|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > 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 glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, 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 > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > 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 glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, 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 > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > 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 glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, 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 > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > 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 - 2 - 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 - 2 - 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 glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work, glob_last; n := glob_max_terms; m := n - 3; 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 - 3; 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 > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > 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 glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, 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 > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > 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[1,3] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (2)) * factorial_3(0,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > temporary := temporary / glob_h * (3.0); > array_y_higher[3,1] := 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[1,4] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (2)) * factorial_3(1,3); > 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 > ; > 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[1,5] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (2)) * factorial_3(2,4); > 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 > ; > 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[1,6] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (2)) * factorial_3(3,5); > 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 > ; > 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[1,7] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (2)) * factorial_3(4,6); > 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 > ; > 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 := 2; > 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 glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, 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, 3] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h^2*factorial_3(0, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary; temporary := temporary*3.0/glob_h; array_y_higher[3, 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, 4] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h^2*factorial_3(1, 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 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, 5] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h^2*factorial_3(2, 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 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, 6] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h^2*factorial_3(3, 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 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, 7] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h^2*factorial_3(4, 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 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 := 2; 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) > if (nnn <= glob_max_terms) then # if number 13 > ret := array_fact_1[nnn]; > else > ret := nnn!; > fi;# end if 13 > ; > ret; > # End Function number 17 > end; Warning, `ret` is implicitly declared local to procedure `factorial_1` factorial_1 := proc(nnn) local ret; if nnn <= glob_max_terms then ret := array_fact_1[nnn] else ret := nnn! end if; ret end proc > # Begin Function number 18 > factorial_3 := proc(mmm,nnn) > if (nnn <= glob_max_terms) and (mmm <= glob_max_terms) then # if number 13 > ret := array_fact_2[mmm,nnn]; > else > ret := (mmm!)/(nnn!); > fi;# end if 13 > ; > ret; > # End Function number 18 > end; Warning, `ret` is implicitly declared local to procedure `factorial_3` factorial_3 := proc(mmm, nnn) local ret; if nnn <= glob_max_terms and mmm <= glob_max_terms then ret := array_fact_2[mmm, nnn] else ret := mmm!/nnn! end if; ret end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 2.0 - cos(x); > end; exact_soln_y := proc(x) 2.0 - cos(x) end proc > exact_soln_yp := proc(x) > sin(x); > end; exact_soln_yp := proc(x) sin(x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > ALWAYS, > glob_iolevel, > #Top Generate Globals Decl > glob_current_iter, > glob_orig_start_sec, > glob_smallish_float, > glob_no_eqs, > glob_log10_relerr, > glob_dump_analytic, > glob_look_poles, > years_in_century, > djd_debug, > glob_html_log, > glob_normmax, > glob_iter, > glob_max_trunc_err, > glob_hmin, > glob_h, > sec_in_min, > glob_max_minutes, > glob_unchanged_h_cnt, > glob_optimal_clock_start_sec, > centuries_in_millinium, > glob_optimal_expect_sec, > glob_curr_iter_when_opt, > glob_small_float, > glob_max_iter, > glob_almost_1, > hours_in_day, > glob_dump, > glob_log10relerr, > glob_hmax, > glob_percent_done, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_max_hours, > glob_log10_abserr, > glob_large_float, > glob_clock_start_sec, > glob_display_flag, > glob_log10normmin, > glob_max_sec, > glob_disp_incr, > glob_optimal_done, > djd_debug2, > glob_max_opt_iter, > glob_log10abserr, > MAX_UNCHANGED, > glob_abserr, > days_in_year, > glob_warned2, > glob_warned, > glob_relerr, > glob_hmin_init, > glob_not_yet_start_msg, > glob_clock_sec, > glob_subiter_method, > glob_start, > glob_last_good_h, > glob_reached_optimal_h, > glob_initial_pass, > glob_not_yet_finished, > min_in_hour, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2, > array_const_0D0, > #END CONST > array_last_rel_error, > array_y_init, > array_tmp0, > array_tmp1_g, > array_tmp1, > array_tmp2, > array_y, > array_x, > array_1st_rel_error, > array_pole, > array_norms, > array_type_pole, > array_fact_1, > array_m1, > array_real_pole, > array_y_set_initial, > array_y_higher, > array_complex_pole, > array_fact_2, > array_poles, > array_y_higher_work2, > array_y_higher_work, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > glob_max_terms := 30; > DEBUGL := 3; > INFO := 2; > DEBUGMASSIVE := 4; > ALWAYS := 1; > glob_iolevel := 5; > glob_current_iter := 0; > glob_orig_start_sec := 0.0; > glob_smallish_float := 0.1e-100; > glob_no_eqs := 0; > glob_log10_relerr := 0.1e-10; > glob_dump_analytic := false; > glob_look_poles := false; > years_in_century := 100.0; > djd_debug := true; > glob_html_log := true; > glob_normmax := 0.0; > glob_iter := 0; > glob_max_trunc_err := 0.1e-10; > glob_hmin := 0.00000000001; > glob_h := 0.1; > sec_in_min := 60.0; > glob_max_minutes := 0.0; > glob_unchanged_h_cnt := 0; > glob_optimal_clock_start_sec := 0.0; > centuries_in_millinium := 10.0; > glob_optimal_expect_sec := 0.1; > glob_curr_iter_when_opt := 0; > glob_small_float := 0.1e-50; > glob_max_iter := 1000; > glob_almost_1 := 0.9990; > hours_in_day := 24.0; > glob_dump := false; > glob_log10relerr := 0.0; > glob_hmax := 1.0; > glob_percent_done := 0.0; > glob_optimal_start := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_max_hours := 0.0; > glob_log10_abserr := 0.1e-10; > glob_large_float := 9.0e100; > glob_clock_start_sec := 0.0; > glob_display_flag := true; > glob_log10normmin := 0.1; > glob_max_sec := 10000.0; > glob_disp_incr := 0.1; > glob_optimal_done := false; > djd_debug2 := true; > glob_max_opt_iter := 10; > glob_log10abserr := 0.0; > MAX_UNCHANGED := 10; > glob_abserr := 0.1e-10; > days_in_year := 365.0; > glob_warned2 := false; > glob_warned := false; > glob_relerr := 0.1e-10; > glob_hmin_init := 0.001; > glob_not_yet_start_msg := true; > glob_clock_sec := 0.0; > glob_subiter_method := 3; > glob_start := 0; > glob_last_good_h := 0.1; > glob_reached_optimal_h := false; > glob_initial_pass := true; > glob_not_yet_finished := true; > min_in_hour := 60.0; > #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/h2sinpostode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 2 ) = sin(x);"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 50;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.1;"); > omniout_str(ALWAYS,"x_end := 5.0 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"array_y_init[1 + 1] := exact_soln_yp(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.00001;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100;"); > 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,"2.0 - cos(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"exact_soln_yp := proc(x)"); > omniout_str(ALWAYS,"sin(x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 50; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_last_rel_error:= Array(0..(max_terms + 1),[]); > array_y_init:= Array(0..(max_terms + 1),[]); > array_tmp0:= Array(0..(max_terms + 1),[]); > array_tmp1_g:= Array(0..(max_terms + 1),[]); > array_tmp1:= Array(0..(max_terms + 1),[]); > array_tmp2:= Array(0..(max_terms + 1),[]); > array_y:= Array(0..(max_terms + 1),[]); > array_x:= Array(0..(max_terms + 1),[]); > array_1st_rel_error:= Array(0..(max_terms + 1),[]); > array_pole:= Array(0..(max_terms + 1),[]); > array_norms:= Array(0..(max_terms + 1),[]); > array_type_pole:= Array(0..(max_terms + 1),[]); > array_fact_1:= Array(0..(max_terms + 1),[]); > array_m1:= Array(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_y_higher := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_complex_pole := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_fact_2 := Array(0..(max_terms+ 1) ,(0..max_terms+ 1),[]); > array_poles := Array(0..(1+ 1) ,(0..3+ 1),[]); > array_y_higher_work2 := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > array_y_higher_work := Array(0..(3+ 1) ,(0..max_terms+ 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y_init[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1_g[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_fact_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_real_pole[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_y_set_initial[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=3 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 <=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 <=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_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 <=3 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 <=3 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_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_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_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_2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2[1] := 2; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #Initing Factorial Tables > iiif := 0; > while iiif <= glob_max_terms do # do number 2 > jjjf := 0; > while jjjf <= glob_max_terms do # do number 3 > temp1 := iiif !; > temp2 := jjjf !; > array_fact_1[iiif] := temp1; > array_fact_2[iiif,jjjf] := temp1/temp2; > jjjf := jjjf + 1; > od;# end do number 3 > ; > iiif := iiif + 1; > od;# end do number 2 > ; > #Done Initing Factorial Tables > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.1; > x_end := 5.0 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > array_y_init[1 + 1] := exact_soln_yp(x_start); > glob_h := 0.00001; > glob_look_poles := true; > glob_max_iter := 100; > #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] := false; > 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 := 2; > #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 := 2; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #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 := 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 := 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 , 2 ) = 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,"2012-06-16T22:07:56-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"h2sin") > ; > logitem_str(html_log_file,"diff ( y , x , 2 ) = 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," 091 ") > ; > logitem_str(html_log_file,"h2sin diffeq.mxt") > ; > logitem_str(html_log_file,"h2sin maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly for speeding 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; Warning, `iiif` is implicitly declared local to procedure `mainprog` Warning, `jjjf` is implicitly declared local to procedure `mainprog` Warning, `temp1` is implicitly declared local to procedure `mainprog` Warning, `temp2` is implicitly declared local to procedure `mainprog` mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp, iiif, jjjf, temp1, temp2; global glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, ALWAYS, glob_iolevel, glob_current_iter, glob_orig_start_sec, glob_smallish_float, glob_no_eqs, glob_log10_relerr, glob_dump_analytic, glob_look_poles, years_in_century, djd_debug, glob_html_log, glob_normmax, glob_iter, glob_max_trunc_err, glob_hmin, glob_h, sec_in_min, glob_max_minutes, glob_unchanged_h_cnt, glob_optimal_clock_start_sec, centuries_in_millinium, glob_optimal_expect_sec, glob_curr_iter_when_opt, glob_small_float, glob_max_iter, glob_almost_1, hours_in_day, glob_dump, glob_log10relerr, glob_hmax, glob_percent_done, glob_optimal_start, glob_max_rel_trunc_err, glob_max_hours, glob_log10_abserr, glob_large_float, glob_clock_start_sec, glob_display_flag, glob_log10normmin, glob_max_sec, glob_disp_incr, glob_optimal_done, djd_debug2, glob_max_opt_iter, glob_log10abserr, MAX_UNCHANGED, glob_abserr, days_in_year, glob_warned2, glob_warned, glob_relerr, glob_hmin_init, glob_not_yet_start_msg, glob_clock_sec, glob_subiter_method, glob_start, glob_last_good_h, glob_reached_optimal_h, glob_initial_pass, glob_not_yet_finished, min_in_hour, array_const_2, array_const_0D0, array_last_rel_error, array_y_init, array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_y, array_x, array_1st_rel_error, array_pole, array_norms, array_type_pole, array_fact_1, array_m1, array_real_pole, array_y_set_initial, array_y_higher, array_complex_pole, array_fact_2, array_poles, array_y_higher_work2, array_y_higher_work, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; glob_max_terms := 30; DEBUGL := 3; INFO := 2; DEBUGMASSIVE := 4; ALWAYS := 1; glob_iolevel := 5; glob_current_iter := 0; glob_orig_start_sec := 0.; glob_smallish_float := 0.1*10^(-100); glob_no_eqs := 0; glob_log10_relerr := 0.1*10^(-10); glob_dump_analytic := false; glob_look_poles := false; years_in_century := 100.0; djd_debug := true; glob_html_log := true; glob_normmax := 0.; glob_iter := 0; glob_max_trunc_err := 0.1*10^(-10); glob_hmin := 0.1*10^(-10); glob_h := 0.1; sec_in_min := 60.0; glob_max_minutes := 0.; glob_unchanged_h_cnt := 0; glob_optimal_clock_start_sec := 0.; centuries_in_millinium := 10.0; glob_optimal_expect_sec := 0.1; glob_curr_iter_when_opt := 0; glob_small_float := 0.1*10^(-50); glob_max_iter := 1000; glob_almost_1 := 0.9990; hours_in_day := 24.0; glob_dump := false; glob_log10relerr := 0.; glob_hmax := 1.0; glob_percent_done := 0.; glob_optimal_start := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_max_hours := 0.; glob_log10_abserr := 0.1*10^(-10); glob_large_float := 0.90*10^101; glob_clock_start_sec := 0.; glob_display_flag := true; glob_log10normmin := 0.1; glob_max_sec := 10000.0; glob_disp_incr := 0.1; glob_optimal_done := false; djd_debug2 := true; glob_max_opt_iter := 10; glob_log10abserr := 0.; MAX_UNCHANGED := 10; glob_abserr := 0.1*10^(-10); days_in_year := 365.0; glob_warned2 := false; glob_warned := false; glob_relerr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_not_yet_start_msg := true; glob_clock_sec := 0.; glob_subiter_method := 3; glob_start := 0; glob_last_good_h := 0.1; glob_reached_optimal_h := false; glob_initial_pass := true; glob_not_yet_finished := true; min_in_hour := 60.0; 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/h2sinpostode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 2 ) = sin(x);"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 50;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.1;"); omniout_str(ALWAYS, "x_end := 5.0 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "array_y_init[1 + 1] := exact_soln_yp(x_start);"); omniout_str(ALWAYS, "glob_h := 0.00001;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100;"); 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, "2.0 - cos(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "exact_soln_yp := proc(x)"); omniout_str(ALWAYS, "sin(x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 50; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_last_rel_error := Array(0 .. max_terms + 1, []); array_y_init := Array(0 .. max_terms + 1, []); array_tmp0 := Array(0 .. max_terms + 1, []); array_tmp1_g := Array(0 .. max_terms + 1, []); array_tmp1 := Array(0 .. max_terms + 1, []); array_tmp2 := Array(0 .. max_terms + 1, []); array_y := Array(0 .. max_terms + 1, []); array_x := Array(0 .. max_terms + 1, []); array_1st_rel_error := Array(0 .. max_terms + 1, []); array_pole := Array(0 .. max_terms + 1, []); array_norms := Array(0 .. max_terms + 1, []); array_type_pole := Array(0 .. max_terms + 1, []); array_fact_1 := Array(0 .. max_terms + 1, []); array_m1 := Array(0 .. max_terms + 1, []); array_real_pole := Array(0 .. 2, 0 .. 4, []); array_y_set_initial := Array(0 .. 3, 0 .. max_terms + 1, []); array_y_higher := Array(0 .. 4, 0 .. max_terms + 1, []); array_complex_pole := Array(0 .. 2, 0 .. 4, []); array_fact_2 := Array(0 .. max_terms + 1, 0 .. max_terms + 1, []); array_poles := Array(0 .. 2, 0 .. 4, []); array_y_higher_work2 := Array(0 .. 4, 0 .. max_terms + 1, []); array_y_higher_work := Array(0 .. 4, 0 .. max_terms + 1, []); 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_y_init[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1_g[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_y[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_x[term] := 0.; term := term + 1 end do ; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_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_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_fact_1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_real_pole[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 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 <= 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 <= 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_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 3 do term := 1; while term <= max_terms do array_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_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_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[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_2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2[term] := 0.; term := term + 1 end do; array_const_2[1] := 2; 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 temp1 := iiif!; temp2 := jjjf!; array_fact_1[iiif] := temp1; array_fact_2[iiif, jjjf] := temp1/temp2; jjjf := jjjf + 1 end do; iiif := iiif + 1 end do; x_start := 0.1; x_end := 5.0; array_y_init[1] := exact_soln_y(x_start); array_y_init[2] := exact_soln_yp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; 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] := false; 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 := 2; 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 := 2; 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 := 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 := 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 , 2 ) = 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, "2012-06-16T22:07:56-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "h2sin"); logitem_str(html_log_file, "diff ( y , x , 2 ) = 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, " 091 "); logitem_str(html_log_file, "h2sin diffeq.mxt"); logitem_str(html_log_file, "h2sin maple results"); logitem_str(html_log_file, "Test of revised logic - mostly for speeding 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/h2sinpostode.ode################# diff ( y , x , 2 ) = sin(x); ! #BEGIN FIRST INPUT BLOCK Digits := 50; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.1; x_end := 5.0 ; array_y_init[0 + 1] := exact_soln_y(x_start); array_y_init[1 + 1] := exact_soln_yp(x_start); glob_h := 0.00001; glob_look_poles := true; glob_max_iter := 100; #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) 2.0 - cos(x); end; exact_soln_yp := proc(x) sin(x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0.1 y[1] (analytic) = 1.0049958347219742339044380121961 y[1] (numeric) = 1.0049958347219742339044380121961 absolute error = 0 relative error = 0 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.101 y[1] (analytic) = 1.005096165624023340621597000171 y[1] (numeric) = 1.0050957182211592450002505135296 absolute error = 4.4740286409562134648664143211856e-07 relative error = 4.4513438554195169991043675258269e-05 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.102 y[1] (analytic) = 1.0051974914298239146653143235401 y[1] (numeric) = 1.005195702548706583302547040273 absolute error = 1.7888811173313627672832671789245e-06 relative error = 0.00017796314978729235509063066070597 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.103 y[1] (analytic) = 1.0052998120380501586788328071734 y[1] (numeric) = 1.0052957886994694202844078633664 absolute error = 4.0233385807383944249438070110668e-06 relative error = 0.00040021280542984054764995263739006 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.104 y[1] (analytic) = 1.0054031273463814729626255055154 y[1] (numeric) = 1.0053959776681991042118998418611 absolute error = 7.1496781823687507256636542783716e-06 relative error = 0.00071112551651189997611342783179656 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.105 y[1] (analytic) = 1.0055074372515025577949868753959 y[1] (numeric) = 1.0054962704495441653928110527955 absolute error = 1.1166801958392402175822600431405e-05 relative error = 0.0011105638352030712751795164792041 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.106 y[1] (analytic) = 1.0056127416491035167473238881278 y[1] (numeric) = 1.0055966680380493215282033707819 absolute error = 1.6073611054195219120517345855789e-05 relative error = 0.0015983897566608113409636112367587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.107 y[1] (analytic) = 1.0057190404338799609940437656082 y[1] (numeric) = 1.0056971714281544831677776456682 absolute error = 2.1869005725477826266119939983739e-05 relative error = 0.0021744647208869844587317596349434 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.108 y[1] (analytic) = 1.0058263334995331146169340305467 y[1] (numeric) = 1.005797781614193759270046022827 absolute error = 2.8551885339355346888007719695583e-05 relative error = 0.0028386496145925970756197855112094 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=3.8MB, alloc=3.0MB, time=0.16 x[1] = 0.109 y[1] (analytic) = 1.0059346207387699209039295664461 y[1] (numeric) = 1.0058984995903944628683058458161 absolute error = 3.6121148375458035623720629926680e-05 relative error = 0.003590804773070664377958475585722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.11 y[1] (analytic) = 1.0060439020433031496421603885802 y[1] (numeric) = 1.0059993263508761168434094753551 absolute error = 4.4575692427032798750913225041804e-05 relative error = 0.0044307899820771566224000135581127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.111 y[1] (analytic) = 1.006154177303851505405172832928 y[1] (numeric) = 1.0061002628896494598043242517632 absolute error = 5.3914414202045600848581164818357e-05 relative error = 0.0053584644797199729619917450140278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.112 y[1] (analytic) = 1.0062654464101397368342158758533 y[1] (numeric) = 1.0062013102006154520774767202177 absolute error = 6.4136209524284756739155635679122e-05 relative error = 0.0063736869583558903026784493966881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.113 y[1] (analytic) = 1.0063777092508987469134833032515 y[1] (numeric) = 1.0063024692775642818058751294045 absolute error = 7.5239973334465107608173847021135e-05 relative error = 0.0074763155664954345224412270103994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.114 y[1] (analytic) = 1.0064909657138657042392014539315 y[1] (numeric) = 1.0064037411141743711590041043565 absolute error = 8.7224599691333080197349574984850e-05 relative error = 0.0086662079107156211844073651526171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.115 y[1] (analytic) = 1.0066052156857841552824512681535 y[1] (numeric) = 1.0065051267040113826544852835008 absolute error = 0.00010008898177277262796598465268132 relative error = 0.0099432210575805126767984523509175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.116 y[1] (analytic) = 1.006720459052404137645612378511 y[1] (numeric) = 1.0066066270405272255924975981734 absolute error = 0.00011383201187691205311478033762765 relative error = 0.011307211535569538516530725993234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.117 y[1] (analytic) = 1.006836695698482294312315986721 y[1] (numeric) = 1.0067082431170590626039507600962 absolute error = 0.00012845258142323170836522662481455 relative error = 0.012758035337013525359649167121704 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.118 y[1] (analytic) = 1.00695392550778198889079227638 y[1] (numeric) = 1.0068099759268283163134054085616 absolute error = 0.00014394958095367257738686781832511 relative error = 0.014295547920038383070572035326086 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.119 y[1] (analytic) = 1.0070721483630734218504971183478 y[1] (numeric) = 1.0069118264629396761177332543212 absolute error = 0.00016032190013374573276386402662099 relative error = 0.015919604210516393013352042546884 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.12 y[1] (analytic) = 1.0071913641461337477519018321424 y[1] (numeric) = 1.007013795718380105081510441435 absolute error = 0.00017756842775364267039139070738924 relative error = 0.017630058604025044541830710467689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.121 y[1] (analytic) = 1.0073115727377471934693287735644 y[1] (numeric) = 1.0071158846860178469501372316063 absolute error = 0.00019568805172934651919154195807825 relative error = 0.019426764967813365481679992354109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.122 y[1] (analytic) = 1.007432774017705177406714525728 y[1] (numeric) = 1.0072180943586014332816769977992 absolute error = 0.00021467965910374412503752792882016 relative error = 0.021309576642775692215896153803612 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.123 y[1] (analytic) = 1.0075549678648064297061814777427 y[1] (numeric) = 1.0073204257287586906984073952165 absolute error = 0.00023454213604773900777408252621605 relative error = 0.023278346445432824806341221629062 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.124 y[1] (analytic) = 1.007678154156857113449297582485 y[1] (numeric) = 1.0074228797889957482590764580047 absolute error = 0.00025527436786136519022112448032273 relative error = 0.025332926669920512407422886143564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.125 y[1] (analytic) = 1.0078023327706709468509030922117 y[1] (numeric) = 1.0075254575316960449528562493478 absolute error = 0.00027687523897490189804684286399888 relative error = 0.027473169089985214053970275817319 % h = 0.001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=0.37 NO POLE x[1] = 0.126 y[1] (analytic) = 1.0079275035820693264453820781963 y[1] (numeric) = 1.0076281599491193373159865709119 absolute error = 0.00029934363294998912939550728441699 relative error = 0.029698924960987079733806047087311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.127 y[1] (analytic) = 1.0080536664658814512652555481279 y[1] (numeric) = 1.007730988033400707172101114916 absolute error = 0.00032267843248074409315443321189479 relative error = 0.032010045021910096486440114398572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.128 y[1] (analytic) = 1.0081808212959444480119719826911 y[1] (numeric) = 1.007833942776549569497228318419 absolute error = 0.00034687851939487851474366427211748 relative error = 0.034406379497379344102722290523378 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.129 y[1] (analytic) = 1.0083089679451034972187701205446 y[1] (numeric) = 1.0079370251704486804104590547394 absolute error = 0.00037194277465481680831106580517724 relative error = 0.036887778099685304836195154709988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.13 y[1] (analytic) = 1.0084381062852119604054878288482 y[1] (numeric) = 1.0080402362068531452912731712587 absolute error = 0.00039787007835881511421465758951754 relative error = 0.039454090030815171375289491708572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.131 y[1] (analytic) = 1.0085682361871315082251899045384 y[1] (numeric) = 1.0081435768773894270245167561967 absolute error = 0.00042465930974208120067314834170255 relative error = 0.042105163984491097166407359161258 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.132 y[1] (analytic) = 1.008699357520732249602486659737 y[1] (numeric) = 1.0082470481735543543740218893022 absolute error = 0.00045230934717789522846477043480233 relative error = 0.044840848148215333021346790606859 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.133 y[1] (analytic) = 1.0088314701548928618634141529829 y[1] (numeric) = 1.008350651086714130485860502753 absolute error = 0.00048081906817873137755365022995618 relative error = 0.047660990205322193788441708191829 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.134 y[1] (analytic) = 1.0089645739575007218567459364203 y[1] (numeric) = 1.0084543866081033415222238489321 absolute error = 0.00051018734939738033452208748821259 relative error = 0.050565437337036798715225020181236 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.135 y[1] (analytic) = 1.0090986687954520380666051976395 y[1] (numeric) = 1.0085582557288239654269189411156 absolute error = 0.00054041306662807263968625652390713 relative error = 0.053554036224540528981376165914977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.136 y[1] (analytic) = 1.009233754534651983716245183572 y[1] (numeric) = 1.0086622594398443808234732014945 absolute error = 0.0005714950948076028927719820774893 relative error = 0.056626633051043145734190432634776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.137 y[1] (analytic) = 1.0093698310400148308628648026684 y[1] (numeric) = 1.0087663987319983760468384183427 absolute error = 0.00060343230801645481602638432570626 relative error = 0.059783073503861511814809927591339 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.138 y[1] (analytic) = 1.0095068981754640854833253105561 y[1] (numeric) = 1.0088706745959841583096849805449 absolute error = 0.0006362235794799271736403300112537 relative error = 0.063023202776504860221988703314704 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.139 y[1] (analytic) = 1.0096449558039326235506329934705 y[1] (numeric) = 1.0089750880223633630042772231072 absolute error = 0.00066986778156926054635577036326944 relative error = 0.066346865570766552221230597524698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.14 y[1] (analytic) = 1.0097840037873628281010517729886 y[1] (numeric) = 1.0090796400015600631409205816934 absolute error = 0.0007043637858027649601311912952295 relative error = 0.069753906098822267870741090893181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.141 y[1] (analytic) = 1.0099240419867067272917086649643 y[1] (numeric) = 1.0091843315238597789239711176555 absolute error = 0.00073971046284694836773754730876573 relative error = 0.073244168085334571601776970217549 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=4.3MB, time=0.58 x[1] = 0.142 y[1] (analytic) = 1.0100650702619261334485540350706 y[1] (numeric) = 1.0092891635794084874663978374691 absolute error = 0.00077590668251764598215619760151107 relative error = 0.076817494769563795359662711524955 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.143 y[1] (analytic) = 1.0102070884719927831045376030009 y[1] (numeric) = 1.0093941371582116326438880919257 absolute error = 0.00081295131378115046064951107514749 relative error = 0.080473728907485181682973002815054 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.144 y[1] (analytic) = 1.0103500964748884780278601571639 y[1] (numeric) = 1.0094992532501331350894862008967 absolute error = 0.00085084322475534293837395626723361 relative error = 0.084212712773912228972159280903462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.145 y[1] (analytic) = 1.010494094127605227240159951634 y[1] (numeric) = 1.009604512844894402329755308946 absolute error = 0.00088958128271082491040464268797492 relative error = 0.088034288164626181075226968326538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.146 y[1] (analytic) = 1.0106390812861453900244917671803 y[1] (numeric) = 1.0097099169320733390634523355486 absolute error = 0.0009291643540720509610394316317186 relative error = 0.091938296398511603196951507662105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.147 y[1] (analytic) = 1.0107850578055218199229556284092 y[1] (numeric) = 1.0098154665011033575837057411557 absolute error = 0.00096959130441846233924988725345647 relative error = 0.095924578319697986019557381182767 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.148 y[1] (analytic) = 1.0109320235397580097238311794022 y[1] (numeric) = 1.0099211625412723883446856868484 absolute error = 0.0010108609984856213791454925538494 relative error = 0.099992974299707319806776989043915 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.149 y[1] (analytic) = 1.0110799783418882374380727307282 y[1] (numeric) = 1.0100270060417218906737560208251 absolute error = 0.0010529723001663467643167099030922 relative error = 0.10414332423960758014975729123105 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.15 y[1] (analytic) = 1.0112289220639577132650190013457 y[1] (numeric) = 1.0101329979914458636300973794905 absolute error = 0.0010959240725118496349216218551644 relative error = 0.10837546757217206690239308591347 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.151 y[1] (analytic) = 1.0113788545570227275471705896988 y[1] (numeric) = 1.0102391393792898570107905444383 absolute error = 0.0011397151777328705363800452605004 relative error = 0.11268924326404453774533812518902 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.152 y[1] (analytic) = 1.0115297756711507997138872192414 y[1] (numeric) = 1.0103454311939499825053490491637 absolute error = 0.0011843444772008172085381700777126 relative error = 0.11708448981791007771218022104408 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.153 y[1] (analytic) = 1.0116816852554208282138558147042 y[1] (numeric) = 1.0104518744239719249996898808896 absolute error = 0.0012298108314489032141659338145418 relative error = 0.12156104527467164590806516958416 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.154 y[1] (analytic) = 1.0118345831579232414361794766499 y[1] (numeric) = 1.0105584700577499540305309734543 absolute error = 0.0012761131001732874056485031955492 relative error = 0.1261187472156322405504176576527 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.155 y[1] (analytic) = 1.0119884692257601496199364332395 y[1] (numeric) = 1.0106652190835259353912040367795 absolute error = 0.0013232501422342142287323964600211 relative error = 0.13075743276468262336333608809746 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.156 y[1] (analytic) = 1.0121433433050454977520570596639 y[1] (numeric) = 1.0107721224893883428898711170249 absolute error = 0.0013712208156571548621859426389912 relative error = 0.1354769385904945442617330814973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.157 y[1] (analytic) = 1.0122992052409052194533660673757 y[1] (numeric) = 1.0108791812632712702611331291296 absolute error = 0.0014200239776339491922329382460149 relative error = 0.14027710090871940716835473482982 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.158 y[1] (analytic) = 1.0124560548774773918526359770927 y[1] (numeric) = 1.0109863963929534432320184500495 absolute error = 0.0014696584845239486206175270432052 relative error = 0.14515775548419231771643983171698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=15.2MB, alloc=4.3MB, time=0.80 x[1] = 0.159 y[1] (analytic) = 1.0126138920579123914484970015328 y[1] (numeric) = 1.01109376886605723174333950662 absolute error = 0.0015201231918551597051574949128816 relative error = 0.15011873763314145350297523389322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.16 y[1] (analytic) = 1.0127727166243730509590474759817 y[1] (numeric) = 1.0112012996700476623274051366048 absolute error = 0.0015714169543253886316423393768437 relative error = 0.15515988222540269747226560807499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.161 y[1] (analytic) = 1.0129325284180348171590079870977 y[1] (numeric) = 1.0113089897922314306430763451371 absolute error = 0.0016235386258033865159316419605707 relative error = 0.16028102368663947492686426480785 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.162 y[1] (analytic) = 1.0130933272790859097042613628125 y[1] (numeric) = 1.0114168402197559141691529214131 absolute error = 0.001676487059329995535108441399416 relative error = 0.16548199600056773458280685447175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.163 y[1] (analytic) = 1.0132551130467274809436196988004 y[1] (numeric) = 1.0115248519396081850570782221715 absolute error = 0.0017302611071192958865414766289363 relative error = 0.17076263271118601400855046916745 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.164 y[1] (analytic) = 1.0134178855591737767176586097624 y[1] (numeric) = 1.0116330259386140231439492691698 absolute error = 0.0017848596205597535737093405926905 relative error = 0.17612276692501052971204666717648 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.165 y[1] (analytic) = 1.0135816446536522981444579067051 y[1] (numeric) = 1.0117413632034369291268191475661 absolute error = 0.0018402814502153690176387591390046 relative error = 0.18156223131331523206796723973486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.166 y[1] (analytic) = 1.0137463901664039643920869144861 y[1] (numeric) = 1.011849864720577137899278530822 absolute error = 0.0018965254458268264928083836641401 relative error = 0.1870808581143767652072551902025 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.167 y[1] (analytic) = 1.0139121219326832764376716571557 y[1] (numeric) = 1.0119585314763706320513029954618 absolute error = 0.0019535904563126443863686616938611 relative error = 0.19267847913572427192388924755133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.168 y[1] (analytic) = 1.014078839786758481812880152039 y[1] (numeric) = 1.0120673644569881555333526257596 absolute error = 0.0020114753297703262795275262793827 relative error = 0.19835492575639398358902698606227 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.169 y[1] (analytic) = 1.0142465435619117403356610670895 y[1] (numeric) = 1.0121763646484342274857102441716 absolute error = 0.0020701789134775128499508229179364 relative error = 0.2041100289291885350005278107114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.17 y[1] (analytic) = 1.0144152330904392908280700097875 y[1] (numeric) = 1.012285533036546156234044438094 absolute error = 0.0021297000538931345940255716935162 relative error = 0.20994361918294094403625107576575 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.171 y[1] (analytic) = 1.0145849082036516188200167297711 y[1] (numeric) = 1.0123948706069930534521833873005 absolute error = 0.0021900375966585653678333424706044 relative error = 0.21585552662478319592247465922856 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.172 y[1] (analytic) = 1.0147555687318736252387655314679 y[1] (numeric) = 1.0125043783452748484930853292042 absolute error = 0.0022511903865987767456802022636294 relative error = 0.22184558094241937187428348888998 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.173 y[1] (analytic) = 1.0149272145044447960840202072392 y[1] (numeric) = 1.0126140572367213028889913308908 absolute error = 0.0023131572677234931950288763484057 relative error = 0.22791361140640326181283372255566 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.174 y[1] (analytic) = 1.0150998453497193730884238159675 y[1] (numeric) = 1.0127239082664910250217458676878 absolute error = 0.0023759370832283480666779482796583 relative error = 0.23405944687242040081500428654355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.175 y[1] (analytic) = 1.0152734610950665253633026466005 y[1] (numeric) = 1.0128339324195704849642705378687 absolute error = 0.002439528675496040399032108731765 relative error = 0.24028291578357446890410087957772 % h = 0.001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.01 NO POLE x[1] = 0.176 y[1] (analytic) = 1.0154480615668705220294827209227 y[1] (numeric) = 1.0129441306807730294941760719338 absolute error = 0.0025039308860974925353066489888684 relative error = 0.24658384617267799374597580694321 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.177 y[1] (analytic) = 1.0156236465905309058330062047525 y[1] (numeric) = 1.0130545040347378972804976227762 absolute error = 0.0025691425557930085525085819763306 relative error = 0.25296206566454729577316742227489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.178 y[1] (analytic) = 1.0158002159904626677455741118622 y[1] (numeric) = 1.0131650534659292342445381499133 absolute error = 0.0026351625245334335010359619489468 relative error = 0.25941740147830161522044266917608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.179 y[1] (analytic) = 1.0159777695900964225495407001936 y[1] (numeric) = 1.0132757799586351090958045368604 absolute error = 0.0027019896314613134537361633332012 relative error = 0.26594968042966636051844222757284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.18 y[1] (analytic) = 1.0161563072118785854072839753885 y[1] (numeric) = 1.0133866844969665290440209056265 absolute error = 0.0027696227149120563632630697619566 relative error = 0.27255872893328041745797692449857 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.181 y[1] (analytic) = 1.0163358286772715494147757322793 y[1] (numeric) = 1.0134977680648564556882034162382 absolute error = 0.0028380606124150937265723160411266 relative error = 0.2792443730050074585059030592748 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.182 y[1] (analytic) = 1.016516333806753864139173580784 y[1] (numeric) = 1.0136090316460588210837806621341 absolute error = 0.002907302160695043055392918649895 relative error = 0.28600643826425119162440966203284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.183 y[1] (analytic) = 1.0166978224198204151402564186277 y[1] (numeric) = 1.013720476224147543988743594228 absolute error = 0.0029773461956728711515128243997231 relative error = 0.29284474993627448791897884587015 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.184 y[1] (analytic) = 1.0168802943349826044755238294719 y[1] (numeric) = 1.0138321027825155462898087274084 absolute error = 0.0030481915524670581857151020635368 relative error = 0.29975913285452232741622757138952 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.185 y[1] (analytic) = 1.0170637493697685321887789013652 y[1] (numeric) = 1.0139439123043737696095782032293 absolute error = 0.0031198370653947625792006981359076 relative error = 0.30674941146294850225130141437309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.186 y[1] (analytic) = 1.0172481873407231787820129769491 y[1] (numeric) = 1.0140559057727501920956801015506 absolute error = 0.0031922815679729866863328753985459 relative error = 0.31381540981834601652546426170808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.187 y[1] (analytic) = 1.0174336080634085886704098635492 y[1] (numeric) = 1.0141680841704888453928722119054 absolute error = 0.0032655238929197432775376516438083 relative error = 0.32095695159268112207800805924744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.188 y[1] (analytic) = 1.0176200113524040546202860481617 y[1] (numeric) = 1.0142804484802488317990922924087 absolute error = 0.0033395628721552228211937557529859 relative error = 0.32817386007543092940258945360299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.189 y[1] (analytic) = 1.0178073970213063031697824794125 y[1] (numeric) = 1.0143929996845033416064376600758 absolute error = 0.003414397336802961563344819336693 relative error = 0.33546595817592453292658091787088 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.19 y[1] (analytic) = 1.0179957648827296810321224958101 y[1] (numeric) = 1.0145057387655386706280567714876 absolute error = 0.0034900261171910104040657243225026 relative error = 0.34283306842568758986299809400855 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.191 y[1] (analytic) = 1.0181851147483063424812494970519 y[1] (numeric) = 1.014618666705453237911935266831 absolute error = 0.0035664480428531045693142302208885 relative error = 0.35027501298079029183802784285018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.192 y[1] (analytic) = 1.0183754464286864377196569727608 y[1] (numeric) = 1.0147317844861566036425587634455 absolute error = 0.0036436619425298340770982093153195 relative error = 0.35779161362419866849312794391107 % h = 0.001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=1.22 NO POLE x[1] = 0.193 y[1] (analytic) = 1.0185667597335383022282225208382 y[1] (numeric) = 1.0148450930893684872314344971314 absolute error = 0.0037216666441698149967880237068086 relative error = 0.3653826917681291622590944657901 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.194 y[1] (analytic) = 1.0187590544715486470978565056148 y[1] (numeric) = 1.0149585934966177855974537206167 absolute error = 0.0038004609749308615004027849981455 relative error = 0.37304806845640641350039132672171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.195 y[1] (analytic) = 1.0189523304504227503427750241667 y[1] (numeric) = 1.0150722866892415916380765787374 absolute error = 0.0038800437611811587046984454292246 relative error = 0.38078756436682419523140313498434 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.196 y[1] (analytic) = 1.0191465874768846491952058675394 y[1] (numeric) = 1.0151861736483842128923209890663 absolute error = 0.0039604138285004363028848784731118 relative error = 0.38860099981350943661210155127464 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.197 y[1] (analytic) = 1.019341825356677333381335182191 y[1] (numeric) = 1.0153002553549961903965368649174 absolute error = 0.0040415700016811429847983172735747 relative error = 0.39648819474928927443890152091406 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.198 y[1] (analytic) = 1.0195380438945629393783015557216 y[1] (numeric) = 1.0154145327898333177339468248721 absolute error = 0.004123511104729621644354730849505 relative error = 0.40444896876806107185722101503127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.199 y[1] (analytic) = 1.0197352428943229456520432699139 y[1] (numeric) = 1.0155290069334556602789343392032 absolute error = 0.0042062359608672853731089307107901 relative error = 0.41248314110716534353544049067451 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.2 y[1] (analytic) = 1.0199334221587583688758034832518 y[1] (numeric) = 1.0156436787662265746370600688273 absolute error = 0.0042897433925317942387434144245287 relative error = 0.4205905306497615265555800868166 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.201 y[1] (analytic) = 1.020132581489689961129097124429 y[1] (numeric) = 1.0157585492683117282817869566882 absolute error = 0.0043740322213782328473101677408091 relative error = 0.42877095592720653629406743654944 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.202 y[1] (analytic) = 1.0203327206879584080769422978976 y[1] (numeric) = 1.0158736194196781193888944347632 absolute error = 0.0044591012682802886880478631343812 relative error = 0.43702423512143604658645057983392 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.203 y[1] (analytic) = 1.0205338395534245281291580222406 y[1] (numeric) = 1.0159888902000930968695619121974 absolute error = 0.0045449493533314312595961100432164 relative error = 0.44535018606734843349281235550229 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.204 y[1] (analytic) = 1.020735937884969472579529142089 y[1] (numeric) = 1.0161043625891233806031015114011 absolute error = 0.0046315752958460919764276306879673 relative error = 0.4537486262551913220059582512812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.205 y[1] (analytic) = 1.0209390154804949267246382744327 y[1] (numeric) = 1.0162200375661340818703198192942 absolute error = 0.0047189779143608448543184551384765 relative error = 0.46221937283295067507217227870183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.206 y[1] (analytic) = 1.0211430721369233119621636705127 y[1] (numeric) = 1.0163359161102877239884882202572 absolute error = 0.0048071560266355879736754502555295 relative error = 0.47076224260874236432445816583521 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.207 y[1] (analytic) = 1.0213481076501979888684408950116 y[1] (numeric) = 1.0164519992005432631489011757328 absolute error = 0.0048961084496547257195397192787785 relative error = 0.47937705205320616196069904331715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.208 y[1] (analytic) = 1.0215541218152834612550852449989 y[1] (numeric) = 1.016568287815655109458001612843 absolute error = 0.0049858339996283517970836321559579 relative error = 0.48806361730190209323407072599558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=26.7MB, alloc=4.3MB, time=1.44 x[1] = 0.209 y[1] (analytic) = 1.0217611144261655812044708520247 y[1] (numeric) = 1.0166847829341721481830523808098 absolute error = 0.005076331491993433021418471214944 relative error = 0.49682175415770908906032442192644 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.21 y[1] (analytic) = 1.0219690852758517550838614319007 y[1] (numeric) = 1.016801485534436761203332529431 absolute error = 0.0051675997414149938805289024696649 relative error = 0.50565127809322587828620686173352 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.211 y[1] (analytic) = 1.0221780341563711505379866680538 y[1] (numeric) = 1.0169183965945838486678369583297 absolute error = 0.0052596375617873018701497097241011 relative error = 0.51455200425317405920530193599665 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.212 y[1] (analytic) = 1.0223879608587749044598572358949 y[1] (numeric) = 1.0170355170925398508604577791985 absolute error = 0.0053524437662350535993994566964208 relative error = 0.52352374745680328995195033080775 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.213 y[1] (analytic) = 1.0225988651731363319396104974034 y[1] (numeric) = 1.0171528480060217702736255257749 absolute error = 0.0054460171671145616659849716284305 relative error = 0.53256632220029853745062461032682 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.214 y[1] (analytic) = 1.0228107468885511361911779170994 y[1] (numeric) = 1.0172703903125361938913881378247 absolute error = 0.0055403565760149422997897792747625 relative error = 0.54167954265918932464719883332253 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.215 y[1] (analytic) = 1.0230236057931376194565642727558 y[1] (numeric) = 1.0173881449893783156829054359735 absolute error = 0.0056354608037593037736588367823371 relative error = 0.5508632226907609157999461073258 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.216 y[1] (analytic) = 1.0232374416740368948875277565849 y[1] (numeric) = 1.0175061130136309593073365938105 absolute error = 0.0057313286604059355801911627743976 relative error = 0.56011717583646737966181635492496 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.217 y[1] (analytic) = 1.0234522543174130994044490852411 y[1] (numeric) = 1.0176242953621636010310979022955 absolute error = 0.0058279589552494983733511829455889 relative error = 0.5694412153243464704415817453364 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.218 y[1] (analytic) = 1.023668043508453607532176759785 y[1] (numeric) = 1.0177426930116313928584679091291 absolute error = 0.0059253504968222146737088506558933 relative error = 0.57883515407143626648978036279151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.219 y[1] (analytic) = 1.0238848090313692462126346397834 y[1] (numeric) = 1.0178613069384741858765168024009 absolute error = 0.0060235020928950603361178373825302 relative error = 0.58829880468619350671603125319715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.22 y[1] (analytic) = 1.0241025506693945105939770189553 y[1] (numeric) = 1.0179801381189155538153366935044 absolute error = 0.0061224125504789567786403254509177 relative error = 0.59783197947091356480722740425068 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.221 y[1] (analytic) = 1.0243212682047877807960754132258 y[1] (numeric) = 1.0180991875289618168245492390066 absolute error = 0.0062220806758259639715261742192559 relative error = 0.60743449042415200138132874559052 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.222 y[1] (analytic) = 1.0245409614188315396521202957203 y[1] (numeric) = 1.0182184561444010654670668248834 absolute error = 0.0063225052744304741850534708369803 relative error = 0.61710614924314763427896606106847 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.223 y[1] (analytic) = 1.024761630091832591426120037115 y[1] (numeric) = 1.018337944940802184931083319279 absolute error = 0.006423685151030406495036717836016 relative error = 0.62684676732624706726481982483092 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.224 y[1] (analytic) = 1.0249832740031222815060783338625 y[1] (numeric) = 1.0184576548935138794612701817163 absolute error = 0.0065256191096084020448081521461848 relative error = 0.63665615577533061748274633114132 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.225 y[1] (analytic) = 1.0252058929310567170726304311345 y[1] (numeric) = 1.0185775869776636970101534974815 absolute error = 0.006628305953393020062476933653052 relative error = 0.64653412539823958208287789489296 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.4MB, time=1.66 x[1] = 0.226 y[1] (analytic) = 1.0254294866530169887429174718627 y[1] (numeric) = 1.018697742168157054110647285724 absolute error = 0.006731744484859934632270186138694 relative error = 0.65648048671120478451541505226355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.227 y[1] (analytic) = 1.0256540549454093931894773280223 y[1] (numeric) = 1.0188181214396762609707182086582 absolute error = 0.0068359335057331322187591193640741 relative error = 0.66649504994127634106454717328435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.228 y[1] (analytic) = 1.0258795975836656567339292952864 y[1] (numeric) = 1.0189387257666795467911565871197 absolute error = 0.0069408718169861099427727081667 relative error = 0.67657762502875458827687418321514 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.229 y[1] (analytic) = 1.0261061143422431599152290573844 y[1] (numeric) = 1.0190595561234000853074284046246 absolute error = 0.0070465582188430746078006527597401 relative error = 0.68672802162962211202184654019507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.23 y[1] (analytic) = 1.0263336049946251630322693519284 y[1] (numeric) = 1.0191806134838450205565827579988 absolute error = 0.0071529915107801424756865939295559 relative error = 0.69694604911797681900708348606926 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.231 y[1] (analytic) = 1.0265620693133210326606007951267 y[1] (numeric) = 1.0193018988217944928701889875883 absolute error = 0.0072601704915265397904118075384178 relative error = 0.70723151658846599165896102074005 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.232 y[1] (analytic) = 1.0267915070698664691430463486806 y[1] (numeric) = 1.0194234131108006650942774940319 absolute error = 0.0073680939590658040487688546487534 relative error = 0.71758423285872126736857108586102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.233 y[1] (analytic) = 1.0270219180348237350539819382704 y[1] (numeric) = 1.0195451573241867490372580215751 absolute error = 0.0074767607106369860167239166953832 relative error = 0.7280040064717944831950320130783 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.234 y[1] (analytic) = 1.027253301977781884637054759369 y[1] (numeric) = 1.0196671324350460321467889599254 absolute error = 0.0075861695427358524902657994435774 relative error = 0.73849064569859432721216722218421 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.235 y[1] (analytic) = 1.0274856586673569942161098326828 y[1] (numeric) = 1.0197893394162409044165709876986 absolute error = 0.0076963192511160897995388449841596 relative error = 0.74904395854032373778075416837745 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.236 y[1] (analytic) = 1.0277189878711923935790943983139 y[1] (numeric) = 1.0199117792404018855240381505809 absolute error = 0.0078072086307905080550562477330372 relative error = 0.75966375273091799212686825532722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.237 y[1] (analytic) = 1.0279532893559588983347087647578 y[1] (numeric) = 1.0200344528799266521999192364356 absolute error = 0.0079188364760322461347895283221969 relative error = 0.77034983573948342570729637012124 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.238 y[1] (analytic) = 1.0281885628873550432415712561047 y[1] (numeric) = 1.0201573613069790658306420777116 absolute error = 0.0080312015803759774109291783931062 relative error = 0.78110201477273672394556127492851 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.239 y[1] (analytic) = 1.0284248082301073165096639283 y[1] (numeric) = 1.0202805054934882002945531786676 absolute error = 0.0081443027366191162151107496323543 relative error = 0.79192009677744472802677062619783 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.24 y[1] (analytic) = 1.0286620251479703950738247530366 y[1] (numeric) = 1.0204038864111473700329248311126 absolute error = 0.0082581387368230250408999219239815 relative error = 0.80280388844286469654627210479313 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.241 y[1] (analytic) = 1.0289002134037273808390509958078 y[1] (numeric) = 1.0205275050314131583567216475738 absolute error = 0.0083727083723142224823293482340289 relative error = 0.8137531962031849649159481515686 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.242 y[1] (analytic) = 1.0291393727591900378973775428355 y[1] (numeric) = 1.0206513623255044459900982050444 absolute error = 0.0084880104336855919072793377911256 relative error = 0.82476782623996594454290913813691 % h = 0.001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.4MB, time=1.87 NO POLE x[1] = 0.243 y[1] (analytic) = 1.0293795029751990307160929600163 y[1] (numeric) = 1.0207754592644014398515992557331 absolute error = 0.0086040437107975908644937042831533 relative error = 0.83584758448458140390833139241183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.244 y[1] (analytic) = 1.0296206038116241632970550956892 y[1] (numeric) = 1.0208997968188447020740337235342 absolute error = 0.008720806992779461223021372154923 relative error = 0.84699227662065997378922517926585 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.245 y[1] (analytic) = 1.0298626750273646193068670679285 y[1] (numeric) = 1.0210243759593341792639934662624 absolute error = 0.0088382990680304400428736016661032 relative error = 0.85820170808652681898299625173214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.246 y[1] (analytic) = 1.0301057163803492031776735062069 y[1] (numeric) = 1.0211491976561282320019875440539 absolute error = 0.0089565187242209711756859621530799 relative error = 0.86947568407764541901377158916547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.247 y[1] (analytic) = 1.0303497276275365821783359466519 y[1] (numeric) = 1.0212742628792426645841624937181 absolute error = 0.0090754647482939175941734529337431 relative error = 0.88081400954905940042058398653047 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.248 y[1] (analytic) = 1.0305947085249155294557453097401 y[1] (numeric) = 1.021399572598449755006578867239 absolute error = 0.0091951359264657744491664425011041 relative error = 0.89221648921783436335063972481027 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.249 y[1] (analytic) = 1.0308406588275051680460284191387 y[1] (numeric) = 1.0215251277832772851930140500678 absolute error = 0.0093155310442278828530143690708952 relative error = 0.90368292756549964530601701930365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.25 y[1] (analytic) = 1.0310875782893552158554045505058 y[1] (numeric) = 1.0216509294030075714672611313252 absolute error = 0.0094366488863476443881434191805973 relative error = 0.91521312884048996501924860589624 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.251 y[1] (analytic) = 1.0313354666635462316104470294153 y[1] (numeric) = 1.0217769784266764952708933535319 absolute error = 0.0095584882368697363395536758834278 relative error = 0.92680689706058688956231789470279 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.252 y[1] (analytic) = 1.0315843237021898617775039281638 y[1] (numeric) = 1.0219032758230725341274634240224 absolute error = 0.0096810478791173276500405041414088 relative error = 0.93846403601536006792463272024492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.253 y[1] (analytic) = 1.0318341491564290884510309420608 y[1] (numeric) = 1.0220298225607357928541067237634 absolute error = 0.0098043265956932955969242182974607 relative error = 0.95018434926860817442852188817101 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.254 y[1] (analytic) = 1.0320849427764384782105885568886 y[1] (numeric) = 1.0221566196079570350215172018903 absolute error = 0.0099283231684814431890713549982422 relative error = 0.96196764016079950548571541837957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.255 y[1] (analytic) = 1.0323367043114244319462546505563 y[1] (numeric) = 1.0222836679327767146632644959084 absolute error = 0.010053036378647717282990154647915 relative error = 0.97381371181151217333510748968185 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.256 y[1] (analytic) = 1.0325894335096254356522027035565 y[1] (numeric) = 1.0224109685029840082354205681577 absolute error = 0.01017846500664142741678213539886 relative error = 0.98572236712187384054084939787698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.257 y[1] (analytic) = 1.032843130118312312188194824666 y[1] (numeric) = 1.0225385222861158468274638988366 absolute error = 0.010304607832196465360730925829342 relative error = 0.99769340877700093917046606415399 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.258 y[1] (analytic) = 1.0330977938837884740087378304194 y[1] (numeric) = 1.0226663302494559486254290245985 absolute error = 0.010431463634332525383308805820919 relative error = 1.0097266392484373187152214128834 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.259 y[1] (analytic) = 1.0333534245513901768596496492213 y[1] (numeric) = 1.0227943933600338516282689594906 absolute error = 0.010559031191356325231380689730741 relative error = 1.0218218607965922669593628390539 % h = 0.001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.4MB, time=2.09 NO POLE x[1] = 0.26 y[1] (analytic) = 1.0336100218654867744417823535499 y[1] (numeric) = 1.0229227125846239466183977817934 absolute error = 0.010687309280862827823384571756511 relative error = 1.0339788754731778481511404920861 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.261 y[1] (analytic) = 1.0338675855694809740416471565521 y[1] (numeric) = 1.0230512888897445103873804161366 absolute error = 0.010816296679736463654266740415459 relative error = 1.0461974851236455029766106262367 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.262 y[1] (analytic) = 1.0341261154058090931286857424248 y[1] (numeric) = 1.0231801232416567392177363851208 absolute error = 0.010945992164152353910949357303996 relative error = 1.0584774913896218549871811466581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.263 y[1] (analytic) = 1.0343856111159413169189313333345 y[1] (numeric) = 1.0233092166063637826218240485621 absolute error = 0.011076394509577534297107284772382 relative error = 1.0708186957113436682836289806043 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.264 y[1] (analytic) = 1.0346460724403819569048019292326 y[1] (numeric) = 1.023438569949609777338771591393 absolute error = 0.011207502490772179566030337839576 relative error = 1.0832208993300919014129002204868 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.265 y[1] (analytic) = 1.0349074991186697103507671907983 y[1] (numeric) = 1.0235681842368788815904207632103 absolute error = 0.01133931488179082876034642758805 relative error = 1.0956839032906248025893822448789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.266 y[1] (analytic) = 1.0351698908893779207546294698607 y[1] (numeric) = 1.0236980604333943095972491134431 absolute error = 0.01147183045598361115738035641754 relative error = 1.1082075084436099915094992819214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.267 y[1] (analytic) = 1.0354332474901148392741585260421 y[1] (numeric) = 1.0238281995041173663552362061411 absolute error = 0.011605047985997472918922319901091 relative error = 1.1207915154480554731874161262363 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.268 y[1] (analytic) = 1.0356975686575238871188185030108 y[1] (numeric) = 1.0239586024137464826746390374337 absolute error = 0.011738966243777404444179465577116 relative error = 1.1334357247737395294003258784693 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.269 y[1] (analytic) = 1.0359628541272839189063247726353 y[1] (numeric) = 1.0240892701267162504816416168071 absolute error = 0.011873584000567668424683155828193 relative error = 1.1461399367036394334942335039782 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.27 y[1] (analytic) = 1.0362291036341094869837672905078 y[1] (numeric) = 1.0242202036071964583838434104661 absolute error = 0.012008900026913028599923880041673 relative error = 1.1589039513363589344653144980787 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.271 y[1] (analytic) = 1.0364963169117511067130361417346 y[1] (numeric) = 1.024351403819091127500551081215 absolute error = 0.012144913092659979212485060519587 relative error = 1.1717275685885544563978137310874 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.272 y[1] (analytic) = 1.0367644936929955227202839915894 y[1] (numeric) = 1.0244828717260375475588376944829 absolute error = 0.012281621966957975161446297106491 relative error = 1.1846105881973599595070402970897 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.273 y[1] (analytic) = 1.0370336337096659761091591915901 y[1] (numeric) = 1.0246146082914053132563332943556 absolute error = 0.012419025418260662852825897234528 relative error = 1.1975528097228104092052965155329 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.274 y[1] (analytic) = 1.0373037366926224726375423277883 y[1] (numeric) = 1.0247466144782953608917104867426 absolute error = 0.012557122214327111745831841045744 relative error = 1.2105540325502637997795396848868 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.275 y[1] (analytic) = 1.0375748023717620518575180345561 y[1] (numeric) = 1.0248788912495390052638283991128 absolute error = 0.012695911122223046593689635443315 relative error = 1.223614055892821679442200255303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.276 y[1] (analytic) = 1.0378468304760190572183129339225 y[1] (numeric) = 1.025011439567696976840498117576 absolute error = 0.01283539090832208037781481634653 relative error = 1.2367326787937481236908562082642 % h = 0.001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=2.31 NO POLE x[1] = 0.277 y[1] (analytic) = 1.0381198207333654071319295975428 y[1] (numeric) = 1.025144260395058459197832432463 absolute error = 0.012975560338306947934097165079764 relative error = 1.2499097001288871040883769859309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.278 y[1] (analytic) = 1.0383937728708108670012054656899 y[1] (numeric) = 1.0252773546936401267311424529759 absolute error = 0.013116418177170740270063012714029 relative error = 1.2631449186090781997526876271988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.279 y[1] (analytic) = 1.0386686866144033222100246952314 y[1] (numeric) = 1.0254107234251851826383433799298 absolute error = 0.013257963189218139571681315301653 relative error = 1.2764381327825705990244511141503 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.28 y[1] (analytic) = 1.0389445616892290520754099464035 y[1] (numeric) = 1.0255443675511623971768314531026 absolute error = 0.013400194138066654898578493300946 relative error = 1.2897891410374353389617105324191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.281 y[1] (analytic) = 1.0392213978194130047612201563121 y[1] (numeric) = 1.0256782880327651461947938162331 absolute error = 0.013543109786647858566426340078961 relative error = 1.3031977416039757304928586720203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.282 y[1] (analytic) = 1.0394991947281190731531793854871 y[1] (numeric) = 1.0258124858309104499379127682796 absolute error = 0.013686708897208623215266617207502 relative error = 1.3166637325571359172431972618787 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.283 y[1] (analytic) = 1.0397779521375503716949608624835 y[1] (numeric) = 1.0259469619062380121324255941527 absolute error = 0.013830990231312359562535268330853 relative error = 1.3301869118189075162357972136636 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.284 y[1] (analytic) = 1.0400576697689495141850493904688 y[1] (numeric) = 1.0260817172191092593455008917846 absolute error = 0.013975952549840254839548498684165 relative error = 1.3437670771607342888543610734706 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.285 y[1] (analytic) = 1.040338347342598892534104318956 y[1] (numeric) = 1.0262167527296063806238920350764 absolute error = 0.014121594612992511910212283879632 relative error = 1.3574040262059147906443053222156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.286 y[1] (analytic) = 1.0406199845778209564825443233454 y[1] (numeric) = 1.0263520693975313674118281339912 absolute error = 0.014267915180289589070716189354195 relative error = 1.3710975564320029487183091613463 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.287 y[1] (analytic) = 1.0409025811929784942780742747098 y[1] (numeric) = 1.0264876681824050537491025738215 absolute error = 0.014414913010573440528971700888284 relative error = 1.3848474651732065157241038600242 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.288 y[1] (analytic) = 1.0411861369054749143128735223236 y[1] (numeric) = 1.0266235500434661567503189354629 absolute error = 0.014562586862008757562554586860626 relative error = 1.398653549622783349525288471215 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.289 y[1] (analytic) = 1.0414706514317545277201639517677 y[1] (numeric) = 1.0267597159396703173662538173675 absolute error = 0.014710935492084210353910134400204 relative error = 1.4125156068354354679404395538445 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.29 y[1] (analytic) = 1.0417561244873028319298752220681 y[1] (numeric) = 1.0268961668296891414282957977345 absolute error = 0.014859957657613690501579424333599 relative error = 1.4264334337297008280817202329187 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.291 y[1] (analytic) = 1.0420425557866467951831236262249 y[1] (numeric) = 1.0270329036719092409769194924199 absolute error = 0.015009652114737554206204133804998 relative error = 1.4404068270903427800315732170081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.292 y[1] (analytic) = 1.0423299450433551420052200606774 y[1] (numeric) = 1.0271699274244312758751533800097 absolute error = 0.015160017618923866130066680667656 relative error = 1.454435583570737144794888962737 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.293 y[1] (analytic) = 1.0426182919700386396369216307212 y[1] (numeric) = 1.0273072390450689957079997805109 absolute error = 0.015311052924969643928921850210321 relative error = 1.4685194996952568666642596824018 % h = 0.001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.52 NO POLE x[1] = 0.294 y[1] (analytic) = 1.0429075962783503854236404606493 y[1] (numeric) = 1.0274448394913482819687650881586 absolute error = 0.015462756787002103454875372490715 relative error = 1.4826583718616541903375479516722 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.295 y[1] (analytic) = 1.0431978576789860951623223194319 y[1] (numeric) = 1.0275827297205061905332580719307 absolute error = 0.015615127958479904629064247501251 relative error = 1.4968519963434403133300008734765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.296 y[1] (analytic) = 1.0434890758816843924057067150814 y[1] (numeric) = 1.0277209106894899944228137694909 absolute error = 0.015768165192194397982892945590489 relative error = 1.5111001692922624644275126425767 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.297 y[1] (analytic) = 1.0437812505952270987236791534653 y[1] (numeric) = 1.0278593833549562268571002114573 absolute error = 0.015921867240270871866578942008008 relative error = 1.525402686740278359133365452146 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.298 y[1] (analytic) = 1.0440743815274395249214253002402 y[1] (numeric) = 1.0279981486732697245976649231092 absolute error = 0.016076232854169800323760377131093 relative error = 1.5397593446025279832678464773284 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.299 y[1] (analytic) = 1.0443684683851907632140958277764 y[1] (numeric) = 1.0281372076005026715831778599069 absolute error = 0.016231260784688091630917967869567 relative error = 1.5541699386793026560885326202928 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.3 y[1] (analytic) = 1.044663510874393980357689772432 y[1] (numeric) = 1.0282765610924336428573271415011 absolute error = 0.0163869497819603375003626309309 relative error = 1.568634264658511324508740237345 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.301 y[1] (analytic) = 1.0449595087000067117358632713184 y[1] (numeric) = 1.0284162101045466487903236562564 absolute error = 0.016543298595460062945539615062072 relative error = 1.5831521181180440402026395947571 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.302 y[1] (analytic) = 1.0452564615660311564023695917739 y[1] (numeric) = 1.0285561555920301795949703147057 absolute error = 0.016700305974000976807399277068218 relative error = 1.5977232945281325715978186936192 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.303 y[1] (analytic) = 1.0455543691755144730788354111266 y[1] (numeric) = 1.0286963985097762501382514357851 absolute error = 0.016857970665738222940583975341482 relative error = 1.6123475892537081029696337179017 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.304 y[1] (analytic) = 1.0458532312305490771075773489994 y[1] (numeric) = 1.028836939812379445049397454182 absolute error = 0.01701629141816963205817989481746 relative error = 1.6270247975567559730664890230318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.305 y[1] (analytic) = 1.0461530474322729383591617993617 y[1] (numeric) = 1.02897778045413596412537984065 absolute error = 0.017175266978136974233781958711715 relative error = 1.6417547145986674059112336011077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.306 y[1] (analytic) = 1.0464538174808698800944101547946 y[1] (numeric) = 1.0291189213890426680347908297187 absolute error = 0.017334896091827212059619325075844 relative error = 1.6565371354425881866411286184881 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.307 y[1] (analytic) = 1.0467555410755698787805505609893 y[1] (numeric) = 1.0292603635707961243210622508372 absolute error = 0.017495177504773754459488310152022 relative error = 1.6713718550557642354673171867602 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.308 y[1] (analytic) = 1.0470582179146493648612163853508 y[1] (numeric) = 1.0294021079527916537059774596532 absolute error = 0.017656109961857711155238925697574 relative error = 1.686258668311884033054398244785 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.309 y[1] (analytic) = 1.0473618476954315244799906297348 y[1] (numeric) = 1.0295441554881223766944300658372 absolute error = 0.017817692207309147785560563897599 relative error = 1.7011973699934178508415565254536 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.31 y[1] (analytic) = 1.0476664301142866021571945637978 y[1] (numeric) = 1.0296865071295782604813828526133 absolute error = 0.017979922984708341675811711184532 relative error = 1.7161877547939537400487152669842 % h = 0.001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=2.74 NO POLE x[1] = 0.311 y[1] (analytic) = 1.0479719648666322044196179021966 y[1] (numeric) = 1.029829163829645166161979980957 absolute error = 0.018142801036987038257637921239593 relative error = 1.7312296173205302333343428003723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.312 y[1] (analytic) = 1.0482784516469336043828868959338 y[1] (numeric) = 1.0299721265405038962457652682709 absolute error = 0.018306325106429708137121627662845 relative error = 1.7463227520959657132958435827592 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.313 y[1] (analytic) = 1.0485858901487040472861657555049 y[1] (numeric) = 1.0301153962140292424759590272381 absolute error = 0.018470493934674804810206728266806 relative error = 1.761466953561184402228883818371 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.314 y[1] (analytic) = 1.0488942800645050569788858711721 y[1] (numeric) = 1.0302589738017890339547456454983 absolute error = 0.018635306262716023024140225673831 relative error = 1.7766620160775389277885266693584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.315 y[1] (analytic) = 1.0492036210859467433591963436608 y[1] (numeric) = 1.0304028602550431855755237807803 absolute error = 0.018800760830903557783672562880512 relative error = 1.791907733929129419422667352214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.316 y[1] (analytic) = 1.0495139129036881107638283868539 y[1] (numeric) = 1.0305470565247427467630707391603 absolute error = 0.018966856378945364000757647693644 relative error = 1.807203901325119090676949275276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.317 y[1] (analytic) = 1.0498251552074373673090652126448 y[1] (numeric) = 1.0306915635615289505225722962021 absolute error = 0.019133591645908416786492916442731 relative error = 1.8225503124020462627000939239906 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.318 y[1] (analytic) = 1.0501373476859522351825080570062 y[1] (numeric) = 1.0308363823157322627984689118722 absolute error = 0.019300965370219972384039145133974 relative error = 1.837946761226132784509374560111 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.319 y[1] (analytic) = 1.0504504900270402618853280555329 y[1] (numeric) = 1.0309815137373714321440689803018 absolute error = 0.019468976289668829741259075231026 relative error = 1.8533930417955888058077920791049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.32 y[1] (analytic) = 1.0507645819175591324246927262339 y[1] (numeric) = 1.0311269587761525397028794447049 absolute error = 0.019637623141406592721813281528996 relative error = 1.8688889480429138583773556713398 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.321 y[1] (analytic) = 1.0510796230434169824560548671731 y[1] (numeric) = 1.031272718381468049502603796042 absolute error = 0.019806904661948932953451071131042 relative error = 1.8844342738371942023067163571498 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.322 y[1] (analytic) = 1.0513956130895727123749907266948 y[1] (numeric) = 1.031418793502395859062757161353 absolute error = 0.019976819587176853312233565341873 relative error = 1.9000288129863963935462331102455 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.323 y[1] (analytic) = 1.051712551740036302358273354424 y[1] (numeric) = 1.0315651850876983503168478740637 absolute error = 0.02014736665233795204142548036038 relative error = 1.9156723592396570295193542423 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.324 y[1] (analytic) = 1.0520304386778691283538660919921 y[1] (numeric) = 1.0317118940858214408500746040071 absolute error = 0.020318544592047687503791487984954 relative error = 1.9313647062895686297559560868147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.325 y[1] (analytic) = 1.0523492735851842790195202135225 y[1] (numeric) = 1.031858921444893635453487809382 absolute error = 0.020490352140290643566032404140525 relative error = 1.9471056477744616087509818852005 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.326 y[1] (analytic) = 1.0526690561431468736096597773046 y[1] (numeric) = 1.032006268112725077995563956408 absolute error = 0.020662788030421795614095820896585 relative error = 1.9628949772806822984903512358987 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.327 y[1] (analytic) = 1.0529897860319743808102358017967 y[1] (numeric) = 1.0321539350368066036121406350257 memory used=53.4MB, alloc=4.4MB, time=2.95 absolute error = 0.020835850995167777198095166771062 relative error = 1.9787324883448669783256496137147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.328 y[1] (analytic) = 1.0533114629309369385212309311322 y[1] (numeric) = 1.0323019231643087912156603806256 absolute error = 0.021009539766628147305570550506544 relative error = 1.994617974456211870119543399716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.329 y[1] (analytic) = 1.0536340865183576745864948076487 y[1] (numeric) = 1.0324502334420810163246706924851 absolute error = 0.021183853076276658261824115163607 relative error = 2.0105512290587390568251836844401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.33 y[1] (analytic) = 1.0539576564716130284705894216338 y[1] (numeric) = 1.0325988668166505042145274193322 absolute error = 0.021358789654962524256062002301553 relative error = 2.0265320455535582829050469262311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.331 y[1] (analytic) = 1.0542821724671330738823227614669 y[1] (numeric) = 1.0327478242342213833902483612566 absolute error = 0.021534348232911690492074400210313 relative error = 2.0425602173011245952376974758427 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.332 y[1] (analytic) = 1.0546076341804018423446481406519 y[1] (numeric) = 1.0328971066406737393824636150327 absolute error = 0.021710527539728102962184525619218 relative error = 2.0586355376234917834048311387453 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.333 y[1] (analytic) = 1.0549340412859576477106056318672 y[1] (numeric) = 1.0330467149815626688674088668277 absolute error = 0.021887326304394978843196765039478 relative error = 2.0747577998065615784956554667646 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.334 y[1] (analytic) = 1.0552613934573934116249810921192 y[1] (numeric) = 1.0331966502021173341119075122211 absolute error = 0.02206474325527607751307357989809 relative error = 2.0909267971023285698111664888948 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.335 y[1] (analytic) = 1.0555896903673569899313573173679 y[1] (numeric) = 1.0333469132472400177442871584757 absolute error = 0.022242777120116972187070158892191 relative error = 2.1071423227311207990971782557447 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.336 y[1] (analytic) = 1.0559189316875515000242309195995 y[1] (numeric) = 1.0334975050615051778521757380643 absolute error = 0.02242142662604632217205518153517 relative error = 2.1234041698838359921820360427088 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.337 y[1] (analytic) = 1.056249117088735649145867574257 y[1] (numeric) = 1.0336484265891585034081221355772 absolute error = 0.022600690499577145737745438679803 relative error = 2.1397121317241733881427815055224 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.338 y[1] (analytic) = 1.0565802462407240636275673412012 y[1] (numeric) = 1.0337996787741159700239859023114 absolute error = 0.02278056746660809360358143888985 relative error = 2.1560660013908611263721236935077 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.339 y[1] (analytic) = 1.0569123188123876190750108179637 y[1] (numeric) = 1.033951262559962896035040304073 absolute error = 0.022961056252424723039970513890653 relative error = 2.1724655719998791521678888000189 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.34 y[1] (analytic) = 1.0572453344716537714973559399734 y[1] (numeric) = 1.0341031788899529989147326180116 absolute error = 0.023142155581700772582623321961776 relative error = 2.1889106366466776017166590810411 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.341 y[1] (analytic) = 1.0575792928855068893797542986879 y[1] (numeric) = 1.0342554287070074520210452636465 absolute error = 0.02332386417849943735870903504144 relative error = 2.2054009884083906275940527325754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.342 y[1] (analytic) = 1.0579141937199885866989549051397 y[1] (numeric) = 1.0344080129537139416754010216458 absolute error = 0.023506180766274645023553883493821 relative error = 2.2219364203460456261555269335588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.343 y[1] (analytic) = 1.0582500366401980568816623833228 y[1] (numeric) = 1.0345609325723257245750552613758 absolute error = 0.023689104067872332306607121947004 relative error = 2.2385167255067678284436910000438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=57.2MB, alloc=4.4MB, time=3.17 x[1] = 0.344 y[1] (analytic) = 1.0585868213102924077053156350886 y[1] (numeric) = 1.0347141885047606855399177647466 absolute error = 0.023872632805531722165397870342 relative error = 2.2551416969259802164908809438205 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.345 y[1] (analytic) = 1.0589245473934869971409520758003 y[1] (numeric) = 1.0348677816926003955947463994579 absolute error = 0.024056765700886601546205676342427 relative error = 2.2718111276295987271491559903523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.346 y[1] (analytic) = 1.0592632145520557701378215979091 y[1] (numeric) = 1.0350217130770891703876545593683 absolute error = 0.024241501474966599750167038540755 relative error = 2.2885248106362227058339171136914 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.347 y[1] (analytic) = 1.0596028224473315963494134778678 y[1] (numeric) = 1.0351759835991331289458739534067 absolute error = 0.024426838848198467403539524461137 relative error = 2.3052825389593205728220027388639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.348 y[1] (analytic) = 1.0599433707397066088005585003815 y[1] (numeric) = 1.0353305941992992527697139871803 absolute error = 0.024612776540407356030844513201282 relative error = 2.3220841056094106650003728169886 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.349 y[1] (analytic) = 1.0602848590886325434952676329222 y[1] (numeric) = 1.0354855458178144452656586432449 absolute error = 0.024799313270818098229608989677257 relative error = 2.3389293035962372162173348909972 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.35 y[1] (analytic) = 1.0606272871526210799649676426963 y[1] (numeric) = 1.0356408393945645915195414268602 absolute error = 0.02498644775805648844542621583611 relative error = 2.3558179259309414396446799609817 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.351 y[1] (analytic) = 1.0609706545892441827567931078597 y[1] (numeric) = 1.0357964758690936184107386039774 absolute error = 0.025174178720150564346054503882374 relative error = 2.3727497656282276758160673744593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.352 y[1] (analytic) = 1.0613149610551344438615933347137 y[1] (numeric) = 1.0359524561806025550683206171873 absolute error = 0.02536250487453188879327271752645 relative error = 2.3897246157085245702645120814573 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.353 y[1] (analytic) = 1.0616602062059854260813117529063 y[1] (numeric) = 1.0361087812679485936701012234001 absolute error = 0.025551424938036832411210529506215 relative error = 2.4067422692001412449398699081692 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.354 y[1] (analytic) = 1.0620063896965520073353944212866 y[1] (numeric) = 1.0362654520696441505855235541282 absolute error = 0.025740937626907856749870867158465 relative error = 2.423802519141418427845772545426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.355 y[1] (analytic) = 1.062353511180650725905883338033 y[1] (numeric) = 1.0364224695238559278633219554084 absolute error = 0.025931041656794798042561382624681 relative error = 2.4409051585828745055945192782154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.356 y[1] (analytic) = 1.0627015703111601266208493099901 y[1] (numeric) = 1.0365798345684039750648981196235 absolute error = 0.026121735742756151555951190366632 relative error = 2.4580499805893464638379726891225 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.357 y[1] (analytic) = 1.0630505667400211079758181978111 y[1] (numeric) = 1.036737548140760751444349675769 absolute error = 0.026313018599260356531468522042103 relative error = 2.4752367782421256807925162722477 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.358 y[1] (analytic) = 1.0634005001182372701928434155077 y[1] (numeric) = 1.0368956111780501884760890580575 absolute error = 0.026504888940187081716754357450167 relative error = 2.4924653446410885393365987473226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.359 y[1] (analytic) = 1.0637513700958752642168766253643 y[1] (numeric) = 1.0370540246170467527309901251648 absolute error = 0.026697345478828511485886500199514 relative error = 2.5097354729068218234202985518212 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.36 y[1] (analytic) = 1.0641031763220651416490876318753 y[1] (numeric) = 1.0372127893941745091019996538923 absolute error = 0.026890386927890632547087977982911 relative error = 2.5270469561827428647876782310724 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.4MB, time=3.38 x[1] = 0.361 y[1] (analytic) = 1.064455918445000705616783541413 y[1] (numeric) = 1.0373719064455061843801504815564 absolute error = 0.027084011999494521236633059856648 relative error = 2.5443995876372144062744479966373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.362 y[1] (analytic) = 1.0648095961119398625795763177395 y[1] (numeric) = 1.0375313767067622311819127210133 absolute error = 0.027278219405177631397663596726207 relative error = 2.5617931604656541482056063709421 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.363 y[1] (analytic) = 1.0651642089692049750714469272204 y[1] (numeric) = 1.0376912011133098922288191208913 absolute error = 0.027473007855895082842627806329142 relative error = 2.5792274678926389446802594071654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.364 y[1] (analytic) = 1.0655197566621832153783533317088 y[1] (numeric) = 1.0378513806001622649803002913251 absolute error = 0.027668376062020950398053040383762 relative error = 2.5967023031740036167937243306488 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.365 y[1] (analytic) = 1.0658762388353269201510286515192 y[1] (numeric) = 1.038011916101977366620665162281 absolute error = 0.027864322733349553530363489238259 relative error = 2.6142174595989343501102844926775 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.366 y[1] (analytic) = 1.0662336551321539459526148857234 y[1] (numeric) = 1.0381728085530571994011616874133 absolute error = 0.028060846579096746551453198310065 relative error = 2.6317727304920566439635661992263 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.367 y[1] (analytic) = 1.0665920051952480257407766421643 y[1] (numeric) = 1.0383340588873468163380524513144 absolute error = 0.02825794630790120940272419084991 relative error = 2.6493679092155177804254402557274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.368 y[1] (analytic) = 1.0669512886662591262839383951033 y[1] (numeric) = 1.0384956680384333872676394820033 absolute error = 0.028455620627825739016298913100054 relative error = 2.6670027891710637810485979741002 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.369 y[1] (analytic) = 1.0673115051859038065112878542941 y[1] (numeric) = 1.0386576369395452652591722135523 absolute error = 0.028653868246358541252115640741836 relative error = 2.6846771638021108197524989814525 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.37 y[1] (analytic) = 1.0676726543939655767961870955091 y[1] (numeric) = 1.0388199665235510533865721858643 absolute error = 0.028852687870414523409614909644812 relative error = 2.7023908265958110604872225543499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.371 y[1] (analytic) = 1.0680347359292952591726321691378 y[1] (numeric) = 1.038982657722958671859907709799 absolute error = 0.029052078206336587312724459338754 relative error = 2.7201435710851128885748615245181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.372 y[1] (analytic) = 1.0683977494298113484844009704265 y[1] (numeric) = 1.0391457114699144255175513660952 absolute error = 0.02925203795989692296684960433132 relative error = 2.7379351908508155048934642510759 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.373 y[1] (analytic) = 1.0687616945325003744665282222431 y[1] (numeric) = 1.0393091286962020716799528458543 absolute error = 0.029452565836298302786575376388837 relative error = 2.7557654795236178523341419650484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.374 y[1] (analytic) = 1.0691265708734172647587454889206 y[1] (numeric) = 1.0394729103332418883659592787347 absolute error = 0.029653660540175376392786210185899 relative error = 2.7736342307861618442278022433009 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.375 y[1] (analytic) = 1.0694923780876857088505232077704 y[1] (numeric) = 1.0396370573120897428726148324584 absolute error = 0.029855320775595965977908375312001 relative error = 2.7915412383750698647040307863492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.376 y[1] (analytic) = 1.0698591158094985229573507932542 y[1] (numeric) = 1.0398015705634361607193710037535 absolute error = 0.030057545246062362237979789500716 relative error = 2.8094862960829765112109094295969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.377 y[1] (analytic) = 1.070226783672118015827889937563 y[1] (numeric) = 1.0399664510176053949576386564434 absolute error = 0.030260332654512620870251281119606 relative error = 2.827469197760554549691014829637 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=64.8MB, alloc=4.4MB, time=3.60 x[1] = 0.378 y[1] (analytic) = 1.0705953813078763554816353004824 y[1] (numeric) = 1.0401316996045544958466124970547 absolute error = 0.030463681703321859635022803427634 relative error = 2.8454897373185350531754760036641 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.379 y[1] (analytic) = 1.070964908348175936876715850913 y[1] (numeric) = 1.040297317253872380896298312041 absolute error = 0.030667591094303555980417538871969 relative error = 2.8635477087297216948247663769324 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.38 y[1] (analytic) = 1.0713353644234897505074691922754 y[1] (numeric) = 1.0404633048947789052786729235173 absolute error = 0.030872059528710845228796268758189 relative error = 2.8816429060309991667118537762635 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.381 y[1] (analytic) = 1.0717067491633617519314202742562 y[1] (numeric) = 1.0406296634561239326079064522685 absolute error = 0.031077085707237819323513821987722 relative error = 2.8997751233253356959104165128071 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.382 y[1] (analytic) = 1.0720790621964072322252949639468 y[1] (numeric) = 1.0407963938663864060905761077325 absolute error = 0.031282668330020826134718856214287 relative error = 2.9179441547837796297180419914842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.383 y[1] (analytic) = 1.072452303150313189369698020393 y[1] (numeric) = 1.0409634970536734200468003546651 absolute error = 0.031488806096639769322897665727839 relative error = 2.9361497946474500621116428863422 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.384 y[1] (analytic) = 1.0728264716518387005620840879077 y[1] (numeric) = 1.0411309739457192918032219352772 absolute error = 0.031695497706119408758862152630519 relative error = 2.9543918372295214737997416012651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.385 y[1] (analytic) = 1.0732015673268152954576493952072 y[1] (numeric) = 1.0412988254698846339587678537822 absolute error = 0.031902741856930661498881541425028 relative error = 2.9726700769172023585037733179921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.386 y[1] (analytic) = 1.0735775898001473303377709195101 y[1] (numeric) = 1.041467052553155427024114057518 absolute error = 0.032110537246991903313656861992103 relative error = 2.9909843081737078083681282956925 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.387 y[1] (analytic) = 1.0739545386958123632056188471909 y[1] (numeric) = 1.0416356561221420924357821750998 absolute error = 0.032318882573670270769836672091087 relative error = 3.0093343255402260316662821602895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.388 y[1] (analytic) = 1.0743324136368615298085672354074 y[1] (numeric) = 1.041804637103078565945795297431 absolute error = 0.032527776533782963862771937976364 relative error = 3.0277199236378787762380356941172 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.389 y[1] (analytic) = 1.0747112142454199205870268523226 y[1] (numeric) = 1.0419739964218213713878194118393 absolute error = 0.032737217823598549199207440483356 relative error = 3.046140897169675632360590149773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.39 y[1] (analytic) = 1.0750909401426869585493232471189 y[1] (numeric) = 1.0421437350038486948207167231177 absolute error = 0.032947205138838263728606524001238 relative error = 3.0645970409224621890239074648619 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.391 y[1] (analytic) = 1.0754715909489367780722421749589 y[1] (numeric) = 1.0423138537742594590504367178426 absolute error = 0.033157737174677319021805457116299 relative error = 3.083088149768862017848534102288 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.392 y[1] (analytic) = 1.0758531662835186046268635763786 y[1] (numeric) = 1.0424843536577723985311704499983 absolute error = 0.033368812625746206095693126380265 relative error = 3.1016140186692124591517897968798 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.393 y[1] (analytic) = 1.0762356657648571354293043853106 y[1] (numeric) = 1.042655235578725134646693146678 absolute error = 0.033580430186132000782611238632621 relative error = 3.1201744426734941849359255246005 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.394 y[1] (analytic) = 1.0766190890104529210159895150267 y[1] (numeric) = 1.0428265004610732513728198524412 absolute error = 0.033792588549379669643169662585515 relative error = 3.1387692169232545138395258552731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=68.6MB, alloc=4.4MB, time=3.81 x[1] = 0.395 y[1] (analytic) = 1.0770034356368827477430694467591 y[1] (numeric) = 1.0429981492283893713218984497944 absolute error = 0.034005286408493376421170996964735 relative error = 3.1573981366535244533610568928072 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.396 y[1] (analytic) = 1.0773887052598000212096019216175 y[1] (numeric) = 1.0431701828038622321702640112264 absolute error = 0.034218522455937789039337910391055 relative error = 3.1760609971947294449310296974357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.397 y[1] (analytic) = 1.0777748974939351506041143126486 y[1] (numeric) = 1.0433426021102957634695780552651 absolute error = 0.034432295383639387134536257383519 relative error = 3.1947575939745937876767479319792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.398 y[1] (analytic) = 1.0781620119530959339741623305114 y[1] (numeric) = 1.0435154080701081638429758951409 absolute error = 0.034646603882987770131186435370527 relative error = 3.2134877225200387169910250492457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.399 y[1] (analytic) = 1.0785500482501679444184997932385 y[1] (numeric) = 1.0436886016053309785669448838322 absolute error = 0.03486144664483696585155490940636 relative error = 3.2322511784590741142835782725234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.4 y[1] (analytic) = 1.0789390059971149172014732679482 y[1] (numeric) = 1.0438621836376081775398559735375 absolute error = 0.035076822359506739661617294410664 relative error = 3.2510477575226838245610216100754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.401 y[1] (analytic) = 1.0793288848049791377892544701431 y[1] (numeric) = 1.0440361550881952336380706209662 absolute error = 0.035292729716783904151183849176926 relative error = 3.269877255546704558748475944648 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.402 y[1] (analytic) = 1.0797196842838818308075223843971 y[1] (numeric) = 1.0442105168779582014605446822636 absolute error = 0.035509167405923629346977702133568 relative error = 3.2887394684736983579327786705387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.403 y[1] (analytic) = 1.0801114040430235499202061487794 y[1] (numeric) = 1.0443852699273727964628505528907 absolute error = 0.035726134115650753457355595888627 relative error = 3.3076341923548185969740962978037 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.404 y[1] (analytic) = 1.0805040436906845686288988243055 y[1] (numeric) = 1.044560415156523474481538418359 absolute error = 0.035943628534161094147360405946509 relative error = 3.3265612233516695051994088540651 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.405 y[1] (analytic) = 1.0808976028342252719925512500355 y[1] (numeric) = 1.0447359534851025116497570913819 absolute error = 0.036161649349122760342794158653561 relative error = 3.3455203577381591821578328022669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.406 y[1] (analytic) = 1.0812920810800865492670542641556 y[1] (numeric) = 1.0449118858324090847050545197468 absolute error = 0.036380195247677464561999744408765 relative error = 3.3645113919023460866840676360995 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.407 y[1] (analytic) = 1.0816874780337901874643166514964 y[1] (numeric) = 1.0450882131173483516902776570292 absolute error = 0.036599264916441835774038994467209 relative error = 3.3835341223482789777823784579494 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.408 y[1] (analytic) = 1.0820837932999392658304452584406 y[1] (numeric) = 1.045264936258430533048490995173 absolute error = 0.036818857041508732781954263267647 relative error = 3.4025883456978302861094508977127 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.409 y[1] (analytic) = 1.0824810264822185512426327970737 y[1] (numeric) = 1.0454420561737699931128326639416 absolute error = 0.037038970308448558129800133132031 relative error = 3.4216738586925228951001639720059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.41 y[1] (analytic) = 1.082879177183394894524357941723 y[1] (numeric) = 1.0456195737810843219922266073082 absolute error = 0.03725960340231057253213133441479 relative error = 3.4407904581953503110458092568276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.411 y[1] (analytic) = 1.0832782450053176276785014027179 y[1] (numeric) = 1.0457974899976934178538689509944 absolute error = 0.037480755007624209824632451723478 relative error = 3.4599379411925902016995294649116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=72.4MB, alloc=4.4MB, time=4.02 x[1] = 0.412 y[1] (analytic) = 1.0836782295489189620379807442877 y[1] (numeric) = 1.045975805740518569603406278597 absolute error = 0.037702423808400392434574465690668 relative error = 3.4791161047956112832487446623669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.413 y[1] (analytic) = 1.084079130414214387333505795996 y[1] (numeric) = 1.0461545219260815399637231360459 absolute error = 0.037924608488132847369782659950154 relative error = 3.4983247462426735357590684768662 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.414 y[1] (analytic) = 1.0844809472003030716780555899898 y[1] (numeric) = 1.0463336394705036489532556855306 absolute error = 0.038147307729799422724799904459249 relative error = 3.5175636629007217274586783598177 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.415 y[1] (analytic) = 1.0848836795053682624676768396186 y[1] (numeric) = 1.046513159289504857764748030505 absolute error = 0.038370520215863404702928809113579 relative error = 3.5368326522671722284962819553265 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.416 y[1] (analytic) = 1.0852873269266776881982030586595 y[1] (numeric) = 1.0466930822984028530453673329375 absolute error = 0.038594244628274835152835725721983 relative error = 3.5561315119716930950697046569448 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.417 y[1] (analytic) = 1.0856918890605839611974925044623 y[1] (numeric) = 1.046873409412112131579093442615 absolute error = 0.038818479648471829618399061847308 relative error = 3.5754600397779774050857003271778 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.418 y[1] (analytic) = 1.0860973655025249812727822128099 y[1] (numeric) = 1.0470541415451430853722983560353 absolute error = 0.039043223957381895900483856774629 relative error = 3.5948180335855098267748468131465 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.419 y[1] (analytic) = 1.0865037558470243402727544771743 y[1] (numeric) = 1.0472352796116010871434304192321 absolute error = 0.03926847623542325312932405794219 relative error = 3.6142052914313264019483192845654 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.42 y[1] (analytic) = 1.0869110596876917275639112103343 y[1] (numeric) = 1.0474168245251855762177177847716 absolute error = 0.039494235162506151346193425562714 relative error = 3.6336216114917675258459265886507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.421 y[1] (analytic) = 1.087319276617223336420850712016 y[1] (numeric) = 1.0475987771991891448278052281419 absolute error = 0.03972049941803419159304548387415 relative error = 3.6530667920842241057870378740336 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.422 y[1] (analytic) = 1.0877284062274022713300404523114 y[1] (numeric) = 1.0477811385464966248212380228215 absolute error = 0.039947267680905646508802429489901 relative error = 3.6725406316688768810979078678222 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.423 y[1] (analytic) = 1.0881384481090989562066785671375 y[1] (numeric) = 1.0479639094795841747757061664678 absolute error = 0.040174538629514781430972400669684 relative error = 3.692042928850428887050418654901 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.424 y[1] (analytic) = 1.088549401852271543524235848908 y[1] (numeric) = 1.0481470909105183675229618429042 absolute error = 0.040402310941753176001274006003844 relative error = 3.7115734823798310458083829376653 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.425 y[1] (analytic) = 1.0889612670459663243562691029099 y[1] (numeric) = 1.0483306837509552780823225959131 absolute error = 0.040630583295011046273946506996717 relative error = 3.7311320911560008676382879523402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.426 y[1] (analytic) = 1.0893740432783181393300958276049 y[1] (numeric) = 1.0485146889121395720046722812558 absolute error = 0.040859354366178567325423546349049 relative error = 3.7507185542275342459016899632113 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.427 y[1] (analytic) = 1.089787730136550790491919265217 y[1] (numeric) = 1.048699107304903594127871452841 absolute error = 0.041088622831647196364047812375954 relative error = 3.7703326707944103296063861009545 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.428 y[1] (analytic) = 1.0902023272069774540829919575135 y[1] (numeric) = 1.0488839398396664577444884275575 absolute error = 0.041318387367310996338503529955998 relative error = 3.7899742402096894575529828826207 % h = 0.001 TOP MAIN SOLVE Loop memory used=76.2MB, alloc=4.4MB, time=4.24 NO POLE x[1] = 0.429 y[1] (analytic) = 1.0906178340750010942264050306518 y[1] (numeric) = 1.0490691874264331341827618609626 absolute error = 0.041548646648567960043643169689236 relative error = 3.8096430619812041383725387502585 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.43 y[1] (analytic) = 1.0910342503251148775240895223366 y[1] (numeric) = 1.0492548509747935428017052527887 absolute error = 0.041779399350321334722384269547818 relative error = 3.8293389357732430610095711691878 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.431 y[1] (analytic) = 1.09145157554090258856361515432 y[1] (numeric) = 1.0494409313939216414012633870873 absolute error = 0.042010644146980947162351767232735 relative error = 3.8490616614082281204628770874593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.432 y[1] (analytic) = 1.0918698093050390463343710434825 y[1] (numeric) = 1.0496274295925745170484302967777 absolute error = 0.042242379712464529285940746704797 relative error = 3.8688110388683844438543088025454 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.433 y[1] (analytic) = 1.0922889511992905215527119353457 y[1] (numeric) = 1.0498143464790914773202379264082 absolute error = 0.042474604720199044232474008937561 relative error = 3.8885868682974034021528655131999 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.434 y[1] (analytic) = 1.0927090008045151548956526349088 y[1] (numeric) = 1.0500016829613931419645242500637 absolute error = 0.042707317843122012931128384845138 relative error = 3.9083889500020985931381941333091 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.435 y[1] (analytic) = 1.0931299577006633761426924011461 y[1] (numeric) = 1.050189439946980534979389183577 absolute error = 0.042940517753682841163303217569132 relative error = 3.9282170844540547814438314664667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.436 y[1] (analytic) = 1.0935518214667783242253501633781 y[1] (numeric) = 1.0503776183429341771122462115113 absolute error = 0.043174203123844147113103951866796 relative error = 3.9480710722912697817762538177337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.437 y[1] (analytic) = 1.0939745916809962681839905100158 y[1] (numeric) = 1.0505662190559131787793772297883 absolute error = 0.043408372625083089404613280227458 relative error = 3.9679507143197892716610198623462 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.438 y[1] (analytic) = 1.0943982679205470290315194928856 y[1] (numeric) = 1.0507552429921543334068976843289 absolute error = 0.043643024928392695624621808556739 relative error = 3.9878558115153345203219884870033 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.439 y[1] (analytic) = 1.0948228497617544025235283834771 y[1] (numeric) = 1.0509446910574712111940386646685 absolute error = 0.043878158704283191329489718808606 relative error = 4.0077861650249230205537558322784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.44 y[1] (analytic) = 1.0952483367800365828344626110016 y[1] (numeric) = 1.0511345641572532532996521891873 absolute error = 0.04411377262278332953481042181434 relative error = 4.0277415761684820107010754368212 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.441 y[1] (analytic) = 1.0956747285499065871393922061318 y[1] (numeric) = 1.0513248631964648664528454953762 absolute error = 0.044349865353441720686546710755579 relative error = 4.0477218464404548741120928354791 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.442 y[1] (analytic) = 1.0961020246449726811009591686834 y[1] (numeric) = 1.0515155890796445179886497244273 absolute error = 0.044586435565328163112309444256084 relative error = 4.067726777511400403684731892522 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.443 y[1] (analytic) = 1.0965302246379388052610762723304 y[1] (numeric) = 1.0517067427109038313096279644059 absolute error = 0.044823481927034973951448307924442 relative error = 4.0877561712295849193775053344543 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.444 y[1] (analytic) = 1.0969593281006050023369509146883 y[1] (numeric) = 1.0518983249939266817743271903205 absolute error = 0.045061003106678320562623724367839 relative error = 4.1078098296225672268073772396318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.445 y[1] (analytic) = 1.0973893346038678454210067167782 y[1] (numeric) = 1.0520903368319682930134782125622 absolute error = 0.045298997771899552407528504215951 relative error = 4.1278875548987764053080715780561 % h = 0.001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=4.45 NO POLE x[1] = 0.446 y[1] (analytic) = 1.0978202437177208670842746719854 y[1] (numeric) = 1.0522827791278543336748473174411 absolute error = 0.045537464589866533409427354544288 relative error = 4.1479891494490824140723892872119 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.447 y[1] (analytic) = 1.0982520550112549893828247411573 y[1] (numeric) = 1.0524756527839800145976428548888 absolute error = 0.045776402227274974785181886268518 relative error = 4.1681144158483595052516579107071 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.448 y[1] (analytic) = 1.0986847680526589547668078874449 y[1] (numeric) = 1.0526689587023091864173795988491 absolute error = 0.046015809350349768349428288595828 relative error = 4.1882631568570424331343836871572 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.449 y[1] (analytic) = 1.0991183824092197578916776418816 y[1] (numeric) = 1.0528626977843734376021032754149 absolute error = 0.046255684624846320289574366466754 relative error = 4.2084351754226754487744974080558 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.45 y[1] (analytic) = 1.0995528976473230783311593885136 y[1] (numeric) = 1.053056870931271192920877222412 absolute error = 0.046496026716051885410282166101602 relative error = 4.2286302746814540696872736957931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.451 y[1] (analytic) = 1.0999883133324537141915346561489 y[1] (numeric) = 1.0532514790436668123454327118689 absolute error = 0.046736834288786901846101944280009 relative error = 4.2488482579597596144780499967941 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.452 y[1] (analytic) = 1.1004246290291960166268068024775 y[1] (numeric) = 1.0534465230217896903858840336466 absolute error = 0.046978106007406326240922768830905 relative error = 4.2690889287756864925152680301433 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.453 y[1] (analytic) = 1.100861844301234325254313575431 y[1] (numeric) = 1.0536420037654333558614090044374 absolute error = 0.047219840535800969392904570993542 relative error = 4.2893520908405622390050982493341 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.454 y[1] (analytic) = 1.101299958711353404470351136208 y[1] (numeric) = 1.0538379221739545721067951313792 absolute error = 0.047462036537398832363556004828842 relative error = 4.3096375480604602860699787143789 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.455 y[1] (analytic) = 1.1017389718214388806653732283767 y[1] (numeric) = 1.0540342791462724376157512236622 absolute error = 0.047704692675166443049622004714543 relative error = 4.329945104537705460677795364257 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.456 y[1] (analytic) = 1.1021788831924776803383282778904 y[1] (numeric) = 1.0542310755808674871218838087424 absolute error = 0.047947807611610193216444469147972 relative error = 4.3502745645723722005121428367668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.457 y[1] (analytic) = 1.1026196923845584691096963097179 y[1] (numeric) = 1.0544283123757807931182372721108 absolute error = 0.048191380008777675991459037607173 relative error = 4.3706257326637754791171255960816 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.458 y[1] (analytic) = 1.1030613989568720916327866680871 y[1] (numeric) = 1.0546259904286130678162962010021 absolute error = 0.048435408528259023816490467085079 relative error = 4.3909984135119544318924801700876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.459 y[1] (analytic) = 1.1035040024677120124028566290802 y[1] (numeric) = 1.0548241106365237655453479729673 absolute error = 0.048679891831188246857508656112844 relative error = 4.4113924120191486747564128230784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.46 y[1] (analytic) = 1.1039475024744747574636100964996 y[1] (numeric) = 1.0550226738962301855931031898718 absolute error = 0.048924828578244571870506906627841 relative error = 4.4318075332912673075344451285718 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.461 y[1] (analytic) = 1.104391898533660357010634674543 y[1] (numeric) = 1.0552216811040065754884711166233 absolute error = 0.049170217429653781522163557919649 relative error = 4.4522435826393505943727348767968 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.462 y[1] (analytic) = 1.1048371902008727888913345138855 y[1] (numeric) = 1.0554211331556832347273868417815 absolute error = 0.049416057045189554163947672103984 relative error = 4.4727003655810243137137838476421 % h = 0.001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=4.67 NO POLE x[1] = 0.463 y[1] (analytic) = 1.1052833770308204230009154312754 y[1] (numeric) = 1.0556210309466456189425864341448 absolute error = 0.049662346084174804058328997130561 relative error = 4.4931776878419467706111495794811 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.464 y[1] (analytic) = 1.1057304585773164665739779066934 y[1] (numeric) = 1.0558213753718334445182259254669 absolute error = 0.04990908320548302205575198122659 relative error = 4.5136753553572484643977378253129 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.465 y[1] (analytic) = 1.1061784343932794103712726665209 y[1] (numeric) = 1.0560221673257397936502395046073 absolute error = 0.050156267067539616721033161913622 relative error = 4.5341931742729644049594584492644 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.466 y[1] (analytic) = 1.1066273040307334757611726659979 y[1] (numeric) = 1.0562234077024102198533318626857 absolute error = 0.050403896328323255907840803312124 relative error = 4.5547309509474590711024726990664 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.467 y[1] (analytic) = 1.1070770670408090626954143895363 y[1] (numeric) = 1.0564250973954418539154991821704 absolute error = 0.050651969645367208779915207365925 relative error = 4.5752884919528440047379367952738 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.468 y[1] (analytic) = 1.107527722973743198578660493185 y[1] (numeric) = 1.0566272372979825103009728153069 absolute error = 0.050900485675760688277687677878075 relative error = 4.5958656040763880348430483886377 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.469 y[1] (analytic) = 1.1079792713788799880314349197206 y[1] (numeric) = 1.0568298283027297940024792488696 absolute error = 0.051149443076150194028955670851018 relative error = 4.6164620943219201253913215173576 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.47 y[1] (analytic) = 1.1084317118046710635459807234666 y[1] (numeric) = 1.0570328713019302078437095028988 absolute error = 0.051398840502740855702271220567836 relative error = 4.6370777699112248416783451914534 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.471 y[1] (analytic) = 1.1088850437986760370345899490213 y[1] (numeric) = 1.0572363671873782602328906608832 absolute error = 0.051648676611297776801699288138086 relative error = 4.6577124382854304297018136690468 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.472 y[1] (analytic) = 1.1093392669075629522699540156011 y[1] (numeric) = 1.0574403168504155733683517777392 absolute error = 0.051898950057147378901602237861863 relative error = 4.6783659071063895034863459771071 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.473 y[1] (analytic) = 1.1097943806771087382170821666872 y[1] (numeric) = 1.0576447211819299918969759599476 absolute error = 0.052149659495178746320106206739641 relative error = 4.6990379842580523354745314567052 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.474 y[1] (analytic) = 1.1102503846521996632563346530956 y[1] (numeric) = 1.057849581072354692026429959322 absolute error = 0.052400803579844971229904693773558 relative error = 4.7197284778478327453357403508838 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.475 y[1] (analytic) = 1.1107072783768317902971164264731 y[1] (numeric) = 1.0580548974116672910920621681044 absolute error = 0.052652380965164499205054258368677 relative error = 4.7404371962079665827735170540258 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.476 y[1] (analytic) = 1.1111650613941114327817762295659 y[1] (numeric) = 1.0582606710893889575793594484153 absolute error = 0.052904390304722475202416781150622 relative error = 4.7611639478968628001408220385532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.477 y[1] (analytic) = 1.1116237332462556115792550793985 y[1] (numeric) = 1.0584669029945835216028527735289 absolute error = 0.053156830251672089976402305869525 relative error = 4.781908541700447110900000182603 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.478 y[1] (analytic) = 1.1120832934745925127680272497516 y[1] (numeric) = 1.0586735940158565858423612019919 absolute error = 0.053409699458735926925666047759613 relative error = 4.8026707866334982301911218369747 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.479 y[1] (analytic) = 1.1125437416195619463078759700387 y[1] (numeric) = 1.058880745041354636937463248269 absolute error = 0.05366299657820730937041272176969 relative error = 4.8234504919409766939982621682422 % h = 0.001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=4.88 NO POLE x[1] = 0.48 y[1] (analytic) = 1.1130050772207158056000451688413 y[1] (numeric) = 1.0590883569587641573410842553688 absolute error = 0.053916720261951648258960913472438 relative error = 4.8442474670993462536283478557717 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.481 y[1] (analytic) = 1.1134672998167185279353077019906 y[1] (numeric) = 1.0592964306553107376330879157902 absolute error = 0.054170869161407790302219786200492 relative error = 4.8650615218178878424414019428734 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.482 y[1] (analytic) = 1.1139304089453475558294896171662 y[1] (numeric) = 1.0595049670177581892947596271213 absolute error = 0.054425441927589366534729990044915 relative error = 4.8858924660400061119943514668485 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.483 y[1] (analytic) = 1.1143944041434937992459891195241 y[1] (numeric) = 1.0597139669324076579450689077365 absolute error = 0.054680437211086141300920211787547 relative error = 4.9067401099445285349830224206934 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.484 y[1] (analytic) = 1.1148592849471620987048280158762 y[1] (numeric) = 1.0599234312850967370395976362532 absolute error = 0.054935853662065361665230379623093 relative error = 4.9276042639469970725885267129868 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.485 y[1] (analytic) = 1.1153250508914716892777725284065 y[1] (numeric) = 1.0601333609611985820330204157463 absolute error = 0.055191689930273107244752112660205 relative error = 4.9484847387009524040549402551471 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.486 y[1] (analytic) = 1.115791701510656665469059482842 y[1] (numeric) = 1.0603437568456210250060229001684 absolute error = 0.055447944665035640463036582673577 relative error = 4.9693813450992107165449743607096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.487 y[1] (analytic) = 1.1162592363380664469812629903921 y[1] (numeric) = 1.0605546198228056897575434559804 absolute error = 0.055704616515260757223719534411729 relative error = 4.9902938942751330535392486140683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.488 y[1] (analytic) = 1.1167276549061662453658358576272 y[1] (numeric) = 1.0607659507767271073632230666792 absolute error = 0.055961704129439138002612790948009 relative error = 5.0112221976038872202627766613819 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.489 y[1] (analytic) = 1.117196956746537531557859073795 y[1] (numeric) = 1.0609777505908918322009479216992 absolute error = 0.056219206155645699356911152095894 relative error = 5.0321660667037022448393714796459 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.49 y[1] (analytic) = 1.1176671413898785042945318408633 y[1] (numeric) = 1.061190020148337558444368664069 absolute error = 0.056477121241540945850163176794324 relative error = 5.0531253134371153940908581572312 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.491 y[1] (analytic) = 1.1181382083660045594169337278386 y[1] (numeric) = 1.0614027603316322370252798032337 absolute error = 0.056735448034372322391653924604953 relative error = 5.0740997499122117431132447166912 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.492 y[1] (analytic) = 1.1186101572038487600545896476376 y[1] (numeric) = 1.0616159720228731930657423305864 absolute error = 0.05699418518097556698884731705125 relative error = 5.0950891884838562979763397546933 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.493 y[1] (analytic) = 1.1190829874314623076923674719854 y[1] (numeric) = 1.0618296561036862437808321055156 absolute error = 0.05725333132777606391153536646984 relative error = 5.1160934417549186711067144708918 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.494 y[1] (analytic) = 1.1195566985760150141192372174827 y[1] (numeric) = 1.0620438134552248168528961091451 absolute error = 0.057512885120790197266341108337605 relative error = 5.1371123225774903091263808936849 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.495 y[1] (analytic) = 1.1200312901637957742584198541208 y[1] (numeric) = 1.0622584449581690692781981914364 absolute error = 0.057772845205626704980221662684423 relative error = 5.1581456440540942731310927520923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.496 y[1] (analytic) = 1.1205067617202130398784529061372 y[1] (numeric) = 1.062473551492725006686835464936 absolute error = 0.058033210227488033191617441201297 relative error = 5.179193219538887571602765535081 % h = 0.001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=5.09 NO POLE x[1] = 0.497 y[1] (analytic) = 1.1209831127697952941846991341835 y[1] (numeric) = 1.0626891339386236031368060251759 absolute error = 0.058293978831171691047893109007559 relative error = 5.2002548626388560463601529476579 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.498 y[1] (analytic) = 1.1214603428361915272908237073372 y[1] (numeric) = 1.0629051931751199213831082035881 absolute error = 0.058555149661071605907715503749061 relative error = 5.2213303872150018121606034213608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.499 y[1] (analytic) = 1.1219384514421717125697643935207 y[1] (numeric) = 1.0631217300809922336227510837584 absolute error = 0.058816721361179478947013309762381 relative error = 5.2424196073835232507734478490297 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.5 y[1] (analytic) = 1.1224174381096272838837184173962 y[1] (numeric) = 1.0633387455345411427165555359378 absolute error = 0.059078692575086141167162881458341 relative error = 5.263522337516987560552333652523 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.501 y[1] (analytic) = 1.1228973023595716136926687557886 y[1] (numeric) = 1.0635562404135887038886245479366 absolute error = 0.059341061945982909804044207852002 relative error = 5.284638392245495862739616098838 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.502 y[1] (analytic) = 1.1233780437121404920409717621522 y[1] (numeric) = 1.063774215595477546904361152856 absolute error = 0.059603828116662945136610609296213 relative error = 5.3057675864578408659407409750357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.503 y[1] (analytic) = 1.1238596616865926064215271335312 y[1] (numeric) = 1.0639926719570699987279117755691 absolute error = 0.059866989729522607693615357962084 relative error = 5.326909735302657090410398914102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.504 y[1] (analytic) = 1.1243421558013100225170503558855 y[1] (numeric) = 1.0642116103747472066599123404327 absolute error = 0.060130545426562815857138015452862 relative error = 5.3480646541895636539950965093766 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.505 y[1] (analytic) = 1.1248255255737986658179668865485 y[1] (numeric) = 1.0644310317244082619564140024105 absolute error = 0.06039449384939040386155288413801 relative error = 5.3692321587902996217786686195557 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.506 y[1] (analytic) = 1.1253097705206888041164464559633 y[1] (numeric) = 1.0646509368814693239298648826112 absolute error = 0.060658833639219480186581573352192 relative error = 5.3904120650398519216781457825853 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.507 y[1] (analytic) = 1.1257948901577355308760949947039 y[1] (numeric) = 1.0648713267208627445330237071841 absolute error = 0.060923563436872786343071287519816 relative error = 5.4116041891375758284372863358311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.508 y[1] (analytic) = 1.1262808839998192494768208161278 y[1] (numeric) = 1.0650922021170361934266807655877 absolute error = 0.061188681882783056050140050540062 relative error = 5.4328083475483080186639806701054 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.509 y[1] (analytic) = 1.126767751560946158334390809836 y[1] (numeric) = 1.0653135639439517835320611204355 absolute error = 0.061454187616994374802329689400445 relative error = 5.4540243570034721997556310921861 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.51 y[1] (analytic) = 1.1272554923542487368941915264245 y[1] (numeric) = 1.0655354130750851970687845164453 absolute error = 0.061720079279163539825407009979226 relative error = 5.4752520345021773157535011772457 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.511 y[1] (analytic) = 1.1277441058919862324987091598053 y[1] (numeric) = 1.0657577503834248120792559504565 absolute error = 0.061986355508561420419453209348814 relative error = 5.4964911973123083333629094789142 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.512 y[1] (analytic) = 1.1282335916855451481282415596589 y[1] (numeric) = 1.0659805767414708294403603780547 absolute error = 0.062253014944074318687881181604132 relative error = 5.5177416629716096115710103270594 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.513 y[1] (analytic) = 1.1287239492454397310143545333464 y[1] (numeric) = 1.0662038930212344003633345450344 absolute error = 0.062520056224205330651019988312005 relative error = 5.5390032492887608584877555547658 % h = 0.001 TOP MAIN SOLVE Loop memory used=95.3MB, alloc=4.4MB, time=5.31 NO POLE x[1] = 0.514 y[1] (analytic) = 1.1292151780813124621255938238659 y[1] (numeric) = 1.0664277000942367543826884437554 absolute error = 0.062787477987075707742905380110554 relative error = 5.5602757743444456792284618057118 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.515 y[1] (analytic) = 1.1297072777019345465249632781811 y[1] (numeric) = 1.0666519988315083278350484053996 absolute error = 0.063055278870426218689914872781512 relative error = 5.5815590564924127188482151064731 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.516 y[1] (analytic) = 1.1302002476152064045986788484863 y[1] (numeric) = 1.0668767901035878928287933492124 absolute error = 0.063323457511618511769885499273886 relative error = 5.6028529143605294045291242463202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.517 y[1] (analytic) = 1.1306940873281581641557071976931 y[1] (numeric) = 1.0671020747805216867053552190183 absolute error = 0.063592012547636477450351978674734 relative error = 5.6241571668518282914111838664676 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.518 y[1] (analytic) = 1.1311887963469501533975968096429 y[1] (numeric) = 1.0673278537318625419930541456405 absolute error = 0.063860942615087611404542664002435 relative error = 5.6454716331455460166462237734465 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.519 y[1] (analytic) = 1.1316843741768733947581086342535 y[1] (numeric) = 1.0675541278266690168543383813134 absolute error = 0.0641302463502043779037702529401 relative error = 5.6667961326981548664420996843171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.52 y[1] (analytic) = 1.1321808203223500996121524280115 y[1] (numeric) = 1.0677808979335045260272985587795 absolute error = 0.064399922388845573584853869232014 relative error = 5.6881304852443869610509192866594 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.521 y[1] (analytic) = 1.1326781342869341638535340809147 y[1] (numeric) = 1.06800816492043647226232533348 absolute error = 0.064669969366497691591208747434691 relative error = 5.7094745107982510628406931300474 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.522 y[1] (analytic) = 1.1331763155733116643410183521593 y[1] (numeric) = 1.0682359296550353782547789721128 absolute error = 0.064940385918276286086239380046523 relative error = 5.7308280296540420127743495087097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.523 y[1] (analytic) = 1.1336753636833013562122105685491 y[1] (numeric) = 1.0684641930043740190745389548125 absolute error = 0.065211170678927337137671613736595 relative error = 5.7521908623873428008035532719993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.524 y[1] (analytic) = 1.1341752781178551710647599717881 y[1] (numeric) = 1.0686929558350265550933011613338 absolute error = 0.0654823222828286159714588104543 relative error = 5.7735628298560192758672176085956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.525 y[1] (analytic) = 1.1346760583770587160043865334936 y[1] (numeric) = 1.0689222190130676654104897138662 absolute error = 0.065753839363991050593896819627377 relative error = 5.7949437532012075013659925639817 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.526 y[1] (analytic) = 1.135177703960131773559232189945 y[1] (numeric) = 1.0691519834040716817786500504978 absolute error = 0.066025720556060091780582139447184 relative error = 5.8163334538482937621643517138221 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.527 y[1] (analytic) = 1.1356802143654288024600365822581 y[1] (numeric) = 1.0693822498731117230291893038612 absolute error = 0.066297964492317079430847278396896 relative error = 5.8377317535078872293511764464827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.528 y[1] (analytic) = 1.1361835890904394392856365218521 y[1] (numeric) = 1.0696130192847588299993295591509 absolute error = 0.066570569805680609286306962701122 relative error = 5.8591384741767852891679531967988 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.529 y[1] (analytic) = 1.1366878276317890009732875357502 y[1] (numeric) = 1.0698442925030811009611390644856 absolute error = 0.066843535128707900012148471264613 relative error = 5.8805534381389315426908502833667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.53 y[1] (analytic) = 1.1371929294852389881933049814358 y[1] (numeric) = 1.0700760703916428275535059645121 absolute error = 0.067116859093596160639799016923676 relative error = 5.9019764679663664830290253682458 % h = 0.001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.4MB, time=5.53 NO POLE x[1] = 0.531 y[1] (analytic) = 1.1376988941456875895875213566629 y[1] (numeric) = 1.0703083538135036312179186252061 absolute error = 0.067390540332183958369602731456848 relative error = 5.923407386520170856976529687888 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.532 y[1] (analytic) = 1.138205721107170186871055565808 y[1] (numeric) = 1.0705411436312176001389161140162 absolute error = 0.067664577475952586732139451791826 relative error = 5.9448460169514017182291188757277 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.533 y[1] (analytic) = 1.1387134098628598607968890410339 y[1] (numeric) = 1.07077444070683242669007189483 absolute error = 0.067938969156027434106817146203895 relative error = 5.9662921827020211794501502596873 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.534 y[1] (analytic) = 1.1392219599050678979827427537335 y[1] (numeric) = 1.071008245901888545386373291706 absolute error = 0.068213714003179352596369462027462 relative error = 5.9877457075058178706415408922517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.535 y[1] (analytic) = 1.1397313707252442985997482894172 y[1] (numeric) = 1.0712425600774182713438587689199 absolute error = 0.068488810647826027255889520497218 relative error = 6.009206415389321111446477247678 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.536 y[1] (analytic) = 1.1402416418139782849224052974161 y[1] (numeric) = 1.0714773840939449392473745676168 absolute error = 0.068764257720033345675030729799245 relative error = 6.030674130672707805180204561489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.537 y[1] (analytic) = 1.1407527726609988107393167654858 y[1] (numeric) = 1.0717127188114820428273117312404 absolute error = 0.069040053849516767912005034245376 relative error = 6.0521486779707020625537793227373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.538 y[1] (analytic) = 1.1412647627551750716241927086173 y[1] (numeric) = 1.0719485650895323748461840429306 absolute error = 0.069316197665642696778008665686731 relative error = 6.073629882193467563223140660304 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.539 y[1] (analytic) = 1.1417776115845170160666120010953 y[1] (numeric) = 1.0721849237870871675959068882404 absolute error = 0.06959268779742984847070511285486 relative error = 6.095117568547492663462243560673 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.54 y[1] (analytic) = 1.1422913186361758574620312210822 y[1] (numeric) = 1.0724217957626252339066365458205 absolute error = 0.069869522873550623555394675261742 relative error = 6.1166115625364682584242973551109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.541 y[1] (analytic) = 1.1428058833964445869605285177651 y[1] (numeric) = 1.0726591818741121086680288971617 absolute error = 0.070146701522332478292499620603349 relative error = 6.1381116899621584076193651265304 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.542 y[1] (analytic) = 1.1433213053507584871737696523608 y[1] (numeric) = 1.072897082978999190863776034065 absolute error = 0.070424222371759296309993618295868 relative error = 6.1596177769252637323997020863373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.543 y[1] (analytic) = 1.1438375839836956467396825060591 y[1] (numeric) = 1.0731354999342228861202787292296 absolute error = 0.070702084049472760619403776829488 relative error = 6.1811296498262775944062421030665 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.544 y[1] (analytic) = 1.1443547187789774757443254902696 y[1] (numeric) = 1.0733744335962037497703122212176 absolute error = 0.070980285182773725974013269052011 relative error = 6.2026471353663350640905800389866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.545 y[1] (analytic) = 1.1448727092194692220004344373497 y[1] (numeric) = 1.0736138848208456304325422500556 absolute error = 0.071258824398623591567892187294065 relative error = 6.2241700605480546885866420468092 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.546 y[1] (analytic) = 1.1453915547871804881821316933069 y[1] (numeric) = 1.0738538544635348141077477638875 absolute error = 0.071537700323645674074383929419417 relative error = 6.2456982526763730683649852417823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.547 y[1] (analytic) = 1.1459112549632657498152802778119 y[1] (numeric) = 1.0740943433791391687926062003834 absolute error = 0.071816911584126581022674077428451 relative error = 6.2672315393593722522603210070065 % h = 0.001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.4MB, time=5.74 NO POLE x[1] = 0.548 y[1] (analytic) = 1.1464318092280248741229651212096 y[1] (numeric) = 1.0743353524220072896118967290492 absolute error = 0.072096456806017584511068392160362 relative error = 6.2887697485090999606194114902458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.549 y[1] (analytic) = 1.1469532170609036397255825330915 y[1] (numeric) = 1.0745768824459676444699763221609 absolute error = 0.072376334614935995255606210930551 relative error = 6.3103127083423826464719455531516 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.55 y[1] (analytic) = 1.1474754779404942571950182023822 y[1] (numeric) = 1.0748189343043277202223830027779 absolute error = 0.072656543636166536972635199604334 relative error = 6.3318602473816314047813575485813 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.551 y[1] (analytic) = 1.1479985913445358904623931748063 y[1] (numeric) = 1.0750615088498731693684200981596 absolute error = 0.072937082494662721093973076646739 relative error = 6.3534121944556407399858089036237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.552 y[1] (analytic) = 1.1485225567499151790788564000321 y[1] (numeric) = 1.0753046069348669572655748059308 absolute error = 0.073217949815048221813281594101221 relative error = 6.3749683787003802021917077149375 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.553 y[1] (analytic) = 1.1490473736326667613289015877443 y[1] (numeric) = 1.0755482294110485098666238585063 absolute error = 0.073499144221618251462277729237922 relative error = 6.3965286295597789025331946234183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.554 y[1] (analytic) = 1.1495730414679737981956852593716 y[1] (numeric) = 1.0757923771296328619802785485967 absolute error = 0.073780664338340936215406710774866 relative error = 6.4180927767865029183609733954668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.555 y[1] (analytic) = 1.150099559730168498177822030195 y[1] (numeric) = 1.0760370509413098060562208550812 absolute error = 0.074062508788858692121601175113742 relative error = 6.4396606504427255990727112304237 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.556 y[1] (analytic) = 1.1506269278927326429571323050854 y[1] (numeric) = 1.0762822516962430414953818841396 absolute error = 0.074344676196489601461750420945758 relative error = 6.4612320809008907835449762335903 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.557 y[1] (analytic) = 1.1511551454282981139168167201663 y[1] (numeric) = 1.0765279802440693244863133152933 absolute error = 0.074627165184228789430503404873023 relative error = 6.482806898844468940273317200199 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.558 y[1] (analytic) = 1.1516842118086474195095308122717 y[1] (numeric) = 1.0767742374338976183685020159145 absolute error = 0.074909974374749801141028796357182 relative error = 6.5043849352687062414726233688784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.559 y[1] (analytic) = 1.1522141265047142234748325481675 y[1] (numeric) = 1.0770210241143082445234774608175 absolute error = 0.07519310239040597895135508735 relative error = 6.5259660214813665825343287069573 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.56 y[1] (analytic) = 1.1527448889865838739054744961337 y[1] (numeric) = 1.0772683411333520337945610657531 absolute error = 0.075476547853231840110913430380557 relative error = 6.5475499891034665583803462296242 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.561 y[1] (analytic) = 1.153276498723493933162011573659 y[1] (numeric) = 1.077516189338549478436106014988 absolute error = 0.075760309384944454725905558671032 relative error = 6.5691366700700034083958325372382 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.562 y[1] (analytic) = 1.1538089551838347086351944566842 y[1] (numeric) = 1.0777645695768898845930756336563 absolute error = 0.076044385606944824042118823027966 relative error = 6.5907258966306759417639909478209 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.563 y[1] (analytic) = 1.1543422578351497843556178880455 y[1] (numeric) = 1.0780134826948305253118078252366 absolute error = 0.076328775140319259043810062808855 relative error = 6.6123175013505984551661231335016 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.564 y[1] (analytic) = 1.1548764061441365534500922755127 y[1] (numeric) = 1.0782629295382957940828125633177 absolute error = 0.076613476605840759367279712195046 relative error = 6.6339113171110076549490339293462 % h = 0.001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=5.96 NO POLE x[1] = 0.565 y[1] (analytic) = 1.1554113995766467514442061230971 y[1] (numeric) = 1.0785129109526763589164488947853 absolute error = 0.076898488623970392527757228311779 relative error = 6.655507177109962595999681919422 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.566 y[1] (analytic) = 1.1559472375976869904105459931083 y[1] (numeric) = 1.0787634277828283169523273786834 absolute error = 0.077183809814858673458218614424847 relative error = 6.6771049148630376497036495265363 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.567 y[1] (analytic) = 1.1564839196714192939620398507875 y[1] (numeric) = 1.0790144808730723496032833512762 absolute error = 0.077469438798346944358756499511344 relative error = 6.6987043642040085134995807064274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.568 y[1] (analytic) = 1.157021445261161633089888798216 y[1] (numeric) = 1.0792660710671928782347658732666 absolute error = 0.077755374193968754855122924949381 relative error = 6.7203053592855312746762021006276 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.569 y[1] (analytic) = 1.1575598138293884628455513596132 y[1] (numeric) = 1.0795181992084372203804866797142 absolute error = 0.078041614620951242465064679899018 relative error = 6.7419077345798145411919048195023 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.57 y[1] (analytic) = 1.158099024837731259866243636084 y[1] (numeric) = 1.0797708661395147464951729169299 absolute error = 0.078328158698216513371070719154101 relative error = 6.7635113248792846524291191508271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.571 y[1] (analytic) = 1.158639077746979060743417804361 y[1] (numeric) = 1.0800240727025960372452669135283 absolute error = 0.078615005044383023498150890832661 relative error = 6.7851159652972439829268637200064 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.572 y[1] (analytic) = 1.1591799720170790012336805911064 y[1] (numeric) = 1.0802778197393120413384156948642 absolute error = 0.07890215227776695989526489624223 relative error = 6.8067214912685223522648943231776 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.573 y[1] (analytic) = 1.1597217071071368563116125119018 y[1] (numeric) = 1.0805321080907532338925924112956 absolute error = 0.079189599016383622419020100606229 relative error = 6.8283277385501215544018162282861 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.574 y[1] (analytic) = 1.1602642824754175810639478221502 y[1] (numeric) = 1.0807869385974687753456913110814 absolute error = 0.079477343877948805718256511068766 relative error = 6.8499345432218530198973576624409 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.575 y[1] (analytic) = 1.1608076975793458524245742857562 y[1] (numeric) = 1.0810423120994656709064373482481 absolute error = 0.079765385479880181518136937508022 relative error = 6.871541741686968624575732003162 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.576 y[1] (analytic) = 1.1613519518755066117498110266296 y[1] (numeric) = 1.0812982294362079305474509744463 absolute error = 0.080053722439298681202360052183257 relative error = 6.8931491706727846583126424487495 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.577 y[1] (analytic) = 1.1618970448196456082334218877795 y[1] (numeric) = 1.0815546914466157295413081216619 absolute error = 0.080342353373029878692113766117598 relative error = 6.9147566672312989677530062964042 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.578 y[1] (analytic) = 1.162442975866669943160820883031 y[1] (numeric) = 1.0818116989690645695404348396525 absolute error = 0.080631276897605373620386043378459 relative error = 6.9363640687398012868898970980892 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.579 y[1] (analytic) = 1.1629897444706486150019254872046 y[1] (numeric) = 1.0820692528413844402016755081445 absolute error = 0.080920491629264174800249979060058 relative error = 6.9579712129014767695575226400438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.58 y[1] (analytic) = 1.16353735008481306534211267195 y[1] (numeric) = 1.0823273539008589813563729991517 absolute error = 0.081209996183954083985739672798236 relative error = 6.9795779377460027380122757028375 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.581 y[1] (analytic) = 1.1640857921615577256507317563242 y[1] (numeric) = 1.0825860029842246457267986192672 absolute error = 0.08149978917733307992393313705701 relative error = 7.0011840816301386618960137589775 % h = 0.001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=6.17 NO POLE x[1] = 0.582 y[1] (analytic) = 1.1646350701524405648866273036464 y[1] (numeric) = 1.0828452009276698621897691154271 absolute error = 0.081789869224770702696858188219306 relative error = 7.0227894832383093819947440615309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.583 y[1] (analytic) = 1.165185183508183637940124459152 y[1] (numeric) = 1.0831049485668341995882874804607 absolute error = 0.082080234941349438351836978691325 relative error = 7.0443939815831815933238129299283 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.584 y[1] (analytic) = 1.1657361316786736349109282865074 y[1] (numeric) = 1.083365246736807531092043746716 absolute error = 0.082370884941866103818884539791412 relative error = 7.0659974160062336021875234602842 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.585 y[1] (analytic) = 1.1662879141129624312213878253303 y[1] (numeric) = 1.08362609627212919910761140719 absolute error = 0.082661817840833232113776418140281 relative error = 7.0875996261783183719768354413269 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.586 y[1] (analytic) = 1.1668405302592676385645747564985 y[1] (numeric) = 1.0838874980067871807391745538981 absolute error = 0.0829530322524804578254002026004 relative error = 7.1092004521002198725834360589544 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.587 y[1] (analytic) = 1.1673939795649731566866257272142 y[1] (numeric) = 1.0841494527742172538006202726857 absolute error = 0.083244526790755902886005454528472 relative error = 7.1307997341032027484220111891772 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.588 y[1] (analytic) = 1.1679482614766297260027965535271 y[1] (numeric) = 1.0844119614073021633798302823206 absolute error = 0.083536300069327562622966271206547 relative error = 7.1523973128495553201649959280602 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.589 y[1] (analytic) = 1.1685033754399554810466756843086 y[1] (numeric) = 1.0846750247383707889560052535039 absolute error = 0.083828350701584692090670430804723 relative error = 7.1739930293331259354054407557513 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.59 y[1] (analytic) = 1.1690593208998365047520034775093 y[1] (numeric) = 1.0849386435991973120708546904075 absolute error = 0.084120677300639192681148787101805 relative error = 7.1955867248798526835738976971064 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.591 y[1] (analytic) = 1.1696160973003273835665430069271 y[1] (numeric) = 1.085202818821000384554484703477 absolute error = 0.084413278479326999012058303450086 relative error = 7.2171782411482864905444103904978 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.592 y[1] (analytic) = 1.1701737040846517633974472856612 y[1] (numeric) = 1.0854675512344422973068154475445 absolute error = 0.084706152850209466090631838116791 relative error = 7.2387674201301076084727845247994 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.593 y[1] (analytic) = 1.1707321406952029063875669609314 y[1] (numeric) = 1.0857328416696281496353594437634 absolute error = 0.084999299025574756752207517167988 relative error = 7.2603541041506355165173221165154 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.594 y[1] (analytic) = 1.1712914065735442485221417040005 y[1] (numeric) = 1.0859986909561050191501914475192 absolute error = 0.085292715617439229371950256481219 relative error = 7.2819381358693322481981260868896 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.595 y[1] (analytic) = 1.1718515011604099580653176885558 y[1] (numeric) = 1.0862650999228611322169399672748 absolute error = 0.085586401237548825848377721280974 relative error = 7.3035193582802991612559221226849 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.596 y[1] (analytic) = 1.172412423895705494825932721079 y[1] (numeric) = 1.0865320693983250349686299812923 absolute error = 0.085880354497380459857302739786703 relative error = 7.3250976147127671659751044714703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.597 y[1] (analytic) = 1.1729741742185081702520097574644 y[1] (numeric) = 1.0867996002103647648772058403177 absolute error = 0.086174574008143405374803917146655 relative error = 7.3466727488315804280383927869189 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.598 y[1] (analytic) = 1.1735367515670677083533987114403 y[1] (numeric) = 1.0870676931862870228855627846377 absolute error = 0.086469058380780685467835926802624 relative error = 7.3682446046376735620820901024378 % h = 0.001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.4MB, time=6.39 NO POLE x[1] = 0.599 y[1] (analytic) = 1.1741001553788068074520056321979 y[1] (numeric) = 1.0873363491528363461009149434069 absolute error = 0.086763806225970461351090688791062 relative error = 7.3898130264685423322214592190728 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.6 y[1] (analytic) = 1.1746643850903217027590475010446 y[1] (numeric) = 1.0876055689361942810503271228095 absolute error = 0.087058816154127421708720378235113 relative error = 7.4113778589987078759151880383157 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.601 y[1] (analytic) = 1.1752294401373827297787700698751 y[1] (numeric) = 1.0878753533619785574992371274547 absolute error = 0.087354086775404172279532942420362 relative error = 7.4329389472401744676362954895998 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.602 y[1] (analytic) = 1.1757953199549348885380653377883 y[1] (numeric) = 1.0881457032552422628337947964137 absolute error = 0.087649616699692625704270541374552 relative error = 7.4544961365428808389141405780668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.603 y[1] (analytic) = 1.1763620239770984086414244362806 y[1] (numeric) = 1.0884166194404730170078433714919 absolute error = 0.087945404536625391633581064788679 relative error = 7.4760492725951450714084396371112 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.604 y[1] (analytic) = 1.1769295516371693151506608681084 y[1] (numeric) = 1.0886881027415921480553682506846 absolute error = 0.088241448895577167095292617423766 relative error = 7.4975982014241030797713730826316 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.605 y[1] (analytic) = 1.177497902367619995288838220145 y[1] (numeric) = 1.0889601539819538681692376143003 absolute error = 0.088537748385666127119600605844705 relative error = 7.5191427693961407011479748457049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.606 y[1] (analytic) = 1.1780670756000997659678356463513 y[1] (numeric) = 1.0892327739843444503470588449413 absolute error = 0.088834301615755315620776801409969 relative error = 7.5406828232173194082580472644417 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.607 y[1] (analytic) = 1.1786370707654354421389835933405 y[1] (numeric) = 1.0895059635709814056049740954165 absolute error = 0.089131107194454036534009497924031 relative error = 7.5622182099337956630948336436107 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.608 y[1] (analytic) = 1.1792078872936319059662014179512 y[1] (numeric) = 1.089779723563512660760217790723 absolute error = 0.089428163730119245205983627228262 relative error = 7.583748776932233928366612083961 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.609 y[1] (analytic) = 1.1797795246138726768210677237362 y[1] (numeric) = 1.09005405478301573678325828147 absolute error = 0.089725469830856940037809442266142 relative error = 7.6052743719402133538972497255244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.61 y[1] (analytic) = 1.1803519821545204820992534213452 y[1] (numeric) = 1.0903289580499969277203452965351 absolute error = 0.09002302410452355437890812481008 relative error = 7.62679484302662815529057846539 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.611 y[1] (analytic) = 1.1809252593431178288577466964165 y[1] (numeric) = 1.0906044341843904801872842723363 absolute error = 0.090320825158727348670462424080203 relative error = 7.6483100386020817022512237663003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.612 y[1] (analytic) = 1.1814993556063875762722982477992 y[1] (numeric) = 1.0908804840055577734352580648787 absolute error = 0.090618871600829802837040182920517 relative error = 7.6698198074192743340412396741915 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.613 y[1] (analytic) = 1.1820742703702335089145143387088 y[1] (numeric) = 1.0911571083322864999895159786839 absolute error = 0.090917162037947008924998360024928 relative error = 7.6913239985733849196375779568491 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.614 y[1] (analytic) = 1.1826500030597409108480243837716 y[1] (numeric) = 1.0914343079827898468617494738464 absolute error = 0.091215695076951063986274909925148 relative error = 7.7128224615024461802400497481977 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.615 y[1] (analytic) = 1.1832265530991771405431489758368 y[1] (numeric) = 1.0917120837747056773369733387721 absolute error = 0.091514469324471463206175637064708 relative error = 7.7343150459877137918630266586215 % h = 0.001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.4MB, time=6.60 NO POLE x[1] = 0.616 y[1] (analytic) = 1.1838039199119922066094934379379 y[1] (numeric) = 1.0919904365250957133357305416496 absolute error = 0.091813483386896493273762896288281 relative error = 7.7558016021540292858266774551855 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.617 y[1] (analytic) = 1.1843821029208193443458911678558 y[1] (numeric) = 1.092269367050444718352438398382 absolute error = 0.092112735870374625993452769473761 relative error = 7.7772819804701767650450486291244 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.618 y[1] (analytic) = 1.1849611015474755931071202253905 y[1] (numeric) = 1.0925488761666596809706931185644 absolute error = 0.092412225380815912136427106826036 relative error = 7.7987560317492334540887749919013 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.619 y[1] (analytic) = 1.1855409152129623744868157956707 y[1] (numeric) = 1.0928289646890689989563492141342 absolute error = 0.092711950523893375530466581536572 relative error = 7.8202236071489141010796524534389 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.62 y[1] (analytic) = 1.1861215433374660713160003456393 y[1] (numeric) = 1.0931096334324216639291896775474 absolute error = 0.093011909905044407386810668091935 relative error = 7.8416845581719092495527219518697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.621 y[1] (analytic) = 1.1867029853403586074766524752305 y[1] (numeric) = 1.093390883210886446614002257743 absolute error = 0.093312102129472160862650217487454 relative error = 7.8631387366662173984989037750844 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.622 y[1] (analytic) = 1.1872852406401980285297346497202 y[1] (numeric) = 1.0936727148380510826718765827505 absolute error = 0.093612525802146945857858066969678 relative error = 7.8845859948254710688775879285281 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.623 y[1] (analytic) = 1.1878683086547290831570991852689 y[1] (numeric) = 1.0939551291269214591125362975757 absolute error = 0.093913179527807624044562887693238 relative error = 7.9060261851892567949639314849856 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.624 y[1] (analytic) = 1.1884521888008838054166910457999 y[1] (numeric) = 1.0942381268899208012885198049654 absolute error = 0.094214061910963004128171240834523 relative error = 7.9274591606434290589699407598486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.625 y[1] (analytic) = 1.1890368804947820978104651960589 y[1] (numeric) = 1.0945217089388888604720226148025 absolute error = 0.094515171555893237338442581256388 relative error = 7.9488847744204181874517274839146 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.626 y[1] (analytic) = 1.189622383151732315164435442986 y[1] (numeric) = 1.0948058760850811020152137252208 absolute error = 0.094816507066651213149221717765178 relative error = 7.9703028800995322280876267240774 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.627 y[1] (analytic) = 1.1902086961862318493202708853993 y[1] (numeric) = 1.0950906291391678940948378750554 absolute error = 0.095118067047063955225433010343922 relative error = 7.991713331607252825483152993465 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.628 y[1] (analytic) = 1.1907958190119677146378552804441 y[1] (numeric) = 1.0953759689112336970419149229603 absolute error = 0.09541985010073401759594035748382 relative error = 8.0131159832175251147290526935538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.629 y[1] (analytic) = 1.1913837510418171343082238242947 y[1] (numeric) = 1.0956618962107762532573470234243 absolute error = 0.095721854831040881050876800870393 relative error = 8.034510689552041651507988671783 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.63 y[1] (analytic) = 1.1919724916878481274762910342229 y[1] (numeric) = 1.0959484118467057777142436840119 absolute error = 0.096024079841142349762047350211057 relative error = 8.0558973055805203976136692223823 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.631 y[1] (analytic) = 1.1925620403613200971727826093538 y[1] (numeric) = 1.0962355166273441490477742014361 absolute error = 0.096326523733975948125008407917671 relative error = 8.0772756866209767808135123012002 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.632 memory used=122.0MB, alloc=4.4MB, time=6.82 y[1] (analytic) = 1.1931523964726844190547833382246 y[1] (numeric) = 1.0965232113604241012333563865436 absolute error = 0.096629185112260317821426951681048 relative error = 8.0986456883399898480522190950756 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.633 y[1] (analytic) = 1.1937435594315850309543123126502 y[1] (numeric) = 1.0968114968530884158539898999555 absolute error = 0.096932062578496615100322412694666 relative error = 8.1200071667529625310589224422116 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.634 y[1] (analytic) = 1.1943355286468590232343358993665 y[1] (numeric) = 1.0971003739118891149575419309643 absolute error = 0.097235154734969908276793968402143 relative error = 8.1413599782243760434848780328486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.635 y[1] (analytic) = 1.1949283035265372299516281134903 y[1] (numeric) = 1.0973898433427866545047923623327 absolute error = 0.097538460183750575446835751157629 relative error = 8.1627039794680384287619829509183 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.636 y[1] (analytic) = 1.1955218834778448208258872309833 y[1] (numeric) = 1.0976799059511491184090449728829 absolute error = 0.097841977526695702416842258100402 relative error = 8.1840390275473272779347400993695 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.637 y[1] (analytic) = 1.1961162679072018940145166710524 y[1] (numeric) = 1.0979705625417514131681106381976 absolute error = 0.098145705365450480846406032854739 relative error = 8.2053649798754266367796415666103 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.638 y[1] (analytic) = 1.1967114562202240696924773737563 y[1] (numeric) = 1.0982618139187744630894678973824 absolute error = 0.098449642301449606603009476373891 relative error = 8.2266816942155581215863222507733 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.639 y[1] (analytic) = 1.1973074478217230844366180930148 y[1] (numeric) = 1.0985536608858044061094056606619 absolute error = 0.098753786935918678327212432352893 relative error = 8.2479890286812062630342403032583 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.64 y[1] (analytic) = 1.1979042421157073864138892207397 y[1] (numeric) = 1.0988461042458317902069522386005 absolute error = 0.099058137869875596206936982139159 relative error = 8.2692868417363380976570764530482 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.641 y[1] (analytic) = 1.1985018385053827313728449539229 y[1] (numeric) = 1.0991391448012507704133942789503 absolute error = 0.099362693704131960959450674972635 relative error = 8.2905749921956170264445133268531 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.642 y[1] (analytic) = 1.1991002363931527794378378132311 y[1] (numeric) = 1.0994327833538583064181886015422 absolute error = 0.099667453039294473019649211688859 relative error = 8.311853339224610960187561813432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.643 y[1] (analytic) = 1.1996994351806196927053087189588 y[1] (numeric) = 1.09972702070485336077206932524 absolute error = 0.099972414475766331933239393718857 relative error = 8.333121742339994771229147687318 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.644 y[1] (analytic) = 1.2002994342685847336415750281037 y[1] (numeric) = 1.1000218576548360976881520837842 absolute error = 0.10027757661374863595342294431952 relative error = 8.3543800614097470713362614886576 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.645 y[1] (analytic) = 1.2009002330570488642815181348221 y[1] (numeric) = 1.1003172950038070824418365293548 absolute error = 0.1005829380532417818396816054673 relative error = 8.3756281566533413354636114598146 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.646 y[1] (analytic) = 1.2015018309452133462275714356296 y[1] (numeric) = 1.1006133335511664813703077238828 absolute error = 0.10088849739404686485726371174672 relative error = 8.3968658886419313912314066000191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.647 y[1] (analytic) = 1.2021042273314803414484086604078 y[1] (numeric) = 1.1009099740957132624724364185438 absolute error = 0.10119425323576707897597224186393 relative error = 8.4180931182985312939916380769018 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.648 y[1] (analytic) = 1.2027074216134535138767317705792 y[1] (numeric) = 1.1012072174356443966098776214654 absolute error = 0.10150020417780911726685414911372 relative error = 8.4393097068981896074080258140962 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=125.8MB, alloc=4.4MB, time=7.04 x[1] = 0.649 y[1] (analytic) = 1.203311413187938631805556826712 y[1] (numeric) = 1.1015050643685540593101662524844 absolute error = 0.10180634881938457249539057422758 relative error = 8.4605155160681581095246565682583 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.65 y[1] (analytic) = 1.2039162014509441710823954293201 y[1] (numeric) = 1.1018035156914328331726080817909 absolute error = 0.10211268575951133790978734752916 relative error = 8.4817104077880549443472637527175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.651 y[1] (analytic) = 1.2045217857976819191007285387257 y[1] (numeric) = 1.1021025722006669108777635465022 absolute error = 0.10241921359701500822296499222347 relative error = 8.5028942443900222390090912188069 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.652 y[1] (analytic) = 1.2051281656225675795881686825627 y[1] (numeric) = 1.1024022346920372988013214356163 absolute error = 0.10272593093053028078684724694644 relative error = 8.5240668885588782066403467540402 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.653 y[1] (analytic) = 1.2057353403192213781907057628076 y[1] (numeric) = 1.1027025039607190212331588294044 absolute error = 0.1030328363585023569575469334032 relative error = 8.5452282033322637551063898066337 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.654 y[1] (analytic) = 1.2063433092804686688524308781435 y[1] (numeric) = 1.1030033808012803252023830741176 absolute error = 0.10333992847918834365004780402593 relative error = 8.5663780521007836218250155296067 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.655 y[1] (analytic) = 1.2069520718983405409901317819836 y[1] (numeric) = 1.1033048660076818859091509668973 absolute error = 0.10364720589065865508098081508626 relative error = 8.5875162986081420549174973088556 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.656 y[1] (analytic) = 1.207561627564074427462152801609 y[1] (numeric) = 1.1036069603732760127640597190064 absolute error = 0.10395466719079841469809308260268 relative error = 8.6086428069512730609914361746976 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.657 y[1] (analytic) = 1.2081719756681147133309112496125 y[1] (numeric) = 1.1039096646908058560359036579215 absolute error = 0.104262310977308857295007591691 relative error = 8.6297574415804652398959415939886 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.658 y[1] (analytic) = 1.2087831156001133454184615651814 y[1] (numeric) = 1.1042129797524046141085900204666 absolute error = 0.10457013584770873130987154471478 relative error = 8.6508600672994812268312378203201 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.659 y[1] (analytic) = 1.2093950467489304426544976297072 y[1] (numeric) = 1.1045169063495947413480065800027 absolute error = 0.10487814039933570130649104970443 relative error = 8.6719505492656717622354569845765 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.66 y[1] (analytic) = 1.2100077685026349072161829087698 y[1] (numeric) = 1.1048214452732871565796332407428 absolute error = 0.105186323229347750636549668027 relative error = 8.6930287529900844099111481998035 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.661 y[1] (analytic) = 1.2106212802485050364591972807178 y[1] (numeric) = 1.1051265973137804521776891215126 absolute error = 0.10549468293472458428150815920517 relative error = 8.7140945443375669438929049159737 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.662 y[1] (analytic) = 1.2112355813730291356393886208484 y[1] (numeric) = 1.105432363260760103766606039746 absolute error = 0.10580321811226903187278258110244 relative error = 8.7351477895268654245954943950683 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.663 y[1] (analytic) = 1.2118506712619061314244164195866 y[1] (numeric) = 1.1057387439032976805356186941731 absolute error = 0.10611192735860845088879772541347 relative error = 8.7561883551307169848189673079668 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.664 y[1] (analytic) = 1.2124665493000461861947739230711 y[1] (numeric) = 1.1060457400298500561672612315481 absolute error = 0.10642080927019613002751269152294 relative error = 8.7772161080759373462234359243935 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.665 y[1] (analytic) = 1.2130832148715713131335744951767 y[1] (numeric) = 1.1063533524282586203805592688523 absolute error = 0.10672986244331269275301522632444 relative error = 8.7982309156435030869215400371131 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.4MB, time=7.26 x[1] = 0.666 y[1] (analytic) = 1.213700667359815992104487111237 y[1] (numeric) = 1.1066615818857484910897058277151 absolute error = 0.10703908547406750101478128352189 relative error = 8.8192326454686286808710745118591 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.667 y[1] (analytic) = 1.2143189061473277863172051055833 y[1] (numeric) = 1.1069704291889277271790090223123 absolute error = 0.107348476958400059138196083271 relative error = 8.8402211655408383297838350835931 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.668 y[1] (analytic) = 1.2149379306158679597798315074841 y[1] (numeric) = 1.1072798951237865418948987257275 absolute error = 0.10765803549208141788493278175661 relative error = 8.8611963442040326082994536440266 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.669 y[1] (analytic) = 1.2155577401464120955375635131482 y[1] (numeric) = 1.1075899804756965168557788227038 absolute error = 0.10796775967071557868178469044437 relative error = 8.8821580501565499432048447188533 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.67 y[1] (analytic) = 1.2161783341191507146970578551619 y[1] (numeric) = 1.1079006860294098166805110388705 absolute error = 0.10827764808974089801654681629143 relative error = 8.9031061524512229475108750670011 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.671 y[1] (analytic) = 1.2167997119134898962358580450436 y[1] (numeric) = 1.1082120125690584042363157178919 absolute error = 0.10858769934443149199954232715171 relative error = 8.9240405204954296302280023164182 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.672 y[1] (analytic) = 1.2174218729080518975962636795423 y[1] (numeric) = 1.108523960878153256506874298576 absolute error = 0.10889791202989864108938938096632 relative error = 8.9449610240511395027119102659099 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.673 y[1] (analytic) = 1.2180448164806757760630212168607 y[1] (numeric) = 1.1088365317395835810814176237714 absolute error = 0.10920828474109219498160359308932 relative error = 8.9658675332349546024786019309363 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.674 y[1] (analytic) = 1.2186685420084180109242148451658 y[1] (numeric) = 1.1091497259356160332655835919023 absolute error = 0.1095188160728019776586312532635 relative error = 8.9867599185181454554160006093678 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.675 y[1] (analytic) = 1.219293048867553126414735282546 y[1] (numeric) = 1.109463544247893933814827040216 absolute error = 0.10982950461965919259990824232999 relative error = 9.0076380507266819973458582227181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.676 y[1] (analytic) = 1.2199183364335743154417035649992 y[1] (numeric) = 1.1097779874574364872911641262692 absolute error = 0.11014034897613782815053943872991 relative error = 9.0285018010412594759156829960643 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.677 y[1] (analytic) = 1.2205444040811940640912260970796 y[1] (numeric) = 1.1100930563446380010440328508439 absolute error = 0.11045134773655606304719324623574 relative error = 9.0493510409973193538254792371792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.678 y[1] (analytic) = 1.2211712511843447769158564585004 y[1] (numeric) = 1.1104087516892671048160507413653 absolute error = 0.11076249949507767209980571713506 relative error = 9.0701856424850652344183446380974 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.679 y[1] (analytic) = 1.221798877116179403002138679282 y[1] (numeric) = 1.1107250742704659709744500900023 absolute error = 0.11107380284571343202768858927966 relative error = 9.0910054777494738306873992401658 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.68 y[1] (analytic) = 1.2224272812490720628176059159557 y[1] (numeric) = 1.1110420248667495353689705149466 absolute error = 0.11138525638232252744863540100906 relative error = 9.1118104193903009987741290799784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.681 y[1] (analytic) = 1.2230564629546186758366076818755 y[1] (numeric) = 1.1113596042560047188169879869159 absolute error = 0.11169685869861395701961969495963 relative error = 9.1326003403620828570550206851156 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.682 y[1] (analytic) = 1.223686421603637588944338005864 y[1] (numeric) = 1.1116778132154896492166588356858 absolute error = 0.11200860838814793972767917017813 relative error = 9.1533751139741320119343441449203 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=133.5MB, alloc=4.4MB, time=7.48 x[1] = 0.683 y[1] (analytic) = 1.2243171565661702056184361152149 y[1] (numeric) = 1.111996652521832884288856623442 absolute error = 0.11232050404433732132957949177289 relative error = 9.1741346138905289114811165848303 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.684 y[1] (analytic) = 1.2249486672114816158875304615069 y[1] (numeric) = 1.112316122951032634948679142951 absolute error = 0.11263254426044898093885131855584 relative error = 9.1948787141301083480676486775243 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.685 y[1] (analytic) = 1.2255809529080612270660961307334 y[1] (numeric) = 1.1126362252784559893073021689778 absolute error = 0.11294472762960523775879396175567 relative error = 9.2156072890664411311856484966754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.686 y[1] (analytic) = 1.2262140130236233952649949029474 y[1] (numeric) = 1.1129569602788381373049559610317 absolute error = 0.11325705274478525796003894191571 relative error = 9.236320213427810951633633737414 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.687 y[1] (analytic) = 1.2268478469251080576770664509304 y[1] (numeric) = 1.1132783287262815959757998844002 absolute error = 0.11356951819882646170126656653017 relative error = 9.2570173622971864582863892808538 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.688 y[1] (analytic) = 1.2274824539786813656371383923497 y[1] (numeric) = 1.1136003313942554353454698845303 absolute error = 0.1138821225844259302916685078194 relative error = 9.2776986111121885686734064683401 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.689 y[1] (analytic) = 1.2281178335497363184558221354451 y[1] (numeric) = 1.1139229690555945049620729171461 absolute error = 0.11419486449414181349374921829894 relative error = 9.2983638356650530346086574851121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.69 y[1] (analytic) = 1.2287539850028933980264606845022 y[1] (numeric) = 1.1142462424824986610614018030442 absolute error = 0.11450774252039473696505888145807 relative error = 9.3190129121025882841286971537524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.691 y[1] (analytic) = 1.2293909077020012042045937982186 y[1] (numeric) = 1.1145701524465319943671433422862 absolute error = 0.1148207552554692098374504559324 relative error = 9.3396457169261285610099494359686 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.692 y[1] (analytic) = 1.2300286010101370909593051215486 y[1] (numeric) = 1.1148946997186220585268518875181 absolute error = 0.11513390129151503243245323403053 relative error = 9.3602621269914823831491312773473 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.693 y[1] (analytic) = 1.2306670642896078032958151397345 y[1] (numeric) = 1.1152198850690590991844599403758 absolute error = 0.11544717922054870411135519935873 relative error = 9.3808620195088763411030963534397 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.694 y[1] (analytic) = 1.2313062969019501149486830319832 y[1] (numeric) = 1.1155457092674952836900966984047 absolute error = 0.11576058763445483125858633357849 relative error = 9.4014452720428942580959500455305 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.695 y[1] (analytic) = 1.2319462982079314668449797316401 y[1] (numeric) = 1.1158721730829439314479848426092 absolute error = 0.11607412512498753539699488903092 relative error = 9.4220117625124117328120988579777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.696 y[1] (analytic) = 1.2325870675675506063367937297397 y[1] (numeric) = 1.1161992772837787449031852176704 absolute error = 0.11638779028377186143360851206929 relative error = 9.4425613691905260863039567616709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.697 y[1] (analytic) = 1.2332286043400382272024303894814 y[1] (numeric) = 1.1165270226377330411679584180258 absolute error = 0.11670158170230518603447197145562 relative error = 9.4630939707044817343523418935148 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.698 y[1] (analytic) = 1.2338709078838576104156647704838 y[1] (numeric) = 1.1168554099118989842885116533825 absolute error = 0.11701549797195862612715311710128 relative error = 9.4836094460355910066261639511443 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.699 y[1] (analytic) = 1.234513977556705265682407193618 y[1] (numeric) = 1.1171844398727268181528986268552 absolute error = 0.11732953768397844752950856676276 relative error = 9.5041076745191504339958297939395 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=137.3MB, alloc=4.4MB, time=7.69 x[1] = 0.7 y[1] (analytic) = 1.2351578127155115737441400098081 y[1] (numeric) = 1.1175141132860241000408395177637 absolute error = 0.11764369942948747370330049204445 relative error = 9.5245885358443525253618865014922 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.701 y[1] (analytic) = 1.2358024127164414294474832694162 y[1] (numeric) = 1.1178444309169549348162275192071 absolute error = 0.11795798179948649463125575020904 relative error = 9.5450519100541930553667817614012 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.702 y[1] (analytic) = 1.2364477769148948855792462226979 y[1] (numeric) = 1.1181753935300392097630877378442 absolute error = 0.11827238338485567581615848485369 relative error = 9.5654976775453738843632552784895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.703 y[1] (analytic) = 1.2370939046655077974663208163335 y[1] (numeric) = 1.1185070018891518300657536198565 absolute error = 0.11858690277635596740056719647696 relative error = 9.5859257190682013320177862422351 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.704 y[1] (analytic) = 1.2377407953221524683397725861917 y[1] (numeric) = 1.118839256757521954934025422855 absolute error = 0.11890153856463051340574716333673 relative error = 9.6063359157264801259317150892147 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.705 y[1] (analytic) = 1.2383884482379382954624835822915 y[1] (numeric) = 1.1191721588977322343740746085074 absolute error = 0.11921628934020606108840897378415 relative error = 9.6267281489774029466661371890252 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.706 y[1] (analytic) = 1.2390368627652124170197011983717 y[1] (numeric) = 1.1195057090717180466058573849191 absolute error = 0.11953115369349437041384381345263 relative error = 9.6471023006314355905594360070736 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.707 y[1] (analytic) = 1.2396860382555603597718460155734 y[1] (numeric) = 1.1198399080407667361277999812896 absolute error = 0.11984613021479362364404603428383 relative error = 9.6674582528521977717283881023387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.708 y[1] (analytic) = 1.2403359740598066874689310074817 y[1] (numeric) = 1.1201747565655168524295175900959 absolute error = 0.12016121749428983503941341738577 relative error = 9.6877958881563395846451363538876 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.709 y[1] (analytic) = 1.2409866695280156500259436921618 y[1] (numeric) = 1.1205102554059573893533282640216 absolute error = 0.12047641412205826067261542814018 relative error = 9.7081150894134136486829954321121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.71 y[1] (analytic) = 1.2416381240094918334585420558604 y[1] (numeric) = 1.1208464053214270251053224060522 absolute error = 0.12079171868806480835321964980827 relative error = 9.7284157398457429560240290989273 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.711 y[1] (analytic) = 1.2422903368527808105784143127322 y[1] (numeric) = 1.1211832070706133629167478416062 absolute error = 0.12110712978216744766166647112604 relative error = 9.7486977230282844443206267989241 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.712 y[1] (analytic) = 1.2429433074056697924476518052839 y[1] (numeric) = 1.121520661411552172356469811252 absolute error = 0.12142264599411762009118199403194 relative error = 9.7689609228884883155019115575564 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.713 y[1] (analytic) = 1.2435970350151882805914835912195 y[1] (numeric) = 1.121858769101626631295264571488 absolute error = 0.1217382659135616492962190197315 relative error = 9.7892052237061531221137368029394 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.714 y[1] (analytic) = 1.2442515190276087199687205040045 y[1] (numeric) = 1.1221975308975665685227046392291 absolute error = 0.12205398813004215144601586477539 relative error = 9.8094305101132766425782807477453 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.715 y[1] (analytic) = 1.2449067587884471526992557167609 y[1] (numeric) = 1.1225369475554477070173930630512 absolute error = 0.12236981123299944568186265370973 relative error = 9.8296366670939025667558277826464 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.716 y[1] (analytic) = 1.2455627536424638725479680820458 y[1] (numeric) = 1.122877019830690907871303450896 absolute error = 0.12268573381177296467666463114978 relative error = 9.8498235799839630131872413207973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=141.1MB, alloc=4.4MB, time=7.91 x[1] = 0.717 y[1] (analytic) = 1.2462195029336640801643737636656 y[1] (numeric) = 1.1232177484780614148689818298342 absolute error = 0.12300175445560266529539193383137 relative error = 9.8699911344711168993908860740773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.718 y[1] (analytic) = 1.2468770060052985390773709209283 y[1] (numeric) = 1.1235591342516680997223657586206 absolute error = 0.12331787175363043935500516230771 relative error = 9.8901392165945841865823542181614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.719 y[1] (analytic) = 1.2475352621998642324444214506443 y[1] (numeric) = 1.1239011779049627079619754581605 absolute error = 0.12363408429490152448244599248374 relative error = 9.9102677127449760201792936984507 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.72 y[1] (analytic) = 1.2481942708591050205545130377481 y[1] (numeric) = 1.1242438801907391054852310686332 absolute error = 0.12395039066836591506928196911483 relative error = 9.9303765096641207874469324272299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.721 y[1] (analytic) = 1.2488540313240122990842440116342 y[1] (numeric) = 1.1245872418611325257626494848915 absolute error = 0.12426678946287977332159452674267 relative error = 9.950465494444886113632543709919 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.722 y[1] (analytic) = 1.249514542934825658106372752177 y[1] (numeric) = 1.124931263667618817702673563879 absolute error = 0.12458327926720684040369918829794 relative error = 9.9705345545309968179291103014921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.723 y[1] (analytic) = 1.2501758050310335418501726369398 y[1] (numeric) = 1.1252759463610136941758858391726 absolute error = 0.12489985867001984767428679776716 relative error = 9.9905835777168488505998214200643 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.724 y[1] (analytic) = 1.2508378169513739092129327692739 y[1] (numeric) = 1.1256212906914719811993582183739 absolute error = 0.12521652625990192801357455090003 relative error = 10.010612452147319232585783220566 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.725 y[1] (analytic) = 1.2515005780338348950219439758613 y[1] (numeric) = 1.1259672974084868677818884789374 absolute error = 0.12553328062534802724005549692389 relative error = 10.030621066317572018909443044557 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.726 y[1] (analytic) = 1.2521640876156554720463088117698 y[1] (numeric) = 1.1263139672608891564308737171364 absolute error = 0.12585012035476631561543509463344 relative error = 10.050609309072860307175725599511 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.727 y[1] (analytic) = 1.2528283450333261137579135612673 y[1] (numeric) = 1.1266613009968465143215702432306 absolute error = 0.12616704403647959943634331803668 relative error = 10.07057706960832431246175946877 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.728 y[1] (analytic) = 1.2534933496225894578408994734763 y[1] (numeric) = 1.1270092993638627251294887535136 absolute error = 0.12648405025872673271141071996274 relative error = 10.090524237468785529874339397387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.729 y[1] (analytic) = 1.2541591007184409704489697234547 y[1] (numeric) = 1.1273579631087769415266729467816 absolute error = 0.12680113760966402892229677667309 relative error = 10.11045070254853700604192802387 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.73 y[1] (analytic) = 1.2548255976551296112098678414497 y[1] (numeric) = 1.1277072929777629383426090888842 absolute error = 0.12711830467736667286725875256543 relative error = 10.130356355091129740795054516685 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.731 y[1] (analytic) = 1.2554928397661584989763626059028 y[1] (numeric) = 1.1280572897163283663905133643838 absolute error = 0.12743555004983013258584924151907 relative error = 10.150241085689155240275421309004 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.732 y[1] (analytic) = 1.2561608263842855783230736492765 y[1] (numeric) = 1.1284079540693140069597431889745 absolute error = 0.12775287231497157136333046030195 relative error = 10.170104785284024242699888185669 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.733 y[1] (analytic) = 1.2568295568415242867884712799312 y[1] (numeric) = 1.1287592867808930269750779901885 absolute error = 0.12807027006063125981339328974262 relative error = 10.189947345165741637990769740474 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.4MB, time=8.13 x[1] = 0.734 y[1] (analytic) = 1.2574990304691442228613832781104 y[1] (numeric) = 1.1291112885945702348236142970445 absolute error = 0.12838774187457398803776898106582 relative error = 10.209768656972677602468562065629 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.735 y[1] (analytic) = 1.2581692465976718147113406795812 y[1] (numeric) = 1.1294639602531813368500193116835 absolute error = 0.12870528634449047786132136789766 relative error = 10.229568612691334969787311831589 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.736 y[1] (analytic) = 1.2588402045568909896620938166407 y[1] (numeric) = 1.1298173024988921945208864676749 absolute error = 0.12902290205799879514120734896585 relative error = 10.249347104656112859276360035042 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.737 y[1] (analytic) = 1.2595119036758438444076291430284 y[1] (numeric) = 1.1301713160731980822589358105762 absolute error = 0.12934058760264576214869333245227 relative error = 10.269104025549066582835138003191 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.738 y[1] (analytic) = 1.2601843432828313159700166267826 y[1] (numeric) = 1.1305260017169229459478013664837 absolute error = 0.12965834156590837002221526029891 relative error = 10.288839268399663851510069107857 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.739 y[1] (analytic) = 1.2608575227054138533984167532507 y[1] (numeric) = 1.1308813601702186621081469937255 absolute error = 0.12997616253519519129026975952523 relative error = 10.308552726584537302864440424418 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.74 y[1] (analytic) = 1.2615314412704120902085754393012 y[1] (numeric) = 1.1312373921725642977458515415181 absolute error = 0.13029404909784779246272389778306 relative error = 10.328244293827233370233358625382 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.741 y[1] (analytic) = 1.2622060983039075175621344192991 y[1] (numeric) = 1.1315940984627653708730034673417 absolute error = 0.1306119998411421466891309519574 relative error = 10.347913864197957514936598079956 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.742 y[1] (analytic) = 1.2628814931312431581850839235906 y[1] (numeric) = 1.1319514797789531117024443919758 absolute error = 0.1309300133522900464826395316148 relative error = 10.367561332113315842502290788614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.743 y[1] (analytic) = 1.2635576250770242410246837310994 y[1] (numeric) = 1.1323095368585837245166003975913 absolute error = 0.13124808821844051650808333350808 relative error = 10.387186592336053123934001760527 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.744 y[1] (analytic) = 1.2642344934651188766441779391716 y[1] (numeric) = 1.1326682704384376502113392000064 absolute error = 0.13156622302668122643283873916522 relative error = 10.40678953997478724303278408213 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.745 y[1] (analytic) = 1.2649120976186587333546280560096 y[1] (numeric) = 1.1330276812546188295155906511868 absolute error = 0.1318844163640399038390374048228 relative error = 10.426370070483740090764319563065 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.746 y[1] (analytic) = 1.2655904368600397140831882839174 y[1] (numeric) = 1.1333877700425539668874673523086 absolute error = 0.13220266681748574719572093160881 relative error = 10.445928079662464927639227811854 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.747 y[1] (analytic) = 1.2662695105109226339771461251409 y[1] (numeric) = 1.1337485375369917950876214812027 absolute error = 0.13252097297393083888952464393824 relative error = 10.465463463655570235052073213782 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.748 y[1] (analytic) = 1.2669493178922338987430507063167 y[1] (numeric) = 1.1341099844720023404305732607616 absolute error = 0.13283933342023155831247744555517 relative error = 10.484976118952440076501519877726 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.749 y[1] (analytic) = 1.2676298583241661837202504824584 y[1] (numeric) = 1.134472111580976188714745816919 absolute error = 0.13315774674318999500550466553945 relative error = 10.504465942386950989590483501904 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.75 y[1] (analytic) = 1.2683111311261791136881612469999 y[1] (numeric) = 1.1348349195966237518319404961072 absolute error = 0.13347621152955536185622075089274 relative error = 10.523932831137185429681010589524 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=148.7MB, alloc=4.4MB, time=8.34 x[1] = 0.751 y[1] (analytic) = 1.2689931356169999434065846406836 y[1] (numeric) = 1.1351984092509745350569860326545 absolute error = 0.13379472636602540834959860802904 relative error = 10.54337668272514178605398382719 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.752 y[1] (analytic) = 1.2696758711146242388883966190315 y[1] (numeric) = 1.1355625812753764050182942764133 absolute error = 0.13411328983924783387010234261821 relative error = 10.56279739501644099139861201825 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.753 y[1] (analytic) = 1.270359336936316559403924605769 y[1] (numeric) = 1.1359274364004948583500545100017 absolute error = 0.13443190053582170105387009576736 relative error = 10.582194866220029745431018030561 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.754 y[1] (analytic) = 1.2710435323986111402163313278786 y[1] (numeric) = 1.1362929753563122910267977034034 absolute error = 0.13475055704229884918953362447523 relative error = 10.601568994887880373415093057121 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.755 y[1] (analytic) = 1.2717284568173125760473225969591 y[1] (numeric) = 1.1366591988721272683810613713015 absolute error = 0.13506925794518530766626122565761 relative error = 10.620919679914687340332144375679 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.756 y[1] (analytic) = 1.2724141095074965052724955712377 y[1] (numeric) = 1.137026107676553795804885015419 absolute error = 0.13538800183094270946761055581874 relative error = 10.640246820537560441418730999905 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.757 y[1] (analytic) = 1.2731004897835102948456433029448 y[1] (numeric) = 1.1373937024975205901358654503111 absolute error = 0.1357067872859897047097778526337 relative error = 10.659550316335714689764461402764 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.758 y[1] (analytic) = 1.2737875969589737259513306468032 y[1] (numeric) = 1.137761984062270351728500626493 absolute error = 0.13602561289670337422283002031024 relative error = 10.678830067230156921633424118059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.759 y[1] (analytic) = 1.274475430346779680385055877114 y[1] (numeric) = 1.1381309530973590372115498794981 absolute error = 0.13634447724942064317350599761589 relative error = 10.698085973483369140144339736614 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.76 y[1] (analytic) = 1.275163989259094827660311633333 y[1] (numeric) = 1.1385006103286551329321378474463 absolute error = 0.13666337893043969472817378588671 relative error = 10.717317935698988617915465849598 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.761 y[1] (analytic) = 1.2758532730073603128418580871366 y[1] (numeric) = 1.1388709564813389290873286129581 absolute error = 0.13698231652602138375452947417846 relative error = 10.736525854821484779250759085473 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.762 y[1] (analytic) = 1.2765432809022924451045204977583 y[1] (numeric) = 1.1392419922799017945438959377793 absolute error = 0.13730128862239065056062455997904 relative error = 10.755709632135832882413804763302 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.763 y[1] (analytic) = 1.2772340122538833870168225968583 y[1] (numeric) = 1.1396137184481454523470147702857 absolute error = 0.13762029380573793466980782657261 relative error = 10.774869169267184522505569059727 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.764 y[1] (analytic) = 1.277925466371401844548766519348 y[1] (numeric) = 1.1399861357091812559185985171166 absolute error = 0.13793933066222058863016800223132 relative error = 10.794004368180534975431115167555 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.765 y[1] (analytic) = 1.2786176425633937578030692724491 y[1] (numeric) = 1.1403592447854294659460058805392 absolute error = 0.13825839777796429185706339190995 relative error = 10.813115131180387403409057909563 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.766 y[1] (analytic) = 1.2793105401376829924691650118068 y[1] (numeric) = 1.1407330463986185279618403727754 absolute error = 0.13857749373906446450732463903142 relative error = 10.83220136091041394244571485216 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.767 y[1] (analytic) = 1.2800041584013720319992816707128 y[1] (numeric) = 1.1411075412697843506155649274343 absolute error = 0.13889661713158768138371674327848 relative error = 10.851262960353113692163650321271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=152.5MB, alloc=4.4MB, time=8.55 x[1] = 0.768 y[1] (analytic) = 1.2806984966608426705058997664195 y[1] (numeric) = 1.1414827301192695846376533363724 absolute error = 0.13921576654157308586824643004715 relative error = 10.870299832829467628341606029484 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.769 y[1] (analytic) = 1.2813935542217567063799004861449 y[1] (numeric) = 1.1418586136667229024969995477723 absolute error = 0.13953494055503380388290093837259 relative error = 10.889311881998590458489672442029 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.77 y[1] (analytic) = 1.2820893303890566366287094346757 y[1] (numeric) = 1.1422351926310982787523051679694 absolute error = 0.13985413775795835787640426670624 relative error = 10.908299011857379440749982693181 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.771 y[1] (analytic) = 1.2827858244669663519337417054856 y[1] (numeric) = 1.1426124677306542710981648155796 absolute error = 0.14017335673631208083557688990597 relative error = 10.927261126740160186379209957997 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.772 y[1] (analytic) = 1.2834830357589918324264532179796 y[1] (numeric) = 1.1429904396829533021065682817824 absolute error = 0.14049259607603853031988493619728 relative error = 10.946198131318329466034723821168 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.773 y[1] (analytic) = 1.2841809635679218441823025448716 y[1] (numeric) = 1.1433691092048609416645377551974 absolute error = 0.14081185436306090251776478967426 relative error = 10.965109930599995040051415489441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.774 y[1] (analytic) = 1.2848796071958286364319267357915 y[1] (numeric) = 1.1437484770125451901086176736581 absolute error = 0.14113113018328344632330906213341 relative error = 10.983996429929612532860939780716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.775 y[1] (analytic) = 1.2855789659440686394888339260045 y[1] (numeric) = 1.1441285438214757620569340683321 absolute error = 0.14145042212259287743189985767244 relative error = 11.002857534987619371669447795519 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.776 y[1] (analytic) = 1.2862790391132831633929148026071 y[1] (numeric) = 1.1445093103464233709395395680688 absolute error = 0.14176972876685979245337523453835 relative error = 11.021693151790065809473802128737 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.777 y[1] (analytic) = 1.2869798260033990972690742847478 y[1] (numeric) = 1.1448907773014590142277595335715 absolute error = 0.14208904870194008304131475117639 relative error = 11.040503186688243052459780494282 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.778 y[1] (analytic) = 1.2876813259136296094002840592981 y[1] (numeric) = 1.1452729453999532593632540919861 absolute error = 0.14240838051367635003702996731203 relative error = 11.059287546368308511788887785245 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.779 y[1] (analytic) = 1.28838353814247484801435589898 y[1] (numeric) = 1.1456558153545755303875101427866 absolute error = 0.14272772278789931762684575619343 relative error = 11.078046137850908199743114938552 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.78 y[1] (analytic) = 1.2890864619877226427837349762354 y[1] (numeric) = 1.1460393878772933952724767054046 absolute error = 0.14304707411042924751125827083083 relative error = 11.096778868490796290159309566976 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.781 y[1] (analytic) = 1.289790096746449207037611673102 y[1] (numeric) = 1.1464236636793718539530562779092 absolute error = 0.1433664330670773530845553951928 relative error = 11.115485645976451863046762201955 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.782 y[1] (analytic) = 1.2904944417150198406856496750424 y[1] (numeric) = 1.1468086434713726270621641741857 absolute error = 0.14368579824364721362348550085673 relative error = 11.134166378329692853243167186436 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.783 y[1] (analytic) = 1.2911994961890896338526274250576 y[1] (numeric) = 1.147194327963153445369067104495 absolute error = 0.14400516822593618848356032056267 relative error = 11.152820973905287222925292784822 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.784 y[1] (analytic) = 1.2919052594636041712232893035015 y[1] (numeric) = 1.147580717863867339921711561016 absolute error = 0.14432454159973683130157774248546 relative error = 11.171449341390561377751494942438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=156.4MB, alloc=4.4MB, time=8.77 x[1] = 0.785 y[1] (analytic) = 1.2926117308328002370967021888034 y[1] (numeric) = 1.1479678138819619328937518659831 absolute error = 0.14464391695083830420295032282026 relative error = 11.190051389805005846373637323532 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.786 y[1] (analytic) = 1.2933189095902065211494123448021 y[1] (numeric) = 1.1483556167251787291369870353313 absolute error = 0.14496329286502779201242530947075 relative error = 11.208627028499878243016040766787 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.787 y[1] (analytic) = 1.2940267950286443249066968715924 y[1] (numeric) = 1.1487441271005524084399149053545 absolute error = 0.14528266792809191646678196623785 relative error = 11.227176167157803532778782090587 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.788 y[1] (analytic) = 1.2947353864402282689212032486917 y[1] (numeric) = 1.149133345714410118493111263762 absolute error = 0.14560204072581815042809198492962 relative error = 11.245698715792371619281999215087 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.789 y[1] (analytic) = 1.2954446831163670006582697919461 y[1] (numeric) = 1.1495232732723707685621410196967 absolute error = 0.14592140984399623209612877224946 relative error = 11.264194584747732274226840790274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.79 y[1] (analytic) = 1.296154684347763903087219138915 y[1] (numeric) = 1.1499139104793443238687077397435 absolute error = 0.14624077386841957921851139917155 relative error = 11.282663684698187428407327862404 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.791 y[1] (analytic) = 1.2968653894244178039779161714986 y[1] (numeric) = 1.1503052580395311006807471687215 absolute error = 0.14656013138488670329716900277716 relative error = 11.301105926647780843665676496618 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.792 y[1] (analytic) = 1.2975767976356236859018810793109 y[1] (numeric) = 1.1506973166564210621121696451055 absolute error = 0.14687948097920262378971143420543 relative error = 11.319521221929885185241567609933 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.793 y[1] (analytic) = 1.2982889082699733969372475627432 y[1] (numeric) = 1.1510900870327931146329556112775 absolute error = 0.14719882123718028230429195146569 relative error = 11.337909482206786513923447452235 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.794 y[1] (analytic) = 1.2990017206153563620768554708199 y[1] (numeric) = 1.1514835698707144052903077084532 absolute error = 0.14751815074464195678654776236662 relative error = 11.356270619469266217367203086626 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.795 y[1] (analytic) = 1.2997152339589602953387664658126 y[1] (numeric) = 1.1518777658715396196415622350731 absolute error = 0.14783746808742067569720423073948 relative error = 11.374604546036180399904485735074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.796 y[1] (analytic) = 1.3004294475872719125784906041565 y[1] (numeric) = 1.1522726757359102803995620356875 absolute error = 0.14815677185136163217892856846903 relative error = 11.392911174554036750119554828008 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.797 y[1] (analytic) = 1.3011443607860776450022110215024 y[1] (numeric) = 1.1526683001637540467911921749061 absolute error = 0.14847606062232359821101884659632 relative error = 11.411190417996568905429790871929 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.798 y[1] (analytic) = 1.3018599728404643533802932087375 y[1] (numeric) = 1.1530646398542840146297790378152 absolute error = 0.14879533298618033875051417092227 relative error = 11.429442189664308332860979658164 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.799 y[1] (analytic) = 1.3025762830348200429603646655274 y[1] (numeric) = 1.1534616955059980171020527844079 absolute error = 0.14911458752882202585831188111952 relative error = 11.447666403184153745164107696599 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.8 y[1] (analytic) = 1.3032932906528345790792500183577 y[1] (numeric) = 1.1538594678166779262703723710043 absolute error = 0.14943382283615665280887764735338 relative error = 11.465862972508938071375732874921 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.801 y[1] (analytic) = 1.3040109949775004034730459911998 y[1] (numeric) = 1.1542579574833889552909116363803 absolute error = 0.14975303749411144818213435481951 relative error = 11.484031811916993000879009007501 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=160.2MB, alloc=4.4MB, time=8.98 x[1] = 0.802 y[1] (analytic) = 1.3047293952911132512846199187868 y[1] (numeric) = 1.1546571652024789613485042343594 absolute error = 0.15007223008863428993611568442738 relative error = 11.502172836011711119977151925877 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.803 y[1] (analytic) = 1.3054484908752728687678147950589 y[1] (numeric) = 1.1550570916695777493088444779652 absolute error = 0.15039139920569511945897031709364 relative error = 11.520285959721105659945541838322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.804 y[1] (analytic) = 1.3061682810108837316876431526351 y[1] (numeric) = 1.1554577375795963760887404428759 absolute error = 0.15071054343128735559890270975917 relative error = 11.538371098297367875482765599056 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.805 y[1] (analytic) = 1.3068887649781557644157513731752 y[1] (numeric) = 1.1558591036267264557451149598684 absolute error = 0.15102966135142930867063641330677 relative error = 11.556428167316422072434717013993 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.806 y[1] (analytic) = 1.3076099420566050597204353332294 y[1] (numeric) = 1.1562611905044394652834494071953 absolute error = 0.15134875155216559443698592603412 relative error = 11.574457082677478303619397091396 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.807 y[1] (analytic) = 1.3083318115250545992504875956188 y[1] (numeric) = 1.156663998905486051186364494391 absolute error = 0.15166781261956854806412310122776 relative error = 11.592457760602582751533292930106 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.808 y[1] (analytic) = 1.3090543726616349747121556625597 y[1] (numeric) = 1.1570675295218953366630315088699 absolute error = 0.15198684313973963804912415368985 relative error = 11.610430117636165816673167418582 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.809 y[1] (analytic) = 1.3097776247437851097384901136345 y[1] (numeric) = 1.1574717830449742296201067758463 absolute error = 0.15230584169881088011838333778821 relative error = 11.628374070644587930159765774188 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.81 y[1] (analytic) = 1.3105015670482529824503607593199 y[1] (numeric) = 1.1578767601653067313548813605859 absolute error = 0.152624806882946251095479398734 relative error = 11.646289536815683109302342848667 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.811 y[1] (analytic) = 1.311226198851096348708418249117 y[1] (numeric) = 1.1582824615727532459713373197788 absolute error = 0.15294373727834310273708092933825 relative error = 11.664176433658300274695040713045 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.812 y[1] (analytic) = 1.3119515194276834660552778823829 y[1] (numeric) = 1.1586888879564498905198010859229 absolute error = 0.15326263147123357553547679645993 relative error = 11.682034679001842347388002949138 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.813 y[1] (analytic) = 1.3126775280526938183472016797382 y[1] (numeric) = 1.1590960400048078058608838450056 absolute error = 0.15358148804788601248631783473261 relative error = 11.699864190995803144627703936569 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.814 y[1] (analytic) = 1.3134042240001188410745540834315 y[1] (numeric) = 1.1595039184055124682543980434852 absolute error = 0.15390030559460637282015603994623 relative error = 11.717664888109302092612301840262 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.815 y[1] (analytic) = 1.3141316065432626473703059662622 y[1] (numeric) = 1.1599125238455230016739384355999 absolute error = 0.15421908269773964569636753066224 relative error = 11.735436689130616774658896565496 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.816 y[1] (analytic) = 1.314859674954742754705860940622 y[1] (numeric) = 1.1603218570110714908478153563648 absolute error = 0.15453781794367126385804558425722 relative error = 11.753179513166713333130392232607 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.817 y[1] (analytic) = 1.315588428506490812273477271886 y[1] (numeric) = 1.1607319185876622950270271792665 absolute error = 0.15485650991882851724645009261953 relative error = 11.770893279642774743420231293223 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.818 y[1] (analytic) = 1.316317866469753329054558013794 y[1] (numeric) = 1.1611427092600713624809581906264 absolute error = 0.15517515720968196657359982316757 relative error = 11.788577908301726978243587811445 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=164.0MB, alloc=4.4MB, time=9.20 x[1] = 0.819 y[1] (analytic) = 1.3170479881150924025730812975917 y[1] (numeric) = 1.1615542297123455457214873848768 absolute error = 0.15549375840274685685159391271495 relative error = 11.806233319203763080433684198368 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.82 y[1] (analytic) = 1.3177787927123864483334420215631 y[1] (numeric) = 1.161966480627801917456192956584 absolute error = 0.15581231208458453087724906497905 relative error = 11.823859432725865162391732333492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.821 y[1] (analytic) = 1.3185102795308309299419755031717 y[1] (numeric) = 1.1623794626890270872713365359582 absolute error = 0.15613081684180384267063896721349 relative error = 11.841456169561324350288600033285 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.822 y[1] (analytic) = 1.3192424478389390899114329723498 y[1] (numeric) = 1.162793176577876519045310484807 absolute error = 0.15644927126106257086612248754284 relative error = 11.859023450719258691065670721547 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.823 y[1] (analytic) = 1.3199752969045426811476781015192 y[1] (numeric) = 1.1632076229754738490932308394299 absolute error = 0.15676767392906883205444726208926 relative error = 11.876561197524129040231501388991 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.824 y[1] (analytic) = 1.3207088259947926991178730857087 y[1] (numeric) = 1.1636228025622102050433577558035 absolute error = 0.15708602343258249407451532990514 relative error = 11.894069331615252948399794956059 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.825 y[1] (analytic) = 1.3214430343761601146994221046441 y[1] (numeric) = 1.1640387160177435254460245805801 absolute error = 0.15740431835841658925339752406402 relative error = 11.911547774946316564462891413079 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.826 y[1] (analytic) = 1.3221779213144366077089393179268 y[1] (numeric) = 1.1644553640209978801157559389138 absolute error = 0.15772255729343872759318337901299 relative error = 11.928996449784884573243451029871 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.827 y[1] (analytic) = 1.3229134860747353011105078643946 y[1] (numeric) = 1.16487274725016279120725449694 absolute error = 0.15804073882457250990325336745462 relative error = 11.94641527871190818541525591139 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.828 y[1] (analytic) = 1.3236497279214914959024956574681 y[1] (numeric) = 1.1652908663826925550259353228643 absolute error = 0.15835886153879894087656033460378 relative error = 11.963804184621231197432096619997 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.829 y[1] (analytic) = 1.3243866461184634066821930897261 y[1] (numeric) = 1.1657097220953055645736860360703 absolute error = 0.15867692402315784210850705365583 relative error = 11.981163090719094139151541865709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.83 y[1] (analytic) = 1.3251242399287328978875370821355 y[1] (numeric) = 1.1661293150639836328305301984294 absolute error = 0.15899492486474926505700688370617 relative error = 11.998491920523636526788014744744 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.831 y[1] (analytic) = 1.3258625086147062207151852362717 y[1] (numeric) = 1.1665496459639713167728706660932 absolute error = 0.15931286265073490394231457017849 relative error = 12.01579059786439723877702202957 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.832 y[1] (analytic) = 1.3266014514381147507142031715169 y[1] (numeric) = 1.1669707154697752421289888834685 absolute error = 0.15963073596833950858521428804842 relative error = 12.033059046881813032079606910073 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.833 y[1] (analytic) = 1.3273410676600157260546274536119 y[1] (numeric) = 1.1673925242551634288724753638195 absolute error = 0.15994854340485229718215208979245 relative error = 12.050297192026715216403123669365 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.834 y[1] (analytic) = 1.3280813565407929864701658460576 y[1] (numeric) = 1.1678150729931646174542658630102 absolute error = 0.16026628354762836901589998304734 relative error = 12.067504958059824503761268346801 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.835 y[1] (analytic) = 1.3288223173401577128742959417292 y[1] (numeric) = 1.1682383623560675957739570142956 absolute error = 0.16058395498409011710033892743361 relative error = 12.084682270051244050742945776786 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=167.8MB, alloc=4.4MB, time=9.41 x[1] = 0.836 y[1] (analytic) = 1.3295639493171491676490225586661 y[1] (numeric) = 1.1686623930154205268910744527882 absolute error = 0.16090155630172864075794810587791 relative error = 12.101829053379950710806013760677 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.837 y[1] (analytic) = 1.3303062517301354356055536113409 y[1] (numeric) = 1.1690871656420302774769657182781 absolute error = 0.16121908608810515812858789306278 relative error = 12.118945233733284513858222779894 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.838 y[1] (analytic) = 1.3310492238368141656161534967937 y[1] (numeric) = 1.1695126809059617470079894844554 absolute error = 0.16153654293085241860816401233827 relative error = 12.136030737106436390333767824799 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.839 y[1] (analytic) = 1.3317928648942133129164323638407 y[1] (numeric) = 1.1699389394765371977006719212914 absolute error = 0.16185392541767611521576044254935 relative error = 12.153085489801934156919790812975 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.84 y[1] (analytic) = 1.3325371741586918820773289631291 y[1] (numeric) = 1.1703659420223355851895002553656 absolute error = 0.16217123213635629688782870776356 relative error = 12.170109418429126781032920903234 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.841 y[1] (analytic) = 1.3332821508859406706460441061175 y[1] (numeric) = 1.17079368921119188994802285029 absolute error = 0.16248846167474878069802125582747 relative error = 12.187102449903666941091518962502 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.842 y[1] (analytic) = 1.3340277943309830134551810921098 y[1] (numeric) = 1.1712221817101964494539243860735 absolute error = 0.16280561262078656400125670603631 relative error = 12.204064511446991899574704679971 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.843 y[1] (analytic) = 1.334774103748175527599348794266 y[1] (numeric) = 1.171651420185694291098743972297 absolute error = 0.16312268356248123650060482196897 relative error = 12.22099553058580270580449349846 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.844 y[1] (analytic) = 1.3355210783912088580784824280462 y[1] (numeric) = 1.1720814053032844658429032853248 absolute error = 0.16343967308792439223557914272136 relative error = 12.237895435151541745332458782114 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.845 y[1] (analytic) = 1.3362687175131084241071363588314 y[1] (numeric) = 1.1725121377278193826167110744685 absolute error = 0.16375657978528904149042528436295 relative error = 12.254764153279868652757265581659 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.846 y[1] (analytic) = 1.3370170203662351660890026394896 y[1] (numeric) = 1.1729436181234041434680096360437 absolute error = 0.16407340224283102262099300344593 relative error = 12.271601613410134604744199095673 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.847 y[1] (analytic) = 1.3377659862022862932559083034306 y[1] (numeric) = 1.1733758471533958794571281076181 absolute error = 0.16439013904889041379878019581254 relative error = 12.288407744284855009962436544969 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.848 y[1] (analytic) = 1.3385156142722960319705437742155 y[1] (numeric) = 1.1738088254804030872998066874412 absolute error = 0.16470678879189294467073708677434 relative error = 12.30518247494918061260028874663 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.849 y[1] (analytic) = 1.3392659038266363746921740890535 y[1] (numeric) = 1.1742425537662849667587551360768 absolute error = 0.16502335006035140793341895297665 relative error = 12.321925734750367026062970247392 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.85 y[1] (analytic) = 1.3400168541150178296045839705385 y[1] (numeric) = 1.1746770326721507587845081686252 absolute error = 0.16533982144286707082007580191329 relative error = 12.338637453337242713401647489288 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.851 y[1] (analytic) = 1.3407684643864901709055071187423 y[1] (numeric) = 1.1751122628583590844062395966229 absolute error = 0.1656562015281310864992675221194 relative error = 12.355317560659675430966566153499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.852 y[1] (analytic) = 1.3415207338894431897567894342973 y[1] (numeric) = 1.1755482449845172843731963287523 absolute error = 0.16597248890492590538359310554495 relative error = 12.371965986968037151720974564151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=171.6MB, alloc=4.4MB, time=9.63 x[1] = 0.853 y[1] (analytic) = 1.3422736618716074458945352223685 y[1] (numeric) = 1.1759849797094807595474125888713 absolute error = 0.16628868216212668634712263349713 relative error = 12.388582662812667484596342818888 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.854 y[1] (analytic) = 1.3430272475800550198984847674315 y[1] (numeric) = 1.1764224676913523120483639585941 absolute error = 0.16660477988870270785012080883749 relative error = 12.405167519043335606213030117003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.855 y[1] (analytic) = 1.3437814902612002661198710095412 y[1] (numeric) = 1.1768607095874814871502200997135 absolute error = 0.16692078067371877896965090982769 relative error = 12.421720486808700721234078531827 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.856 y[1] (analytic) = 1.3445363891608005662670023942965 y[1] (numeric) = 1.177299706054463915932354259159 absolute error = 0.16723668310633665033464813513751 relative error = 12.438241497555771067563213158104 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.857 y[1] (analytic) = 1.3452919435239570836478183109831 y[1] (numeric) = 1.1777394577481406586837669059236 absolute error = 0.16755248577581642496405140505953 relative error = 12.454730483029361482541409076841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.858 y[1] (analytic) = 1.3460481525951155180686628763995 y[1] (numeric) = 1.1781799653235975490620800954835 absolute error = 0.16786818727151796900658278091598 relative error = 12.471187375271549546239547822225 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.859 y[1] (analytic) = 1.3468050156180668613885221656564 y[1] (numeric) = 1.1786212294351645390077584026603 absolute error = 0.16818378618290232238076376299616 relative error = 12.487612106621130317887732893707 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.86 y[1] (analytic) = 1.3475625318359481537279693357761 y[1] (numeric) = 1.1790632507364150444142115086506 absolute error = 0.1684992810995331093137578271255 relative error = 12.504004609713069681424768200332 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.861 y[1] (analytic) = 1.3483207004912432403320614332074 y[1] (numeric) = 1.1795060298801652915544327720661 absolute error = 0.16881467061107794877762866114134 relative error = 12.520364817477956316094128006242 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.862 y[1] (analytic) = 1.3490795208257835290864310224247 y[1] (numeric) = 1.1799495675184736642648273572899 absolute error = 0.16912995330730986482160366513475 relative error = 12.536692663141452307955464801458 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.863 y[1] (analytic) = 1.3498389920807487486858151195816 y[1] (numeric) = 1.1803938643026400518868827362692 absolute error = 0.16944512777810869679893238331241 relative error = 12.552988080223742418123315369274 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.864 y[1] (analytic) = 1.3505991134966677074542632627533 y[1] (numeric) = 1.1808389208832051979673336220157 absolute error = 0.16976019261346250948692964073755 relative error = 12.569251002538982023487177962672 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.865 y[1] (analytic) = 1.3513598843134190528162658986232 y[1] (numeric) = 1.1812847379099500497174726335987 absolute error = 0.17007514640346900309879326502447 relative error = 12.585481364194743745609547722053 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.866 y[1] (analytic) = 1.3521213037702320314180436145485 y[1] (numeric) = 1.1817313160318951082322572332622 absolute error = 0.17038998773833692318578638128631 relative error = 12.601679099591462783440816033432 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.867 y[1] (analytic) = 1.3528833711056872498982370947791 y[1] (numeric) = 1.1821786558972997794698627165078 absolute error = 0.17070471520838747042837437827129 relative error = 12.617844143421880965432165191218 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.868 y[1] (analytic) = 1.3536460855577174363072370302028 y[1] (numeric) = 1.1826267581536617259923302755348 absolute error = 0.17101932740405571031490675466799 relative error = 12.633976430670489536569725227246 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.869 y[1] (analytic) = 1.3544094463636082021743925623505 y[1] (numeric) = 1.1830756234477162194679583953353 absolute error = 0.17133382291589198270643416701518 relative error = 12.650075896612970695795307815214 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=175.4MB, alloc=4.4MB, time=9.85 x[1] = 0.87 y[1] (analytic) = 1.3551734527599988052223361945172 y[1] (numeric) = 1.1835252524254354939360850800004 absolute error = 0.17164820033456331128625111451678 relative error = 12.66614247681563789922099545782 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.871 y[1] (analytic) = 1.3559381039828829127276624557363 y[1] (numeric) = 1.1839756457320280998349076443997 absolute error = 0.17196245825085481289275481133654 relative error = 12.682176107134874944486745396271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.872 y[1] (analytic) = 1.3567033992676093655271969569926 y[1] (numeric) = 1.1844268040119382587929860433614 absolute error = 0.17227659525567110673421091363117 relative error = 12.698176723716573851551969515358 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.873 y[1] (analytic) = 1.3574693378488829426690918334692 y[1] (numeric) = 1.1848787279088452191850749467957 absolute error = 0.17259060994003772348401688667354 relative error = 12.714144262995571555153776601824 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.874 y[1] (analytic) = 1.3582359189607651267079829217956 y[1] (numeric) = 1.1853314180656626124529290048756 absolute error = 0.17290450089510251425505391691999 relative error = 12.73007866169508542410621428238 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.875 y[1] (analytic) = 1.359003141836674869643443377204 y[1] (numeric) = 1.1857848751245378101917249824166 absolute error = 0.17321826671213705945171839478734 relative error = 12.745979856826147622556427436548 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.876 y[1] (analytic) = 1.3597710057093893595009677922045 y[1] (numeric) = 1.1862390997268512820027436759791 absolute error = 0.17353190598253807749822411622541 relative error = 12.761847785687038328255160447848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.877 y[1] (analytic) = 1.3605395098110447875547202358586 y[1] (numeric) = 1.1866940925132159541129537609581 absolute error = 0.17384541729782883344176647490041 relative error = 12.777682385862717822840474907049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.878 y[1] (analytic) = 1.3613086533731371161912789909657 y[1] (numeric) = 1.1871498541234765687621389490235 absolute error = 0.17415879924966054742914004194214 relative error = 12.793483595224257469074934878807 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.879 y[1] (analytic) = 1.3620784356265228474136101254846 y[1] (numeric) = 1.1876063851967090443582090687296 absolute error = 0.17447205042981380305540105675503 relative error = 12.809251351928269589917831136655 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.88 y[1] (analytic) = 1.3628488558014197919845013942779 y[1] (numeric) = 1.1880636863712198364013349139301 absolute error = 0.17478516943019995558316648034781 relative error = 12.824985594416336264255276392773 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.881 y[1] (analytic) = 1.3636199131274078392086873278103 y[1] (numeric) = 1.1885217582845452991775459358103 absolute error = 0.17509815484286254003114139200003 relative error = 12.840686261414437054052208013186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.882 y[1] (analytic) = 1.3643916068334297273528957257406 y[1] (numeric) = 1.1889806015734510482224290848851 absolute error = 0.17541100525997867913046664085549 relative error = 12.856353291932375677631485514097 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.883 y[1] (analytic) = 1.3651639361477918147030451354242 y[1] (numeric) = 1.189440216873931323555566339212 absolute error = 0.17572371927386049114747879621219 relative error = 12.871986625263205643726369762189 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.884 y[1] (analytic) = 1.3659369002981648512578222581931 y[1] (numeric) = 1.1899006048212083536863476843268 absolute error = 0.17603629547695649757147457386622 relative error = 12.887586200982654860893721715435 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.885 y[1] (analytic) = 1.3667104985115847510578675899006 y[1] (numeric) = 1.1903617660497317203917955390382 absolute error = 0.17634873246185303066607205086236 relative error = 12.903151958948549236816263188697 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.886 y[1] (analytic) = 1.3674847300144533651497969666091 y[1] (numeric) = 1.1908237011931777242670358492015 absolute error = 0.17666102882127564088276111740765 relative error = 12.918683839300235281963202941169 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=179.2MB, alloc=4.5MB, time=10.07 x[1] = 0.887 y[1] (analytic) = 1.3682595940325392551842860514642 y[1] (numeric) = 1.1912864108844487510490502989496 absolute error = 0.17697318314809050413523575251458 relative error = 12.934181782458001732019450774412 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.888 y[1] (analytic) = 1.3690350897909784676474441647341 y[1] (numeric) = 1.1917498957556726387143433155751 absolute error = 0.17728519403530582893310084915903 relative error = 12.949645729122500203434522697679 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.889 y[1] (analytic) = 1.369811216514275308724703225707 y[1] (numeric) = 1.1922141564382020453511567703437 absolute error = 0.17759706007607326337354645536334 relative error = 12.965075620274164896383083941879 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.89 y[1] (analytic) = 1.3705879734263031197964469426197 y[1] (numeric) = 1.1926791935626138178068645029723 absolute error = 0.17790877986368930198958243964748 relative error = 12.98047139717263135936988604873 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.891 y[1] (analytic) = 1.3713653597503050535646047550548 y[1] (numeric) = 1.1931450077587083611111780223238 absolute error = 0.17822035199159669245342673273097 relative error = 12.995833001356154329652631774293 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.892 y[1] (analytic) = 1.3721433747088948508094344022757 y[1] (numeric) = 1.1936115996555090086757939600612 absolute error = 0.17853177505338584213364044221454 relative error = 13.011160374641024663597049456689 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.893 y[1] (analytic) = 1.3729220175240576177757163607833 y[1] (numeric) = 1.1940789698812613932711130775599 absolute error = 0.17884304764279622450460328322348 relative error = 13.026453459120985371019179119841 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.894 y[1] (analytic) = 1.373701287417150604187582764963 y[1] (numeric) = 1.1945471190634328187806598493083 absolute error = 0.17915416835371778540692291565467 relative error = 13.041712197166646767510568215657 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.895 y[1] (analytic) = 1.3744811836089039818912027960585 y[1] (numeric) = 1.1950160478287116327338308683236 absolute error = 0.17946513578019234915737192773495 relative error = 13.056936531424900758682747826486 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.896 y[1] (analytic) = 1.3752617053194216241245458968532 y[1] (numeric) = 1.195485756803006599617599540782 absolute error = 0.17977594851641502450694635607116 relative error = 13.07212640481833427020801262163 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.897 y[1] (analytic) = 1.3760428517681818854134435423582 y[1] (numeric) = 1.1959562466114462749678037581078 absolute error = 0.18008660515673561044563978425035 relative error = 13.087281760544641837474162133309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.898 y[1] (analytic) = 1.3768246221740383820931696705131 y[1] (numeric) = 1.1964275178783783802406424551797 absolute error = 0.18039710429566000185252721533343 relative error = 13.102402542076037368611479219292 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.899 y[1] (analytic) = 1.3776070157552207734547592513822 y[1] (numeric) = 1.1968995712273691784650061831069 absolute error = 0.18070744452785159498975306827522 relative error = 13.117488693158665094590826125419 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.9 y[1] (analytic) = 1.3783900317293355435152838485929 y[1] (numeric) = 1.1973724072812028506762660441925 absolute error = 0.18101762444813269283901780440038 relative error = 13.132540157812009720032331548863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.901 y[1] (analytic) = 1.3791736693133667834113024028072 y[1] (numeric) = 1.1978460266618808731321445552418 absolute error = 0.18132764265148591027915784756537 relative error = 13.147556880328305788304725713186 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.902 y[1] (analytic) = 1.3799579277236769744147048438388 y[1] (numeric) = 1.1983204299906213953112912232949 absolute error = 0.18163749773305557910341362054385 relative error = 13.162538805271946274435956863522 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.903 y[1] (analytic) = 1.380742806176007771570165515639 y[1] (numeric) = 1.1987956178878586186951848351545 absolute error = 0.18194718828814915287498068048448 relative error = 13.17748587747889041929629392256 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=183.1MB, alloc=4.5MB, time=10.29 x[1] = 0.904 y[1] (analytic) = 1.3815283038854807879534227767624 y[1] (numeric) = 1.1992715909732421763339836787553 absolute error = 0.18225671291223861161943909800709 relative error = 13.192398042056070818455688446973 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.905 y[1] (analytic) = 1.3823144200665983795496005180982 y[1] (numeric) = 1.1997483498656365131969441304734 absolute error = 0.18256607020096186635265638762479 relative error = 13.207275244380799779057736604884 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.906 y[1] (analytic) = 1.3831011539332444307507867196122 y[1] (numeric) = 1.2002258951831202673080272579059 absolute error = 0.18287525875012416344275946170632 relative error = 13.222117430100174957993150756478 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.907 y[1] (analytic) = 1.3838885046986851404720835485838 y[1] (numeric) = 1.2007042275429856516673123024602 absolute error = 0.18318427715569948880477124612354 relative error = 13.23692454513048429459622244475 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.908 y[1] (analytic) = 1.3846764715755698088853428833566 y[1] (numeric) = 1.201183347561737836958835120292 absolute error = 0.1834931240138319719265077630646 relative error = 13.251696535656610251028336257546 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.909 y[1] (analytic) = 1.3854650537759316247698005289301 y[1] (numeric) = 1.2016632558550943350454688736976 absolute error = 0.18380179792083728972433165523256 relative error = 13.266433348131433373453179155676 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.91 y[1] (analytic) = 1.3862542505111884534788217738253 y[1] (numeric) = 1.2021439530379843832514634780322 absolute error = 0.18411029747320407022735829579309 relative error = 13.281134929275235187048884508438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.911 y[1] (analytic) = 1.3870440609921436255219703215436 y[1] (numeric) = 1.2026254397245483294332595215616 absolute error = 0.18441862126759529608871079998199 relative error = 13.295801226075100437842956255048 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.912 y[1] (analytic) = 1.387834484428986725761612014616 y[1] (numeric) = 1.2031077165281370178391915873815 absolute error = 0.18472676790084970792242042723453 relative error = 13.310432185784318694296438319373 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.913 y[1] (analytic) = 1.3886255200312943832232641547054 y[1] (numeric) = 1.2035907840613111757586951176523 absolute error = 0.18503473596998320746456903705313 relative error = 13.325027755921785321504429631299 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.914 y[1] (analytic) = 1.3894171670080310615189006084766 y[1] (numeric) = 1.2040746429358408009616301708887 absolute error = 0.18534252407219026055727043758787 relative error = 13.339587884271401840820697820033 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.915 y[1] (analytic) = 1.390209424567549849882422275997 y[1] (numeric) = 1.2045592937627045499283346329315 absolute error = 0.18565013080484529995408764306545 relative error = 13.354112518881475687654816795637 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.916 y[1] (analytic) = 1.3910022919175932548165018862618 y[1] (numeric) = 1.2050447371520891268710186514958 absolute error = 0.18595755476550412794548323476604 relative error = 13.368601608064119380130946962098 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.917 y[1] (analytic) = 1.3917957682652939923500114730661 y[1] (numeric) = 1.2055309737133886735471112728512 absolute error = 0.18626479455190531880290020021488 relative error = 13.383055100394649111238093629204 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.918 y[1] (analytic) = 1.3925898528171757809052402738607 y[1] (numeric) = 1.2060180040552041598651694672363 absolute error = 0.18657184876197162104007080662432 relative error = 13.397472944710982777042421216441 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.919 y[1] (analytic) = 1.3933845447791541347741101844421 y[1] (numeric) = 1.2065058287853427752839589370476 absolute error = 0.18687871599381135949015124739452 relative error = 13.411855090113037453472969959084 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.92 y[1] (analytic) = 1.3941798433565371582025952933256 y[1] (numeric) = 1.2069944485108173210053153086708 absolute error = 0.18718539484571983719727998465485 relative error = 13.426201485962126334132919907937 % h = 0.001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=10.50 NO POLE x[1] = 0.921 y[1] (analytic) = 1.3949757477540263400825514114488 y[1] (numeric) = 1.2074838638378456029613935150442 absolute error = 0.18749188391618073712115789640463 relative error = 13.440512081880355141529375916986 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.922 y[1] (analytic) = 1.3957722571757173492501609054418 y[1] (numeric) = 1.2079740753718498255969123816521 absolute error = 0.18779818180386752365324852378966 relative error = 13.454786827750018024055508879283 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.923 y[1] (analytic) = 1.3965693708251008303901975360864 y[1] (numeric) = 1.2084650837174559864470006336551 absolute error = 0.18810428710764484394319690243135 relative error = 13.469025673712992950999784526359 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.924 y[1] (analytic) = 1.3973670879050632005453153977649 y[1] (numeric) = 1.2089568894784932715112497462588 absolute error = 0.18841019842656992903406565150608 relative error = 13.483228570170136617797943460485 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.925 y[1] (analytic) = 1.3981654076178874462295654496762 y[1] (numeric) = 1.2094494932579934514245782642204 absolute error = 0.18871591435989399480498718545579 relative error = 13.497395467780678873684366536579 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.926 y[1] (analytic) = 1.3989643291652539211453425253694 y[1] (numeric) = 1.2099428956581902784255114195752 absolute error = 0.18902143350706364271983110579412 relative error = 13.511526317461616683840470030193 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.927 y[1] (analytic) = 1.3997638517482411445029651037137 y[1] (numeric) = 1.2104370972805188841224790792562 absolute error = 0.18932675446772226038048602445743 relative error = 13.525621070387107638078826983021 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.928 y[1] (analytic) = 1.4005639745673265999420895217925 y[1] (numeric) = 1.2109320987256151780587342562568 absolute error = 0.18963187584171142188335526553576 relative error = 13.539679677987863018042806455346 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.929 y[1] (analytic) = 1.4013646968223875350541597083728 y[1] (numeric) = 1.2114279005933152470764936193682 absolute error = 0.18993679622907228797766608900456 relative error = 13.553702091950540434842662867866 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.93 y[1] (analytic) = 1.402166017712701761505092915567 y[1] (numeric) = 1.2119245034826547554809006373023 absolute error = 0.19024151423004700602419227826471 relative error = 13.567688264217136048990194900081 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.931 y[1] (analytic) = 1.4029679364369484557574013260696 y[1] (numeric) = 1.2124219079918683460044111931847 absolute error = 0.19054602844508010975299013288488 relative error = 13.581638146984376384435329230109 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.932 y[1] (analytic) = 1.4037704521932089603909488139114 y[1] (numeric) = 1.2129201147183890415722007049844 absolute error = 0.19085033747481991881874810892698 relative error = 13.595551692703109748449270437202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.933 y[1] (analytic) = 1.4045735641789675860215415380431 y[1] (numeric) = 1.2134191242588476478691909864216 absolute error = 0.19115443992011993815235055162154 relative error = 13.609428854077697269040196314039 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.934 y[1] (analytic) = 1.4053772715911124138165504502244 y[1] (numeric) = 1.2139189372090721567092942812784 absolute error = 0.19145833438204025710725616894596 relative error = 13.623269584065403561528869306102 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.935 y[1] (analytic) = 1.4061815736259360986067632016613 y[1] (numeric) = 1.2144195541640871502074711018174 absolute error = 0.19176201946184894839929209984386 relative error = 13.637073835875787035852981450311 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.936 y[1] (analytic) = 1.4069864694791366725936623366093 y[1] (numeric) = 1.2149209757181132057551976992014 absolute error = 0.19206549376102346683846463740786 relative error = 13.650841562970089856110553649278 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.937 y[1] (analytic) = 1.4077919583458183496513260657285 y[1] (numeric) = 1.2154232024645663017999381903968 absolute error = 0.19236875588125204785138787533171 relative error = 13.664572719060627563794272000799 % h = 0.001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=10.72 NO POLE x[1] = 0.938 y[1] (analytic) = 1.4085980394204923302221473173594 y[1] (numeric) = 1.2159262349960572244292155620397 absolute error = 0.19267180442443510579293175531976 relative error = 13.678267258110178376110265799096 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.939 y[1] (analytic) = 1.409404711897077606805566171065 y[1] (numeric) = 1.216430073904390974759874967143 absolute error = 0.19297463799268663204569120392203 relative error = 13.691925134331372170716515314407 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.94 y[1] (analytic) = 1.410211974968901770039010184776 y[1] (numeric) = 1.2169347197805661771331319253335 absolute error = 0.19327725518833559290587825944252 relative error = 13.705546302186079168157824105356 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.941 y[1] (analytic) = 1.4110198278287018153702365346646 y[1] (numeric) = 1.2174401732147744881159972315197 absolute error = 0.19357965461392732725423930314484 relative error = 13.719130716384798323216101973726 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.942 y[1] (analytic) = 1.4118282696686249503202692954725 y[1] (numeric) = 1.2179464347964000063096695715178 absolute error = 0.19388183487222494401059972395468 relative error = 13.73267833188604543633658226856 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.943 y[1] (analytic) = 1.4126372996802294023361245984231 y[1] (numeric) = 1.2184535051140186829654860361924 absolute error = 0.19418379456621071937063856223068 relative error = 13.746189103895740996232542605728 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.944 y[1] (analytic) = 1.41344691705448522723251581406 y[1] (numeric) = 1.2189613847553977334090199181144 absolute error = 0.19448553229908749382349589594561 relative error = 13.759662987866597764713112695422 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.945 y[1] (analytic) = 1.4142571209817751182217303183736 y[1] (numeric) = 1.2194700743074950492729143665867 absolute error = 0.1947870466742800689488159517869 relative error = 13.773099939497508114720838353692 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.946 y[1] (analytic) = 1.4150679106518952155308688124071 y[1] (numeric) = 1.2199795743564586115390396681573 absolute error = 0.19508833629543660399182914424977 relative error = 13.786499914732931132507828390926 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.947 y[1] (analytic) = 1.4158792852540559166056375781701 y[1] (numeric) = 1.2204898854876259043905611104128 absolute error = 0.19538939976643001221507646775726 relative error = 13.799862869762279494821542380923 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.948 y[1] (analytic) = 1.4166912439768826868998834671338 y[1] (numeric) = 1.2210010082855233298745035769346 absolute error = 0.19569023569135935702537989019923 relative error = 13.813188761019306131913583765608 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.949 y[1] (analytic) = 1.4175037860084168712500608318425 y[1] (numeric) = 1.2215129433338656233753982108062 absolute error = 0.19599084267455124787466262103627 relative error = 13.826477545181490687127245774091 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.95 y[1] (analytic) = 1.4183169105361165058338190262395 y[1] (numeric) = 1.2220256912155552699005956729751 absolute error = 0.1962912193205612359332233532644 relative error = 13.839729179169425783762018648426 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.951 y[1] (analytic) = 1.4191306167468571307118985161905 y[1] (numeric) = 1.2225392525126819211778297101076 absolute error = 0.19659136423417520953406880608293 relative error = 13.852943620146203109855807074784 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.952 y[1] (analytic) = 1.419944903826932602952523058373 y[1] (numeric) = 1.223053627806521813565613934324 absolute error = 0.19689127602041078938690912404893 relative error = 13.866120825516799331468227906671 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.953 y[1] (analytic) = 1.4207597709620559103374748232099 y[1] (numeric) = 1.2235688176775371867770539043705 absolute error = 0.19719095328451872356042091883937 relative error = 13.879260752927461844991061610497 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.954 y[1] (analytic) = 1.4215752173373599856490387558386 y[1] (numeric) = 1.2240848227053757034176557843646 absolute error = 0.19749039463198428223138297147407 relative error = 13.892363360265094378954717723314 % h = 0.001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=10.94 NO POLE x[1] = 0.955 y[1] (analytic) = 1.4223912421373985215370018882395 y[1] (numeric) = 1.2246016434688698693377120422595 absolute error = 0.19778959866852865219928984597993 relative error = 13.905428605656642455742446333715 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.956 y[1] (analytic) = 1.4232078445461467859648927355918 y[1] (numeric) = 1.2251192805460364547998438355926 absolute error = 0.19808856400011033116504889999919 relative error = 13.918456447468478723566985511492 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.957 y[1] (analytic) = 1.4240250237470024382346453306867 y[1] (numeric) = 1.2256377345140759164622789169259 absolute error = 0.19838728923292652177236641376071 relative error = 13.931446844305788169007380037159 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.958 y[1] (analytic) = 1.4248427789227863455888718718004 y[1] (numeric) = 1.226157005949371820178443075656 absolute error = 0.1986857729734145254104287961445 relative error = 13.944399755011953220346841022531 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.959 y[1] (analytic) = 1.4256611092557434003899273818234 y[1] (numeric) = 1.2266770954274902646134423165492 absolute error = 0.19898401382825313577648506527422 relative error = 13.957315138667938751895740357687 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.96 y[1] (analytic) = 1.4264800139275433378749491996481 y[1] (numeric) = 1.2271980035231793056780121584765 absolute error = 0.1992820104043640321969370411716 relative error = 13.970192954591676999427149643586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.961 y[1] (analytic) = 1.4272994921192815544860535488458 y[1] (numeric) = 1.2277197308103683817805096193475 absolute error = 0.19957976130891317270554392949835 relative error = 13.983033162337452396795741634974 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.962 y[1] (analytic) = 1.4281195430114799267748708535018 y[1] (numeric) = 1.2282422778621677398975226352045 absolute error = 0.19987726514931218687734821829738 relative error = 13.995835721695286343754374473133 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.963 y[1] (analytic) = 1.4289401657840876308806008967442 y[1] (numeric) = 1.2287656452508678624636708428209 absolute error = 0.20017452053321976841693005392329 relative error = 14.008600592690321914926276366557 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.964 y[1] (analytic) = 1.4297613596164819625807683439772 y[1] (numeric) = 1.2292898335479388950811708359532 absolute error = 0.20047152606854306749959750802391 relative error = 14.021327735582208519834442100372 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.965 y[1] (analytic) = 1.4305831236874691579138585801337 y[1] (numeric) = 1.2298148433240300750497381856351 absolute error = 0.20076828036343908286412039449859 relative error = 14.034017110864486523833644029069 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.966 y[1] (analytic) = 1.4314054571752852143730132383785 y[1] (numeric) = 1.230340675148969160717397694563 absolute error = 0.20106478202631605365561554381551 relative error = 14.046668679263971839734350225166 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.967 y[1] (analytic) = 1.4322283592575967126699642266353 y[1] (numeric) = 1.2308673295917618616527725347167 absolute error = 0.20136102966583485101719169191862 relative error = 14.059282401740140499851832398574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.968 y[1] (analytic) = 1.4330518291115016390683844880724 y[1] (numeric) = 1.231394807220591269639422095877 absolute error = 0.20165702189091036942896239219538 relative error = 14.071858239484513218157837233856 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.969 y[1] (analytic) = 1.4338758659135302082858331622636 y[1] (numeric) = 1.2319231086028172904927975506554 absolute error = 0.20195275731071291779303561160826 relative error = 14.084396153920039952156388068304 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.97 y[1] (analytic) = 1.4347004688396456869634722451501 y[1] (numeric) = 1.2324522343049760767003833190338 absolute error = 0.20224823453466961026308892611638 relative error = 14.096896106700484474049580492171 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.971 y[1] (analytic) = 1.4355256370652452177027312781524 y[1] (numeric) = 1.2329821848927794608855917922244 absolute error = 0.20254345217246575681713948592802 relative error = 14.109358059709808960703636619847 % h = 0.001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.5MB, time=11.16 NO POLE x[1] = 0.972 y[1] (analytic) = 1.4363513697651606436680960298383 y[1] (numeric) = 1.2335129609311143900959778519086 absolute error = 0.20283840883404625357211817792975 relative error = 14.121781975061558611869989570187 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.973 y[1] (analytic) = 1.4371776661136593337551965674268 y[1] (numeric) = 1.2340445629840423609163388965926 absolute error = 0.20313310312961697283885767083415 relative error = 14.134167815098246306060783205493 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.974 y[1] (analytic) = 1.4380045252844450083233695501071 y[1] (numeric) = 1.2345769916147988554072652619334 absolute error = 0.20342753366964615291610428817368 relative error = 14.146515542390737303422893498505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.975 y[1] (analytic) = 1.4388319464506585654918690116816 y[1] (numeric) = 1.2351102473857927778697050964369 absolute error = 0.2037216990648657876221639152447 relative error = 14.158825119737634004899408098845 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.976 y[1] (analytic) = 1.4396599287848789079988993363885 y[1] (numeric) = 1.2356443308586058924361069279168 absolute error = 0.20401559792627301556279240847166 relative error = 14.171096510164660776912440815437 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.977 y[1] (analytic) = 1.4404884714591237706226435689417 y[1] (numeric) = 1.2361792425939922614887023295251 absolute error = 0.20430922886513150913394123941658 relative error = 14.183329676924048850746208867175 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.978 y[1] (analytic) = 1.4413175736448505481634596378282 y[1] (numeric) = 1.2367149831518776849054902670239 absolute error = 0.20460259049297286325796937080421 relative error = 14.195524583493921305754463915454 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.979 y[1] (analytic) = 1.4421472345129571239864165097351 y[1] (numeric) = 1.2372515530913591401344838812686 absolute error = 0.20489568142159798385193262846644 relative error = 14.207681193577678145461644101264 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.98 y[1] (analytic) = 1.4429774532337826991233417326401 y[1] (numeric) = 1.2377889529707042230967796316075 absolute error = 0.20518850026307847602656210103254 relative error = 14.219799471103381475572504575584 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.981 y[1] (analytic) = 1.4438082289771086219335512655861 y[1] (numeric) = 1.2383271833473505899190078970838 absolute error = 0.20548104562975803201454336850229 relative error = 14.231879380223140792850489331581 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.982 y[1] (analytic) = 1.4446395609121592183224319344801 y[1] (numeric) = 1.2388662447779053994957233029414 absolute error = 0.20577331613425381882670863153869 relative error = 14.243920885312498393770728504588 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.983 y[1] (analytic) = 1.4454714482076026225170462954026 y[1] (numeric) = 1.2394061378181447568822922099991 absolute error = 0.20606531038945786563475408540345 relative error = 14.255923950969814911799283672472 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.984 y[1] (analytic) = 1.4463038900315516083979291298914 y[1] (numeric) = 1.2399468630230131575188339739576 absolute error = 0.20635702700853845087909515593381 relative error = 14.267888542015654992096120023777 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.985 y[1] (analytic) = 1.4471368855515644213862442404742 y[1] (numeric) = 1.2404884209466229322857717506535 absolute error = 0.20664846460494148910047248982077 relative error = 14.279814623492173112385259510505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.986 y[1] (analytic) = 1.4479704339346456108854696593607 y[1] (numeric) = 1.2410308121422536933915477916621 absolute error = 0.20693962179239191749392186769859 relative error = 14.291702160662499558681664200684 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.987 y[1] (analytic) = 1.4488045343472468632767788286789 y[1] (numeric) = 1.2415740371623517810930573424881 absolute error = 0.20723049718489508218372148619088 relative error = 14.303551119010126564510614914779 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.988 y[1] (analytic) = 1.4496391859552678354672847569453 y[1] (numeric) = 1.2421180965585297112493544228635 absolute error = 0.20752108939673812421793033408181 relative error = 14.315361464238294622201687779251 % h = 0.001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.5MB, time=11.37 NO POLE x[1] = 0.989 y[1] (analytic) = 1.4504743879240569889903136035916 y[1] (numeric) = 1.2426629908815656237091819354023 absolute error = 0.20781139704249136528113166818939 relative error = 14.327133162269378974785891457319 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.99 y[1] (analytic) = 1.4513101394184124246568735913464 y[1] (numeric) = 1.2432087206814027315328777150336 absolute error = 0.20810141873700969312399587631282 relative error = 14.338866179244276296971111406771 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.991 y[1] (analytic) = 1.4521464396025827177574845950707 y[1] (numeric) = 1.243755286507148771049207297264 absolute error = 0.20839115309543394670827729780668 relative error = 14.350560481521791573617715440438 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.992 y[1] (analytic) = 1.4529832876402677538135332052885 y[1] (numeric) = 1.2443026889070754527476733483882 absolute error = 0.20868059873319230106585985690028 relative error = 14.362216035678025184083007988093 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.993 y[1] (analytic) = 1.4538206826946195648773175151265 y[1] (numeric) = 1.2448509284286179130068508652943 absolute error = 0.20896975426600165187046664983219 relative error = 14.373832808505760200750179628194 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.994 y[1] (analytic) = 1.4546586239282431663799453306873 y[1] (numeric) = 1.2454000056183741666592964164817 absolute error = 0.20925861830986899972064891420564 relative error = 14.385410767013849910004484511489 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.995 y[1] (analytic) = 1.4554971105031973945262489570286 y[1] (numeric) = 1.2459499210221045603935788593375 absolute error = 0.20954718948109283413267009769116 relative error = 14.396949878426605563866592061593 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.996 y[1] (analytic) = 1.4563361415809957442358791649033 y[1] (numeric) = 1.2465006751847312269939781315955 absolute error = 0.20983546639626451724190103330778 relative error = 14.40845011018318437044040162404 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.997 y[1] (analytic) = 1.4571757163226072076297403972349 y[1] (numeric) = 1.2470522686503375404183978772321 absolute error = 0.21012344767226966721134252000289 relative error = 14.419911429936977731280080347151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.998 y[1] (analytic) = 1.4580158338884571130609287289657 y[1] (numeric) = 1.2476047019621675717150368288423 absolute error = 0.21041113192628954134589190012342 relative error = 14.431333805554999733728686305799 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.999 y[1] (analytic) = 1.4588564934384279646893335494061 y[1] (numeric) = 1.248157975662625545778363029779 absolute error = 0.21069851777580241891097051962719 relative error = 14.44271720511727590622847150179 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1 y[1] (analytic) = 1.459697694131860282599063392557 y[1] (numeric) = 1.2487120902932752989449341400351 absolute error = 0.21098560383858498365412925252194 relative error = 14.4540615969162322445508236595 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.001 y[1] (analytic) = 1.4605394351275534434578557980465 y[1] (numeric) = 1.2492670463948397374296062300045 absolute error = 0.21127238873271370602824956804198 relative error = 14.46536694945608451684180243863 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.002 y[1] (analytic) = 1.4613817155837665217176305433427 y[1] (numeric) = 1.2498228445072002966026726258663 absolute error = 0.21155887107656622511495791747643 relative error = 14.476633231452227855327355552125 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.003 y[1] (analytic) = 1.4622245346582191313553450467597 y[1] (numeric) = 1.2503794851693964011084735294098 absolute error = 0.21184504948882273024687151734982 relative error = 14.487860411830626642470564039723 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.004 y[1] (analytic) = 1.4630678915080922681533102004696 y[1] (numeric) = 1.250936968919624925826016293645 absolute error = 0.21213092258846734232729390682456 relative error = 14.499048459727204699321664328357 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.005 memory used=206.0MB, alloc=4.5MB, time=11.59 y[1] (analytic) = 1.4639117852900291525181243532775 y[1] (numeric) = 1.2514952962952396576721453935329 absolute error = 0.21241648899478949484597895974458 relative error = 14.510197344487235783750128420636 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.006 y[1] (analytic) = 1.4647562151601360728373826242936 y[1] (numeric) = 1.2520544678327507582478002886221 absolute error = 0.21270174732738531458958233567145 relative error = 14.521307035664734406196753291616 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.007 y[1] (analytic) = 1.4656011802739832293733181908644 y[1] (numeric) = 1.252614484067824227327898531288 absolute error = 0.21298669620615900204541965957645 relative error = 14.532377503021846970532517030812 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.008 y[1] (analytic) = 1.4664466797866055786925316571923 y[1] (numeric) = 1.2531753455352813671953806306468 absolute error = 0.21327133425132421149715102654548 relative error = 14.543408716528243247559903118574 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.009 y[1] (analytic) = 1.467292712852503678630964073983 y[1] (numeric) = 1.2537370527690982478199523380557 absolute error = 0.21355566008340543081101173592732 relative error = 14.554400646360508188641476140418 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.01 y[1] (analytic) = 1.4681392786256445337932686442208 y[1] (numeric) = 1.2542996063024051728820591754113 absolute error = 0.21383967232323936091120946880949 relative error = 14.565353262901534086889712875534 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.011 y[1] (analytic) = 1.4689863762594624415857356157674 y[1] (numeric) = 1.254863006667486146642627182228 absolute error = 0.21412336959197629494310843353947 relative error = 14.576266536739913093301452691719 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.012 y[1] (analytic) = 1.4698340049068598387819243279326 y[1] (numeric) = 1.2554272543957783416591030117105 absolute error = 0.2144067505110814971228213162221 relative error = 14.587140438669330095169831172698 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.013 y[1] (analytic) = 1.4706821637202081486201558464535 y[1] (numeric) = 1.2559923500178715673483256597374 absolute error = 0.21468981370233658127183018671606 relative error = 14.597974939687955964056201519049 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.014 y[1] (analytic) = 1.4715308518513486284320190894609 y[1] (numeric) = 1.2565582940635077393967612638375 absolute error = 0.21497255778784088903525782562344 relative error = 14.608770010997841180554330113751 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.015 y[1] (analytic) = 1.472380068451593217801042815998 y[1] (numeric) = 1.2571250870615803500186315618821 absolute error = 0.21525498139001286778241125411595 relative error = 14.619525624004309843029076330384 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.016 y[1] (analytic) = 1.4732298126717253872506853184886 y[1] (numeric) = 1.2576927295401339390624657523197 absolute error = 0.21553708313159144818821956616897 relative error = 14.630241750315354067461832778297 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.017 y[1] (analytic) = 1.4740800836620009874607931312371 y[1] (numeric) = 1.2582612220263635659666046493565 absolute error = 0.21581886163563742149418848188055 relative error = 14.64091836174102878548521130624 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.018 y[1] (analytic) = 1.4749308805721490990116795385718 y[1] (numeric) = 1.2588305650466142825641851775364 absolute error = 0.21610031552553481644749436103541 relative error = 14.651555430292846947639812795512 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.019 y[1] (analytic) = 1.4757822025513728826549731386242 y[1] (numeric) = 1.2594007591263806067381324006894 absolute error = 0.21638144342499227591684073793482 relative error = 14.662152928183175138836415626397 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.02 y[1] (analytic) = 1.4766340487483504301103861919662 y[1] (numeric) = 1.2599718047903059969266854302157 absolute error = 0.21666224395804443318370076175046 relative error = 14.672710827824629612957559248623 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.021 y[1] (analytic) = 1.4774864183112356153875519584076 y[1] (numeric) = 1.260543702562182327479982707133 absolute error = 0.21694271574905328790756925127452 relative error = 14.683229101829472753483286068174 % h = 0.001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=11.80 NO POLE x[1] = 1.022 y[1] (analytic) = 1.4783393103876589466320797001881 y[1] (numeric) = 1.2611164529649493648682313012594 absolute error = 0.21722285742270958176384839892871 relative error = 14.693707723009009966976737409734 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.023 y[1] (analytic) = 1.4791927241247284184949755055798 y[1] (numeric) = 1.2616900565206942447419840193189 absolute error = 0.21750266760403417375299148626097 relative error = 14.704146664372987016216378146755 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.024 y[1] (analytic) = 1.4800466586690303650245765635492 y[1] (numeric) = 1.2622645137506509498450472616482 absolute error = 0.21778214491837941517952930190098 relative error = 14.714545899128987799712850220151 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.025 y[1] (analytic) = 1.4809011131666303130801459976169 y[1] (numeric) = 1.2628398251751997887805417145545 absolute error = 0.21806128799143052429960428306244 relative error = 14.724905400681832584299828192617 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.026 y[1] (analytic) = 1.4817560867630738362662748453913 y[1] (numeric) = 1.2634159913138668756306371122187 absolute error = 0.21834009544920696063563773317262 relative error = 14.735225142632976697439770699202 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.027 y[1] (analytic) = 1.4826115786033874093872372494439 y[1] (numeric) = 1.2639930126853236104304814483673 absolute error = 0.21861856591806379895675580107655 relative error = 14.74550509877990968583713063716 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.028 y[1] (analytic) = 1.4834675878320792634204444052437 y[1] (numeric) = 1.2645708898073861604968441637395 absolute error = 0.21889669802469310292360024150419 relative error = 14.755745243115554946903404660431 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.029 y[1] (analytic) = 1.4843241135931402410081422927682 y[1] (numeric) = 1.2651496231970149426119919806637 absolute error = 0.21917449039612529839615031210453 relative error = 14.765945549827669839570369468003 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.03 y[1] (analytic) = 1.4851811550300446524664977001626 y[1] (numeric) = 1.2657292133703141060633152008238 absolute error = 0.21945194165973054640318249933889 relative error = 14.776105993298246280899968952903 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.031 y[1] (analytic) = 1.4860387112857511323112165304354 y[1] (numeric) = 1.266309660842531016539221426547 absolute error = 0.21972905044322011577199510388841 relative error = 14.78622654810291183489158295217 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.032 y[1] (analytic) = 1.4868967815027034962988378656402 y[1] (numeric) = 1.266890966128055740881812809675 absolute error = 0.22000581537464775541702505596524 relative error = 14.796307189010331299839825540825 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.033 y[1] (analytic) = 1.4877553648228315989828467473245 y[1] (numeric) = 1.2674731297404205326968620752993 absolute error = 0.22028223508241106628598467202517 relative error = 14.80634789098160880054858896825 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.034 y[1] (analytic) = 1.4886144603875521917837481172009 y[1] (numeric) = 1.2680561521922993188216017103416 absolute error = 0.22055830819525287296214640685925 relative error = 14.816348629169690391659768857775 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.035 y[1] (analytic) = 1.4894740673377697815722438480409 y[1] (numeric) = 1.2686400339955071866508398491471 absolute error = 0.22083403334226259492140399889381 relative error = 14.826309378918767178307977584638 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.036 y[1] (analytic) = 1.4903341848138774897646542816843 y[1] (numeric) = 1.2692247756609998723219155299322 absolute error = 0.22110940915287761744273875175215 relative error = 14.836230115763678960265576209556 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.037 y[1] (analytic) = 1.4911948119557579119297251788145 y[1] (numeric) = 1.2698103776988732497590051370887 absolute error = 0.22138443425688466217072004172586 relative error = 14.846110815429318405695531361683 % h = 0.001 TOP MAIN SOLVE Loop memory used=213.6MB, alloc=4.5MB, time=12.01 NO POLE x[1] = 1.038 y[1] (analytic) = 1.4920559479027839779059604737648 y[1] (numeric) = 1.2703968406183628205772909849955 absolute error = 0.22165910728442115732866948876936 relative error = 14.85595145383003576058293241306 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.039 y[1] (analytic) = 1.4929175917938198124286207170946 y[1] (numeric) = 1.2709841649278432048475021391268 absolute error = 0.22193342686597660758111857796775 relative error = 14.865752007069044099869486535494 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.04 y[1] (analytic) = 1.4937797427672215962655265790078 y[1] (numeric) = 1.2715723511348276327213367098733 absolute error = 0.22220739163239396354418986913456 relative error = 14.875512451437825126268945139499 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.041 y[1] (analytic) = 1.4946423999608384278608062778836 y[1] (numeric) = 1.2721613997459674369182739936114 absolute error = 0.22248100021487099094253228427219 relative error = 14.885232763415535522695205114226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.042 y[1] (analytic) = 1.4955055625120131854857252902416 y[1] (numeric) = 1.2727513112670515460742839741677 absolute error = 0.22275425124496163941144131607394 relative error = 14.89491291966841386418877255895 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.043 y[1] (analytic) = 1.4963692295575833898957361913855 y[1] (numeric) = 1.2733420862030059789529408359241 absolute error = 0.22302714335457741094279535546142 relative error = 14.904552897049188095181375653659 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.044 y[1] (analytic) = 1.4972334002338820674928859697465 y[1] (numeric) = 1.2739337250578933395194462774113 absolute error = 0.2232996751759887279734396923352 relative error = 14.914152672596483577892767282918 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.045 y[1] (analytic) = 1.4980980736767386139927176525903 y[1] (numeric) = 1.2745262283349123128780675513219 absolute error = 0.22357184534182630111465010126844 relative error = 14.923712223534231717608167319076 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.046 y[1] (analytic) = 1.4989632490214796585948025762604 y[1] (numeric) = 1.2751195965363971620734942934662 absolute error = 0.2238436524850824965213082827942 relative error = 14.933231527271079170539359395083 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.047 y[1] (analytic) = 1.499828925402929928656039130494 y[1] (numeric) = 1.2757138301638172257566173392693 absolute error = 0.22411509523911270289942179122465 relative error = 14.942710561399797639927177852148 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.048 y[1] (analytic) = 1.5006951019554131148658533035871 y[1] (numeric) = 1.2763089297177764167152318619906 absolute error = 0.22438617223763669815062144159645 relative error = 14.952149303696694265997997623322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.049 y[1] (analytic) = 1.5015617778127527369224358532785 y[1] (numeric) = 1.27690489569801272127016630192 absolute error = 0.22465688211474001565226955135848 relative error = 14.961547732121022615341873392309 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.05 y[1] (analytic) = 1.5024289521082730097091504271879 y[1] (numeric) = 1.2775017286033976995373376903801 absolute error = 0.22492722350487531017181273680779 relative error = 14.970905824814394275235164720808 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.051 y[1] (analytic) = 1.5032966239747997099702464564727 y[1] (numeric) = 1.278099428931935986556233106438 absolute error = 0.22519719504286372341401335003472 relative error = 14.980223560100191058385831232295 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.052 y[1] (analytic) = 1.5041647925446610434850101470624 y[1] (numeric) = 1.2786979971807647942853161378029 absolute error = 0.22546679536389624919969400925941 relative error = 14.989500916482977823535086632272 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.053 y[1] (analytic) = 1.5050334569496885127394863943916 y[1] (numeric) = 1.2792974338461534144648563504624 absolute error = 0.22573602310353509827463004392916 relative error = 14.998737872647915917304762583059 % h = 0.001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.5MB, time=12.23 NO POLE x[1] = 1.054 y[1] (analytic) = 1.5059026163212177850949039499833 y[1] (numeric) = 1.2798977394235027223476789041855 absolute error = 0.22600487689771506274722504579779 relative error = 15.007934407460177242635553475813 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.055 y[1] (analytic) = 1.5067722697900895614519356715277 y[1] (numeric) = 1.2804989144073446812983305831025 absolute error = 0.22627335538274488015360508842518 relative error = 15.017090499964358959117291185938 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.056 y[1] (analytic) = 1.5076424164866504454099251922705 y[1] (numeric) = 1.2811009592913418482611576421541 absolute error = 0.22654145719530859714876755011643 relative error = 15.0262061293838988204685351849 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.057 y[1] (analytic) = 1.508513055540753812920210850555 y[1] (numeric) = 1.2817038745682868800977900012895 absolute error = 0.2268091809724669328224208492655 relative error = 15.035281275120491154379058128201 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.058 y[1] (analytic) = 1.5093841860817606824326772262677 y[1] (numeric) = 1.2823076607301020407945254498905 absolute error = 0.22707652535165864163815177637717 relative error = 15.044315916753503489885260454517 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.059 y[1] (analytic) = 1.5102558072385405855346641377078 y[1] (numeric) = 1.2829123182678387095401066539942 absolute error = 0.22734348897070187599455748371357 relative error = 15.053310034039393837405159815645 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.06 y[1] (analytic) = 1.5111279181394724380813624600436 y[1] (numeric) = 1.2835178476716768896743828884967 absolute error = 0.22761007046779554840697957154685 relative error = 15.062263606911128626516372504031 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.061 y[1] (analytic) = 1.5120005179124454118168256350344 y[1] (numeric) = 1.284124249430924718508347545637 absolute error = 0.22787626848152069330847808939738 relative error = 15.07117661547760130651743463965 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.062 y[1] (analytic) = 1.5128736056848598064847252510766 y[1] (numeric) = 1.2847315240340179780160415996795 absolute error = 0.22814208165084182846868365139706 relative error = 15.080049040023051614769900898703 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.063 y[1] (analytic) = 1.513747180583627922427978582893 y[1] (numeric) = 1.2853396719685196063988123358541 absolute error = 0.22840750861510831602916624703894 relative error = 15.088880861006485517775908183226 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.064 y[1] (analytic) = 1.5146212417351749336763754913097 y[1] (numeric) = 1.2859486937211192105224157792519 absolute error = 0.22867254801405572315395971205787 relative error = 15.097672059061095829903301005899 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.065 y[1] (analytic) = 1.5154957882654397615213315955666 y[1] (numeric) = 1.2865585897776325792274503865355 absolute error = 0.22893719848780718229388120903102 relative error = 15.10642261499368351462798465349 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.066 y[1] (analytic) = 1.5163708192998759485768941434805 y[1] (numeric) = 1.2871693606230011975136086899883 absolute error = 0.22920145867687475106328545349221 relative error = 15.11513250978407967312090154322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.067 y[1] (analytic) = 1.5172463339634525333261265185295 y[1] (numeric) = 1.2877810067412917615982327096104 absolute error = 0.22946532722216077172789380891911 relative error = 15.123801724584568224964915739551 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.068 y[1] (analytic) = 1.5181223313806549251519968375448 y[1] (numeric) = 1.2883935286156956948496580746673 absolute error = 0.2297288027649592303023387628775 relative error = 15.132430240719309285744940487656 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.069 y[1] (analytic) = 1.5189988106754857798518956081959 y[1] (numeric) = 1.2890069267285286645958309213045 absolute error = 0.2299918839469571152560646868914 relative error = 15.14101803968376324621285397024 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=221.2MB, alloc=4.5MB, time=12.45 x[1] = 1.07 y[1] (analytic) = 1.5198757709714658756349069318241 y[1] (numeric) = 1.2896212015612300998086807575726 absolute error = 0.2302545694102357758262261742515 relative error = 15.149565103144115557687119425355 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.071 y[1] (analytic) = 1.5207532113916349896009572544251 y[1] (numeric) = 1.2902363535943627096647316114483 absolute error = 0.23051685779727227993622564297678 relative error = 15.15807141293670222830555738613 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.072 y[1] (analytic) = 1.521631131058552774700965186707 y[1] (numeric) = 1.2908523833076120029824329012021 absolute error = 0.23077874775094077171853228550486 relative error = 15.166536951067436034708410223754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.073 y[1] (analytic) = 1.5225095290942996371771154331449 y[1] (numeric) = 1.2914692911797858085366905907397 absolute error = 0.23104023791451382864042484240525 relative error = 15.174961699711233453687692490375 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.074 y[1] (analytic) = 1.5233884046204776144823793898327 y[1] (numeric) = 1.2920870776888137962510783153468 absolute error = 0.23130132693166381823130107448583 relative error = 15.183345641211442318297834859586 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.075 y[1] (analytic) = 1.5242677567582112536784044916836 y[1] (numeric) = 1.2927057433117469992682072855874 absolute error = 0.23156201344646425441019720609617 relative error = 15.191688758079270202881804832999 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.076 y[1] (analytic) = 1.5251475846281484903108939111643 y[1] (numeric) = 1.2933252885247573368987328989431 absolute error = 0.2318222961033911534121610122212 relative error = 15.199991032993213541426223899074 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.077 y[1] (analytic) = 1.5260278873504615277615977332555 y[1] (numeric) = 1.2939457138031371384494751101503 absolute error = 0.23208217354732438931212262310525 relative error = 15.208252448798487483618498565448 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.078 y[1] (analytic) = 1.5269086640448477170760362547213 y[1] (numeric) = 1.2945670196212986679311287320728 absolute error = 0.23234164442354904914490752264851 relative error = 15.216472988506456492938641702061 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.079 y[1] (analytic) = 1.527789913830530437266075580037 y[1] (numeric) = 1.2951892064527736496460389593611 absolute error = 0.23260070737775678762003662067589 relative error = 15.224652635294065691078280986709 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.08 y[1] (analytic) = 1.528671635826259976086475211474 y[1] (numeric) = 1.2958122747702127946565165270828 absolute error = 0.23285936105604718142995868439113 relative error = 15.232791372503272952939332987505 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.081 y[1] (analytic) = 1.5295538291503144112845268568664 y[1] (numeric) = 1.2964362250453853281341660359699 absolute error = 0.23311760410492908315036082089645 relative error = 15.240889183640481756424964592339 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.082 y[1] (analytic) = 1.5304364929205004923219032054952 y[1] (numeric) = 1.2970610577491785175907000949149 absolute error = 0.23337543517132197473120311058033 relative error = 15.248946052375974791195768141076 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.083 y[1] (analytic) = 1.5313196262541545225678349503138 y[1] (numeric) = 1.2976867733515972019907110498625 absolute error = 0.2336328529025573205771239004513 relative error = 15.256961962543348330524542763201 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.084 y[1] (analytic) = 1.5322032282681432419627338634115 y[1] (numeric) = 1.2983133723217633217468711862861 absolute error = 0.2338898559463799202158626771254 relative error = 15.264936898138947370343702096449 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.085 y[1] (analytic) = 1.533087298078864710151379261166 y[1] (numeric) = 1.2989408551279154495980314100089 absolute error = 0.23414644295094926055334785115708 relative error = 15.272870843321301539540117779271 % h = 0.001 TOP MAIN SOLVE Loop NO POLE memory used=225.0MB, alloc=4.5MB, time=12.67 x[1] = 1.086 y[1] (analytic) = 1.5339718348022491900847847259714 y[1] (numeric) = 1.299569222237408322370687528233 absolute error = 0.23440261256484086771409719773844 relative error = 15.280763782410561785513158883754 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.087 y[1] (analytic) = 1.5348568375537600320898614827493 y[1] (numeric) = 1.3001984741167123736242823692702 absolute error = 0.23465836343704765846557911347907 relative error = 15.288615699887937838972799792015 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.088 y[1] (analytic) = 1.5357423054483945584059943606521 y[1] (numeric) = 1.3008286112314132671808110956343 absolute error = 0.23491369421698129122518326501778 relative error = 15.296426580395136461915942917792 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.089 y[1] (analytic) = 1.5366282376006849481876458034578 y[1] (numeric) = 1.3014596340462114315391961808496 absolute error = 0.23516860355447351664844962260826 relative error = 15.30419640873380048268053812983 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.09 y[1] (analytic) = 1.5375146331246991229721029261249 y[1] (numeric) = 1.3020915430249215951748976355628 absolute error = 0.23542309009977752779720529056204 relative error = 15.311925169864948621938677732404 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.091 y[1] (analytic) = 1.5384014911340416326114821498343 y[1] (numeric) = 1.3027243386304723227252231833097 absolute error = 0.23567715250356930988625896652456 relative error = 15.319612848908416113451604382639 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.092 y[1] (analytic) = 1.5392888107418545416681054835882 y[1] (numeric) = 1.3033580213249055520608022005858 absolute error = 0.23593078941694898960730328300236 relative error = 15.327259431142296123371489350086 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.093 y[1] (analytic) = 1.5401765910608183162723620570624 y[1] (numeric) = 1.3039925915693761322436863497111 absolute error = 0.23618399949144218402867570735138 relative error = 15.334864902002381971836920021165 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.094 y[1] (analytic) = 1.5410648312031527114421680469252 y[1] (numeric) = 1.3046280498241513623725389463472 absolute error = 0.236436781379001349069629100578 relative error = 15.342429247081610160571278483848 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.095 y[1] (analytic) = 1.5419535302806176588631376772364 y[1] (numeric) = 1.3052643965486105313153742164418 absolute error = 0.23668913373200712754776346079462 relative error = 15.349952452129504210155597354536 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.096 y[1] (analytic) = 1.5428426874045141551285775138303 y[1] (numeric) = 1.3059016322012444583303067098201 absolute error = 0.23694105520326969679827080401024 relative error = 15.357434503051619310610044682408 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.097 y[1] (analytic) = 1.5437323016856851504384158127608 y[1] (numeric) = 1.3065397572396550345747702496371 absolute error = 0.23719254444603011586364556312369 relative error = 15.364875385908987788880916733322 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.098 y[1] (analytic) = 1.5446223722345164377561782239551 y[1] (numeric) = 1.3071787721205547655036649084339 absolute error = 0.23744360011396167225251331552117 relative error = 15.372275086917565396792905657314 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.099 y[1] (analytic) = 1.5455128981609375424231206931733 y[1] (numeric) = 1.3078186772997663141568896126116 absolute error = 0.2376942208611712282662310805617 relative error = 15.379633592447678422989458416529 % h = 0.001 TOP MAIN SOLVE Loop NO POLE x[1] = 1.1 y[1] (analytic) = 1.5464038785744226122286299482153 y[1] (numeric) = 1.3084594732322220453367170877529 absolute error = 0.23794440534220056689191286046237 relative error = 15.386950889023471632347253824546 % h = 0.001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 2 ) = sin(x); Iterations = 1000 Total Elapsed Time = 12 Seconds Elapsed Time(since restart) = 12 Seconds Expected Time Remaining = 49 Seconds Optimized Time Remaining = 49 Seconds Time to Timeout = 14 Minutes 47 Seconds Percent Done = 20.43 % > quit memory used=228.5MB, alloc=4.5MB, time=12.85