|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 1 - 1; > while ((m >= 10) and ((abs(array_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 - 1 - 1; > cnt := 0; > while ((cnt < 5) and (n >= 10)) do # do number 2 > if (abs(array_y_higher[1,n]) > glob_small_float) then # if number 1 > cnt := cnt + 1; > else > cnt := 0; > fi;# end if 1 > ; > n := n - 1; > od;# end do number 2 > ; > m := n + cnt; > if (m <= 10) then # if number 1 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > elif (abs(array_y_higher[1,m]) >= (glob_large_float)) or (abs(array_y_higher[1,m-1]) >=(glob_large_float)) or (abs(array_y_higher[1,m-2]) >= (glob_large_float)) or (abs(array_y_higher[1,m-3]) >= (glob_large_float)) or (abs(array_y_higher[1,m-4]) >= (glob_large_float)) or (abs(array_y_higher[1,m-5]) >= (glob_large_float)) then # if number 2 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > rm0 := (array_y_higher[1,m])/(array_y_higher[1,m-1]); > rm1 := (array_y_higher[1,m-1])/(array_y_higher[1,m-2]); > rm2 := (array_y_higher[1,m-2])/(array_y_higher[1,m-3]); > rm3 := (array_y_higher[1,m-3])/(array_y_higher[1,m-4]); > rm4 := (array_y_higher[1,m-4])/(array_y_higher[1,m-5]); > nr1 := convfloat(m-1)*rm0 - 2.0*convfloat(m-2)*rm1 + convfloat(m-3)*rm2; > nr2 := convfloat(m-2)*rm1 - 2.0*convfloat(m-3)*rm2 + convfloat(m-4)*rm3; > dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3; > dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4; > ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; > ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; > if ((abs(nr1 * dr2 - nr2 * dr1) <= glob_small_float) or (abs(dr1) <= glob_small_float)) then # if number 3 > array_complex_pole[1,1] := glob_large_float; > array_complex_pole[1,2] := glob_large_float; > else > if (abs(nr1*dr2 - nr2 * dr1) > glob_small_float) then # if number 4 > rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1)); > #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1) > ord_no := (rcs*nr1 - ds1)/(2.0*dr1) -convfloat(m)/2.0; > if (abs(rcs) > glob_small_float) then # if number 5 > if (rcs > 0.0) then # if number 6 > rad_c := sqrt(rcs) * glob_h; > else > rad_c := glob_large_float; > fi;# end if 6 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 5 > else > rad_c := glob_large_float; > ord_no := glob_large_float; > fi;# end if 4 > fi;# end if 3 > ; > array_complex_pole[1,1] := rad_c; > array_complex_pole[1,2] := ord_no; > fi;# end if 2 > ; > #BOTTOM RADII COMPLEX EQ = 1 > found := false; > #TOP WHICH RADII EQ = 1 > if not found and ((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float)) and ((array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > found := true; > array_type_pole[1] := 2; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] <> glob_large_float) and (array_real_pole[1,2] <> glob_large_float) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float) or (array_complex_pole[1,1] <= 0.0 ) or (array_complex_pole[1,2] <= 0.0))) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and (((array_real_pole[1,1] = glob_large_float) or (array_real_pole[1,2] = glob_large_float)) and ((array_complex_pole[1,1] = glob_large_float) or (array_complex_pole[1,2] = glob_large_float))) then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > found := true; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_real_pole[1,1] < array_complex_pole[1,1]) and (array_real_pole[1,1] > 0.0) and (array_real_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_real_pole[1,1]; > array_poles[1,2] := array_real_pole[1,2]; > found := true; > array_type_pole[1] := 1; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Real estimate of pole used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found and ((array_complex_pole[1,1] <> glob_large_float) and (array_complex_pole[1,2] <> glob_large_float) and (array_complex_pole[1,1] > 0.0) and (array_complex_pole[1,2] > 0.0)) then # if number 2 > array_poles[1,1] := array_complex_pole[1,1]; > array_poles[1,2] := array_complex_pole[1,2]; > array_type_pole[1] := 2; > found := true; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"Complex estimate of poles used"); > fi;# end if 3 > ; > fi;# end if 2 > ; > if not found then # if number 2 > array_poles[1,1] := glob_large_float; > array_poles[1,2] := glob_large_float; > array_type_pole[1] := 3; > if (glob_display_flag) then # if number 3 > omniout_str(ALWAYS,"NO POLE"); > fi;# end if 3 > ; > fi;# end if 2 > ; > #BOTTOM WHICH RADII EQ = 1 > array_pole[1] := glob_large_float; > array_pole[2] := glob_large_float; > #TOP WHICH RADIUS EQ = 1 > if array_pole[1] > array_poles[1,1] then # if number 2 > array_pole[1] := array_poles[1,1]; > array_pole[2] := array_poles[1,2]; > fi;# end if 2 > ; > #BOTTOM WHICH RADIUS EQ = 1 > #BOTTOM CHECK FOR POLE > display_pole(); > # End Function number 6 > end; check_for_pole := proc() local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; n := glob_max_terms; m := n - 2; 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 - 2; cnt := 0; while cnt < 5 and 10 <= n do if glob_small_float < abs(array_y_higher[1, n]) then cnt := cnt + 1 else cnt := 0 end if; n := n - 1 end do; m := n + cnt; if m <= 10 then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float elif glob_large_float <= abs(array_y_higher[1, m]) or glob_large_float <= abs(array_y_higher[1, m - 1]) or glob_large_float <= abs(array_y_higher[1, m - 2]) or glob_large_float <= abs(array_y_higher[1, m - 3]) or glob_large_float <= abs(array_y_higher[1, m - 4]) or glob_large_float <= abs(array_y_higher[1, m - 5]) then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else rm0 := array_y_higher[1, m]/array_y_higher[1, m - 1]; rm1 := array_y_higher[1, m - 1]/array_y_higher[1, m - 2]; rm2 := array_y_higher[1, m - 2]/array_y_higher[1, m - 3]; rm3 := array_y_higher[1, m - 3]/array_y_higher[1, m - 4]; rm4 := array_y_higher[1, m - 4]/array_y_higher[1, m - 5]; nr1 := convfloat(m - 1)*rm0 - 2.0*convfloat(m - 2)*rm1 + convfloat(m - 3)*rm2; nr2 := convfloat(m - 2)*rm1 - 2.0*convfloat(m - 3)*rm2 + convfloat(m - 4)*rm3; dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3; dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4; ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3; ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4; if abs(nr1*dr2 - nr2*dr1) <= glob_small_float or abs(dr1) <= glob_small_float then array_complex_pole[1, 1] := glob_large_float; array_complex_pole[1, 2] := glob_large_float else if glob_small_float < abs(nr1*dr2 - nr2*dr1) then rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1); ord_no := (rcs*nr1 - ds1)/(2.0*dr1) - convfloat(m)/2.0; if glob_small_float < abs(rcs) then if 0. < rcs then rad_c := sqrt(rcs)*glob_h else rad_c := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if else rad_c := glob_large_float; ord_no := glob_large_float end if end if; array_complex_pole[1, 1] := rad_c; array_complex_pole[1, 2] := ord_no end if; found := false; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; found := true; array_type_pole[1] := 2; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found and array_real_pole[1, 1] <> glob_large_float and array_real_pole[1, 2] <> glob_large_float and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float or array_complex_pole[1, 1] <= 0. or array_complex_pole[1, 2] <= 0.) then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and (array_real_pole[1, 1] = glob_large_float or array_real_pole[1, 2] = glob_large_float) and ( array_complex_pole[1, 1] = glob_large_float or array_complex_pole[1, 2] = glob_large_float) then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; found := true; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; if not found and array_real_pole[1, 1] < array_complex_pole[1, 1] and 0. < array_real_pole[1, 1] and 0. < array_real_pole[1, 2] then array_poles[1, 1] := array_real_pole[1, 1]; array_poles[1, 2] := array_real_pole[1, 2]; found := true; array_type_pole[1] := 1; if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used") end if end if; if not found and array_complex_pole[1, 1] <> glob_large_float and array_complex_pole[1, 2] <> glob_large_float and 0. < array_complex_pole[1, 1] and 0. < array_complex_pole[1, 2] then array_poles[1, 1] := array_complex_pole[1, 1]; array_poles[1, 2] := array_complex_pole[1, 2]; array_type_pole[1] := 2; found := true; if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used") end if end if; if not found then array_poles[1, 1] := glob_large_float; array_poles[1, 2] := glob_large_float; array_type_pole[1] := 3; if glob_display_flag then omniout_str(ALWAYS, "NO POLE") end if end if; array_pole[1] := glob_large_float; array_pole[2] := glob_large_float; if array_poles[1, 1] < array_pole[1] then array_pole[1] := array_poles[1, 1]; array_pole[2] := array_poles[1, 2] end if; display_pole() end proc > # Begin Function number 7 > get_norms := proc() > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > > local kkk, order_d, adj2, temporary, term; > #TOP ATOMALL > #END OUTFILE1 > #BEGIN ATOMHDR1 > # emit pre mult $eq_no = 1 i = 1 > array_tmp1[1] := (array_y[1] * (array_y[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[1,2] then # if number 1 > if (1 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[1] * (glob_h ^ (1)) * factorial_3(0,1); > array_y[2] := temporary; > array_y_higher[1,2] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,1] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 2; > #END ATOMHDR1 > #BEGIN ATOMHDR2 > # emit pre mult $eq_no = 1 i = 2 > array_tmp1[2] := ats(2,array_y,array_y,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[1,3] then # if number 1 > if (2 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[2] * (glob_h ^ (1)) * factorial_3(1,2); > array_y[3] := temporary; > array_y_higher[1,3] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,2] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 3; > #END ATOMHDR2 > #BEGIN ATOMHDR3 > # emit pre mult $eq_no = 1 i = 3 > array_tmp1[3] := ats(3,array_y,array_y,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[1,4] then # if number 1 > if (3 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[3] * (glob_h ^ (1)) * factorial_3(2,3); > array_y[4] := temporary; > array_y_higher[1,4] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,3] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 4; > #END ATOMHDR3 > #BEGIN ATOMHDR4 > # emit pre mult $eq_no = 1 i = 4 > array_tmp1[4] := ats(4,array_y,array_y,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[1,5] then # if number 1 > if (4 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[4] * (glob_h ^ (1)) * factorial_3(3,4); > array_y[5] := temporary; > array_y_higher[1,5] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,4] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 5; > #END ATOMHDR4 > #BEGIN ATOMHDR5 > # emit pre mult $eq_no = 1 i = 5 > array_tmp1[5] := ats(5,array_y,array_y,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[1,6] then # if number 1 > if (5 <= glob_max_terms) then # if number 2 > temporary := array_tmp2[5] * (glob_h ^ (1)) * factorial_3(4,5); > array_y[6] := temporary; > array_y_higher[1,6] := temporary; > temporary := temporary / glob_h * (2.0); > array_y_higher[2,5] := temporary > ; > fi;# end if 2 > ; > fi;# end if 1 > ; > kkk := 6; > #END ATOMHDR5 > #BEGIN OUTFILE3 > #Top Atomall While Loop-- outfile3 > while (kkk <= glob_max_terms) do # do number 1 > #END OUTFILE3 > #BEGIN OUTFILE4 > #emit mult $eq_no = 1 > array_tmp1[kkk] := ats(kkk,array_y,array_y,1); > #emit add $eq_no = 1 > array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; > #emit assign $eq_no = 1 > order_d := 1; > if (kkk + order_d + 1 <= glob_max_terms) then # if number 1 > if not array_y_set_initial[1,kkk + order_d] then # if number 2 > temporary := array_tmp2[kkk] * (glob_h ^ (order_d)) / factorial_3((kkk - 1),(kkk + order_d - 1)); > array_y[kkk + order_d] := temporary; > array_y_higher[1,kkk + order_d] := temporary; > term := kkk + order_d - 1; > adj2 := 2; > while (adj2 <= order_d + 1) and (term >= 1) do # do number 2 > temporary := temporary / glob_h * convfp(adj2); > array_y_higher[adj2,term] := temporary; > adj2 := adj2 + 1; > term := term - 1; > od;# end do number 2 > fi;# end if 2 > fi;# end if 1 > ; > kkk := kkk + 1; > od;# end do number 1 > ; > #BOTTOM ATOMALL > #END OUTFILE4 > #BEGIN OUTFILE5 > # End Function number 8 > end; atomall := proc() local kkk, order_d, adj2, temporary, term; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; array_tmp1[1] := array_y[1]*array_y[1]; array_tmp2[1] := array_const_0D0[1] + array_tmp1[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp2[1]*glob_h*factorial_3(0, 1); array_y[2] := temporary; array_y_higher[1, 2] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 1] := temporary end if end if; kkk := 2; array_tmp1[2] := ats(2, array_y, array_y, 1); array_tmp2[2] := array_const_0D0[2] + array_tmp1[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp2[2]*glob_h*factorial_3(1, 2); array_y[3] := temporary; array_y_higher[1, 3] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 2] := temporary end if end if; kkk := 3; array_tmp1[3] := ats(3, array_y, array_y, 1); array_tmp2[3] := array_const_0D0[3] + array_tmp1[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp2[3]*glob_h*factorial_3(2, 3); array_y[4] := temporary; array_y_higher[1, 4] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 3] := temporary end if end if; kkk := 4; array_tmp1[4] := ats(4, array_y, array_y, 1); array_tmp2[4] := array_const_0D0[4] + array_tmp1[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp2[4]*glob_h*factorial_3(3, 4); array_y[5] := temporary; array_y_higher[1, 5] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 4] := temporary end if end if; kkk := 5; array_tmp1[5] := ats(5, array_y, array_y, 1); array_tmp2[5] := array_const_0D0[5] + array_tmp1[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp2[5]*glob_h*factorial_3(4, 5); array_y[6] := temporary; array_y_higher[1, 6] := temporary; temporary := temporary*2.0/glob_h; array_y_higher[2, 5] := temporary end if end if; kkk := 6; while kkk <= glob_max_terms do array_tmp1[kkk] := ats(kkk, array_y, array_y, 1); array_tmp2[kkk] := array_const_0D0[kkk] + array_tmp1[kkk]; order_d := 1; if kkk + order_d + 1 <= glob_max_terms then if not array_y_set_initial[1, kkk + order_d] then temporary := array_tmp2[kkk]*glob_h^order_d/ factorial_3(kkk - 1, kkk + order_d - 1); array_y[kkk + order_d] := temporary; array_y_higher[1, kkk + order_d] := temporary; term := kkk + order_d - 1; adj2 := 2; while adj2 <= order_d + 1 and 1 <= term do temporary := temporary*convfp(adj2)/glob_h; array_y_higher[adj2, term] := temporary; adj2 := adj2 + 1; term := term - 1 end do end if end if; kkk := kkk + 1 end do end proc > #BEGIN ATS LIBRARY BLOCK > omniout_str := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s\n",str); > fi; > # End Function number 1 > end; omniout_str := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s\n", str) end if end proc > omniout_str_noeol := proc(iolevel,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > printf("%s",str); > fi; > # End Function number 1 > end; omniout_str_noeol := proc(iolevel, str) global glob_iolevel; if iolevel <= glob_iolevel then printf("%s", str) end if end proc > omniout_labstr := proc(iolevel,label,str) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(label,str); > fi; > # End Function number 1 > end; omniout_labstr := proc(iolevel, label, str) global glob_iolevel; if iolevel <= glob_iolevel then print(label, str) end if end proc > omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 4 then > printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel); > else > printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 4 then printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel) else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel) end if end if end proc > omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > if vallen = 5 then > printf("%-30s = %-32d %s\n",prelabel,value, postlabel); > else > printf("%-30s = %-32d %s \n",prelabel,value, postlabel); > fi; > fi; > # End Function number 1 > end; omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then if vallen = 5 then printf("%-30s = %-32d %s\n", prelabel, value, postlabel) else printf("%-30s = %-32d %s \n", prelabel, value, postlabel) end if end if end proc > omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel) > global glob_iolevel; > if (glob_iolevel >= iolevel) then > print(prelabel,"[",elemnt,"]",value, postlabel); > fi; > # End Function number 1 > end; omniout_float_arr := proc( iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) global glob_iolevel; if iolevel <= glob_iolevel then print(prelabel, "[", elemnt, "]", value, postlabel) end if end proc > dump_series := proc(iolevel,dump_label,series_name, > array_series,numb) > global glob_iolevel; > local i; > if (glob_iolevel >= iolevel) then > i := 1; > while (i <= numb) do > print(dump_label,series_name > ,i,array_series[i]); > i := i + 1; > od; > fi; > # End Function number 1 > end; dump_series := proc(iolevel, dump_label, series_name, array_series, numb) local i; global glob_iolevel; if iolevel <= glob_iolevel then i := 1; while i <= numb do print(dump_label, series_name, i, array_series[i]); i := i + 1 end do end if end proc > dump_series_2 := proc(iolevel,dump_label,series_name2, > array_series2,numb,subnum,array_x) > global glob_iolevel; > local i,sub,ts_term; > if (glob_iolevel >= iolevel) then > sub := 1; > while (sub <= subnum) do > i := 1; > while (i <= numb) do > print(dump_label,series_name2,sub,i,array_series2[sub,i]); > od; > sub := sub + 1; > od; > fi; > # End Function number 1 > end; dump_series_2 := proc( iolevel, dump_label, series_name2, array_series2, numb, subnum, array_x) local i, sub, ts_term; global glob_iolevel; if iolevel <= glob_iolevel then sub := 1; while sub <= subnum do i := 1; while i <= numb do print(dump_label, series_name2, sub, i, array_series2[sub, i]) end do; sub := sub + 1 end do end if end proc > cs_info := proc(iolevel,str) > global glob_iolevel,glob_correct_start_flag,glob_h,glob_reached_optimal_h; > if (glob_iolevel >= iolevel) then > print("cs_info " , str , " glob_correct_start_flag = " , glob_correct_start_flag , "glob_h := " , glob_h , "glob_reached_optimal_h := " , glob_reached_optimal_h) > fi; > # End Function number 1 > end; cs_info := proc(iolevel, str) global glob_iolevel, glob_correct_start_flag, glob_h, glob_reached_optimal_h; if iolevel <= glob_iolevel then print("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h) end if end proc > # Begin Function number 2 > logitem_time := proc(fd,secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := (secs_in); > if (secs > 0.0) then # if number 1 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > fprintf(fd,""); > if (millinium_int > 0) then # if number 2 > fprintf(fd,"%d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 3 > fprintf(fd,"%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 4 > fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 5 > fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 6 > fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 7 > fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int); > else > fprintf(fd,"%d Seconds",sec_int); > fi;# end if 7 > else > fprintf(fd,"Unknown"); > fi;# end if 6 > fprintf(fd,""); > # End Function number 2 > end; logitem_time := proc(fd, secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := secs_in; if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); fprintf(fd, ""); if 0 < millinium_int then fprintf(fd, "%d Millinia %d Centuries %\ d Years %d Days %d Hours %d Minutes %d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then fprintf(fd, "%d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then fprintf(fd, "%d Years %d Days %d Hours %d Minutes %d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then fprintf(fd, "%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then fprintf(fd, "%d Hours %d Minutes %d Seconds", hours_int, minutes_int, sec_int) elif 0 < minutes_int then fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int) else fprintf(fd, "%d Seconds", sec_int) end if else fprintf(fd, "Unknown") end if; fprintf(fd, "") end proc > omniout_timestr := proc (secs_in) > global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; > local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; > secs := convfloat(secs_in); > if (secs > 0.0) then # if number 6 > sec_in_millinium := convfloat(sec_in_min * min_in_hour * hours_in_day * days_in_year * years_in_century * centuries_in_millinium); > milliniums := convfloat(secs / sec_in_millinium); > millinium_int := floor(milliniums); > centuries := (milliniums - millinium_int)*centuries_in_millinium; > cent_int := floor(centuries); > years := (centuries - cent_int) * years_in_century; > years_int := floor(years); > days := (years - years_int) * days_in_year; > days_int := floor(days); > hours := (days - days_int) * hours_in_day; > hours_int := floor(hours); > minutes := (hours - hours_int) * min_in_hour; > minutes_int := floor(minutes); > seconds := (minutes - minutes_int) * sec_in_min; > sec_int := floor(seconds); > > if (millinium_int > 0) then # if number 7 > printf(" = %d Millinia %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",millinium_int,cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (cent_int > 0) then # if number 8 > printf(" = %d Centuries %d Years %d Days %d Hours %d Minutes %d Seconds\n",cent_int,years_int,days_int,hours_int,minutes_int,sec_int); > elif (years_int > 0) then # if number 9 > printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int); > elif (days_int > 0) then # if number 10 > printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int); > elif (hours_int > 0) then # if number 11 > printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int); > elif (minutes_int > 0) then # if number 12 > printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int); > else > printf(" = %d Seconds\n",sec_int); > fi;# end if 12 > else > printf(" Unknown\n"); > fi;# end if 11 > # End Function number 2 > end; omniout_timestr := proc(secs_in) local cent_int, centuries, days, days_int, hours, hours_int, millinium_int, milliniums, minutes, minutes_int, sec_in_millinium, sec_int, seconds, secs, years, years_int; global centuries_in_millinium, days_in_year, hours_in_day, min_in_hour, sec_in_min, years_in_century; secs := convfloat(secs_in); if 0. < secs then sec_in_millinium := convfloat(sec_in_min*min_in_hour*hours_in_day* days_in_year*years_in_century*centuries_in_millinium); milliniums := convfloat(secs/sec_in_millinium); millinium_int := floor(milliniums); centuries := (milliniums - millinium_int)*centuries_in_millinium; cent_int := floor(centuries); years := (centuries - cent_int)*years_in_century; years_int := floor(years); days := (years - years_int)*days_in_year; days_int := floor(days); hours := (days - days_int)*hours_in_day; hours_int := floor(hours); minutes := (hours - hours_int)*min_in_hour; minutes_int := floor(minutes); seconds := (minutes - minutes_int)*sec_in_min; sec_int := floor(seconds); if 0 < millinium_int then printf(" = %d Millinia %d Centuries %d\ Years %d Days %d Hours %d Minutes %d Seconds\n", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < cent_int then printf(" = %d Centuries %d Years %d Days \ %d Hours %d Minutes %d Seconds\n", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < years_int then printf( " = %d Years %d Days %d Hours %d Minutes %d Seconds\n", years_int, days_int, hours_int, minutes_int, sec_int) elif 0 < days_int then printf( " = %d Days %d Hours %d Minutes %d Seconds\n", days_int, hours_int, minutes_int, sec_int) elif 0 < hours_int then printf( " = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int, sec_int) elif 0 < minutes_int then printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int) else printf(" = %d Seconds\n", sec_int) end if else printf(" Unknown\n") end if end proc > > # Begin Function number 3 > ats := proc( > mmm_ats,array_a,array_b,jjj_ats) > local iii_ats, lll_ats,ma_ats, ret_ats; > ret_ats := 0.0; > if (jjj_ats <= mmm_ats) then # if number 11 > ma_ats := mmm_ats + 1; > iii_ats := jjj_ats; > while (iii_ats <= mmm_ats) do # do number 1 > lll_ats := ma_ats - iii_ats; > ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; > iii_ats := iii_ats + 1; > od;# end do number 1 > fi;# end if 11 > ; > ret_ats > # End Function number 3 > end; ats := proc(mmm_ats, array_a, array_b, jjj_ats) local iii_ats, lll_ats, ma_ats, ret_ats; ret_ats := 0.; if jjj_ats <= mmm_ats then ma_ats := mmm_ats + 1; iii_ats := jjj_ats; while iii_ats <= mmm_ats do lll_ats := ma_ats - iii_ats; ret_ats := ret_ats + array_a[iii_ats]*array_b[lll_ats]; iii_ats := iii_ats + 1 end do end if; ret_ats end proc > > # Begin Function number 4 > att := proc( > mmm_att,array_aa,array_bb,jjj_att) > global glob_max_terms; > local al_att, iii_att,lll_att, ma_att, ret_att; > ret_att := 0.0; > if (jjj_att <= mmm_att) then # if number 11 > ma_att := mmm_att + 2; > iii_att := jjj_att; > while (iii_att <= mmm_att) do # do number 1 > lll_att := ma_att - iii_att; > al_att := (lll_att - 1); > if (lll_att <= glob_max_terms) then # if number 12 > ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]* convfp(al_att); > fi;# end if 12 > ; > iii_att := iii_att + 1; > od;# end do number 1 > ; > ret_att := ret_att / convfp(mmm_att) ; > fi;# end if 11 > ; > ret_att; > # End Function number 4 > end; att := proc(mmm_att, array_aa, array_bb, jjj_att) local al_att, iii_att, lll_att, ma_att, ret_att; global glob_max_terms; ret_att := 0.; if jjj_att <= mmm_att then ma_att := mmm_att + 2; iii_att := jjj_att; while iii_att <= mmm_att do lll_att := ma_att - iii_att; al_att := lll_att - 1; if lll_att <= glob_max_terms then ret_att := ret_att + array_aa[iii_att]*array_bb[lll_att]*convfp(al_att) end if; iii_att := iii_att + 1 end do; ret_att := ret_att/convfp(mmm_att) end if; ret_att end proc > # Begin Function number 5 > display_pole := proc() > global ALWAYS,glob_display_flag, glob_large_float, array_pole; > if ((array_pole[1] <> glob_large_float) and (array_pole[1] > 0.0) and (array_pole[2] <> glob_large_float) and (array_pole[2]> 0.0) and glob_display_flag) then # if number 11 > omniout_float(ALWAYS,"Radius of convergence ",4, array_pole[1],4," "); > omniout_float(ALWAYS,"Order of pole ",4, array_pole[2],4," "); > fi;# end if 11 > # End Function number 5 > end; display_pole := proc() global ALWAYS, glob_display_flag, glob_large_float, array_pole; if array_pole[1] <> glob_large_float and 0. < array_pole[1] and array_pole[2] <> glob_large_float and 0. < array_pole[2] and glob_display_flag then omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole[1], 4, " "); omniout_float(ALWAYS, "Order of pole ", 4, array_pole[2], 4, " ") end if end proc > # Begin Function number 6 > logditto := proc(file) > fprintf(file,""); > fprintf(file,"ditto"); > fprintf(file,""); > # End Function number 6 > end; logditto := proc(file) fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, "") end proc > # Begin Function number 7 > logitem_integer := proc(file,n) > fprintf(file,""); > fprintf(file,"%d",n); > fprintf(file,""); > # End Function number 7 > end; logitem_integer := proc(file, n) fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, "") end proc > # Begin Function number 8 > logitem_str := proc(file,str) > fprintf(file,""); > fprintf(file,str); > fprintf(file,""); > # End Function number 8 > end; logitem_str := proc(file, str) fprintf(file, ""); fprintf(file, str); fprintf(file, "") end proc > # Begin Function number 9 > log_revs := proc(file,revs) > fprintf(file,revs); > # End Function number 9 > end; log_revs := proc(file, revs) fprintf(file, revs) end proc > # Begin Function number 10 > logitem_float := proc(file,x) > fprintf(file,""); > fprintf(file,"%g",x); > fprintf(file,""); > # End Function number 10 > end; logitem_float := proc(file, x) fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, "") end proc > # Begin Function number 11 > logitem_pole := proc(file,pole) > fprintf(file,""); > if pole = 0 then # if number 11 > fprintf(file,"NA"); > elif pole = 1 then # if number 12 > fprintf(file,"Real"); > elif pole = 2 then # if number 13 > fprintf(file,"Complex"); > else > fprintf(file,"No Pole"); > fi;# end if 13 > fprintf(file,""); > # End Function number 11 > end; logitem_pole := proc(file, pole) fprintf(file, ""); if pole = 0 then fprintf(file, "NA") elif pole = 1 then fprintf(file, "Real") elif pole = 2 then fprintf(file, "Complex") else fprintf(file, "No Pole") end if; fprintf(file, "") end proc > # Begin Function number 12 > logstart := proc(file) > fprintf(file,""); > # End Function number 12 > end; logstart := proc(file) fprintf(file, "") end proc > # Begin Function number 13 > logend := proc(file) > fprintf(file,"\n"); > # End Function number 13 > end; logend := proc(file) fprintf(file, "\n") end proc > # Begin Function number 14 > chk_data := proc() > global glob_max_iter,ALWAYS, glob_max_terms; > local errflag; > errflag := false; > > if ((glob_max_terms < 15) or (glob_max_terms > 512)) then # if number 13 > omniout_str(ALWAYS,"Illegal max_terms = -- Using 30"); > glob_max_terms := 30; > fi;# end if 13 > ; > if (glob_max_iter < 2) then # if number 13 > omniout_str(ALWAYS,"Illegal max_iter"); > errflag := true; > fi;# end if 13 > ; > if (errflag) then # if number 13 > > quit; > fi;# end if 13 > # End Function number 14 > end; chk_data := proc() local errflag; global glob_max_iter, ALWAYS, glob_max_terms; errflag := false; if glob_max_terms < 15 or 512 < glob_max_terms then omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"); glob_max_terms := 30 end if; if glob_max_iter < 2 then omniout_str(ALWAYS, "Illegal max_iter"); errflag := true end if; if errflag then quit end if end proc > > # Begin Function number 15 > comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec) > global glob_small_float; > local ms2, rrr, sec_left, sub1, sub2; > ; > ms2 := clock_sec; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (sub1 = 0.0) then # if number 13 > sec_left := 0.0; > else > if (abs(sub2) > 0.0) then # if number 14 > rrr := (sub1/sub2); > sec_left := rrr * ms2 - ms2; > else > sec_left := 0.0; > fi;# end if 14 > fi;# end if 13 > ; > sec_left; > # End Function number 15 > end; comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec) local ms2, rrr, sec_left, sub1, sub2; global glob_small_float; ms2 := clock_sec; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if sub1 = 0. then sec_left := 0. else if 0. < abs(sub2) then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2 else sec_left := 0. end if end if; sec_left end proc > > # Begin Function number 16 > comp_percent := proc(t_end2,t_start2,t2) > global glob_small_float; > local rrr, sub1, sub2; > sub1 := (t_end2-t_start2); > sub2 := (t2-t_start2); > if (abs(sub2) > glob_small_float) then # if number 13 > rrr := (100.0*sub2)/sub1; > else > rrr := 0.0; > fi;# end if 13 > ; > rrr > # End Function number 16 > end; comp_percent := proc(t_end2, t_start2, t2) local rrr, sub1, sub2; global glob_small_float; sub1 := t_end2 - t_start2; sub2 := t2 - t_start2; if glob_small_float < abs(sub2) then rrr := 100.0*sub2/sub1 else rrr := 0. end if; rrr end proc > > # Begin Function number 17 > factorial_1 := proc(nnn) > nnn!; > > # End Function number 17 > end; factorial_1 := proc(nnn) nnn! end proc > > # Begin Function number 18 > factorial_3 := proc(mmm2,nnn2) > (mmm2!)/(nnn2!); > > # End Function number 18 > end; factorial_3 := proc(mmm2, nnn2) mmm2!/nnn2! end proc > # Begin Function number 19 > convfp := proc(mmm) > (mmm); > > # End Function number 19 > end; convfp := proc(mmm) mmm end proc > # Begin Function number 20 > convfloat := proc(mmm) > (mmm); > > # End Function number 20 > end; convfloat := proc(mmm) mmm end proc > elapsed_time_seconds := proc() > time(); > end; elapsed_time_seconds := proc() time() end proc > > > > #END ATS LIBRARY BLOCK > #BEGIN USER DEF BLOCK > #BEGIN USER DEF BLOCK > exact_soln_y := proc(x) > 1.0/(1.0 - x); > end; exact_soln_y := proc(x) 1.0/(1.0 - x) end proc > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > ALWAYS, > glob_max_terms, > DEBUGL, > INFO, > DEBUGMASSIVE, > glob_iolevel, > #Top Generate Globals Decl > glob_log10relerr, > glob_start, > glob_abserr, > glob_hmin_init, > glob_almost_1, > glob_display_flag, > glob_dump, > glob_normmax, > glob_orig_start_sec, > glob_look_poles, > days_in_year, > min_in_hour, > glob_html_log, > glob_max_minutes, > glob_max_sec, > glob_unchanged_h_cnt, > glob_smallish_float, > glob_log10_relerr, > djd_debug, > glob_percent_done, > glob_max_iter, > glob_last_good_h, > centuries_in_millinium, > glob_current_iter, > glob_optimal_start, > glob_max_rel_trunc_err, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_iter, > glob_warned, > glob_max_hours, > glob_relerr, > glob_hmax, > glob_not_yet_finished, > glob_clock_sec, > glob_curr_iter_when_opt, > glob_warned2, > glob_optimal_clock_start_sec, > glob_reached_optimal_h, > djd_debug2, > glob_max_opt_iter, > glob_subiter_method, > glob_log10abserr, > glob_no_eqs, > glob_hmin, > MAX_UNCHANGED, > glob_large_float, > years_in_century, > hours_in_day, > glob_optimal_expect_sec, > glob_small_float, > glob_log10_abserr, > glob_clock_start_sec, > glob_log10normmin, > glob_max_trunc_err, > glob_dump_analytic, > glob_disp_incr, > glob_not_yet_start_msg, > sec_in_min, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_0D0, > array_const_1, > #END CONST > array_y, > array_x, > array_last_rel_error, > array_type_pole, > array_tmp0, > array_tmp1, > array_tmp2, > array_norms, > array_y_init, > array_1st_rel_error, > array_m1, > array_pole, > array_real_pole, > array_y_higher_work, > array_y_set_initial, > array_y_higher_work2, > array_y_higher, > array_complex_pole, > array_poles, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > ALWAYS := 1; > glob_max_terms := 30; > DEBUGL := 3; > INFO := 2; > DEBUGMASSIVE := 4; > glob_iolevel := 5; > glob_log10relerr := 0.0; > glob_start := 0; > glob_abserr := 0.1e-10; > glob_hmin_init := 0.001; > glob_almost_1 := 0.9990; > glob_display_flag := true; > glob_dump := false; > glob_normmax := 0.0; > glob_orig_start_sec := 0.0; > glob_look_poles := false; > days_in_year := 365.0; > min_in_hour := 60.0; > glob_html_log := true; > glob_max_minutes := 0.0; > glob_max_sec := 10000.0; > glob_unchanged_h_cnt := 0; > glob_smallish_float := 0.1e-100; > glob_log10_relerr := 0.1e-10; > djd_debug := true; > glob_percent_done := 0.0; > glob_max_iter := 1000; > glob_last_good_h := 0.1; > centuries_in_millinium := 10.0; > glob_current_iter := 0; > glob_optimal_start := 0.0; > glob_max_rel_trunc_err := 0.1e-10; > glob_h := 0.1; > glob_optimal_done := false; > glob_initial_pass := true; > glob_iter := 0; > glob_warned := false; > glob_max_hours := 0.0; > glob_relerr := 0.1e-10; > glob_hmax := 1.0; > glob_not_yet_finished := true; > glob_clock_sec := 0.0; > glob_curr_iter_when_opt := 0; > glob_warned2 := false; > glob_optimal_clock_start_sec := 0.0; > glob_reached_optimal_h := false; > djd_debug2 := true; > glob_max_opt_iter := 10; > glob_subiter_method := 3; > glob_log10abserr := 0.0; > glob_no_eqs := 0; > glob_hmin := 0.00000000001; > MAX_UNCHANGED := 10; > glob_large_float := 9.0e100; > years_in_century := 100.0; > hours_in_day := 24.0; > glob_optimal_expect_sec := 0.1; > glob_small_float := 0.1e-50; > glob_log10_abserr := 0.1e-10; > glob_clock_start_sec := 0.0; > glob_log10normmin := 0.1; > glob_max_trunc_err := 0.1e-10; > glob_dump_analytic := false; > glob_disp_incr := 0.1; > glob_not_yet_start_msg := true; > sec_in_min := 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/nonlinear1postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = y * y;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 32;"); > omniout_str(ALWAYS,"max_terms := 30;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#END FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"x_start := 0.0;"); > omniout_str(ALWAYS,"x_end := 0.5 ;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.01;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000000;"); > omniout_str(ALWAYS,"#END SECOND INPUT BLOCK"); > omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK"); > omniout_str(ALWAYS,"glob_h := 0.0001 ;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 1000;"); > omniout_str(ALWAYS,"glob_max_minutes := 15;"); > omniout_str(ALWAYS,"#END OVERRIDE BLOCK"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK"); > omniout_str(ALWAYS,"exact_soln_y := proc(x)"); > omniout_str(ALWAYS,"1.0/(1.0 - x);"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 32; > max_terms := 30; > #END FIRST INPUT BLOCK > #START OF INITS AFTER INPUT BLOCK > glob_max_terms := max_terms; > glob_html_log := true; > #END OF INITS AFTER INPUT BLOCK > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_tmp0:= Array(1..(max_terms + 1),[]); > array_tmp1:= Array(1..(max_terms + 1),[]); > array_tmp2:= Array(1..(max_terms + 1),[]); > array_norms:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > 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_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_type_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_norms[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_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_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_higher_work[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=2 do # do number 2 > term := 1; > while term <= max_terms do # do number 3 > array_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 <=2 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 <=2 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 <=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 > ; > #BEGIN ARRAYS DEFINED AND INITIALIZATED > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_const_1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_1[1] := 1; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := 0.0; > x_end := 0.5 ; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.01; > glob_look_poles := true; > glob_max_iter := 1000000; > #END SECOND INPUT BLOCK > #BEGIN OVERRIDE BLOCK > glob_h := 0.0001 ; > 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] := false; > 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 := 1; > #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 := 1; > #START PART 1 SUM AND ADJUST > #START SUM AND ADJUST EQ =1 > #sum_and_adjust array_y > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 2; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[2,iii] := array_y_higher[2,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 2; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 2; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 2; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #BEFORE ADJUST SUBSERIES EQ =1 > ord := 1; > calc_term := 1; > #adjust_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > array_y_higher_work[1,iii] := array_y_higher[1,iii] / (glob_h ^ (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1); > iii := iii - 1; > od;# end do number 3 > ; > #AFTER ADJUST SUBSERIES EQ =1 > #BEFORE SUM SUBSERIES EQ =1 > temp_sum := 0.0; > ord := 1; > calc_term := 1; > #sum_subseriesarray_y > iii := glob_max_terms; > while (iii >= calc_term) do # do number 3 > temp_sum := temp_sum + array_y_higher_work[ord,iii]; > iii := iii - 1; > od;# end do number 3 > ; > array_y_higher_work2[ord,calc_term] := temp_sum * (glob_h ^ (calc_term - 1)) / (convfp(calc_term - 1)!); > #AFTER SUM SUBSERIES EQ =1 > #END SUM AND ADJUST EQ =1 > #END PART 1 > #START PART 2 MOVE TERMS to REGULAR Array > term_no := glob_max_terms; > while (term_no >= 1) do # do number 3 > array_y[term_no] := array_y_higher_work2[1,term_no]; > ord := 1; > while ord <= order_diff do # do number 4 > array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no]; > ord := ord + 1; > od;# end do number 4 > ; > term_no := term_no - 1; > od;# end do number 3 > ; > #END PART 2 HEVE MOVED TERMS to REGULAR Array > display_alot(current_iter) > ; > od;# end do number 2 > ;#right paren 0001C > omniout_str(ALWAYS,"Finished!"); > if (glob_iter >= glob_max_iter) then # if number 2 > omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!") > fi;# end if 2 > ; > if (elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec )) then # if number 2 > omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!") > fi;# end if 2 > ; > glob_clock_sec := elapsed_time_seconds(); > omniout_str(INFO,"diff ( y , x , 1 ) = y * y;"); > 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,"2012-06-13T18:11:49-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"nonlinear1") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = y * y;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"nonlinear1 diffeq.mxt") > ; > logitem_str(html_log_file,"nonlinear1 maple results") > ; > logitem_str(html_log_file,"Test of revised logic - mostly affecting systems of eqs") > ; > logend(html_log_file) > ; > ; > fi;# end if 2 > ; > if glob_html_log then # if number 2 > fclose(html_log_file); > fi;# end if 2 > ; > ;; > #END OUTFILEMAIN > # End Function number 8 > end; mainprog := proc() local d1, d2, d3, d4, est_err_2, niii, done_once, term, ord, order_diff, term_no, html_log_file, rows, r_order, sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it, log10norm, max_terms, opt_iter, tmp; global ALWAYS, glob_max_terms, DEBUGL, INFO, DEBUGMASSIVE, glob_iolevel, glob_log10relerr, glob_start, glob_abserr, glob_hmin_init, glob_almost_1, glob_display_flag, glob_dump, glob_normmax, glob_orig_start_sec, glob_look_poles, days_in_year, min_in_hour, glob_html_log, glob_max_minutes, glob_max_sec, glob_unchanged_h_cnt, glob_smallish_float, glob_log10_relerr, djd_debug, glob_percent_done, glob_max_iter, glob_last_good_h, centuries_in_millinium, glob_current_iter, glob_optimal_start, glob_max_rel_trunc_err, glob_h, glob_optimal_done, glob_initial_pass, glob_iter, glob_warned, glob_max_hours, glob_relerr, glob_hmax, glob_not_yet_finished, glob_clock_sec, glob_curr_iter_when_opt, glob_warned2, glob_optimal_clock_start_sec, glob_reached_optimal_h, djd_debug2, glob_max_opt_iter, glob_subiter_method, glob_log10abserr, glob_no_eqs, glob_hmin, MAX_UNCHANGED, glob_large_float, years_in_century, hours_in_day, glob_optimal_expect_sec, glob_small_float, glob_log10_abserr, glob_clock_start_sec, glob_log10normmin, glob_max_trunc_err, glob_dump_analytic, glob_disp_incr, glob_not_yet_start_msg, sec_in_min, array_const_0D0, array_const_1, array_y, array_x, array_last_rel_error, array_type_pole, array_tmp0, array_tmp1, array_tmp2, array_norms, array_y_init, array_1st_rel_error, array_m1, array_pole, array_real_pole, array_y_higher_work, array_y_set_initial, array_y_higher_work2, array_y_higher, array_complex_pole, array_poles, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; ALWAYS := 1; glob_max_terms := 30; DEBUGL := 3; INFO := 2; DEBUGMASSIVE := 4; glob_iolevel := 5; glob_log10relerr := 0.; glob_start := 0; glob_abserr := 0.1*10^(-10); glob_hmin_init := 0.001; glob_almost_1 := 0.9990; glob_display_flag := true; glob_dump := false; glob_normmax := 0.; glob_orig_start_sec := 0.; glob_look_poles := false; days_in_year := 365.0; min_in_hour := 60.0; glob_html_log := true; glob_max_minutes := 0.; glob_max_sec := 10000.0; glob_unchanged_h_cnt := 0; glob_smallish_float := 0.1*10^(-100); glob_log10_relerr := 0.1*10^(-10); djd_debug := true; glob_percent_done := 0.; glob_max_iter := 1000; glob_last_good_h := 0.1; centuries_in_millinium := 10.0; glob_current_iter := 0; glob_optimal_start := 0.; glob_max_rel_trunc_err := 0.1*10^(-10); glob_h := 0.1; glob_optimal_done := false; glob_initial_pass := true; glob_iter := 0; glob_warned := false; glob_max_hours := 0.; glob_relerr := 0.1*10^(-10); glob_hmax := 1.0; glob_not_yet_finished := true; glob_clock_sec := 0.; glob_curr_iter_when_opt := 0; glob_warned2 := false; glob_optimal_clock_start_sec := 0.; glob_reached_optimal_h := false; djd_debug2 := true; glob_max_opt_iter := 10; glob_subiter_method := 3; glob_log10abserr := 0.; glob_no_eqs := 0; glob_hmin := 0.1*10^(-10); MAX_UNCHANGED := 10; glob_large_float := 0.90*10^101; years_in_century := 100.0; hours_in_day := 24.0; glob_optimal_expect_sec := 0.1; glob_small_float := 0.1*10^(-50); glob_log10_abserr := 0.1*10^(-10); glob_clock_start_sec := 0.; glob_log10normmin := 0.1; glob_max_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; glob_disp_incr := 0.1; glob_not_yet_start_msg := true; sec_in_min := 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/nonlinear1postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = y * y;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 32;"); omniout_str(ALWAYS, "max_terms := 30;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#END FIRST INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK"); omniout_str(ALWAYS, "x_start := 0.0;"); omniout_str(ALWAYS, "x_end := 0.5 ;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.01;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000000;"); omniout_str(ALWAYS, "#END SECOND INPUT BLOCK"); omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK"); omniout_str(ALWAYS, "glob_h := 0.0001 ;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 1000;"); omniout_str(ALWAYS, "glob_max_minutes := 15;"); omniout_str(ALWAYS, "#END OVERRIDE BLOCK"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK"); omniout_str(ALWAYS, "exact_soln_y := proc(x)"); omniout_str(ALWAYS, "1.0/(1.0 - x);"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 32; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_tmp0 := Array(1 .. max_terms + 1, []); array_tmp1 := Array(1 .. max_terms + 1, []); array_tmp2 := Array(1 .. max_terms + 1, []); array_norms := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_poles := Array(1 .. 2, 1 .. 4, []); 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_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_type_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_norms[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_1st_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_pole[term] := 0.; term := term + 1 end do; 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_higher_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_set_initial[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_y_higher_work2[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 2 do term := 1; while term <= max_terms do array_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 <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_const_1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_1[term] := 0.; term := term + 1 end do; array_const_1[1] := 1; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := 0.; x_end := 0.5; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; glob_h := 0.0001; 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] := false; 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 := 1; 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 := 1; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[2, iii] := array_y_higher[2, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 2; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 2; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do array_y_higher_work[1, iii] := array_y_higher[1, iii]/( glob_h^(calc_term - 1)* factorial_3(iii - calc_term, iii - 1)); iii := iii - 1 end do; temp_sum := 0.; ord := 1; calc_term := 1; iii := glob_max_terms; while calc_term <= iii do temp_sum := temp_sum + array_y_higher_work[ord, iii]; iii := iii - 1 end do; array_y_higher_work2[ord, calc_term] := temp_sum*glob_h^(calc_term - 1)/convfp(calc_term - 1)!; term_no := glob_max_terms; while 1 <= term_no do array_y[term_no] := array_y_higher_work2[1, term_no]; ord := 1; while ord <= order_diff do array_y_higher[ord, term_no] := array_y_higher_work2[ord, term_no]; ord := ord + 1 end do; term_no := term_no - 1 end do; display_alot(current_iter) end do; omniout_str(ALWAYS, "Finished!"); if glob_max_iter <= glob_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!") end if; if convfloat(glob_max_sec) <= elapsed_time_seconds() - convfloat(glob_orig_start_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!") end if; glob_clock_sec := elapsed_time_seconds(); omniout_str(INFO, "diff ( y , x , 1 ) = y * y;"); 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, "2012-06-13T18:11:49-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "nonlinear1"); logitem_str(html_log_file, "diff ( y , x , 1 ) = y * y;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "nonlinear1 diffeq.mxt"); logitem_str(html_log_file, "nonlinear1 maple results"); logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"); logend(html_log_file) end if; if glob_html_log then fclose(html_log_file) end if end proc > mainprog(); ##############ECHO OF PROBLEM################# ##############temp/nonlinear1postode.ode################# diff ( y , x , 1 ) = y * y; ! #BEGIN FIRST INPUT BLOCK Digits := 32; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := 0.0; x_end := 0.5 ; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.01; glob_look_poles := true; glob_max_iter := 1000000; #END SECOND INPUT BLOCK #BEGIN OVERRIDE BLOCK glob_h := 0.0001 ; glob_look_poles := true; glob_max_iter := 1000; glob_max_minutes := 15; #END OVERRIDE BLOCK ! #BEGIN USER DEF BLOCK exact_soln_y := proc(x) 1.0/(1.0 - x); end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = 0 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0001 y[1] (analytic) = 1.0001000100010001000100010001 y[1] (numeric) = 1.0001000100010001000100360539925 absolute error = 3.50538925e-23 relative error = 3.5050387110750000000000000000000e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0002 y[1] (analytic) = 1.0002000400080016003200640128026 y[1] (numeric) = 1.000200040008001600320134152153 absolute error = 7.01393504e-23 relative error = 7.0125322529919999999999999999997e-21 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0003 y[1] (analytic) = 1.0003000900270081024307292187656 y[1] (numeric) = 1.0003000900270081024308344751669 absolute error = 1.052564013e-22 relative error = 1.0522482437961000000000000000000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0004 y[1] (analytic) = 1.0004001600640256102440976390556 y[1] (numeric) = 1.000400160064025610244238044128 absolute error = 1.404050724e-22 relative error = 1.4034891037104000000000000000000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0005 y[1] (analytic) = 1.0005002501250625312656328164082 y[1] (numeric) = 1.0005002501250625312658084017993 absolute error = 1.755853911e-22 relative error = 1.7549759840445000000000000000000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0006 y[1] (analytic) = 1.0006003602161296778066840104062 y[1] (numeric) = 1.0006003602161296778068948077912 absolute error = 2.107973850e-22 relative error = 2.1067090656900000000000000000001e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0007 y[1] (analytic) = 1.0007004903432402681877314119884 y[1] (numeric) = 1.0007004903432402681879774530698 absolute error = 2.460410814e-22 relative error = 2.4586885264302000000000000000000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0008 y[1] (analytic) = 1.0008006405124099279423538831065 y[1] (numeric) = 1.0008006405124099279426351996145 absolute error = 2.813165080e-22 relative error = 2.8109145479360000000000000000000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0009 y[1] (analytic) = 1.000900810729656691021919727755 y[1] (numeric) = 1.0009008107296566910222363514472 absolute error = 3.166236922e-22 relative error = 3.1633873087701999999999999999999e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=2.8MB, time=0.13 NO POLE x[1] = 0.001 y[1] (analytic) = 1.001001001001001001001001001001 y[1] (numeric) = 1.0010010010010010010013529636626 absolute error = 3.519626616e-22 relative error = 3.5161069893840000000000000000000e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0011 y[1] (analytic) = 1.0011012113324657122835118630494 y[1] (numeric) = 1.0011012113324657122838991964931 absolute error = 3.873334437e-22 relative error = 3.8690737691192999999999999999998e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0012 y[1] (analytic) = 1.0012014417300760913095714857829 y[1] (numeric) = 1.0012014417300760913099942218493 absolute error = 4.227360664e-22 relative error = 4.2222878312032000000000000000002e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0013 y[1] (analytic) = 1.0013016921998598177630920196255 y[1] (numeric) = 1.0013016921998598177635501901824 absolute error = 4.581705569e-22 relative error = 4.5757493517603000000000000000001e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0014 y[1] (analytic) = 1.0014019627478469857800921289806 y[1] (numeric) = 1.0014019627478469857805857659237 absolute error = 4.936369431e-22 relative error = 4.9294585137965999999999999999999e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0015 y[1] (analytic) = 1.0015022533800701051577366049074 y[1] (numeric) = 1.0015022533800701051582657401601 absolute error = 5.291352527e-22 relative error = 5.2834154982094999999999999999998e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0016 y[1] (analytic) = 1.0016025641025641025641025641026 y[1] (numeric) = 1.0016025641025641025646672296159 absolute error = 5.646655133e-22 relative error = 5.6376204847871999999999999999998e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0017 y[1] (analytic) = 1.0017028949213663227486727436642 y[1] (numeric) = 1.001702894921366322749272971417 absolute error = 6.002277528e-22 relative error = 5.9920736562024000000000000000002e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0018 y[1] (analytic) = 1.0018032458425165297535564015227 y[1] (numeric) = 1.0018032458425165297541922235215 absolute error = 6.358219988e-22 relative error = 6.3467751920216000000000000000003e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0019 y[1] (analytic) = 1.0019036168720569081254383328324 y[1] (numeric) = 1.0019036168720569081261097811115 absolute error = 6.714482791e-22 relative error = 6.7017252736970999999999999999999e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.002 y[1] (analytic) = 1.0020040080160320641282565130261 y[1] (numeric) = 1.0020040080160320641289636196476 absolute error = 7.071066215e-22 relative error = 7.0569240825699999999999999999997e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0021 y[1] (analytic) = 1.0021044192804890269566088786452 y[1] (numeric) = 1.0021044192804890269573516756991 absolute error = 7.427970539e-22 relative error = 7.4123718008680999999999999999997e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0022 y[1] (analytic) = 1.0022048506714772499498897574664 y[1] (numeric) = 1.0022048506714772499506682770707 absolute error = 7.785196043e-22 relative error = 7.7680686117054000000000000000002e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0023 y[1] (analytic) = 1.0023053021950486118071564598577 y[1] (numeric) = 1.002305302195048611807970734158 absolute error = 8.142743003e-22 relative error = 8.1240146940930999999999999999998e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0024 y[1] (analytic) = 1.0024057738572574178027265437049 y[1] (numeric) = 1.0024057738572574178035766048749 absolute error = 8.500611700e-22 relative error = 8.4802102319199999999999999999999e-20 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=3.8MB, time=0.29 NO POLE x[1] = 0.0025 y[1] (analytic) = 1.0025062656641604010025062656642 y[1] (numeric) = 1.0025062656641604010033921459054 absolute error = 8.858802412e-22 relative error = 8.8366554059699999999999999999997e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0026 y[1] (analytic) = 1.0026067776218167234810507319029 y[1] (numeric) = 1.002606777621816723481972463445 absolute error = 9.217315421e-22 relative error = 9.1933504009054000000000000000004e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0027 y[1] (analytic) = 1.0027073097362879775393562619071 y[1] (numeric) = 1.0027073097362879775403138770076 absolute error = 9.576151005e-22 relative error = 9.5502953972865000000000000000005e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0028 y[1] (analytic) = 1.0028078620136381869233854793422 y[1] (numeric) = 1.0028078620136381869243790102866 absolute error = 9.935309444e-22 relative error = 9.9074905775567999999999999999996e-20 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0029 y[1] (analytic) = 1.0029084344599338080433256443687 y[1] (numeric) = 1.0029084344599338080443551234707 absolute error = 1.0294791020e-21 relative error = 1.0264936126042000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.003 y[1] (analytic) = 1.0030090270812437311935807422267 y[1] (numeric) = 1.003009027081243731194646201828 absolute error = 1.0654596013e-21 relative error = 1.0622632224961000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0031 y[1] (analytic) = 1.0031096398836392817734978433143 y[1] (numeric) = 1.0031096398836392817745993157847 absolute error = 1.1014724704e-21 relative error = 1.0980579057417600000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0032 y[1] (analytic) = 1.0032102728731942215088282504013 y[1] (numeric) = 1.0032102728731942215099657681387 absolute error = 1.1375177374e-21 relative error = 1.1338776806403200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0033 y[1] (analytic) = 1.0033109260559847496739239490318 y[1] (numeric) = 1.0033109260559847496750975444623 absolute error = 1.1735954305e-21 relative error = 1.1697225655793500000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0034 y[1] (analytic) = 1.0034115994380895043146698775838 y[1] (numeric) = 1.0034115994380895043158795831616 absolute error = 1.2097055778e-21 relative error = 1.2055925788354800000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0035 y[1] (analytic) = 1.0035122930255895634721525338685 y[1] (numeric) = 1.0035122930255895634733983820761 absolute error = 1.2458482076e-21 relative error = 1.2414877388734000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0036 y[1] (analytic) = 1.003613006824568446407065435568 y[1] (numeric) = 1.0036130068245684464083474589161 absolute error = 1.2820233481e-21 relative error = 1.2774080640468400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0037 y[1] (analytic) = 1.0037137408411121148248519522232 y[1] (numeric) = 1.0037137408411121148261701832507 absolute error = 1.3182310275e-21 relative error = 1.3133535726982500000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0038 y[1] (analytic) = 1.0038144950813089741015860269022 y[1] (numeric) = 1.0038144950813089741029404981763 absolute error = 1.3544712741e-21 relative error = 1.3493242832584200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0039 y[1] (analytic) = 1.0039152695512498745105913060938 y[1] (numeric) = 1.00391526955124987451198205021 absolute error = 1.3907441162e-21 relative error = 1.3853202141468200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=11.4MB, alloc=3.9MB, time=0.44 x[1] = 0.004 y[1] (analytic) = 1.0040160642570281124497991967871 y[1] (numeric) = 1.0040160642570281124512262463694 absolute error = 1.4270495823e-21 relative error = 1.4213413839708000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0041 y[1] (analytic) = 1.0041168792047394316698463701175 y[1] (numeric) = 1.004116879204739431671309757818 absolute error = 1.4633877005e-21 relative error = 1.4573878109279500000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0042 y[1] (analytic) = 1.0042177144004820245029122313718 y[1] (numeric) = 1.0042177144004820245044119898712 absolute error = 1.4997584994e-21 relative error = 1.4934595137025199999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0043 y[1] (analytic) = 1.0043185698503565330922968765692 y[1] (numeric) = 1.0043185698503565330938330385766 absolute error = 1.5361620074e-21 relative error = 1.5295565107681800000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0044 y[1] (analytic) = 1.0044194455604660506227400562475 y[1] (numeric) = 1.0044194455604660506243126545002 absolute error = 1.5725982527e-21 relative error = 1.5656788203881200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0045 y[1] (analytic) = 1.0045203415369161225514816675038 y[1] (numeric) = 1.0045203415369161225530907347678 absolute error = 1.6090672640e-21 relative error = 1.6018264613119999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0046 y[1] (analytic) = 1.0046212577858147478400642957605 y[1] (numeric) = 1.0046212577858147478417098648303 absolute error = 1.6455690698e-21 relative error = 1.6379994520789200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0047 y[1] (analytic) = 1.0047221943132723801868783281423 y[1] (numeric) = 1.0047221943132723801885604318408 absolute error = 1.6821036985e-21 relative error = 1.6741978111170499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0048 y[1] (analytic) = 1.0048231511254019292604501607717 y[1] (numeric) = 1.0048231511254019292621688319505 absolute error = 1.7186711788e-21 relative error = 1.7104215571417600000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0049 y[1] (analytic) = 1.0049241282283187619334740227113 y[1] (numeric) = 1.0049241282283187619352292942504 absolute error = 1.7552715391e-21 relative error = 1.7466707085584100000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.005 y[1] (analytic) = 1.0050251256281407035175879396985 y[1] (numeric) = 1.0050251256281407035193798445066 absolute error = 1.7919048081e-21 relative error = 1.7829452840595000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0051 y[1] (analytic) = 1.0051261433309880389988943612423 y[1] (numeric) = 1.0051261433309880390007229322568 absolute error = 1.8285710145e-21 relative error = 1.8192453023260500000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0052 y[1] (analytic) = 1.0052271813429835142742259750704 y[1] (numeric) = 1.0052271813429835142760912452571 absolute error = 1.8652701867e-21 relative error = 1.8555707817291599999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0053 y[1] (analytic) = 1.0053282396702523373881572333367 y[1] (numeric) = 1.0053282396702523373900592356904 absolute error = 1.9020023537e-21 relative error = 1.8919217412253900000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0054 y[1] (analytic) = 1.0054293183189221797707621154233 y[1] (numeric) = 1.0054293183189221797727008829673 absolute error = 1.9387675440e-21 relative error = 1.9282981992624000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0055 y[1] (analytic) = 1.0055304172951231774761186525892 y[1] (numeric) = 1.0055304172951231774780942183756 absolute error = 1.9755657864e-21 relative error = 1.9647001745748000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=3.9MB, time=0.59 NO POLE x[1] = 0.0056 y[1] (analytic) = 1.0056315366049879324215607401448 y[1] (numeric) = 1.0056315366049879324235731372544 absolute error = 2.0123971096e-21 relative error = 2.0011276857862400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0057 y[1] (analytic) = 1.0057326762546515136276777632505 y[1] (numeric) = 1.005732676254651513629727024793 absolute error = 2.0492615425e-21 relative error = 2.0375807517077500000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0058 y[1] (analytic) = 1.0058338362502514584590625628646 y[1] (numeric) = 1.0058338362502514584611487219785 absolute error = 2.0861591139e-21 relative error = 2.0740593910393800000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0059 y[1] (analytic) = 1.0059350165979277738658082687858 y[1] (numeric) = 1.0059350165979277738679313586384 absolute error = 2.1230898526e-21 relative error = 2.1105636224696600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.006 y[1] (analytic) = 1.006036217303822937625754527163 y[1] (numeric) = 1.0060362173038229376279145809504 absolute error = 2.1600537874e-21 relative error = 2.1470934646756000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0061 y[1] (analytic) = 1.0061374383740818995874836502666 y[1] (numeric) = 1.006137438374081899589680701214 absolute error = 2.1970509474e-21 relative error = 2.1836489366208600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0062 y[1] (analytic) = 1.0062386798148520829140672167438 y[1] (numeric) = 1.0062386798148520829163012981051 absolute error = 2.2340813613e-21 relative error = 2.2202300568599400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0063 y[1] (analytic) = 1.0063399416322833853275636510013 y[1] (numeric) = 1.0063399416322833853298347960595 absolute error = 2.2711450582e-21 relative error = 2.2568368443333400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0064 y[1] (analytic) = 1.006441223832528180354267310789 y[1] (numeric) = 1.0064412238325281803565755528561 absolute error = 2.3082420671e-21 relative error = 2.2934693178705600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0065 y[1] (analytic) = 1.0065425264217413185707096124811 y[1] (numeric) = 1.0065425264217413185730549848979 absolute error = 2.3453724168e-21 relative error = 2.3301274960908000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0066 y[1] (analytic) = 1.0066438494060801288504127239783 y[1] (numeric) = 1.0066438494060801288527952601148 absolute error = 2.3825361365e-21 relative error = 2.3668113979990999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0067 y[1] (analytic) = 1.0067451927917044196113963555824 y[1] (numeric) = 1.0067451927917044196138160888377 absolute error = 2.4197332553e-21 relative error = 2.4035210424894900000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0068 y[1] (analytic) = 1.0068465565847764800644381796214 y[1] (numeric) = 1.0068465565847764800668951434236 absolute error = 2.4569638022e-21 relative error = 2.4402564483450400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0069 y[1] (analytic) = 1.0069479407914610814620884100292 y[1] (numeric) = 1.0069479407914610814645826378355 absolute error = 2.4942278063e-21 relative error = 2.4770176344365300000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.007 y[1] (analytic) = 1.0070493454179254783484390735146 y[1] (numeric) = 1.0070493454179254783509705988114 absolute error = 2.5315252968e-21 relative error = 2.5138046197224000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=19.0MB, alloc=3.9MB, time=0.75 x[1] = 0.0071 y[1] (analytic) = 1.0071507704703394098096485043811 y[1] (numeric) = 1.0071507704703394098122173606839 absolute error = 2.5688563028e-21 relative error = 2.5506174230501200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0072 y[1] (analytic) = 1.0072522159548751007252215954875 y[1] (numeric) = 1.0072522159548751007278278163411 absolute error = 2.6062208536e-21 relative error = 2.5874560634540800000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0073 y[1] (analytic) = 1.0073536818777072630200463382694 y[1] (numeric) = 1.0073536818777072630226899572477 absolute error = 2.6436189783e-21 relative error = 2.6243205597584099999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0074 y[1] (analytic) = 1.0074551682450130969171871851703 y[1] (numeric) = 1.0074551682450130969198682358766 absolute error = 2.6810507063e-21 relative error = 2.6612109310733799999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0075 y[1] (analytic) = 1.007556675062972292191435768262 y[1] (numeric) = 1.0075566750629722921941542843288 absolute error = 2.7185160668e-21 relative error = 2.6981271962989999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0076 y[1] (analytic) = 1.0076582023377670294236195082628 y[1] (numeric) = 1.0076582023377670294263755233519 absolute error = 2.7560150891e-21 relative error = 2.7350693744228400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0077 y[1] (analytic) = 1.0077597500755819812556686485942 y[1] (numeric) = 1.0077597500755819812584621963967 absolute error = 2.7935478025e-21 relative error = 2.7720374844207499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0078 y[1] (analytic) = 1.0078613182826043136464422495465 y[1] (numeric) = 1.0078613182826043136492733637829 absolute error = 2.8311142364e-21 relative error = 2.8090315453560799999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0079 y[1] (analytic) = 1.0079629069650236871283136780566 y[1] (numeric) = 1.0079629069650236871311823924769 absolute error = 2.8687144203e-21 relative error = 2.8460515763796300000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.008 y[1] (analytic) = 1.0080645161290322580645161290323 y[1] (numeric) = 1.0080645161290322580674224774156 absolute error = 2.9063483833e-21 relative error = 2.8830975962335999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0081 y[1] (analytic) = 1.0081661457808246799072487145882 y[1] (numeric) = 1.0081661457808246799101927307433 absolute error = 2.9440161551e-21 relative error = 2.9201696242436899999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0082 y[1] (analytic) = 1.0082677959265981044565436579956 y[1] (numeric) = 1.0082677959265981044595253757607 absolute error = 2.9817177651e-21 relative error = 2.9572676794261799999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0083 y[1] (analytic) = 1.0083694665725521831198951295755 y[1] (numeric) = 1.0083694665725521831229145828184 absolute error = 3.0194532429e-21 relative error = 2.9943917809839299999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0084 y[1] (analytic) = 1.0084711577248890681726502622025 y[1] (numeric) = 1.0084711577248890681757074848204 absolute error = 3.0572226179e-21 relative error = 3.0315419479096400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0085 y[1] (analytic) = 1.0085728693898134140191628845184 y[1] (numeric) = 1.0085728693898134140222579104381 absolute error = 3.0950259197e-21 relative error = 3.0687181993825500000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0086 y[1] (analytic) = 1.0086746015735323784547105103893 y[1] (numeric) = 1.0086746015735323784578433735672 absolute error = 3.1328631779e-21 relative error = 3.1059205545700600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.0MB, time=0.91 NO POLE x[1] = 0.0087 y[1] (analytic) = 1.0087763542822556239281751235751 y[1] (numeric) = 1.0087763542822556239313458579971 absolute error = 3.1707344220e-21 relative error = 3.1431490325286000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0088 y[1] (analytic) = 1.0088781275221953188054882970137 y[1] (numeric) = 1.0088781275221953188086969366955 absolute error = 3.2086396818e-21 relative error = 3.1804036526001600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0089 y[1] (analytic) = 1.0089799212995661386338411865604 y[1] (numeric) = 1.0089799212995661386370877655473 absolute error = 3.2465789869e-21 relative error = 3.2176844339165900000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.009 y[1] (analytic) = 1.0090817356205852674066599394551 y[1] (numeric) = 1.0090817356205852674099444918221 absolute error = 3.2845523670e-21 relative error = 3.2549913956970000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0091 y[1] (analytic) = 1.0091835704914723988293470582299 y[1] (numeric) = 1.0091835704914723988326696180817 absolute error = 3.3225598518e-21 relative error = 3.2923245571486200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0092 y[1] (analytic) = 1.0092854259184497375857892612031 y[1] (numeric) = 1.0092854259184497375891498626741 absolute error = 3.3606014710e-21 relative error = 3.3296839374667999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0093 y[1] (analytic) = 1.0093873019077420006056323811446 y[1] (numeric) = 1.0093873019077420006090310583992 absolute error = 3.3986772546e-21 relative error = 3.3670695561322200000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0094 y[1] (analytic) = 1.0094891984655764183323238441349 y[1] (numeric) = 1.009489198465576418335760631367 absolute error = 3.4367872321e-21 relative error = 3.4044814321182599999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0095 y[1] (analytic) = 1.0095911155981827359919232710752 y[1] (numeric) = 1.0095911155981827359953982025088 absolute error = 3.4749314336e-21 relative error = 3.4419195849808000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0096 y[1] (analytic) = 1.0096930533117932148626817447496 y[1] (numeric) = 1.0096930533117932148661948546383 absolute error = 3.5131098887e-21 relative error = 3.4793840337684800000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0097 y[1] (analytic) = 1.009795011612642633545390285772 y[1] (numeric) = 1.0097950116126426335489416083995 absolute error = 3.5513226275e-21 relative error = 3.5168747980132500000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0098 y[1] (analytic) = 1.0098969905069682892344980811957 y[1] (numeric) = 1.0098969905069682892380876508755 absolute error = 3.5895696798e-21 relative error = 3.5543918969379600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0099 y[1] (analytic) = 1.009998990001009998990001009999 y[1] (numeric) = 1.0099989900010099989936288610746 absolute error = 3.6278510756e-21 relative error = 3.5919353499515600000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.01 y[1] (analytic) = 1.010101010101010101010101010101 y[1] (numeric) = 1.0101010101010101010137671769459 absolute error = 3.6661668449e-21 relative error = 3.6295051764510000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0101 y[1] (analytic) = 1.0102030508132134559046368320032 y[1] (numeric) = 1.0102030508132134559083413490208 absolute error = 3.7045170176e-21 relative error = 3.6671013957222400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0102 y[1] (analytic) = 1.0103051121438674479692867245908 y[1] (numeric) = 1.0103051121438674479730296262146 absolute error = 3.7429016238e-21 relative error = 3.7047240272372400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.0MB, time=1.06 NO POLE x[1] = 0.0103 y[1] (analytic) = 1.0104071940992219864605435990704 y[1] (numeric) = 1.010407194099221986464324919764 absolute error = 3.7813206936e-21 relative error = 3.7423730904559200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0104 y[1] (analytic) = 1.0105092966855295068714632174616 y[1] (numeric) = 1.0105092966855295068752829917186 absolute error = 3.8197742570e-21 relative error = 3.7800486047272000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0105 y[1] (analytic) = 1.0106114199090449722081859525013 y[1] (numeric) = 1.0106114199090449722120442148454 absolute error = 3.8582623441e-21 relative error = 3.8177505894869499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0106 y[1] (analytic) = 1.0107135637760258742672326662624 y[1] (numeric) = 1.0107135637760258742711294512475 absolute error = 3.8967849851e-21 relative error = 3.8554790642579399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0107 y[1] (analytic) = 1.010815728292732234913575255231 y[1] (numeric) = 1.0108157282927322349175105974412 absolute error = 3.9353422102e-21 relative error = 3.8932340485508599999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0108 y[1] (analytic) = 1.0109179134654266073594824100283 y[1] (numeric) = 1.0109179134654266073634563440779 absolute error = 3.9739340496e-21 relative error = 3.9310155618643200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0109 y[1] (analytic) = 1.0110201193003740774441411384087 y[1] (numeric) = 1.0110201193003740774481536989421 absolute error = 4.0125605334e-21 relative error = 3.9688236235859399999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.011 y[1] (analytic) = 1.0111223458038422649140546006067 y[1] (numeric) = 1.0111223458038422649181058222987 absolute error = 4.0512216920e-21 relative error = 4.0066582533879999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0111 y[1] (analytic) = 1.0112245929821013247042168065527 y[1] (numeric) = 1.0112245929821013247083067241084 absolute error = 4.0899175557e-21 relative error = 4.0445194708317300000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0112 y[1] (analytic) = 1.0113268608414239482200647249191 y[1] (numeric) = 1.0113268608414239482241933730737 absolute error = 4.1286481546e-21 relative error = 4.0824072952684800000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0113 y[1] (analytic) = 1.0114291493880853646202083544048 y[1] (numeric) = 1.011429149388085364624375767924 absolute error = 4.1674135192e-21 relative error = 4.1203217464330399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0114 y[1] (analytic) = 1.0115314586283633420999393081125 y[1] (numeric) = 1.0115314586283633421041455217924 absolute error = 4.2062136799e-21 relative error = 4.1582628439491399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0115 y[1] (analytic) = 1.0116337885685381891755184623166 y[1] (numeric) = 1.0116337885685381891797635109837 absolute error = 4.2450486671e-21 relative error = 4.1962306074283500000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0116 y[1] (analytic) = 1.0117361392148927559692432213679 y[1] (numeric) = 1.011736139214892755973527139879 absolute error = 4.2839185111e-21 relative error = 4.2342250563712399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0117 y[1] (analytic) = 1.0118385105737124354952949509258 y[1] (numeric) = 1.0118385105737124354996177741684 absolute error = 4.3228232426e-21 relative error = 4.2722462106615800000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=30.5MB, alloc=4.0MB, time=1.22 x[1] = 0.0118 y[1] (analytic) = 1.0119409026512851649463671321595 y[1] (numeric) = 1.0119409026512851649507288950513 absolute error = 4.3617628918e-21 relative error = 4.3102940896767599999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0119 y[1] (analytic) = 1.012043315453901426981074790001 y[1] (numeric) = 1.0120433154539014269854755274904 absolute error = 4.4007374894e-21 relative error = 4.3483687132761400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.012 y[1] (analytic) = 1.0121457489878542510121457489879 y[1] (numeric) = 1.0121457489878542510165854960537 absolute error = 4.4397470658e-21 relative error = 4.3864701010103999999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0121 y[1] (analytic) = 1.0122482032594392144953942706752 y[1] (numeric) = 1.0122482032594392144998730623269 absolute error = 4.4787916517e-21 relative error = 4.4245982727144299999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0122 y[1] (analytic) = 1.01235067827495444421947762705 y[1] (numeric) = 1.0123506782749544442239954983277 absolute error = 4.5178712777e-21 relative error = 4.4627532481120600000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0123 y[1] (analytic) = 1.0124531740407006175964361648274 y[1] (numeric) = 1.0124531740407006176009931508017 absolute error = 4.5569859743e-21 relative error = 4.5009350468161099999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0124 y[1] (analytic) = 1.0125556905629809639530174159579 y[1] (numeric) = 1.0125556905629809639576135517301 absolute error = 4.5961357722e-21 relative error = 4.5391436886247199999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0125 y[1] (analytic) = 1.0126582278481012658227848101266 y[1] (numeric) = 1.0126582278481012658274201308288 absolute error = 4.6353207022e-21 relative error = 4.5773791934224999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0126 y[1] (analytic) = 1.012760785902369860239011545473 y[1] (numeric) = 1.0127607859023698602436860862679 absolute error = 4.6745407949e-21 relative error = 4.6156415808842599999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0127 y[1] (analytic) = 1.0128633647320976400283601742125 y[1] (numeric) = 1.0128633647320976400330739702936 absolute error = 4.7137960811e-21 relative error = 4.6539308708700300000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0128 y[1] (analytic) = 1.0129659643435980551053484602917 y[1] (numeric) = 1.0129659643435980551101015468833 absolute error = 4.7530865916e-21 relative error = 4.6922470832275200000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0129 y[1] (analytic) = 1.0130685847431871137676020666599 y[1] (numeric) = 1.013068584743187113772394479017 absolute error = 4.7924123571e-21 relative error = 4.7305902376934100000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.013 y[1] (analytic) = 1.0131712259371833839918946301925 y[1] (numeric) = 1.013171225937183383996726403601 absolute error = 4.8317734085e-21 relative error = 4.7689603541895000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0131 y[1] (analytic) = 1.0132738879319079947309757827541 y[1] (numeric) = 1.0132738879319079947358469525307 absolute error = 4.8711697766e-21 relative error = 4.8073574525265399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0132 y[1] (analytic) = 1.0133765707336846372111876773409 y[1] (numeric) = 1.0133765707336846372160982788333 absolute error = 4.9106014924e-21 relative error = 4.8457815527003200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0133 y[1] (analytic) = 1.0134792743488395662308705786967 y[1] (numeric) = 1.0134792743488395662358206472834 absolute error = 4.9500685867e-21 relative error = 4.8842326744968899999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=34.3MB, alloc=4.0MB, time=1.38 NO POLE x[1] = 0.0134 y[1] (analytic) = 1.0135819987837016014595580782485 y[1] (numeric) = 1.0135819987837016014645476493391 absolute error = 4.9895710906e-21 relative error = 4.9227108379859600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0135 y[1] (analytic) = 1.0136847440446021287379624936645 y[1] (numeric) = 1.0136847440446021287429916026993 absolute error = 5.0291090348e-21 relative error = 4.9612160628301999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0136 y[1] (analytic) = 1.0137875101378751013787510137875 y[1] (numeric) = 1.0137875101378751013838196962381 absolute error = 5.0686824506e-21 relative error = 4.9997483692718400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0137 y[1] (analytic) = 1.0138902970698570414681131501572 y[1] (numeric) = 1.013890297069857041473221441526 absolute error = 5.1082913688e-21 relative error = 5.0383077770474399999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0138 y[1] (analytic) = 1.0139931048468870411681200567836 y[1] (numeric) = 1.0139931048468870411732679926043 absolute error = 5.1479358207e-21 relative error = 5.0768943063743400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0139 y[1] (analytic) = 1.0140959334753067640198762802961 y[1] (numeric) = 1.0140959334753067640250638961333 absolute error = 5.1876158372e-21 relative error = 5.1155079770629200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.014 y[1] (analytic) = 1.0141987829614604462474645030426 y[1] (numeric) = 1.0141987829614604462526918344921 absolute error = 5.2273314495e-21 relative error = 5.1541488092070000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0141 y[1] (analytic) = 1.0143016533116948980626838421747 y[1] (numeric) = 1.0143016533116948980679509248634 absolute error = 5.2670826887e-21 relative error = 5.1928168227893299999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0142 y[1] (analytic) = 1.0144045445323595049705822682086 y[1] (numeric) = 1.0144045445323595049758891377947 absolute error = 5.3068695861e-21 relative error = 5.2315120379773799999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0143 y[1] (analytic) = 1.0145074566298062290757837070102 y[1] (numeric) = 1.0145074566298062290811303991831 absolute error = 5.3466921729e-21 relative error = 5.2702344748275300000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0144 y[1] (analytic) = 1.0146103896103896103896103896104 y[1] (numeric) = 1.0146103896103896103949969400906 absolute error = 5.3865504802e-21 relative error = 5.3089841532851199999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0145 y[1] (analytic) = 1.0147133434804667681380010147133 y[1] (numeric) = 1.0147133434804667681434274592527 absolute error = 5.4264445394e-21 relative error = 5.3477610935787000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0146 y[1] (analytic) = 1.0148163182463974020702252892226 y[1] (numeric) = 1.0148163182463974020756916636043 absolute error = 5.4663743817e-21 relative error = 5.3865653157271800000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0147 y[1] (analytic) = 1.0149193139145437937683954125647 y[1] (numeric) = 1.0149193139145437937739017526031 absolute error = 5.5063400384e-21 relative error = 5.4253968398355200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0148 y[1] (analytic) = 1.0150223304912708079577750710516 y[1] (numeric) = 1.0150223304912708079633214125926 absolute error = 5.5463415410e-21 relative error = 5.4642556861931999999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0149 y[1] (analytic) = 1.0151253679829458938178865089839 y[1] (numeric) = 1.0151253679829458938234728879047 absolute error = 5.5863789208e-21 relative error = 5.5031418748800799999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=38.1MB, alloc=4.1MB, time=1.53 NO POLE x[1] = 0.015 y[1] (analytic) = 1.0152284263959390862944162436548 y[1] (numeric) = 1.0152284263959390863000426958641 absolute error = 5.6264522093e-21 relative error = 5.5420554261605000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0151 y[1] (analytic) = 1.0153315057366230074119199918773 y[1] (numeric) = 1.0153315057366230074175865533152 absolute error = 5.6665614379e-21 relative error = 5.5809963601877100000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0152 y[1] (analytic) = 1.015434606011372867587327376117 y[1] (numeric) = 1.015434606011372867593034082755 absolute error = 5.7067066380e-21 relative error = 5.6199646971023999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0153 y[1] (analytic) = 1.0155377272265664669442469787753 y[1] (numeric) = 1.0155377272265664669499938666165 absolute error = 5.7468878412e-21 relative error = 5.6589604572296399999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0154 y[1] (analytic) = 1.0156408693885841966280723136299 y[1] (numeric) = 1.0156408693885841966338594187089 absolute error = 5.7871050790e-21 relative error = 5.6979836607834000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0155 y[1] (analytic) = 1.0157440325038090401218892839005 y[1] (numeric) = 1.0157440325038090401277166422834 absolute error = 5.8273583829e-21 relative error = 5.7370343279650499999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0156 y[1] (analytic) = 1.0158472165786265745631856968712 y[1] (numeric) = 1.0158472165786265745690533446559 absolute error = 5.8676477847e-21 relative error = 5.7761124792586799999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0157 y[1] (analytic) = 1.0159504216194249720613634054658 y[1] (numeric) = 1.0159504216194249720672713787816 absolute error = 5.9079733158e-21 relative error = 5.8152181347419400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0158 y[1] (analytic) = 1.0160536476325950010160536476326 y[1] (numeric) = 1.0160536476325950010220019826405 absolute error = 5.9483350079e-21 relative error = 5.8543513147751800000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0159 y[1] (analytic) = 1.0161568946245300274362361548623 y[1] (numeric) = 1.0161568946245300274422248877551 absolute error = 5.9887328928e-21 relative error = 5.8935120398044800000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.016 y[1] (analytic) = 1.016260162601626016260162601626 y[1] (numeric) = 1.0162601626016260162661917686282 absolute error = 6.0291670022e-21 relative error = 5.9327003301648000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0161 y[1] (analytic) = 1.0163634515702815326760849679846 y[1] (numeric) = 1.0163634515702815326821546053523 absolute error = 6.0696373677e-21 relative error = 5.9719162060800299999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0162 y[1] (analytic) = 1.016466761536897743443789388087 y[1] (numeric) = 1.0164667615368977434498995321083 absolute error = 6.1101440213e-21 relative error = 6.0111596881549400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0163 y[1] (analytic) = 1.0165700925078784182169360577412 y[1] (numeric) = 1.0165700925078784182230867447357 absolute error = 6.1506869945e-21 relative error = 6.0504307964896499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0164 y[1] (analytic) = 1.0166734444896299308662057747052 y[1] (numeric) = 1.0166734444896299308723970410246 absolute error = 6.1912663194e-21 relative error = 6.0897295517618399999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0165 y[1] (analytic) = 1.016776817488561260803253685816 y[1] (numeric) = 1.0167768174885612608094855678437 absolute error = 6.2318820277e-21 relative error = 6.1290559742429499999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.1MB, time=1.69 NO POLE x[1] = 0.0166 y[1] (analytic) = 1.0168802115110839943054708155379 y[1] (numeric) = 1.0168802115110839943117433496894 absolute error = 6.2725341515e-21 relative error = 6.1684100845851000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0167 y[1] (analytic) = 1.0169836265636123258415539509814 y[1] (numeric) = 1.0169836265636123258478671737039 absolute error = 6.3132227225e-21 relative error = 6.2077919030342499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0168 y[1] (analytic) = 1.0170870626525630593978844589097 y[1] (numeric) = 1.0170870626525630594042384066824 absolute error = 6.3539477727e-21 relative error = 6.2472014501186399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0169 y[1] (analytic) = 1.0171905197843556098057166107212 y[1] (numeric) = 1.0171905197843556098121113200554 absolute error = 6.3947093342e-21 relative error = 6.2866387464520199999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.017 y[1] (analytic) = 1.0172939979654120040691759918616 y[1] (numeric) = 1.0172939979654120040756114993006 absolute error = 6.4355074390e-21 relative error = 6.3261038125370000000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0171 y[1] (analytic) = 1.0173974972021568826940685725913 y[1] (numeric) = 1.0173974972021568827005449147103 absolute error = 6.4763421190e-21 relative error = 6.3655966687651000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0172 y[1] (analytic) = 1.017501017501017501017501017501 y[1] (numeric) = 1.0175010175010175010240182309074 absolute error = 6.5172134064e-21 relative error = 6.4051173358099200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0173 y[1] (analytic) = 1.0176045588684237305383128116414 y[1] (numeric) = 1.0176045588684237305448709329747 absolute error = 6.5581213333e-21 relative error = 6.4446658342339100000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0174 y[1] (analytic) = 1.0177081213108080602483207815998 y[1] (numeric) = 1.0177081213108080602549198475316 absolute error = 6.5990659318e-21 relative error = 6.4842421845866800000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0175 y[1] (analytic) = 1.0178117048346055979643765903308 y[1] (numeric) = 1.0178117048346055979710166375648 absolute error = 6.6400472340e-21 relative error = 6.5238464074049999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0176 y[1] (analytic) = 1.0179153094462540716612377850163 y[1] (numeric) = 1.0179153094462540716679188502886 absolute error = 6.6810652723e-21 relative error = 6.5634785235075199999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0177 y[1] (analytic) = 1.0180189351521938308052529777054 y[1] (numeric) = 1.0180189351521938308119750977842 absolute error = 6.7221200788e-21 relative error = 6.6031385534052399999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0178 y[1] (analytic) = 1.0181225819588678476888617389534 y[1] (numeric) = 1.0181225819588678476956249506391 absolute error = 6.7632116857e-21 relative error = 6.6428265176945399999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0179 y[1] (analytic) = 1.0182262498727217187659097851543 y[1] (numeric) = 1.0182262498727217187727141252797 absolute error = 6.8043401254e-21 relative error = 6.6825424371553399999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.018 y[1] (analytic) = 1.0183299389002036659877800407332 y[1] (numeric) = 1.0183299389002036659946255461634 absolute error = 6.8455054302e-21 relative error = 6.7222863324564000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=45.7MB, alloc=4.1MB, time=1.85 x[1] = 0.0181 y[1] (analytic) = 1.0184336490477645381403401568388 y[1] (numeric) = 1.0184336490477645381472268644712 absolute error = 6.8867076324e-21 relative error = 6.7620582242535599999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0182 y[1] (analytic) = 1.0185373803218578121817070686494 y[1] (numeric) = 1.0185373803218578121886350154138 absolute error = 6.9279467644e-21 relative error = 6.8018581332879200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0183 y[1] (analytic) = 1.018641132728939594580829173882 y[1] (numeric) = 1.0186411327289395945877983967407 absolute error = 6.9692228587e-21 relative error = 6.8416860803857900000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0184 y[1] (analytic) = 1.0187449062754686226568867155664 y[1] (numeric) = 1.018744906275468622663897251514 absolute error = 7.0105359476e-21 relative error = 6.8815420861641600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0185 y[1] (analytic) = 1.0188487009679062659195109526235 y[1] (numeric) = 1.0188487009679062659265628386871 absolute error = 7.0518860636e-21 relative error = 6.9214261714234000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0186 y[1] (analytic) = 1.0189525168127165274098227022621 y[1] (numeric) = 1.0189525168127165274169159755013 absolute error = 7.0932732392e-21 relative error = 6.9613383569508799999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0187 y[1] (analytic) = 1.0190563538163660450422908386834 y[1] (numeric) = 1.0190563538163660450494255361904 absolute error = 7.1346975070e-21 relative error = 7.0012786636190999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0188 y[1] (analytic) = 1.0191602119853240929474113330616 y[1] (numeric) = 1.0191602119853240929545874919612 absolute error = 7.1761588996e-21 relative error = 7.0412471122875199999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0189 y[1] (analytic) = 1.0192640913260625828152074202426 y[1] (numeric) = 1.0192640913260625828224250776921 absolute error = 7.2176574495e-21 relative error = 7.0812437237044499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.019 y[1] (analytic) = 1.0193679918450560652395514780836 y[1] (numeric) = 1.019367991845056065246810671273 absolute error = 7.2591931894e-21 relative error = 7.1212685188013999999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0191 y[1] (analytic) = 1.0194719135487817310633092058314 y[1] (numeric) = 1.0194719135487817310706099719833 absolute error = 7.3007661519e-21 relative error = 7.1613215183987099999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0192 y[1] (analytic) = 1.0195758564437194127243066884176 y[1] (numeric) = 1.0195758564437194127316490647874 absolute error = 7.3423763698e-21 relative error = 7.2014027434998400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0193 y[1] (analytic) = 1.0196798205363515856021209340267 y[1] (numeric) = 1.0196798205363515856095049579023 absolute error = 7.3840238756e-21 relative error = 7.2415122148009200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0194 y[1] (analytic) = 1.0197838058331633693656944727718 y[1] (numeric) = 1.019783805833163369373120181474 absolute error = 7.4257087022e-21 relative error = 7.2816499533773199999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0195 y[1] (analytic) = 1.0198878123406425293217746047935 y[1] (numeric) = 1.0198878123406425293292420356759 absolute error = 7.4674308824e-21 relative error = 7.3218159801931999999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0196 y[1] (analytic) = 1.0199918400652794777641778865769 y[1] (numeric) = 1.0199918400652794777716870770259 absolute error = 7.5091904490e-21 relative error = 7.3620103161996000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.1MB, time=2.02 NO POLE x[1] = 0.0197 y[1] (analytic) = 1.0200958890135672753238804447618 y[1] (numeric) = 1.0200958890135672753314314321966 absolute error = 7.5509874348e-21 relative error = 7.4022329823344400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0198 y[1] (analytic) = 1.0201999591920016323199347072026 y[1] (numeric) = 1.0201999591920016323275275290753 absolute error = 7.5928218727e-21 relative error = 7.4424839996205400000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0199 y[1] (analytic) = 1.0203040506070809101112131415162 y[1] (numeric) = 1.0203040506070809101188478353117 absolute error = 7.6346937955e-21 relative error = 7.4827633889695499999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.02 y[1] (analytic) = 1.0204081632653061224489795918367 y[1] (numeric) = 1.0204081632653061224566561950731 absolute error = 7.6766032364e-21 relative error = 7.5230711716720000000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0201 y[1] (analytic) = 1.0205122971731809368302888049801 y[1] (numeric) = 1.0205122971731809368380073552082 absolute error = 7.7185502281e-21 relative error = 7.5634073685151900000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0202 y[1] (analytic) = 1.0206164523372116758522147377016 y[1] (numeric) = 1.0206164523372116758599752725053 absolute error = 7.7605348037e-21 relative error = 7.6037720006652599999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0203 y[1] (analytic) = 1.0207206287639073185669082372155 y[1] (numeric) = 1.0207206287639073185747107942118 absolute error = 7.8025569963e-21 relative error = 7.6441650892751099999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0204 y[1] (analytic) = 1.0208248264597795018374846876276 y[1] (numeric) = 1.0208248264597795018453293044665 absolute error = 7.8446168389e-21 relative error = 7.6845866553864400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0205 y[1] (analytic) = 1.020929045431342521694742215416 y[1] (numeric) = 1.0209290454313425217026289297806 absolute error = 7.8867143646e-21 relative error = 7.7250367201257000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0206 y[1] (analytic) = 1.0210332856851133346947110475802 y[1] (numeric) = 1.0210332856851133347026398971866 absolute error = 7.9288496064e-21 relative error = 7.7655153045081599999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0207 y[1] (analytic) = 1.0211375472276115592770346165629 y[1] (numeric) = 1.0211375472276115592850056391606 absolute error = 7.9710225977e-21 relative error = 7.8060224299276099999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0208 y[1] (analytic) = 1.0212418300653594771241830065359 y[1] (numeric) = 1.0212418300653594771321962399075 absolute error = 8.0132333716e-21 relative error = 7.8465581174707200000000000000004e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0209 y[1] (analytic) = 1.021346134204882034521499336125 y[1] (numeric) = 1.0213461342048820345295548180862 absolute error = 8.0554819612e-21 relative error = 7.8871223882109200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.021 y[1] (analytic) = 1.0214504596527068437180796731359 y[1] (numeric) = 1.0214504596527068437261774415357 absolute error = 8.0977683998e-21 relative error = 7.9277152634041999999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0211 y[1] (analytic) = 1.0215548064153641842884870773317 y[1] (numeric) = 1.0215548064153641842966271700525 absolute error = 8.1400927208e-21 relative error = 7.9683367643911200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0212 y[1] (analytic) = 1.0216591744993870044953003677973 y[1] (numeric) = 1.0216591744993870045034828227547 absolute error = 8.1824549574e-21 relative error = 8.0089869123031200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=53.4MB, alloc=4.1MB, time=2.17 NO POLE x[1] = 0.0213 y[1] (analytic) = 1.0217635639113109226524982119138 y[1] (numeric) = 1.0217635639113109226607230670567 absolute error = 8.2248551429e-21 relative error = 8.0496657283562299999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0214 y[1] (analytic) = 1.021867974657674228489679133456 y[1] (numeric) = 1.0218679746576742284979464267668 absolute error = 8.2672933108e-21 relative error = 8.0903732339488799999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0215 y[1] (analytic) = 1.021972406745017884517118037813 y[1] (numeric) = 1.0219724067450178845254278073075 absolute error = 8.3097694945e-21 relative error = 8.1311094503682499999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0216 y[1] (analytic) = 1.0220768601798855273916598528209 y[1] (numeric) = 1.0220768601798855274000121365483 absolute error = 8.3522837274e-21 relative error = 8.1718743988881600000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0217 y[1] (analytic) = 1.0221813349688234692834508841869 y[1] (numeric) = 1.0221813349688234692918457202298 absolute error = 8.3948360429e-21 relative error = 8.2126681007690699999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0218 y[1] (analytic) = 1.0222858311183806992435084849724 y[1] (numeric) = 1.0222858311183806992519459114471 absolute error = 8.4374264747e-21 relative error = 8.2534905775515400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0219 y[1] (analytic) = 1.0223903486351088845721296390962 y[1] (numeric) = 1.0223903486351088845806096941524 absolute error = 8.4800550562e-21 relative error = 8.2943418504692200000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.022 y[1] (analytic) = 1.0224948875255623721881390593047 y[1] (numeric) = 1.0224948875255623721966617811257 absolute error = 8.5227218210e-21 relative error = 8.3352219409380000000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0221 y[1] (analytic) = 1.0225994477962981899989774005522 y[1] (numeric) = 1.0225994477962981900075428273548 absolute error = 8.5654268026e-21 relative error = 8.3761308702625400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0222 y[1] (analytic) = 1.0227040294538760482716301902229 y[1] (numeric) = 1.0227040294538760482802383602577 absolute error = 8.6081700348e-21 relative error = 8.4170686600274400000000000000004e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0223 y[1] (analytic) = 1.0228086325048583410043980771198 y[1] (numeric) = 1.0228086325048583410130490286709 absolute error = 8.6509515511e-21 relative error = 8.4580353315104699999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0224 y[1] (analytic) = 1.0229132569558101472995090016367 y[1] (numeric) = 1.022913256955810147308202773022 absolute error = 8.6937713853e-21 relative error = 8.4990309062692799999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0225 y[1] (analytic) = 1.0230179028132992327365728900256 y[1] (numeric) = 1.0230179028132992327453095195967 absolute error = 8.7366295711e-21 relative error = 8.5400554057502499999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0226 y[1] (analytic) = 1.0231225700838960507468794761612 y[1] (numeric) = 1.0231225700838960507556590023036 absolute error = 8.7795261424e-21 relative error = 8.5811088515817600000000000000004e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0227 y[1] (analytic) = 1.0232272587741737439885398547017 y[1] (numeric) = 1.0232272587741737439973623158344 absolute error = 8.8224611327e-21 relative error = 8.6221912649877100000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0228 y[1] (analytic) = 1.0233319688907081457224723700368 y[1] (numeric) = 1.0233319688907081457313378046128 absolute error = 8.8654345760e-21 relative error = 8.6633026676672000000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=57.2MB, alloc=4.1MB, time=2.33 NO POLE x[1] = 0.0229 y[1] (analytic) = 1.0234367004400777811892334459114 y[1] (numeric) = 1.0234367004400777811981418924175 absolute error = 8.9084465061e-21 relative error = 8.7044430811103099999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.023 y[1] (analytic) = 1.0235414534288638689866939611054 y[1] (numeric) = 1.0235414534288638689956454580624 absolute error = 8.9514969570e-21 relative error = 8.7456125269890000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0231 y[1] (analytic) = 1.0236462278636503224485617770499 y[1] (numeric) = 1.0236462278636503224575563630123 absolute error = 8.9945859624e-21 relative error = 8.7868110266685599999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0232 y[1] (analytic) = 1.023751023751023751023751023751 y[1] (numeric) = 1.0237510237510237510327887373076 absolute error = 9.0377135566e-21 relative error = 8.8280386020868800000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0233 y[1] (analytic) = 1.0238558410975734616565987508959 y[1] (numeric) = 1.0238558410975734616656796306691 absolute error = 9.0808797732e-21 relative error = 8.8692952744844399999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0234 y[1] (analytic) = 1.0239606799098914601679295515052 y[1] (numeric) = 1.0239606799098914601770536361517 absolute error = 9.1240846465e-21 relative error = 8.9105810657719000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0235 y[1] (analytic) = 1.024065540194572452636968766001 y[1] (numeric) = 1.0240655401945724526461360942114 absolute error = 9.1673282104e-21 relative error = 8.9518959974556000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0236 y[1] (analytic) = 1.0241704219582138467841048750512 y[1] (numeric) = 1.0241704219582138467933154855502 absolute error = 9.2106104990e-21 relative error = 8.9932400912236000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0237 y[1] (analytic) = 1.0242753252074157533545016900543 y[1] (numeric) = 1.0242753252074157533637556216008 absolute error = 9.2539315465e-21 relative error = 9.0346133688479499999999999999999e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0238 y[1] (analytic) = 1.0243802499487809875025609506249 y[1] (numeric) = 1.0243802499487809875118582420119 absolute error = 9.2972913870e-21 relative error = 9.0760158519893999999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0239 y[1] (analytic) = 1.0244851961889150701772359389407 y[1] (numeric) = 1.0244851961889150701865766289954 absolute error = 9.3406900547e-21 relative error = 9.1174475623926699999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.024 y[1] (analytic) = 1.0245901639344262295081967213115 y[1] (numeric) = 1.0245901639344262295175808488952 absolute error = 9.3841275837e-21 relative error = 9.1589085216911999999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0241 y[1] (analytic) = 1.0246951531919254021928476278307 y[1] (numeric) = 1.0246951531919254022022752318391 absolute error = 9.4276040084e-21 relative error = 9.2003987517975600000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0242 y[1] (analytic) = 1.0248001639680262348841975814716 y[1] (numeric) = 1.0248001639680262348936687008346 absolute error = 9.4711193630e-21 relative error = 9.2419182744154000000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0243 y[1] (analytic) = 1.0249051962693450855795838884903 y[1] (numeric) = 1.0249051962693450855890985621721 absolute error = 9.5146736818e-21 relative error = 9.2834671113322600000000000000001e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=61.0MB, alloc=4.1MB, time=2.50 x[1] = 0.0244 y[1] (analytic) = 1.025010250102501025010250102501 y[1] (numeric) = 1.0250102501025010250198083695001 absolute error = 9.5582669991e-21 relative error = 9.3250452843219600000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0245 y[1] (analytic) = 1.0251153254741158380317785750897 y[1] (numeric) = 1.025115325474115838041380474439 absolute error = 9.6018993493e-21 relative error = 9.3666528152421500000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0246 y[1] (analytic) = 1.0252204223908140250153783063359 y[1] (numeric) = 1.0252204223908140250250238771028 absolute error = 9.6455707669e-21 relative error = 9.4082897260342599999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0247 y[1] (analytic) = 1.0253255408592228032400287091151 y[1] (numeric) = 1.0253255408592228032497179904014 absolute error = 9.6892812863e-21 relative error = 9.4499560385283900000000000000004e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0248 y[1] (analytic) = 1.0254306808859721082854799015587 y[1] (numeric) = 1.0254306808859721082952129325005 absolute error = 9.7330309418e-21 relative error = 9.4916517744433599999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0249 y[1] (analytic) = 1.0255358424776945954261101425495 y[1] (numeric) = 1.0255358424776945954358869623177 absolute error = 9.7768197682e-21 relative error = 9.5333769559718199999999999999998e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.025 y[1] (analytic) = 1.025641025641025641025641025641 y[1] (numeric) = 1.0256410256410256410354616734409 absolute error = 9.8206477999e-21 relative error = 9.5751316049025000000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0251 y[1] (analytic) = 1.0257462303826033439327110472869 y[1] (numeric) = 1.0257462303826033439425755623583 absolute error = 9.8645150714e-21 relative error = 9.6169157431078600000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0252 y[1] (analytic) = 1.0258514567090685268773081657776 y[1] (numeric) = 1.025851456709068526887216587395 absolute error = 9.9084216174e-21 relative error = 9.6587293926415200000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0253 y[1] (analytic) = 1.025956704627064737868061967785 y[1] (numeric) = 1.0259567046270647378780143352574 absolute error = 9.9523674724e-21 relative error = 9.7005725753482799999999999999996e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0254 y[1] (analytic) = 1.026061974143238251590396059922 y[1] (numeric) = 1.0260619741432382516003924125933 absolute error = 9.9963526713e-21 relative error = 9.7424453134489800000000000000002e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0255 y[1] (analytic) = 1.0261672652642380708055413032324 y[1] (numeric) = 1.026167265264238070815581680481 absolute error = 1.00403772486e-20 relative error = 9.7843476287607000000000000000003e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0256 y[1] (analytic) = 1.0262725779967159277504105090312 y[1] (numeric) = 1.0262725779967159277604949502703 absolute error = 1.00844412391e-20 relative error = 9.8262795433790400000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0257 y[1] (analytic) = 1.0263779123473262855383352150262 y[1] (numeric) = 1.0263779123473262855484637597038 absolute error = 1.01285446776e-20 relative error = 9.8682410793856799999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0258 y[1] (analytic) = 1.0264832683227263395606651611579 y[1] (numeric) = 1.0264832683227263395708378487568 absolute error = 1.01726875989e-20 relative error = 9.9102322588483799999999999999997e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0259 y[1] (analytic) = 1.0265886459295760188892310851042 y[1] (numeric) = 1.0265886459295760188994479551421 absolute error = 1.02168700379e-20 relative error = 9.9522531039183900000000000000000e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.1MB, time=2.66 NO POLE x[1] = 0.026 y[1] (analytic) = 1.0266940451745379876796714579055 y[1] (numeric) = 1.0266940451745379876899325499349 absolute error = 1.02610920294e-20 relative error = 9.9943036366356000000000000000004e-19 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0261 y[1] (analytic) = 1.0267994660642776465756237806756 y[1] (numeric) = 1.0267994660642776465859291342838 absolute error = 1.03053536082e-20 relative error = 1.0036383879025980000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0262 y[1] (analytic) = 1.0269049086054631341137810638735 y[1] (numeric) = 1.0269049086054631341241307186828 absolute error = 1.03496548093e-20 relative error = 1.0078493853296340000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0263 y[1] (analytic) = 1.0270103728047653281298141111225 y[1] (numeric) = 1.0270103728047653281402081067903 absolute error = 1.03939956678e-20 relative error = 1.0120633581736860000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0264 y[1] (analytic) = 1.027115858668857847165160230074 y[1] (numeric) = 1.0271158586688578471755986062925 absolute error = 1.04383762185e-20 relative error = 1.0162803086331600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0265 y[1] (analytic) = 1.0272213662044170518746789933231 y[1] (numeric) = 1.0272213662044170518851617898197 absolute error = 1.04827964966e-20 relative error = 1.0205002389440100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0266 y[1] (analytic) = 1.0273268954181220464351756728991 y[1] (numeric) = 1.0273268954181220464457029294362 absolute error = 1.05272565371e-20 relative error = 1.0247231513213140000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0267 y[1] (analytic) = 1.0274324463166546799547929723621 y[1] (numeric) = 1.0274324463166546799653647287371 absolute error = 1.05717563750e-20 relative error = 1.0289490479787500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0268 y[1] (analytic) = 1.0275380189066995478832716810522 y[1] (numeric) = 1.0275380189066995478938879770978 absolute error = 1.06162960456e-20 relative error = 1.0331779311577920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0269 y[1] (analytic) = 1.0276436131949439934230808755524 y[1] (numeric) = 1.0276436131949439934337417511364 absolute error = 1.06608755840e-20 relative error = 1.0374098030790400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.027 y[1] (analytic) = 1.0277492291880781089414182939363 y[1] (numeric) = 1.0277492291880781089521237889617 absolute error = 1.07054950254e-20 relative error = 1.0416446659714200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0271 y[1] (analytic) = 1.0278548668927947373830815088909 y[1] (numeric) = 1.027854866892794737393831663296 absolute error = 1.07501544051e-20 relative error = 1.0458825220721790000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0272 y[1] (analytic) = 1.0279605263157894736842105263158 y[1] (numeric) = 1.027960526315789473695005380074 absolute error = 1.07948537582e-20 relative error = 1.0501233735976960000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0273 y[1] (analytic) = 1.0280662074637606661869024365169 y[1] (numeric) = 1.0280662074637606661977420296371 absolute error = 1.08395931202e-20 relative error = 1.0543672228018540000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0274 y[1] (analytic) = 1.0281719103434094180546987456303 y[1] (numeric) = 1.0281719103434094180655831181566 absolute error = 1.08843725263e-20 relative error = 1.0586140719079380000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0275 y[1] (analytic) = 1.0282776349614395886889460154242 y[1] (numeric) = 1.0282776349614395886998752074362 absolute error = 1.09291920120e-20 relative error = 1.0628639231670000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.1MB, time=2.81 NO POLE x[1] = 0.0276 y[1] (analytic) = 1.0283833813245577951460304401481 y[1] (numeric) = 1.0283833813245577951570044917607 absolute error = 1.09740516126e-20 relative error = 1.0671167788092240000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0277 y[1] (analytic) = 1.0284891494394734135554869896123 y[1] (numeric) = 1.0284891494394734135665059409759 absolute error = 1.10189513636e-20 relative error = 1.0713726410828280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0278 y[1] (analytic) = 1.0285949393128985805389837482 y[1] (numeric) = 1.0285949393128985805500476395004 absolute error = 1.10638913004e-20 relative error = 1.0756315122248880000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0279 y[1] (analytic) = 1.0287007509515481946301820800329 y[1] (numeric) = 1.0287007509515481946412909514915 absolute error = 1.11088714586e-20 relative error = 1.0798933944905060000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.028 y[1] (analytic) = 1.0288065843621399176954732510288 y[1] (numeric) = 1.0288065843621399177066271429025 absolute error = 1.11538918737e-20 relative error = 1.0841582901236400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0281 y[1] (analytic) = 1.028912439551394176355592139109 y[1] (numeric) = 1.0289124395513941763667910916902 absolute error = 1.11989525812e-20 relative error = 1.0884262013668280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0282 y[1] (analytic) = 1.0290183165260341634081086643342 y[1] (numeric) = 1.0290183165260341634193527179511 absolute error = 1.12440536169e-20 relative error = 1.0926971304903420000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0283 y[1] (analytic) = 1.0291242152927858392507975712669 y[1] (numeric) = 1.029124215292785839262086766283 absolute error = 1.12891950161e-20 relative error = 1.0969710797144369999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0284 y[1] (analytic) = 1.0292301358583779333058871963771 y[1] (numeric) = 1.0292301358583779333172215731919 absolute error = 1.13343768148e-20 relative error = 1.1012480513259680000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0285 y[1] (analytic) = 1.0293360782295419454451878538343 y[1] (numeric) = 1.0293360782295419454565674528829 absolute error = 1.13795990486e-20 relative error = 1.1055280475714900000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0286 y[1] (analytic) = 1.0294420424130121474161004735433 y[1] (numeric) = 1.0294420424130121474275253352966 absolute error = 1.14248617533e-20 relative error = 1.1098110707155620000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0287 y[1] (analytic) = 1.0295480284155255842685061258108 y[1] (numeric) = 1.0295480284155255842799762907753 absolute error = 1.14701649645e-20 relative error = 1.1140971230018850000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0288 y[1] (analytic) = 1.0296540362438220757825370675453 y[1] (numeric) = 1.0296540362438220757940525762635 absolute error = 1.15155087182e-20 relative error = 1.1183862067115840000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0289 y[1] (analytic) = 1.0297600659046442178972299454227 y[1] (numeric) = 1.0297600659046442179087908384729 absolute error = 1.15608930502e-20 relative error = 1.1226783241049220000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.029 y[1] (analytic) = 1.029866117404737384140061791967 y[1] (numeric) = 1.0298661174047373841516681099633 absolute error = 1.16063179963e-20 relative error = 1.1269734774407300000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0291 y[1] (analytic) = 1.0299721907508497270573694510248 y[1] (numeric) = 1.0299721907508497270690212346173 absolute error = 1.16517835925e-20 relative error = 1.1312716689958250000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=72.4MB, alloc=4.1MB, time=2.98 NO POLE x[1] = 0.0292 y[1] (analytic) = 1.0300782859497321796456530696333 y[1] (numeric) = 1.030078285949732179657350359508 absolute error = 1.16972898747e-20 relative error = 1.1355729010358760000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0293 y[1] (analytic) = 1.0301844030081384567837642938086 y[1] (numeric) = 1.0301844030081384567955071306875 absolute error = 1.17428368789e-20 relative error = 1.1398771758348230000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0294 y[1] (analytic) = 1.0302905419328250566659798063054 y[1] (numeric) = 1.0302905419328250566777682309465 absolute error = 1.17884246411e-20 relative error = 1.1441844956651660000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0295 y[1] (analytic) = 1.0303967027305512622359608449253 y[1] (numeric) = 1.0303967027305512622477948981227 absolute error = 1.18340531974e-20 relative error = 1.1484948628076700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0296 y[1] (analytic) = 1.0305028854080791426215993404782 y[1] (numeric) = 1.030502885408079142633479063062 absolute error = 1.18797225838e-20 relative error = 1.1528082795319519999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0297 y[1] (analytic) = 1.0306090899721735545707513140266 y[1] (numeric) = 1.0306090899721735545826767468632 absolute error = 1.19254328366e-20 relative error = 1.1571247481352980000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0298 y[1] (analytic) = 1.0307153164296021438878581735725 y[1] (numeric) = 1.0307153164296021438998293575643 absolute error = 1.19711839918e-20 relative error = 1.1614442708844360000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0299 y[1] (analytic) = 1.030821564787135346871456550871 y[1] (numeric) = 1.0308215647871353468834735269567 absolute error = 1.20169760857e-20 relative error = 1.1657668500737570000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.03 y[1] (analytic) = 1.0309278350515463917525773195876 y[1] (numeric) = 1.030927835051546391764640128742 absolute error = 1.20628091544e-20 relative error = 1.1700924879768000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0301 y[1] (analytic) = 1.0310341272296113001340344365398 y[1] (numeric) = 1.031034127229611300146143119774 absolute error = 1.21086832342e-20 relative error = 1.1744211868850580000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0302 y[1] (analytic) = 1.0311404413281088884306042482986 y[1] (numeric) = 1.03114044132810888844275884666 absolute error = 1.21545983614e-20 relative error = 1.1787529490885720000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0303 y[1] (analytic) = 1.0312467773538207693100959059503 y[1] (numeric) = 1.0312467773538207693222964605226 absolute error = 1.22005545723e-20 relative error = 1.1830877768759310000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0304 y[1] (analytic) = 1.0313531353135313531353135313531 y[1] (numeric) = 1.0313531353135313531475600832565 absolute error = 1.22465519034e-20 relative error = 1.1874256725536640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0305 y[1] (analytic) = 1.0314595152140278494069107787519 y[1] (numeric) = 1.0314595152140278494192033691428 absolute error = 1.22925903909e-20 relative error = 1.1917666383977550000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0306 y[1] (analytic) = 1.0315659170621002682071384361461 y[1] (numeric) = 1.0315659170621002682194771062174 absolute error = 1.23386700713e-20 relative error = 1.1961106767118220000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0307 y[1] (analytic) = 1.0316723408645414216444857113381 y[1] (numeric) = 1.0316723408645414216568705023193 memory used=76.2MB, alloc=4.1MB, time=3.13 absolute error = 1.23847909812e-20 relative error = 1.2004577898077160000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0308 y[1] (analytic) = 1.0317787866281469252992158481222 y[1] (numeric) = 1.0317787866281469253116468012792 absolute error = 1.24309531570e-20 relative error = 1.2048079799764400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0309 y[1] (analytic) = 1.0318852543597151996697967186049 y[1] (numeric) = 1.0318852543597151996822738752401 absolute error = 1.24771566352e-20 relative error = 1.2091612495172320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.031 y[1] (analytic) = 1.0319917440660474716202270381837 y[1] (numeric) = 1.0319917440660474716327504396361 absolute error = 1.25234014524e-20 relative error = 1.2135176007375600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0311 y[1] (analytic) = 1.0320982557539477758282588502425 y[1] (numeric) = 1.0320982557539477758408285378878 absolute error = 1.25696876453e-20 relative error = 1.2178770359531170000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0312 y[1] (analytic) = 1.0322047894302229562345169281585 y[1] (numeric) = 1.0322047894302229562471329434089 absolute error = 1.26160152504e-20 relative error = 1.2222395574587520000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0313 y[1] (analytic) = 1.032311345101682667492515742748 y[1] (numeric) = 1.0323113451016826675051781270524 absolute error = 1.26623843044e-20 relative error = 1.2266051675672280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0314 y[1] (analytic) = 1.0324179227751393764195746438158 y[1] (numeric) = 1.0324179227751393764322834386599 absolute error = 1.27087948441e-20 relative error = 1.2309738685995260000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0315 y[1] (analytic) = 1.0325245224574083634486319050077 y[1] (numeric) = 1.032524522457408363461387151914 absolute error = 1.27552469063e-20 relative error = 1.2353456628751550000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0316 y[1] (analytic) = 1.0326311441553077240809582817018 y[1] (numeric) = 1.0326311441553077240937600222294 absolute error = 1.28017405276e-20 relative error = 1.2397205526927840000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0317 y[1] (analytic) = 1.0327377878756583703397707322111 y[1] (numeric) = 1.0327377878756583703526190079561 absolute error = 1.28482757450e-20 relative error = 1.2440985403883500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0318 y[1] (analytic) = 1.0328444536252840322247469531089 y[1] (numeric) = 1.0328444536252840322376418057041 absolute error = 1.28948525952e-20 relative error = 1.2484796282672640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0319 y[1] (analytic) = 1.0329511414110112591674413800227 y[1] (numeric) = 1.0329511414110112591803828511379 absolute error = 1.29414711152e-20 relative error = 1.2528638186625120000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.032 y[1] (analytic) = 1.0330578512396694214876033057851 y[1] (numeric) = 1.0330578512396694215005914371269 absolute error = 1.29881313418e-20 relative error = 1.2572511138862400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0321 y[1] (analytic) = 1.0331645831180907118503977683645 y[1] (numeric) = 1.0331645831180907118634326016765 absolute error = 1.30348333120e-20 relative error = 1.2616415162684800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0322 y[1] (analytic) = 1.0332713370531101467245298615416 y[1] (numeric) = 1.0332713370531101467376114386045 absolute error = 1.30815770629e-20 relative error = 1.2660350281474620000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.1MB, time=3.29 NO POLE x[1] = 0.0323 y[1] (analytic) = 1.0333781130515655678412731218353 y[1] (numeric) = 1.0333781130515655678544014844667 absolute error = 1.31283626314e-20 relative error = 1.2704316518405780000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0324 y[1] (analytic) = 1.0334849111202976436544026457214 y[1] (numeric) = 1.0334849111202976436675778357761 absolute error = 1.31751900547e-20 relative error = 1.2748313896927720000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0325 y[1] (analytic) = 1.0335917312661498708010335917313 y[1] (numeric) = 1.0335917312661498708142556511011 absolute error = 1.32220593698e-20 relative error = 1.2792342440281500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0326 y[1] (analytic) = 1.0336985734959685755633657225553 y[1] (numeric) = 1.0336985734959685755766346931692 absolute error = 1.32689706139e-20 relative error = 1.2836402171886860000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0327 y[1] (analytic) = 1.0338054378166029153313346428202 y[1] (numeric) = 1.0338054378166029153446505666444 absolute error = 1.33159238242e-20 relative error = 1.2880493115148660000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0328 y[1] (analytic) = 1.033912324234904880066170388751 y[1] (numeric) = 1.0339123242349048800795333077888 absolute error = 1.33629190378e-20 relative error = 1.2924615293360160000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0329 y[1] (analytic) = 1.0340192327577292937648640264709 y[1] (numeric) = 1.0340192327577292937782739827628 absolute error = 1.34099562919e-20 relative error = 1.2968768729896490000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.033 y[1] (analytic) = 1.0341261633919338159255429162358 y[1] (numeric) = 1.0341261633919338159389999518598 absolute error = 1.34570356240e-20 relative error = 1.3012953448408000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0331 y[1] (analytic) = 1.0342331161443789430137553004447 y[1] (numeric) = 1.034233116144378943027259457516 absolute error = 1.35041570713e-20 relative error = 1.3057169472239970000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0332 y[1] (analytic) = 1.0343400910219280099296648738105 y[1] (numeric) = 1.0343400910219280099432161944816 absolute error = 1.35513206711e-20 relative error = 1.3101416824819480000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0333 y[1] (analytic) = 1.0344470880314471914761559946209 y[1] (numeric) = 1.0344470880314471914897545210817 absolute error = 1.35985264608e-20 relative error = 1.3145695529655360000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0334 y[1] (analytic) = 1.0345541071798055038278501965653 y[1] (numeric) = 1.0345541071798055038414959710432 absolute error = 1.36457744779e-20 relative error = 1.3190005610338140000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0335 y[1] (analytic) = 1.0346611484738748060010346611485 y[1] (numeric) = 1.0346611484738748060147277259083 absolute error = 1.36930647598e-20 relative error = 1.3234347090346700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0336 y[1] (analytic) = 1.0347682119205298013245033112583 y[1] (numeric) = 1.0347682119205298013382437086023 absolute error = 1.37403973440e-20 relative error = 1.3278719993241600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0337 y[1] (analytic) = 1.034875297526648038911311187002 y[1] (numeric) = 1.03487529752664803892509895927 absolute error = 1.37877722680e-20 relative error = 1.3323124342568400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0338 y[1] (analytic) = 1.034982405299109915131442765473 y[1] (numeric) = 1.0349824052991099151452779550425 absolute error = 1.38351895695e-20 relative error = 1.3367560162050900000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.1MB, time=3.46 NO POLE x[1] = 0.0339 y[1] (analytic) = 1.0350895352447986750853948866577 y[1] (numeric) = 1.0350895352447986750992775359437 absolute error = 1.38826492860e-20 relative error = 1.3412027475204600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.034 y[1] (analytic) = 1.0351966873706004140786749482402 y[1] (numeric) = 1.0351966873706004140926050996953 absolute error = 1.39301514551e-20 relative error = 1.3456526305626600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0341 y[1] (analytic) = 1.0353038616834040790972150326121 y[1] (numeric) = 1.0353038616834040791111927287266 absolute error = 1.39776961145e-20 relative error = 1.3501056676995550000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0342 y[1] (analytic) = 1.0354110581901014702837026299441 y[1] (numeric) = 1.0354110581901014702977279132461 absolute error = 1.40252833020e-20 relative error = 1.3545618613071600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0343 y[1] (analytic) = 1.0355182768975872424148286217252 y[1] (numeric) = 1.0355182768975872424289015347804 absolute error = 1.40729130552e-20 relative error = 1.3590212137406640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0344 y[1] (analytic) = 1.0356255178127589063794531897266 y[1] (numeric) = 1.0356255178127589063935737751386 absolute error = 1.41205854120e-20 relative error = 1.3634837273827200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0345 y[1] (analytic) = 1.0357327809425168306576903158985 y[1] (numeric) = 1.0357327809425168306718586163087 absolute error = 1.41683004102e-20 relative error = 1.3679494046048100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0346 y[1] (analytic) = 1.0358400662937642428009115392583 y[1] (numeric) = 1.035840066293764242815127597346 absolute error = 1.42160580877e-20 relative error = 1.3724182477865580000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0347 y[1] (analytic) = 1.0359473738734072309126696363825 y[1] (numeric) = 1.0359473738734072309269334948647 absolute error = 1.42638584822e-20 relative error = 1.3768902592867660000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0348 y[1] (analytic) = 1.0360547036883547451305428926647 y[1] (numeric) = 1.0360547036883547451448545942966 absolute error = 1.43117016319e-20 relative error = 1.3813654415109880000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0349 y[1] (analytic) = 1.0361620557455185991089006320589 y[1] (numeric) = 1.0361620557455185991232602196334 absolute error = 1.43595875745e-20 relative error = 1.3858437968149949999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.035 y[1] (analytic) = 1.0362694300518134715025906735751 y[1] (numeric) = 1.0362694300518134715169981899234 absolute error = 1.44075163483e-20 relative error = 1.3903253276109500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0351 y[1] (analytic) = 1.0363768266141569074515493833558 y[1] (numeric) = 1.0363768266141569074660048713469 absolute error = 1.44554879911e-20 relative error = 1.3948100362612390000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0352 y[1] (analytic) = 1.0364842454394693200663349917081 y[1] (numeric) = 1.0364842454394693200808384942492 absolute error = 1.45035025411e-20 relative error = 1.3992979251653280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0353 y[1] (analytic) = 1.0365916865346739919145848450295 y[1] (numeric) = 1.0365916865346739919291364050658 absolute error = 1.45515600363e-20 relative error = 1.4037889967018610000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0354 y[1] (analytic) = 1.0366991499066970765083972631142 y[1] (numeric) = 1.0366991499066970765229969236291 absolute error = 1.45996605149e-20 relative error = 1.4082832532672540000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.1MB, time=3.62 NO POLE x[1] = 0.0355 y[1] (analytic) = 1.0368066355624675997926386728875 y[1] (numeric) = 1.0368066355624675998072864769026 absolute error = 1.46478040151e-20 relative error = 1.4127806972563950000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0356 y[1] (analytic) = 1.0369141435089174616341766901701 y[1] (numeric) = 1.0369141435089174616488726807452 absolute error = 1.46959905751e-20 relative error = 1.4172813310626439999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0357 y[1] (analytic) = 1.0370216737529814373120398216323 y[1] (numeric) = 1.0370216737529814373267840418655 absolute error = 1.47442202332e-20 relative error = 1.4217851570874760000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0358 y[1] (analytic) = 1.0371292263015971790085044596557 y[1] (numeric) = 1.0371292263015971790232969526834 absolute error = 1.47924930277e-20 relative error = 1.4262921777308340000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0359 y[1] (analytic) = 1.0372368011617052173011098433772 y[1] (numeric) = 1.0372368011617052173159506523741 absolute error = 1.48408089969e-20 relative error = 1.4308023953911290000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.036 y[1] (analytic) = 1.037344398340248962655601659751 y[1] (numeric) = 1.0373443983402489626704908279301 absolute error = 1.48891681791e-20 relative error = 1.4353158124652400000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0361 y[1] (analytic) = 1.0374520178441747069198049590206 y[1] (numeric) = 1.0374520178441747069347425296334 absolute error = 1.49375706128e-20 relative error = 1.4398324313677920000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0362 y[1] (analytic) = 1.0375596596804316248184270595559 y[1] (numeric) = 1.0375596596804316248334130758923 absolute error = 1.49860163364e-20 relative error = 1.4443522545022320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0363 y[1] (analytic) = 1.0376673238559717754487911175677 y[1] (numeric) = 1.0376673238559717754638256229561 absolute error = 1.50345053884e-20 relative error = 1.4488752842801080000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0364 y[1] (analytic) = 1.037775010377750103777501037775 y[1] (numeric) = 1.0377750103777501037925840755823 absolute error = 1.50830378073e-20 relative error = 1.4534015231114280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0365 y[1] (analytic) = 1.0378827192527244421380384016606 y[1] (numeric) = 1.0378827192527244421531700152923 absolute error = 1.51316136317e-20 relative error = 1.4579309734142950000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0366 y[1] (analytic) = 1.0379904504878555117292920905128 y[1] (numeric) = 1.0379904504878555117444723234129 absolute error = 1.51802329001e-20 relative error = 1.4624636375956340000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0367 y[1] (analytic) = 1.0380982040901069241150212810132 y[1] (numeric) = 1.0380982040901069241302501766645 absolute error = 1.52288956513e-20 relative error = 1.4669995180897290000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0368 y[1] (analytic) = 1.0382059800664451827242524916944 y[1] (numeric) = 1.0382059800664451827395300936182 absolute error = 1.52776019238e-20 relative error = 1.4715386173004159999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0369 y[1] (analytic) = 1.0383137784238396843526113591527 y[1] (numeric) = 1.0383137784238396843679377109091 absolute error = 1.53263517564e-20 relative error = 1.4760809376588840000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.037 y[1] (analytic) = 1.0384215991692627206645898234683 y[1] (numeric) = 1.038421599169262720679964968656 absolute error = 1.53751451877e-20 relative error = 1.4806264815755100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.1MB, time=3.77 NO POLE x[1] = 0.0371 y[1] (analytic) = 1.0385294423096894796967494028456 y[1] (numeric) = 1.0385294423096894797121733851022 absolute error = 1.54239822566e-20 relative error = 1.4851752514880140000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0372 y[1] (analytic) = 1.0386373078520980473618612380557 y[1] (numeric) = 1.0386373078520980473773341010576 absolute error = 1.54728630019e-20 relative error = 1.4897272498229320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0373 y[1] (analytic) = 1.0387451958034694089539835878259 y[1] (numeric) = 1.0387451958034694089695053752884 absolute error = 1.55217874625e-20 relative error = 1.4942824790148750000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0374 y[1] (analytic) = 1.0388531061707874506544774568876 y[1] (numeric) = 1.0388531061707874506700482125648 absolute error = 1.55707556772e-20 relative error = 1.4988409414872720000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0375 y[1] (analytic) = 1.038961038961038961038961038961 y[1] (numeric) = 1.038961038961038961054580806646 absolute error = 1.56197676850e-20 relative error = 1.5034026396812500000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0376 y[1] (analytic) = 1.0390689941812136325852036575229 y[1] (numeric) = 1.0390689941812136326008724810476 absolute error = 1.56688235247e-20 relative error = 1.5079675760171279999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0377 y[1] (analytic) = 1.0391769718383040631819598877689 y[1] (numeric) = 1.0391769718383040631976778110044 absolute error = 1.57179232355e-20 relative error = 1.5125357529521650000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0378 y[1] (analytic) = 1.0392849719393057576387445437539 y[1] (numeric) = 1.0392849719393057576545116106102 absolute error = 1.57670668563e-20 relative error = 1.5171071729131860000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0379 y[1] (analytic) = 1.0393929944912171291965492152583 y[1] (numeric) = 1.0393929944912171292123654696845 absolute error = 1.58162544262e-20 relative error = 1.5216818383447020000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.038 y[1] (analytic) = 1.039501039501039501039501039501 y[1] (numeric) = 1.0395010395010395010553665254854 absolute error = 1.58654859844e-20 relative error = 1.5262597516992800000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0381 y[1] (analytic) = 1.0396091069757771078074643933881 y[1] (numeric) = 1.039609106975777107823379154958 absolute error = 1.59147615699e-20 relative error = 1.5308409154086810000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0382 y[1] (analytic) = 1.0397171969224370971095861925556 y[1] (numeric) = 1.0397171969224370971255502737777 absolute error = 1.59640812221e-20 relative error = 1.5354253319415780000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0383 y[1] (analytic) = 1.0398253093480295310387854840387 y[1] (numeric) = 1.0398253093480295310547989290187 absolute error = 1.60134449800e-20 relative error = 1.5400130037266000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0384 y[1] (analytic) = 1.0399334442595673876871880199667 y[1] (numeric) = 1.0399334442595673877032508728498 absolute error = 1.60628528831e-20 relative error = 1.5446039332388960000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0385 y[1] (analytic) = 1.04004160166406656266250650026 y[1] (numeric) = 1.0400416016640665626786188052305 absolute error = 1.61123049705e-20 relative error = 1.5491981229135750000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=95.3MB, alloc=4.1MB, time=3.93 x[1] = 0.0386 y[1] (analytic) = 1.0401497815685458706053671728729 y[1] (numeric) = 1.0401497815685458706215289741545 absolute error = 1.61618012816e-20 relative error = 1.5537955752130240000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0387 y[1] (analytic) = 1.0402579839800270467075834807032 y[1] (numeric) = 1.0402579839800270467237948225591 absolute error = 1.62113418559e-20 relative error = 1.5583962926076670000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0388 y[1] (analytic) = 1.0403662089055347482313774448606 y[1] (numeric) = 1.0403662089055347482476383715933 absolute error = 1.62609267327e-20 relative error = 1.5630002775471240000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0389 y[1] (analytic) = 1.0404744563520965560295494745604 y[1] (numeric) = 1.0404744563520965560458600305119 absolute error = 1.63105559515e-20 relative error = 1.5676075324986650000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.039 y[1] (analytic) = 1.0405827263267429760665972944849 y[1] (numeric) = 1.0405827263267429760829575240366 absolute error = 1.63602295517e-20 relative error = 1.5722180599183700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0391 y[1] (analytic) = 1.0406910188365074409407846810282 y[1] (numeric) = 1.0406910188365074409571946286011 absolute error = 1.64099475729e-20 relative error = 1.5768318622799610000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0392 y[1] (analytic) = 1.0407993338884263114071606994172 y[1] (numeric) = 1.0407993338884263114236204094718 absolute error = 1.64597100546e-20 relative error = 1.5814489420459679999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0393 y[1] (analytic) = 1.0409076714895388779015301342771 y[1] (numeric) = 1.0409076714895388779180396513137 absolute error = 1.65095170366e-20 relative error = 1.5860693017061620000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0394 y[1] (analytic) = 1.0410160316468873620653758067874 y[1] (numeric) = 1.0410160316468873620819351753458 absolute error = 1.65593685584e-20 relative error = 1.5906929437199040000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0395 y[1] (analytic) = 1.0411244143675169182717334721499 y[1] (numeric) = 1.0411244143675169182883427368096 absolute error = 1.66092646597e-20 relative error = 1.5953198705641850000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0396 y[1] (analytic) = 1.0412328196584756351520199916701 y[1] (numeric) = 1.0412328196584756351686791970503 absolute error = 1.66592053802e-20 relative error = 1.5999500847144080000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0397 y[1] (analytic) = 1.0413412475268145371238154743309 y[1] (numeric) = 1.0413412475268145371405246650906 absolute error = 1.67091907597e-20 relative error = 1.6045835886539910000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0398 y[1] (analytic) = 1.041449697979587585919600083316 y[1] (numeric) = 1.0414496979795875859363593041539 absolute error = 1.67592208379e-20 relative error = 1.6092203848551580000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0399 y[1] (analytic) = 1.0415581710238516821164462035205 y[1] (numeric) = 1.0415581710238516821332554991753 absolute error = 1.68092956548e-20 relative error = 1.6138604758173479999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.04 y[1] (analytic) = 1.0416666666666666666666666666667 y[1] (numeric) = 1.0416666666666666666835260819169 absolute error = 1.68594152502e-20 relative error = 1.6185038640191999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0401 y[1] (analytic) = 1.041775184915095322429419731222 y[1] (numeric) = 1.041775184915095322446329310886 absolute error = 1.69095796640e-20 relative error = 1.6231505519473600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=99.1MB, alloc=4.1MB, time=4.08 NO POLE x[1] = 0.0402 y[1] (analytic) = 1.0418837257762033757032715148989 y[1] (numeric) = 1.0418837257762033757202313038351 absolute error = 1.69597889362e-20 relative error = 1.6278005420964760000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0403 y[1] (analytic) = 1.0419922892570594977597165780973 y[1] (numeric) = 1.041992289257059497776726621204 absolute error = 1.70100431067e-20 relative error = 1.6324538369499990000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0404 y[1] (analytic) = 1.0421008753647353063776573572322 y[1] (numeric) = 1.0421008753647353063947176994477 absolute error = 1.70603422155e-20 relative error = 1.6371104389993800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0405 y[1] (analytic) = 1.0422094841063053673788431474726 y[1] (numeric) = 1.0422094841063053673959538337754 absolute error = 1.71106863028e-20 relative error = 1.6417703507536600000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0406 y[1] (analytic) = 1.042318115488847196164269335001 y[1] (numeric) = 1.0423181154888471961814304104096 absolute error = 1.71610754086e-20 relative error = 1.6464335747010840000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0407 y[1] (analytic) = 1.042426769519441259251537579485 y[1] (numeric) = 1.0424267695194412592687490890581 absolute error = 1.72115095731e-20 relative error = 1.6511001133474830000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0408 y[1] (analytic) = 1.04253544620517097581317764804 y[1] (numeric) = 1.0425354462051709758304396368765 absolute error = 1.72619888365e-20 relative error = 1.6557699691970800000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0409 y[1] (analytic) = 1.0426441455531227192159316025441 y[1] (numeric) = 1.042644145553122719233244115783 absolute error = 1.73125132389e-20 relative error = 1.6604431447428989999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.041 y[1] (analytic) = 1.0427528675703858185610010427529 y[1] (numeric) = 1.0427528675703858185783641255737 absolute error = 1.73630828208e-20 relative error = 1.6651196425147199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0411 y[1] (analytic) = 1.042861612264052560225258108249 y[1] (numeric) = 1.0428616122640525602426718058714 absolute error = 1.74136976224e-20 relative error = 1.6697994650119360000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0412 y[1] (analytic) = 1.0429703796412181894034209428452 y[1] (numeric) = 1.0429703796412181894208853005291 absolute error = 1.74643576839e-20 relative error = 1.6744826147323320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0413 y[1] (analytic) = 1.0430791697089809116511943256493 y[1] (numeric) = 1.0430791697089809116687093886951 absolute error = 1.75150630458e-20 relative error = 1.6791690942008460000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0414 y[1] (analytic) = 1.0431879824744418944293761735865 y[1] (numeric) = 1.043187982474441894446941987335 absolute error = 1.75658137485e-20 relative error = 1.6838589059312100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0415 y[1] (analytic) = 1.0432968179447052686489306207616 y[1] (numeric) = 1.0432968179447052686665472305941 absolute error = 1.76166098325e-20 relative error = 1.6885520524451250000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0416 y[1] (analytic) = 1.0434056761268781302170283806344 y[1] (numeric) = 1.0434056761268781302346958319726 absolute error = 1.76674513382e-20 relative error = 1.6932485362530880000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0417 y[1] (analytic) = 1.0435145570280705415840550975686 y[1] (numeric) = 1.0435145570280705416017734358749 absolute error = 1.77183383063e-20 relative error = 1.6979483598927290000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.1MB, time=4.24 NO POLE x[1] = 0.0418 y[1] (analytic) = 1.0436234606553955332915883949071 y[1] (numeric) = 1.0436234606553955333093576656843 absolute error = 1.77692707772e-20 relative error = 1.7026515258713040000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0419 y[1] (analytic) = 1.0437323870159691055213443273145 y[1] (numeric) = 1.043732387015969105539164576106 absolute error = 1.78202487915e-20 relative error = 1.7073580367136150000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.042 y[1] (analytic) = 1.0438413361169102296450939457202 y[1] (numeric) = 1.0438413361169102296629652181103 absolute error = 1.78712723901e-20 relative error = 1.7120678949715800000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0421 y[1] (analytic) = 1.0439503079653408497755506837875 y[1] (numeric) = 1.0439503079653408497934730254008 absolute error = 1.79223416133e-20 relative error = 1.7167811031380069999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0422 y[1] (analytic) = 1.0440593025683858843182292754228 y[1] (numeric) = 1.0440593025683858843362027319251 absolute error = 1.79734565023e-20 relative error = 1.7214976637902940000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0423 y[1] (analytic) = 1.0441683199331732275242769134384 y[1] (numeric) = 1.0441683199331732275423015305359 absolute error = 1.80246170975e-20 relative error = 1.7262175794275750000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0424 y[1] (analytic) = 1.0442773600668337510442773600668 y[1] (numeric) = 1.0442773600668337510623531835066 absolute error = 1.80758234398e-20 relative error = 1.7309408525952480000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0425 y[1] (analytic) = 1.0443864229765013054830287206266 y[1] (numeric) = 1.0443864229765013055011557961967 absolute error = 1.81270755701e-20 relative error = 1.7356674858370750000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0426 y[1] (analytic) = 1.044495508669312721955295592229 y[1] (numeric) = 1.0444955086693127219734739657582 absolute error = 1.81783735292e-20 relative error = 1.7403974816856079999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0427 y[1] (analytic) = 1.0446046171524078136425363000104 y[1] (numeric) = 1.0446046171524078136607660173687 absolute error = 1.82297173583e-20 relative error = 1.7451308427100590000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0428 y[1] (analytic) = 1.0447137484329293773506059339741 y[1] (numeric) = 1.0447137484329293773688870410721 absolute error = 1.82811070980e-20 relative error = 1.7498675714205600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0429 y[1] (analytic) = 1.0448229025180231950684359001149 y[1] (numeric) = 1.0448229025180231950867684429045 absolute error = 1.83325427896e-20 relative error = 1.7546076703926160000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.043 y[1] (analytic) = 1.0449320794148380355276907001045 y[1] (numeric) = 1.0449320794148380355460747245784 absolute error = 1.83840244739e-20 relative error = 1.7593511421522300000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0431 y[1] (analytic) = 1.0450412791305256557634026544048 y[1] (numeric) = 1.045041279130525655781838206597 absolute error = 1.84355521922e-20 relative error = 1.7640979892716180000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0432 y[1] (analytic) = 1.0451505016722408026755852842809 y[1] (numeric) = 1.0451505016722408026940724102664 absolute error = 1.84871259855e-20 relative error = 1.7688482142926400000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0433 y[1] (analytic) = 1.0452597470471412145918260687781 y[1] (numeric) = 1.045259747047141214610364814673 absolute error = 1.85387458949e-20 relative error = 1.7736018197650830000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.1MB, time=4.40 NO POLE x[1] = 0.0434 y[1] (analytic) = 1.0453690152623876228308592933305 y[1] (numeric) = 1.0453690152623876228494497052924 absolute error = 1.85904119619e-20 relative error = 1.7783588082753540000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0435 y[1] (analytic) = 1.0454783063251437532671197072661 y[1] (numeric) = 1.0454783063251437532857618314935 absolute error = 1.86421242274e-20 relative error = 1.7831191823508100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0436 y[1] (analytic) = 1.0455876202425763278962777080719 y[1] (numeric) = 1.0455876202425763279149715908049 absolute error = 1.86938827330e-20 relative error = 1.7878829445841200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0437 y[1] (analytic) = 1.0456969570218550664017567708878 y[1] (numeric) = 1.0456969570218550664205024584075 absolute error = 1.87456875197e-20 relative error = 1.7926500975089110000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0438 y[1] (analytic) = 1.0458063166701526877222338422924 y[1] (numeric) = 1.0458063166701526877410313809215 absolute error = 1.87975386291e-20 relative error = 1.7974206437145420000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0439 y[1] (analytic) = 1.0459156991946449116201234180525 y[1] (numeric) = 1.045915699194644911638972854155 absolute error = 1.88494361025e-20 relative error = 1.8021945857600250000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.044 y[1] (analytic) = 1.0460251046025104602510460251046 y[1] (numeric) = 1.046025104602510460269947405086 absolute error = 1.89013799814e-20 relative error = 1.8069719262218400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0441 y[1] (analytic) = 1.0461345329009310597342818286432 y[1] (numeric) = 1.0461345329009310597532351989505 absolute error = 1.89533703073e-20 relative error = 1.8117526676748069999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0442 y[1] (analytic) = 1.046243984097091441724210085792 y[1] (numeric) = 1.0462439840970914417432154929137 absolute error = 1.90054071217e-20 relative error = 1.8165368126920860000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0443 y[1] (analytic) = 1.0463534581981793449827351679397 y[1] (numeric) = 1.0463534581981793450017926584059 absolute error = 1.90574904662e-20 relative error = 1.8213243638547340000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0444 y[1] (analytic) = 1.0464629552113855169526998744244 y[1] (numeric) = 1.0464629552113855169718094948067 absolute error = 1.91096203823e-20 relative error = 1.8261153237325880000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0445 y[1] (analytic) = 1.0465724751439037153322867608582 y[1] (numeric) = 1.0465724751439037153514485577699 absolute error = 1.91617969117e-20 relative error = 1.8309096949129350000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0446 y[1] (analytic) = 1.046682018002930709650408205987 y[1] (numeric) = 1.0466820180029307096696222260832 absolute error = 1.92140200962e-20 relative error = 1.8357074799909480000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0447 y[1] (analytic) = 1.046791583795666282843085941589 y[1] (numeric) = 1.0467915837956662828623522315664 absolute error = 1.92662899774e-20 relative error = 1.8405086815410220000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0448 y[1] (analytic) = 1.0469011725293132328308207705193 y[1] (numeric) = 1.0469011725293132328501393771163 absolute error = 1.93186065970e-20 relative error = 1.8453133021454399999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0449 y[1] (analytic) = 1.0470107842110773740969531986179 y[1] (numeric) = 1.047010784211077374116324168615 absolute error = 1.93709699971e-20 memory used=110.6MB, alloc=4.1MB, time=4.56 relative error = 1.8501213444230210000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.045 y[1] (analytic) = 1.0471204188481675392670157068063 y[1] (numeric) = 1.0471204188481675392864390870255 absolute error = 1.94233802192e-20 relative error = 1.8549328109336000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0451 y[1] (analytic) = 1.0472300764477955806890773903026 y[1] (numeric) = 1.0472300764477955807085532276081 absolute error = 1.94758373055e-20 relative error = 1.8597477043021950000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0452 y[1] (analytic) = 1.047339757017176372015081692501 y[1] (numeric) = 1.0473397570171763720346100337987 absolute error = 1.95283412977e-20 relative error = 1.8645660271043960000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0453 y[1] (analytic) = 1.0474494605635278097831779616633 y[1] (numeric) = 1.0474494605635278098027588539012 absolute error = 1.95808922379e-20 relative error = 1.8693877819523130000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0454 y[1] (analytic) = 1.0475591870940708150010475591871 y[1] (numeric) = 1.0475591870940708150206810493551 absolute error = 1.96334901680e-20 relative error = 1.8742129714372800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0455 y[1] (analytic) = 1.0476689366160293347302252488214 y[1] (numeric) = 1.0476689366160293347499113839515 absolute error = 1.96861351301e-20 relative error = 1.8790415981680450000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0456 y[1] (analytic) = 1.0477787091366303436714165968148 y[1] (numeric) = 1.0477787091366303436911554239812 absolute error = 1.97388271664e-20 relative error = 1.8838736647612159999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0457 y[1] (analytic) = 1.0478885046631038457508121135911 y[1] (numeric) = 1.0478885046631038457706036799101 absolute error = 1.97915663190e-20 relative error = 1.8887091738221700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0458 y[1] (analytic) = 1.0479983232026828757073988681618 y[1] (numeric) = 1.0479983232026828757272432207918 absolute error = 1.98443526300e-20 relative error = 1.8935481279546000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0459 y[1] (analytic) = 1.0481081647626035006812703070957 y[1] (numeric) = 1.0481081647626035007011674932373 absolute error = 1.98971861416e-20 relative error = 1.8983905297700560000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.046 y[1] (analytic) = 1.0482180293501048218029350104822 y[1] (numeric) = 1.0482180293501048218228850773783 absolute error = 1.99500668961e-20 relative error = 1.9032363818879400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0461 y[1] (analytic) = 1.0483279169724289757836251179369 y[1] (numeric) = 1.0483279169724289758036281128727 absolute error = 2.00029949358e-20 relative error = 1.9080856869259620000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0462 y[1] (analytic) = 1.0484378276368211365066051583141 y[1] (numeric) = 1.0484378276368211365266611286172 absolute error = 2.00559703031e-20 relative error = 1.9129384475096780000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0463 y[1] (analytic) = 1.0485477613505295166194820174059 y[1] (numeric) = 1.0485477613505295166395910104461 absolute error = 2.01089930402e-20 relative error = 1.9177946662438740000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0464 y[1] (analytic) = 1.0486577181208053691275167785235 y[1] (numeric) = 1.0486577181208053691476788417132 absolute error = 2.01620631897e-20 relative error = 1.9226543457697920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=114.4MB, alloc=4.1MB, time=4.72 NO POLE x[1] = 0.0465 y[1] (analytic) = 1.0487676979549029889879391714735 y[1] (numeric) = 1.0487676979549029890081543522675 absolute error = 2.02151807940e-20 relative error = 1.9275174887079000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0466 y[1] (analytic) = 1.0488777008600797147052653660583 y[1] (numeric) = 1.0488777008600797147255337119539 absolute error = 2.02683458956e-20 relative error = 1.9323840976865040000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0467 y[1] (analytic) = 1.0489877268435959299276198468478 y[1] (numeric) = 1.0489877268435959299479414053848 absolute error = 2.03215585370e-20 relative error = 1.9372541753322100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0468 y[1] (analytic) = 1.0490977759127150650440621065883 y[1] (numeric) = 1.0490977759127150650644369253492 absolute error = 2.03748187609e-20 relative error = 1.9421277242889880000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0469 y[1] (analytic) = 1.0492078480747035987829188962333 y[1] (numeric) = 1.0492078480747035988033470228432 absolute error = 2.04281266099e-20 relative error = 1.9470047471895690000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.047 y[1] (analytic) = 1.0493179433368310598111227701994 y[1] (numeric) = 1.0493179433368310598316042523259 absolute error = 2.04814821265e-20 relative error = 1.9518852466554499999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0471 y[1] (analytic) = 1.049428061706370028334557666072 y[1] (numeric) = 1.0494280617063700283550925514257 absolute error = 2.05348853537e-20 relative error = 1.9567692253540730000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0472 y[1] (analytic) = 1.0495382031905961376994122586062 y[1] (numeric) = 1.0495382031905961377200005949403 absolute error = 2.05883363341e-20 relative error = 1.9616566859130480000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0473 y[1] (analytic) = 1.0496483677967880759945418284875 y[1] (numeric) = 1.0496483677967880760151836635979 absolute error = 2.06418351104e-20 relative error = 1.9665476309678079999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0474 y[1] (analytic) = 1.049758555532227587654839386941 y[1] (numeric) = 1.0497585555322275876755347686666 absolute error = 2.06953817256e-20 relative error = 1.9714420631806560000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0475 y[1] (analytic) = 1.0498687664041994750656167979003 y[1] (numeric) = 1.0498687664041994750863657741227 absolute error = 2.07489762224e-20 relative error = 1.9763399851835999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0476 y[1] (analytic) = 1.0499790004199916001679966400672 y[1] (numeric) = 1.0499790004199916001887992587111 absolute error = 2.08026186439e-20 relative error = 1.9812413996450360000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0477 y[1] (analytic) = 1.0500892575868948860653155518219 y[1] (numeric) = 1.0500892575868948860861718608549 absolute error = 2.08563090330e-20 relative error = 1.9861463092125900000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0478 y[1] (analytic) = 1.0501995379122033186305398025625 y[1] (numeric) = 1.0501995379122033186514498499951 absolute error = 2.09100474326e-20 relative error = 1.9910547165321720000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0479 y[1] (analytic) = 1.0503098414032139481146938346812 y[1] (numeric) = 1.0503098414032139481356576685671 absolute error = 2.09638338859e-20 relative error = 1.9959666242765390000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.048 y[1] (analytic) = 1.0504201680672268907563025210084 y[1] (numeric) = 1.0504201680672268907773201894443 absolute error = 2.10176684359e-20 relative error = 2.0008820350976800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=118.2MB, alloc=4.1MB, time=4.88 NO POLE x[1] = 0.0481 y[1] (analytic) = 1.050530517911545330391847883181 y[1] (numeric) = 1.0505305179115453304129194343067 absolute error = 2.10715511257e-20 relative error = 2.0058009516553830000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0482 y[1] (analytic) = 1.0506408909434755200672410170204 y[1] (numeric) = 1.0506408909434755200883664990189 absolute error = 2.11254819985e-20 relative error = 2.0107233766172300000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0483 y[1] (analytic) = 1.0507512871703267836503099716297 y[1] (numeric) = 1.0507512871703267836714894327273 absolute error = 2.11794610976e-20 relative error = 2.0156493126585920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0484 y[1] (analytic) = 1.0508617065994115174443043295502 y[1] (numeric) = 1.0508617065994115174655378180164 absolute error = 2.12334884662e-20 relative error = 2.0205787624435920000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0485 y[1] (analytic) = 1.0509721492380451918024172359432 y[1] (numeric) = 1.0509721492380451918237048000907 absolute error = 2.12875641475e-20 relative error = 2.0255117286346250000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0486 y[1] (analytic) = 1.0510826150935463527433256253942 y[1] (numeric) = 1.051082615093546352764667313579 absolute error = 2.13416881848e-20 relative error = 2.0304482139018719999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0487 y[1] (analytic) = 1.051193104173236623567749395564 y[1] (numeric) = 1.0511931041732366235891452561857 absolute error = 2.13958606217e-20 relative error = 2.0353882209423209999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0488 y[1] (analytic) = 1.0513036164844407064760302775442 y[1] (numeric) = 1.0513036164844407064974803590457 absolute error = 2.14500815015e-20 relative error = 2.0403317524226799999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0489 y[1] (analytic) = 1.0514141520344863841867311534013 y[1] (numeric) = 1.0514141520344863842082355042691 absolute error = 2.15043508678e-20 relative error = 2.0452788110364580000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.049 y[1] (analytic) = 1.0515247108307045215562565720294 y[1] (numeric) = 1.0515247108307045215778152407933 absolute error = 2.15586687639e-20 relative error = 2.0502293994468900000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0491 y[1] (analytic) = 1.0516352928804290671994952150594 y[1] (numeric) = 1.0516352928804290672211082502928 absolute error = 2.16130352334e-20 relative error = 2.0551835203440060000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0492 y[1] (analytic) = 1.0517458981909970551114850652082 y[1] (numeric) = 1.0517458981909970551331525155282 absolute error = 2.16674503200e-20 relative error = 2.0601411764256000000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0493 y[1] (analytic) = 1.0518565267697486062901020300831 y[1] (numeric) = 1.0518565267697486063118239441503 absolute error = 2.17219140672e-20 relative error = 2.0651023703687040000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0494 y[1] (analytic) = 1.0519671786240269303597727750894 y[1] (numeric) = 1.0519671786240269303815492016082 absolute error = 2.17764265188e-20 relative error = 2.0700671048771280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0495 y[1] (analytic) = 1.0520778537611783271962125197265 y[1] (numeric) = 1.0520778537611783272180435074448 absolute error = 2.18309877183e-20 relative error = 2.0750353826244149999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0496 y[1] (analytic) = 1.0521885521885521885521885521886 y[1] (numeric) = 1.0521885521885521885740741498983 absolute error = 2.18855977097e-20 relative error = 2.0800072063298879999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.1MB, time=5.04 NO POLE x[1] = 0.0497 y[1] (analytic) = 1.0522992739135009996843102178259 y[1] (numeric) = 1.0522992739135009997062504743627 absolute error = 2.19402565368e-20 relative error = 2.0849825786921040000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0498 y[1] (analytic) = 1.0524100189433803409808461376552 y[1] (numeric) = 1.0524100189433803410028411018985 absolute error = 2.19949642433e-20 relative error = 2.0899615023983660000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0499 y[1] (analytic) = 1.0525207872855488895905694137459 y[1] (numeric) = 1.052520787285548889612619134619 absolute error = 2.20497208731e-20 relative error = 2.0949439801532310000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.05 y[1] (analytic) = 1.0526315789473684210526315789474 y[1] (numeric) = 1.0526315789473684210747361054176 absolute error = 2.21045264702e-20 relative error = 2.0999300146689999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0501 y[1] (analytic) = 1.0527423939362038109274660490578 y[1] (numeric) = 1.0527423939362038109496254301364 absolute error = 2.21593810786e-20 relative error = 2.1049196086562140000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0502 y[1] (analytic) = 1.052853232259423036428721836176 y[1] (numeric) = 1.0528532322594230364509361209183 absolute error = 2.22142847423e-20 relative error = 2.1099127648236540000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0503 y[1] (analytic) = 1.0529640939243971780562282826156 y[1] (numeric) = 1.0529640939243971780784975201208 absolute error = 2.22692375052e-20 relative error = 2.1149094858688439999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0504 y[1] (analytic) = 1.0530749789385004212299915754002 y[1] (numeric) = 1.0530749789385004212523158148118 absolute error = 2.23242394116e-20 relative error = 2.1199097745255359999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0505 y[1] (analytic) = 1.0531858873091100579252238020011 y[1] (numeric) = 1.0531858873091100579476030925067 absolute error = 2.23792905056e-20 relative error = 2.1249136335067199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0506 y[1] (analytic) = 1.053296819043606488308405308616 y[1] (numeric) = 1.0532968190436064883308396994474 absolute error = 2.24343908314e-20 relative error = 2.1299210655331159999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0507 y[1] (analytic) = 1.0534077741493732223743811229327 y[1] (numeric) = 1.0534077741493732223968706633659 absolute error = 2.24895404332e-20 relative error = 2.1349320733236760000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0508 y[1] (analytic) = 1.0535187526337968815844922039612 y[1] (numeric) = 1.0535187526337968816070369433165 absolute error = 2.25447393553e-20 relative error = 2.1399466596050760000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0509 y[1] (analytic) = 1.053629754504267200505742282162 y[1] (numeric) = 1.053629754504267200528342269804 absolute error = 2.25999876420e-20 relative error = 2.1449648271022200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.051 y[1] (analytic) = 1.0537407797681770284510010537408 y[1] (numeric) = 1.0537407797681770284736563390784 absolute error = 2.26552853376e-20 relative error = 2.1499865785382400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0511 y[1] (analytic) = 1.0538518284329223311202444936242 y[1] (numeric) = 1.0538518284329223311429551261108 absolute error = 2.27106324866e-20 relative error = 2.1550119166534740000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0512 y[1] (analytic) = 1.0539629005059021922428330522766 y[1] (numeric) = 1.05396290050590219226559908141 absolute error = 2.27660291334e-20 relative error = 2.1600408441769919999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.1MB, time=5.21 NO POLE x[1] = 0.0513 y[1] (analytic) = 1.0540739959945188152208285021609 y[1] (numeric) = 1.0540739959945188152436499774834 absolute error = 2.28214753225e-20 relative error = 2.1650733638455749999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0514 y[1] (analytic) = 1.0541851149061775247733502002952 y[1] (numeric) = 1.0541851149061775247962271713937 absolute error = 2.28769710985e-20 relative error = 2.1701094784037099999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0515 y[1] (analytic) = 1.0542962572482867685819715340011 y[1] (numeric) = 1.054296257248286768604904050507 absolute error = 2.29325165059e-20 relative error = 2.1751491905846149999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0516 y[1] (analytic) = 1.0544074230282581189371573175875 y[1] (numeric) = 1.0544074230282581189601454291769 absolute error = 2.29881115894e-20 relative error = 2.1801925031386960000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0517 y[1] (analytic) = 1.0545186122535062743857429083623 y[1] (numeric) = 1.0545186122535062744087866647559 absolute error = 2.30437563936e-20 relative error = 2.1852394188050880000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0518 y[1] (analytic) = 1.0546298249314490613794558110103 y[1] (numeric) = 1.0546298249314490614025552619735 absolute error = 2.30994509632e-20 relative error = 2.1902899403306240000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0519 y[1] (analytic) = 1.0547410610695074359244805400274 y[1] (numeric) = 1.0547410610695074359476357353703 absolute error = 2.31551953429e-20 relative error = 2.1953440704603490000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.052 y[1] (analytic) = 1.0548523206751054852320675105485 y[1] (numeric) = 1.0548523206751054852552785001261 absolute error = 2.32109895776e-20 relative error = 2.2004018119564800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0521 y[1] (analytic) = 1.0549636037556704293701867285579 y[1] (numeric) = 1.05496360375567042939345356227 absolute error = 2.32668337121e-20 relative error = 2.2054631675699589999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0522 y[1] (analytic) = 1.0550749103186326229162270521207 y[1] (numeric) = 1.0550749103186326229395497799121 absolute error = 2.33227277914e-20 relative error = 2.2105281400688920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0523 y[1] (analytic) = 1.055186240371425556610741795927 y[1] (numeric) = 1.0551862403714255566341204677872 absolute error = 2.33786718602e-20 relative error = 2.2155967321911540000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0524 y[1] (analytic) = 1.0552975939214858590122414520895 y[1] (numeric) = 1.0552975939214858590356761180531 absolute error = 2.34346659636e-20 relative error = 2.2206689467107360000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0525 y[1] (analytic) = 1.0554089709762532981530343007916 y[1] (numeric) = 1.0554089709762532981765250109382 absolute error = 2.34907101466e-20 relative error = 2.2257447863903499999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0526 y[1] (analytic) = 1.0555203715431707831961156850327 y[1] (numeric) = 1.0555203715431707832196624894871 absolute error = 2.35468044544e-20 relative error = 2.2308242540098560000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0527 y[1] (analytic) = 1.0556317956296843660931067243745 y[1] (numeric) = 1.0556317956296843661167096733064 absolute error = 2.36029489319e-20 relative error = 2.2359073523188870000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=129.7MB, alloc=4.1MB, time=5.37 x[1] = 0.0528 y[1] (analytic) = 1.0557432432432432432432432432432 y[1] (numeric) = 1.0557432432432432432669023868675 absolute error = 2.36591436243e-20 relative error = 2.2409940840936960000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0529 y[1] (analytic) = 1.0558547143912997571534156900011 y[1] (numeric) = 1.0558547143912997571771310785778 absolute error = 2.37153885767e-20 relative error = 2.2460844520992569999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.053 y[1] (analytic) = 1.0559662090813093980992608236536 y[1] (numeric) = 1.0559662090813093981230325074882 absolute error = 2.37716838346e-20 relative error = 2.2511784591366200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0531 y[1] (analytic) = 1.0560777273207308057873059457176 y[1] (numeric) = 1.0560777273207308058111339751606 absolute error = 2.38280294430e-20 relative error = 2.2562761079576700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0532 y[1] (analytic) = 1.0561892691170257710181664554288 y[1] (numeric) = 1.0561892691170257710420508808762 absolute error = 2.38844254474e-20 relative error = 2.2613774013598320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0533 y[1] (analytic) = 1.05630083447765923735079750713 y[1] (numeric) = 1.0563008344776592373747383790231 absolute error = 2.39408718931e-20 relative error = 2.2664823421197770000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0534 y[1] (analytic) = 1.0564124234100993027678005493345 y[1] (numeric) = 1.05641242341009930279179791816 absolute error = 2.39973688255e-20 relative error = 2.2715909330218299999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0535 y[1] (analytic) = 1.0565240359218172213417855256207 y[1] (numeric) = 1.0565240359218172213658394419109 absolute error = 2.40539162902e-20 relative error = 2.2767031768674300000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0536 y[1] (analytic) = 1.0566356720202874049027895181741 y[1] (numeric) = 1.0566356720202874049269000325067 absolute error = 2.41105143326e-20 relative error = 2.2818190764372640000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0537 y[1] (analytic) = 1.0567473317129874247067526154496 y[1] (numeric) = 1.0567473317129874247309197784478 absolute error = 2.41671629982e-20 relative error = 2.2869386345196660000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0538 y[1] (analytic) = 1.0568590150073980131050517860917 y[1] (numeric) = 1.0568590150073980131292756484243 absolute error = 2.42238623326e-20 relative error = 2.2920618539106120000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0539 y[1] (analytic) = 1.0569707219110030652150935419089 y[1] (numeric) = 1.0569707219110030652393741542903 absolute error = 2.42806123814e-20 relative error = 2.2971887374042540000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.054 y[1] (analytic) = 1.0570824524312896405919661733615 y[1] (numeric) = 1.0570824524312896406163035865519 absolute error = 2.43374131904e-20 relative error = 2.3023192878118400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0541 y[1] (analytic) = 1.0571942065757479649011523416852 y[1] (numeric) = 1.0571942065757479649255466064904 absolute error = 2.43942648052e-20 relative error = 2.3074535079238679999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0542 y[1] (analytic) = 1.0573059843518714315923028124339 y[1] (numeric) = 1.0573059843518714316167539797056 absolute error = 2.44511672717e-20 relative error = 2.3125914005573860000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0543 y[1] (analytic) = 1.057417785767156603574072115893 y[1] (numeric) = 1.0574177857671566035985802365286 absolute error = 2.45081206356e-20 relative error = 2.3177329685086920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=133.5MB, alloc=4.1MB, time=5.52 NO POLE x[1] = 0.0544 y[1] (analytic) = 1.0575296108291032148900169204738 y[1] (numeric) = 1.0575296108291032149145820454166 absolute error = 2.45651249428e-20 relative error = 2.3228782145911679999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0545 y[1] (analytic) = 1.0576414595452141723955579058699 y[1] (numeric) = 1.0576414595452141724201800861092 absolute error = 2.46221802393e-20 relative error = 2.3280271416258150000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0546 y[1] (analytic) = 1.0577533319229955574360059234187 y[1] (numeric) = 1.0577533319229955574606852099895 absolute error = 2.46792865708e-20 relative error = 2.3331797524034319999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0547 y[1] (analytic) = 1.0578652279699566275256532317783 y[1] (numeric) = 1.0578652279699566275503896757618 absolute error = 2.47364439835e-20 relative error = 2.3383360497602549999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0548 y[1] (analytic) = 1.0579771476936098180279305966991 y[1] (numeric) = 1.0579771476936098180527242492225 absolute error = 2.47936525234e-20 relative error = 2.3434960365117680000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0549 y[1] (analytic) = 1.0580890911014707438366310443339 y[1] (numeric) = 1.0580890911014707438614819565705 absolute error = 2.48509122366e-20 relative error = 2.3486597154810660000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.055 y[1] (analytic) = 1.0582010582010582010582010582011 y[1] (numeric) = 1.0582010582010582010831092813702 absolute error = 2.49082231691e-20 relative error = 2.3538270894799499999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0551 y[1] (analytic) = 1.0583130489998941686951000105831 y[1] (numeric) = 1.0583130489998941687200655959504 absolute error = 2.49655853673e-20 relative error = 2.3589981613561770000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0552 y[1] (analytic) = 1.0584250635055038103302286198137 y[1] (numeric) = 1.0584250635055038103552516186909 absolute error = 2.50229988772e-20 relative error = 2.3641729339178560000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0553 y[1] (analytic) = 1.0585371017254154758124272255743 y[1] (numeric) = 1.0585371017254154758375076893194 absolute error = 2.50804637451e-20 relative error = 2.3693514099995969999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0554 y[1] (analytic) = 1.0586491636671607029430446749947 y[1] (numeric) = 1.0586491636671607029681826550122 absolute error = 2.51379800175e-20 relative error = 2.3745335924530500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0555 y[1] (analytic) = 1.0587612493382742191635786130228 y[1] (numeric) = 1.0587612493382742191887741607633 absolute error = 2.51955477405e-20 relative error = 2.3797194840902249999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0556 y[1] (analytic) = 1.0588733587462939432443879711986 y[1] (numeric) = 1.0588733587462939432696411381593 absolute error = 2.52531669607e-20 relative error = 2.3849090877685080000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0557 y[1] (analytic) = 1.0589854918987609869744784496452 y[1] (numeric) = 1.0589854918987609869997892873696 absolute error = 2.53108377244e-20 relative error = 2.3901024063150920000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0558 y[1] (analytic) = 1.0590976488032196568523617877568 y[1] (numeric) = 1.059097648803219656877730347835 absolute error = 2.53685600782e-20 relative error = 2.3952994425836440000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0559 y[1] (analytic) = 1.0592098294672174557779896197437 y[1] (numeric) = 1.0592098294672174558034159538122 absolute error = 2.54263340685e-20 relative error = 2.4005001994070849999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.1MB, time=5.68 NO POLE x[1] = 0.056 y[1] (analytic) = 1.0593220338983050847457627118644 y[1] (numeric) = 1.0593220338983050847712468716065 absolute error = 2.54841597421e-20 relative error = 2.4057046796542400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0561 y[1] (analytic) = 1.0594342621040364445386163788537 y[1] (numeric) = 1.0594342621040364445641584159991 absolute error = 2.55420371454e-20 relative error = 2.4109128861543060000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0562 y[1] (analytic) = 1.0595465140919686374231828777283 y[1] (numeric) = 1.0595465140919686374487828440535 absolute error = 2.55999663252e-20 relative error = 2.4161248217723760000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0563 y[1] (analytic) = 1.0596587898696619688460315778319 y[1] (numeric) = 1.0596587898696619688716895251601 absolute error = 2.56579473282e-20 relative error = 2.4213404893622340000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0564 y[1] (analytic) = 1.0597710894446799491309877066554 y[1] (numeric) = 1.0597710894446799491567036868564 absolute error = 2.57159802010e-20 relative error = 2.4265598917663599999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0565 y[1] (analytic) = 1.0598834128245892951775304716481 y[1] (numeric) = 1.0598834128245892952033045366388 absolute error = 2.57740649907e-20 relative error = 2.4317830318725450000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0566 y[1] (analytic) = 1.0599957600169599321602713589146 y[1] (numeric) = 1.0599957600169599321861035606585 absolute error = 2.58322017439e-20 relative error = 2.4370099125195259999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0567 y[1] (analytic) = 1.0601081310293649952295134103679 y[1] (numeric) = 1.0601081310293649952554038008756 absolute error = 2.58903905077e-20 relative error = 2.4422405365913409999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0568 y[1] (analytic) = 1.0602205258693808312128922815946 y[1] (numeric) = 1.0602205258693808312388409129236 absolute error = 2.59486313290e-20 relative error = 2.4474749069512799999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0569 y[1] (analytic) = 1.0603329445445870003180998833634 y[1] (numeric) = 1.0603329445445870003441068076181 absolute error = 2.60069242547e-20 relative error = 2.4527130264607569999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.057 y[1] (analytic) = 1.0604453870625662778366914103924 y[1] (numeric) = 1.0604453870625662778627566797243 absolute error = 2.60652693319e-20 relative error = 2.4579548979981699999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0571 y[1] (analytic) = 1.0605578534309046558489765616714 y[1] (numeric) = 1.0605578534309046558751002282792 absolute error = 2.61236666078e-20 relative error = 2.4632005244494620000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0572 y[1] (analytic) = 1.0606703436571913449299957573186 y[1] (numeric) = 1.0606703436571913449561778734479 absolute error = 2.61821161293e-20 relative error = 2.4684499086704040000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0573 y[1] (analytic) = 1.0607828577490187758565821576323 y[1] (numeric) = 1.0607828577490187758828227755761 absolute error = 2.62406179438e-20 relative error = 2.4737030535620260000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0574 y[1] (analytic) = 1.0608953957139826013155102906853 y[1] (numeric) = 1.0608953957139826013418094627837 absolute error = 2.62991720984e-20 relative error = 2.4789599619951840000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0575 y[1] (analytic) = 1.0610079575596816976127320954907 y[1] (numeric) = 1.061007957559681697639089874131 absolute error = 2.63577786403e-20 relative error = 2.4842206368482750000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.1MB, time=5.84 NO POLE x[1] = 0.0576 y[1] (analytic) = 1.061120543293718166383701188455 y[1] (numeric) = 1.061120543293718166410117626072 absolute error = 2.64164376170e-20 relative error = 2.4894850810260800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0577 y[1] (analytic) = 1.0612331529236973363047861615197 y[1] (numeric) = 1.0612331529236973363312613105954 absolute error = 2.64751490757e-20 relative error = 2.4947532974032110000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0578 y[1] (analytic) = 1.0613457864572277648057737210783 y[1] (numeric) = 1.0613457864572277648323076341423 absolute error = 2.65339130640e-20 relative error = 2.5000252888900800000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0579 y[1] (analytic) = 1.061458443901921239783462477444 y[1] (numeric) = 1.0614584439019212398100552070732 absolute error = 2.65927296292e-20 relative error = 2.5053010583669320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.058 y[1] (analytic) = 1.0615711252653927813163481953291 y[1] (numeric) = 1.0615711252653927813429997941479 absolute error = 2.66515988188e-20 relative error = 2.5105806087309600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0581 y[1] (analytic) = 1.0616838305552606433804013164879 y[1] (numeric) = 1.0616838305552606434071118371684 absolute error = 2.67105206805e-20 relative error = 2.5158639428962950000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0582 y[1] (analytic) = 1.0617965597791463155659375663623 y[1] (numeric) = 1.061796559779146315592707061624 absolute error = 2.67694952617e-20 relative error = 2.5211510637469060000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0583 y[1] (analytic) = 1.0619093129446745247955824572582 y[1] (numeric) = 1.0619093129446745248224109798683 absolute error = 2.68285226101e-20 relative error = 2.5264419741931169999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0584 y[1] (analytic) = 1.0620220900594732370433305012744 y[1] (numeric) = 1.062022090059473237070218104048 absolute error = 2.68876027736e-20 relative error = 2.5317366771621760000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0585 y[1] (analytic) = 1.0621348911311736590546999468933 y[1] (numeric) = 1.0621348911311736590816466826929 absolute error = 2.69467357996e-20 relative error = 2.5370351755323399999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0586 y[1] (analytic) = 1.0622477161674102400679838538347 y[1] (numeric) = 1.0622477161674102400949897755709 absolute error = 2.70059217362e-20 relative error = 2.5423374722458680000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0587 y[1] (analytic) = 1.0623605651758206735365983214703 y[1] (numeric) = 1.0623605651758206735636634821013 absolute error = 2.70651606310e-20 relative error = 2.5476435701960300000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0588 y[1] (analytic) = 1.0624734381640458988525286867828 y[1] (numeric) = 1.0624734381640458988796531393148 absolute error = 2.71244525320e-20 relative error = 2.5529534723118400000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0589 y[1] (analytic) = 1.0625863351397301030708745085538 y[1] (numeric) = 1.0625863351397301030980583060408 absolute error = 2.71837974870e-20 relative error = 2.5582671815015700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.059 y[1] (analytic) = 1.0626992561105207226354941551541 y[1] (numeric) = 1.0626992561105207226627373506982 absolute error = 2.72431955441e-20 relative error = 2.5635847006998100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=144.9MB, alloc=4.1MB, time=6.00 x[1] = 0.0591 y[1] (analytic) = 1.0628122010840684451057498140079 y[1] (numeric) = 1.0628122010840684451330524607591 absolute error = 2.73026467512e-20 relative error = 2.5689060328204079999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0592 y[1] (analytic) = 1.0629251700680272108843537414966 y[1] (numeric) = 1.0629251700680272109117158926531 absolute error = 2.73621511565e-20 relative error = 2.5742311808035200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0593 y[1] (analytic) = 1.063038163070054214946316572765 y[1] (numeric) = 1.063038163070054214973738281573 absolute error = 2.74217088080e-20 relative error = 2.5795601475685599999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0594 y[1] (analytic) = 1.0631511800978099085689985115883 y[1] (numeric) = 1.0631511800978099085964798313424 absolute error = 2.74813197541e-20 relative error = 2.5848929360706460000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0595 y[1] (analytic) = 1.063264221158958001063264221159 y[1] (numeric) = 1.0632642211589580010908052052016 absolute error = 2.75409840426e-20 relative error = 2.5902295492065299999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0596 y[1] (analytic) = 1.0633772862611654615057422373458 y[1] (numeric) = 1.0633772862611654615333429390679 absolute error = 2.76007017221e-20 relative error = 2.5955699899462840000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0597 y[1] (analytic) = 1.063490375412102520472189726683 y[1] (numeric) = 1.0634903754121025204998501995237 absolute error = 2.76604728407e-20 relative error = 2.6009142612110209999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0598 y[1] (analytic) = 1.06360348861944267177196341204 y[1] (numeric) = 1.0636034886194426717996837094869 absolute error = 2.77202974469e-20 relative error = 2.6062623659575380000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0599 y[1] (analytic) = 1.0637166258908626741835974896288 y[1] (numeric) = 1.0637166258908626742113776652178 absolute error = 2.77801755890e-20 relative error = 2.6116143071218899999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.06 y[1] (analytic) = 1.0638297872340425531914893617021 y[1] (numeric) = 1.0638297872340425532193294690177 absolute error = 2.78401073156e-20 relative error = 2.6169700876664000000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0601 y[1] (analytic) = 1.0639429726566656027236940100011 y[1] (numeric) = 1.063942972656665602751594102676 absolute error = 2.79000926749e-20 relative error = 2.6223297105138509999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0602 y[1] (analytic) = 1.0640561821664183868908278357097 y[1] (numeric) = 1.0640561821664183869187879674254 absolute error = 2.79601317157e-20 relative error = 2.6276931786414860000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0603 y[1] (analytic) = 1.0641694157709907417260827923805 y[1] (numeric) = 1.064169415770990741754103016867 absolute error = 2.80202244865e-20 relative error = 2.6330604949964050000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0604 y[1] (analytic) = 1.0642826734780757769263516389953 y[1] (numeric) = 1.0642826734780757769544320100312 absolute error = 2.80803710359e-20 relative error = 2.6384316625331640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0605 y[1] (analytic) = 1.0643959552953698775944651410325 y[1] (numeric) = 1.0643959552953698776226057124451 absolute error = 2.81405714126e-20 relative error = 2.6438066842137699999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0606 y[1] (analytic) = 1.0645092612305727059825420481158 y[1] (numeric) = 1.0645092612305727060107428737812 absolute error = 2.82008256654e-20 relative error = 2.6491855630076760000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=148.7MB, alloc=4.1MB, time=6.16 NO POLE x[1] = 0.0607 y[1] (analytic) = 1.0646225912913872032364526775258 y[1] (numeric) = 1.0646225912913872032647138113688 absolute error = 2.82611338430e-20 relative error = 2.6545683018729900000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0608 y[1] (analytic) = 1.0647359454855195911413969335605 y[1] (numeric) = 1.0647359454855195911697184295547 absolute error = 2.83214959942e-20 relative error = 2.6599549037752639999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0609 y[1] (analytic) = 1.0648493238206793738685975934405 y[1] (numeric) = 1.0648493238206793738969795056085 absolute error = 2.83819121680e-20 relative error = 2.6653453716968800000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.061 y[1] (analytic) = 1.0649627263045793397231096911608 y[1] (numeric) = 1.064962726304579339751552073574 absolute error = 2.84423824132e-20 relative error = 2.6707397085994800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0611 y[1] (analytic) = 1.0650761529449355628927468313984 y[1] (numeric) = 1.0650761529449355629212497381773 absolute error = 2.85029067789e-20 relative error = 2.6761379174709210000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0612 y[1] (analytic) = 1.0651896037494674051981252662974 y[1] (numeric) = 1.0651896037494674052266887516114 absolute error = 2.85634853140e-20 relative error = 2.6815400012783200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0613 y[1] (analytic) = 1.0653030787258975178438265686588 y[1] (numeric) = 1.0653030787258975178724506867264 absolute error = 2.86241180676e-20 relative error = 2.6869459630056120000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0614 y[1] (analytic) = 1.0654165778819518431706797357767 y[1] (numeric) = 1.0654165778819518431993645408656 absolute error = 2.86848050889e-20 relative error = 2.6923558056441540000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0615 y[1] (analytic) = 1.0655301012253596164091635588705 y[1] (numeric) = 1.0655301012253596164379091052975 absolute error = 2.87455464270e-20 relative error = 2.6977695321739500000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0616 y[1] (analytic) = 1.0656436487638533674339300937766 y[1] (numeric) = 1.0656436487638533674627364359077 absolute error = 2.88063421311e-20 relative error = 2.7031871455824240000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0617 y[1] (analytic) = 1.0657572205051689225194500692742 y[1] (numeric) = 1.0657572205051689225483172615246 absolute error = 2.88671922504e-20 relative error = 2.7086086488550320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0618 y[1] (analytic) = 1.0658708164570454060967810701343 y[1] (numeric) = 1.0658708164570454061257091669686 absolute error = 2.89280968343e-20 relative error = 2.7140340449940260000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0619 y[1] (analytic) = 1.0659844366272252425114593326937 y[1] (numeric) = 1.0659844366272252425404483886259 absolute error = 2.89890559322e-20 relative error = 2.7194633369996820000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.062 y[1] (analytic) = 1.0660980810234541577825159914712 y[1] (numeric) = 1.0660980810234541578115660610646 absolute error = 2.90500695934e-20 relative error = 2.7248965278609200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0621 y[1] (analytic) = 1.0662117496534811813626186160571 y[1] (numeric) = 1.0662117496534811813917297539246 absolute error = 2.91111378675e-20 relative error = 2.7303336205928250000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0622 y[1] (analytic) = 1.0663254425250586478993388782256 y[1] (numeric) = 1.0663254425250586479285111390294 absolute error = 2.91722608038e-20 relative error = 2.7357746181803640000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=152.5MB, alloc=4.1MB, time=6.32 NO POLE x[1] = 0.0623 y[1] (analytic) = 1.0664391596459421989975471899328 y[1] (numeric) = 1.0664391596459421990267806283848 absolute error = 2.92334384520e-20 relative error = 2.7412195236440400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0624 y[1] (analytic) = 1.0665529010238907849829351535836 y[1] (numeric) = 1.0665529010238907850122298244453 absolute error = 2.92946708617e-20 relative error = 2.7466683399929920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0625 y[1] (analytic) = 1.0666666666666666666666666666667 y[1] (numeric) = 1.0666666666666666666960226247492 absolute error = 2.93559580825e-20 relative error = 2.7521210702343749999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0626 y[1] (analytic) = 1.0667804565820354171111585235758 y[1] (numeric) = 1.06678045658203541714057582374 absolute error = 2.94173001642e-20 relative error = 2.7575777173921080000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0627 y[1] (analytic) = 1.0668942707777659233969913581564 y[1] (numeric) = 1.0668942707777659234264700553128 absolute error = 2.94786971564e-20 relative error = 2.7630382844693720000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0628 y[1] (analytic) = 1.0670081092616303883909517712335 y[1] (numeric) = 1.0670081092616303884204919203424 absolute error = 2.95401491089e-20 relative error = 2.7685027744861079999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0629 y[1] (analytic) = 1.0671219720414043325152064881016 y[1] (numeric) = 1.0671219720414043325448081441733 absolute error = 2.96016560717e-20 relative error = 2.7739711904790070000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.063 y[1] (analytic) = 1.0672358591248665955176093916756 y[1] (numeric) = 1.0672358591248665955472726097702 absolute error = 2.96632180946e-20 relative error = 2.7794435354640199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0631 y[1] (analytic) = 1.0673497705197993382431422777244 y[1] (numeric) = 1.067349770519799338272867112952 absolute error = 2.97248352276e-20 relative error = 2.7849198124738440000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0632 y[1] (analytic) = 1.0674637062339880444064901793339 y[1] (numeric) = 1.0674637062339880444362766868545 absolute error = 2.97865075206e-20 relative error = 2.7904000245298080000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0633 y[1] (analytic) = 1.0675776662752215223657521084659 y[1] (numeric) = 1.0675776662752215223956003434896 absolute error = 2.98482350237e-20 relative error = 2.7958841746699790000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0634 y[1] (analytic) = 1.0676916506512919068972880632073 y[1] (numeric) = 1.0676916506512919069271980809944 absolute error = 2.99100177871e-20 relative error = 2.8013722659397860000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0635 y[1] (analytic) = 1.0678056593699946609717031500267 y[1] (numeric) = 1.0678056593699946610016750058874 absolute error = 2.99718558607e-20 relative error = 2.8068643013545550000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0636 y[1] (analytic) = 1.0679196924391285775309696710807 y[1] (numeric) = 1.0679196924391285775610034203756 absolute error = 3.00337492949e-20 relative error = 2.8123602839744360000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0637 y[1] (analytic) = 1.0680337498664957812666880273417 y[1] (numeric) = 1.0680337498664957812967837254815 absolute error = 3.00956981398e-20 relative error = 2.8178602168294739999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0638 y[1] (analytic) = 1.0681478316599017303994872890408 y[1] (numeric) = 1.0681478316599017304296449914867 absolute error = 3.01577024459e-20 relative error = 2.8233641029851580000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.1MB, time=6.48 NO POLE x[1] = 0.0639 y[1] (analytic) = 1.0682619378271552184595662856532 y[1] (numeric) = 1.0682619378271552184897860479166 absolute error = 3.02197622634e-20 relative error = 2.8288719454768740000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.064 y[1] (analytic) = 1.0683760683760683760683760683761 y[1] (numeric) = 1.0683760683760683760986579460186 absolute error = 3.02818776425e-20 relative error = 2.8343837473379999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0641 y[1] (analytic) = 1.0684902233144566727214445987819 y[1] (numeric) = 1.0684902233144566727517886474159 absolute error = 3.03440486340e-20 relative error = 2.8398995116560600000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0642 y[1] (analytic) = 1.0686044026501389185723445180594 y[1] (numeric) = 1.0686044026501389186027507933476 absolute error = 3.04062752882e-20 relative error = 2.8454192414697560000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0643 y[1] (analytic) = 1.0687186063909372662178048519825 y[1] (numeric) = 1.0687186063909372662482734096381 absolute error = 3.04685576556e-20 relative error = 2.8509429398344919999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0644 y[1] (analytic) = 1.0688328345446772124839675074818 y[1] (numeric) = 1.0688328345446772125144984032688 absolute error = 3.05308957870e-20 relative error = 2.8564706098317200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0645 y[1] (analytic) = 1.0689470871191876002137894174238 y[1] (numeric) = 1.0689470871191876002443827071566 absolute error = 3.05932897328e-20 relative error = 2.8620022545034400000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0646 y[1] (analytic) = 1.0690613641223006200555911909344 y[1] (numeric) = 1.0690613641223006200862469304781 absolute error = 3.06557395437e-20 relative error = 2.8675378769176979999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0647 y[1] (analytic) = 1.0691756655618518122527531273388 y[1] (numeric) = 1.0691756655618518122834713726095 absolute error = 3.07182452707e-20 relative error = 2.8730774801685710000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0648 y[1] (analytic) = 1.0692899914456800684345594525235 y[1] (numeric) = 1.0692899914456800684653402594879 absolute error = 3.07808069644e-20 relative error = 2.8786210673106880000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0649 y[1] (analytic) = 1.069404341781627633408191637258 y[1] (numeric) = 1.0694043417816276334390350619336 absolute error = 3.08434246756e-20 relative error = 2.8841686414153560000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.065 y[1] (analytic) = 1.069518716577540106951871657754 y[1] (numeric) = 1.0695187165775401069827777562092 absolute error = 3.09060984552e-20 relative error = 2.8897202055612000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0651 y[1] (analytic) = 1.0696331158412664456091560594716 y[1] (numeric) = 1.0696331158412664456401248878259 absolute error = 3.09688283543e-20 relative error = 2.8952757628435070000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0652 y[1] (analytic) = 1.0697475395806589644843816859221 y[1] (numeric) = 1.0697475395806589645154133003459 absolute error = 3.10316144238e-20 relative error = 2.9008353163368240000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0653 y[1] (analytic) = 1.0698619878035733390392639349524 y[1] (numeric) = 1.069861987803573339070358391667 absolute error = 3.10944567146e-20 relative error = 2.9063988691136620000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=160.2MB, alloc=4.1MB, time=6.64 x[1] = 0.0654 y[1] (analytic) = 1.0699764605178686068906484057351 y[1] (numeric) = 1.0699764605178686069218057610131 absolute error = 3.11573552780e-20 relative error = 2.9119664242818799999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0655 y[1] (analytic) = 1.070090957731407169609416800428 y[1] (numeric) = 1.0700909577314071696406371105931 absolute error = 3.12203101651e-20 relative error = 2.9175379849285950000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0656 y[1] (analytic) = 1.0702054794520547945205479452055 y[1] (numeric) = 1.0702054794520547945518312666325 absolute error = 3.12833214270e-20 relative error = 2.9231135541388799999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0657 y[1] (analytic) = 1.070320025687680616504334796104 y[1] (numeric) = 1.0703200256876806165356811852191 absolute error = 3.13463891151e-20 relative error = 2.9286931350237930000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0658 y[1] (analytic) = 1.0704345964461571397987582958681 y[1] (numeric) = 1.0704345964461571398301678091486 absolute error = 3.14095132805e-20 relative error = 2.9342767306643100000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0659 y[1] (analytic) = 1.0705491917353602398030189487207 y[1] (numeric) = 1.0705491917353602398344916426953 absolute error = 3.14726939746e-20 relative error = 2.9398643441673860000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.066 y[1] (analytic) = 1.0706638115631691648822269807281 y[1] (numeric) = 1.0706638115631691649137629119769 absolute error = 3.15359312488e-20 relative error = 2.9454559786379199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0661 y[1] (analytic) = 1.0707784559374665381732519541707 y[1] (numeric) = 1.0707784559374665382048511793254 absolute error = 3.15992251547e-20 relative error = 2.9510516371974330000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0662 y[1] (analytic) = 1.070893124866138359391732705076 y[1] (numeric) = 1.0708931248661383594233952808197 absolute error = 3.16625757437e-20 relative error = 2.9566513229467060000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0663 y[1] (analytic) = 1.0710078183570740066402484738139 y[1] (numeric) = 1.0710078183570740066719744568811 absolute error = 3.17259830672e-20 relative error = 2.9622550389844639999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0664 y[1] (analytic) = 1.0711225364181662382176520994002 y[1] (numeric) = 1.0711225364181662382494415465772 absolute error = 3.17894471770e-20 relative error = 2.9678627884447199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0665 y[1] (analytic) = 1.071237279057311194429566148902 y[1] (numeric) = 1.0712372790573111944614191170267 absolute error = 3.18529681247e-20 relative error = 2.9734745744407449999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0666 y[1] (analytic) = 1.0713520462824083994000428540819 y[1] (numeric) = 1.0713520462824083994319594000438 absolute error = 3.19165459619e-20 relative error = 2.9790904000837459999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0667 y[1] (analytic) = 1.0714668381013607628843887281689 y[1] (numeric) = 1.0714668381013607629163689089094 absolute error = 3.19801807405e-20 relative error = 2.9847102685108649999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0668 y[1] (analytic) = 1.0715816545220745820831547363909 y[1] (numeric) = 1.0715816545220745821151986089032 absolute error = 3.20438725123e-20 relative error = 2.9903341828478360000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0669 y[1] (analytic) = 1.0716964955524595434572928946522 y[1] (numeric) = 1.0716964955524595434894005159812 absolute error = 3.21076213290e-20 relative error = 2.9959621462089900000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.1MB, time=6.80 NO POLE x[1] = 0.067 y[1] (analytic) = 1.0718113612004287245444801714898 y[1] (numeric) = 1.0718113612004287245766515987324 absolute error = 3.21714272426e-20 relative error = 3.0015941617345800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0671 y[1] (analytic) = 1.0719262514738985957766105691928 y[1] (numeric) = 1.0719262514738985958088458594979 absolute error = 3.22352903051e-20 relative error = 3.0072302325627790000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0672 y[1] (analytic) = 1.0720411663807890222984562607204 y[1] (numeric) = 1.0720411663807890223307554712888 absolute error = 3.22992105684e-20 relative error = 3.0128703618203520000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0673 y[1] (analytic) = 1.0721561059290232657874986598049 y[1] (numeric) = 1.0721561059290232658198618478895 absolute error = 3.23631880846e-20 relative error = 3.0185145526506419999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0674 y[1] (analytic) = 1.0722710701265279862749303023804 y[1] (numeric) = 1.0722710701265279863073575252864 absolute error = 3.24272229060e-20 relative error = 3.0241628082135600000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0675 y[1] (analytic) = 1.0723860589812332439678284182306 y[1] (numeric) = 1.072386058981233244000319733315 absolute error = 3.24913150844e-20 relative error = 3.0298151316202999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0676 y[1] (analytic) = 1.0725010725010725010725010725011 y[1] (numeric) = 1.0725010725010725011050565371734 absolute error = 3.25554646723e-20 relative error = 3.0354715260452519999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0677 y[1] (analytic) = 1.0726161106939826236190067574815 y[1] (numeric) = 1.0726161106939826236516264292034 absolute error = 3.26196717219e-20 relative error = 3.0411319946327370000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0678 y[1] (analytic) = 1.0727311735679038832868483158121 y[1] (numeric) = 1.0727311735679038833195322520976 absolute error = 3.26839362855e-20 relative error = 3.0467965405343099999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0679 y[1] (analytic) = 1.0728462611307799592318420770304 y[1] (numeric) = 1.0728462611307799592645903354459 absolute error = 3.27482584155e-20 relative error = 3.0524651669087549999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.068 y[1] (analytic) = 1.0729613733905579399141630901288 y[1] (numeric) = 1.0729613733905579399469757282931 absolute error = 3.28126381643e-20 relative error = 3.0581378769127599999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0681 y[1] (analytic) = 1.073076510355188324927567335551 y[1] (numeric) = 1.0730765103551883249604444111355 absolute error = 3.28770755845e-20 relative error = 3.0638146737195550000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0682 y[1] (analytic) = 1.0731916720326250268297918008156 y[1] (numeric) = 1.073191672032625026862733371544 absolute error = 3.29415707284e-20 relative error = 3.0694955604723120000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0683 y[1] (analytic) = 1.0733068584308253729741333047118 y[1] (numeric) = 1.0733068584308253730071394283605 absolute error = 3.30061236487e-20 relative error = 3.0751805403493790000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0684 y[1] (analytic) = 1.073422069557750107342206955775 y[1] (numeric) = 1.073422069557750107375277690173 absolute error = 3.30707343980e-20 relative error = 3.0808696165176800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0685 y[1] (analytic) = 1.0735373054213633923778851315083 y[1] (numeric) = 1.0735373054213633924110205345373 absolute error = 3.31354030290e-20 relative error = 3.0865627921513500000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=167.8MB, alloc=4.1MB, time=6.96 NO POLE x[1] = 0.0686 y[1] (analytic) = 1.0736525660296328108224178655787 y[1] (numeric) = 1.0736525660296328108556179951731 absolute error = 3.32001295944e-20 relative error = 3.0922600704224160000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0687 y[1] (analytic) = 1.0737678513905293675507355309782 y[1] (numeric) = 1.0737678513905293675840004451252 absolute error = 3.32649141470e-20 relative error = 3.0979614545101100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0688 y[1] (analytic) = 1.0738831615120274914089347079038 y[1] (numeric) = 1.0738831615120274914422644646435 absolute error = 3.33297567397e-20 relative error = 3.1036669476008639999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0689 y[1] (analytic) = 1.0739984964021050370529481258726 y[1] (numeric) = 1.073998496402105037086342783298 absolute error = 3.33946574254e-20 relative error = 3.1093765528789940000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.069 y[1] (analytic) = 1.0741138560687432867883995703545 y[1] (numeric) = 1.0741138560687432868218591866114 absolute error = 3.34596162569e-20 relative error = 3.1150902735173899999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0691 y[1] (analytic) = 1.0742292405199269524116446449672 y[1] (numeric) = 1.0742292405199269524451692782546 absolute error = 3.35246332874e-20 relative error = 3.1208081127240660000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0692 y[1] (analytic) = 1.0743446497636441770519982810486 y[1] (numeric) = 1.0743446497636441770855879896183 absolute error = 3.35897085697e-20 relative error = 3.1265300736676759999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0693 y[1] (analytic) = 1.0744600838078865370151498871817 y[1] (numeric) = 1.0744600838078865370488047293388 absolute error = 3.36548421571e-20 relative error = 3.1322561595612970000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0694 y[1] (analytic) = 1.0745755426606490436277670320224 y[1] (numeric) = 1.0745755426606490436614870661251 absolute error = 3.37200341027e-20 relative error = 3.1379863735972619999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0695 y[1] (analytic) = 1.0746910263299301450832885545406 y[1] (numeric) = 1.0746910263299301451170738390003 absolute error = 3.37852844597e-20 relative error = 3.1437207189750849999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0696 y[1] (analytic) = 1.0748065348237317282889079965606 y[1] (numeric) = 1.074806534823731728322758589842 absolute error = 3.38505932814e-20 relative error = 3.1494591989014560000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0697 y[1] (analytic) = 1.0749220681500591207137482532516 y[1] (numeric) = 1.0749220681500591207476642138727 absolute error = 3.39159606211e-20 relative error = 3.1552018165809330000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0698 y[1] (analytic) = 1.0750376263169210922382283379918 y[1] (numeric) = 1.0750376263169210922722097245239 absolute error = 3.39813865321e-20 relative error = 3.1609485752159420000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0699 y[1] (analytic) = 1.0751532093323298570046231588001 y[1] (numeric) = 1.075153209332329857038670029868 absolute error = 3.40468710679e-20 relative error = 3.1666994780253790000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.07 y[1] (analytic) = 1.0752688172043010752688172043011 y[1] (numeric) = 1.075268817204301075302929618583 absolute error = 3.41124142819e-20 relative error = 3.1724545282166999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0701 y[1] (analytic) = 1.0753844499408538552532530379611 y[1] (numeric) = 1.0753844499408538552874310541888 absolute error = 3.41780162277e-20 relative error = 3.1782137290138229999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.1MB, time=7.13 NO POLE x[1] = 0.0702 y[1] (analytic) = 1.0755001075500107550010755001076 y[1] (numeric) = 1.0755001075500107550353191770664 absolute error = 3.42436769588e-20 relative error = 3.1839770836292239999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0703 y[1] (analytic) = 1.0756157900397977842314725180166 y[1] (numeric) = 1.0756157900397977842657819145455 absolute error = 3.43093965289e-20 relative error = 3.1897445952918329999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0704 y[1] (analytic) = 1.0757314974182444061962134251291 y[1] (numeric) = 1.0757314974182444062305886001208 absolute error = 3.43751749917e-20 relative error = 3.1955162672284320000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0705 y[1] (analytic) = 1.0758472296933835395373856912318 y[1] (numeric) = 1.0758472296933835395718267036327 absolute error = 3.44410124009e-20 relative error = 3.2012921026636550000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0706 y[1] (analytic) = 1.0759629868732515601463309662148 y[1] (numeric) = 1.075962986873251560180837875025 absolute error = 3.45069088102e-20 relative error = 3.2070721048199879999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0707 y[1] (analytic) = 1.0760787689658883030237813407941 y[1] (numeric) = 1.0760787689658883030583542050678 absolute error = 3.45728642737e-20 relative error = 3.2128562769549410000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0708 y[1] (analytic) = 1.0761945759793370641411967283685 y[1] (numeric) = 1.0761945759793370641758356072135 absolute error = 3.46388788450e-20 relative error = 3.2186446222774000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0709 y[1] (analytic) = 1.0763104079216446023033042729523 y[1] (numeric) = 1.0763104079216446023380092255306 absolute error = 3.47049525783e-20 relative error = 3.2244371440498530000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.071 y[1] (analytic) = 1.0764262648008611410118406889128 y[1] (numeric) = 1.0764262648008611410466117744402 absolute error = 3.47710855274e-20 relative error = 3.2302338454954600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0711 y[1] (analytic) = 1.0765421466250403703304984390139 y[1] (numeric) = 1.0765421466250403703653357167603 absolute error = 3.48372777464e-20 relative error = 3.2360347298630960000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0712 y[1] (analytic) = 1.0766580534022394487510766580534 y[1] (numeric) = 1.076658053402239448785980187343 absolute error = 3.49035292896e-20 relative error = 3.2418398004180480000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0713 y[1] (analytic) = 1.0767739851405190050608377301604 y[1] (numeric) = 1.0767739851405190050958075703714 absolute error = 3.49698402110e-20 relative error = 3.2476490603955700000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0714 y[1] (analytic) = 1.0768899418479431402110704286022 y[1] (numeric) = 1.076889941847943140246106639167 absolute error = 3.50362105648e-20 relative error = 3.2534625130473280000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0715 y[1] (analytic) = 1.0770059235325794291868605277329 y[1] (numeric) = 1.0770059235325794292219631681383 absolute error = 3.51026404054e-20 relative error = 3.2592801616413900000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0716 y[1] (analytic) = 1.0771219302024989228780697975011 y[1] (numeric) = 1.0771219302024989229132389272881 absolute error = 3.51691297870e-20 relative error = 3.2651020094250799999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=175.4MB, alloc=4.1MB, time=7.28 x[1] = 0.0717 y[1] (analytic) = 1.077237961865776149951524291716 y[1] (numeric) = 1.0772379618657761499867599704801 absolute error = 3.52356787641e-20 relative error = 3.2709280596714030000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0718 y[1] (analytic) = 1.0773540185304891187244128420599 y[1] (numeric) = 1.0773540185304891187597151294509 absolute error = 3.53022873910e-20 relative error = 3.2767583156326200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0719 y[1] (analytic) = 1.0774701002047193190388966706174 y[1] (numeric) = 1.0774701002047193190742656263397 absolute error = 3.53689557223e-20 relative error = 3.2825927805866630000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.072 y[1] (analytic) = 1.0775862068965517241379310344828 y[1] (numeric) = 1.0775862068965517241733667182953 absolute error = 3.54356838125e-20 relative error = 3.2884314577999999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0721 y[1] (analytic) = 1.0777023386140747925422998167906 y[1] (numeric) = 1.0777023386140747925778022885069 absolute error = 3.55024717163e-20 relative error = 3.2942743505554770000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0722 y[1] (analytic) = 1.0778184953653804699288639793059 y[1] (numeric) = 1.0778184953653804699644332987941 absolute error = 3.55693194882e-20 relative error = 3.3001214621151960000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0723 y[1] (analytic) = 1.0779346771585641910100247924976 y[1] (numeric) = 1.0779346771585641910456610196805 absolute error = 3.56362271829e-20 relative error = 3.3059727957576329999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0724 y[1] (analytic) = 1.0780508840017248814144027598103 y[1] (numeric) = 1.0780508840017248814501059546656 absolute error = 3.57031948553e-20 relative error = 3.3118283547776279999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0725 y[1] (analytic) = 1.0781671159029649595687331536388 y[1] (numeric) = 1.078167115902964959604503376199 absolute error = 3.57702225602e-20 relative error = 3.3176881424585500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0726 y[1] (analytic) = 1.0782833728703903385809790813026 y[1] (numeric) = 1.0782833728703903386168163916549 absolute error = 3.58373103523e-20 relative error = 3.3235521620723019999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0727 y[1] (analytic) = 1.0783996549121104281246630001078 y[1] (numeric) = 1.0783996549121104281605674583946 absolute error = 3.59044582868e-20 relative error = 3.3294204169349640000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0728 y[1] (analytic) = 1.0785159620362381363244176013805 y[1] (numeric) = 1.0785159620362381363603892677989 absolute error = 3.59716664184e-20 relative error = 3.3352929103140480000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0729 y[1] (analytic) = 1.0786322942508898716427569841441 y[1] (numeric) = 1.0786322942508898716787959189464 absolute error = 3.60389348023e-20 relative error = 3.3411696455212330000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.073 y[1] (analytic) = 1.0787486515641855447680690399137 y[1] (numeric) = 1.0787486515641855448041753034072 absolute error = 3.61062634935e-20 relative error = 3.3470506258474500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0731 y[1] (analytic) = 1.0788650339842485705038299708706 y[1] (numeric) = 1.0788650339842485705400036234179 absolute error = 3.61736525473e-20 relative error = 3.3529358546092370000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0732 y[1] (analytic) = 1.0789814415192058696590418644799 y[1] (numeric) = 1.0789814415192058696952829664986 absolute error = 3.62411020187e-20 relative error = 3.3588253350931160000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.2MB, alloc=4.1MB, time=7.44 NO POLE x[1] = 0.0733 y[1] (analytic) = 1.0790978741771878709398942484083 y[1] (numeric) = 1.0790978741771878709762028603714 absolute error = 3.63086119631e-20 relative error = 3.3647190706204770000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0734 y[1] (analytic) = 1.0792143319663285128426505503993 y[1] (numeric) = 1.079214331966328512879026732835 absolute error = 3.63761824357e-20 relative error = 3.3706170644919620000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0735 y[1] (analytic) = 1.0793308148947652455477603885591 y[1] (numeric) = 1.0793308148947652455842042020511 absolute error = 3.64438134920e-20 relative error = 3.3765193200338000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0736 y[1] (analytic) = 1.0794473229706390328151986183074 y[1] (numeric) = 1.0794473229706390328517101234948 absolute error = 3.65115051874e-20 relative error = 3.3824258405607360000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0737 y[1] (analytic) = 1.0795638562020943538810320630465 y[1] (numeric) = 1.0795638562020943539176113206238 absolute error = 3.65792575773e-20 relative error = 3.3883366293852990000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0738 y[1] (analytic) = 1.0796804145972792053552148564025 y[1] (numeric) = 1.0796804145972792053918619271197 absolute error = 3.66470707172e-20 relative error = 3.3942516898270640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0739 y[1] (analytic) = 1.079796998164345103120613324695 y[1] (numeric) = 1.0797969981643451031573282693577 absolute error = 3.67149446627e-20 relative error = 3.4001710252126469999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.074 y[1] (analytic) = 1.0799136069114470842332613390929 y[1] (numeric) = 1.0799136069114470842700442185624 absolute error = 3.67828794695e-20 relative error = 3.4060946388756999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0741 y[1] (analytic) = 1.0800302408467437088238470677179 y[1] (numeric) = 1.0800302408467437088606979429112 absolute error = 3.68508751933e-20 relative error = 3.4120225341476470000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0742 y[1] (analytic) = 1.08014689997839706200043205876 y[1] (numeric) = 1.0801468999783970620373509906498 absolute error = 3.69189318898e-20 relative error = 3.4179547143576840000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0743 y[1] (analytic) = 1.0802635843145727557524035864751 y[1] (numeric) = 1.08026358431457275578939063609 absolute error = 3.69870496149e-20 relative error = 3.4238911828512930000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0744 y[1] (analytic) = 1.0803802938634399308556611927398 y[1] (numeric) = 1.0803802938634399308927164211642 absolute error = 3.70552284244e-20 relative error = 3.4298319429624640000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0745 y[1] (analytic) = 1.0804970286331712587790383576445 y[1] (numeric) = 1.0804970286331712588161618260187 absolute error = 3.71234683742e-20 relative error = 3.4357769980322100000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0746 y[1] (analytic) = 1.0806137886319429435919602334126 y[1] (numeric) = 1.0806137886319429436291520029328 absolute error = 3.71917695202e-20 relative error = 3.4417263513993079999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0747 y[1] (analytic) = 1.0807305738679347238733383767427 y[1] (numeric) = 1.0807305738679347239105985086613 absolute error = 3.72601319186e-20 relative error = 3.4476800064280579999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0748 y[1] (analytic) = 1.0808473843493298746217034154777 y[1] (numeric) = 1.0808473843493298746590319711032 absolute error = 3.73285556255e-20 relative error = 3.4536379664712600000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=183.1MB, alloc=4.2MB, time=7.60 NO POLE x[1] = 0.0749 y[1] (analytic) = 1.080964220084315209166576586315 y[1] (numeric) = 1.0809642200843152092039736270118 absolute error = 3.73970406968e-20 relative error = 3.4596002348609680000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.075 y[1] (analytic) = 1.0810810810810810810810810810811 y[1] (numeric) = 1.08108108108108108111854666827 absolute error = 3.74655871889e-20 relative error = 3.4655668149732499999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0751 y[1] (analytic) = 1.081197967347821386095794139907 y[1] (numeric) = 1.0811979673478213861333283350651 absolute error = 3.75341951581e-20 relative error = 3.4715377101726690000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0752 y[1] (analytic) = 1.0813148788927335640138408304498 y[1] (numeric) = 1.0813148788927335640514436951104 absolute error = 3.76028646606e-20 relative error = 3.4775129238122880000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0753 y[1] (analytic) = 1.0814318157240186006272304531199 y[1] (numeric) = 1.0814318157240186006649020488726 absolute error = 3.76715957527e-20 relative error = 3.4834924592521690000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0754 y[1] (analytic) = 1.0815487778498810296344365130867 y[1] (numeric) = 1.0815487778498810296721769015776 absolute error = 3.77403884909e-20 relative error = 3.4894763198686140000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0755 y[1] (analytic) = 1.081665765278528934559221200649 y[1] (numeric) = 1.0816657652785289345970304435807 absolute error = 3.78092429317e-20 relative error = 3.4954645090356650000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0756 y[1] (analytic) = 1.0817827780181739506707053223713 y[1] (numeric) = 1.0817827780181739507085834815029 absolute error = 3.78781591316e-20 relative error = 3.5014570301251039999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0757 y[1] (analytic) = 1.0818998160770312669046846262036 y[1] (numeric) = 1.0818998160770312669426317633509 absolute error = 3.79471371473e-20 relative error = 3.5074538865249390000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0758 y[1] (analytic) = 1.082016879463319627786193464618 y[1] (numeric) = 1.0820168794633196278242096416533 absolute error = 3.80161770353e-20 relative error = 3.5134550816024260000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0759 y[1] (analytic) = 1.0821339681852613353533167406125 y[1] (numeric) = 1.0821339681852613353914020194648 absolute error = 3.80852788523e-20 relative error = 3.5194606187410430000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.076 y[1] (analytic) = 1.0822510822510822510822510822511 y[1] (numeric) = 1.0822510822510822511204055249063 absolute error = 3.81544426552e-20 relative error = 3.5254705013404799999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0761 y[1] (analytic) = 1.0823682216690117978136161922286 y[1] (numeric) = 1.0823682216690117978518398607294 absolute error = 3.82236685008e-20 relative error = 3.5314847327889120000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0762 y[1] (analytic) = 1.0824853864472829616800173197662 y[1] (numeric) = 1.0824853864472829617183102762121 absolute error = 3.82929564459e-20 relative error = 3.5375033164722419999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0763 y[1] (analytic) = 1.0826025765941322940348598029663 y[1] (numeric) = 1.0826025765941322940732221095138 absolute error = 3.83623065475e-20 relative error = 3.5435262557925750000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0764 y[1] (analytic) = 1.082719792117799913382416630576 y[1] (numeric) = 1.0827197921177999134208483494384 absolute error = 3.84317188624e-20 relative error = 3.5495535541312640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.2MB, time=7.75 NO POLE x[1] = 0.0765 y[1] (analytic) = 1.0828370330265295073091499729291 y[1] (numeric) = 1.0828370330265295073476511663769 absolute error = 3.85011934478e-20 relative error = 3.5555852149043299999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0766 y[1] (analytic) = 1.0829542993285683344162876326619 y[1] (numeric) = 1.0829542993285683344548583630228 absolute error = 3.85707303609e-20 relative error = 3.5616212415255060000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0767 y[1] (analytic) = 1.0830715910321672262536553666197 y[1] (numeric) = 1.0830715910321672262922956962784 absolute error = 3.86403296587e-20 relative error = 3.5676616373877710000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0768 y[1] (analytic) = 1.0831889081455805892547660311958 y[1] (numeric) = 1.0831889081455805892934760225943 absolute error = 3.87099913985e-20 relative error = 3.5737064059095200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0769 y[1] (analytic) = 1.0833062506770664066731665041707 y[1] (numeric) = 1.0833062506770664067119462198082 absolute error = 3.87797156375e-20 relative error = 3.5797555504976250000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.077 y[1] (analytic) = 1.0834236186348862405200433369447 y[1] (numeric) = 1.0834236186348862405588928393778 absolute error = 3.88495024331e-20 relative error = 3.5858090745751300000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0771 y[1] (analytic) = 1.0835410120273052335030880918843 y[1] (numeric) = 1.0835410120273052335420074437269 absolute error = 3.89193518426e-20 relative error = 3.5918669815535539999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0772 y[1] (analytic) = 1.0836584308625921109666233203294 y[1] (numeric) = 1.083658430862592111005612584253 absolute error = 3.89892639236e-20 relative error = 3.5979292748698080000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0773 y[1] (analytic) = 1.0837758751490191828329901376395 y[1] (numeric) = 1.0837758751490191828720493763729 absolute error = 3.90592387334e-20 relative error = 3.6039959579308180000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0774 y[1] (analytic) = 1.0838933448948623455451983524821 y[1] (numeric) = 1.0838933448948623455843276288118 absolute error = 3.91292763297e-20 relative error = 3.6100670341781220000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0775 y[1] (analytic) = 1.0840108401084010840108401084011 y[1] (numeric) = 1.0840108401084010840500394851712 absolute error = 3.91993767701e-20 relative error = 3.6161425070417249999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0776 y[1] (analytic) = 1.0841283607979184735472679965308 y[1] (numeric) = 1.0841283607979184735865375366431 absolute error = 3.92695401123e-20 relative error = 3.6222223799585520000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0777 y[1] (analytic) = 1.0842459069717011818280385991543 y[1] (numeric) = 1.0842459069717011818673783655682 absolute error = 3.93397664139e-20 relative error = 3.6283066563539970000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0778 y[1] (analytic) = 1.0843634786380394708306224246367 y[1] (numeric) = 1.0843634786380394708700324803696 absolute error = 3.94100557329e-20 relative error = 3.6343953396880380000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0779 y[1] (analytic) = 1.0844810758052271987853811950981 y[1] (numeric) = 1.0844810758052271988248616032251 absolute error = 3.94804081270e-20 relative error = 3.6404884333906700000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.078 y[1] (analytic) = 1.0845986984815618221258134490239 y[1] (numeric) = 1.0845986984815618221653642726779 absolute error = 3.95508236540e-20 memory used=190.7MB, alloc=4.2MB, time=7.92 relative error = 3.6465859408987999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0781 y[1] (analytic) = 1.0847163466753443974400694218462 y[1] (numeric) = 1.0847163466753443974796907242183 absolute error = 3.96213023721e-20 relative error = 3.6526878656838990000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0782 y[1] (analytic) = 1.0848340203948795834237361683662 y[1] (numeric) = 1.0848340203948795834634280127055 absolute error = 3.96918443393e-20 relative error = 3.6587942111966740000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0783 y[1] (analytic) = 1.0849517196484756428338938917218 y[1] (numeric) = 1.0849517196484756428736563413353 absolute error = 3.97624496135e-20 relative error = 3.6649049808762950000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0784 y[1] (analytic) = 1.0850694444444444444444444444444 y[1] (numeric) = 1.0850694444444444444842775626974 absolute error = 3.98331182530e-20 relative error = 3.6710201781964800000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0785 y[1] (analytic) = 1.085187194791101465002712967987 y[1] (numeric) = 1.0851871947911014650426168183029 absolute error = 3.99038503159e-20 relative error = 3.6771398066101849999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0786 y[1] (analytic) = 1.0853049706967657911873236379423 y[1] (numeric) = 1.0853049706967657912272982838028 absolute error = 3.99746458605e-20 relative error = 3.6832638695864699999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0787 y[1] (analytic) = 1.0854227721697601215673504830131 y[1] (numeric) = 1.0854227721697601216073959879583 absolute error = 4.00455049452e-20 relative error = 3.6893923706012760000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0788 y[1] (analytic) = 1.0855405992184107685627442466348 y[1] (numeric) = 1.085540599218410768602860674263 absolute error = 4.01164276282e-20 relative error = 3.6955253131097840000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0789 y[1] (analytic) = 1.0856584518510476604060362609923 y[1] (numeric) = 1.0856584518510476604462236749603 absolute error = 4.01874139680e-20 relative error = 3.7016627005924800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.079 y[1] (analytic) = 1.0857763300760043431053203040174 y[1] (numeric) = 1.0857763300760043431455787680406 absolute error = 4.02584640232e-20 relative error = 3.7078045365367199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0791 y[1] (analytic) = 1.0858942339016179824085134107938 y[1] (numeric) = 1.085894233901617982448842988646 absolute error = 4.03295778522e-20 relative error = 3.7139508244090980000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0792 y[1] (analytic) = 1.086012163336229365768896611642 y[1] (numeric) = 1.0860121633362293658092973671558 absolute error = 4.04007555138e-20 relative error = 3.7201015677107040000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0793 y[1] (analytic) = 1.0861301183881829043119365700011 y[1] (numeric) = 1.0861301183881829043524085670675 absolute error = 4.04719970664e-20 relative error = 3.7262567699034480000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0794 y[1] (analytic) = 1.0862480990658266348033890940691 y[1] (numeric) = 1.086248099065826634843932396638 absolute error = 4.05433025689e-20 relative error = 3.7324164344929339999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0795 y[1] (analytic) = 1.0863661053775122216186854970125 y[1] (numeric) = 1.0863661053775122216593001690925 absolute error = 4.06146720800e-20 relative error = 3.7385805649640000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=194.5MB, alloc=4.2MB, time=8.08 x[1] = 0.0796 y[1] (analytic) = 1.0864841373315949587136027813994 y[1] (numeric) = 1.086484137331594958754288887058 absolute error = 4.06861056586e-20 relative error = 3.7447491648175440000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0797 y[1] (analytic) = 1.0866021949364337715962186243616 y[1] (numeric) = 1.0866021949364337716369762277252 absolute error = 4.07576033636e-20 relative error = 3.7509222375521080000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0798 y[1] (analytic) = 1.0867202782003912193001521408389 y[1] (numeric) = 1.0867202782003912193409813060928 absolute error = 4.08291652539e-20 relative error = 3.7570997866638780000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0799 y[1] (analytic) = 1.0868383871318334963590914031084 y[1] (numeric) = 1.0868383871318334963999921944968 absolute error = 4.09007913884e-20 relative error = 3.7632818156466839999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.08 y[1] (analytic) = 1.0869565217391304347826086956522 y[1] (numeric) = 1.0869565217391304348235811774787 absolute error = 4.09724818265e-20 relative error = 3.7694683280379999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0801 y[1] (analytic) = 1.0870746820306555060332644852701 y[1] (numeric) = 1.0870746820306555060743087218973 absolute error = 4.10442366272e-20 relative error = 3.7756593273361280000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0802 y[1] (analytic) = 1.0871928680147858230050010871929 y[1] (numeric) = 1.0871928680147858230461171430424 absolute error = 4.11160558495e-20 relative error = 3.7818548170370099999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0803 y[1] (analytic) = 1.0873110796999021420028270088072 y[1] (numeric) = 1.0873110796999021420440149483601 absolute error = 4.11879395529e-20 relative error = 3.7880548006802130000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0804 y[1] (analytic) = 1.087429317094388864723792953458 y[1] (numeric) = 1.0874293170943888647650528412546 absolute error = 4.12598877966e-20 relative error = 3.7942592817753360000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0805 y[1] (analytic) = 1.0875475802066340402392604676455 y[1] (numeric) = 1.0875475802066340402805923682855 absolute error = 4.13319006400e-20 relative error = 3.8004682638479999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0806 y[1] (analytic) = 1.0876658690450293669784642157929 y[1] (numeric) = 1.0876658690450293670198681939355 absolute error = 4.14039781426e-20 relative error = 3.8066817504306440000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0807 y[1] (analytic) = 1.0877841836179701947133688676167 y[1] (numeric) = 1.0877841836179701947548449879805 absolute error = 4.14761203638e-20 relative error = 3.8128997450441339999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0808 y[1] (analytic) = 1.0879025239338555265448215839861 y[1] (numeric) = 1.0879025239338555265863699113493 absolute error = 4.15483273632e-20 relative error = 3.8191222512253439999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0809 y[1] (analytic) = 1.0880208900010880208900010880209 y[1] (numeric) = 1.0880208900010880209316216872213 absolute error = 4.16205992004e-20 relative error = 3.8253492725087640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.081 y[1] (analytic) = 1.0881392818280739934711643090316 y[1] (numeric) = 1.0881392818280739935128572449666 absolute error = 4.16929359350e-20 relative error = 3.8315808124264999999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0811 y[1] (analytic) = 1.088257699423223419305691587768 y[1] (numeric) = 1.0882576994232234193474569253949 absolute error = 4.17653376269e-20 relative error = 3.8378168745358409999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=198.3MB, alloc=4.2MB, time=8.24 NO POLE x[1] = 0.0812 y[1] (analytic) = 1.088376142794949934697431432303 y[1] (numeric) = 1.0883761427949499347392692366388 absolute error = 4.18378043358e-20 relative error = 3.8440574623733040000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0813 y[1] (analytic) = 1.0884946119516708392293458147382 y[1] (numeric) = 1.0884946119516708392712561508597 absolute error = 4.19103361215e-20 relative error = 3.8503025794822050000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0814 y[1] (analytic) = 1.0886131069018070977574569997823 y[1] (numeric) = 1.0886131069018070977994399328262 absolute error = 4.19829330439e-20 relative error = 3.8565522294126539999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0815 y[1] (analytic) = 1.0887316276537833424060968971149 y[1] (numeric) = 1.088731627653783342448152492278 absolute error = 4.20555951631e-20 relative error = 3.8628064157307349999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0816 y[1] (analytic) = 1.0888501742160278745644599303136 y[1] (numeric) = 1.0888501742160278746065882528527 absolute error = 4.21283225391e-20 relative error = 3.8690651419909440000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0817 y[1] (analytic) = 1.0889687465969726668844604159861 y[1] (numeric) = 1.088968746596972666926661531218 absolute error = 4.22011152319e-20 relative error = 3.8753284117453769999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0818 y[1] (analytic) = 1.0890873448050533652798954476149 y[1] (numeric) = 1.0890873448050533653221694209167 absolute error = 4.22739733018e-20 relative error = 3.8815962285712760000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0819 y[1] (analytic) = 1.0892059688487092909269142794903 y[1] (numeric) = 1.0892059688487092909692611762991 absolute error = 4.23468968088e-20 relative error = 3.8878685960159279999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.082 y[1] (analytic) = 1.0893246187363834422657952069717 y[1] (numeric) = 1.0893246187363834423082150927851 absolute error = 4.24198858134e-20 relative error = 3.8941455176701199999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0821 y[1] (analytic) = 1.0894432944765224970040309401896 y[1] (numeric) = 1.0894432944765224970465238805654 absolute error = 4.24929403758e-20 relative error = 3.9004269970946819999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0822 y[1] (analytic) = 1.0895619960775768141207234691654 y[1] (numeric) = 1.0895619960775768141632895297218 absolute error = 4.25660605564e-20 relative error = 3.9067130378663920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0823 y[1] (analytic) = 1.0896807235480004358722894192002 y[1] (numeric) = 1.0896807235480004359149286656159 absolute error = 4.26392464157e-20 relative error = 3.9130036435687889999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0824 y[1] (analytic) = 1.0897994768962510897994768962511 y[1] (numeric) = 1.0897994768962510898421893942653 absolute error = 4.27124980142e-20 relative error = 3.9192988177829920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0825 y[1] (analytic) = 1.0899182561307901907356948228883 y[1] (numeric) = 1.0899182561307901907784806383008 absolute error = 4.27858154125e-20 relative error = 3.9255985640968749999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0826 y[1] (analytic) = 1.0900370612600828428166557662961 y[1] (numeric) = 1.0900370612600828428595149649673 absolute error = 4.28591986712e-20 relative error = 3.9319028860958879999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0827 y[1] (analytic) = 1.0901558922925978414913332606563 y[1] (numeric) = 1.0901558922925978415342659085073 absolute error = 4.29326478510e-20 relative error = 3.9382117873722299999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=202.1MB, alloc=4.2MB, time=8.40 NO POLE x[1] = 0.0828 y[1] (analytic) = 1.090274749236807675534234627126 y[1] (numeric) = 1.0902747492368076755772407901388 absolute error = 4.30061630128e-20 relative error = 3.9445252715340160000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0829 y[1] (analytic) = 1.0903936321011885290589902954967 y[1] (numeric) = 1.0903936321011885291020700397138 absolute error = 4.30797442171e-20 relative error = 3.9508433421502409999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.083 y[1] (analytic) = 1.0905125408942202835332606324973 y[1] (numeric) = 1.0905125408942202835764140240224 absolute error = 4.31533915251e-20 relative error = 3.9571660028516699999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0831 y[1] (analytic) = 1.0906314756243865197949612825826 y[1] (numeric) = 1.0906314756243865198381883875802 absolute error = 4.32271049976e-20 relative error = 3.9634932572299440000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0832 y[1] (analytic) = 1.0907504363001745200698080279232 y[1] (numeric) = 1.0907504363001745201131089126188 absolute error = 4.33008846956e-20 relative error = 3.9698251088926080000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0833 y[1] (analytic) = 1.0908694229300752699901821751936 y[1] (numeric) = 1.0908694229300752700335569058738 absolute error = 4.33747306802e-20 relative error = 3.9761615614539340000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0834 y[1] (analytic) = 1.0909884355225834606153174776347 y[1] (numeric) = 1.0909884355225834606587661206473 absolute error = 4.34486430126e-20 relative error = 3.9825026185349160000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0835 y[1] (analytic) = 1.0911074740861974904528096017458 y[1] (numeric) = 1.0911074740861974904963322234996 absolute error = 4.35226217538e-20 relative error = 3.9888482837357699999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0836 y[1] (analytic) = 1.0912265386294194674814491488433 y[1] (numeric) = 1.0912265386294194675250458158086 absolute error = 4.35966669653e-20 relative error = 3.9951985607000920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0837 y[1] (analytic) = 1.0913456291607552111753792426061 y[1] (numeric) = 1.0913456291607552112190500213143 absolute error = 4.36707787082e-20 relative error = 4.0015534530323660000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0838 y[1] (analytic) = 1.0914647456887142545295786946082 y[1] (numeric) = 1.0914647456887142545733236516521 absolute error = 4.37449570439e-20 relative error = 4.0079129643621179999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0839 y[1] (analytic) = 1.0915838882218098460866717607248 y[1] (numeric) = 1.0915838882218098461304909627588 absolute error = 4.38192020340e-20 relative error = 4.0142770983347400000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.084 y[1] (analytic) = 1.0917030567685589519650655021834 y[1] (numeric) = 1.0917030567685589520089590159232 absolute error = 4.38935137398e-20 relative error = 4.0206458585656800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0841 y[1] (analytic) = 1.0918222513374822578884157659133 y[1] (numeric) = 1.0918222513374822579323836581363 absolute error = 4.39678922230e-20 relative error = 4.0270192487045700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0842 y[1] (analytic) = 1.0919414719371041712164227997379 y[1] (numeric) = 1.0919414719371041712604651372831 absolute error = 4.40423375452e-20 relative error = 4.0333972723894160000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0843 y[1] (analytic) = 1.092060718575952822976957518838 y[1] (numeric) = 1.092060718575952823021074368606 absolute error = 4.41168497680e-20 relative error = 4.0397799332557600000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.2MB, time=8.56 NO POLE x[1] = 0.0844 y[1] (analytic) = 1.0921799912625600698995194408038 y[1] (numeric) = 1.092179991262560069943710869757 absolute error = 4.41914289532e-20 relative error = 4.0461672349549920000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0845 y[1] (analytic) = 1.0922992900054614964500273074822 y[1] (numeric) = 1.0922992900054614964942933826448 absolute error = 4.42660751626e-20 relative error = 4.0525591811360300000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0846 y[1] (analytic) = 1.0924186148131964168669434127158 y[1] (numeric) = 1.0924186148131964169112842011737 absolute error = 4.43407884579e-20 relative error = 4.0589557754361659999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0847 y[1] (analytic) = 1.0925379656943078771987326559598 y[1] (numeric) = 1.0925379656943078772431482248612 absolute error = 4.44155689014e-20 relative error = 4.0653570215451420000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0848 y[1] (analytic) = 1.0926573426573426573426573426573 y[1] (numeric) = 1.0926573426573426573871477592122 absolute error = 4.44904165549e-20 relative error = 4.0717629231044480000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0849 y[1] (analytic) = 1.0927767457108512730849087531417 y[1] (numeric) = 1.0927767457108512731294740846221 absolute error = 4.45653314804e-20 relative error = 4.0781734837714040000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.085 y[1] (analytic) = 1.0928961748633879781420765027322 y[1] (numeric) = 1.0928961748633879781867168164723 absolute error = 4.46403137401e-20 relative error = 4.0845887072191500000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0851 y[1] (analytic) = 1.093015630123510766203956716581 y[1] (numeric) = 1.0930156301235107662486720799771 absolute error = 4.47153633961e-20 relative error = 4.0910085971091890000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0852 y[1] (analytic) = 1.0931351114997813729777000437254 y[1] (numeric) = 1.0931351114997813730224905242361 absolute error = 4.47904805107e-20 relative error = 4.0974331571188360000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0853 y[1] (analytic) = 1.0932546190007652782333005356948 y[1] (numeric) = 1.093254619000765278278166200841 absolute error = 4.48656651462e-20 relative error = 4.1038623909229139999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0854 y[1] (analytic) = 1.0933741526350317078504264159195 y[1] (numeric) = 1.0933741526350317078953673332846 absolute error = 4.49409173651e-20 relative error = 4.1102963022120460000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0855 y[1] (analytic) = 1.0934937124111536358665937670858 y[1] (numeric) = 1.0934937124111536359116100043154 absolute error = 4.50162372296e-20 relative error = 4.1167348946469200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0856 y[1] (analytic) = 1.0936132983377077865266841644794 y[1] (numeric) = 1.0936132983377077865717757892817 absolute error = 4.50916248023e-20 relative error = 4.1231781719223120000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0857 y[1] (analytic) = 1.0937329104232746363338072842612 y[1] (numeric) = 1.0937329104232746363789743644069 absolute error = 4.51670801457e-20 relative error = 4.1296261377213509999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0858 y[1] (analytic) = 1.0938525486764384161015095165172 y[1] (numeric) = 1.0938525486764384161467521198398 absolute error = 4.52426033226e-20 relative error = 4.1360787957520919999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0859 y[1] (analytic) = 1.0939722131057871130073296138278 y[1] (numeric) = 1.0939722131057871130526478082234 absolute error = 4.53181943956e-20 relative error = 4.1425361497017960000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.2MB, time=8.71 NO POLE x[1] = 0.086 y[1] (analytic) = 1.0940919037199124726477024070022 y[1] (numeric) = 1.0940919037199124726930962604295 absolute error = 4.53938534273e-20 relative error = 4.1489982032552200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0861 y[1] (analytic) = 1.0942116205274100010942116205274 y[1] (numeric) = 1.0942116205274100011396812010081 absolute error = 4.54695804807e-20 relative error = 4.1554649601311730000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0862 y[1] (analytic) = 1.0943313635368789669511928211863 y[1] (numeric) = 1.0943313635368789669967381968049 absolute error = 4.55453756186e-20 relative error = 4.1619364240276679999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0863 y[1] (analytic) = 1.0944511327569224034146875342016 y[1] (numeric) = 1.0944511327569224034603087731056 absolute error = 4.56212389040e-20 relative error = 4.1684125986584800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0864 y[1] (analytic) = 1.0945709281961471103327495621716 y[1] (numeric) = 1.0945709281961471103784467325714 absolute error = 4.56971703998e-20 relative error = 4.1748934877257280000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0865 y[1] (analytic) = 1.0946907498631636562671045429666 y[1] (numeric) = 1.0946907498631636563128777131357 absolute error = 4.57731701691e-20 relative error = 4.1813790949472850000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0866 y[1] (analytic) = 1.0948105977665863805561637836654 y[1] (numeric) = 1.0948105977665863806020130219405 absolute error = 4.58492382751e-20 relative error = 4.1878694240476340000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0867 y[1] (analytic) = 1.0949304719150333953793934085186 y[1] (numeric) = 1.0949304719150333954253187832994 absolute error = 4.59253747808e-20 relative error = 4.1943644787304639999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0868 y[1] (analytic) = 1.0950503723171265878230398598336 y[1] (numeric) = 1.0950503723171265878690414395833 absolute error = 4.60015797497e-20 relative error = 4.2008642627426039999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0869 y[1] (analytic) = 1.0951702989814916219472127915891 y[1] (numeric) = 1.0951702989814916219932906448341 absolute error = 4.60778532450e-20 relative error = 4.2073687798009500000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.087 y[1] (analytic) = 1.0952902519167579408543263964951 y[1] (numeric) = 1.0952902519167579409004805918252 absolute error = 4.61541953301e-20 relative error = 4.2138780336381299999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0871 y[1] (analytic) = 1.0954102311315587687589002081279 y[1] (numeric) = 1.0954102311315587688051308141964 absolute error = 4.62306060685e-20 relative error = 4.2203920279933650000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0872 y[1] (analytic) = 1.0955302366345311130587204206836 y[1] (numeric) = 1.0955302366345311131050275062071 absolute error = 4.63070855235e-20 relative error = 4.2269107665850800000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0873 y[1] (analytic) = 1.0956502684343157664073627698039 y[1] (numeric) = 1.0956502684343157664537464035628 absolute error = 4.63836337589e-20 relative error = 4.2334342531748029999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0874 y[1] (analytic) = 1.0957703265395573087880780188472 y[1] (numeric) = 1.0957703265395573088345382696855 absolute error = 4.64602508383e-20 relative error = 4.2399624915032580000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=213.6MB, alloc=4.2MB, time=8.87 x[1] = 0.0875 y[1] (analytic) = 1.0958904109589041095890410958904 y[1] (numeric) = 1.0958904109589041096355780327157 absolute error = 4.65369368253e-20 relative error = 4.2464954853086250000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0876 y[1] (analytic) = 1.0960105217010083296799649276633 y[1] (numeric) = 1.0960105217010083297265786194471 absolute error = 4.66136917838e-20 relative error = 4.2530332383539120000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0877 y[1] (analytic) = 1.0961306587745259234900800175381 y[1] (numeric) = 1.0961306587745259235367705333156 absolute error = 4.66905157775e-20 relative error = 4.2595757543813250000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0878 y[1] (analytic) = 1.0962508221881166410874808156106 y[1] (numeric) = 1.0962508221881166411342482244811 absolute error = 4.67674088705e-20 relative error = 4.2661230371670100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0879 y[1] (analytic) = 1.0963710119504440302598399298323 y[1] (numeric) = 1.0963710119504440303066843009588 absolute error = 4.68443711265e-20 relative error = 4.2726750904480649999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.088 y[1] (analytic) = 1.0964912280701754385964912280702 y[1] (numeric) = 1.09649122807017543864341263068 absolute error = 4.69214026098e-20 relative error = 4.2792319180137599999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0881 y[1] (analytic) = 1.0966114705559820155718828818949 y[1] (numeric) = 1.0966114705559820156188813852793 absolute error = 4.69985033844e-20 relative error = 4.2857935236234360000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0882 y[1] (analytic) = 1.0967317394165387146304014038166 y[1] (numeric) = 1.0967317394165387146774770773309 absolute error = 4.70756735143e-20 relative error = 4.2923599110338740000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0883 y[1] (analytic) = 1.0968520346605242952725677306131 y[1] (numeric) = 1.096852034660524295319720643677 absolute error = 4.71529130639e-20 relative error = 4.2989310840357630000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0884 y[1] (analytic) = 1.0969723562966213251426064063186 y[1] (numeric) = 1.0969723562966213251898366284159 absolute error = 4.72302220973e-20 relative error = 4.3055070463898679999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0885 y[1] (analytic) = 1.0970927043335161821173889193637 y[1] (numeric) = 1.0970927043335161821646965200427 absolute error = 4.73076006790e-20 relative error = 4.3120878018908499999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0886 y[1] (analytic) = 1.0972130787798990563967522492868 y[1] (numeric) = 1.0972130787798990564441372981602 absolute error = 4.73850488734e-20 relative error = 4.3186733543216760000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0887 y[1] (analytic) = 1.0973334796444639525951936793592 y[1] (numeric) = 1.0973334796444639526426562461041 absolute error = 4.74625667449e-20 relative error = 4.3252637074627369999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0888 y[1] (analytic) = 1.0974539069359086918349429323968 y[1] (numeric) = 1.0974539069359086918824830867551 absolute error = 4.75401543583e-20 relative error = 4.3318588651282960000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0889 y[1] (analytic) = 1.0975743606629349138404126879596 y[1] (numeric) = 1.0975743606629349138880304997375 absolute error = 4.76178117779e-20 relative error = 4.3384588310844690000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.089 y[1] (analytic) = 1.0976948408342480790340285400659 y[1] (numeric) = 1.0976948408342480790817240791344 absolute error = 4.76955390685e-20 relative error = 4.3450636091403499999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=217.4MB, alloc=4.2MB, time=9.03 NO POLE x[1] = 0.0891 y[1] (analytic) = 1.0978153474585574706334394554836 y[1] (numeric) = 1.0978153474585574706812127917785 absolute error = 4.77733362949e-20 relative error = 4.3516732031024410000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0892 y[1] (analytic) = 1.0979358805445761967501097935881 y[1] (numeric) = 1.0979358805445761967979609971099 absolute error = 4.78512035218e-20 relative error = 4.3582876167655439999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0893 y[1] (analytic) = 1.098056440101021192489293949709 y[1] (numeric) = 1.0980564401010211925372230905232 absolute error = 4.79291408142e-20 relative error = 4.3649068539491940000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0894 y[1] (analytic) = 1.0981770261366132220513946848232 y[1] (numeric) = 1.0981770261366132220994018330601 absolute error = 4.80071482369e-20 relative error = 4.3715309184521140000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0895 y[1] (analytic) = 1.0982976386600768808347062053817 y[1] (numeric) = 1.0982976386600768808827914312366 absolute error = 4.80852258549e-20 relative error = 4.3781598140886449999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0896 y[1] (analytic) = 1.0984182776801405975395430579965 y[1] (numeric) = 1.0984182776801405975877064317299 absolute error = 4.81633737334e-20 relative error = 4.3847935446887359999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0897 y[1] (analytic) = 1.0985389432055366362737559046468 y[1] (numeric) = 1.0985389432055366363219974965843 absolute error = 4.82415919375e-20 relative error = 4.3914321140706250000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0898 y[1] (analytic) = 1.0986596352450010986596352450011 y[1] (numeric) = 1.0986596352450010987079551255334 absolute error = 4.83198805323e-20 relative error = 4.3980755260499460000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0899 y[1] (analytic) = 1.0987803538072739259422041533897 y[1] (numeric) = 1.0987803538072739259906023929729 absolute error = 4.83982395832e-20 relative error = 4.4047237844670320000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.09 y[1] (analytic) = 1.0989010989010989010989010989011 y[1] (numeric) = 1.0989010989010989011473777680565 absolute error = 4.84766691554e-20 relative error = 4.4113768931414000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0901 y[1] (analytic) = 1.099021870535223650950653918013 y[1] (numeric) = 1.0990218705352236509992090873274 absolute error = 4.85551693144e-20 relative error = 4.4180348559172559999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0902 y[1] (analytic) = 1.0991426687183996482743460101121 y[1] (numeric) = 1.0991426687183996483229797502379 absolute error = 4.86337401258e-20 relative error = 4.4246976766452840000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0903 y[1] (analytic) = 1.0992634934593822139166758271958 y[1] (numeric) = 1.0992634934593822139653882088507 absolute error = 4.87123816549e-20 relative error = 4.4313653591462529999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0904 y[1] (analytic) = 1.0993843447669305189094107299912 y[1] (numeric) = 1.0993843447669305189582018239586 absolute error = 4.87910939674e-20 relative error = 4.4380379072747040000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0905 y[1] (analytic) = 1.0995052226498075865860362836723 y[1] (numeric) = 1.0995052226498075866349061608013 absolute error = 4.88698771290e-20 relative error = 4.4447153248825500000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0906 y[1] (analytic) = 1.0996261271167802946998020672971 y[1] (numeric) = 1.0996261271167802947487507985024 absolute error = 4.89487312053e-20 relative error = 4.4513976158099820000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=221.2MB, alloc=4.2MB, time=9.19 NO POLE x[1] = 0.0907 y[1] (analytic) = 1.0997470581766193775431650720334 y[1] (numeric) = 1.0997470581766193775921927282956 absolute error = 4.90276562622e-20 relative error = 4.4580847839218460000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0908 y[1] (analytic) = 1.0998680158380994280686317641883 y[1] (numeric) = 1.0998680158380994281177384165538 absolute error = 4.91066523655e-20 relative error = 4.4647768330712600000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0909 y[1] (analytic) = 1.0999890001099989000109998900011 y[1] (numeric) = 1.0999890001099989000601856095823 absolute error = 4.91857195812e-20 relative error = 4.4714737671268920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.091 y[1] (analytic) = 1.10011001100110011001100110011 y[1] (numeric) = 1.1001100110011001100602659580853 absolute error = 4.92648579753e-20 relative error = 4.4781755899547700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0911 y[1] (analytic) = 1.1002310485201892397403454725492 y[1] (numeric) = 1.100231048520189239789689540163 absolute error = 4.93440676138e-20 relative error = 4.4848823054182820000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0912 y[1] (analytic) = 1.1003521126760563380281690140845 y[1] (numeric) = 1.1003521126760563380775923626473 absolute error = 4.94233485628e-20 relative error = 4.4915939173872640000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0913 y[1] (analytic) = 1.1004732034774953229888852206449 y[1] (numeric) = 1.1004732034774953230383879215335 absolute error = 4.95027008886e-20 relative error = 4.4983104297470819999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0914 y[1] (analytic) = 1.1005943209333039841514417785604 y[1] (numeric) = 1.1005943209333039842010239032179 absolute error = 4.95821246575e-20 relative error = 4.5050318463804500000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0915 y[1] (analytic) = 1.100715465052283984589983489268 y[1] (numeric) = 1.1007154650522839846396451092037 absolute error = 4.96616199357e-20 relative error = 4.5117581711583450000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0916 y[1] (analytic) = 1.1008366358432408630559225011008 y[1] (numeric) = 1.1008366358432408631056636878905 absolute error = 4.97411867897e-20 relative error = 4.5184894079763480000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0917 y[1] (analytic) = 1.1009578333149840361114169327315 y[1] (numeric) = 1.1009578333149840361612377580174 absolute error = 4.98208252859e-20 relative error = 4.5252255607182969999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0918 y[1] (analytic) = 1.1010790574763268002642589737943 y[1] (numeric) = 1.1010790574763268003141595092853 absolute error = 4.99005354910e-20 relative error = 4.5319666332926200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0919 y[1] (analytic) = 1.1012003083360863341041735491686 y[1] (numeric) = 1.10120030833608633415415386664 absolute error = 4.99803174714e-20 relative error = 4.5387126295778340000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.092 y[1] (analytic) = 1.1013215859030837004405286343612 y[1] (numeric) = 1.1013215859030837004905888056551 absolute error = 5.00601712939e-20 relative error = 4.5454635534861200000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0921 y[1] (analytic) = 1.1014428901861438484414583103866 y[1] (numeric) = 1.1014428901861438484915984074117 absolute error = 5.01400970251e-20 relative error = 4.5522194089088290000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0922 y[1] (analytic) = 1.1015642211940956157743996474994 y[1] (numeric) = 1.1015642211940956158246197422314 absolute error = 5.02200947320e-20 relative error = 4.5589801997709600000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=225.0MB, alloc=4.2MB, time=9.35 NO POLE x[1] = 0.0923 y[1] (analytic) = 1.1016855789357717307480445080974 y[1] (numeric) = 1.1016855789357717307983446725787 absolute error = 5.03001644813e-20 relative error = 4.5657459299676010000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0924 y[1] (analytic) = 1.1018069634200088144557073600705 y[1] (numeric) = 1.1018069634200088145060876664106 absolute error = 5.03803063401e-20 relative error = 4.5725166034274760000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0925 y[1] (analytic) = 1.1019283746556473829201101928375 y[1] (numeric) = 1.1019283746556473829705707132127 absolute error = 5.04605203752e-20 relative error = 4.5792922240493999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0926 y[1] (analytic) = 1.1020498126515318492395856292704 y[1] (numeric) = 1.1020498126515318492901264359243 absolute error = 5.05408066539e-20 relative error = 4.5860727957748860000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0927 y[1] (analytic) = 1.1021712774165105257356993276755 y[1] (numeric) = 1.1021712774165105257863204929187 absolute error = 5.06211652432e-20 relative error = 4.5928583225155360000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0928 y[1] (analytic) = 1.1022927689594356261022927689594 y[1] (numeric) = 1.1022927689594356261529943651698 absolute error = 5.07015962104e-20 relative error = 4.5996488082074880000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0929 y[1] (analytic) = 1.1024142872891632675559475250799 y[1] (numeric) = 1.1024142872891632676067296247026 absolute error = 5.07820996227e-20 relative error = 4.6064442567751170000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.093 y[1] (analytic) = 1.1025358324145534729878721058434 y[1] (numeric) = 1.1025358324145534730387347813909 absolute error = 5.08626755475e-20 relative error = 4.6132446721582500000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0931 y[1] (analytic) = 1.1026574043444701731172124820818 y[1] (numeric) = 1.102657404344470173168155806134 absolute error = 5.09433240522e-20 relative error = 4.6200500582940180000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0932 y[1] (analytic) = 1.1027790030877812086457873842082 y[1] (numeric) = 1.1027790030877812086968114294125 absolute error = 5.10240452043e-20 relative error = 4.6268604191259240000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0933 y[1] (analytic) = 1.1029006286533583324142494761222 y[1] (numeric) = 1.1029006286533583324653543151935 absolute error = 5.11048390713e-20 relative error = 4.6336757585947710000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0934 y[1] (analytic) = 1.1030222810500772115596735054048 y[1] (numeric) = 1.1030222810500772116108592111257 absolute error = 5.11857057209e-20 relative error = 4.6404960806567940000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0935 y[1] (analytic) = 1.1031439602868174296745725317154 y[1] (numeric) = 1.1031439602868174297258391769362 absolute error = 5.12666452208e-20 relative error = 4.6473213892655200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0936 y[1] (analytic) = 1.1032656663724624889673433362754 y[1] (numeric) = 1.1032656663724624890186909939141 absolute error = 5.13476576387e-20 relative error = 4.6541516883717679999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0937 y[1] (analytic) = 1.103387399315899812424142116297 y[1] (numeric) = 1.1033873993158998124755708593395 absolute error = 5.14287430425e-20 relative error = 4.6609869819417750000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE memory used=228.8MB, alloc=4.2MB, time=9.51 x[1] = 0.0938 y[1] (analytic) = 1.10350915912602074597219156919 y[1] (numeric) = 1.10350915912602074602370147069 absolute error = 5.15099015000e-20 relative error = 4.6678272739300000000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0939 y[1] (analytic) = 1.103630945811720560644520472354 y[1] (numeric) = 1.1036309458117205606961116054333 absolute error = 5.15911330793e-20 relative error = 4.6746725683153730000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.094 y[1] (analytic) = 1.1037527593818984547461368653422 y[1] (numeric) = 1.1037527593818984547978093031905 absolute error = 5.16724378483e-20 relative error = 4.6815228690559799999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0941 y[1] (analytic) = 1.103874599845457556021635942157 y[1] (numeric) = 1.1038745998454575560733897580322 absolute error = 5.17538158752e-20 relative error = 4.6883781801343679999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0942 y[1] (analytic) = 1.10399646721130492382424376242 y[1] (numeric) = 1.1039964672113049238760790296482 absolute error = 5.18352672282e-20 relative error = 4.6952385055303559999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0943 y[1] (analytic) = 1.1041183614883515512862978911339 y[1] (numeric) = 1.1041183614883515513382146831095 absolute error = 5.19167919756e-20 relative error = 4.7021038492300920000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0944 y[1] (analytic) = 1.1042402826855123674911660777385 y[1] (numeric) = 1.104240282685512367543164467924 absolute error = 5.19983901855e-20 relative error = 4.7089742151988800000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0945 y[1] (analytic) = 1.1043622308117062396466040861403 y[1] (numeric) = 1.1043622308117062396986841480666 absolute error = 5.20800619263e-20 relative error = 4.7158496074264649999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0946 y[1] (analytic) = 1.1044842058758559752595537883808 y[1] (numeric) = 1.1044842058758559753117155956475 absolute error = 5.21618072667e-20 relative error = 4.7227300299270180000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0947 y[1] (analytic) = 1.1046062078868883243123826355904 y[1] (numeric) = 1.1046062078868883243646262618654 absolute error = 5.22436262750e-20 relative error = 4.7296154866757500000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0948 y[1] (analytic) = 1.1047282368537339814405656208573 y[1] (numeric) = 1.1047282368537339814928911398772 absolute error = 5.23255190199e-20 relative error = 4.7365059816813479999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0949 y[1] (analytic) = 1.1048502927853275881118108496299 y[1] (numeric) = 1.1048502927853275881642183351999 absolute error = 5.24074855700e-20 relative error = 4.7434015189406999999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.095 y[1] (analytic) = 1.1049723756906077348066298342541 y[1] (numeric) = 1.1049723756906077348591193602483 absolute error = 5.24895259942e-20 relative error = 4.7503021024751000000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0951 y[1] (analytic) = 1.1050944855785169632003536302354 y[1] (numeric) = 1.1050944855785169632529252705964 absolute error = 5.25716403610e-20 relative error = 4.7572077362668899999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0952 y[1] (analytic) = 1.1052166224580017683465959328028 y[1] (numeric) = 1.1052166224580017683992497615423 absolute error = 5.26538287395e-20 relative error = 4.7641184243499600000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0953 y[1] (analytic) = 1.1053387863380126008621642533436 y[1] (numeric) = 1.1053387863380126009149003445422 absolute error = 5.27360911986e-20 relative error = 4.7710341707373420000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=232.7MB, alloc=4.2MB, time=9.68 NO POLE x[1] = 0.0954 y[1] (analytic) = 1.1054609772275038691134202962635 y[1] (numeric) = 1.1054609772275038691662387240708 absolute error = 5.28184278073e-20 relative error = 4.7779549794483580000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0955 y[1] (analytic) = 1.105583195135433941404090657822 y[1] (numeric) = 1.1055831951354339414569914964566 absolute error = 5.29008386346e-20 relative error = 4.7848808544995700000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0956 y[1] (analytic) = 1.1057054400707651481645289694825 y[1] (numeric) = 1.1057054400707651482175122932323 absolute error = 5.29833237498e-20 relative error = 4.7918117999319120000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0957 y[1] (analytic) = 1.1058277120424637841424306093111 y[1] (numeric) = 1.1058277120424637841954964925331 absolute error = 5.30658832220e-20 relative error = 4.7987478197654599999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0958 y[1] (analytic) = 1.10595001105950011059500110595 y[1] (numeric) = 1.1059500110595001106481496230706 absolute error = 5.31485171206e-20 relative error = 4.8056889180446520000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0959 y[1] (analytic) = 1.1060723371308483574825793606902 y[1] (numeric) = 1.1060723371308483575358105862051 absolute error = 5.32312255149e-20 relative error = 4.8126350988021090000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.096 y[1] (analytic) = 1.1061946902654867256637168141593 y[1] (numeric) = 1.1061946902654867257170308226336 absolute error = 5.33140084743e-20 relative error = 4.8195863660767200000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0961 y[1] (analytic) = 1.1063170704723973890917136851422 y[1] (numeric) = 1.1063170704723973891451105512106 absolute error = 5.33968660684e-20 relative error = 4.8265427239226759999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0962 y[1] (analytic) = 1.1064394777605664970126134100465 y[1] (numeric) = 1.1064394777605664970660932084132 absolute error = 5.34797983667e-20 relative error = 4.8335041763823459999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0963 y[1] (analytic) = 1.1065619121389841761646564125263 y[1] (numeric) = 1.1065619121389841762182192179652 absolute error = 5.35628054389e-20 relative error = 4.8404707275133929999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0964 y[1] (analytic) = 1.106684373616644532979194333776 y[1] (numeric) = 1.1066843736166445330328402211307 absolute error = 5.36458873547e-20 relative error = 4.8474423813706920000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0965 y[1] (analytic) = 1.1068068622025456557830658550083 y[1] (numeric) = 1.1068068622025456558367948991922 absolute error = 5.37290441839e-20 relative error = 4.8544191420153650000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0966 y[1] (analytic) = 1.1069293779056896170024352446314 y[1] (numeric) = 1.1069293779056896170562475206277 absolute error = 5.38122759963e-20 relative error = 4.8614010135057420000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0967 y[1] (analytic) = 1.1070519207350824753680947636444 y[1] (numeric) = 1.1070519207350824754219903465064 absolute error = 5.38955828620e-20 relative error = 4.8683879999244600000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0968 y[1] (analytic) = 1.1071744906997342781222320637732 y[1] (numeric) = 1.1071744906997342781762110286241 absolute error = 5.39789648509e-20 relative error = 4.8753801053332880000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0969 y[1] (analytic) = 1.1072970878086590632266637138744 y[1] (numeric) = 1.1072970878086590632807261359074 absolute error = 5.40624220330e-20 relative error = 4.8823773338002300000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=236.5MB, alloc=4.2MB, time=9.84 NO POLE x[1] = 0.097 y[1] (analytic) = 1.1074197120708748615725359911406 y[1] (numeric) = 1.1074197120708748616266819456191 absolute error = 5.41459544785e-20 relative error = 4.8893796894085500000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0971 y[1] (analytic) = 1.1075423634954036991914940746484 y[1] (numeric) = 1.1075423634954036992457236369059 absolute error = 5.42295622575e-20 relative error = 4.8963871762296749999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0972 y[1] (analytic) = 1.1076650420912715994683207797962 y[1] (numeric) = 1.1076650420912715995226340252368 absolute error = 5.43132454406e-20 relative error = 4.9033997983773680000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0973 y[1] (analytic) = 1.1077877478675085853550459731915 y[1] (numeric) = 1.1077877478675085854094429772894 absolute error = 5.43970040979e-20 relative error = 4.9104175599174330000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0974 y[1] (analytic) = 1.1079104808331486815865278085531 y[1] (numeric) = 1.1079104808331486816410086468529 absolute error = 5.44808382998e-20 relative error = 4.9174404649399479999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0975 y[1] (analytic) = 1.1080332409972299168975069252078 y[1] (numeric) = 1.1080332409972299169520716733248 absolute error = 5.45647481170e-20 relative error = 4.9244685175592499999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0976 y[1] (analytic) = 1.108156028368794326241134751773 y[1] (numeric) = 1.1081560283687943262957834853931 absolute error = 5.46487336201e-20 relative error = 4.9315017218778240000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0977 y[1] (analytic) = 1.108278842956887953008977058628 y[1] (numeric) = 1.1082788429568879530637098535074 absolute error = 5.47327948794e-20 relative error = 4.9385400819682619999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0978 y[1] (analytic) = 1.1084016847705608512524939037907 y[1] (numeric) = 1.1084016847705608513073108357568 absolute error = 5.48169319661e-20 relative error = 4.9455836019815420000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0979 y[1] (analytic) = 1.1085245538188670879059971178362 y[1] (numeric) = 1.1085245538188670879608982627868 absolute error = 5.49011449506e-20 relative error = 4.9526322859936259999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.098 y[1] (analytic) = 1.1086474501108647450110864745011 y[1] (numeric) = 1.1086474501108647450660719084051 absolute error = 5.49854339040e-20 relative error = 4.9596861381408000000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0981 y[1] (analytic) = 1.1087703736556159219425656946446 y[1] (numeric) = 1.1087703736556159219976354935417 absolute error = 5.50697988971e-20 relative error = 4.9667451625294490000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0982 y[1] (analytic) = 1.1088933244621867376358394322466 y[1] (numeric) = 1.1088933244621867376909936722475 absolute error = 5.51542400009e-20 relative error = 4.9738093632811620000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0983 y[1] (analytic) = 1.1090163025396473328157923921482 y[1] (numeric) = 1.1090163025396473328710311494347 absolute error = 5.52387572865e-20 relative error = 4.9808787445237049999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0984 y[1] (analytic) = 1.1091393078970718722271517302573 y[1] (numeric) = 1.1091393078970718722824750810825 absolute error = 5.53233508252e-20 relative error = 4.9879533104000320000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0985 y[1] (analytic) = 1.1092623405435385468663338879645 y[1] (numeric) = 1.1092623405435385469217419086526 absolute error = 5.54080206881e-20 relative error = 4.9950330650322150000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=240.3MB, alloc=4.2MB, time=10.01 NO POLE x[1] = 0.0986 y[1] (analytic) = 1.1093854004881295762147770135345 y[1] (numeric) = 1.109385400488129576270269780481 absolute error = 5.54927669465e-20 relative error = 5.0021180125575100000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0987 y[1] (analytic) = 1.109508487739931210473760124265 y[1] (numeric) = 1.1095084877399312105293377139368 absolute error = 5.55775896718e-20 relative error = 5.0092081571193339999999999999998e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0988 y[1] (analytic) = 1.1096316023080337328007101642255 y[1] (numeric) = 1.109631602308033732856372653161 absolute error = 5.56624889355e-20 relative error = 5.0163035028672599999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0989 y[1] (analytic) = 1.1097547442015314615469981134169 y[1] (numeric) = 1.109754744201531461602745578226 absolute error = 5.57474648091e-20 relative error = 5.0234040539480010000000000000002e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.099 y[1] (analytic) = 1.1098779134295227524972253052164 y[1] (numeric) = 1.1098779134295227525530578225805 absolute error = 5.58325173641e-20 relative error = 5.0305098145054100000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0991 y[1] (analytic) = 1.1100011100011100011100011100011 y[1] (numeric) = 1.1100011100011100011659187566733 absolute error = 5.59176466722e-20 relative error = 5.0376207886984980000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0992 y[1] (analytic) = 1.1101243339253996447602131438721 y[1] (numeric) = 1.1101243339253996448162159966772 absolute error = 5.60028528051e-20 relative error = 5.0447369806834080000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0993 y[1] (analytic) = 1.1102475852115021649827911624292 y[1] (numeric) = 1.1102475852115021650388792982639 absolute error = 5.60881358347e-20 relative error = 5.0518583946314290000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0994 y[1] (analytic) = 1.1103708638685320897179658005774 y[1] (numeric) = 1.1103708638685320897741392964102 absolute error = 5.61734958328e-20 relative error = 5.0589850347019680000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0995 y[1] (analytic) = 1.1104941699056079955580233203776 y[1] (numeric) = 1.110494169905607995614282253249 absolute error = 5.62589328714e-20 relative error = 5.0661169050695699999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0996 y[1] (analytic) = 1.1106175033318525099955575299867 y[1] (numeric) = 1.1106175033318525100519019770093 absolute error = 5.63444470226e-20 relative error = 5.0732540099149039999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0997 y[1] (analytic) = 1.1107408641563923136732200377652 y[1] (numeric) = 1.1107408641563923137296500761237 absolute error = 5.64300383585e-20 relative error = 5.0803963534157550000000000000000e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0998 y[1] (analytic) = 1.1108642523883581426349700066652 y[1] (numeric) = 1.1108642523883581426914857136164 absolute error = 5.65157069512e-20 relative error = 5.0875439397470239999999999999999e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.0999 y[1] (analytic) = 1.1109876680368847905788245750472 y[1] (numeric) = 1.1109876680368847906354260279202 absolute error = 5.66014528730e-20 relative error = 5.0946967730987300000000000000001e-18 % h = 0.0001 TOP MAIN SOLVE Loop NO POLE x[1] = 0.1 y[1] (analytic) = 1.1111111111111111111111111111111 y[1] (numeric) = 1.1111111111111111111677983873072 absolute error = 5.66872761961e-20 relative error = 5.1018548576490000000000000000001e-18 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = y * y; Iterations = 1000 Total Elapsed Time = 10 Seconds Elapsed Time(since restart) = 10 Seconds Expected Time Remaining = 40 Seconds Optimized Time Remaining = 40 Seconds Time to Timeout = 14 Minutes 49 Seconds Percent Done = 20.02 % > quit memory used=243.9MB, alloc=4.2MB, time=10.15