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=152.5MB, alloc=4.5MB, time=8.36 x[1] = 0.641 y[1] (analytic) = 0.40200276161110207318625054258986 y[1] (numeric) = 0.38259228371796352046195235069993 absolute error = 0.01941047789313855272429819188993 relative error = 4.8284439179838946028689562084303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.642 y[1] (analytic) = 0.40120156258178475405243616672017 y[1] (numeric) = 0.3816915696321746050650673954324 absolute error = 0.01950999294961014898736877128777 relative error = 4.8628905690348715667438329073043 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.643 y[1] (analytic) = 0.40040096235085495326574621610695 y[1] (numeric) = 0.38079114948427074939782037896788 absolute error = 0.01960981286658420386792583713907 relative error = 4.8975438898673096949158874341338 % 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 = 0.01970993784546214404527826290018 relative error = 4.9324050074049875397879187931773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.645 y[1] (analytic) = 0.39880156148595896464849201010053 y[1] (numeric) = 0.37899119339971346781890893656538 absolute error = 0.01981036808624549682958307353515 relative error = 4.9674750551203600937128889108037 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.646 y[1] (analytic) = 0.3980027624513935084305154067426 y[1] (numeric) = 0.37809165866385781827018060459051 absolute error = 0.01991110378753569016033480215209 relative error = 5.0027551730793210089288153345997 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.647 y[1] (analytic) = 0.39720456541401543438424020351384 y[1] (numeric) = 0.37719242026748158037928610288681 absolute error = 0.02001214514653385400495410062703 relative error = 5.0382465079863157764981230939617 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.648 y[1] (analytic) = 0.39640697117202171337132288239725 y[1] (numeric) = 0.37629347881298109021364867678696 absolute error = 0.02011349235904062315767420561029 relative error = 5.0739502132298089846831672859365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.649 y[1] (analytic) = 0.39560998052300652091929983903959 y[1] (numeric) = 0.37539483490355057948037737802736 absolute error = 0.02021514561945594143892246101223 relative error = 5.1098674489281088082499280223558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.65 y[1] (analytic) = 0.39481359426396043962747832139406 y[1] (numeric) = 0.37449648914318157233208562382339 absolute error = 0.02031710512077886729539269757067 relative error = 5.1459993819755519115946938066127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.651 y[1] (analytic) = 0.39401781319126966217642024629276 y[1] (numeric) = 0.37359844213666228137541737688132 absolute error = 0.02041937105460738080100286941144 relative error = 5.1823471860890519803380358847378 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.652 y[1] (analytic) = 0.39322263810071519494181588439859 y[1] (numeric) = 0.37270069448957700288288493777041 absolute error = 0.02052194361113819205893094662818 relative error = 5.2189120418550151281307370559302 % 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 = 0.02062482297916655100492066182971 relative error = 5.2556951367766254578718317706021 % 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 = 0.02072800934608605861204730733328 relative error = 5.2926976653215040893538543392172 % h = 0.001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=8.57 NO POLE x[1] = 0.655 y[1] (analytic) = 0.39084075667058521656348124135303 y[1] (numeric) = 0.37000925377269673706634886313089 absolute error = 0.02083150289788847949713237822214 relative error = 5.3299208289697449985291500917299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.656 y[1] (analytic) = 0.39004801345425448825244775327319 y[1] (numeric) = 0.36911270963509093232345329843592 absolute error = 0.02093530381916355592899445483727 relative error = 5.3673658362623310471381096712908 % 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 = 0.02103941229309882323872231643681 relative error = 5.4050339028499336153599273919988 % 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 = 5.4429262515420992844435084271331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.659 y[1] (analytic) = 0.38767344668479865132692622696415 y[1] (numeric) = 0.36642489406011071192217510514078 absolute error = 0.02124855262468793940475112182337 relative error = 5.4810441123568270509550646801994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.66 y[1] (analytic) = 0.3868831480265662113848545206037 y[1] (numeric) = 0.36552956318486202882582266400833 absolute error = 0.02135358484170418255903185659537 relative error = 5.5193887225705395893444150262453 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.661 y[1] (analytic) = 0.38609346248513465180727674557586 y[1] (numeric) = 0.36463453715502960598250313836873 absolute error = 0.02145892533010504582477360720713 relative error = 5.5579613267684521149887739207238 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.662 y[1] (analytic) = 0.38530439085018944821862622039934 y[1] (numeric) = 0.36373981658412513813649252602325 absolute error = 0.02156457426606431008213369437609 relative error = 5.5967631768953424357256680064652 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.663 y[1] (analytic) = 0.38451593391080216980813914682333 y[1] (numeric) = 0.36284540208644969862025511345199 absolute error = 0.02167053182435247118788403337134 relative error = 5.6357955323067258161404221898808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.664 y[1] (analytic) = 0.38372809245542969025835117655314 y[1] (numeric) = 0.36195129427709312505342133510401 absolute error = 0.02177679817833656520492984144913 relative error = 5.6750596598204383155333285504718 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.665 y[1] (analytic) = 0.38294086727191339928828943345192 y[1] (numeric) = 0.36105749377193340425300141125166 absolute error = 0.02188337349997999503528802220026 relative error = 5.7145568337686322975621431399191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.666 y[1] (analytic) = 0.38215425914747841481214844796039 y[1] (numeric) = 0.36016400118763605635544985414421 absolute error = 0.02199025795984235845669859381618 relative error = 5.7542883360501878470420038215365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.667 y[1] (analytic) = 0.38136826886873279571423784499337 y[1] (numeric) = 0.35927081714165351815119672034496 absolute error = 0.02209745172707927756304112464841 relative error = 5.7942554561835438672923512284388 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=160.2MB, alloc=4.5MB, time=8.78 x[1] = 0.668 y[1] (analytic) = 0.38058289722166675524098901029949 y[1] (numeric) = 0.35837794225222452563226227466921 absolute error = 0.02220495496944222960872673563028 relative error = 5.8344594913599526697541579208556 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.669 y[1] (analytic) = 0.37979814499165187501080734321209 y[1] (numeric) = 0.35748537713837349575357251805695 absolute error = 0.02231276785327837925723482515514 relative error = 5.8749017464971619063659909548581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.67 y[1] (analytic) = 0.37901401296344031964255608587341 y[1] (numeric) = 0.35659312241990990740859381801322 absolute error = 0.02242089054353041223396226786019 relative error = 5.9155835342935277343894842191497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.671 y[1] (analytic) = 0.37823050192116405200345710038291 y[1] (numeric) = 0.35570117871742768161990566592991 absolute error = 0.022529323203736370383551434453 relative error = 5.9565061752825631430190847981118 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.672 y[1] (analytic) = 0.37744761264833404907719334590347 y[1] (numeric) = 0.35480954665230456094533137066465 absolute error = 0.02263806599602948813186197523882 relative error = 5.9976709978879254112029409312348 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.673 y[1] (analytic) = 0.37666534592783951845299718755764 y[1] (numeric) = 0.3539182268467014881002472821943 absolute error = 0.02274711908113803035274990536334 relative error = 6.0390793384788467066470704892544 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.674 y[1] (analytic) = 0.37588370254194711543650804796045 y[1] (numeric) = 0.35302721992356198379669192298213 absolute error = 0.02285648261838513163981612497832 relative error = 6.0807325414260118769791159589036 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.675 y[1] (analytic) = 0.3751026832723001607831822904657 y[1] (numeric) = 0.35213652650661152379989718789759 absolute error = 0.02296615676568863698328510256811 relative error = 6.1226319591578875255167585588798 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.676 y[1] (analytic) = 0.37432228889991785905503760065086 y[1] (numeric) = 0.3512461472203569152028645561057 absolute error = 0.02307614167956094385217304454516 relative error = 6.1647789522175065060250114073422 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.677 y[1] (analytic) = 0.37354252020519451760151350923091 y[1] (numeric) = 0.35035608269008567191961004029772 absolute error = 0.02318643751510884568190346893319 relative error = 6.2071748893197120132619991375919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.678 y[1] (analytic) = 0.37276337796789876616522907547561 y[1] (numeric) = 0.34946633354186538939770237996627 absolute error = 0.02329704442603337676752669550934 relative error = 6.2498211474088654890103980804599 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.679 y[1] (analytic) = 0.3719848629671727771134181253074 y[1] (numeric) = 0.34857690040254311855071976613443 absolute error = 0.02340796256462965856269835917297 relative error = 6.2927191117170226066774768912182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.68 y[1] (analytic) = 0.37120697598153148629582181257975 y[1] (numeric) = 0.34768778389974473891125116503008 absolute error = 0.02351919208178674738457064754967 relative error = 6.3358701758225816414267440002152 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.681 y[1] (analytic) = 0.37042971778886181452981764557857 y[1] (numeric) = 0.34679898466187433100506908765181 absolute error = 0.02363073312698748352474855792676 relative error = 6.3792757417094085771847603350946 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=164.0MB, alloc=4.5MB, time=9.00 x[1] = 0.682 y[1] (analytic) = 0.36965308916642188971356349355254 y[1] (numeric) = 0.34591050331811354794710143100137 absolute error = 0.02374258584830834176646206255117 relative error = 6.4229372198264433467539825691832 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.683 y[1] (analytic) = 0.36887709089084026956793446006375 y[1] (numeric) = 0.34502234049842098625983079495845 absolute error = 0.0238547503924192833081036651053 relative error = 6.4668560291477916466629184589284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.684 y[1] (analytic) = 0.36810172373811516500802988115697 y[1] (numeric) = 0.34413449683353155591475045634605 absolute error = 0.02396722690458360909327942481092 relative error = 6.5110335972333068143048432630155 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.685 y[1] (analytic) = 0.36732698848361366414502707677567 y[1] (numeric) = 0.34324697295495584959750695867795 absolute error = 0.02408001552865781454752011809772 relative error = 6.555471360289666301362374550501 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.686 y[1] (analytic) = 0.36655288590207095691915785350657 y[1] (numeric) = 0.34235976949497951119736005239311 absolute error = 0.02419311640709144572179780111346 relative error = 6.6001707632319473244939511172829 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.687 y[1] (analytic) = 0.36577941676758956036458312561155 y[1] (numeric) = 0.34147288708666260352159149606452 absolute error = 0.02430652968092695684299162954703 relative error = 6.6451332597457063217764202273702 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.688 y[1] (analytic) = 0.36500658185363854450694038940761 y[1] (numeric) = 0.34058632636383897523549500412091 absolute error = 0.0244202554897995692714453852867 relative error = 6.6903603123495668914623080902528 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.689 y[1] (analytic) = 0.36423438193305275889433815338313 y[1] (numeric) = 0.33970008796111562702858040103864 absolute error = 0.02453429397193713186575775234449 relative error = 6.7358533924583209382278269840642 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.69 y[1] (analytic) = 0.36346281777803205976257079299128 y[1] (numeric) = 0.33881417251387207700762581574687 absolute error = 0.02464864526415998275494497724441 relative error = 6.7816139804465478012652492272705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.691 y[1] (analytic) = 0.36269189016014053783532666484154 y[1] (numeric) = 0.33792858065825972531721252314081 absolute error = 0.02476330950188081251811414170073 relative error = 6.827643565712756188318040080389 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.692 y[1] (analytic) = 0.36192159985030574676016168001679 y[1] (numeric) = 0.33704331303120121798837781211539 absolute error = 0.0248782868191045287717838679014 relative error = 6.8739436467440537900762731495762 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.693 y[1] (analytic) = 0.36115194761881793218100990047802 y[1] (numeric) = 0.33615837027038981001602203141334 absolute error = 0.02499357734842812216498786906468 relative error = 6.9205157311813495002506366883742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.694 y[1] (analytic) = 0.36038293423532926144800208598196 y[1] (numeric) = 0.33527375301428872766570673582767 absolute error = 0.02510918122104053378229535015429 relative error = 6.9673613358850932181331617529454 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.695 y[1] (analytic) = 0.35961456046885305396536248162878 y[1] (numeric) = 0.3343894619021305300104816259072 absolute error = 0.02522509856672252395488085572158 relative error = 7.0144819870015582625391500463634 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=167.8MB, alloc=4.5MB, time=9.21 x[1] = 0.696 y[1] (analytic) = 0.35884682708776301217815349807899 y[1] (numeric) = 0.33350549757391646969837874428499 absolute error = 0.025341329513846542479774753794 relative error = 7.0618792200296714787152407926902 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.697 y[1] (analytic) = 0.35807973485979245319863729763077 y[1] (numeric) = 0.33262186067041585295121316108226 absolute error = 0.02545787418937660024742413654851 relative error = 7.1095545798883961731008276883867 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.698 y[1] (analytic) = 0.35731328455203354107302265973213 y[1] (numeric) = 0.3317385518331653987953301495337 absolute error = 0.02557473271886814227769251019843 relative error = 7.1575096209846730647519213184306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.699 y[1] (analytic) = 0.35654747693093651968936485911696 y[1] (numeric) = 0.3308555717044685975249396210337 absolute error = 0.02569190522646792216442523808326 relative error = 7.2057459072819244967859602895106 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.7 y[1] (analytic) = 0.35578231276230894632738564860128 y[1] (numeric) = 0.32997292092739506839867935621549 absolute error = 0.02580939183491387792870629238579 relative error = 7.2542650123691272063910267094309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.701 y[1] (analytic) = 0.35501779281131492585097979665585 y[1] (numeric) = 0.32909060014577991657004933544651 absolute error = 0.02592719266553500928093046120934 relative error = 7.303068519530459007771551269505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.702 y[1] (analytic) = 0.35425391784247434554417398718465 y[1] (numeric) = 0.32820861000422308925236023825208 absolute error = 0.02604530783825125629181374893257 relative error = 7.3521580218155247988831462443468 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.703 y[1] (analytic) = 0.35349068861966211059130324548666 y[1] (numeric) = 0.3273269511480887311188399466652 absolute error = 0.02616373747157337947246329882146 relative error = 7.4015351221101673599500425429566 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.704 y[1] (analytic) = 0.35272810590610738020216941016085 y[1] (numeric) = 0.32644562422350453893854265234225 absolute error = 0.0262824816826028412636267578186 relative error = 7.451201433207868469568207752466 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.705 y[1] (analytic) = 0.35196617046439280438294552573213 y[1] (numeric) = 0.32556462987736111544870593148175 absolute error = 0.02640154058703168893423959425038 relative error = 7.5011585778817459226841828019441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.706 y[1] (analytic) = 0.35120488305645376135358938503038 y[1] (numeric) = 0.3246839687573113224642019151352 absolute error = 0.02652091429914243888938746989518 relative error = 7.5514081889571520939127127919826 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.707 y[1] (analytic) = 0.35044424444357759561252880384534 y[1] (numeric) = 0.32380364151176963322472944540499 absolute error = 0.02664060293180796238779935844035 relative error = 7.6019519093848797495242023305469 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.708 y[1] (analytic) = 0.3496842553864028566493805631088 y[1] (numeric) = 0.32292364878991148398039487028317 absolute error = 0.02676060659649137266898569282563 relative error = 7.652791392314980872004861180665 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.709 y[1] (analytic) = 0.34892491664491853830646430582142 y[1] (numeric) = 0.32204399124167262481632989149632 absolute error = 0.0268809254032459134901344143251 relative error = 7.7039283011712043223772119910943 % h = 0.001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=9.42 NO POLE x[1] = 0.71 y[1] (analytic) = 0.34816622897846331878987202714716 y[1] (numeric) = 0.32116466951774846971699564068458 absolute error = 0.02700155946071484907287638646258 relative error = 7.7553643097260582274756261349764 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.711 y[1] (analytic) = 0.3474081931457248013308531465424 y[1] (numeric) = 0.32028568426959344587082291955651 absolute error = 0.02712250887613135546003022698589 relative error = 7.8071011021765030421100839175427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.712 y[1] (analytic) = 0.34665080990473875549827450047127 y[1] (numeric) = 0.31940703614942034221583929932542 absolute error = 0.02724377375531841328243520114585 relative error = 7.8591403732202812995309012167853 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.713 y[1] (analytic) = 0.34589408001288835916291394318423 y[1] (numeric) = 0.31852872581019965722693453374574 absolute error = 0.02736535420268870193597940943849 relative error = 7.9114838281328901278373394806135 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.714 y[1] (analytic) = 0.34513800422690344111434559120292 y[1] (numeric) = 0.31765075390565894594541649842966 absolute error = 0.02748725032124449516892909277326 relative error = 7.9641331828452026749635693634687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.715 y[1] (analytic) = 0.344382583302859724331174094563 y[1] (numeric) = 0.31677312109028216625151062683367 absolute error = 0.02760946221257755807966346772933 relative error = 8.0170901640217446506362776248269 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.716 y[1] (analytic) = 0.34362781799617806990537466451765 y[1] (numeric) = 0.31589582801930902438045657036117 absolute error = 0.02773198997686904552491809415648 relative error = 8.0703565091396322602393198635388 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.717 y[1] (analytic) = 0.34287370906162372162149493329869 y[1] (numeric) = 0.3150188753487343196828565664298 absolute error = 0.02785483371288940193863836686889 relative error = 8.1239339665681778728523981624345 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.718 y[1] (analytic) = 0.3421202572533055511914740666705 y[1] (numeric) = 0.31414226373530728862993075410071 absolute error = 0.02797799351799826256154331256979 relative error = 8.177824295649169833863097194841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.719 y[1] (analytic) = 0.34136746332467530414583389439473 y[1] (numeric) = 0.31326599383653094806433543195961 absolute error = 0.02810146948814435608149846243512 relative error = 8.2320292667778329014952059417925 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.72 y[1] (analytic) = 0.34061532802852684638199616735183 y[1] (numeric) = 0.31239006631066143769720100737672 absolute error = 0.02822526171786540868479515997511 relative error = 8.2865506614844758563616950030857 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.721 y[1] (analytic) = 0.3398638521169954113704793929394 y[1] (numeric) = 0.31151448181670736185204714005284 absolute error = 0.02834937030028804951843225288656 relative error = 8.3413902725168329037487729475594 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.722 y[1] (analytic) = 0.33911303634155684801972804248768 y[1] (numeric) = 0.31063924101442913045623333588156 absolute error = 0.02847379532712771756349470660612 relative error = 8.3965499039231055597790242365914 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=175.4MB, alloc=4.5MB, time=9.63 x[1] = 0.723 y[1] (analytic) = 0.33836288145302686920032626580041 y[1] (numeric) = 0.30976434456433829928060399962207 absolute error = 0.02859853688868856991972226617834 relative error = 8.4520313711357117848978069519032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.724 y[1] (analytic) = 0.33761338820156030092934758854468 y[1] (numeric) = 0.30888979312769690942798770668259 absolute error = 0.02872359507386339150135988186209 relative error = 8.5078365010557492012890902433165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.725 y[1] (analytic) = 0.33686455733665033221559140807746 y[1] (numeric) = 0.30801558736651682607121120546002 absolute error = 0.02884896997013350614438020261744 relative error = 8.5639671321381793048661293154047 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.726 y[1] (analytic) = 0.33611638960712776556645644240991 y[1] (numeric) = 0.30714172794355907644128941216681 absolute error = 0.0289746616635686891251670302431 relative error = 8.6204251144777396574103634721795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.727 y[1] (analytic) = 0.33536888576116026815720062537343 y[1] (numeric) = 0.3062682155223331870664534098998 absolute error = 0.02910067023882708109074721547363 relative error = 8.6772123098955911202603996987781 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.728 y[1] (analytic) = 0.33462204654625162366333627866526 y[1] (numeric) = 0.30539505076709652026267921286783 absolute error = 0.02922699577915510340065706579743 relative error = 8.7343305920267072676937984052379 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.729 y[1] (analytic) = 0.33387587270924098475690872831604 y[1] (numeric) = 0.30452223434285360987638080519406 absolute error = 0.02935363836638737488052792312198 relative error = 8.7917818464080131958096683030759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.73 y[1] (analytic) = 0.33313036499630212626740586923847 y[1] (numeric) = 0.30364976691535549627993171154467 absolute error = 0.0294805980809466299874741576938 relative error = 8.8495679705672810213220366974502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.731 y[1] (analytic) = 0.33238552415294269900804551688526 y[1] (numeric) = 0.3027776491510990606206801040068 absolute error = 0.02960787500184363838736541287846 relative error = 8.9076908741127894442249989878957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.732 y[1] (analytic) = 0.33164135092400348426818671966681 y[1] (numeric) = 0.30190588171732635832412319614533 absolute error = 0.02973546920667712594406352352148 relative error = 8.9661524788237548288033553326318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.733 y[1] (analytic) = 0.33089784605365764897261053965515 y[1] (numeric) = 0.3010344652820239518519074210084 absolute error = 0.02986338077163369712070311864675 relative error = 9.024954718741541338949583724923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.734 y[1] (analytic) = 0.33015501028541000150841514223148 y[1] (numeric) = 0.30016340051392224271532163502601 absolute error = 0.02999160977148775879309350720547 relative error = 9.0840995402616577462225325101955 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.735 y[1] (analytic) = 0.32941284436209624822026936771989 y[1] (numeric) = 0.29929268808249480274495133425277 absolute error = 0.03012015627960144547531803346712 relative error = 9.1435889022265486125582847702532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.736 y[1] (analytic) = 0.32867134902588225057476828969201 y[1] (numeric) = 0.29842232865795770461716261324484 absolute error = 0.03024902036792454595760567644717 relative error = 9.2034247760191876340325858697055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=179.2MB, alloc=4.5MB, time=9.84 x[1] = 0.737 y[1] (analytic) = 0.32793052501826328299463359552502 y[1] (numeric) = 0.2975523229112688516380853400314 absolute error = 0.03037820210699443135654825549362 relative error = 9.2636091456574810175905613728528 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.738 y[1] (analytic) = 0.32719037308006329136350095495073 y[1] (numeric) = 0.29668267151412730678576576314149 absolute error = 0.03050770156593598457773519180924 relative error = 9.3241440078894888492169098397707 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.739 y[1] (analytic) = 0.32645089395143415220203587174673 y[1] (numeric) = 0.29581337513897262101115950847783 absolute error = 0.0306375188124615311908763632689 relative error = 9.3850313722894724996322579090147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.74 y[1] (analytic) = 0.32571208837185493251611884239183 y[1] (numeric) = 0.29494443445898416079863666498857 absolute error = 0.03076765391287077171748217740326 relative error = 9.446273261354776202283040803765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.741 y[1] (analytic) = 0.32497395708013115031783997343909 y[1] (numeric) = 0.29407585014808043498667139857587 absolute error = 0.03089810693205071533116857486322 relative error = 9.5078717106035510281574534183105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.742 y[1] (analytic) = 0.32423650081439403582004253655019 y[1] (numeric) = 0.2932076228809184208493892734956 absolute error = 0.03102887793347561497065326305459 relative error = 9.5698287686733295728232484003152 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.743 y[1] (analytic) = 0.32349972031209979330515426658597 y[1] (numeric) = 0.29233975333289288943964619964467 absolute error = 0.0311599669792069038655080669413 relative error = 9.632146497420459763059193893724 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.744 y[1] (analytic) = 0.32276361631002886366904453386027 y[1] (numeric) = 0.29147224218013573019431366260084 absolute error = 0.03129137412989313347473087125943 relative error = 9.694826972020406283555816776767 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.745 y[1] (analytic) = 0.32202818954428518764064484663867 y[1] (numeric) = 0.29060509009951527480244563107346 absolute error = 0.03142309944476991283819921556521 relative error = 9.7578722810689282184078388561511 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.746 y[1] (analytic) = 0.32129344075029546967806946419994 y[1] (numeric) = 0.28973829776863562033700327354196 absolute error = 0.03155514298165984934106619065798 relative error = 9.8212845266841415975258781948864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.747 y[1] (analytic) = 0.32055937066280844254197222427846 y[1] (numeric) = 0.28887186586583595165081435230085 absolute error = 0.03168750479697249089115787197761 relative error = 9.8850658246094756346741768359573 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.748 y[1] (analytic) = 0.31982598001589413254687501146943 y[1] (numeric) = 0.2880057950701898630374448988955 absolute error = 0.03182018494570426950943011257393 relative error = 9.949218304317531541610201168995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.749 y[1] (analytic) = 0.3190932695429431254912026152071 y[1] (numeric) = 0.28714008606150467915766151002042 absolute error = 0.03195318348143844633354110518668 relative error = 10.013744109114852901777047531046 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.75 y[1] (analytic) = 0.31836123997666583326675804722011 y[1] (numeric) = 0.28627473952032077523216333736114 absolute error = 0.03208650045634505803459470985897 relative error = 10.078645396247616687197016453702 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=183.1MB, alloc=4.5MB, time=10.06 x[1] = 0.751 y[1] (analytic) = 0.31762989204909176114837170892742 y[1] (numeric) = 0.28540975612791089650126357859112 absolute error = 0.0322201359211808646471081303363 relative error = 10.143924337008254103651078844412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.752 y[1] (analytic) = 0.3168992264915687757644571190647 y[1] (numeric) = 0.28454513656627947695220100978542 absolute error = 0.03235408992528929881225610927928 relative error = 10.209583116843010551921076220157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.753 y[1] (analytic) = 0.31616924403476237374920523092425 y[1] (numeric) = 0.28368088151816195731476283188288 absolute error = 0.03248836251660041643444239904137 relative error = 10.275623935460454096836454049958 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.754 y[1] (analytic) = 0.31543994540865495107714868695348 y[1] (numeric) = 0.28281699166702410232590083551706 absolute error = 0.03262295374163084875124785143642 relative error = 10.34204900694094194112245471481 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.755 y[1] (analytic) = 0.31471133134254507308082667608652 y[1] (numeric) = 0.28195346769706131726402361954297 absolute error = 0.03275786364548375581680305654355 relative error = 10.408860559847054507609584283797 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.756 y[1] (analytic) = 0.31398340256504674515228037608347 y[1] (numeric) = 0.28109031029319796375364832891031 absolute error = 0.03289309227184878139863204717316 relative error = 10.476060837335006841252666416204 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.757 y[1] (analytic) = 0.31325615980408868412910827932099 y[1] (numeric) = 0.28022752014108667484109610717459 absolute error = 0.0330286396630020092880121721464 relative error = 10.543652097267047151640024079701 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.758 y[1] (analytic) = 0.31252960378691359036581001591817 y[1] (numeric) = 0.2793650979271076693419161878935 absolute error = 0.03316450585980592102389382802467 relative error = 10.611636612324852427267672223144 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.759 y[1] (analytic) = 0.31180373524007742049114660279324 y[1] (numeric) = 0.27850304433836806546072427742731 absolute error = 0.03330069090170935503042232536593 relative error = 10.680016670123931164828523163704 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.76 y[1] (analytic) = 0.31107855488944866085224436123027 y[1] (numeric) = 0.2776413600627011936841416092478 absolute error = 0.03343719482674746716810275198247 relative error = 10.748794573329043370141441085812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.761 y[1] (analytic) = 0.31035406346020760164616905879138 y[1] (numeric) = 0.2767800457886659089475217767593 absolute error = 0.03357401767154169269864728203208 relative error = 10.817972639770648102138755796588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.762 y[1] (analytic) = 0.30963026167684561173969614393974 y[1] (numeric) = 0.2759191022055459020761531778478 absolute error = 0.03371115947129970966354296609194 relative error = 10.88755320256238894756306966872 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.763 y[1] (analytic) = 0.30890715026316441417800225354293 y[1] (numeric) = 0.27505853000334901050162562989816 absolute error = 0.03384862025981540367637662364477 relative error = 10.957538610219627931714668963235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.764 y[1] (analytic) = 0.30818472994227536238300248450447 y[1] (numeric) = 0.27419832987280652825405043885553 absolute error = 0.03398640006946883412895204564894 relative error = 11.027931226779038489759682152009 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=10.27 NO POLE x[1] = 0.765 y[1] (analytic) = 0.30746300143659871704205723112624 y[1] (numeric) = 0.27333850250537251523082393005328 absolute error = 0.03412449893122620181123330107296 relative error = 11.09873343191926824377671623432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.766 y[1] (analytic) = 0.30674196546786292368777169943441 y[1] (numeric) = 0.2724790485932231057426251719864 absolute error = 0.03426291687463981794514652744801 relative error = 11.169947621082682452906757149312 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.767 y[1] (analytic) = 0.30602162275710389096961051860939 y[1] (numeric) = 0.27161996882925581633733934697506 absolute error = 0.03440165392784807463227117163433 relative error = 11.241576205598199127698664024991 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.768 y[1] (analytic) = 0.30530197402466426961804917784491 y[1] (numeric) = 0.2707612639070888529025989447372 absolute error = 0.03454071011757541671545023310771 relative error = 11.313621612805226925031958073888 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.769 y[1] (analytic) = 0.30458301999019273210198332442474 y[1] (numeric) = 0.26990293452106041704763567627128 absolute error = 0.03468008546913231505434764815346 relative error = 11.386086286178717066871466629576 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.77 y[1] (analytic) = 0.30386476137264325298011626554779 y[1] (numeric) = 0.26904498136622801176513672613942 absolute error = 0.03481978000641524121497953940837 relative error = 11.458972685455340654586719856803 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.771 y[1] (analytic) = 0.30314719889027438994704432245398 y[1] (numeric) = 0.2681874051383677463737996812369 absolute error = 0.03495979375190664357324464121708 relative error = 11.532283286760802880675133722687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.772 y[1] (analytic) = 0.30243033326064856557475899070575 y[1] (numeric) = 0.26733020653397364074228119343506 absolute error = 0.03510012672667492483247779727069 relative error = 11.606020582738305771484607931029 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.773 y[1] (analytic) = 0.30171416520063134975028416506311 y[1] (numeric) = 0.26647338625025692879523515209104 absolute error = 0.03524077895037442095504901297207 relative error = 11.680187082678171227961225677886 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.774 y[1] (analytic) = 0.30099869542639074281016599125526 y[1] (numeric) = 0.26561694498514536130213686032811 absolute error = 0.03538175044124538150802913092715 relative error = 11.754785312648636266574616859742 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.775 y[1] (analytic) = 0.30028392465339645937253221009913 y[1] (numeric) = 0.26476088343728250794959042620435 absolute error = 0.03552304121611395142294178389478 relative error = 11.829817815627832499420946679068 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.776 y[1] (analytic) = 0.29956985359641921286743716184588 y[1] (numeric) = 0.26390520230602705869781729640404 absolute error = 0.03566465129039215416961986544184 relative error = 11.905287151636962031095487574806 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.777 y[1] (analytic) = 0.29885648296953000076620792035069 y[1] (numeric) = 0.26304990229145212442202457590513 absolute error = 0.03580658067807787634418334444556 relative error = 11.981195897874682090287761352068 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=190.7MB, alloc=4.5MB, time=10.48 x[1] = 0.778 y[1] (analytic) = 0.29814381348609939051050632766018 y[1] (numeric) = 0.26219498409434453683935249219607 absolute error = 0.03594882939175485367115383546411 relative error = 12.057546648852710856207110824954 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.779 y[1] (analytic) = 0.29743184585879680614182099989582 y[1] (numeric) = 0.26134044841620414772210107703631 absolute error = 0.03609139744259265841971992285951 relative error = 12.134342016532667083920466155049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.78 y[1] (analytic) = 0.29672058079958981563210267488208 y[1] (numeric) = 0.26048629595924312739793685247527 absolute error = 0.03623428484034668823416582240681 relative error = 12.211584630464156278502585996417 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.781 y[1] (analytic) = 0.2960100190197434189162555708243 y[1] (numeric) = 0.25963252742638526253778102086476 absolute error = 0.03637749159335815637847454995954 relative error = 12.289277137924116315588145265543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.782 y[1] (analytic) = 0.29530016122981933662719672348589 y[1] (numeric) = 0.25877914352126525323208137091801 absolute error = 0.03652101770855408339511535256788 relative error = 12.367422204057435555501076165036 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.783 y[1] (analytic) = 0.29459100813967529953419456674599 y[1] (numeric) = 0.25792614494822800935617082348496 absolute error = 0.03666486319144729017802374326103 relative error = 12.446022512018856649646318554322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.784 y[1] (analytic) = 0.29388256045846433868519731813999 y[1] (numeric) = 0.25707353241232794622541625162654 absolute error = 0.03680902804613639245978106651345 relative error = 12.525080763116179391309783408872 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.785 y[1] (analytic) = 0.29317481889463407625386102699527 y[1] (numeric) = 0.25622130661932827954086191978044 absolute error = 0.03695351227530579671299910721483 relative error = 12.60459967695477611845148131416 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.786 y[1] (analytic) = 0.292467784155926017091986438075 y[1] (numeric) = 0.25536946827570031962607259631619 absolute error = 0.03709831588022569746591384175881 relative error = 12.684581991583433333522444910116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.787 y[1] (analytic) = 0.29176145694937484098807311823418 y[1] (numeric) = 0.25451801808862276495588210257763 absolute error = 0.03724343886075207603219101565655 relative error = 12.765030463641533364816741096579 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.788 y[1] (analytic) = 0.29105583798130769563269858747478 y[1] (numeric) = 0.25366695676598099497775376960533 absolute error = 0.03738888121532670065494481786945 relative error = 12.845947868507590055414426986674 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.789 y[1] (analytic) = 0.29035092795734349029142948896187 y[1] (numeric) = 0.25281628501636636222645998111957 absolute error = 0.0375346429409771280649695078423 relative error = 12.927337000449152629409101982203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.79 y[1] (analytic) = 0.2896467275823921901859711250308 y[1] (numeric) = 0.25196600354907548373278868802537 absolute error = 0.03768072403331670645318243700543 relative error = 13.00920067277409205087455095222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.791 y[1] (analytic) = 0.28894323756065411158426097797705 y[1] (numeric) = 0.25111611307410953172698548567401 absolute error = 0.03782712448654457985727549230304 relative error = 13.091541717983284358939127057009 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=194.5MB, alloc=4.5MB, time=10.69 x[1] = 0.792 y[1] (analytic) = 0.28824045859561921760021112547646 y[1] (numeric) = 0.25026661430217352363764055037979 absolute error = 0.03797384429344569396257057509667 relative error = 13.174362987924705632434724515679 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.793 y[1] (analytic) = 0.2875383913900664147038037508348 y[1] (numeric) = 0.249417507944675611386730436246 absolute error = 0.0381208834453908033170733145888 relative error = 13.257667353948953409900657238489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.794 y[1] (analytic) = 0.28683703664606284994224323791253 y[1] (numeric) = 0.24856879471372636998152543719905 absolute error = 0.03826824193233647996071780071348 relative error = 13.341457707066209565283190904228 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.795 y[1] (analytic) = 0.28613639506496320887286762951401 y[1] (numeric) = 0.24772047532213808540407392226414 absolute error = 0.03841591974282512346879370724987 relative error = 13.425736958104659816511070639785 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.796 y[1] (analytic) = 0.28543646734740901420852151627135 y[1] (numeric) = 0.2468725504834240417989757545387 absolute error = 0.03856391686398497240954576173265 relative error = 13.510508037870385223278843909571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.797 y[1] (analytic) = 0.28473725419332792517609171059139 y[1] (numeric) = 0.24602502091179780796015760603093 absolute error = 0.03871223328153011721593410456046 relative error = 13.595773897308741211866310092332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.798 y[1] (analytic) = 0.28403875630193303758890634707191 y[1] (numeric) = 0.24517788732217252311736368152853 absolute error = 0.03886086897976051447154266554338 relative error = 13.681537507667239848697766319768 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.799 y[1] (analytic) = 0.28334097437172218463369733692953 y[1] (numeric) = 0.24433115043016018202307606494742 absolute error = 0.03900982394156200261062127198211 relative error = 13.7678018606599512706331243715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8 y[1] (analytic) = 0.28264390910047723837282538941861 y[1] (numeric) = 0.24348481095207091934057960118061 absolute error = 0.039159098148406319032245788238 relative error = 13.85456996863344036871924474173 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.801 y[1] (analytic) = 0.28194756118526341196246609795798 y[1] (numeric) = 0.24263886960491229333388692532255 absolute error = 0.03930869158035111862857917263543 relative error = 13.941844864734255013349317626939 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.802 y[1] (analytic) = 0.28125193132242856258745487272111 y[1] (numeric) = 0.24179332710638856886023994928438 absolute error = 0.03945860421603999372721492343673 relative error = 14.029629603077982302516719301069 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.803 y[1] (analytic) = 0.28055702020760249511348778478693 y[1] (numeric) = 0.24094818417489999966590481323875 absolute error = 0.03960883603270249544758297154818 relative error = 14.117927258919889511143954967808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.804 y[1] (analytic) = 0.27986282853569626645737466959218 y[1] (numeric) = 0.24010344152954210998597800603951 absolute error = 0.03975938700615415647139666355267 relative error = 14.206740928827166618354110250579 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.805 y[1] (analytic) = 0.27916935700090149067604011937443 y[1] (numeric) = 0.23925909989010497544892205475022 absolute error = 0.03991025711079651522711806462421 relative error = 14.296073730852787491069303109203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=198.3MB, alloc=4.5MB, time=10.91 x[1] = 0.806 y[1] (analytic) = 0.27847660629668964477496727554668 y[1] (numeric) = 0.23841515997707250328654987868595 absolute error = 0.04006144631961714148841739686073 relative error = 14.385928804711007006506181860159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.807 y[1] (analytic) = 0.27778457711581137523677861250211 y[1] (numeric) = 0.23757162251162171185017759792396 absolute error = 0.04021295460418966338660101457815 relative error = 14.476309311954511603031384635075 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.808 y[1] (analytic) = 0.27709327015029580527064718421017 y[1] (numeric) = 0.23672848821562200943366628007041 absolute error = 0.04036478193467379583698090413976 relative error = 14.567218436153240958479508756178 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.809 y[1] (analytic) = 0.2764026860914498427832310841352 y[1] (numeric) = 0.23588575781163447240407380218136 absolute error = 0.04051692827981537037915728195384 relative error = 14.658659383074898707462609657296 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.81 y[1] (analytic) = 0.27571282562985748907182314748546 y[1] (numeric) = 0.23504343202291112264063869712587 absolute error = 0.04066939360694636643118445035959 relative error = 14.750635380867170324454270244406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.811 y[1] (analytic) = 0.27502368945537914824040720258509 y[1] (numeric) = 0.23420151157339420428281854534731 absolute error = 0.04082217788198494395758865723778 relative error = 14.843149680241666517554213661702 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.812 y[1] (analytic) = 0.27433527825715093733931145525542 y[1] (numeric) = 0.2333599971877154597881061639241 absolute error = 0.04097528106943547755120529133132 relative error = 14.936205554659610698873295774654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.813 y[1] (analytic) = 0.27364759272358399722914886649459 y[1] (numeric) = 0.23251888959119540530034753505343 absolute error = 0.04112870313238859192880133144116 relative error = 15.029806300519289321466199943367 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.814 y[1] (analytic) = 0.27296063354236380416973365945774 y[1] (numeric) = 0.2316781895098426053292861055796 absolute error = 0.04128244403252119884044755387814 relative error = 15.123955237345284099723640273495 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.815 y[1] (analytic) = 0.27227440140044948213466236676389 y[1] (numeric) = 0.23083789767035294674205877796226 absolute error = 0.04143650373009653539260358880163 relative error = 15.218655707979505360161429555285 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.816 y[1] (analytic) = 0.2715888969840731158522471034912 y[1] (numeric) = 0.22999801480010891206736960112807 absolute error = 0.04159088218396420378487750236313 relative error = 15.313911078774046002655160265904 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.817 y[1] (analytic) = 0.27090412097873906457348802486997 y[1] (numeric) = 0.22915854162717885211306785697151 absolute error = 0.04174557935156021246042016789846 relative error = 15.409724739785875788411975998983 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.818 y[1] (analytic) = 0.27022007406922327656777120064388 y[1] (numeric) = 0.22831947888031625789785792486615 absolute error = 0.04190059518890701866991327577773 relative error = 15.506100104973395910391202639171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.819 y[1] (analytic) = 0.26953675693957260434697741034436 y[1] (numeric) = 0.2274808272889590318978689924158 absolute error = 0.04205592965061357244910841792856 relative error = 15.603040612394874044530433858148 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=11.12 NO POLE x[1] = 0.82 y[1] (analytic) = 0.26885417027310412061868663531228 y[1] (numeric) = 0.22664258758322875860881336581519 absolute error = 0.04221158268987536200987326949709 relative error = 15.700549724408780326050751591251 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.821 y[1] (analytic) = 0.26817231475240443496916229420547 y[1] (numeric) = 0.22580476049392997442446281760103 absolute error = 0.04236755425847446054469947660444 relative error = 15.798630927876044944352606983001 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.822 y[1] (analytic) = 0.2674911910593290112767985389509 y[1] (numeric) = 0.22496734675254943683217309325621 absolute error = 0.04252384430677957444462544569469 relative error = 15.897287734364258302621772664177 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.823 y[1] (analytic) = 0.26681079987500148585671319763723 y[1] (numeric) = 0.22413034709125539292618738108181 absolute error = 0.04268045278374609293052581655542 relative error = 15.996523680353834944292782544253 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.824 y[1] (analytic) = 0.26613114187981298633716821969816 y[1] (numeric) = 0.22329376224289684723945023197251 absolute error = 0.04283737963691613909771798772565 relative error = 16.096342327446162708016291562009 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.825 y[1] (analytic) = 0.26545221775342145126849874690922 y[1] (numeric) = 0.22245759294100282889466409722033 absolute error = 0.04299462481241862237383464968889 relative error = 16.196747262573758835798531862671 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.826 y[1] (analytic) = 0.26477402817475095046523120121228 y[1] (numeric) = 0.22162183991978165807532133322926 absolute error = 0.04315218825496929238990986798302 relative error = 16.297742098212455025578070849723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.827 y[1] (analytic) = 0.26409657382199100608207004719305 y[1] (numeric) = 0.22078650391412021181744520204756 absolute error = 0.04331006990787079426462484514549 relative error = 16.399330472595633689730802833626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.828 y[1] (analytic) = 0.26341985537259591442443215316827 y[1] (numeric) = 0.21995158565958318912277407591551 absolute error = 0.04346826971301272530165807725276 relative error = 16.501516049930537954902812135572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.829 y[1] (analytic) = 0.26274387350328406849420694029164 y[1] (numeric) = 0.21911708589241237539412373258328 absolute error = 0.04362678761087169310008320770836 relative error = 16.60430252061667821621759965889 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.83 y[1] (analytic) = 0.26206862889003728127141977386192 y[1] (numeric) = 0.21828300534952590619366330597519 absolute error = 0.04378562354051137507775646788673 relative error = 16.707693601466358340345236513377 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.831 y[1] (analytic) = 0.26139412220810010973247531511345 y[1] (numeric) = 0.21744934476851753032484113386318 absolute error = 0.04394477743958257940763418125027 relative error = 16.811693035927344897213283861658 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.832 y[1] (analytic) = 0.26072035413197917960565681518938 y[1] (numeric) = 0.21661610488765587223869742056216 absolute error = 0.04410424924432330736695939462722 relative error = 16.916304594307703089340717795486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=205.9MB, alloc=4.5MB, time=11.33 x[1] = 0.833 y[1] (analytic) = 0.26004732533544251086455659574197 y[1] (numeric) = 0.21578328644588369376530130827311 absolute error = 0.04426403888955881709925528746886 relative error = 17.021532074002823340945491802694 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.834 y[1] (analytic) = 0.25937503649151884396011222267346 y[1] (numeric) = 0.21495089018281715517105062557538 absolute error = 0.04442414630870168878906159709808 relative error = 17.12737929972466280617359421098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.835 y[1] (analytic) = 0.25870348827249696679192214092496 y[1] (numeric) = 0.21411891683874507554257325570683 absolute error = 0.04458457143375189124934888521813 relative error = 17.233850123733226357083334955847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.836 y[1] (analytic) = 0.2580326813499250424195137989418 y[1] (numeric) = 0.21328736715462819249796974066882 absolute error = 0.04474531419529684992154405827298 relative error = 17.340948426070311917454947821725 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.837 y[1] (analytic) = 0.25736261639460993751423655149115 y[1] (numeric) = 0.21245624187209842122613740985172 absolute error = 0.04490637452251151628809914163943 relative error = 17.448678114795545318145263165329 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.838 y[1] (analytic) = 0.25669329407661655155245088888304 y[1] (numeric) = 0.21162554173345811285491699379515 absolute error = 0.04506775234315843869753389508789 relative error = 17.557043126224730163634071996852 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.839 y[1] (analytic) = 0.25602471506526714675068479934958 y[1] (numeric) = 0.21079526748167931214880335487443 absolute error = 0.04522944758358783460188144447515 relative error = 17.666047425170538517677801412722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.84 y[1] (analytic) = 0.25535688002914067874342732937035 y[1] (numeric) = 0.20996541986040301453696263714072 absolute error = 0.04539146016873766420646469222963 relative error = 17.775695005185568538663265209553 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.841 y[1] (analytic) = 0.25468978963607212800422866409446 y[1] (numeric) = 0.20913599961393842247229880723577 absolute error = 0.04555379002213370553192985685869 relative error = 17.885989888807795522406648040791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.842 y[1] (analytic) = 0.25402344455315183201077530670349 y[1] (numeric) = 0.20830700748726220112231322725276 absolute error = 0.04571643706588963088846207945073 relative error = 17.996936127808443141838746858329 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.843 y[1] (analytic) = 0.25335784544672481815460819158468 y[1] (numeric) = 0.20747844422601773339250156862161 absolute error = 0.04587940122070708476210662296307 relative error = 18.10853780344230200932618398162 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.844 y[1] (analytic) = 0.25269299298239013739615082154036 y[1] (numeric) = 0.20665031057651437428303304355983 absolute error = 0.04604268240587576311311777798053 relative error = 18.220799026700523028370330977328 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.845 y[1] (analytic) = 0.2520288878250001986657137739502 y[1] (numeric) = 0.20582260728572670457945759734749 absolute error = 0.04620628053927349408625617660271 relative error = 18.333723938565913347172726113332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.846 y[1] (analytic) = 0.25136553063866010401114117482621 y[1] (numeric) = 0.20499533510129378387818737065692 absolute error = 0.04637019553736632013295380416929 relative error = 18.447316710270763077130711682647 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=209.8MB, alloc=4.5MB, time=11.54 x[1] = 0.847 y[1] (analytic) = 0.25070292208672698449276399305858 y[1] (numeric) = 0.20416849477151840294749940639346 absolute error = 0.04653442731520858154526458666512 relative error = 18.561581543557231294803960545931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.848 y[1] (analytic) = 0.25004106283180933682632425984381 y[1] (numeric) = 0.20334208704536633542480723998224 absolute error = 0.04669897578644300140151701986157 relative error = 18.676522670940320206346843812267 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.849 y[1] (analytic) = 0.24937995353576636077453357031556 y[1] (numeric) = 0.20251611267246558885094967576703 absolute error = 0.04686384086330077192358389454853 relative error = 18.792144355973466718909816589644 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.85 y[1] (analytic) = 0.24871959485970729728792847576453 y[1] (numeric) = 0.20169057240310565504224571517 absolute error = 0.04702902245660164224568276059453 relative error = 18.908450893516781034153054976447 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.851 y[1] (analytic) = 0.24805998746399076739568462553681 y[1] (numeric) = 0.20086546698823675980106526449492 absolute error = 0.04719452047575400759461936104189 relative error = 19.025446610007962254866662973319 % 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 = 0.04736033482875499988138485600083 relative error = 19.143135863735921376834413908968 % 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 = 0.04752646542219057970401624475285 relative error = 19.261523045117142424594085844671 % 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 = 0.04769291216123562976162798321078 relative error = 19.380612576974812881720265004581 % 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 = 0.0478596749496540496795213827114 relative error = 19.500408914820754963769703810402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.856 y[1] (analytic) = 0.24477324275047132132773006648732 y[1] (numeric) = 0.19674648906067246908245310144788 absolute error = 0.04802675368979885224527696503944 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 = 0.04836185862762580957475634175698 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) = 0.19428036876243693622570961857632 absolute error = 0.04852988462296044160169521661266 relative error = 19.986752596453174150810645966372 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.86 y[1] (analytic) = 0.24215743710472302770541127047135 y[1] (numeric) = 0.1934592109393964145549789607513 absolute error = 0.04869822616532661315043230972005 relative error = 20.110150961114877585949980787165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=213.6MB, alloc=4.5MB, time=11.75 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) = 0.19181822325198835540525164648455 absolute error = 0.04903585547094358108908793353281 relative error = 20.359155107915900354215826893615 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.863 y[1] (analytic) = 0.24020353792517346858315780320164 y[1] (numeric) = 0.19099839490460968134608990157144 absolute error = 0.0492051430205637872370679016302 relative error = 20.484770310040908027249217435492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.864 y[1] (analytic) = 0.2395537569238137591287784200408 y[1] (numeric) = 0.19017901123385919307523701788749 absolute error = 0.04937474568995456605354140215331 relative error = 20.611133936696060333899400075211 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.865 y[1] (analytic) = 0.23890473636863375534249590988562 y[1] (numeric) = 0.18936007299985824316830449733086 absolute error = 0.04954466336877551217419141255476 relative error = 20.738250786425313689824502978502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.866 y[1] (analytic) = 0.23825647690865395831926959685314 y[1] (numeric) = 0.18854158096337758497917358194355 absolute error = 0.04971489594527637334009601490959 relative error = 20.866125693756796888031167602406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.867 y[1] (analytic) = 0.23760897919213377401727663990728 y[1] (numeric) = 0.18772353588583661186930529759084 absolute error = 0.04988544330629716214797134231644 relative error = 20.994763529520965886015577190795 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.868 y[1] (analytic) = 0.23696224386657086499856009629705 y[1] (numeric) = 0.18690593852930259578841054411424 absolute error = 0.05005630533726826921014955218281 relative error = 21.12416920117200841983668105965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.869 y[1] (analytic) = 0.23631627157870050293142031765021 y[1] (numeric) = 0.18608878965648992520724165122448 absolute error = 0.05022748192221057772417866642573 relative error = 21.254347653112536191307744711578 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.87 y[1] (analytic) = 0.23567106297449492185519717627715 y[1] (numeric) = 0.18527209003075934240326746727944 absolute error = 0.05039897294373557945192970899771 relative error = 21.385303867021602866329460629104 % 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 = 0.05057077828304549210809516164031 relative error = 21.517042862186086621335314928609 % 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 = 0.05074289781993337815796134937684 relative error = 21.649569695835476480990720550998 % 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 = 0.05108807899857026670351047650786 relative error = 21.917007299252847993212152483189 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.6MB, time=11.97 NO POLE x[1] = 0.875 y[1] (analytic) = 0.23245649776397296036542453294546 y[1] (numeric) = 0.18119535737111225357528858402195 absolute error = 0.05126114039286070679013594892351 relative error = 22.051928376254390840451401027242 % 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 = 0.05160820416217399256680377170788 relative error = 22.324201143281973373671576530816 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.878 y[1] (analytic) = 0.23053696401713715226972775121205 y[1] (numeric) = 0.17875475773585049188558403313598 absolute error = 0.05178220628128666038414371807607 relative error = 22.461563377505651573506091184628 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.879 y[1] (analytic) = 0.22989865750844477230729502683122 y[1] (numeric) = 0.17794213579136210553360866964374 absolute error = 0.05195652171708266677368635718748 relative error = 22.599749942069222108902733218414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.88 y[1] (analytic) = 0.22926112110103070879035486924401 y[1] (numeric) = 0.17712997076294443079206289774045 absolute error = 0.05213115033808627799829197150356 relative error = 22.738766210217187817871584238224 % 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 = 0.05230609201141373764862639867986 relative error = 22.878617596309645353911286033193 % 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 = 0.05248134660277339952690636725425 relative error = 23.01930955619338456757844447299 % 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 = 0.05265691397646586193853450346005 relative error = 23.160847587576858946205060168938 % 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 = 0.05283279399538410339148971754023 relative error = 23.303237230409073036297070547846 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.885 y[1] (analytic) = 0.22608501286991831495710414761512 y[1] (numeric) = 0.17307602634890469525376687743125 absolute error = 0.05300898652101361970333727018387 relative error = 23.446484067262433384448329663187 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.886 y[1] (analytic) = 0.22545211043143946326293915322968 y[1] (numeric) = 0.17226661901800690074721774114385 absolute error = 0.05318549141343256251572141208583 relative error = 23.590593723719610152934436957505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.887 y[1] (analytic) = 0.22481998254078563447399837107075 y[1] (numeric) = 0.17145767400947375525779628892181 absolute error = 0.05336230853131187921620208214894 relative error = 23.735571868764457195656363104984 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=221.2MB, alloc=4.6MB, time=12.18 x[1] = 0.888 y[1] (analytic) = 0.22418862983008466656678812483747 y[1] (numeric) = 0.17064919209816921229949238233414 absolute error = 0.05353943773191545426729574250333 relative error = 23.881424215177039018934015766089 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.889 y[1] (analytic) = 0.22355805293068921762955218375027 y[1] (numeric) = 0.16984117405958896568697316243614 absolute error = 0.05371687887110025194257902131413 relative error = 24.028156519932813699956593143764 % 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 = 0.05389463180331646046971242728558 relative error = 24.175774584606021493634338892792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.891 y[1] (analytic) = 0.22229922908734582223684384457509 y[1] (numeric) = 0.16822653270573818465660385172519 absolute error = 0.0540726963816076375802399928499 relative error = 24.324284255777329526322438072301 % 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 = 0.05425107245761085746601929625356 relative error = 24.473691425445783652562382951851 % 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 = 0.0544297598815568591421349061229 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 = 0.05460875850227019621614688560825 relative error = 24.775222057864483335879824932467 % 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) = 0.16419810149975271042540265119327 absolute error = 0.05496768872226707240911456048834 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) = 0.16339382243636444328388148234701 absolute error = 0.05514762001217015931448999833289 relative error = 25.234399203325997606332768708087 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.898 y[1] (analytic) = 0.21791787613354185228333124736692 y[1] (numeric) = 0.16259001425346186571230352479712 absolute error = 0.0553278618800799865710277225698 relative error = 25.389317692401986077771140060547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.899 y[1] (analytic) = 0.21729509190060779491828897618233 y[1] (numeric) = 0.16178667773281531841973164845415 absolute error = 0.05550841416779247649855732772818 relative error = 25.545176231215747130989862460147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9 y[1] (analytic) = 0.21667309037251661153861768428645 y[1] (numeric) = 0.16098381365681831738919200708825 absolute error = 0.0556892767156982941494256771982 relative error = 25.701981090477892336736958703956 % 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 = 0.05587044936278300691781855010679 relative error = 25.859738590227577356510240703399 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=225.0MB, alloc=4.6MB, time=12.39 x[1] = 0.902 y[1] (analytic) = 0.21543143791808544498721276287073 y[1] (numeric) = 0.15937950597145819943303293360787 absolute error = 0.05605193194662724555417982926286 relative error = 26.018455100290491154213355968127 % h = 0.001 TOP MAIN SOLVE Loop 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 = 26.338790882373839958232284940283 % 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 = 0.05659823767345279515910942146275 relative error = 26.50042314716941779300446126525 % 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 = 0.05678095835204842607350331898959 relative error = 26.663040408779450223007669173373 % 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 = 0.05696398813423842079305022107121 relative error = 26.826649293006335852137888117627 % 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 = 0.0571473268491772501735430559373 relative error = 26.99125647829232412623878177548 % 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 = 0.05733097432461561485699610957635 relative error = 27.156868696213211959234153312176 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.91 y[1] (analytic) = 0.21049626031004958812104248212845 y[1] (numeric) = 0.15298132992314897060011245251487 absolute error = 0.05751493038690061752093002961358 relative error = 27.323492731977395154265989275854 % 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 = 0.057699194860975936531254676716 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) = 0.15138658106597051049353030338025 absolute error = 0.05788376757038200099857617065617 relative error = 27.659803669064546916459522292798 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.913 y[1] (analytic) = 0.2086585785876018138010267943691 y[1] (numeric) = 0.15058993025034564656327371962664 absolute error = 0.05806864833725616723775307474246 relative error = 27.829504413535059427072421180694 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.914 y[1] (analytic) = 0.20804759988020658339188045106857 y[1] (numeric) = 0.14979376289787368676135519199471 absolute error = 0.05825383698233289663052525907386 relative error = 28.000244663180611730768328815749 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.915 y[1] (analytic) = 0.20743741312514547674500726750837 y[1] (numeric) = 0.14899807980020154185396968750253 absolute error = 0.05843933332494393489103758000584 relative error = 28.172031479050460288871014445919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=228.8MB, alloc=4.6MB, time=12.61 x[1] = 0.916 y[1] (analytic) = 0.20682801893260519807261933043264 y[1] (numeric) = 0.14820288174958670533854022011457 absolute error = 0.05862513718301849273407911031807 relative error = 28.344871978936984868018929645866 % 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 = 0.05881124837308342794585725186009 relative error = 28.518773337914125941350871471792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.918 y[1] (analytic) = 0.20561161067187051983215106836788 y[1] (numeric) = 0.14661394396160709097502640845196 absolute error = 0.05899766671026342885712465991592 relative error = 28.693742788881731932435433054032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.919 y[1] (analytic) = 0.20500459782008427963139730153571 y[1] (numeric) = 0.14582020581180308041292179535976 absolute error = 0.05918439200828119921847550617595 relative error = 28.869787623115890107738053034991 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.92 y[1] (analytic) = 0.20439837996363396973172389751838 y[1] (numeric) = 0.14502695588417632525409769248315 absolute error = 0.05937142407945764447762620503523 relative error = 29.046915190825315957945571119095 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.921 y[1] (analytic) = 0.20379295770873739606528773573527 y[1] (numeric) = 0.14423419497402533660679340978221 absolute error = 0.05955876273471205945849432595306 relative error = 29.225132901713876959088300330919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.922 y[1] (analytic) = 0.20318833166081676307680958963652 y[1] (numeric) = 0.14344192387725444563492157682602 absolute error = 0.0597464077835623174418880128105 relative error = 29.404448225549327671389047783082 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.923 y[1] (analytic) = 0.20258450242449806830142013383096 y[1] (numeric) = 0.14265014339037300765380330423876 absolute error = 0.0599343590341250606476168295922 relative error = 29.584868692738334217407703643863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.924 y[1] (analytic) = 0.20198147060361049773871279445357 y[1] (numeric) = 0.14185885431049460562087924415599 absolute error = 0.06012261629311589211783355029758 relative error = 29.766401894907867281624663718266 % 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 = 0.06031117936584956900141500975545 relative error = 29.949055485493043891407494324032 % h = 0.001 TOP MAIN SOLVE Loop NO POLE 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 = 0.06068922216680142764981064384032 relative error = 30.317754758264372042357137313484 % 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 = 0.06087870149864665341609780923385 relative error = 30.503816061743984316308418974536 % 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 = 0.06106848585148920897161866236141 relative error = 30.691028997448305210506404896878 % h = 0.001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.6MB, time=12.81 NO POLE x[1] = 0.93 y[1] (analytic) = 0.19838005911622284791568078408935 y[1] (numeric) = 0.13712148409258027762833889547324 absolute error = 0.06125857502364257028734188861611 relative error = 30.879401536902280285054031940627 % 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 = 0.06144896881202055655814364540243 relative error = 31.068941717106116417535596119689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.932 y[1] (analytic) = 0.19718599518810742273101194568898 y[1] (numeric) = 0.13554632817596988944204050227671 absolute error = 0.06163966701213753328897144341227 relative error = 31.259657641170609984561817795529 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.933 y[1] (analytic) = 0.19659016714664117338782511274851 y[1] (numeric) = 0.13475949772853255660736351154009 absolute error = 0.06183066941810861678046160120842 relative error = 31.451557478959608312743823615791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.934 y[1] (analytic) = 0.19599514251494082658629213935434 y[1] (numeric) = 0.13397316669229094657248635183913 absolute error = 0.06202197582264988001380578751521 relative error = 31.644649467739695545256067310582 % 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 = 0.06221358601707855993466076636679 relative error = 31.838941912837195377478947449168 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.936 y[1] (analytic) = 0.19480750586013216434455342896323 y[1] (numeric) = 0.13240200606881889820865936774251 absolute error = 0.06240549979131326613589406122072 relative error = 32.034443188302584443356365723988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.937 y[1] (analytic) = 0.19421489502466040474329199864048 y[1] (numeric) = 0.13161717809078621380433514333196 absolute error = 0.06259771693387419093895685530852 relative error = 32.231161737582411483426112368695 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.938 y[1] (analytic) = 0.19362308997422647172511617197774 y[1] (numeric) = 0.13083285274234315085144212511005 absolute error = 0.06279023723188332087367404686769 relative error = 32.429106074198818796353135556299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.939 y[1] (analytic) = 0.19303209130063536640687307489267 y[1] (numeric) = 0.13004903082957071685063309540963 absolute error = 0.06298306047106464955623997948304 relative error = 32.628284782436763868595924358035 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.94 y[1] (analytic) = 0.19244189959488571312978020136585 y[1] (numeric) = 0.12926571315914132116457323180686 absolute error = 0.06317618643574439196520696955899 relative error = 32.828706518039040491950138407842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.941 y[1] (analytic) = 0.19185251544716916846085032210711 y[1] (numeric) = 0.1284829005383179683455979671546 absolute error = 0.06336961490885120011525235495251 relative error = 33.030380008909200116534383847763 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.942 y[1] (analytic) = 0.19126393944686983100128410017909 y[1] (numeric) = 0.12770059377495345087277570916176 absolute error = 0.06356334567191638012850839101733 relative error = 33.233314055822475647711354195773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=236.5MB, alloc=4.6MB, time=13.03 x[1] = 0.943 y[1] (analytic) = 0.19067617218256365200242060513652 y[1] (numeric) = 0.1269187936774895412991826823887 absolute error = 0.06375737850507411070323792274782 relative error = 33.437517533144811379881831473554 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.944 y[1] (analytic) = 0.19008921424201784678983510968148 y[1] (numeric) = 0.12613750105495618381019774531646 absolute error = 0.06395171318706166297963736436502 relative error = 33.642999389560104268465558498471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.945 y[1] (analytic) = 0.18950306621219030699617274468771 y[1] (numeric) = 0.12535671671697068519362562412768 absolute error = 0.06414634949521962180254712056003 relative error = 33.849768648805763274116069817994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.946 y[1] (analytic) = 0.18891772867922901360330577971155 y[1] (numeric) = 0.12457644147373690522245759300853 absolute error = 0.06434128720549210838084818670302 relative error = 34.057834410416695070738737734655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.947 y[1] (analytic) = 0.18833320222847145079440148678306 y[1] (numeric) = 0.12379667613604444645107921814349 absolute error = 0.06453652609242700434332226863957 relative error = 34.267205850477825991633464030841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.948 y[1] (analytic) = 0.18774948744444402061648673536087 y[1] (numeric) = 0.12301742151526784342573536912774 absolute error = 0.06473206592917617719075136623313 relative error = 34.477892222385271696515097606735 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.949 y[1] (analytic) = 0.18716658491086145845409465583714 y[1] (numeric) = 0.12223867842336575131006328726459 absolute error = 0.06492790648749570714403136857255 relative error = 34.689902857616267676733991028835 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.95 y[1] (analytic) = 0.18658449521062624931457789789744 y[1] (numeric) = 0.12146044767288013392650508514725 absolute error = 0.06512404753774611538807281275019 relative error = 34.903247166507975377193254291047 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.951 y[1] (analytic) = 0.18600321892582804492567219837358 y[1] (numeric) = 0.12068273007693545121441163604477 absolute error = 0.06532048884889259371126056232881 relative error = 35.117934639045280401714461152309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.952 y[1] (analytic) = 0.1854227566377430816458931609772 y[1] (numeric) = 0.11990552644923784610565039492057 absolute error = 0.06551723018850523554024276605663 relative error = 35.333974845657700984425353949157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.953 y[1] (analytic) = 0.18484310892683359918834833746895 y[1] (numeric) = 0.11912883760407433081853027540798 absolute error = 0.06571427132275926836981806206097 relative error = 35.551377438025526653626517947657 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.954 y[1] (analytic) = 0.18426427637274726015854588640262 y[1] (numeric) = 0.11835266435631197257085728875007 absolute error = 0.06591161201643528758768859765255 relative error = 35.770152149895308787043798162313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.955 y[1] (analytic) = 0.18368625955431657040678027158725 y[1] (numeric) = 0.11757700752139707871293523158032 absolute error = 0.06610925203291949169384504000693 relative error = 35.990308797904826558904059169694 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.956 y[1] (analytic) = 0.18310905904955830019567464783323 y[1] (numeric) = 0.11680186791535438128132628947549 absolute error = 0.06630719113420391891434835835774 relative error = 36.211857282417653610408508580283 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=240.3MB, alloc=4.6MB, time=13.24 x[1] = 0.957 y[1] (analytic) = 0.18253267543567290618345876639169 y[1] (numeric) = 0.11602724635478622097418700245219 absolute error = 0.0665054290808866852092717639395 relative error = 36.434807588367452636455317680123 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.958 y[1] (analytic) = 0.18195710928904395422356041676126 y[1] (numeric) = 0.11525314365687173054899561700312 absolute error = 0.06670396563217222367456479975814 relative error = 36.659169786112126973427332441073 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.959 y[1] (analytic) = 0.18138236118523754298108760522243 y[1] (numeric) = 0.11447956063936601764348742687761 absolute error = 0.06690280054587152533760017834482 relative error = 36.884954032297960196067708347131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.96 y[1] (analytic) = 0.18080843169900172836677785356957 y[1] (numeric) = 0.11370649812059934702061528160304 absolute error = 0.06710193357840238134616257196653 relative error = 37.112170570733876686483767460049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.961 y[1] (analytic) = 0.18023532140426594878899018404309 y[1] (numeric) = 0.11293395691947632223835301771843 absolute error = 0.06730136448478962655063716632466 relative error = 37.340829733275958125725956631897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.962 y[1] (analytic) = 0.17966303087414045122431453842204 y[1] (numeric) = 0.11216193785547506674516014284864 absolute error = 0.0675010930186653844791543955734 relative error = 37.570941940722352878774660800235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.963 y[1] (analytic) = 0.17909156068091571810737256061982 y[1] (numeric) = 0.1113904417486464044019266770862 absolute error = 0.06770111893226931370544588353362 relative error = 37.802517703718717297734709390055 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.964 y[1] (analytic) = 0.1785209113960618950403828529345 y[1] (numeric) = 0.11061946941961303943121762966766 absolute error = 0.06790144197644885560916522326684 relative error = 38.03556762367433005619960996134 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.965 y[1] (analytic) = 0.17795108359022821932306299634073 y[1] (numeric) = 0.10984902168956873579463716163167 absolute error = 0.06810206190065948352842583470906 relative error = 38.270102393689022750731001638916 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.966 y[1] (analytic) = 0.17738207783324244930343980487371 y[1] (numeric) = 0.10907909938027749599913305702619 absolute error = 0.06830297845296495330430674784752 relative error = 38.506132799491072163842203957267 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.967 y[1] (analytic) = 0.17681389469411029455013846324732 y[1] (numeric) = 0.10830970331407273933306269629197 absolute error = 0.06850419138003755521707576695535 relative error = 38.74366972038620177742949016057 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.968 y[1] (analytic) = 0.1762465347410148468467203753698 y[1] (numeric) = 0.10754083431385647953284229568782 absolute error = 0.06870570042715836731387807968198 relative error = 38.982724130217842356925343900115 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.969 y[1] (analytic) = 0.17567999854131601200863872937179 y[1] (numeric) = 0.10677249320309850188100174603992 absolute error = 0.06890750533821751012763698333187 relative error = 39.223307098338803695232315274411 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.97 y[1] (analytic) = 0.17511428666154994252337996214366 y[1] (numeric) = 0.10600468080583553973646795269177 absolute error = 0.06910960585571440278691200945189 relative error = 39.465429790594511912425661800208 % h = 0.001 TOP MAIN SOLVE Loop memory used=244.1MB, alloc=4.6MB, time=13.45 NO POLE x[1] = 0.971 y[1] (analytic) = 0.17454939966742847101435848319357 y[1] (numeric) = 0.10523739794667045049790014630273 absolute error = 0.06931200172075802051645833689084 relative error = 39.709103470317969052993159978793 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.972 y[1] (analytic) = 0.17398533812383854452913119388423 y[1] (numeric) = 0.10447064545077139100090120109133 absolute error = 0.0695146926730671535282299927929 relative error = 39.954339499336594107730957989861 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.973 y[1] (analytic) = 0.17342210259484165965249751378665 y[1] (numeric) = 0.10370442414387099234992956324314 absolute error = 0.06971767845097066730256795054351 relative error = 40.201149338991107013069312107593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.974 y[1] (analytic) = 0.17285969364367329844504980100387 y[1] (numeric) = 0.10293873485226553418573695750264 absolute error = 0.06992095879140776425931284350123 relative error = 40.449544551166619647310577955459 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.975 y[1] (analytic) = 0.17229811183274236520773822786723 y[1] (numeric) = 0.10217357840281411838915760444251 absolute error = 0.07012453342992824681858062342472 relative error = 40.69953679933610035178817518165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.976 y[1] (analytic) = 0.17173735772363062407301334739332 y[1] (numeric) = 0.10140895562293784222207524455224 absolute error = 0.07032840210069278185093810284108 relative error = 40.951137849616381056079200321627 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.977 y[1] (analytic) = 0.17117743187709213742310875931219 y[1] (numeric) = 0.10064486734061897090639482811021 absolute error = 0.07053256453647316651671393120198 relative error = 41.204359571836878680920586580402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.978 y[1] (analytic) = 0.17061833485305270513602545733743 y[1] (numeric) = 0.099881314384400109641846291798567 absolute error = 0.070737020468652595494179165538863 relative error = 41.459213940621205131201079476207 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.979 y[1] (analytic) = 0.17006006721060930465977861164691 y[1] (numeric) = 0.099118297583383375063448404188049 absolute error = 0.070941769627225929596330207458861 relative error = 41.715713036481842875157270038245 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.98 y[1] (analytic) = 0.16950262950802953191546671228085 y[1] (numeric) = 0.098355817767229566139461222559988 absolute error = 0.071146811740799965776005489720862 relative error = 41.973869046928065835536903659607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.981 y[1] (analytic) = 0.16894602230275104302972217034147 y[1] (numeric) = 0.097593875766157334510656263043854 absolute error = 0.071352146536593708519065907297616 relative error = 42.233694267587288094869384437638 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.982 y[1] (analytic) = 0.168390246151380996897101644497 y[1] (numeric) = 0.096832472410942354271734044731074 absolute error = 0.071557773740438642625367599765926 relative error = 42.495201103340025740982248818735 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.983 y[1] (analytic) = 0.1678353016096954985729735303534 y[1] (numeric) = 0.096071608532916491195719226278376 absolute error = 0.071763693076779007377254304075024 relative error = 42.758402069468660051421914726059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.984 y[1] (analytic) = 0.16728118923263904349745921975985 y[1] (numeric) = 0.095311284963966971402164110536306 absolute error = 0.071969904268672072095295109223544 relative error = 43.023309792820193137394251775513 % h = 0.001 TOP MAIN SOLVE Loop memory used=247.9MB, alloc=4.6MB, time=13.66 NO POLE x[1] = 0.985 y[1] (analytic) = 0.16672790957432396255098390606041 y[1] (numeric) = 0.094551502536535549469991848930121 absolute error = 0.072176407037788413080992057130289 relative error = 43.2899370129831901401714089979 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.986 y[1] (analytic) = 0.16617546318802986794199187969491 y[1] (numeric) = 0.093792262083617675995811232680541 absolute error = 0.072383201104412191946180647014369 relative error = 43.558296583479105096571161639368 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.987 y[1] (analytic) = 0.16562385062620309992738042638742 y[1] (numeric) = 0.093033564438761664598535512480195 absolute error = 0.072590286187441435328844913907225 relative error = 43.828401472968190666078852902651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.988 y[1] (analytic) = 0.16507307244045617436620560744248 y[1] (numeric) = 0.092275410436067858371138241937521 absolute error = 0.072797662004388315995067365504959 relative error = 44.100264766470195041445080214705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.989 y[1] (analytic) = 0.16452312918156723110721236839716 y[1] (numeric) = 0.091517800910187795780379692962823 absolute error = 0.073005328271379435326832675434337 relative error = 44.373899666600052548170548953842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.99 y[1] (analytic) = 0.16397402139947948321074058845289 y[1] (numeric) = 0.090760736696323376015337943300548 absolute error = 0.073213284703156107195402645152342 relative error = 44.649319494818777677220065035102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.991 y[1] (analytic) = 0.16342574964330066700555784873517 y[1] (numeric) = 0.090004218630226023785579287607159 absolute error = 0.073421531013074643219978561128011 relative error = 44.926537692699775590649148830857 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.992 y[1] (analytic) = 0.16287831446130249298116886250245 y[1] (numeric) = 0.089248247548195853569803173834576 absolute error = 0.073630066913106639411365688667874 relative error = 45.205567823210785492660014382693 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.993 y[1] (analytic) = 0.16233171640092009751615067494915 y[1] (numeric) = 0.088492824287080833315797416204609 absolute error = 0.073838892113839264200353258744541 relative error = 45.486423572011676670032058005568 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.994 y[1] (analytic) = 0.16178595600875149544306190422175 y[1] (numeric) = 0.087737949684275947592539984749486 absolute error = 0.074048006324475547850521919472264 relative error = 45.769118748768320477022040324889 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.995 y[1] (analytic) = 0.16124103383055703345047345869323 y[1] (numeric) = 0.086983624577722360195284219246935 absolute error = 0.074257409252834673255189239446295 relative error = 46.053667288482765071850964425208 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.996 y[1] (analytic) = 0.16069695041125884432266732841958 y[1] (numeric) = 0.086229849805906576204464862394833 absolute error = 0.074467100605352268118202466024747 relative error = 46.340083252839943305962564563324 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.997 y[1] (analytic) = 0.16015370629494030201754921103397 y[1] (numeric) = 0.085476626207859603499262853249559 absolute error = 0.074677080087080698518286357784411 relative error = 46.628380831571147824551365731092 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=251.7MB, alloc=4.6MB, time=13.87 x[1] = 0.998 y[1] (analytic) = 0.15961130202484547758331989412072 y[1] (numeric) = 0.084723954623156113726667367293378 absolute error = 0.074887347401689363856652526827342 relative error = 46.918574343834511158640786135529 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.999 y[1] (analytic) = 0.15906973814337859591444947735228 y[1] (numeric) = 0.083971835891913602726874133998906 absolute error = 0.075097902251464993187575343353374 relative error = 47.210678239612732376493933631953 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1 y[1] (analytic) = 0.1585290151921034933474976783697 y[1] (numeric) = 0.083220270854791550415859606422369 absolute error = 0.075308744337311942931638071947331 relative error = 47.504707101128295716638256518249 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.001 y[1] (analytic) = 0.15798913371174307609732262654106 y[1] (numeric) = 0.082469260352990580125971100181469 absolute error = 0.075519873358752495971351526359591 relative error = 47.800675644276430547583781345159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.002 y[1] (analytic) = 0.15745009424217877953421970834405 y[1] (numeric) = 0.081718805228251617405373561157681 absolute error = 0.075731289013927162128846147186369 relative error = 48.098598720076065991744729537197 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.003 y[1] (analytic) = 0.15691189732245002830253118718872 y[1] (numeric) = 0.080968906322855048277194162406095 absolute error = 0.075942990999594980025337024782625 relative error = 48.398491316139037614495603934741 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.004 y[1] (analytic) = 0.15637454349075369728126647902573 y[1] (numeric) = 0.080219564479619876959206471058075 absolute error = 0.076154979011133820322060007967655 relative error = 48.700368558157807715094111958873 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.005 y[1] (analytic) = 0.15583803328444357338727212307505 y[1] (numeric) = 0.079470780541902883044896465462364 absolute error = 0.076367252742540690342375657612686 relative error = 49.004245711411964965802932683929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.006 y[1] (analytic) = 0.15530236724002981822148964446015 y[1] (numeric) = 0.078722555353597778146753221428401 absolute error = 0.076579811886432040074736423031749 relative error = 49.310138182293773430389068505751 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.007 y[1] (analytic) = 0.1547675458931784315588386624451 y[1] (numeric) = 0.077974889759134362002627624210865 absolute error = 0.076792656134044069556211038234235 relative error = 49.618061519853045354753118879155 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.008 y[1] (analytic) = 0.15423356977871071568226175434684 y[1] (numeric) = 0.077227784603477678046002999806424 absolute error = 0.077005785175233037636258754540416 relative error = 49.928031417361616562252808280671 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.009 y[1] (analytic) = 0.15370043943060274056146674103291 y[1] (numeric) = 0.076481240732127168441022095221682 absolute error = 0.077219198698475572120444645811228 relative error = 50.24006371389770780587953088061 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.01 y[1] (analytic) = 0.15316815538198480987690121521799 y[1] (numeric) = 0.075735258991115828583115372614928 absolute error = 0.077432896390868981293785842603062 relative error = 50.554174395950460030400839195199 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.011 y[1] (analytic) = 0.15263671816514092788949328854018 y[1] (numeric) = 0.074989840227009361066076116612941 absolute error = 0.077646877938131566823417171927239 relative error = 50.870379599044936181507039991598 % h = 0.001 TOP MAIN SOLVE Loop memory used=255.5MB, alloc=4.6MB, time=14.08 NO POLE x[1] = 1.012 y[1] (analytic) = 0.15210612831150826715669168763168 y[1] (numeric) = 0.074244985286905329116428387657239 absolute error = 0.077861143024602938040263299974441 relative error = 51.188695609387886967542539079646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.013 y[1] (analytic) = 0.15157638635167663709533748309973 y[1] (numeric) = 0.073500695018432309495934386941264 absolute error = 0.078075691333244327599403096158466 relative error = 51.509138865534582834244119406747 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.014 y[1] (analytic) = 0.15104749281538795339189888850143 y[1] (numeric) = 0.072756970269749044873088330360558 absolute error = 0.078290522545638908518810558140872 relative error = 51.831725960077019355767254224796 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.015 y[1] (analytic) = 0.15051944823153570826059971903376 y[1] (numeric) = 0.072013811889543595664444459911416 absolute error = 0.078505636341992112596155259122344 relative error = 52.156473641353808277913505618111 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.016 y[1] (analytic) = 0.14999225312816444154997125176595 y[1] (numeric) = 0.071271220727032491346627351139316 absolute error = 0.078721032401131950203343900626634 relative error = 52.483398815182071573670921543425 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.017 y[1] (analytic) = 0.14946590803246921269835638081839 y[1] (numeric) = 0.070529197631959881239873204556112 absolute error = 0.078936710400509331458483176262278 relative error = 52.812518546611661088778133984563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.018 y[1] (analytic) = 0.14894041347079507353889411193989 y[1] (numeric) = 0.069787743454596684763951337413915 absolute error = 0.079152670016198388774942774525975 relative error = 53.143850061702031667894643646484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.019 y[1] (analytic) = 0.14841576996863654195451159145488 y[1] (numeric) = 0.069046859045739741167315619843365 absolute error = 0.079368910922896800787195971611515 relative error = 53.477410749322101062018623185274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.02 y[1] (analytic) = 0.14789197805063707638345001454462 y[1] (numeric) = 0.068306545256710958730336126134003 absolute error = 0.079585432793926117653113888410617 relative error = 53.813218162973435426995528574774 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.021 y[1] (analytic) = 0.14736903824058855117584990729276 y[1] (numeric) = 0.067566802939356463443461797854186 absolute error = 0.079802235301232087732388109438574 relative error = 54.15129002263710483330489924833 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.022 y[1] (analytic) = 0.14684695106143073280192042586617 y[1] (numeric) = 0.066827632946045747161165440576947 absolute error = 0.080019318115384985640754985289223 relative error = 54.491644216644558920841973451927 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.023 y[1] (analytic) = 0.1463257170352507569122164646183 y[1] (numeric) = 0.066089036129670815232522900195811 absolute error = 0.080236680905579941679693564422489 relative error = 54.834298803572878651213216158569 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.024 y[1] (analytic) = 0.14580533668328260625054651279403 y[1] (numeric) = 0.065351013343645333609278788180355 absolute error = 0.080454323339637272641267724613675 relative error = 55.179272014164766036274749430701 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=259.4MB, alloc=4.6MB, time=14.29 x[1] = 1.025 y[1] (analytic) = 0.14528581052590658942003334688506 y[1] (numeric) = 0.064613565441903775432251647634727 absolute error = 0.080672245084002813987781699250333 relative error = 55.526582253273639757441416829705 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.026 y[1] (analytic) = 0.14476713908264882050284879253134 y[1] (numeric) = 0.06387669327890056709693197368282 absolute error = 0.08089044580374825340591681884852 relative error = 55.876248101834210737911596377845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.027 y[1] (analytic) = 0.14424932287218069953414293619066 y[1] (numeric) = 0.063140397709609233799127022510943 absolute error = 0.081108925162571465735015913679717 relative error = 56.228288318858917991668219917211 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.028 y[1] (analytic) = 0.1437323624123183938306873126038 y[1] (numeric) = 0.06240467958952154456150686335195 absolute error = 0.08132768282279684926918044925185 relative error = 56.582721843460611451259799827484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.029 y[1] (analytic) = 0.14321625822002232017475073936883 y[1] (numeric) = 0.06166953977464665674190664679355 absolute error = 0.08154671844537566343284409257528 relative error = 56.939567796901874973318590279731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.03 y[1] (analytic) = 0.14270101081139662785372561470558 y[1] (numeric) = 0.060934979121510260024240581037225 absolute error = 0.081766031689886367829485033668355 relative error = 57.29884548467138933897150251753 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.031 y[1] (analytic) = 0.14218662070168868255602163874092 y[1] (numeric) = 0.060200998487153719892883625122448 absolute error = 0.081985622214534962663138013618472 relative error = 57.660574398587741808232723186096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.032 y[1] (analytic) = 0.14167308840528855112374306237812 y[1] (numeric) = 0.059467598729133220591377424663134 absolute error = 0.082205489676155330532365637714986 relative error = 58.024774218931095655680632786912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.033 y[1] (analytic) = 0.14116041443572848716266471103004 y[1] (numeric) = 0.058734780705518907566317531318966 absolute error = 0.082425633730209579596347179711074 relative error = 58.3914648166031401118182360936 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.034 y[1] (analytic) = 0.14064859930568241751002117319736 y[1] (numeric) = 0.058002545274894029397279462042916 absolute error = 0.082646054030788388112741711154444 relative error = 58.76066625531574826315710508289 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.035 y[1] (analytic) = 0.14013764352696542956062268605983 y[1] (numeric) = 0.057270893296354079213641668107387 absolute error = 0.082866750230611350346981017952443 relative error = 59.132398793808777726970992736329 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.036 y[1] (analytic) = 0.13962754761053325945181039192184 y[1] (numeric) = 0.056539825629505935599163997014473 absolute error = 0.083087721981027323852646394907367 relative error = 59.506682888097456316619452309801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.037 y[1] (analytic) = 0.1391183120664817811077627805146 y[1] (numeric) = 0.055809343134467002985180742640271 absolute error = 0.083308968932014778122582037874329 relative error = 59.883539193749802453189599952688 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.038 y[1] (analytic) = 0.13860993740404649614366427280568 y[1] (numeric) = 0.055079446671864351533267890348567 absolute error = 0.083530490732182144610396382457113 relative error = 60.262988568194537761855701492362 % h = 0.001 TOP MAIN SOLVE Loop memory used=263.2MB, alloc=4.6MB, time=14.51 NO POLE x[1] = 1.039 y[1] (analytic) = 0.13810242413160202463024604210498 y[1] (numeric) = 0.054350137102833856508244674334975 absolute error = 0.083752287028768168122001367770005 relative error = 60.64505207305995711978774901436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.04 y[1] (analytic) = 0.13759577275666159671920830788383 y[1] (numeric) = 0.053621415289019337142370074128246 absolute error = 0.083974357467642259576838233755584 relative error = 61.029750976544229399695539067747 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.041 y[1] (analytic) = 0.13708998378587654513003247684256 y[1] (numeric) = 0.052893282092571694991595385980503 absolute error = 0.084196701693304850138437090862057 relative error = 61.417106755817610282287279555957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.042 y[1] (analytic) = 0.13658505772503579849869064437203 y[1] (numeric) = 0.052165738376148051784734512822008 absolute error = 0.084419319348887746713956131550022 relative error = 61.807141099457056795235847747648 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.043 y[1] (analytic) = 0.13608099507906537558875910765756 y[1] (numeric) = 0.051438785002910886766414123538342 absolute error = 0.084642210076154488822344984119218 relative error = 62.199875909913741678938772980691 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.044 y[1] (analytic) = 0.13557779635202788036544167926943 y[1] (numeric) = 0.050712422836527173534666338547943 absolute error = 0.084865373515500706830775340721487 relative error = 62.595333306013974283761772738082 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.045 y[1] (analytic) = 0.13507546204712199793300772717468 y[1] (numeric) = 0.049986652741167516374027104015386 absolute error = 0.085088809305954481558980623159294 relative error = 62.993535625494043472978707081812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.046 y[1] (analytic) = 0.13457399266668199133614900369011 y[1] (numeric) = 0.049261475581505286085003921530059 absolute error = 0.085312517085176705251145082160051 relative error = 63.394505427569506943750046420208 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.047 y[1] (analytic) = 0.1340733887121771992257584619777 y[1] (numeric) = 0.048536892222715755310777103710493 absolute error = 0.085536496489461443914981358267207 relative error = 63.798265495539460488784676394759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.048 y[1] (analytic) = 0.13357365068421153438963339426183 y[1] (numeric) = 0.047812903530475233361999228961035 absolute error = 0.085760747153736301027634165300795 relative error = 64.20483883942633000745579918381 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.049 y[1] (analytic) = 0.13307477908252298314860436102333 y[1] (numeric) = 0.047089510370960200540557970509305 absolute error = 0.085985268711562782608046390514025 relative error = 64.614248698651738540825007629822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.05 y[1] (analytic) = 0.13257677440598310561859051499973 y[1] (numeric) = 0.046366713610846441963167975889478 absolute error = 0.086210060795136663655422539110252 relative error = 65.02651854474901025409006925419 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.051 y[1] (analytic) = 0.1320796371525965368390810578947 y[1] (numeric) = 0.045644514117308180885657973207318 absolute error = 0.086435123035288355953423084687382 relative error = 65.44167208411288312632108784455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=267.0MB, alloc=4.6MB, time=14.73 x[1] = 1.052 y[1] (analytic) = 0.13158336781950048876854170127377 y[1] (numeric) = 0.044922912758017211528819779827651 absolute error = 0.086660455061483277239721921446119 relative error = 65.859733260787012134987038219247 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.053 y[1] (analytic) = 0.13108796690296425314724413619817 y[1] (numeric) = 0.044201910401142031406686387562984 absolute error = 0.086886056501822221740557748635186 relative error = 66.28072625928985494579402046161 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.054 y[1] (analytic) = 0.13059343489838870522801564872615 y[1] (numeric) = 0.043481507915346973158106796012897 absolute error = 0.087111926983041732069908852713253 relative error = 66.704675507479542540947436722323 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.055 y[1] (analytic) = 0.13009977230030580837540515049052 y[1] (numeric) = 0.042761706169791335882485762407019 absolute error = 0.087338066130514472492919388083501 relative error = 67.131605679458347845400221942932 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.056 y[1] (analytic) = 0.12960697960237811953376102514534 y[1] (numeric) = 0.042042506034128515980557132139443 absolute error = 0.087564473568249603553203893005897 relative error = 67.56154169851737624534639721602 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.057 y[1] (analytic) = 0.12911505729739829556471532256259 y[1] (numeric) = 0.041323908378505137501059909148837 absolute error = 0.087791148918893158063655413413753 relative error = 67.994508740122112940654829477899 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.058 y[1] (analytic) = 0.12862400587728860045456796325345 y[1] (numeric) = 0.04060591407356018199418671939569 absolute error = 0.08801809180372841846038124385776 relative error = 68.430532234939473337709201903749 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.059 y[1] (analytic) = 0.12813382583310041339206374558905 y[1] (numeric) = 0.039888523990424117872674813915731 absolute error = 0.088245301842676295519388931673319 relative error = 68.869637871907014175932314346696 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.06 y[1] (analytic) = 0.12764451765501373771705407800258 y[1] (numeric) = 0.03917173900071802928141025028596 absolute error = 0.08847277865429570843564382771662 relative error = 69.311851601344974794942666909866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.061 y[1] (analytic) = 0.12715608183233671074053448747008 y[1] (numeric) = 0.038455559976552744476416382826514 absolute error = 0.088700521855783966264118104643566 relative error = 69.757199638111829894749644543731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.062 y[1] (analytic) = 0.12666851885350511443654808419172 y[1] (numeric) = 0.037739987790527963714098282477246 absolute error = 0.088928531062977150722449801714474 relative error = 70.205708464804047323688347274646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.063 y[1] (analytic) = 0.12618182920608188700644429052911 y[1] (numeric) = 0.037025023315731386651615197031916 absolute error = 0.089156805890350500354829093497194 relative error = 70.657404835000756853094060684569 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.064 y[1] (analytic) = 0.12569601337675663531598126989944 y[1] (numeric) = 0.036310667425737839259253651284824 absolute error = 0.089385345951018796056727618614616 relative error = 71.112315776554048569310522063226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.065 y[1] (analytic) = 0.12521107185134514820575961848314 y[1] (numeric) = 0.035596920994608400245674274644023 absolute error = 0.089614150856736747960085343839117 relative error = 71.570468594925632437932804474572 % h = 0.001 TOP MAIN SOLVE Loop memory used=270.8MB, alloc=4.6MB, time=14.94 NO POLE x[1] = 1.066 y[1] (analytic) = 0.12472700511478891067547400927103 y[1] (numeric) = 0.034883784896889526996905930891488 absolute error = 0.089843220217899383678568078379542 relative error = 72.031890876570603777751687106523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.067 y[1] (analytic) = 0.12424381365115461894246860415874 y[1] (numeric) = 0.03417126000761218102996121102327 absolute error = 0.09007255364354243791250739313547 relative error = 72.496610492369072828371618665563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.068 y[1] (analytic) = 0.1237614979436336963750811754925 y[1] (numeric) = 0.033459347202290952961947835481269 absolute error = 0.090302150741342743413133340011231 relative error = 72.964655601106430311735019530555 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.069 y[1] (analytic) = 0.12328005847454181030126000368204 y[1] (numeric) = 0.032748047356923186995550996592298 absolute error = 0.090532011117618623305709007089742 relative error = 73.436054653003034879757864053589 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.07 y[1] (analytic) = 0.12279949572531838969293674222318 y[1] (numeric) = 0.032037361347988104921762155659142 absolute error = 0.090762134377330284771174586564038 relative error = 73.910836393294122614064993129182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.071 y[1] (analytic) = 0.1223198101765261437266375657173 y[1] (numeric) = 0.031327290052445929640730291901812 absolute error = 0.090992520124080214085907273815488 relative error = 74.389029865860753305655540567193 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.072 y[1] (analytic) = 0.12184100230785058122081404023625 y[1] (numeric) = 0.030617834347737008201612082324704 absolute error = 0.091223167960113573019201957911546 relative error = 74.870664416912623098627542794971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.073 y[1] (analytic) = 0.12136307259809953095037427866185 y[1] (numeric) = 0.029908995111780934362297972586404 absolute error = 0.091454077486318596588076306075446 relative error = 75.355769698723588239399754244958 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.074 y[1] (analytic) = 0.12088602152520266283889406642884 y[1] (numeric) = 0.029200773222975670669891579072953 absolute error = 0.091685248302226992169002487355887 relative error = 75.844375673420760137900693585301 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.075 y[1] (analytic) = 0.12040984956621101002898676542027 y[1] (numeric) = 0.028493169560196670062820341622001 absolute error = 0.091916680006014339966166423798269 relative error = 76.336512616828047726826249037709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.076 y[1] (analytic) = 0.11993455719729649183130992560556 y[1] (numeric) = 0.027786185002795996995455824714005 absolute error = 0.092148372194500494835854100891555 relative error = 76.832211122365039206341809562217 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.077 y[1] (analytic) = 0.11946014489375143755268565537494 y[1] (numeric) = 0.027079820430601448086122542436925 absolute error = 0.092380324463149989466563112938015 relative error = 77.331502105002131691739123336523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.078 y[1] (analytic) = 0.11898661312998811120381092241007 y[1] (numeric) = 0.026374076723915672289374659142318 absolute error = 0.092612536406072438914436263267752 relative error = 77.834416805272834047944969279307 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=274.6MB, alloc=4.6MB, time=15.15 x[1] = 1.079 y[1] (analytic) = 0.11851396237953823708703307734115 y[1] (numeric) = 0.02566895476351529059342039344281 absolute error = 0.09284500761602294649361268389834 relative error = 78.340986793344185304992805846864 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.08 y[1] (analytic) = 0.11804219311505252626466501237524 y[1] (numeric) = 0.024964455430650015243574428053177 absolute error = 0.093077737684402511021090584322063 relative error = 78.851243973146248510370702039639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.081 y[1] (analytic) = 0.11757130580830020390831348654134 y[1] (numeric) = 0.024260579607041768492619101949235 absolute error = 0.093310726201258435415694384592105 relative error = 79.365220586561657695501221584791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.082 y[1] (analytic) = 0.11710130093016853752969326818436 y[1] (numeric) = 0.023557328174883800878955634409909 absolute error = 0.093543972755284736650737633774451 relative error = 79.882949217676213822640095225455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.083 y[1] (analytic) = 0.11663217895066236609339886385476 y[1] (numeric) = 0.022854702016839809033427102717772 absolute error = 0.093777476933822557059971761136988 relative error = 80.404462797091544143550722044278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.084 y[1] (analytic) = 0.11616394033890363001210472078256 y[1] (numeric) = 0.022152702016043053015695366621568 absolute error = 0.094011238322860576996409354160992 relative error = 80.929794606300858350978118357019 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.085 y[1] (analytic) = 0.11569658556313090202466390769669 y[1] (numeric) = 0.021451329056095473181054603110241 absolute error = 0.094245256507035428843609304586449 relative error = 81.458978282128854246978867741862 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.086 y[1] (analytic) = 0.11523011509069891895757439585166 y[1] (numeric) = 0.020750584021066806578564584611329 absolute error = 0.094479531069632112379009811240331 relative error = 81.992047821236845397551292625896 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.087 y[1] (analytic) = 0.11476452938807811437028117875633 y[1] (numeric) = 0.020050467795493702881387302406825 absolute error = 0.094714061592584411488893876349505 relative error = 82.529037584694203399965128548331 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.088 y[1] (analytic) = 0.11429982892085415208478158526382 y[1] (numeric) = 0.019350981264378839850211004856203 absolute error = 0.094948847656475312234570580407617 relative error = 83.069982302617227967155457250756 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.089 y[1] (analytic) = 0.11383601415372746060000025637812 y[1] (numeric) = 0.018652125313190038330646186928856 absolute error = 0.095183888840537422269354069449264 relative error = 83.614917078876579042201171159405 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.09 y[1] (analytic) = 0.11337308555051276839139937136395 y[1] (numeric) = 0.017953900827859376785478533576212 absolute error = 0.095419184722653391605920837787738 relative error = 84.163877395874426605176464093285 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.091 y[1] (analytic) = 0.1129110435741386400962888235106 y[1] (numeric) = 0.017256308694782305362664284616793 absolute error = 0.095654734879356334733624538893807 relative error = 84.716899119392495734717092413821 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.092 y[1] (analytic) = 0.11244988868664701358530016020116 y[1] (numeric) = 0.016559349800816759499953953065027 absolute error = 0.095890538885830254085346207136133 relative error = 85.274018503512206847910219184524 % h = 0.001 TOP MAIN SOLVE Loop memory used=278.4MB, alloc=4.6MB, time=15.36 NO POLE x[1] = 1.093 y[1] (analytic) = 0.11198962134919273792048721577454 y[1] (numeric) = 0.015863025033282273067030792206225 absolute error = 0.096126596315910464853456423568315 relative error = 85.835272195608133875289818070476 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.094 y[1] (analytic) = 0.11153024202204311220051547904107 y[1] (numeric) = 0.015167335279959091046050869205348 absolute error = 0.096362906742084021154464609835722 relative error = 86.400697241416026443761856781701 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.095 y[1] (analytic) = 0.11107175116457742529340135022401 y[1] (numeric) = 0.01447228142908728175147206463556 absolute error = 0.09659946973549014354192928558845 relative error = 86.970331090176665950435925966001 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.096 y[1] (analytic) = 0.11061414923528649645726155454927 y[1] (numeric) = 0.013777864369365848590059778023571 absolute error = 0.096836284865920647867201776525699 relative error = 87.544211599856849726129548679794 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.097 y[1] (analytic) = 0.11015743669177221684953209169568 y[1] (numeric) = 0.013084084989951841361957579332054 absolute error = 0.097073351701820375487574512363626 relative error = 88.122377042448822320558696182912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.098 y[1] (analytic) = 0.10970161399074709192511521184868 y[1] (numeric) = 0.01239094418045946710371150523442 absolute error = 0.09731066981028762482140370661426 relative error = 88.70486610934949830405544093152 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.099 y[1] (analytic) = 0.10924668158803378472391202017221 y[1] (numeric) = 0.011698442830959200474137157083564 absolute error = 0.097548238757074584249774863088646 relative error = 89.291717916820846885493743859278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.1 y[1] (analytic) = 0.1087926399385646600481974221283 y[1] (numeric) = 0.011006581831976893683919214633347 absolute error = 0.097786058106587766364278207494953 relative error = 89.8829720115328351057084086864 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 3 ) = sin(x); Iterations = 1000 Total Elapsed Time = 15 Seconds Elapsed Time(since restart) = 15 Seconds Expected Time Remaining = 1 Minutes 0 Seconds Optimized Time Remaining = 1 Minutes 0 Seconds Time to Timeout = 14 Minutes 44 Seconds Percent Done = 20.43 % > quit memory used=280.8MB, alloc=4.6MB, time=15.48