|\^/| Maple 12 (IBM INTEL LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > #BEGIN OUTFILE1 > > # Begin Function number 3 > display_alot := proc(iter) > global > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > glob_last; > > local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; > #TOP DISPLAY ALOT > if (iter >= 0) then # if number 1 > ind_var := array_x[1]; > omniout_float(ALWAYS,"x[1] ",33,ind_var,20," "); > analytic_val_y := exact_soln_y(ind_var); > omniout_float(ALWAYS,"y[1] (analytic) ",33,analytic_val_y,20," "); > term_no := 1; > numeric_val := array_y[term_no]; > abserr := abs(numeric_val - analytic_val_y); > omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," "); > if (abs(analytic_val_y) <> 0.0) then # if number 2 > relerr := abserr*100.0/abs(analytic_val_y); > else > relerr := -1.0 ; > fi;# end if 2 > ; > if glob_iter = 1 then # if number 2 > array_1st_rel_error[1] := relerr; > else > array_last_rel_error[1] := relerr; > fi;# end if 2 > ; > omniout_float(ALWAYS,"absolute error ",4,abserr,20," "); > omniout_float(ALWAYS,"relative error ",4,relerr,20,"%"); > omniout_float(ALWAYS,"h ",4,glob_h,20," "); > #BOTTOM DISPLAY ALOT > fi;# end if 1 > ; > # End Function number 3 > end; display_alot := proc(iter) local abserr, analytic_val_y, ind_var, numeric_val, relerr, term_no; global DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, glob_last; if 0 <= iter then ind_var := array_x[1]; omniout_float(ALWAYS, "x[1] ", 33, ind_var, 20, " "); analytic_val_y := exact_soln_y(ind_var); omniout_float(ALWAYS, "y[1] (analytic) ", 33, analytic_val_y, 20, " "); term_no := 1; numeric_val := array_y[term_no]; abserr := abs(numeric_val - analytic_val_y); omniout_float(ALWAYS, "y[1] (numeric) ", 33, numeric_val, 20, " "); if abs(analytic_val_y) <> 0. then relerr := abserr*100.0/abs(analytic_val_y) else relerr := -1.0 end if; if glob_iter = 1 then array_1st_rel_error[1] := relerr else array_last_rel_error[1] := relerr end if; omniout_float(ALWAYS, "absolute error ", 4, abserr, 20, " "); omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"); omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ") end if end proc > # Begin Function number 4 > adjust_for_pole := proc(h_param) > global > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > glob_last; > > local hnew, sz2, tmp; > #TOP ADJUST FOR POLE > > hnew := h_param; > glob_normmax := glob_small_float; > if (abs(array_y_higher[1,1]) > glob_small_float) then # if number 1 > tmp := abs(array_y_higher[1,1]); > if (tmp < glob_normmax) then # if number 2 > glob_normmax := tmp; > fi;# end if 2 > fi;# end if 1 > ; > if (glob_look_poles and (abs(array_pole[1]) > glob_small_float) and (array_pole[1] <> glob_large_float)) then # if number 1 > sz2 := array_pole[1]/10.0; > if (sz2 < hnew) then # if number 2 > omniout_float(INFO,"glob_h adjusted to ",20,h_param,12,"due to singularity."); > omniout_str(INFO,"Reached Optimal"); > newline(); > return(hnew); > fi;# end if 2 > fi;# end if 1 > ; > if (not glob_reached_optimal_h) then # if number 1 > glob_reached_optimal_h := true; > glob_curr_iter_when_opt := glob_current_iter; > glob_optimal_clock_start_sec := elapsed_time_seconds(); > glob_optimal_start := array_x[1]; > fi;# end if 1 > ; > hnew := sz2; > #END block > #BOTTOM ADJUST FOR POLE > # End Function number 4 > end; adjust_for_pole := proc(h_param) local hnew, sz2, tmp; global DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, glob_last; hnew := h_param; glob_normmax := glob_small_float; if glob_small_float < abs(array_y_higher[1, 1]) then tmp := abs(array_y_higher[1, 1]); if tmp < glob_normmax then glob_normmax := tmp end if end if; if glob_look_poles and glob_small_float < abs(array_pole[1]) and array_pole[1] <> glob_large_float then sz2 := array_pole[1]/10.0; if sz2 < hnew then omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."); omniout_str(INFO, "Reached Optimal"); newline(); return hnew end if end if; if not glob_reached_optimal_h then glob_reached_optimal_h := true; glob_curr_iter_when_opt := glob_current_iter; glob_optimal_clock_start_sec := elapsed_time_seconds(); glob_optimal_start := array_x[1] end if; hnew := sz2 end proc > # Begin Function number 5 > prog_report := proc(x_start,x_end) > global > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > glob_last; > > local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; > #TOP PROGRESS REPORT > clock_sec1 := elapsed_time_seconds(); > total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); > glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); > left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); > expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h) ,convfloat( clock_sec1) - convfloat(glob_orig_start_sec)); > opt_clock_sec := convfloat( clock_sec1) - convfloat(glob_optimal_clock_start_sec); > glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) +convfloat( glob_h) ,convfloat( opt_clock_sec)); > percent_done := comp_percent(convfloat(x_end),convfloat(x_start),convfloat(array_x[1]) + convfloat(glob_h)); > glob_percent_done := percent_done; > omniout_str_noeol(INFO,"Total Elapsed Time "); > omniout_timestr(convfloat(total_clock_sec)); > omniout_str_noeol(INFO,"Elapsed Time(since restart) "); > omniout_timestr(convfloat(glob_clock_sec)); > if convfloat(percent_done) < convfloat(100.0) then # if number 1 > omniout_str_noeol(INFO,"Expected Time Remaining "); > omniout_timestr(convfloat(expect_sec)); > omniout_str_noeol(INFO,"Optimized Time Remaining "); > omniout_timestr(convfloat(glob_optimal_expect_sec)); > fi;# end if 1 > ; > omniout_str_noeol(INFO,"Time to Timeout "); > omniout_timestr(convfloat(left_sec)); > omniout_float(INFO, "Percent Done ",33,percent_done,4,"%"); > #BOTTOM PROGRESS REPORT > # End Function number 5 > end; prog_report := proc(x_start, x_end) local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec; global DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, glob_last; clock_sec1 := elapsed_time_seconds(); total_clock_sec := convfloat(clock_sec1) - convfloat(glob_orig_start_sec); glob_clock_sec := convfloat(clock_sec1) - convfloat(glob_clock_start_sec); left_sec := convfloat(glob_max_sec) + convfloat(glob_orig_start_sec) - convfloat(clock_sec1); expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(clock_sec1) - convfloat(glob_orig_start_sec)); opt_clock_sec := convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec); glob_optimal_expect_sec := comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h), convfloat(opt_clock_sec)); percent_done := comp_percent(convfloat(x_end), convfloat(x_start), convfloat(array_x[1]) + convfloat(glob_h)); glob_percent_done := percent_done; omniout_str_noeol(INFO, "Total Elapsed Time "); omniout_timestr(convfloat(total_clock_sec)); omniout_str_noeol(INFO, "Elapsed Time(since restart) "); omniout_timestr(convfloat(glob_clock_sec)); if convfloat(percent_done) < convfloat(100.0) then omniout_str_noeol(INFO, "Expected Time Remaining "); omniout_timestr(convfloat(expect_sec)); omniout_str_noeol(INFO, "Optimized Time Remaining "); omniout_timestr(convfloat(glob_optimal_expect_sec)) end if; omniout_str_noeol(INFO, "Time to Timeout "); omniout_timestr(convfloat(left_sec)); omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%") end proc > # Begin Function number 6 > check_for_pole := proc() > global > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > glob_last; > > local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found; > #TOP CHECK FOR POLE > #IN RADII REAL EQ = 1 > #Computes radius of convergence and r_order of pole from 3 adjacent Taylor series terms. EQUATUON NUMBER 1 > #Applies to pole of arbitrary r_order on the real axis, > #Due to Prof. George Corliss. > n := glob_max_terms; > m := n - 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 DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, 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 > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > glob_last; > > local iii; > if (not glob_initial_pass) then # if number 2 > set_z(array_norms,glob_max_terms+1); > #TOP GET NORMS > iii := 1; > while (iii <= glob_max_terms) do # do number 2 > if (abs(array_y[iii]) > array_norms[iii]) then # if number 3 > array_norms[iii] := abs(array_y[iii]); > fi;# end if 3 > ; > iii := iii + 1; > od;# end do number 2 > #GET NORMS > ; > fi;# end if 2 > ; > # End Function number 7 > end; get_norms := proc() local iii; global DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, glob_last; if not glob_initial_pass then set_z(array_norms, glob_max_terms + 1); iii := 1; while iii <= glob_max_terms do if array_norms[iii] < abs(array_y[iii]) then array_norms[iii] := abs(array_y[iii]) end if; iii := iii + 1 end do end if end proc > # Begin Function number 8 > atomall := proc() > global > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > 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_m1[1] * (array_const_2D0[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp2[1] := (array_tmp1[1] / (array_x[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp3[1] := (array_tmp2[1] / (array_x[1])); > #emit pre div $eq_no = 1 i = 1 > array_tmp4[1] := (array_tmp3[1] / (array_x[1])); > #emit pre add $eq_no = 1 i = 1 > array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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_m1,array_const_2D0,1); > #emit pre div $eq_no = 1 i = 2 > array_tmp2[2] := ((array_tmp1[2] - ats(2,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 2 > array_tmp3[2] := ((array_tmp2[2] - ats(2,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 2 > array_tmp4[2] := ((array_tmp3[2] - ats(2,array_x,array_tmp4,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 2 > array_tmp5[2] := array_const_0D0[2] + array_tmp4[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_tmp5[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_m1,array_const_2D0,1); > #emit pre div $eq_no = 1 i = 3 > array_tmp2[3] := ((array_tmp1[3] - ats(3,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 3 > array_tmp3[3] := ((array_tmp2[3] - ats(3,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 3 > array_tmp4[3] := ((array_tmp3[3] - ats(3,array_x,array_tmp4,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 3 > array_tmp5[3] := array_const_0D0[3] + array_tmp4[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_tmp5[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_m1,array_const_2D0,1); > #emit pre div $eq_no = 1 i = 4 > array_tmp2[4] := ((array_tmp1[4] - ats(4,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 4 > array_tmp3[4] := ((array_tmp2[4] - ats(4,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 4 > array_tmp4[4] := ((array_tmp3[4] - ats(4,array_x,array_tmp4,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 4 > array_tmp5[4] := array_const_0D0[4] + array_tmp4[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_tmp5[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_m1,array_const_2D0,1); > #emit pre div $eq_no = 1 i = 5 > array_tmp2[5] := ((array_tmp1[5] - ats(5,array_x,array_tmp2,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 5 > array_tmp3[5] := ((array_tmp2[5] - ats(5,array_x,array_tmp3,2))/array_x[1]); > #emit pre div $eq_no = 1 i = 5 > array_tmp4[5] := ((array_tmp3[5] - ats(5,array_x,array_tmp4,2))/array_x[1]); > #emit pre add $eq_no = 1 i = 5 > array_tmp5[5] := array_const_0D0[5] + array_tmp4[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_tmp5[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_m1,array_const_2D0,1); > #emit div $eq_no = 1 > array_tmp2[kkk] := ((array_tmp1[kkk] - ats(kkk,array_x,array_tmp2,2))/array_x[1]); > #emit div $eq_no = 1 > array_tmp3[kkk] := ((array_tmp2[kkk] - ats(kkk,array_x,array_tmp3,2))/array_x[1]); > #emit div $eq_no = 1 > array_tmp4[kkk] := ((array_tmp3[kkk] - ats(kkk,array_x,array_tmp4,2))/array_x[1]); > #emit add $eq_no = 1 > array_tmp5[kkk] := array_const_0D0[kkk] + array_tmp4[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_tmp5[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 DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, glob_last; array_tmp1[1] := array_m1[1]*array_const_2D0[1]; array_tmp2[1] := array_tmp1[1]/array_x[1]; array_tmp3[1] := array_tmp2[1]/array_x[1]; array_tmp4[1] := array_tmp3[1]/array_x[1]; array_tmp5[1] := array_const_0D0[1] + array_tmp4[1]; if not array_y_set_initial[1, 2] then if 1 <= glob_max_terms then temporary := array_tmp5[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_m1, array_const_2D0, 1); array_tmp2[2] := (array_tmp1[2] - ats(2, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[2] := (array_tmp2[2] - ats(2, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[2] := (array_tmp3[2] - ats(2, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[2] := array_const_0D0[2] + array_tmp4[2]; if not array_y_set_initial[1, 3] then if 2 <= glob_max_terms then temporary := array_tmp5[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_m1, array_const_2D0, 1); array_tmp2[3] := (array_tmp1[3] - ats(3, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[3] := (array_tmp2[3] - ats(3, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[3] := (array_tmp3[3] - ats(3, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[3] := array_const_0D0[3] + array_tmp4[3]; if not array_y_set_initial[1, 4] then if 3 <= glob_max_terms then temporary := array_tmp5[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_m1, array_const_2D0, 1); array_tmp2[4] := (array_tmp1[4] - ats(4, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[4] := (array_tmp2[4] - ats(4, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[4] := (array_tmp3[4] - ats(4, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[4] := array_const_0D0[4] + array_tmp4[4]; if not array_y_set_initial[1, 5] then if 4 <= glob_max_terms then temporary := array_tmp5[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_m1, array_const_2D0, 1); array_tmp2[5] := (array_tmp1[5] - ats(5, array_x, array_tmp2, 2))/array_x[1]; array_tmp3[5] := (array_tmp2[5] - ats(5, array_x, array_tmp3, 2))/array_x[1]; array_tmp4[5] := (array_tmp3[5] - ats(5, array_x, array_tmp4, 2))/array_x[1]; array_tmp5[5] := array_const_0D0[5] + array_tmp4[5]; if not array_y_set_initial[1, 6] then if 5 <= glob_max_terms then temporary := array_tmp5[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_m1, array_const_2D0, 1); array_tmp2[kkk] := (array_tmp1[kkk] - ats(kkk, array_x, array_tmp2, 2))/array_x[1] ; array_tmp3[kkk] := (array_tmp2[kkk] - ats(kkk, array_x, array_tmp3, 2))/array_x[1] ; array_tmp4[kkk] := (array_tmp3[kkk] - ats(kkk, array_x, array_tmp4, 2))/array_x[1] ; array_tmp5[kkk] := array_const_0D0[kkk] + array_tmp4[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_tmp5[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/x/x; > end; exact_soln_y := proc(x) 1.0/(x*x) end proc > > > #END USER DEF BLOCK > #END USER DEF BLOCK > #END OUTFILE5 > # Begin Function number 2 > mainprog := proc() > #BEGIN OUTFIEMAIN > local d1,d2,d3,d4,est_err_2,niii,done_once, > term,ord,order_diff,term_no,html_log_file, > rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter, > x_start,x_end > ,it, log10norm, max_terms, opt_iter, tmp; > #Top Generate Globals Definition > #Bottom Generate Globals Deninition > global > DEBUGL, > INFO, > glob_iolevel, > glob_max_terms, > ALWAYS, > DEBUGMASSIVE, > #Top Generate Globals Decl > glob_no_eqs, > glob_max_iter, > glob_log10_abserr, > glob_look_poles, > glob_almost_1, > centuries_in_millinium, > glob_subiter_method, > glob_abserr, > glob_log10_relerr, > glob_reached_optimal_h, > glob_not_yet_finished, > glob_optimal_start, > days_in_year, > MAX_UNCHANGED, > glob_warned, > glob_max_rel_trunc_err, > glob_not_yet_start_msg, > glob_clock_sec, > min_in_hour, > glob_display_flag, > glob_optimal_clock_start_sec, > djd_debug, > glob_optimal_expect_sec, > glob_normmax, > glob_orig_start_sec, > glob_max_sec, > glob_unchanged_h_cnt, > glob_last_good_h, > glob_large_float, > glob_hmin, > hours_in_day, > glob_small_float, > djd_debug2, > glob_percent_done, > glob_smallish_float, > glob_max_hours, > glob_relerr, > glob_h, > glob_optimal_done, > glob_initial_pass, > glob_current_iter, > glob_curr_iter_when_opt, > glob_max_trunc_err, > glob_dump_analytic, > glob_hmax, > glob_clock_start_sec, > sec_in_min, > glob_html_log, > glob_max_minutes, > glob_log10abserr, > glob_iter, > glob_start, > glob_hmin_init, > years_in_century, > glob_dump, > glob_max_opt_iter, > glob_log10relerr, > glob_warned2, > glob_disp_incr, > glob_log10normmin, > #Bottom Generate Globals Decl > #BEGIN CONST > array_const_2D0, > array_const_1, > array_const_0D0, > #END CONST > array_norms, > array_tmp0, > array_tmp1, > array_tmp2, > array_tmp3, > array_tmp4, > array_tmp5, > array_m1, > array_y, > array_x, > array_type_pole, > array_y_init, > array_pole, > array_last_rel_error, > array_1st_rel_error, > array_y_higher_work2, > array_y_set_initial, > array_y_higher_work, > array_poles, > array_complex_pole, > array_real_pole, > array_y_higher, > glob_last; > glob_last; > ALWAYS := 1; > INFO := 2; > DEBUGL := 3; > DEBUGMASSIVE := 4; > glob_iolevel := INFO; > DEBUGL := 3; > INFO := 2; > glob_iolevel := 5; > glob_max_terms := 30; > ALWAYS := 1; > DEBUGMASSIVE := 4; > glob_no_eqs := 0; > glob_max_iter := 1000; > glob_log10_abserr := 0.1e-10; > glob_look_poles := false; > glob_almost_1 := 0.9990; > centuries_in_millinium := 10.0; > glob_subiter_method := 3; > glob_abserr := 0.1e-10; > glob_log10_relerr := 0.1e-10; > glob_reached_optimal_h := false; > glob_not_yet_finished := true; > glob_optimal_start := 0.0; > days_in_year := 365.0; > MAX_UNCHANGED := 10; > glob_warned := false; > glob_max_rel_trunc_err := 0.1e-10; > glob_not_yet_start_msg := true; > glob_clock_sec := 0.0; > min_in_hour := 60.0; > glob_display_flag := true; > glob_optimal_clock_start_sec := 0.0; > djd_debug := true; > glob_optimal_expect_sec := 0.1; > glob_normmax := 0.0; > glob_orig_start_sec := 0.0; > glob_max_sec := 10000.0; > glob_unchanged_h_cnt := 0; > glob_last_good_h := 0.1; > glob_large_float := 9.0e100; > glob_hmin := 0.00000000001; > hours_in_day := 24.0; > glob_small_float := 0.1e-50; > djd_debug2 := true; > glob_percent_done := 0.0; > glob_smallish_float := 0.1e-100; > glob_max_hours := 0.0; > glob_relerr := 0.1e-10; > glob_h := 0.1; > glob_optimal_done := false; > glob_initial_pass := true; > glob_current_iter := 0; > glob_curr_iter_when_opt := 0; > glob_max_trunc_err := 0.1e-10; > glob_dump_analytic := false; > glob_hmax := 1.0; > glob_clock_start_sec := 0.0; > sec_in_min := 60.0; > glob_html_log := true; > glob_max_minutes := 0.0; > glob_log10abserr := 0.0; > glob_iter := 0; > glob_start := 0; > glob_hmin_init := 0.001; > years_in_century := 100.0; > glob_dump := false; > glob_max_opt_iter := 10; > glob_log10relerr := 0.0; > glob_warned2 := false; > glob_disp_incr := 0.1; > glob_log10normmin := 0.1; > #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/sing3postode.ode#################"); > omniout_str(ALWAYS,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); > omniout_str(ALWAYS,"!"); > omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK"); > omniout_str(ALWAYS,"Digits := 100;"); > 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 := -1.0;"); > omniout_str(ALWAYS,"x_end := -0.7;"); > omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);"); > omniout_str(ALWAYS,"glob_h := 0.1;"); > omniout_str(ALWAYS,"glob_look_poles := true;"); > omniout_str(ALWAYS,"glob_max_iter := 100000;"); > 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/x/x;"); > omniout_str(ALWAYS,"end;"); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,""); > omniout_str(ALWAYS,"#END USER DEF BLOCK"); > omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################"); > glob_unchanged_h_cnt := 0; > glob_warned := false; > glob_warned2 := false; > glob_small_float := 1.0e-200; > glob_smallish_float := 1.0e-64; > glob_large_float := 1.0e100; > glob_almost_1 := 0.99; > glob_log10_abserr := -8.0; > glob_log10_relerr := -8.0; > glob_hmax := 0.01; > #BEGIN FIRST INPUT BLOCK > #BEGIN FIRST INPUT BLOCK > Digits := 100; > 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_norms:= 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_tmp3:= Array(1..(max_terms + 1),[]); > array_tmp4:= Array(1..(max_terms + 1),[]); > array_tmp5:= Array(1..(max_terms + 1),[]); > array_m1:= Array(1..(max_terms + 1),[]); > array_y:= Array(1..(max_terms + 1),[]); > array_x:= Array(1..(max_terms + 1),[]); > array_type_pole:= Array(1..(max_terms + 1),[]); > array_y_init:= Array(1..(max_terms + 1),[]); > array_pole:= Array(1..(max_terms + 1),[]); > array_last_rel_error:= Array(1..(max_terms + 1),[]); > array_1st_rel_error:= Array(1..(max_terms + 1),[]); > array_y_higher_work2 := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_set_initial := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_y_higher_work := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > array_poles := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_complex_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_real_pole := Array(1..(1+ 1) ,(1..3+ 1),[]); > array_y_higher := Array(1..(2+ 1) ,(1..max_terms+ 1),[]); > 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_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_tmp5[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_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_type_pole[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_pole[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_last_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > term := 1; > while term <= max_terms do # do number 2 > array_1st_rel_error[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > 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_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_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 <=1 do # do number 2 > term := 1; > while term <= 3 do # do number 3 > array_poles[ord,term] := 0.0; > term := term + 1; > od;# end do number 3 > ; > ord := ord + 1; > od;# end do number 2 > ; > ord := 1; > while ord <=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_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[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_tmp5 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp5[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp4 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp4[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp3 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp3[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp2 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp2[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_tmp0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_tmp0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_x := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_x[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_y := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_y[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_2D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_2D0[1] := 2.0; > array_const_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_const_0D0 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms + 1 do # do number 2 > array_const_0D0[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_const_0D0[1] := 0.0; > array_m1 := Array(1..(max_terms+1 + 1),[]); > term := 1; > while term <= max_terms do # do number 2 > array_m1[term] := 0.0; > term := term + 1; > od;# end do number 2 > ; > array_m1[1] := -1.0; > #END ARRAYS DEFINED AND INITIALIZATED > #TOP SECOND INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > #END FIRST INPUT BLOCK > #BEGIN SECOND INPUT BLOCK > x_start := -1.0; > x_end := -0.7; > array_y_init[0 + 1] := exact_soln_y(x_start); > glob_h := 0.1; > glob_look_poles := true; > glob_max_iter := 100000; > #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 ) = m1 * 2.0 / x / x / x ;"); > omniout_int(INFO,"Iterations ",32,glob_iter,4," ") > ; > prog_report(x_start,x_end); > if glob_html_log then # if number 2 > logstart(html_log_file); > logitem_str(html_log_file,"2012-06-13T18:31:50-05:00") > ; > logitem_str(html_log_file,"Maple") > ; > logitem_str(html_log_file,"sing3") > ; > logitem_str(html_log_file,"diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;") > ; > logitem_float(html_log_file,x_start) > ; > logitem_float(html_log_file,x_end) > ; > logitem_float(html_log_file,array_x[1]) > ; > logitem_float(html_log_file,glob_h) > ; > logitem_integer(html_log_file,Digits) > ; > ; > logitem_integer(html_log_file,glob_max_terms) > ; > logitem_float(html_log_file,array_1st_rel_error[1]) > ; > logitem_float(html_log_file,array_last_rel_error[1]) > ; > logitem_integer(html_log_file,glob_iter) > ; > logitem_pole(html_log_file,array_type_pole[1]) > ; > if array_type_pole[1] = 1 or array_type_pole[1] = 2 then # if number 3 > logitem_float(html_log_file,array_pole[1]) > ; > logitem_float(html_log_file,array_pole[2]) > ; > 0; > else > logitem_str(html_log_file,"NA") > ; > logitem_str(html_log_file,"NA") > ; > 0; > fi;# end if 3 > ; > logitem_time(html_log_file,convfloat(glob_clock_sec)) > ; > if glob_percent_done < 100.0 then # if number 3 > logitem_time(html_log_file,convfloat(glob_optimal_expect_sec)) > ; > 0 > else > logitem_str(html_log_file,"Done") > ; > 0 > fi;# end if 3 > ; > log_revs(html_log_file," 090 ") > ; > logitem_str(html_log_file,"sing3 diffeq.mxt") > ; > logitem_str(html_log_file,"sing3 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 DEBUGL, INFO, glob_iolevel, glob_max_terms, ALWAYS, DEBUGMASSIVE, glob_no_eqs, glob_max_iter, glob_log10_abserr, glob_look_poles, glob_almost_1, centuries_in_millinium, glob_subiter_method, glob_abserr, glob_log10_relerr, glob_reached_optimal_h, glob_not_yet_finished, glob_optimal_start, days_in_year, MAX_UNCHANGED, glob_warned, glob_max_rel_trunc_err, glob_not_yet_start_msg, glob_clock_sec, min_in_hour, glob_display_flag, glob_optimal_clock_start_sec, djd_debug, glob_optimal_expect_sec, glob_normmax, glob_orig_start_sec, glob_max_sec, glob_unchanged_h_cnt, glob_last_good_h, glob_large_float, glob_hmin, hours_in_day, glob_small_float, djd_debug2, glob_percent_done, glob_smallish_float, glob_max_hours, glob_relerr, glob_h, glob_optimal_done, glob_initial_pass, glob_current_iter, glob_curr_iter_when_opt, glob_max_trunc_err, glob_dump_analytic, glob_hmax, glob_clock_start_sec, sec_in_min, glob_html_log, glob_max_minutes, glob_log10abserr, glob_iter, glob_start, glob_hmin_init, years_in_century, glob_dump, glob_max_opt_iter, glob_log10relerr, glob_warned2, glob_disp_incr, glob_log10normmin, array_const_2D0, array_const_1, array_const_0D0, array_norms, array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_m1, array_y, array_x, array_type_pole, array_y_init, array_pole, array_last_rel_error, array_1st_rel_error, array_y_higher_work2, array_y_set_initial, array_y_higher_work, array_poles, array_complex_pole, array_real_pole, array_y_higher, glob_last; glob_last; ALWAYS := 1; INFO := 2; DEBUGL := 3; DEBUGMASSIVE := 4; glob_iolevel := INFO; DEBUGL := 3; INFO := 2; glob_iolevel := 5; glob_max_terms := 30; ALWAYS := 1; DEBUGMASSIVE := 4; glob_no_eqs := 0; glob_max_iter := 1000; glob_log10_abserr := 0.1*10^(-10); glob_look_poles := false; glob_almost_1 := 0.9990; centuries_in_millinium := 10.0; glob_subiter_method := 3; glob_abserr := 0.1*10^(-10); glob_log10_relerr := 0.1*10^(-10); glob_reached_optimal_h := false; glob_not_yet_finished := true; glob_optimal_start := 0.; days_in_year := 365.0; MAX_UNCHANGED := 10; glob_warned := false; glob_max_rel_trunc_err := 0.1*10^(-10); glob_not_yet_start_msg := true; glob_clock_sec := 0.; min_in_hour := 60.0; glob_display_flag := true; glob_optimal_clock_start_sec := 0.; djd_debug := true; glob_optimal_expect_sec := 0.1; glob_normmax := 0.; glob_orig_start_sec := 0.; glob_max_sec := 10000.0; glob_unchanged_h_cnt := 0; glob_last_good_h := 0.1; glob_large_float := 0.90*10^101; glob_hmin := 0.1*10^(-10); hours_in_day := 24.0; glob_small_float := 0.1*10^(-50); djd_debug2 := true; glob_percent_done := 0.; glob_smallish_float := 0.1*10^(-100); glob_max_hours := 0.; glob_relerr := 0.1*10^(-10); glob_h := 0.1; glob_optimal_done := false; glob_initial_pass := true; glob_current_iter := 0; glob_curr_iter_when_opt := 0; glob_max_trunc_err := 0.1*10^(-10); glob_dump_analytic := false; glob_hmax := 1.0; glob_clock_start_sec := 0.; sec_in_min := 60.0; glob_html_log := true; glob_max_minutes := 0.; glob_log10abserr := 0.; glob_iter := 0; glob_start := 0; glob_hmin_init := 0.001; years_in_century := 100.0; glob_dump := false; glob_max_opt_iter := 10; glob_log10relerr := 0.; glob_warned2 := false; glob_disp_incr := 0.1; glob_log10normmin := 0.1; 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/sing3postode.ode#################"); omniout_str(ALWAYS, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); omniout_str(ALWAYS, "!"); omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK"); omniout_str(ALWAYS, "Digits := 100;"); 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 := -1.0;"); omniout_str(ALWAYS, "x_end := -0.7;"); omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);"); omniout_str(ALWAYS, "glob_h := 0.1;"); omniout_str(ALWAYS, "glob_look_poles := true;"); omniout_str(ALWAYS, "glob_max_iter := 100000;"); 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/x/x;"); omniout_str(ALWAYS, "end;"); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, ""); omniout_str(ALWAYS, "#END USER DEF BLOCK"); omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"); glob_unchanged_h_cnt := 0; glob_warned := false; glob_warned2 := false; glob_small_float := 0.10*10^(-199); glob_smallish_float := 0.10*10^(-63); glob_large_float := 0.10*10^101; glob_almost_1 := 0.99; glob_log10_abserr := -8.0; glob_log10_relerr := -8.0; glob_hmax := 0.01; Digits := 100; max_terms := 30; glob_max_terms := max_terms; glob_html_log := true; array_norms := 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_tmp3 := Array(1 .. max_terms + 1, []); array_tmp4 := Array(1 .. max_terms + 1, []); array_tmp5 := Array(1 .. max_terms + 1, []); array_m1 := Array(1 .. max_terms + 1, []); array_y := Array(1 .. max_terms + 1, []); array_x := Array(1 .. max_terms + 1, []); array_type_pole := Array(1 .. max_terms + 1, []); array_y_init := Array(1 .. max_terms + 1, []); array_pole := Array(1 .. max_terms + 1, []); array_last_rel_error := Array(1 .. max_terms + 1, []); array_1st_rel_error := Array(1 .. max_terms + 1, []); array_y_higher_work2 := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_set_initial := Array(1 .. 3, 1 .. max_terms + 1, []); array_y_higher_work := Array(1 .. 3, 1 .. max_terms + 1, []); array_poles := Array(1 .. 2, 1 .. 4, []); array_complex_pole := Array(1 .. 2, 1 .. 4, []); array_real_pole := Array(1 .. 2, 1 .. 4, []); array_y_higher := Array(1 .. 3, 1 .. max_terms + 1, []); term := 1; while term <= max_terms do array_norms[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp0[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp1[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp2[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp3[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp4[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_tmp5[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_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_type_pole[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_pole[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_last_rel_error[term] := 0.; term := term + 1 end do; term := 1; while term <= max_terms do array_1st_rel_error[term] := 0.; term := term + 1 end do; 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_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_work[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 1 do term := 1; while term <= 3 do array_poles[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; ord := 1; while ord <= 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_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[ord, term] := 0.; term := term + 1 end do; ord := ord + 1 end do; array_tmp5 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp5[term] := 0.; term := term + 1 end do; array_tmp4 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp4[term] := 0.; term := term + 1 end do; array_tmp3 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp3[term] := 0.; term := term + 1 end do; array_tmp2 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp2[term] := 0.; term := term + 1 end do; array_tmp1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp1[term] := 0.; term := term + 1 end do; array_tmp0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_tmp0[term] := 0.; term := term + 1 end do; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_m1[term] := 0.; term := term + 1 end do; array_x := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_x[term] := 0.; term := term + 1 end do; array_y := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_y[term] := 0.; term := term + 1 end do; array_const_2D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_2D0[term] := 0.; term := term + 1 end do; array_const_2D0[1] := 2.0; array_const_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_const_0D0 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms + 1 do array_const_0D0[term] := 0.; term := term + 1 end do; array_const_0D0[1] := 0.; array_m1 := Array(1 .. max_terms + 2, []); term := 1; while term <= max_terms do array_m1[term] := 0.; term := term + 1 end do; array_m1[1] := -1.0; x_start := -1.0; x_end := -0.7; array_y_init[1] := exact_soln_y(x_start); glob_h := 0.1; glob_look_poles := true; glob_max_iter := 100000; 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 ) = m1 * 2.0 / x / x / x ;"); omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "); prog_report(x_start, x_end); if glob_html_log then logstart(html_log_file); logitem_str(html_log_file, "2012-06-13T18:31:50-05:00"); logitem_str(html_log_file, "Maple"); logitem_str(html_log_file, "sing3"); logitem_str(html_log_file, "diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ;"); logitem_float(html_log_file, x_start); logitem_float(html_log_file, x_end); logitem_float(html_log_file, array_x[1]); logitem_float(html_log_file, glob_h); logitem_integer(html_log_file, Digits); logitem_integer(html_log_file, glob_max_terms); logitem_float(html_log_file, array_1st_rel_error[1]); logitem_float(html_log_file, array_last_rel_error[1]); logitem_integer(html_log_file, glob_iter); logitem_pole(html_log_file, array_type_pole[1]); if array_type_pole[1] = 1 or array_type_pole[1] = 2 then logitem_float(html_log_file, array_pole[1]); logitem_float(html_log_file, array_pole[2]); 0 else logitem_str(html_log_file, "NA"); logitem_str(html_log_file, "NA"); 0 end if; logitem_time(html_log_file, convfloat(glob_clock_sec)); if glob_percent_done < 100.0 then logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)) ; 0 else logitem_str(html_log_file, "Done"); 0 end if; log_revs(html_log_file, " 090 "); logitem_str(html_log_file, "sing3 diffeq.mxt"); logitem_str(html_log_file, "sing3 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/sing3postode.ode################# diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; ! #BEGIN FIRST INPUT BLOCK Digits := 100; max_terms := 30; ! #END FIRST INPUT BLOCK #BEGIN SECOND INPUT BLOCK x_start := -1.0; x_end := -0.7; array_y_init[0 + 1] := exact_soln_y(x_start); glob_h := 0.1; glob_look_poles := true; glob_max_iter := 100000; #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/x/x; end; #END USER DEF BLOCK #######END OF ECHO OF PROBLEM################# START of Soultion x[1] = -1 y[1] (analytic) = 1 y[1] (numeric) = 1 absolute error = 0 relative error = 0 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9999 y[1] (analytic) = 1.0002000300040005000600070008001 y[1] (numeric) = 1.0002000300040005000602520392058 absolute error = 2.4503840567080010891440185923523e-22 relative error = 2.4498940044005000560062006800740e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9998 y[1] (analytic) = 1.000400120032008001920448102423 y[1] (numeric) = 1.0004001200320080019209383753572 absolute error = 4.9027293415396864307773666192589e-22 relative error = 4.9007684459122442177925129037058e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9997 y[1] (analytic) = 1.0006002701080405145851047501907 y[1] (numeric) = 1.0006002701080405145858404539527 absolute error = 7.3570376206062313890173758661958e-22 relative error = 7.3526240601672535047447904522399e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9996 y[1] (analytic) = 1.0008004802561280614686851131009 y[1] (numeric) = 1.000800480256128061469666444167 absolute error = 9.8133106617861057608869762110668e-22 relative error = 9.8054615833863827620551883720141e-20 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.008 Order of pole = 4.437 x[1] = -0.9995 y[1] (analytic) = 1.0010007505003126876094375351758 y[1] (numeric) = 1.0010007505003126876106646901993 absolute error = 1.2271550234727019297317806672402e-21 relative error = 1.2259281752379850959775313195181e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9994 y[1] (analytic) = 1.0012010808646484668868161000663 y[1] (numeric) = 1.0012010808646484668882892758774 absolute error = 1.4731758110847869560810298645917e-21 relative error = 1.4714085304547772022570368179249e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9993 y[1] (analytic) = 1.0014014713732015092442023536359 y[1] (numeric) = 1.0014014713732015092459217472423 absolute error = 1.7193936063340692122791333298766e-21 relative error = 1.7169872977880686190758565599901e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9992 y[1] (analytic) = 1.0016019220500499679166872328928 y[1] (numeric) = 1.0016019220500499679186530414795 absolute error = 1.9658085867172613103714336491168e-21 relative error = 1.9626645510960091913220779929958e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9991 y[1] (analytic) = 1.0018024329192840466639172532829 y[1] (numeric) = 1.0018024329192840466661296742128 absolute error = 2.2124209299087804058950942395054e-21 relative error = 2.2084403642958978272766118449007e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.999 y[1] (analytic) = 1.002003004005006007008009010011 y[1] (numeric) = 1.0020030040050060070104682408248 absolute error = 2.4592308137609439213527631189132e-21 relative error = 2.4543148113642357944539789454385e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9989 y[1] (analytic) = 1.0022036353313301754765360527073 y[1] (numeric) = 1.0022036353313301754792422911236 absolute error = 2.7062384163041655048765026839688e-21 relative error = 2.7002879663367800688060352786323e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=3.8MB, alloc=3.1MB, time=0.17 Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9988 y[1] (analytic) = 1.0024043269223829508505921964186 y[1] (numeric) = 1.0024043269223829508535456403344 absolute error = 2.9534439157471512243881828036699e-21 relative error = 2.9463599033085967373474142839243e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9987 y[1] (analytic) = 1.0026050788023028114179353355617 y[1] (numeric) = 1.0026050788023028114211361830522 absolute error = 3.2008474904770959975629638855839e-21 relative error = 3.1925306964341144542615360608904e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9986 y[1] (analytic) = 1.0028058909952403222312158311442 y[1] (numeric) = 1.0028058909952403222346642804632 absolute error = 3.4484493190598802579029265668937e-21 relative error = 3.4388004199271779505461038622425e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.007 Order of pole = 4.437 x[1] = -0.9985 y[1] (analytic) = 1.0030067635253581423712935452252 y[1] (numeric) = 1.0030067635253581423749897948054 absolute error = 3.6962495802402668572283353238830e-21 relative error = 3.6851691480611015972570790816658e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9984 y[1] (analytic) = 1.003207696416831032215647600263 y[1] (numeric) = 1.0032076964168310322195918487159 absolute error = 3.9442484529420982048944545819635e-21 relative error = 3.9316369551687230224101968571050e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9983 y[1] (analytic) = 1.0034086896938458607118829446702 y[1] (numeric) = 1.0034086896938458607160753907864 absolute error = 4.1924461162684936440422678450642e-21 relative error = 4.1782039156424567815991554165451e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9982 y[1] (analytic) = 1.00360974338060161265633780958 y[1] (numeric) = 1.0036097433806016126607786523295 absolute error = 4.4408427495020470651918829491678e-21 relative error = 4.4248701039343480823896833922516e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9981 y[1] (analytic) = 1.0038108575013093959777961455088 y[1] (numeric) = 1.003810857501309395982485584041 absolute error = 4.6894385321050247574878397810391e-21 relative error = 4.6716355945561265625487605209728e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.998 y[1] (analytic) = 1.0040120320801924490263091312886 y[1] (numeric) = 1.0040120320801924490312473649323 absolute error = 4.9382336437195634979059706907750e-21 relative error = 4.9185004620792601221683384318947e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9979 y[1] (analytic) = 1.004213267141486147867129851333 y[1] (numeric) = 1.0042132671414861478723170795971 absolute error = 5.1872282641678688787318983667753e-21 relative error = 5.1654647811350088097429796013067e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9978 y[1] (analytic) = 1.0044145627094380135797652409966 y[1] (numeric) = 1.0044145627094380135852016635701 absolute error = 5.4364225734524138736216911351206e-21 relative error = 5.4125286264144787622609040231112e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9977 y[1] (analytic) = 1.0046159188083077195621494034857 y[1] (numeric) = 1.0046159188083077195678352202374 absolute error = 5.6858167517561376425556314932061e-21 relative error = 5.6596920726686761993680047076280e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9976 y[1] (analytic) = 1.004817335462367098839942405478 y[1] (numeric) = 1.0048173354623670988458778164575 absolute error = 5.9354109794426445759964901908638e-21 relative error = 5.9069551947085614716644647777311e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.006 Order of pole = 4.437 x[1] = -0.9975 y[1] (analytic) = 1.00501881269590015138095866232 y[1] (numeric) = 1.005018812695900151387143867757 absolute error = 6.1852054370564035785641353321599e-21 relative error = 6.1543180674051031631936806813450e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9974 y[1] (analytic) = 1.0052203505332030514147290273741 y[1] (numeric) = 1.0052203505332030514211642276794 absolute error = 6.4352003053229475925387437886411e-21 relative error = 6.4017807656893322481832678828482e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9973 y[1] (analytic) = 1.0054219489985841547572007038074 y[1] (numeric) = 1.0054219489985841547638860995726 absolute error = 6.6853957651490733615053206910656e-21 relative error = 6.6493433645523963020979973331217e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9972 y[1] (analytic) = 1.0056236081163640061405791008245 y[1] (numeric) = 1.0056236081163640061475148928221 absolute error = 6.9357919976230414344526719026632e-21 relative error = 6.8970059390456137670645830489560e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9971 y[1] (analytic) = 1.0058253279108753465483157600729 y[1] (numeric) = 1.0058253279108753465555021492569 absolute error = 7.1863891840147764106404141737708e-21 relative error = 7.1447685642805282717283132574462e-19 % h = 0.0001 TOP MAIN SOLVE Loop memory used=7.6MB, alloc=4.2MB, time=0.38 Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.997 y[1] (analytic) = 1.0060271084064631205552464816717 y[1] (numeric) = 1.0060271084064631205626836691775 absolute error = 7.4371875057760674255480481363532e-21 relative error = 7.3926313154289630056015897799683e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9969 y[1] (analytic) = 1.0062289496274844836728837830417 y[1] (numeric) = 1.0062289496274844836805719701862 absolute error = 7.6881871445407688782205604185025e-21 relative error = 7.6405942677230751479645126434934e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9968 y[1] (analytic) = 1.0064308515983088096998678274491 y[1] (numeric) = 1.0064308515983088097078072157312 absolute error = 7.9393882821250014003254629445832e-21 relative error = 7.8886574964554103513777193144784e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9967 y[1] (analytic) = 1.0066328143433176980775799629094 y[1] (numeric) = 1.0066328143433176980857707540099 absolute error = 8.1907911005273530672366199373089e-21 relative error = 8.1368210769789572798677604525138e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9966 y[1] (analytic) = 1.0068348378869049812509230158376 y[1] (numeric) = 1.0068348378869049812593654116196 absolute error = 8.4423957819290808514606562547831e-21 relative error = 8.3850850847072022018453666774369e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.005 Order of pole = 4.437 x[1] = -0.9965 y[1] (analytic) = 1.0070369222534767320342724875751 y[1] (numeric) = 1.0070369222534767320429666900837 absolute error = 8.6942025086943123187221844794679e-21 relative error = 8.6334495951141836378170335348715e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9964 y[1] (analytic) = 1.0072390674674512709826028056685 y[1] (numeric) = 1.0072390674674512709915490171318 absolute error = 8.9462114633702475670245326282407e-21 relative error = 8.8819146837345470629504246312602e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9963 y[1] (analytic) = 1.0074412735532591737677927855297 y[1] (numeric) = 1.0074412735532591737769912083584 absolute error = 9.1984228286873614090030994742284e-21 relative error = 9.1304804261635996645541657905509e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9962 y[1] (analytic) = 1.0076435405353432785601144618573 y[1] (numeric) = 1.0076435405353432785695652986448 absolute error = 9.4508367875596057978889102630504e-21 relative error = 9.3791468980573651545326760609155e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9961 y[1] (analytic) = 1.0078458684381586934149094529603 y[1] (numeric) = 1.0078458684381586934246129064834 absolute error = 9.7034535230846124974003920695282e-21 relative error = 9.6279141751326386368767544713493e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.996 y[1] (analytic) = 1.0080482572861728036644570248867 y[1] (numeric) = 1.0080482572861728036744132981052 absolute error = 9.9562732185438959958818351769174e-21 relative error = 9.8767823331670415302507146048649e-19 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9959 y[1] (analytic) = 1.0082507071038652793150380260242 y[1] (numeric) = 1.0082507071038652793252473220816 absolute error = 1.0209296057403056665007454670358e-20 relative error = 1.0125751447999076545736932317375e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9958 y[1] (analytic) = 1.0084532179157280824491988666115 y[1] (numeric) = 1.0084532179157280824596613888348 absolute error = 1.0462522223311984163370414920616e-20 relative error = 1.0374821595528182719798745289402e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9957 y[1] (analytic) = 1.0086557897462654746332197213711 y[1] (numeric) = 1.0086557897462654746439356732712 absolute error = 1.0715951900105061085276628794362e-20 relative error = 1.0623992851714790502522716551597e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9956 y[1] (analytic) = 1.0088584226199940243297911372514 y[1] (numeric) = 1.0088584226199940243407607225232 absolute error = 1.0969585271801366855063593264357e-20 relative error = 1.0873265292580376901201347674797e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.004 Order of pole = 4.437 x[1] = -0.9955 y[1] (analytic) = 1.009061116561442614315903232048 y[1] (numeric) = 1.0090611165614426143271266545706 absolute error = 1.1223422522604881867264973607938e-20 relative error = 1.1122638994207520679317400961182e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9954 y[1] (analytic) = 1.0092638715951524491059516734584 y[1] (numeric) = 1.0092638715951524491174291372953 absolute error = 1.1477463836904691872942099576408e-20 relative error = 1.1372114032739957610991063715132e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9953 y[1] (analytic) = 1.0094666877456770623800646319123 y[1] (numeric) = 1.0094666877456770623917963413115 absolute error = 1.1731709399275192612503988792233e-20 relative error = 1.1621690484382635790951261510699e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=11.4MB, alloc=4.3MB, time=0.59 Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9952 y[1] (analytic) = 1.0096695650375823244176549043124 y[1] (numeric) = 1.0096695650375823244296410637069 absolute error = 1.1986159394476294695337965186549e-20 relative error = 1.1871368425401771000092501307476e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9951 y[1] (analytic) = 1.0098725034954464495362014096184 y[1] (numeric) = 1.0098725034954464495484422236259 absolute error = 1.2240814007453628726573393527430e-20 relative error = 1.2121147932124902126678699298040e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.995 y[1] (analytic) = 1.0100755031438600035352642610035 y[1] (numeric) = 1.0100755031438600035477599344268 absolute error = 1.2495673423338750681301505010808e-20 relative error = 1.2371029080940946643255522498326e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9949 y[1] (analytic) = 1.0102785640074259111457376231202 y[1] (numeric) = 1.0102785640074259111584883609477 absolute error = 1.2750737827449347526574743491863e-20 relative error = 1.2621011948300256139332847317324e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9948 y[1] (analytic) = 1.0104816861107594634843445668178 y[1] (numeric) = 1.0104816861107594634973505742231 absolute error = 1.3006007405289443091509517226372e-20 relative error = 1.2871096610714671909899012664563e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9947 y[1] (analytic) = 1.0106848694784883255133781374653 y[1] (numeric) = 1.0106848694784883255266396198078 absolute error = 1.3261482342549604185816696969881e-20 relative error = 1.3121283144757580599828619573018e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9946 y[1] (analytic) = 1.0108881141352525435056928568503 y[1] (numeric) = 1.0108881141352525435192100196754 absolute error = 1.3517162825107146967084657948813e-20 relative error = 1.3371571627063969904245703831591e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.003 Order of pole = 4.437 x[1] = -0.9945 y[1] (analytic) = 1.0110914201057045525149508824427 y[1] (numeric) = 1.0110914201057045525287239314817 absolute error = 1.3773049039026343557140120572883e-20 relative error = 1.3621962134330484324904182735229e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9944 y[1] (analytic) = 1.011294787414509183851127051634 y[1] (numeric) = 1.0112947874145091838651561928045 absolute error = 1.4029141170558628907812502803495e-20 relative error = 1.3872454743315480982647551772184e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9943 y[1] (analytic) = 1.0114982160863436725612770423922 y[1] (numeric) = 1.0114982160863436725755624817983 absolute error = 1.4285439406142807916427955829302e-20 relative error = 1.4123049530839085486009881877132e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9942 y[1] (analytic) = 1.0117017061458976649155728856011 y[1] (numeric) = 1.0117017061458976649301148295335 absolute error = 1.4541943932405262791359714128943e-20 relative error = 1.4373746573783247856020242785830e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9941 y[1] (analytic) = 1.0119052576178732258986100681881 y[1] (numeric) = 1.0119052576178732259134087231243 absolute error = 1.4798654936160160667961851123205e-20 relative error = 1.4624545949091798507272753031989e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.994 y[1] (analytic) = 1.0121088705269848467059904699829 y[1] (numeric) = 1.0121088705269848467210460425873 absolute error = 1.5055572604409661475213992435629e-20 relative error = 1.4875447733770504285324532230129e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9939 y[1] (analytic) = 1.0123125448979594522461853810913 y[1] (numeric) = 1.0123125448979594522614980782156 absolute error = 1.5312697124344126053405000293017e-20 relative error = 1.5126452004887124560483906489503e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9938 y[1] (analytic) = 1.0125162807555364086476828504164 y[1] (numeric) = 1.0125162807555364086632528790997 absolute error = 1.5570028683342324523184104806516e-20 relative error = 1.5377558839571467378051293103904e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9937 y[1] (analytic) = 1.0127200781244675307714236198061 y[1] (numeric) = 1.0127200781244675307872511872751 absolute error = 1.5827567468971644906308420781048e-20 relative error = 1.5628768315015445665075266060428e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9936 y[1] (analytic) = 1.0129239370295170897285299021629 y[1] (numeric) = 1.0129239370295170897446152158319 absolute error = 1.6085313668988301998416252306998e-20 relative error = 1.5880080508473133493686379407163e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.002 Order of pole = 4.437 x[1] = -0.9935 y[1] (analytic) = 1.0131278574954618204033312657082 y[1] (numeric) = 1.0131278574954618204196745331796 absolute error = 1.6343267471337546494156051694347e-20 relative error = 1.6131495497260822401071401115504e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=15.2MB, alloc=4.3MB, time=0.80 Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9934 y[1] (analytic) = 1.0133318395470909289816918904553 y[1] (numeric) = 1.0133318395470909289982933195194 absolute error = 1.6601429064153874365001364316996e-20 relative error = 1.6383013358757077766150685767441e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9933 y[1] (analytic) = 1.01353588320920610048464346681 y[1] (numeric) = 1.0135358832092061005015032654458 absolute error = 1.6859798635761236490082556644996e-20 relative error = 1.6634634170402795243021490191921e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9932 y[1] (analytic) = 1.01373998850662150630732801009 y[1] (numeric) = 1.0137399885066215063244463864647 absolute error = 1.7118376374673248540366591155886e-20 relative error = 1.6886358009701257251230112067341e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9931 y[1] (analytic) = 1.0139441554641638117632548686227 y[1] (numeric) = 1.0139441554641638117806320310923 absolute error = 1.7377162469593401116516578934537e-20 relative error = 1.7138184954218189522935807499563e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.993 y[1] (analytic) = 1.0141483841066721836338762069633 y[1] (numeric) = 1.0141483841066721836515123640728 absolute error = 1.7636157109415270140763308594870e-20 relative error = 1.7390115081581817707029519676663e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9929 y[1] (analytic) = 1.0143526744589982977234852496536 y[1] (numeric) = 1.0143526744589982977413806101369 absolute error = 1.7895360483222727503121418687744e-20 relative error = 1.7642148469482924030270526893094e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9928 y[1] (analytic) = 1.0145570265460063464194415748263 y[1] (numeric) = 1.0145570265460063464375963476065 absolute error = 1.8154772780290151962283349998333e-20 relative error = 1.7894285195674904015504194527220e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9927 y[1] (analytic) = 1.0147614403925730462577277508506 y[1] (numeric) = 1.0147614403925730462761421450407 absolute error = 1.8414394190082640301524684084540e-20 relative error = 1.8146525337973823257024091947321e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9926 y[1] (analytic) = 1.0149659160235876454938416131073 y[1] (numeric) = 1.0149659160235876455125158380095 absolute error = 1.8674224902256218739954945066635e-20 relative error = 1.8398868974258474253141811812441e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1.001 Order of pole = 4.437 x[1] = -0.9925 y[1] (analytic) = 1.015170453463951931679028481876 y[1] (numeric) = 1.0151704534639519316979627469827 absolute error = 1.8934265106658054599448413048384e-20 relative error = 1.8651316182470433296027905825892e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9924 y[1] (analytic) = 1.0153750527385802392418576262221 y[1] (numeric) = 1.0153750527385802392610521412154 absolute error = 1.9194514993326668227589969632780e-20 relative error = 1.8903867040614117418887427691008e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9923 y[1] (analytic) = 1.0155797138723994570751472826707 y[1] (numeric) = 1.0155797138723994570946022574232 absolute error = 1.9454974752492145176971468792058e-20 relative error = 1.9156521626756841400533650811045e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9922 y[1] (analytic) = 1.0157844368903490361282425413691 y[1] (numeric) = 1.0157844368903490361479581859437 absolute error = 1.9715644574576348641174599863255e-20 relative error = 1.9409280019028874827423605168044e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.9921 y[1] (analytic) = 1.0159892218173809970046504163458 y[1] (numeric) = 1.015989221817380997024626940996 absolute error = 1.9976524650193132147776683668263e-20 relative error = 1.9662142295623499213219154809132e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 1 Order of pole = 4.437 x[1] = -0.992 y[1] (analytic) = 1.0161940686784599375650364203954 y[1] (numeric) = 1.0161940686784599375852740355656 absolute error = 2.0237615170148552508716317702283e-20 relative error = 1.9915108534797065175937414463380e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9999 Order of pole = 4.437 x[1] = -0.9919 y[1] (analytic) = 1.0163989774985630405355869690374 y[1] (numeric) = 1.0163989774985630405560858853628 absolute error = 2.0498916325441083028356261997970e-20 relative error = 2.0168178814869049672754381007953e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9998 Order of pole = 4.437 x[1] = -0.9918 y[1] (analytic) = 1.0166039483026800811217419419193 y[1] (numeric) = 1.0166039483026800811425023702266 absolute error = 2.0760428307261826969581433655555e-20 relative error = 2.0421353214222113292525732799203e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9997 Order of pole = 4.437 x[1] = -0.9917 y[1] (analytic) = 1.0168089811158134346273017339674 y[1] (numeric) = 1.0168089811158134346483238852744 absolute error = 2.1022151306994731278270355132940e-20 relative error = 2.0674631811302157606088827282498e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=19.0MB, alloc=4.3MB, time=1.02 Real estimate of pole used Radius of convergence = 0.9996 Order of pole = 4.437 x[1] = -0.9916 y[1] (analytic) = 1.0170140759629780840789131325156 y[1] (numeric) = 1.0170140759629780841001972180318 absolute error = 2.1284085516216800566478879215423e-20 relative error = 2.0928014684618382574410004794321e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9995 Order of pole = 4.437 x[1] = -0.9915 y[1] (analytic) = 1.0172192328692016278559383605834 y[1] (numeric) = 1.0172192328692016278774845917101 absolute error = 2.1546231126698311354675492133427e-20 relative error = 2.1181501912743344014641384071465e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9994 Order of pole = 4.437 x[1] = -0.9914 y[1] (analytic) = 1.0174244518595242873257116304109 y[1] (numeric) = 1.0174244518595242873475202187413 absolute error = 2.1808588330403026573367975569575e-20 relative error = 2.1435093574313011124151412685252e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9993 Order of pole = 4.437 x[1] = -0.9913 y[1] (analytic) = 1.0176297329589989144841875553063 y[1] (numeric) = 1.0176297329589989145062587126258 absolute error = 2.2071157319488410324461688294852e-20 relative error = 2.1688789748026824062593513423709e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9992 Order of pole = 4.437 x[1] = -0.9912 y[1] (analytic) = 1.0178350761926909996019857718056 y[1] (numeric) = 1.0178350761926909996243197100919 absolute error = 2.2333938286305842902690208898550e-20 relative error = 2.1942590512647751592077245551712e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9991 Order of pole = 4.437 x[1] = -0.9911 y[1] (analytic) = 1.0180404815856786788758361281005 y[1] (numeric) = 1.0180404815856786788984330595239 absolute error = 2.2596931423400836077459562529447e-20 relative error = 2.2196495947002348775506477888371e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.999 Order of pole = 4.437 x[1] = -0.991 y[1] (analytic) = 1.0182459491630527420854287986429 y[1] (numeric) = 1.0182459491630527421082889355664 absolute error = 2.2860136923513248635447736747338e-20 relative error = 2.2450506129980814733149148752562e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9989 Order of pole = 4.437 x[1] = -0.9909 y[1] (analytic) = 1.018451478949916640255673688798 y[1] (numeric) = 1.0184514789499166402787972437775 absolute error = 2.3123554979577502184301674495794e-20 relative error = 2.2704621140537050457503266041635e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9988 Order of pole = 4.437 x[1] = -0.9908 y[1] (analytic) = 1.018657070971386493324373497379 y[1] (numeric) = 1.0186570709713864933477606831637 absolute error = 2.3387185784722797217774415850152e-20 relative error = 2.2958841057688716686523879025067e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9987 Order of pole = 4.437 x[1] = -0.9907 y[1] (analytic) = 1.0188627252525910978153148088671 y[1] (numeric) = 1.0188627252525910978389658383994 absolute error = 2.3651029532273329442645544570245e-20 relative error = 2.3213165960517291835275831854388e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9986 Order of pole = 4.437 x[1] = -0.9906 y[1] (analytic) = 1.0190684418186719345167815910911 y[1] (numeric) = 1.0190684418186719345406966775069 absolute error = 2.3915086415748506367768580596601e-20 relative error = 2.3467595928168129986077187313166e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9985 Order of pole = 4.437 x[1] = -0.9905 y[1] (analytic) = 1.0192742206947831761654954781173 y[1] (numeric) = 1.0192742206947831761896748347462 absolute error = 2.4179356628863164155589445472919e-20 relative error = 2.3722131039850518937198287956387e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9984 Order of pole = 4.437 x[1] = -0.9904 y[1] (analytic) = 1.0194800619060916951359872220816 y[1] (numeric) = 1.0194800619060916951604310624471 absolute error = 2.4443840365527784736480614257663e-20 relative error = 2.3976771374837738310181500517325e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9983 Order of pole = 4.437 x[1] = -0.9903 y[1] (analytic) = 1.0196859654777770711354037016783 y[1] (numeric) = 1.0196859654777770711601122394981 absolute error = 2.4708537819848713186236054804962e-20 relative error = 2.4231517012467117715846768292142e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9982 Order of pole = 4.437 x[1] = -0.9902 y[1] (analytic) = 1.01989193143503159890375487901 y[1] (numeric) = 1.0198919314350315989287283281961 absolute error = 2.4973449186128375367072543350689e-20 relative error = 2.4486368032140094979048175148079e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9981 Order of pole = 4.437 x[1] = -0.9901 y[1] (analytic) = 1.0200979598030602959196051004939 y[1] (numeric) = 1.0200979598030602959448436751527 absolute error = 2.5238574658865495832483434134915e-20 relative error = 2.4741324513322274422246803840423e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.998 Order of pole = 4.437 x[1] = -0.99 y[1] (analytic) = 1.0203040506070809101112131415162 y[1] (numeric) = 1.0203040506070809101367170559489 absolute error = 2.5503914432755315996291450328067e-20 relative error = 2.4996386535543485207965250466538e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9979 Order of pole = 4.437 x[1] = -0.9899 y[1] (analytic) = 1.0205102038723239275731253985284 y[1] (numeric) = 1.0205102038723239275988948672311 absolute error = 2.5769468702689812566247553806215e-20 relative error = 2.5251554178397839740189236132293e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=22.8MB, alloc=4.3MB, time=1.24 Real estimate of pole used Radius of convergence = 0.9978 Order of pole = 4.437 x[1] = -0.9898 y[1] (analytic) = 1.0207164196240325802882266362809 y[1] (numeric) = 1.0207164196240325803142618739446 absolute error = 2.6035237663757916242523442342240e-20 relative error = 2.5506827521543792124781836257399e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9977 Order of pole = 4.437 x[1] = -0.9897 y[1] (analytic) = 1.0209226978874628538552527019 y[1] (numeric) = 1.0209226978874628538815539234112 absolute error = 2.6301221511245730681445714545350e-20 relative error = 2.5762206644704196688975927401572e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9976 Order of pole = 4.437 x[1] = -0.9896 y[1] (analytic) = 1.0211290386878834952217696215255 y[1] (numeric) = 1.0211290386878834952483370419661 absolute error = 2.6567420440636751724820235392722e-20 relative error = 2.6017691627666366560010531053213e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9975 Order of pole = 4.437 x[1] = -0.9895 y[1] (analytic) = 1.0213354420505760204226234992433 y[1] (numeric) = 1.0213354420505760204494573338909 absolute error = 2.6833834647612086895195728455188e-20 relative error = 2.6273282550282132302976813486691e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9974 Order of pole = 4.437 x[1] = -0.9894 y[1] (analytic) = 1.0215419080008347223238656420683 y[1] (numeric) = 1.0215419080008347223509661063964 absolute error = 2.7100464328050675157416114925015e-20 relative error = 2.6528979492467900617939580563278e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9973 Order of pole = 4.437 x[1] = -0.9893 y[1] (analytic) = 1.0217484365639666783721573387557 y[1] (numeric) = 1.0217484365639666783995246484337 absolute error = 2.7367309678029506946811614309217e-20 relative error = 2.6784782534204713096400186224722e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9972 Order of pole = 4.437 x[1] = -0.9892 y[1] (analytic) = 1.0219550277652917583496587242502 y[1] (numeric) = 1.021955027765291758377293095144 absolute error = 2.7634370893823844464379117157639e-20 relative error = 2.7040691755538305037166853407259e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9971 Order of pole = 4.437 x[1] = -0.9891 y[1] (analytic) = 1.0221616816301426321344061656138 y[1] (numeric) = 1.0221616816301426321623078137858 absolute error = 2.7901648171907442239302836452529e-20 relative error = 2.7296707236579164321698486187863e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.997 Order of pole = 4.437 x[1] = -0.989 y[1] (analytic) = 1.0223683981838647774661826093091 y[1] (numeric) = 1.022368398183864777494351751018 absolute error = 2.8169141708952767959166741296656e-20 relative error = 2.7552829057502590348988132163826e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9969 Order of pole = 4.437 x[1] = -0.9889 y[1] (analytic) = 1.0225751774518164877178853337574 y[1] (numeric) = 1.0225751774518164877463221854593 absolute error = 2.8436851701831223568210774301443e-20 relative error = 2.7809057298548753030052334361452e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9968 Order of pole = 4.437 x[1] = -0.9888 y[1] (analytic) = 1.0227820194593688796723955551366 y[1] (numeric) = 1.0227820194593688797011003334842 absolute error = 2.8704778347613366633983352596346e-20 relative error = 2.8065392040022751842092692369938e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9967 Order of pole = 4.437 x[1] = -0.9887 y[1] (analytic) = 1.022988924231905901304954338429 y[1] (numeric) = 1.0229889242319059013339272602726 absolute error = 2.8972921843569131982743151656964e-20 relative error = 2.8321833362294674942396032902552e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9966 Order of pole = 4.437 x[1] = -0.9886 y[1] (analytic) = 1.0231958917948243395710492697881 y[1] (numeric) = 1.0231958917948243396002905521752 absolute error = 2.9241282387168053603963671183390e-20 relative error = 2.8578381345799658342039670599116e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9965 Order of pole = 4.437 x[1] = -0.9885 y[1] (analytic) = 1.0234029221735338281998163503456 y[1] (numeric) = 1.0234029221735338282293262105217 absolute error = 2.9509860176079486824294583053342e-20 relative error = 2.8835036071037945139468320601724e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9964 Order of pole = 4.437 x[1] = -0.9884 y[1] (analytic) = 1.0236100153934568554929615756454 y[1] (numeric) = 1.0236100153934568555227402310535 absolute error = 2.9778655408172830751334362927814e-20 relative error = 2.9091797618574944814009305259765e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9963 Order of pole = 4.437 x[1] = -0.9883 y[1] (analytic) = 1.0238171714800287721292066689526 y[1] (numeric) = 1.0238171714800287721592543372341 absolute error = 3.0047668281517750987569209401680e-20 relative error = 2.9348666069041292579392778250756e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9962 Order of pole = 4.437 x[1] = -0.9882 y[1] (analytic) = 1.0240243904586977989742634407605 y[1] (numeric) = 1.0240243904586977990045803397548 absolute error = 3.0316898994384402614833757668993e-20 relative error = 2.9605641503132908797343770440422e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9961 Order of pole = 4.437 x[1] = -0.9881 y[1] (analytic) = 1.0242316723549250348963412508866 y[1] (numeric) = 1.0242316723549250349269275986318 absolute error = 3.0586347745243653449649598514030e-20 relative error = 2.9862724001611058451312942949041e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=26.7MB, alloc=4.3MB, time=1.46 Real estimate of pole used Radius of convergence = 0.996 Order of pole = 4.437 x[1] = -0.988 y[1] (analytic) = 1.0244390171941844645871920536314 y[1] (numeric) = 1.0244390171941844646180480683642 absolute error = 3.0856014732767307569798118045487e-20 relative error = 3.0119913645302410680413014141394e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9959 Order of pole = 4.437 x[1] = -0.9879 y[1] (analytic) = 1.0246464250019629663886975105529 y[1] (numeric) = 1.0246464250019629664198234107087 absolute error = 3.1125900155828329112484678964066e-20 relative error = 3.0377210515099098373627908614983e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9958 Order of pole = 4.437 x[1] = -0.9878 y[1] (analytic) = 1.0248538958037603201250026594959 y[1] (numeric) = 1.0248538958037603201563986637094 absolute error = 3.1396004213501066344451670294097e-20 relative error = 3.0634614691958777824361757725527e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9957 Order of pole = 4.437 x[1] = -0.9877 y[1] (analytic) = 1.0250614296250892149402006326085 y[1] (numeric) = 1.0250614296250892149718669597135 absolute error = 3.1666327105061476004398459419163e-20 relative error = 3.0892126256904688445394962760377e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9956 Order of pole = 4.437 x[1] = -0.9876 y[1] (analytic) = 1.025269026491475257141572920168 y[1] (numeric) = 1.0252690264914752571735097891979 absolute error = 3.1936869029987347918066787941101e-20 relative error = 3.1149745291025712544314613549475e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9955 Order of pole = 4.437 x[1] = -0.9875 y[1] (analytic) = 1.0254766864284569780483896811408 y[1] (numeric) = 1.0254766864284569780805973113288 absolute error = 3.2207630187958529886350661332559e-20 relative error = 3.1407471875476435159486637090078e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9954 Order of pole = 4.437 x[1] = -0.9874 y[1] (analytic) = 1.0256844094615858418462746055023 y[1] (numeric) = 1.0256844094615858418787532162811 absolute error = 3.2478610778857152846790291576688e-20 relative error = 3.1665306091477203956637132655646e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9953 Order of pole = 4.437 x[1] = -0.9873 y[1] (analytic) = 1.0258921956164262534471388374481 y[1] (numeric) = 1.0258921956164262534798886484509 absolute error = 3.2749811002767856308810161984857e-20 relative error = 3.1923248020314189186110431861468e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9952 Order of pole = 4.437 x[1] = -0.9872 y[1] (analytic) = 1.0261000449185555663546884727428 y[1] (numeric) = 1.0261000449185555663877097038028 absolute error = 3.3021231059978014063061794155647e-20 relative error = 3.2181297743339443700871504269617e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9951 Order of pole = 4.437 x[1] = -0.9871 y[1] (analytic) = 1.0263079573935640905355101475635 y[1] (numeric) = 1.0263079573935640905688030187145 absolute error = 3.3292871150977960165232308587235e-20 relative error = 3.2439455341970963035320411334156e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.995 Order of pole = 4.437 x[1] = -0.987 y[1] (analytic) = 1.0265159330670551002957392403166 y[1] (numeric) = 1.0265159330670551003293039717931 absolute error = 3.3564731476461215194680382781646e-20 relative error = 3.2697720897692745544986593814013e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9949 Order of pole = 4.437 x[1] = -0.9869 y[1] (analytic) = 1.0267239719646448421633152120317 y[1] (numeric) = 1.026723971964644842197152024269 absolute error = 3.3836812237324712788261723784749e-20 relative error = 3.2956094492054852607170860216007e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9948 Order of pole = 4.437 x[1] = -0.9868 y[1] (analytic) = 1.0269320741119625427758286150597 y[1] (numeric) = 1.0269320741119625428099377286944 absolute error = 3.4109113634669026449706685991350e-20 relative error = 3.3214576206673468882603026374146e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9947 Order of pole = 4.437 x[1] = -0.9867 y[1] (analytic) = 1.0271402395346504167739643039391 y[1] (numeric) = 1.0271402395346504168083459398089 absolute error = 3.4381635869798596634913179711669e-20 relative error = 3.3473166123230962638183238923698e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9946 Order of pole = 4.437 x[1] = -0.9866 y[1] (analytic) = 1.0273484682583636747005453864266 y[1] (numeric) = 1.0273484682583636747351997655709 absolute error = 3.4654379144221958113518531445144e-20 relative error = 3.3731864323475946130875098189920e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9945 Order of pole = 4.437 x[1] = -0.9865 y[1] (analytic) = 1.0275567603087705309051824568317 y[1] (numeric) = 1.0275567603087705309401098004914 absolute error = 3.4927343659651967607114473041099e-20 relative error = 3.3990670889223336052818778881701e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9944 Order of pole = 4.437 x[1] = -0.9864 y[1] (analytic) = 1.0277651157115522114545326579354 y[1] (numeric) = 1.0277651157115522114897331875534 absolute error = 3.5200529618006031704469953944663e-20 relative error = 3.4249585902354414037732429960050e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9943 Order of pole = 4.437 x[1] = -0.9863 y[1] (analytic) = 1.0279735344924029620481731219276 y[1] (numeric) = 1.027973534492402962083647059149 absolute error = 3.5473937221406335054126988531692e-20 relative error = 3.4508609444816887228670218140401e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=30.5MB, alloc=4.4MB, time=1.68 Real estimate of pole used Radius of convergence = 0.9942 Order of pole = 4.437 x[1] = -0.9862 y[1] (analytic) = 1.0281820166770300559400933449438 y[1] (numeric) = 1.028182016677030055975840911616 absolute error = 3.5747566672180068834735269129597e-20 relative error = 3.4767741598624948907205462686273e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9941 Order of pole = 4.437 x[1] = -0.9861 y[1] (analytic) = 1.028390562291153801865811053946 y[1] (numeric) = 1.0283905622911538019018324721188 absolute error = 3.6021418172859659503491794703217e-20 relative error = 3.5026982445859339184107392460122e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.994 Order of pole = 4.437 x[1] = -0.986 y[1] (analytic) = 1.0285991713605075519751161288464 y[1] (numeric) = 1.0285991713605075520114116207726 absolute error = 3.6295491926182997823052285357442e-20 relative error = 3.5286332068667405751580139615364e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9939 Order of pole = 4.437 x[1] = -0.9859 y[1] (analytic) = 1.0288078439108377097704471469466 y[1] (numeric) = 1.0288078439108377098070169350817 absolute error = 3.6569788135093668167281673772510e-20 relative error = 3.5545790549263164697132667841688e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9938 Order of pole = 4.437 x[1] = -0.9858 y[1] (analytic) = 1.0290165799679037380509051209257 y[1] (numeric) = 1.0290165799679037380877494279284 absolute error = 3.6844307002741178106211486445018e-20 relative error = 3.5805357969927361379148416714106e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9937 Order of pole = 4.437 x[1] = -0.9857 y[1] (analytic) = 1.0292253795574781668619090057931 y[1] (numeric) = 1.0292253795574781668990280545256 absolute error = 3.7119048732481188270572450159058e-20 relative error = 3.6065034413007531364223527444842e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9936 Order of pole = 4.437 x[1] = -0.9856 y[1] (analytic) = 1.0294342427053466014504975543937 y[1] (numeric) = 1.0294342427053466014878915679215 absolute error = 3.7394013527875742496271182458679e-20 relative error = 3.6324819960918061426342599196264e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9935 Order of pole = 4.437 x[1] = -0.9855 y[1] (analytic) = 1.0296431694373077302262821052393 y[1] (numeric) = 1.029643169437307730263951306832 absolute error = 3.7669201592693498249180349036536e-20 relative error = 3.6584714696140250607961009082862e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9934 Order of pole = 4.437 x[1] = -0.9854 y[1] (analytic) = 1.0298521597791733327280548906258 y[1] (numeric) = 1.0298521597791733327659995037567 absolute error = 3.7944613130909957330612195895267e-20 relative error = 3.6844718701222371343062913070803e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9933 Order of pole = 4.437 x[1] = -0.9853 y[1] (analytic) = 1.0300612137567682875960574571853 y[1] (numeric) = 1.030061213756768287634277705532 absolute error = 3.8220248346707696863845889879244e-20 relative error = 3.7104832058779730642264129175138e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9932 Order of pole = 4.437 x[1] = -0.9852 y[1] (analytic) = 1.0302703313959305805499137952208 y[1] (numeric) = 1.0302703313959305805884099026653 absolute error = 3.8496107444476600562079627716081e-20 relative error = 3.7365054851494731340029188657340e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9931 Order of pole = 4.437 x[1] = -0.9851 y[1] (analytic) = 1.0304795127225113123722327773666 y[1] (numeric) = 1.0304795127225113124110049679954 absolute error = 3.8772190628814090278179001051051e-20 relative error = 3.7625387162116933404071925339753e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.993 Order of pole = 4.437 x[1] = -0.985 y[1] (analytic) = 1.0306887577623747068978845113247 y[1] (numeric) = 1.0306887577623747069369330094292 absolute error = 3.9048498104525357836593633104556e-20 relative error = 3.7885829073463115307009057678868e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9929 Order of pole = 4.437 x[1] = -0.9849 y[1] (analytic) = 1.0308980665413981190089552156334 y[1] (numeric) = 1.03089806654139811904828024571 absolute error = 3.9325030076623597147814631534422e-20 relative error = 3.8146380668417335460336302876219e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9928 Order of pole = 4.437 x[1] = -0.9848 y[1] (analytic) = 1.0311074390854720426353852316379 y[1] (numeric) = 1.0311074390854720426749870183882 absolute error = 3.9601786750330236605745931842280e-20 relative error = 3.8407042029930993710796647054368e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9927 Order of pole = 4.437 x[1] = -0.9847 y[1] (analytic) = 1.0313168754205001187612947890477 y[1] (numeric) = 1.0313168754205001188011735573788 absolute error = 3.9878768331075171768363136228020e-20 relative error = 3.8667813241022892899210480386002e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9926 Order of pole = 4.437 x[1] = -0.9846 y[1] (analytic) = 1.0315263755723991434370021466889 y[1] (numeric) = 1.0315263755723991434771581217134 absolute error = 4.0155975024496998322033984169488e-20 relative error = 3.8928694384779300481837391036754e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9925 Order of pole = 4.437 x[1] = -0.9845 y[1] (analytic) = 1.0317359395670990757967387342818 y[1] (numeric) = 1.0317359395670990758371721413183 absolute error = 4.0433407036443245329875123187702e-20 relative error = 3.9189685544354010214339496867230e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9924 Order of pole = 4.437 memory used=34.3MB, alloc=4.4MB, time=1.89 x[1] = -0.9844 y[1] (analytic) = 1.031945567430543046082065925306 y[1] (numeric) = 1.0319455674305430461227769898789 absolute error = 4.0711064572970608764520381252008e-20 relative error = 3.9450786802968403898416279036926e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9923 Order of pole = 4.437 x[1] = -0.9843 y[1] (analytic) = 1.0321552591886873636709980752472 y[1] (numeric) = 1.0321552591886873637119870230875 absolute error = 4.0988947840345185325676276086301e-20 relative error = 3.9711998243911513191180966962484e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9922 Order of pole = 4.437 x[1] = -0.9842 y[1] (analytic) = 1.03236501486750152511283646376 y[1] (numeric) = 1.032365014867501525154103520805 absolute error = 4.1267057045042706542841031257882e-20 relative error = 3.9973319950540081477348609505176e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9921 Order of pole = 4.437 x[1] = -0.9841 y[1] (analytic) = 1.0325748344929682221687187835203 y[1] (numeric) = 1.032574834492968222210264175914 absolute error = 4.1545392393748773163563904366057e-20 relative error = 4.0234752006278625804306052797879e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.992 Order of pole = 4.437 x[1] = -0.984 y[1] (analytic) = 1.0327847180910833498578888227907 y[1] (numeric) = 1.032784718091083349899712776884 absolute error = 4.1823954093359089827622168899632e-20 relative error = 4.0496294494619498880134130770082e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9919 Order of pole = 4.437 x[1] = -0.9839 y[1] (analytic) = 1.0329946656878560145096909929714 y[1] (numeric) = 1.0329946656878560145517937353224 absolute error = 4.2102742350979700027493628402169e-20 relative error = 4.0757947499122951134652460191038e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9918 Order of pole = 4.437 x[1] = -0.9838 y[1] (analytic) = 1.033204677309308541821294356665 y[1] (numeric) = 1.0332046773093085418636761140389 absolute error = 4.2381757373927221355503079472782e-20 relative error = 4.1019711103417192843557317926040e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9917 Order of pole = 4.437 x[1] = -0.9837 y[1] (analytic) = 1.0334147529814764849211508160427 y[1] (numeric) = 1.0334147529814764849638118154124 absolute error = 4.2660999369729081038021678839475e-20 relative error = 4.1281585391198456315723164089159e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9916 Order of pole = 4.437 x[1] = -0.9836 y[1] (analytic) = 1.0336248927304086324381921255644 y[1] (numeric) = 1.0336248927304086324811325941105 absolute error = 4.2940468546123751757098709273145e-20 relative error = 4.1543570446231058143738460877832e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9915 Order of pole = 4.437 x[1] = -0.9835 y[1] (analytic) = 1.0338350965821670165767703973726 y[1] (numeric) = 1.0338350965821670166199905624837 absolute error = 4.3220165111060987759905779464446e-20 relative error = 4.1805666352347461517746523090579e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9914 Order of pole = 4.437 x[1] = -0.9834 y[1] (analytic) = 1.0340453645628269211973467719523 y[1] (numeric) = 1.034045364562826921240846861225 absolute error = 4.3500089272702061256374034164362e-20 relative error = 4.2067873193448338602662222658959e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9913 Order of pole = 4.437 x[1] = -0.9833 y[1] (analytic) = 1.0342556966984768899029329309279 y[1] (numeric) = 1.0342556966984768899467131721673 absolute error = 4.3780241239419999105405492893654e-20 relative error = 4.2330191053502632978835455968919e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9912 Order of pole = 4.437 x[1] = -0.9832 y[1] (analytic) = 1.0344660930152187341312901331465 y[1] (numeric) = 1.0344660930152187341753507543663 absolute error = 4.4060621219799819790040178357884e-20 relative error = 4.2592620016547622146232369304999e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9911 Order of pole = 4.437 x[1] = -0.9831 y[1] (analytic) = 1.0346765535391675412528904594865 y[1] (numeric) = 1.0346765535391675412972316889091 absolute error = 4.4341229422638770681961239364638e-20 relative error = 4.2855160166688980092205424423688e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.991 Order of pole = 4.437 x[1] = -0.983 y[1] (analytic) = 1.0348870782964516826746449561156 y[1] (numeric) = 1.0348870782964516827192670221726 absolute error = 4.4622066056946565595720817529399e-20 relative error = 4.3117811588100839922923473049665e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9909 Order of pole = 4.437 x[1] = -0.9829 y[1] (analytic) = 1.0350976673132128219494033702221 y[1] (numeric) = 1.0350976673132128219943065015541 absolute error = 4.4903131331945622633069952377446e-20 relative error = 4.3380574365025856558533095990912e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9908 Order of pole = 4.437 x[1] = -0.9828 y[1] (analytic) = 1.0353083206156059228912301765375 y[1] (numeric) = 1.0353083206156059229364146019945 absolute error = 4.5184425457071302317776365602649e-20 relative error = 4.3643448581775269492122549585918e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9907 Order of pole = 4.437 x[1] = -0.9827 y[1] (analytic) = 1.0355190382297992576964615972742 y[1] (numeric) = 1.0355190382297992577419275459162 absolute error = 4.5465948641972146021314512231406e-20 relative error = 4.3906434322728965612559749328565e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9906 Order of pole = 4.437 x[1] = -0.9826 memory used=38.1MB, alloc=4.4MB, time=2.11 y[1] (analytic) = 1.0357298201819744150705483224098 y[1] (numeric) = 1.0357298201819744151162960235063 absolute error = 4.5747701096510114679812834262538e-20 relative error = 4.4169531672335542091275807763903e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9905 Order of pole = 4.437 x[1] = -0.9825 y[1] (analytic) = 1.0359406664983263083606886415581 y[1] (numeric) = 1.0359406664983263084067183245888 absolute error = 4.6029683030760827802643701013202e-20 relative error = 4.4432740715112369333065731111175e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9904 Order of pole = 4.437 x[1] = -0.9824 y[1] (analytic) = 1.0361515772050631836942567029889 y[1] (numeric) = 1.0361515772050631837405685976439 absolute error = 4.6311894655013802773042069898011e-20 relative error = 4.4696061535645653990977966549173e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9903 Order of pole = 4.437 x[1] = -0.9823 y[1] (analytic) = 1.0363625523284066281230306196736 y[1] (numeric) = 1.0363625523284066281696249558534 absolute error = 4.6594336179772694441139451705066e-20 relative error = 4.4959494218590502045364579693531e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9902 Order of pole = 4.437 x[1] = -0.9822 y[1] (analytic) = 1.0365735918945915777732251465622 y[1] (numeric) = 1.0365735918945915778201021543779 absolute error = 4.6877007815755535009800315609783e-20 relative error = 4.5223038848670981947163929506072e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9901 Order of pole = 4.437 x[1] = -0.9821 y[1] (analytic) = 1.0367846959298663260013336576258 y[1] (numeric) = 1.0367846959298663260484935673997 absolute error = 4.7159909773894974213648621186664e-20 relative error = 4.5486695510680187825487795702895e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.99 Order of pole = 4.437 x[1] = -0.982 y[1] (analytic) = 1.0369958644604925315557841555328 y[1] (numeric) = 1.0369958644604925316032271977981 absolute error = 4.7443042265338519791672717541832e-20 relative error = 4.5750464289480302759585001670809e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9899 Order of pole = 4.437 x[1] = -0.9819 y[1] (analytic) = 1.0372070975127452267444140511649 y[1] (numeric) = 1.0372070975127452267921404566663 absolute error = 4.7726405501448778253797403396689e-20 relative error = 4.6014345270002662115253663961055e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9898 Order of pole = 4.437 x[1] = -0.9818 y[1] (analytic) = 1.0374183951129128256077684545217 y[1] (numeric) = 1.0374183951129128256557784542155 absolute error = 4.8009999693803695941812496506716e-20 relative error = 4.6278338537247816945774287605215e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9897 Order of pole = 4.437 x[1] = -0.9817 y[1] (analytic) = 1.0376297572872971320982267229113 y[1] (numeric) = 1.0376297572872971321465205479655 absolute error = 4.8293825054196800385047816200729e-20 relative error = 4.6542444176285597457436014790949e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9896 Order of pole = 4.437 x[1] = -0.9816 y[1] (analytic) = 1.0378411840622133482649620166732 y[1] (numeric) = 1.0378411840622133483135398984678 absolute error = 4.8577881794637441951185039076093e-20 relative error = 4.6806662272255176539728422844923e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9895 Order of pole = 4.437 x[1] = -0.9815 y[1] (analytic) = 1.0380526754639900824447386170388 y[1] (numeric) = 1.0380526754639900824936007871661 absolute error = 4.8862170127351035792597444985990e-20 relative error = 4.7070992910365133360271355997055e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9893 Order of pole = 4.437 x[1] = -0.9814 y[1] (analytic) = 1.0382642315189693574585517650928 y[1] (numeric) = 1.0382642315189693575076984553576 absolute error = 4.9146690264779304088609128407050e-20 relative error = 4.7335436175893517024555364044372e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9892 Order of pole = 4.437 x[1] = -0.9813 y[1] (analytic) = 1.038475852253506618814114785166 y[1] (numeric) = 1.0384758522535066188635462275856 absolute error = 4.9431442419580518584065809081113e-20 relative error = 4.7599992154187910300565409794257e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9891 Order of pole = 4.437 x[1] = -0.9812 y[1] (analytic) = 1.0386875376939707429141982603563 y[1] (numeric) = 1.0386875376939707429639146871609 absolute error = 4.9716426804629743424609935484707e-20 relative error = 4.7864660930665493408360596046080e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.989 Order of pole = 4.437 x[1] = -0.9811 y[1] (analytic) = 1.0388992878667440452708260322522 y[1] (numeric) = 1.0388992878667440453208276758852 absolute error = 5.0001643633019078289053335195682e-20 relative error = 4.8129442590813107874682751867151e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9889 Order of pole = 4.437 x[1] = -0.981 y[1] (analytic) = 1.0391111027982222887253328013084 y[1] (numeric) = 1.0391111027982222887756198944265 absolute error = 5.0287093118057901819241227599454e-20 relative error = 4.8394337220187320452666807033839e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9888 Order of pole = 4.437 x[1] = -0.9809 y[1] (analytic) = 1.0393229825148146916742881087077 y[1] (numeric) = 1.039322982514814691724860884181 absolute error = 5.0572775473273115347801976609140e-20 relative error = 4.8659344904414487106725972741758e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9887 Order of pole = 4.437 x[1] = -0.9808 y[1] (analytic) = 1.0395349270429439363012914849282 y[1] (numeric) = 1.0395349270429439363521501758406 absolute error = 5.0858690912409386924177524165689e-20 relative error = 4.8924465729190817062684836040235e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=41.9MB, alloc=4.4MB, time=2.32 Real estimate of pole used Radius of convergence = 0.9886 Order of pole = 4.437 x[1] = -0.9807 y[1] (analytic) = 1.0397469364090461768146435546311 y[1] (numeric) = 1.0397469364090461768657883942805 absolute error = 5.1144839649429395639330009237510e-20 relative error = 4.9189699780282436923233564916083e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9885 Order of pole = 4.437 x[1] = -0.9806 y[1] (analytic) = 1.0399590106395710476908978918741 y[1] (numeric) = 1.0399590106395710477423291137726 absolute error = 5.1431221898514076249520641855321e-20 relative error = 4.9455047143525454848776510540104e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9884 Order of pole = 4.437 x[1] = -0.9805 y[1] (analytic) = 1.0401711497609816719242984240627 y[1] (numeric) = 1.0401711497609816719760162619368 absolute error = 5.1717837874062864099557467398572e-20 relative error = 4.9720507904826024803748582897006e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9883 Order of pole = 4.437 x[1] = -0.9804 y[1] (analytic) = 1.0403833537997546692821071874509 y[1] (numeric) = 1.0403833537997546693341118752416 absolute error = 5.2004687790693940345909222896035e-20 relative error = 4.9986082150160410868472865845578e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9882 Order of pole = 4.437 x[1] = -0.9803 y[1] (analytic) = 1.0405956227823801645658272414177 y[1] (numeric) = 1.040595622782380164618119013281 absolute error = 5.2291771863244477480083054516638e-20 relative error = 5.0251769965575051616633027601310e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9881 Order of pole = 4.437 x[1] = -0.9802 y[1] (analytic) = 1.0408079567353617958783255531551 y[1] (numeric) = 1.0408079567353617959309046434619 absolute error = 5.2579090306770885152664433708578e-20 relative error = 5.0517571437186624558434172698309e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.988 Order of pole = 4.437 x[1] = -0.9801 y[1] (analytic) = 1.0410203556852167228968606688258 y[1] (numeric) = 1.0410203556852167229497273121624 absolute error = 5.2866643336549056298418178596704e-20 relative error = 5.0783486651182110649525871671461e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9879 Order of pole = 4.437 x[1] = -0.98 y[1] (analytic) = 1.0412328196584756351520199916701 y[1] (numeric) = 1.0412328196584756352051744228382 absolute error = 5.3154431168074613562850057271525e-20 relative error = 5.1049515693818858865761195003573e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9878 Order of pole = 4.437 x[1] = -0.9799 y[1] (analytic) = 1.0414453486816827603125714919687 y[1] (numeric) = 1.0414453486816827603660139459857 absolute error = 5.3442454017063156030629020499335e-20 relative error = 5.1315658651424650843865668305834e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9877 Order of pole = 4.437 x[1] = -0.9798 y[1] (analytic) = 1.0416579427813958724762346782012 y[1] (numeric) = 1.0416579427813958725299653903007 absolute error = 5.3730712099450506256270683153358e-20 relative error = 5.1581915610397765588090156243516e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9876 Order of pole = 4.437 x[1] = -0.9797 y[1] (analytic) = 1.041870601984186300466375663178 y[1] (numeric) = 1.0418706019841863005203948688094 absolute error = 5.4019205631392957597483246311893e-20 relative error = 5.1848286657207044242921773382603e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9875 Order of pole = 4.437 x[1] = -0.9796 y[1] (analytic) = 1.0420833263166389361346311633602 y[1] (numeric) = 1.0420833263166389361889390981894 absolute error = 5.4307934829267521851577625492577e-20 relative error = 5.2114771878391954931927010917105e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9874 Order of pole = 4.437 x[1] = -0.9795 y[1] (analytic) = 1.0422961158053522426694662740337 y[1] (numeric) = 1.0422961158053522427240631739434 absolute error = 5.4596899909672177195344124893605e-20 relative error = 5.2381371360562657662801359141454e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9873 Order of pole = 4.437 x[1] = -0.9794 y[1] (analytic) = 1.0425089704769382629106708674496 y[1] (numeric) = 1.042508970476938262965556968539 absolute error = 5.4886101089426116428798572794404e-20 relative error = 5.2648085190400069298699796557626e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9872 Order of pole = 4.437 x[1] = -0.9793 y[1] (analytic) = 1.0427218903580226276697994654987 y[1] (numeric) = 1.0427218903580226277249750040842 absolute error = 5.5175538585569995523201409431317e-20 relative error = 5.2914913454655928595922607652788e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9871 Order of pole = 4.437 x[1] = -0.9792 y[1] (analytic) = 1.0429348754752445640565594429493 y[1] (numeric) = 1.0429348754752445641120246555647 absolute error = 5.5465212615366182473753795709775e-20 relative error = 5.3181856240152861308031082650424e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.987 Order of pole = 4.437 x[1] = -0.9791 y[1] (analytic) = 1.0431479258552569038111524217394 y[1] (numeric) = 1.0431479258552569038669075451357 absolute error = 5.5755123396299006457375389044644e-20 relative error = 5.3448913633784445356467743926267e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9869 Order of pole = 4.437 x[1] = -0.979 y[1] (analytic) = 1.0433610415247260916425737212828 y[1] (numeric) = 1.0433610415247260916986189924289 absolute error = 5.6045271146075007295969011436357e-20 relative error = 5.3716085722515276067755835290074e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=45.7MB, alloc=4.4MB, time=2.53 Real estimate of pole used Radius of convergence = 0.9868 Order of pole = 4.437 x[1] = -0.9789 y[1] (analytic) = 1.0435742225103321935728747342238 y[1] (numeric) = 1.0435742225103321936292103903064 absolute error = 5.6335656082623185225578014593574e-20 relative error = 5.3983372593381031477352901965603e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9867 Order of pole = 4.437 x[1] = -0.9788 y[1] (analytic) = 1.0437874688387689052873931015502 y[1] (numeric) = 1.0437874688387689053440193799743 absolute error = 5.6626278424095250971842727504860e-20 relative error = 5.4250774333488537700233380854104e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9866 Order of pole = 4.437 x[1] = -0.9787 y[1] (analytic) = 1.044000780536743560490955565458 y[1] (numeric) = 1.0440007805367435605478727038469 absolute error = 5.6917138388865876132162953343714e-20 relative error = 5.4518291030015834368275212541575e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9865 Order of pole = 4.437 x[1] = -0.9786 y[1] (analytic) = 1.0442141576309771392700583828489 y[1] (numeric) = 1.0442141576309771393272666190445 absolute error = 5.7208236195532943864974064964663e-20 relative error = 5.4785922770212240134525578506967e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9864 Order of pole = 4.437 x[1] = -0.9785 y[1] (analytic) = 1.0444276001482042764610301868298 y[1] (numeric) = 1.0444276001482042765185297588927 absolute error = 5.7499572062917799886544831514509e-20 relative error = 5.5053669641398418244420959107753e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9863 Order of pole = 4.437 x[1] = -0.9784 y[1] (analytic) = 1.0446411081151732700241821880835 y[1] (numeric) = 1.0446411081151732700819733342936 absolute error = 5.7791146210065503775705692843682e-20 relative error = 5.5321531730966442174036800160888e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9862 Order of pole = 4.437 x[1] = -0.9783 y[1] (analytic) = 1.0448546815586460894239506124776 y[1] (numeric) = 1.0448546815586460894820335713339 absolute error = 5.8082958856245080586916783459388e-20 relative error = 5.5589509126379861335442168301414e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9861 Order of pole = 4.437 x[1] = -0.9782 y[1] (analytic) = 1.0450683205053983840150362757845 y[1] (numeric) = 1.0450683205053983840734112860055 absolute error = 5.8375010220949772772085593716430e-20 relative error = 5.5857601915173766849234867787951e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.986 Order of pole = 4.437 x[1] = -0.9781 y[1] (analytic) = 1.0452820249822194914345462008958 y[1] (numeric) = 1.0452820249822194914932135014197 absolute error = 5.8667300523897292411544742794569e-20 relative error = 5.6125810184954857384332584034259e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9859 Order of pole = 4.437 x[1] = -0.978 y[1] (analytic) = 1.0454957950159124460001421874281 y[1] (numeric) = 1.0454957950159124460591020174132 absolute error = 5.8959829985030073754600925764658e-20 relative error = 5.6394134023401505065095711879084e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9858 Order of pole = 4.437 x[1] = -0.9779 y[1] (analytic) = 1.045709630633293987114201248136 y[1] (numeric) = 1.0457096306332939871734538469605 absolute error = 5.9252598824515526070066685700918e-20 relative error = 5.6662573518263821445857619462901e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9857 Order of pole = 4.437 x[1] = -0.9778 y[1] (analytic) = 1.0459235318611945676739928310728 y[1] (numeric) = 1.0459235318611945677335384383355 absolute error = 5.9545607262746286807187251355154e-20 relative error = 5.6931128757363723552938191559943e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9856 Order of pole = 4.437 x[1] = -0.9777 y[1] (analytic) = 1.0461374987264583624878777509663 y[1] (numeric) = 1.0461374987264583625477166064867 absolute error = 5.9838855520340475067375271371898e-20 relative error = 5.7199799828594999994216589317411e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9855 Order of pole = 4.437 x[1] = -0.9776 y[1] (analytic) = 1.0463515312559432766975337578116 y[1] (numeric) = 1.0463515312559432767576661016298 absolute error = 6.0132343818141945387166867392890e-20 relative error = 5.7468586819923377136339256581072e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9854 Order of pole = 4.437 x[1] = -0.9775 y[1] (analytic) = 1.046565629476520954206212675218 y[1] (numeric) = 1.0465656294765209542666387475952 absolute error = 6.0426072377220541832813020676444e-20 relative error = 5.7737489819386585349639296337722e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9853 Order of pole = 4.437 x[1] = -0.9774 y[1] (analytic) = 1.0467797934150767861130340455916 y[1] (numeric) = 1.0467797934150767861737540870105 absolute error = 6.0720041418872352406920900043609e-20 relative error = 5.8006508915094425320843434280545e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9852 Order of pole = 4.437 x[1] = -0.9773 y[1] (analytic) = 1.0469940230985099191533202237816 y[1] (numeric) = 1.0469940230985099192143344749462 absolute error = 6.1014251164619963767560333060093e-20 relative error = 5.8275644195228834433642880103188e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9851 Order of pole = 4.437 x[1] = -0.9772 y[1] (analytic) = 1.0472083185537332641449778653672 y[1] (numeric) = 1.0472083185537332642062865672034 absolute error = 6.1308701836212716260251217372147e-20 relative error = 5.8544895748043953217204490852815e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=49.5MB, alloc=4.4MB, time=2.75 Real estimate of pole used Radius of convergence = 0.985 Order of pole = 4.437 x[1] = -0.9771 y[1] (analytic) = 1.0474226798076735044409307603228 y[1] (numeric) = 1.0474226798076735045025341539784 absolute error = 6.1603393655626959263248265037537e-20 relative error = 5.8814263661866191862698734521486e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9849 Order of pole = 4.437 x[1] = -0.977 y[1] (analytic) = 1.0476371068872711043876089673546 y[1] (numeric) = 1.0476371068872711044495072941996 absolute error = 6.1898326845066306846540069530851e-20 relative error = 5.9083748025094296807921046029214e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9848 Order of pole = 4.437 x[1] = -0.9769 y[1] (analytic) = 1.0478515998194803177894992087725 y[1] (numeric) = 1.0478515998194803178516927103995 absolute error = 6.2193501626961893744980082857139e-20 relative error = 5.9353348926199417390083261851152e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9847 Order of pole = 4.437 x[1] = -0.9768 y[1] (analytic) = 1.0480661586312691963797614903266 y[1] (numeric) = 1.0480661586312691964422504085506 absolute error = 6.2488918223972631645967688880889e-20 relative error = 5.9623066453725172566851913765679e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9846 Order of pole = 4.437 x[1] = -0.9767 y[1] (analytic) = 1.0482807833496195982969169150157 y[1] (numeric) = 1.0482807833496195983597014918747 absolute error = 6.2784576858985465792098158569981e-20 relative error = 5.9892900696287717705710256549926e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9845 Order of pole = 4.437 x[1] = -0.9766 y[1] (analytic) = 1.0484954740015271965676116644534 y[1] (numeric) = 1.0484954740015271966306921422085 absolute error = 6.3080477755115631899200873368083e-20 relative error = 6.0162851742575811441720998924678e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9844 Order of pole = 4.437 x[1] = -0.9765 y[1] (analytic) = 1.0487102306140014875954621259611 y[1] (numeric) = 1.0487102306140014876588387470968 absolute error = 6.3376621135706913390185804345544e-20 relative error = 6.0432919681350882603766801651754e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9843 Order of pole = 4.437 x[1] = -0.9764 y[1] (analytic) = 1.0489250532140657996559861481475 y[1] (numeric) = 1.0489250532140657997196591553718 absolute error = 6.3673007224331898945118837139570e-20 relative error = 6.0703104601447097209345701414115e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9842 Order of pole = 4.437 x[1] = -0.9763 y[1] (analytic) = 1.0491399418287573013976254123264 y[1] (numeric) = 1.0491399418287573014615950485712 absolute error = 6.3969636244792240367947135980974e-20 relative error = 6.0973406591771425527998713962285e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9841 Order of pole = 4.437 x[1] = -0.9762 y[1] (analytic) = 1.0493548964851270103488639117239 y[1] (numeric) = 1.049354896485127010413130420145 absolute error = 6.4266508421118910770296344318545e-20 relative error = 6.1243825741303709213446964990258e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.984 Order of pole = 4.437 x[1] = -0.9761 y[1] (analytic) = 1.0495699172102398014314475350278 y[1] (numeric) = 1.0495699172102398014960111590054 absolute error = 6.4563623977572463072762024694566e-20 relative error = 6.1514362139096728504515792310291e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9839 Order of pole = 4.437 x[1] = -0.976 y[1] (analytic) = 1.0497850040311744154797097554421 y[1] (numeric) = 1.0497850040311744155445707385807 absolute error = 6.4860983138643288824118346597843e-20 relative error = 6.1785015874276269494923358128787e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9838 Order of pole = 4.437 x[1] = -0.9759 y[1] (analytic) = 1.0500001569750234677660084310183 y[1] (numeric) = 1.0500001569750234678311670171473 absolute error = 6.5158586129051877338867638025207e-20 relative error = 6.2055787036041191472011405585233e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9837 Order of pole = 4.437 x[1] = -0.9758 y[1] (analytic) = 1.0502153760688934565322787266567 y[1] (numeric) = 1.0502153760688934565977351598305 absolute error = 6.5456433173749075153555024420415e-20 relative error = 6.2326675713663494324495889202969e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9836 Order of pole = 4.437 x[1] = -0.9757 y[1] (analytic) = 1.0504306613399047715277071727891 y[1] (numeric) = 1.050430661339904771593461697287 absolute error = 6.5754524497916345802272987532247e-20 relative error = 6.2597681996488386019315304514588e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9835 Order of pole = 4.437 x[1] = -0.9756 y[1] (analytic) = 1.0506460128151917025525318803824 y[1] (numeric) = 1.0506460128151917026185847407093 absolute error = 6.6052860326966029911781286542792e-20 relative error = 6.2868805973934350147654637866260e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9834 Order of pole = 4.437 x[1] = -0.9755 y[1] (analytic) = 1.0508614305219024480079739365348 y[1] (numeric) = 1.0508614305219024480743253774213 absolute error = 6.6351440886541605616668294564181e-20 relative error = 6.3140047735493213540222953274349e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9833 Order of pole = 4.437 x[1] = -0.9754 y[1] (analytic) = 1.0510769144871991234523050095713 y[1] (numeric) = 1.0510769144871991235189552759738 absolute error = 6.6650266402517949294980415288651e-20 relative error = 6.3411407370730213951862729204565e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9832 Order of pole = 4.437 memory used=53.4MB, alloc=4.4MB, time=2.97 x[1] = -0.9753 y[1] (analytic) = 1.0512924647382577701630561971856 y[1] (numeric) = 1.0512924647382577702300055342866 absolute error = 6.6949337101001596624746857204563e-20 relative error = 6.3682884969284067815569154268770e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9831 Order of pole = 4.437 x[1] = -0.9752 y[1] (analytic) = 1.0515080813022683637053731558231 y[1] (numeric) = 1.0515080813022683637726218090314 absolute error = 6.7248653208331003961827656361285e-20 relative error = 6.3954480620867038065997687087534e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.983 Order of pole = 4.437 x[1] = -0.9751 y[1] (analytic) = 1.0517237642064348225065225541478 y[1] (numeric) = 1.0517237642064348225740707690988 absolute error = 6.7548214951076810039513453180219e-20 relative error = 6.4226194415265002032538281947950e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9829 Order of pole = 4.437 x[1] = -0.975 y[1] (analytic) = 1.0519395134779750164365548980934 y[1] (numeric) = 1.0519395134779750165044029206494 absolute error = 6.7848022556042097990306144269355e-20 relative error = 6.4498026442337519402034778396056e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9828 Order of pole = 4.437 x[1] = -0.9749 y[1] (analytic) = 1.0521553291441207753951287796563 y[1] (numeric) = 1.0521553291441207754632768559065 absolute error = 6.8148076250262657690310146606010e-20 relative error = 6.4769976792017900251228049541852e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9827 Order of pole = 4.437 x[1] = -0.9748 y[1] (analytic) = 1.0523712112321178979045016062552 y[1] (numeric) = 1.0523712112321178979729499825162 absolute error = 6.8448376261007248426664628808450e-20 relative error = 6.5042045554313273149001600622383e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9826 Order of pole = 4.437 x[1] = -0.9747 y[1] (analytic) = 1.0525871597692261597086918721504 y[1] (numeric) = 1.0525871597692261597774407949661 absolute error = 6.8748922815777861888447682523546e-20 relative error = 6.5314232819304653328508406264961e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9825 Order of pole = 4.437 x[1] = -0.9746 y[1] (analytic) = 1.0528031747827193223788180380895 y[1] (numeric) = 1.0528031747827193224478677542318 absolute error = 6.9049716142309985481484026215853e-20 relative error = 6.5586538677147010929257871918441e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9824 Order of pole = 4.437 x[1] = -0.9745 y[1] (analytic) = 1.0530192562998851419246190900281 y[1] (numeric) = 1.0530192562998851419939698464967 absolute error = 6.9350756468572865967488453855275e-20 relative error = 6.5858963218069339309241902075776e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9823 Order of pole = 4.437 x[1] = -0.9744 y[1] (analytic) = 1.053235404348025377412161852454 y[1] (numeric) = 1.0532354043480253774818138964768 absolute error = 6.9652044022769773427977862167269e-20 relative error = 6.6131506532374723427179155196055e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9822 Order of pole = 4.437 x[1] = -0.9743 y[1] (analytic) = 1.0534516189544557995877401365351 y[1] (numeric) = 1.0534516189544557996576937155685 absolute error = 6.9953579033338265553385312232862e-20 relative error = 6.6404168710440408294956662648969e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9821 Order of pole = 4.437 x[1] = -0.9742 y[1] (analytic) = 1.0536679001465061995079708080044 y[1] (numeric) = 1.0536679001465061995782261697333 absolute error = 7.0255361728950452257810204307336e-20 relative error = 6.6676949842717867500348086549472e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.982 Order of pole = 4.437 x[1] = -0.9741 y[1] (analytic) = 1.053884247951520397176091864392 y[1] (numeric) = 1.0538842479515203972466492567305 absolute error = 7.0557392338513260619839268767669e-20 relative error = 6.6949850019732871800087989025386e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9819 Order of pole = 4.437 x[1] = -0.974 y[1] (analytic) = 1.0541006623968562501844676159194 y[1] (numeric) = 1.0541006623968562502553272870106 absolute error = 7.0859671091168700149873701101414e-20 relative error = 6.7222869332085557783381583266085e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9818 Order of pole = 4.437 x[1] = -0.9739 y[1] (analytic) = 1.0543171435098856623633060690786 y[1] (numeric) = 1.0543171435098856624344682672949 absolute error = 7.1162198216294128384398394815178e-20 relative error = 6.7496007870450496605929534636358e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9817 Order of pole = 4.437 x[1] = -0.9738 y[1] (analytic) = 1.0545336913179945924355936166292 y[1] (numeric) = 1.0545336913179945925070585905727 absolute error = 7.1464973943502516807629853070822e-20 relative error = 6.7769265725576762794547478206253e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9816 Order of pole = 4.437 x[1] = -0.9737 y[1] (analytic) = 1.0547503058485830626782521424695 y[1] (numeric) = 1.0547503058485830627500201409721 absolute error = 7.1767998502642717100979987753510e-20 relative error = 6.8042642988288003122460017245405e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9815 Order of pole = 4.437 x[1] = -0.9736 y[1] (analytic) = 1.0549669871290651675895236545542 y[1] (numeric) = 1.054966987129065167661594926678 absolute error = 7.2071272123799727720773643539415e-20 relative error = 6.8316139749482505555349065559135e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9814 Order of pole = 4.437 memory used=57.2MB, alloc=4.4MB, time=3.18 x[1] = -0.9735 y[1] (analytic) = 1.0551837351868690825625875637628 y[1] (numeric) = 1.0551837351868690826349623588001 absolute error = 7.2374795037294960804658314363792e-20 relative error = 6.8589756100133268268236495003773e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9813 Order of pole = 4.437 x[1] = -0.9734 y[1] (analytic) = 1.0554005500494370725654157313531 y[1] (numeric) = 1.0554005500494370726380942988268 absolute error = 7.2678567473686509407145150493889e-20 relative error = 6.8863492131288068733281148110297e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9812 Order of pole = 4.437 x[1] = -0.9733 y[1] (analytic) = 1.0556174317442255008268704123724 y[1] (numeric) = 1.0556174317442255008998530020362 absolute error = 7.2982589663769415064720986187319e-20 relative error = 6.9137347934069532878570374468760e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9811 Order of pole = 4.437 x[1] = -0.9732 y[1] (analytic) = 1.0558343802987048375290502271395 y[1] (numeric) = 1.0558343802987048376023370889781 absolute error = 7.3286861838575935690971750666759e-20 relative error = 6.9411323599675204317986348381220e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.981 Order of pole = 4.437 x[1] = -0.9731 y[1] (analytic) = 1.0560513957403596685058892976594 y[1] (numeric) = 1.0560513957403596685794806818888 absolute error = 7.3591384229375813802158258867638e-20 relative error = 6.9685419219377613652227524278258e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9809 Order of pole = 4.437 x[1] = -0.973 y[1] (analytic) = 1.056268478096688703948014690582 y[1] (numeric) = 1.0562684780966887040219108476497 absolute error = 7.3896157067676545073686013118612e-20 relative error = 6.9959634884524347841065685513770e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9808 Order of pole = 4.437 x[1] = -0.9729 y[1] (analytic) = 1.0564856273952047871138673130753 y[1] (numeric) = 1.0564856273952047871880684936605 absolute error = 7.4201180585223647227911282596490e-20 relative error = 7.0233970686538119646919141404812e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9807 Order of pole = 4.437 x[1] = -0.9728 y[1] (analytic) = 1.0567028436634349030470914127424 y[1] (numeric) = 1.0567028436634349031215978677564 absolute error = 7.4506455014000929253726364059696e-20 relative error = 7.0508426716916837149822726768035e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9806 Order of pole = 4.437 x[1] = -0.9727 y[1] (analytic) = 1.0569201269289201873001978374801 y[1] (numeric) = 1.0569201269289201873750098180663 absolute error = 7.4811980586230760958367565008780e-20 relative error = 7.0783003067233673333875357721826e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9805 Order of pole = 4.437 x[1] = -0.9726 y[1] (analytic) = 1.0571374772192159346645062159472 y[1] (numeric) = 1.0571374772192159347396239734816 absolute error = 7.5117757534374342851890089050628e-20 relative error = 7.1057699829137135745245997173909e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9804 Order of pole = 4.437 x[1] = -0.9725 y[1] (analytic) = 1.0573548945618916079063712240865 y[1] (numeric) = 1.0573548945618916079817950101777 absolute error = 7.5423786091131976364754642856458e-20 relative error = 7.1332517094351136221818983198013e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9803 Order of pole = 4.437 x[1] = -0.9724 y[1] (analytic) = 1.0575723789845308465096981079269 y[1] (numeric) = 1.0575723789845308465854281744163 absolute error = 7.5730066489443334398971224704060e-20 relative error = 7.1607454954675060694559773420526e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9802 Order of pole = 4.437 x[1] = -0.9723 y[1] (analytic) = 1.0577899305147314754247526376759 y[1] (numeric) = 1.0577899305147314755007892366384 absolute error = 7.6036598962487732213246196183624e-20 relative error = 7.1882513501983839060682258588921e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9801 Order of pole = 4.437 x[1] = -0.9722 y[1] (analytic) = 1.0580075491801055138232706729068 y[1] (numeric) = 1.0580075491801055138996140566505 absolute error = 7.6343383743684398642579381225621e-20 relative error = 7.2157692828228015128698898678462e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.98 Order of pole = 4.437 x[1] = -0.9721 y[1] (analytic) = 1.0582252350082791838598725234368 y[1] (numeric) = 1.0582252350082791839365229445035 absolute error = 7.6650421066692747652758580180067e-20 relative error = 7.2432993025433816635435035212417e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9799 Order of pole = 4.437 x[1] = -0.972 y[1] (analytic) = 1.0584429880268929194397872952971 y[1] (numeric) = 1.0584429880268929195167450064625 absolute error = 7.6957711165412650230199531240870e-20 relative error = 7.2708414185703225335088833923874e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9798 Order of pole = 4.437 x[1] = -0.9719 y[1] (analytic) = 1.0586608082636013749928924159985 y[1] (numeric) = 1.0586608082636013750701576702725 absolute error = 7.7265254273984706607579997068332e-20 relative error = 7.2983956401214047160418412474577e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9797 Order of pole = 4.437 x[1] = -0.9718 y[1] (analytic) = 1.0588786957460734342540735381089 y[1] (numeric) = 1.0588786957460734343316465887357 absolute error = 7.7573050626790518825717301019047e-20 relative error = 7.3259619764219982456137808668035e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9796 Order of pole = 4.437 x[1] = -0.9717 y[1] (analytic) = 1.0590966505019922190499100249736 y[1] (numeric) = 1.0590966505019922191277911254321 absolute error = 7.7881100458452963632139284946889e-20 relative error = 7.3535404367050696284603545450817e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=61.0MB, alloc=4.4MB, time=3.40 Real estimate of pole used Radius of convergence = 0.9795 Order of pole = 4.437 x[1] = -0.9716 y[1] (analytic) = 1.0593146725590550980916912272305 y[1] (numeric) = 1.0593146725590550981698806312343 absolute error = 7.8189404003836465716799309093290e-20 relative error = 7.3811310302111888803873649987533e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9794 Order of pole = 4.437 x[1] = -0.9715 y[1] (analytic) = 1.0595327619449736957747687635968 y[1] (numeric) = 1.0595327619449736958532667250948 absolute error = 7.8497961498047271285386564141123e-20 relative error = 7.4087337661885365718221085221803e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9793 Order of pole = 4.437 x[1] = -0.9714 y[1] (analytic) = 1.0597509186874739009842500242365 y[1] (numeric) = 1.0597509186874739010630567974129 absolute error = 7.8806773176433721970683616065971e-20 relative error = 7.4363486538929108801183653597595e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9792 Order of pole = 4.437 x[1] = -0.9713 y[1] (analytic) = 1.0599691428142958759070381198505 y[1] (numeric) = 1.0599691428142958759861539591251 absolute error = 7.9115839274586529082423755982899e-20 relative error = 7.4639757025877346491232534013047e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9791 Order of pole = 4.437 x[1] = -0.9712 y[1] (analytic) = 1.0601874343531940648502235044742 y[1] (numeric) = 1.0601874343531940649296486645025 absolute error = 7.9425160028339048196101379757898e-20 relative error = 7.4916149215440624560141714612270e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.979 Order of pole = 4.437 x[1] = -0.9711 y[1] (analytic) = 1.0604057933319372030658325048118 y[1] (numeric) = 1.0604057933319372031455672404855 absolute error = 7.9734735673767554081189275732374e-20 relative error = 7.5192663200405876854140685690027e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9789 Order of pole = 4.437 x[1] = -0.971 y[1] (analytic) = 1.0606242197783083255819379937869 y[1] (numeric) = 1.0606242197783083256619825602341 absolute error = 8.0044566447191515969217353498290e-20 relative error = 7.5469299073636496107932858789681e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9788 Order of pole = 4.437 x[1] = -0.9709 y[1] (analytic) = 1.0608427137201047760401374508444 y[1] (numeric) = 1.0608427137201047761204921034296 absolute error = 8.0354652585173873162168002262333e-20 relative error = 7.5746056928072404831662280016661e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9787 Order of pole = 4.437 x[1] = -0.9708 y[1] (analytic) = 1.0610612751851382155394036564002 y[1] (numeric) = 1.0610612751851382156200686507247 absolute error = 8.0664994324521310981643923951507e-20 relative error = 7.6022936856730126270911307668057e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9786 Order of pole = 4.437 x[1] = -0.9707 y[1] (analytic) = 1.0612799042012346314863132726987 y[1] (numeric) = 1.0612799042012346315672888646009 absolute error = 8.0975591902284537059264943841574e-20 relative error = 7.6299938952702855439812026494096e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9785 Order of pole = 4.437 x[1] = -0.9706 y[1] (analytic) = 1.0614986007962343464516585682108 y[1] (numeric) = 1.0614986007962343465329450137665 absolute error = 8.1286445555758557968750960135299e-20 relative error = 7.6577063309160530227354273259246e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9784 Order of pole = 4.437 x[1] = -0.9705 y[1] (analytic) = 1.0617173649979920270334475475789 y[1] (numeric) = 1.0617173649979920271150451031014 absolute error = 8.1597555522482956200148853581359e-20 relative error = 7.6854310019349902576973250759888e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9783 Order of pole = 4.437 x[1] = -0.9704 y[1] (analytic) = 1.0619361968343766927262977539964 y[1] (numeric) = 1.0619361968343766928082066760367 absolute error = 8.1908922040242167476661838908568e-20 relative error = 7.7131679176594609739499810081959e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9782 Order of pole = 4.437 x[1] = -0.9703 y[1] (analytic) = 1.0621550963332717247972290157957 y[1] (numeric) = 1.0621550963332717248794495611428 absolute error = 8.2220545347065758414540401555581e-20 relative error = 7.7409170874295245599556583645988e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9781 Order of pole = 4.437 x[1] = -0.9702 y[1] (analytic) = 1.0623740635225748751678604139069 y[1] (numeric) = 1.0623740635225748752503928395881 absolute error = 8.2532425681228704526494625904998e-20 relative error = 7.7686785205929432075483254488649e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.978 Order of pole = 4.437 x[1] = -0.9701 y[1] (analytic) = 1.0625930984301982753030167517483 y[1] (numeric) = 1.0625930984301982753858613150296 absolute error = 8.2844563281251668569088384984631e-20 relative error = 7.7964522265051890592874350269610e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9779 Order of pole = 4.437 x[1] = -0.97 y[1] (analytic) = 1.0628122010840684451057498140079 y[1] (numeric) = 1.0628122010840684451889067723938 absolute error = 8.3156958385901279234576526379223e-20 relative error = 7.8242382145294513631813053670211e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9778 Order of pole = 4.437 x[1] = -0.9699 y[1] (analytic) = 1.0630313715121263018187797056808 y[1] (numeric) = 1.063031371512126301902249316915 absolute error = 8.3469611234190410187646854904820e-20 relative error = 7.8520364940366436347884624166562e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=64.8MB, alloc=4.4MB, time=3.62 Real estimate of pole used Radius of convergence = 0.9777 Order of pole = 4.437 x[1] = -0.9698 y[1] (analytic) = 1.0632506097423271689323615676414 y[1] (numeric) = 1.0632506097423271690161440897068 absolute error = 8.3782522065378459447529379437048e-20 relative error = 7.8798470744054108267053129614272e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9776 Order of pole = 4.437 x[1] = -0.9697 y[1] (analytic) = 1.0634699158026407850985829699395 y[1] (numeric) = 1.0634699158026407851826786610584 absolute error = 8.4095691118971629115935959155349e-20 relative error = 7.9076699650221365054485289675276e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9775 Order of pole = 4.437 x[1] = -0.9696 y[1] (analytic) = 1.0636892897210513130520972889368 y[1] (numeric) = 1.0636892897210513131365064075715 absolute error = 8.4409118634723205451294153369592e-20 relative error = 7.9355051752809500357405336849499e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9774 Order of pole = 4.437 x[1] = -0.9695 y[1] (analytic) = 1.0639087315255573485372983793212 y[1] (numeric) = 1.0639087315255573486220211841739 absolute error = 8.4722804852633839289739749034993e-20 relative error = 7.9633527145837337722064904745399e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9773 Order of pole = 4.437 x[1] = -0.9694 y[1] (analytic) = 1.0641282412441719292419418569693 y[1] (numeric) = 1.0641282412441719293269786069823 absolute error = 8.5036750012951826813333111037747e-20 relative error = 7.9912125923401302584912057234088e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9772 Order of pole = 4.437 x[1] = -0.9693 y[1] (analytic) = 1.0643478189049225437372183135645 y[1] (numeric) = 1.0643478189049225438225692679207 absolute error = 8.5350954356173390665965172348865e-20 relative error = 8.0190848179675494338043676281931e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9771 Order of pole = 4.437 x[1] = -0.9692 y[1] (analytic) = 1.0645674645358511404242837888177 y[1] (numeric) = 1.0645674645358511405099492069408 absolute error = 8.5665418123042961417419554199152e-20 relative error = 8.0469694008911758469025530546380e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.977 Order of pole = 4.437 x[1] = -0.9691 y[1] (analytic) = 1.0647871781650141364872528310854 y[1] (numeric) = 1.06478717816501413657323297264 absolute error = 8.5980141554553459376057980525745e-20 relative error = 8.0748663505439758775164451249639e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9769 Order of pole = 4.437 x[1] = -0.969 y[1] (analytic) = 1.0650069598204824268526594821297 y[1] (numeric) = 1.0650069598204824269389546070217 absolute error = 8.6295124891946576750596826081921e-20 relative error = 8.1027756763667049652317146414707e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9767 Order of pole = 4.437 x[1] = -0.9689 y[1] (analytic) = 1.0652268095303413931553915267236 y[1] (numeric) = 1.0652268095303413932420018951004 absolute error = 8.6610368376713060161443313788710e-20 relative error = 8.1306973878079148458320289258581e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9766 Order of pole = 4.437 x[1] = -0.9688 y[1] (analytic) = 1.0654467273226909127111033527648 y[1] (numeric) = 1.0654467273226909127980292250154 absolute error = 8.6925872250592993502060554140805e-20 relative error = 8.1586314943239607951126621388242e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9765 Order of pole = 4.437 x[1] = -0.9687 y[1] (analytic) = 1.0656667132256453674951127725281 y[1] (numeric) = 1.0656667132256453675823544092837 absolute error = 8.7241636755576081150831297762355e-20 relative error = 8.1865780053790088801731916436536e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9764 Order of pole = 4.437 x[1] = -0.9686 y[1] (analytic) = 1.0658867672673336531277871606606 y[1] (numeric) = 1.0658867672673336532153448227945 absolute error = 8.7557662133901931533890951541818e-20 relative error = 8.2145369304450432181977754907574e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9763 Order of pole = 4.437 x[1] = -0.9685 y[1] (analytic) = 1.0661068894758991878664242694969 y[1] (numeric) = 1.066106889475899187954298218125 absolute error = 8.7873948628060341039401089161285e-20 relative error = 8.2425082790018732427315166274844e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9762 Order of pole = 4.437 x[1] = -0.9684 y[1] (analytic) = 1.0663270798794999216036330872592 y[1] (numeric) = 1.06632707987949992169182358374 absolute error = 8.8190496480791578283735368275905e-20 relative error = 8.2704920605371409774614299790214e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9761 Order of pole = 4.437 x[1] = -0.9683 y[1] (analytic) = 1.0665473385063083448722201096882 y[1] (numeric) = 1.0665473385063083449607274156233 absolute error = 8.8507305935086668730050449095329e-20 relative error = 8.2984882845463283175105391018477e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.976 Order of pole = 4.437 x[1] = -0.9682 y[1] (analytic) = 1.0667676653845114978565864006495 y[1] (numeric) = 1.0667676653845114979454107778837 absolute error = 8.8824377234187679659715192672941e-20 relative error = 8.3264969605327643182536396810380e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9759 Order of pole = 4.437 x[1] = -0.9681 y[1] (analytic) = 1.0669880605423109794106408222526 y[1] (numeric) = 1.0669880605423109794997825328742 absolute error = 8.9141710621588005497072101821965e-20 relative error = 8.3545180980076324916632777267258e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=68.6MB, alloc=4.4MB, time=3.83 Real estimate of pole used Radius of convergence = 0.9758 Order of pole = 4.437 x[1] = -0.968 y[1] (analytic) = 1.067208524007922956082234820026 y[1] (numeric) = 1.067208524007922956171694126367 absolute error = 8.9459306341032653488005653251988e-20 relative error = 8.3825517064899781101945009232790e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9757 Order of pole = 4.437 x[1] = -0.9679 y[1] (analytic) = 1.0674290558095781711441241536982 y[1] (numeric) = 1.0674290558095781712339013183347 absolute error = 8.9777164636518529732792856256821e-20 relative error = 8.4105977955067155182169521972149e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9756 Order of pole = 4.437 x[1] = -0.9678 y[1] (analytic) = 1.0676496559755219536314629691482 y[1] (numeric) = 1.0676496559755219537215582549005 absolute error = 9.0095285752294725573712061086684e-20 relative error = 8.4386563745926354510028851966119e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9755 Order of pole = 4.437 x[1] = -0.9677 y[1] (analytic) = 1.0678703245340142273858356121063 y[1] (numeric) = 1.0678703245340142274762492820392 absolute error = 9.0413669932862804337886729006176e-20 relative error = 8.4667274532904123612796920157882e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9754 Order of pole = 4.437 x[1] = -0.9676 y[1] (analytic) = 1.0680910615133295201058315892118 y[1] (numeric) = 1.0680910615133295201965639066348 absolute error = 9.0732317422977088435841565976208e-20 relative error = 8.4948110411506117533555441543249e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9753 Order of pole = 4.437 x[1] = -0.9675 y[1] (analytic) = 1.0683118669417569724041690870607 y[1] (numeric) = 1.0683118669417569724952203155284 absolute error = 9.1051228467644946816249112904714e-20 relative error = 8.5229071477316975248267583691413e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9752 Order of pole = 4.437 x[1] = -0.9674 y[1] (analytic) = 1.0685327408476003468713724649114 y[1] (numeric) = 1.0685327408476003469627428682235 absolute error = 9.1370403312127082777345577489363e-20 relative error = 8.5510157826000393158755097622989e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9751 Order of pole = 4.437 x[1] = -0.9673 y[1] (analytic) = 1.0687536832591780371460091417556 y[1] (numeric) = 1.0687536832591780372376989839576 absolute error = 9.1689842201937822135495385827412e-20 relative error = 8.5791369553299198661665251455410e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.975 Order of pole = 4.437 x[1] = -0.9672 y[1] (analytic) = 1.068974694204823076991491303506 y[1] (numeric) = 1.0689746942048230770835008488889 absolute error = 9.2009545382845401751384626195004e-20 relative error = 8.6072706755035423793514004352858e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9749 Order of pole = 4.437 x[1] = -0.9671 y[1] (analytic) = 1.0691957737128831493794478611011 y[1] (numeric) = 1.069195773712883149471777374202 absolute error = 9.2329513100872258414324252702526e-20 relative error = 8.6354169527110378951891965589068e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9748 Order of pole = 4.437 x[1] = -0.967 y[1] (analytic) = 1.0694169218117205955796720953834 y[1] (numeric) = 1.0694169218117205956723218409857 absolute error = 9.2649745602295318085144612915697e-20 relative error = 8.6635757965504726692919790946726e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9747 Order of pole = 4.437 x[1] = -0.9669 y[1] (analytic) = 1.0696381385297124242566504296667 y[1] (numeric) = 1.0696381385297124243496206728003 absolute error = 9.2970243133646285498163560995853e-20 relative error = 8.6917472166278555605039776236990e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9746 Order of pole = 4.437 x[1] = -0.9668 y[1] (analytic) = 1.0698594238952503205726777759728 y[1] (numeric) = 1.0698594238952503206659687819145 absolute error = 9.3291005941711934122711116459025e-20 relative error = 8.7199312225571454259230515427151e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9745 Order of pole = 4.437 x[1] = -0.9667 y[1] (analytic) = 1.0700807779367406552975649059904 y[1] (numeric) = 1.0700807779367406553911769402639 absolute error = 9.3612034273534396484694328283819e-20 relative error = 8.7481278239602585235731598713807e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9744 Order of pole = 4.437 x[1] = -0.9666 y[1] (analytic) = 1.0703022006826044939249433028815 y[1] (numeric) = 1.0703022006826044940188766312579 absolute error = 9.3933328376411454848686704814493e-20 relative error = 8.7763370304670759227365433873308e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9743 Order of pole = 4.437 x[1] = -0.9665 y[1] (analytic) = 1.0705236921612776057951729551459 y[1] (numeric) = 1.0705236921612776058894278436438 absolute error = 9.4254888497896832261027271709821e-20 relative error = 8.8045588517154509219543382360940e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9742 Order of pole = 4.437 x[1] = -0.9664 y[1] (analytic) = 1.0707452524012104732248585588351 y[1] (numeric) = 1.0707452524012104733194352737209 absolute error = 9.4576714885800483954415023082179e-20 relative error = 8.8327932973512164747043509915516e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9741 Order of pole = 4.437 x[1] = -0.9663 y[1] (analytic) = 1.0709668814308683006429795995053 y[1] (numeric) = 1.0709668814308683007378784072935 absolute error = 9.4898807788188889114485234956486e-20 relative error = 8.8610403770281926227647359856907e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.974 Order of pole = 4.437 memory used=72.4MB, alloc=4.4MB, time=4.04 x[1] = -0.9662 y[1] (analytic) = 1.0711885792787310237336397903881 y[1] (numeric) = 1.0711885792787310238288609578415 absolute error = 9.5221167453385343008854815257121e-20 relative error = 8.8893001004081939372723265840882e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9739 Order of pole = 4.437 x[1] = -0.9661 y[1] (analytic) = 1.0714103459732933185854413483673 y[1] (numeric) = 1.0714103459732933186809851424973 absolute error = 9.5543794129970249479124570704400e-20 relative error = 8.9175724771610369674843829558541e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9738 Order of pole = 4.437 x[1] = -0.966 y[1] (analytic) = 1.0716321815430646108474895944515 y[1] (numeric) = 1.0716321815430646109433562825183 absolute error = 9.5866688066781413796326978272555e-20 relative error = 8.9458575169645476972525297736904e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9737 Order of pole = 4.437 x[1] = -0.9659 y[1] (analytic) = 1.0718540860165690848920333705477 y[1] (numeric) = 1.0718540860165690849882232200607 absolute error = 9.6189849512914335880308757230148e-20 relative error = 8.9741552295045690092176681813047e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9736 Order of pole = 4.437 x[1] = -0.9658 y[1] (analytic) = 1.0720760594223456929837467694596 y[1] (numeric) = 1.0720760594223456930802600481773 absolute error = 9.6513278717722503883538247253366e-20 relative error = 9.0024656244749681567346572816753e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9735 Order of pole = 4.437 x[1] = -0.9657 y[1] (analytic) = 1.0722981017889481644556576801545 y[1] (numeric) = 1.0722981017889481645524946560853 absolute error = 9.6836975930817688139828308674411e-20 relative error = 9.0307887115776442435355713306219e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9734 Order of pole = 4.437 x[1] = -0.9656 y[1] (analytic) = 1.0725202131449450148917286554749 y[1] (numeric) = 1.072520213144945014988889596877 absolute error = 9.7160941402070235478466172603173e-20 relative error = 9.0591245005225357111403497658087e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9733 Order of pole = 4.437 x[1] = -0.9655 y[1] (analytic) = 1.0727423935189195553160956146023 y[1] (numeric) = 1.0727423935189195554135807899839 absolute error = 9.7485175381609363904242381442263e-20 relative error = 9.0874730010276278340236681617259e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9732 Order of pole = 4.437 x[1] = -0.9654 y[1] (analytic) = 1.0729646429394699013889698977194 y[1] (numeric) = 1.0729646429394699014867795758393 absolute error = 9.7809678119823457643871674205197e-20 relative error = 9.1158342228189602225468691763688e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9731 Order of pole = 4.437 x[1] = -0.9653 y[1] (analytic) = 1.0731869614352089826092091954651 y[1] (numeric) = 1.0731869614352089827073436453325 absolute error = 9.8134449867360362559299386046866e-20 relative error = 9.1442081756306343336638035452958e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.973 Order of pole = 4.437 x[1] = -0.9652 y[1] (analytic) = 1.0734093490347645515235628809208 y[1] (numeric) = 1.0734093490347645516220223717959 absolute error = 9.8459490875127681928387647526262e-20 relative error = 9.1725948692048209894094421835095e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9729 Order of pole = 4.437 x[1] = -0.9651 y[1] (analytic) = 1.0736318057667791929425972770271 y[1] (numeric) = 1.0736318057667791930413820784214 absolute error = 9.8784801394293072593476386345563e-20 relative error = 9.2009943132917679031801314751975e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9728 Order of pole = 4.437 x[1] = -0.965 y[1] (analytic) = 1.0738543316599103331633063974872 y[1] (numeric) = 1.0738543316599103332624167791635 absolute error = 9.9110381676284541478314852648995e-20 relative error = 9.2294065176498072138143748658060e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9727 Order of pole = 4.437 x[1] = -0.9649 y[1] (analytic) = 1.0740769267428302491984137043795 y[1] (numeric) = 1.0740769267428302492978499363523 absolute error = 9.9436231972790742473860108421241e-20 relative error = 9.2578314920453630274830349202246e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9726 Order of pole = 4.437 x[1] = -0.9648 y[1] (analytic) = 1.0742995910442260780123704308749 y[1] (numeric) = 1.0742995910442260781121327834107 absolute error = 9.9762352535761273693439642100342e-20 relative error = 9.2862692462529589673978610750626e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9725 Order of pole = 4.437 x[1] = -0.9647 y[1] (analytic) = 1.0745223245927998257640560226283 y[1] (numeric) = 1.0745223245927998258641447662457 absolute error = 1.0008874361740697509777599121597e-19 relative error = 9.3147197900552257313472593921015e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9724 Order of pole = 4.437 x[1] = -0.9646 y[1] (analytic) = 1.0747451274172683770561862565978 y[1] (numeric) = 1.074745127417268377156601662068 absolute error = 1.0041540547020022649037197868248e-19 relative error = 9.3431831332429086570682317140563e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9723 Order of pole = 4.437 x[1] = -0.9645 y[1] (analytic) = 1.0749679995463635041914346012312 y[1] (numeric) = 1.0749679995463635042921769395781 absolute error = 1.0074233834687524588375589231910e-19 relative error = 9.3716592856148752954634227327737e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9722 Order of pole = 4.437 memory used=76.2MB, alloc=4.4MB, time=4.26 x[1] = -0.9644 y[1] (analytic) = 1.0751909410088318764352723871527 y[1] (numeric) = 1.0751909410088318765363419296531 absolute error = 1.0106954250042838823708666223890e-19 relative error = 9.4001482569781229916722246039741e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9721 Order of pole = 4.437 x[1] = -0.9643 y[1] (analytic) = 1.0754139518334350692855333626799 y[1] (numeric) = 1.0754139518334350693869303808641 absolute error = 1.0139701818411844456561981694561e-19 relative error = 9.4286500571477864740048998816190e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.972 Order of pole = 4.437 x[1] = -0.9642 y[1] (analytic) = 1.0756370320489495737487082137064 y[1] (numeric) = 1.0756370320489495738504329793578 absolute error = 1.0172476565146694142253572630497e-19 relative error = 9.4571646959471454507486946989798e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9719 Order of pole = 4.437 x[1] = -0.9641 y[1] (analytic) = 1.0758601816841668056229746326908 y[1] (numeric) = 1.0758601816841668057250274178471 absolute error = 1.0205278515625844075363236801662e-19 relative error = 9.4856921832076322148549252925247e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9718 Order of pole = 4.437 x[1] = -0.964 y[1] (analytic) = 1.0760834007678931147879685267127 y[1] (numeric) = 1.0760834007678931148903496036652 absolute error = 1.0238107695254084012538558380584e-19 relative error = 9.5142325287688392565160321488433e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9717 Order of pole = 4.437 x[1] = -0.9639 y[1] (analytic) = 1.0763066893289497945013019597683 y[1] (numeric) = 1.0763066893289497946040116010629 absolute error = 1.0270964129462567332688052228359e-19 relative error = 9.5427857424785268836416072540159e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9716 Order of pole = 4.437 x[1] = -0.9638 y[1] (analytic) = 1.0765300473961730907018334297115 y[1] (numeric) = 1.0765300473961730908048719081486 absolute error = 1.0303847843708841134611869728942e-19 relative error = 9.5713518341926308502424111391341e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9715 Order of pole = 4.437 x[1] = -0.9637 y[1] (analytic) = 1.0767534749984142113196960854703 y[1] (numeric) = 1.076753474998414211423063674105 absolute error = 1.0336758863476876372120582353834e-19 relative error = 9.5999308137752699927314076451072e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9714 Order of pole = 4.437 x[1] = -0.9636 y[1] (analytic) = 1.0769769721645393355930894954079 y[1] (numeric) = 1.0769769721645393356967864675506 absolute error = 1.0369697214277098026692632553967e-19 relative error = 9.6285226910987538741508555744672e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9713 Order of pole = 4.437 x[1] = -0.9635 y[1] (analytic) = 1.0772005389234296233918405829378 y[1] (numeric) = 1.0772005389234296234958672121543 absolute error = 1.0402662921646415317721115104685e-19 relative error = 9.6571274760435904363345076576409e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9712 Order of pole = 4.437 x[1] = -0.9634 y[1] (analytic) = 1.0774241753039812245477393507502 y[1] (numeric) = 1.0774241753039812246520959108617 absolute error = 1.0435656011148251950400625673264e-19 relative error = 9.6857451784984936600139785361077e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9711 Order of pole = 4.437 x[1] = -0.9633 y[1] (analytic) = 1.0776478813351052881916550202566 y[1] (numeric) = 1.0776478813351052882963417853403 absolute error = 1.0468676508372576401304987136743e-19 relative error = 9.7143758083603912328783547550308e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.971 Order of pole = 4.437 x[1] = -0.9632 y[1] (analytic) = 1.0778716570457279720974382181212 y[1] (numeric) = 1.0778716570457279722024554625106 absolute error = 1.0501724438935932241706738050970e-19 relative error = 9.7430193755344322255961310633570e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9709 Order of pole = 4.437 x[1] = -0.9631 y[1] (analytic) = 1.0780955024647904520326148470073 y[1] (numeric) = 1.0780955024647904521379628452921 absolute error = 1.0534799828481468498689341660071e-19 relative error = 9.7716758899339947758085686400555e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9708 Order of pole = 4.437 x[1] = -0.963 y[1] (analytic) = 1.078319417621248931115877282937 y[1] (numeric) = 1.0783194176212489312215563099638 absolute error = 1.0567902702678970054103147939083e-19 relative error = 9.8003453614806937801035822011192e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9707 Order of pole = 4.437 x[1] = -0.9629 y[1] (analytic) = 1.0785434025440746491813785469369 y[1] (numeric) = 1.0785434025440746492873888778092 absolute error = 1.0601033087224888081416215381514e-19 relative error = 9.8290278001043885939792742932190e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9706 Order of pole = 4.437 x[1] = -0.9628 y[1] (analytic) = 1.0787674572622538921498351039216 y[1] (numeric) = 1.078767457262253892256177014 absolute error = 1.0634191007842370520511173578271e-19 relative error = 9.8577232157431907398062464464918e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9705 Order of pole = 4.437 x[1] = -0.9627 y[1] (analytic) = 1.0789915818047880014064439470509 y[1] (numeric) = 1.0789915818047880015131177119537 absolute error = 1.0667376490281292590479382084924e-19 relative error = 9.8864316183434716227978282408899e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9704 Order of pole = 4.437 x[1] = -0.9626 y[1] (analytic) = 1.0792157762006933831856196310904 y[1] (numeric) = 1.0792157762006933832926255266936 absolute error = 1.0700589560318287340463715640885e-19 relative error = 9.9151530178598702549973767378364e-18 % h = 0.0001 TOP MAIN SOLVE Loop memory used=80.1MB, alloc=4.4MB, time=4.49 Real estimate of pole used Radius of convergence = 0.9703 Order of pole = 4.437 x[1] = -0.9625 y[1] (analytic) = 1.0794400404790015179625569235959 y[1] (numeric) = 1.0794400404790015180698952260335 absolute error = 1.0733830243756776238601380486852e-19 relative error = 9.9438874242553009872918101416476e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9702 Order of pole = 4.437 x[1] = -0.9624 y[1] (analytic) = 1.0796643746687589698516247480495 y[1] (numeric) = 1.0796643746687589699592957337138 absolute error = 1.0767098566426999799118241326187e-19 relative error = 9.9726348475009612494605509833154e-18 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9701 Order of pole = 4.437 x[1] = -0.9623 y[1] (analytic) = 1.0798887787990273960115970983777 y[1] (numeric) = 1.0798887787990273961196010439196 absolute error = 1.0800394554186048247626213391723e-19 relative error = 1.0001395297576339298269065562818e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.97 Order of pole = 4.437 x[1] = -0.9622 y[1] (analytic) = 1.0801132528988835560577266095967 y[1] (numeric) = 1.0801132528988835561660637919258 absolute error = 1.0833718232917892224675349112229e-19 relative error = 1.0030168784469221973616197845170e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9699 Order of pole = 4.437 x[1] = -0.9621 y[1] (analytic) = 1.0803377969974193214806664746474 y[1] (numeric) = 1.0803377969974193215893371709328 absolute error = 1.0867069628533413527612324022487e-19 relative error = 1.0058955318175702462744507479931e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9698 Order of pole = 4.437 x[1] = -0.962 y[1] (analytic) = 1.0805624111237416850722464028077 y[1] (numeric) = 1.0805624111237416851812508904774 absolute error = 1.0900448766970435890797101827835e-19 relative error = 1.0087754908700188072522833103959e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9697 Order of pole = 4.437 x[1] = -0.9619 y[1] (analytic) = 1.0807870953069727703581083203951 y[1] (numeric) = 1.0807870953069727704674468771371 absolute error = 1.0933855674193755804229633918398e-19 relative error = 1.0116567566055408009810313592709e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9696 Order of pole = 4.437 x[1] = -0.9618 y[1] (analytic) = 1.0810118495762498410372075198125 y[1] (numeric) = 1.0810118495762498411468804235744 absolute error = 1.0967290376195173370638524130143e-19 relative error = 1.0145393300262421169911111446552e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9695 Order of pole = 4.437 x[1] = -0.9617 y[1] (analytic) = 1.0812366739607253104281849683256 y[1] (numeric) = 1.0812366739607253105381924973155 absolute error = 1.1000752898993523201083665169626e-19 relative error = 1.0174232121350623933129094035234e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9694 Order of pole = 4.437 x[1] = -0.9616 y[1] (analytic) = 1.0814615684895667509226164933098 y[1] (numeric) = 1.0814615684895667510329589259962 absolute error = 1.1034243268634705349124928857049e-19 relative error = 1.0203084039357757969431739975923e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9693 Order of pole = 4.437 x[1] = -0.9615 y[1] (analytic) = 1.0816865331919569034451445660531 y[1] (numeric) = 1.081686533191956903555822181165 absolute error = 1.1067761511191716283609068198110e-19 relative error = 1.0231949064329918051232549488192e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9692 Order of pole = 4.437 x[1] = -0.9614 y[1] (analytic) = 1.0819115680970936869204984115591 y[1] (numeric) = 1.0819115680970936870315114880867 absolute error = 1.1101307652764679900127065269479e-19 relative error = 1.0260827206321559874301249152844e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9691 Order of pole = 4.437 x[1] = -0.9613 y[1] (analytic) = 1.0821366732341902077474081771593 y[1] (numeric) = 1.0821366732341902078587569943541 absolute error = 1.1134881719480878571194234995575e-19 relative error = 1.0289718475395507886811093100728e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.969 Order of pole = 4.437 x[1] = -0.9612 y[1] (analytic) = 1.0823618486324747692794188981071 y[1] (numeric) = 1.0823618486324747693911037354821 absolute error = 1.1168483737494784235205471105998e-19 relative error = 1.0318622881622963126532574272594e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9689 Order of pole = 4.437 x[1] = -0.9611 y[1] (analytic) = 1.0825870943211908813126100037045 y[1] (numeric) = 1.0825870943211908814246311410344 absolute error = 1.1202113732988089524218096893605e-19 relative error = 1.0347540435083511066182871021683e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9688 Order of pole = 4.437 x[1] = -0.961 y[1] (analytic) = 1.0828124103295972695802261128875 y[1] (numeric) = 1.0828124103295972696925838302092 absolute error = 1.1235771732169738930614859843032e-19 relative error = 1.0376471145865129466940365977097e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9687 Order of pole = 4.437 x[1] = -0.9609 y[1] (analytic) = 1.0830377966869678852542248735854 y[1] (numeric) = 1.0830377966869678853669194511982 absolute error = 1.1269457761275960012699685768655e-19 relative error = 1.0405415024064196240133585748146e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9686 Order of pole = 4.437 x[1] = -0.9608 y[1] (analytic) = 1.0832632534225919144537476055549 y[1] (numeric) = 1.0832632534225919145667793240206 absolute error = 1.1303171846570294639278884789737e-19 relative error = 1.0434372079785497317113921727745e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=83.9MB, alloc=4.4MB, time=4.71 Real estimate of pole used Radius of convergence = 0.9685 Order of pole = 4.437 x[1] = -0.9607 y[1] (analytic) = 1.0834887805657737877605185117905 y[1] (numeric) = 1.0834887805657737878738876519339 absolute error = 1.1336914014343630273280578279059e-19 relative error = 1.0463342323142234527321503946671e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9684 Order of pole = 4.437 x[1] = -0.9606 y[1] (analytic) = 1.0837143781458331897411782290104 y[1] (numeric) = 1.0837143781458331898548850719196 absolute error = 1.1370684290914231294465192849821e-19 relative error = 1.0492325764256033484553611640027e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9683 Order of pole = 4.437 x[1] = -0.9605 y[1] (analytic) = 1.0839400461921050684765574931285 y[1] (numeric) = 1.0839400461921050685906023201548 absolute error = 1.1404482702627770361279944494291e-19 relative error = 1.0521322413256951481445015912640e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9682 Order of pole = 4.437 x[1] = -0.9604 y[1] (analytic) = 1.084165784733939645097896701031 y[1] (numeric) = 1.0841657847339396452122797937895 absolute error = 1.1438309275857359811910313156724e-19 relative error = 1.0550332280283485392169661631392e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9681 Order of pole = 4.437 x[1] = -0.9603 y[1] (analytic) = 1.0843915938007024233300171554003 y[1] (numeric) = 1.0843915938007024234447387957704 absolute error = 1.1472164037003583104581585312696e-19 relative error = 1.0579355375482579583373107429664e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.968 Order of pole = 4.437 x[1] = -0.9602 y[1] (analytic) = 1.084617473421774199041449784749 y[1] (numeric) = 1.0846174734217741991565102548739 absolute error = 1.1506047012494526297163619537403e-19 relative error = 1.0608391709009633833345154482118e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9679 Order of pole = 4.437 x[1] = -0.9601 y[1] (analytic) = 1.0848434236265510698015271362571 y[1] (numeric) = 1.084843423626551069916926718545 absolute error = 1.1539958228785809566132067576837e-19 relative error = 1.0637441291028511259442106497109e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9678 Order of pole = 4.437 x[1] = -0.96 y[1] (analytic) = 1.0850694444444444444444444444444 y[1] (numeric) = 1.0850694444444444445601834215681 absolute error = 1.1573897712360618764939361088308e-19 relative error = 1.0666504131711546253768115178985e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9677 Order of pole = 4.437 x[1] = -0.9599 y[1] (analytic) = 1.0852955359048810526402955841463 y[1] (numeric) = 1.0852955359048810527563742390436 absolute error = 1.1607865489729737021848851990703e-19 relative error = 1.0695580241239552427125077233539e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9676 Order of pole = 4.437 x[1] = -0.9598 y[1] (analytic) = 1.0855216980373029544730897217117 y[1] (numeric) = 1.0855216980373029545895083375861 absolute error = 1.1641861587431576377285572260393e-19 relative error = 1.0724669629801830561240560826853e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9675 Order of pole = 4.437 x[1] = -0.9597 y[1] (analytic) = 1.0857479308711675500257544837942 y[1] (numeric) = 1.0857479308711675501425133441146 absolute error = 1.1675886032032209460757157025968e-19 relative error = 1.0753772307596176569283251260829e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9674 Order of pole = 4.437 x[1] = -0.9596 y[1] (analytic) = 1.0859742344359475889721314685621 y[1] (numeric) = 1.0859742344359475890892308570633 absolute error = 1.1709938850125401207398552954303e-19 relative error = 1.0782888284828889464675417497785e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9673 Order of pole = 4.437 x[1] = -0.9595 y[1] (analytic) = 1.0862006087611311801759699296223 y[1] (numeric) = 1.0862006087611311802934101303057 absolute error = 1.1744020068332640614194212181874e-19 relative error = 1.0812017571714779338211913051673e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9672 Order of pole = 4.437 x[1] = -0.9594 y[1] (analytic) = 1.0864270538762218012969244684188 y[1] (numeric) = 1.0864270538762218014147057655519 absolute error = 1.1778129713303172535931550429158e-19 relative error = 1.0841160178477175343495236664775e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9671 Order of pole = 4.437 x[1] = -0.9593 y[1] (analytic) = 1.0866535698107383084035625763422 y[1] (numeric) = 1.0866535698107383085216852544593 absolute error = 1.1812267811714029520939526442386e-19 relative error = 1.0870316115347933690696190106133e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.967 Order of pole = 4.437 x[1] = -0.9592 y[1] (analytic) = 1.0868801565942149455933878732694 y[1] (numeric) = 1.0868801565942149457118522171721 absolute error = 1.1846434390270063686666278536194e-19 relative error = 1.0899485392567445648649682361543e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9669 Order of pole = 4.437 x[1] = -0.9591 y[1] (analytic) = 1.0871068142562013546198848947389 y[1] (numeric) = 1.0871068142562013547386911894959 absolute error = 1.1880629475703978635149832762984e-19 relative error = 1.0928668020384645555295241434716e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9668 Order of pole = 4.437 x[1] = -0.959 y[1] (analytic) = 1.0873335428262625845265912854566 y[1] (numeric) = 1.0873335428262625846457398164044 absolute error = 1.1914853094776361408435976110322e-19 relative error = 1.0957864009057018836471806945117e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=87.7MB, alloc=4.4MB, time=4.93 Real estimate of pole used Radius of convergence = 0.9667 Order of pole = 4.437 x[1] = -0.9589 y[1] (analytic) = 1.0875603423339791012882032623308 y[1] (numeric) = 1.0875603423339791014076943150736 absolute error = 1.1949105274275714483997467126563e-19 relative error = 1.0987073368850610033076388690205e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9666 Order of pole = 4.437 x[1] = -0.9588 y[1] (analytic) = 1.0877872128089467974587202157334 y[1] (numeric) = 1.0877872128089467975785540761436 absolute error = 1.1983386041018487810208835497471e-19 relative error = 1.1016296110040030836596188338206e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9665 Order of pole = 4.437 x[1] = -0.9587 y[1] (analytic) = 1.0880141542807770018266343231974 y[1] (numeric) = 1.0880141542807770019468112774159 absolute error = 1.2017695421849110881931101342932e-19 relative error = 1.1045532242908468133023793432256e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9664 Order of pole = 4.437 x[1] = -0.9586 y[1] (analytic) = 1.0882411667790964890771710552749 y[1] (numeric) = 1.0882411667790964891976913897113 absolute error = 1.2052033443640024856260824373287e-19 relative error = 1.1074781777747692055165064917721e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9663 Order of pole = 4.437 x[1] = -0.9585 y[1] (analytic) = 1.0884682503335474894615864588019 y[1] (numeric) = 1.0884682503335474895824504601348 absolute error = 1.2086400133291714708497972539425e-19 relative error = 1.1104044724858064043349351451859e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9662 Order of pole = 4.437 x[1] = -0.9584 y[1] (analytic) = 1.0886954049737876984735271083414 y[1] (numeric) = 1.0886954049737876985947350635187 absolute error = 1.2120795517732741428387179429930e-19 relative error = 1.1133321094548544914551675818594e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9661 Order of pole = 4.437 x[1] = -0.9583 y[1] (analytic) = 1.0889226307294902865324586221106 y[1] (numeric) = 1.0889226307294902866540108183498 absolute error = 1.2155219623919774256687039412260e-19 relative error = 1.1162610897136702939936550851241e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.966 Order of pole = 4.437 x[1] = -0.9582 y[1] (analytic) = 1.0891499276303439086741686442362 y[1] (numeric) = 1.0891499276303439087960653690246 absolute error = 1.2189672478837622962122169383657e-19 relative error = 1.1191914142948721930833094362417e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9659 Order of pole = 4.437 x[1] = -0.9581 y[1] (analytic) = 1.0893772957060527142483502007248 y[1] (numeric) = 1.0893772957060527143705917418198 absolute error = 1.2224154109499270158772845991106e-19 relative error = 1.1221230842319409333151124693202e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9658 Order of pole = 4.437 x[1] = -0.958 y[1] (analytic) = 1.0896047349863363566232713420879 y[1] (numeric) = 1.0896047349863363567458579875174 absolute error = 1.2258664542945903663957107298717e-19 relative error = 1.1250561005592204330247930622900e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9657 Order of pole = 4.437 x[1] = -0.9579 y[1] (analytic) = 1.0898322455009300028975369911133 y[1] (numeric) = 1.0898322455009300030204690291758 absolute error = 1.2293203806246948896660288125369e-19 relative error = 1.1279904643119185954255421526489e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9656 Order of pole = 4.437 x[1] = -0.9578 y[1] (analytic) = 1.0900598272795843436189489198401 y[1] (numeric) = 1.0900598272795843437422266391051 absolute error = 1.2327771926500101316567038645638e-19 relative error = 1.1309261765261081205877375829048e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9655 Order of pole = 4.437 x[1] = -0.9577 y[1] (analytic) = 1.0902874803520656025104697853591 y[1] (numeric) = 1.0902874803520656026340934746675 absolute error = 1.2362368930831358903750956343167e-19 relative error = 1.1338632382387273182666517985210e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9654 Order of pole = 4.437 x[1] = -0.9576 y[1] (analytic) = 1.0905152047481555462032971596354 y[1] (numeric) = 1.0905152047481555463272671080993 absolute error = 1.2396994846395054679077042027853e-19 relative error = 1.1368016504875809215791166406967e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9653 Order of pole = 4.437 x[1] = -0.9575 y[1] (analytic) = 1.090743000497651493977053494127 y[1] (numeric) = 1.0907430004976514941013699911308 absolute error = 1.2431649700373889265372271376802e-19 relative error = 1.1397414143113409015301206974948e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9652 Order of pole = 4.437 x[1] = -0.9574 y[1] (analytic) = 1.0909708676303663275070979655619 y[1] (numeric) = 1.0909708676303663276317613007617 absolute error = 1.2466333519978963489419654334126e-19 relative error = 1.1426825307495472823903158996758e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9651 Order of pole = 4.437 x[1] = -0.9573 y[1] (analytic) = 1.0911988061761285006189661548213 y[1] (numeric) = 1.0911988061761285007439766181458 absolute error = 1.2501046332449811024831235706536e-19 relative error = 1.1456250008426089579254112720949e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.965 Order of pole = 4.437 x[1] = -0.9572 y[1] (analytic) = 1.0914268161647820490499435164794 y[1] (numeric) = 1.09142681616478204917530139813 absolute error = 1.2535788165054431075855571420533e-19 relative error = 1.1485688256318045084784329776886e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=91.5MB, alloc=4.4MB, time=5.14 Real estimate of pole used Radius of convergence = 0.9649 Order of pole = 4.437 x[1] = -0.9571 y[1] (analytic) = 1.091654897626186600217778602147 y[1] (numeric) = 1.0916548976261866003434841925979 absolute error = 1.2570559045089321102175296163035e-19 relative error = 1.1515140061592830189058310189058e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9648 Order of pole = 4.437 x[1] = -0.957 y[1] (analytic) = 1.0918830505902173829965420063788 y[1] (numeric) = 1.0918830505902173831225955963776 absolute error = 1.2605358999879509584750479510716e-19 relative error = 1.1544605434680648973684141909410e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9647 Order of pole = 4.437 x[1] = -0.9569 y[1] (analytic) = 1.0921112750867652374996370095149 y[1] (numeric) = 1.0921112750867652376260388900827 absolute error = 1.2640188056778588832763549164352e-19 relative error = 1.1574084386020426949780961122948e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9646 Order of pole = 4.437 x[1] = -0.9568 y[1] (analytic) = 1.0923395711457366248699678974508 y[1] (numeric) = 1.0923395711457366249967183598825 absolute error = 1.2675046243168747831721641543372e-19 relative error = 1.1603576926059819263014363910338e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9645 Order of pole = 4.437 x[1] = -0.9567 y[1] (analytic) = 1.0925679387970536370772719439512 y[1] (numeric) = 1.0925679387970536372043712798158 absolute error = 1.2709933586460805132772321762663e-19 relative error = 1.1633083065255218907209622196366e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9644 Order of pole = 4.437 x[1] = -0.9566 y[1] (analytic) = 1.0927963780706540067226210467599 y[1] (numeric) = 1.0927963780706540068500695479009 absolute error = 1.2744850114094241783288696908886e-19 relative error = 1.1662602814071764946552569275145e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9643 Order of pole = 4.437 x[1] = -0.9565 y[1] (analytic) = 1.0930248889964911168500990143921 y[1] (numeric) = 1.0930248889964911169778969729275 absolute error = 1.2779795853537234298780028557110e-19 relative error = 1.1692136182983350746388032581679e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9641 Order of pole = 4.437 x[1] = -0.9564 y[1] (analytic) = 1.0932534716045340107656605061396 y[1] (numeric) = 1.0932534716045340108938082144625 absolute error = 1.2814770832286687676184032620940e-19 relative error = 1.1721683182472632212625703775045e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.964 Order of pole = 4.437 x[1] = -0.9563 y[1] (analytic) = 1.0934821259247674018631776334705 y[1] (numeric) = 1.0934821259247674019916753842491 absolute error = 1.2849775077868268448597136910453e-19 relative error = 1.1751243823031036039763348610866e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9639 Order of pole = 4.437 x[1] = -0.9562 y[1] (analytic) = 1.093710851987191683457680236658 y[1] (numeric) = 1.0937108519871916835865283228364 absolute error = 1.2884808617836437781499049182597e-19 relative error = 1.1780818115158767967537271510115e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9638 Order of pole = 4.437 x[1] = -0.9561 y[1] (analytic) = 1.0939396498218229386257958561369 y[1] (numeric) = 1.0939396498218229387549945709347 absolute error = 1.2919871479774484610528071008304e-19 relative error = 1.1810406069364821046209962177503e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9637 Order of pole = 4.437 x[1] = -0.956 y[1] (analytic) = 1.0941685194586929500533954237496 y[1] (numeric) = 1.0941685194586929501829450606625 absolute error = 1.2954963691294558820863675449806e-19 relative error = 1.1840007696166983910504864085894e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9636 Order of pole = 4.437 x[1] = -0.9559 y[1] (analytic) = 1.0943974609278492098904507047214 y[1] (numeric) = 1.0943974609278492100203515575218 absolute error = 1.2990085280037704468272949340501e-19 relative error = 1.1869623006091849062198217123276e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9635 Order of pole = 4.437 x[1] = -0.9558 y[1] (analytic) = 1.0946264742593549296131095268801 y[1] (numeric) = 1.0946264742593549297433618896168 absolute error = 1.3025236273673893041877583888712e-19 relative error = 1.1899252009674821161377939195939e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9634 Order of pole = 4.437 x[1] = -0.9557 y[1] (analytic) = 1.0948555594832890498929948393217 y[1] (numeric) = 1.0948555594832890500235990063207 absolute error = 1.3060416699902056768698180385738e-19 relative error = 1.1928894717460125326379524095587e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9633 Order of pole = 4.437 x[1] = -0.9556 y[1] (analytic) = 1.095084716629746250473733648414 y[1] (numeric) = 1.0950847166297462506046899142785 absolute error = 1.3095626586450121960032720988155e-19 relative error = 1.1958551140000815442408945469254e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9632 Order of pole = 4.437 x[1] = -0.9555 y[1] (analytic) = 1.0953139457288369600547218847286 y[1] (numeric) = 1.0953139457288369601860305443394 absolute error = 1.3130865961075042399726137864474e-19 relative error = 1.1988221287858782478862569279042e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9631 Order of pole = 4.437 x[1] = -0.9554 y[1] (analytic) = 1.0955432468106873661821312601916 y[1] (numeric) = 1.0955432468106873663137926087072 absolute error = 1.3166134851562832774387997447268e-19 relative error = 1.2017905171604762815354089703974e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.963 Order of pole = 4.437 memory used=95.3MB, alloc=4.4MB, time=5.38 x[1] = -0.9553 y[1] (analytic) = 1.0957726199054394251471641804554 y[1] (numeric) = 1.0957726199054394252791785133127 absolute error = 1.3201433285728602145615400113992e-19 relative error = 1.2047602801818346576458516018615e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9629 Order of pole = 4.437 x[1] = -0.9552 y[1] (analytic) = 1.0960020650432508718915627832069 y[1] (numeric) = 1.0960020650432508720239303961211 absolute error = 1.3236761291416587464278279333039e-19 relative error = 1.2077314189087985975183250582552e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9628 Order of pole = 4.437 x[1] = -0.9551 y[1] (analytic) = 1.0962315822542952299203781788482 y[1] (numeric) = 1.0962315822542952300530993678132 absolute error = 1.3272118896500187126924368156523e-19 relative error = 1.2107039344011003665176310691514e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9627 Order of pole = 4.437 x[1] = -0.955 y[1] (analytic) = 1.0964611715687618212220059757134 y[1] (numeric) = 1.0964611715687618213550810370022 absolute error = 1.3307506128881994574361184917835e-19 relative error = 1.2136778277193601101681759674689e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9626 Order of pole = 4.437 x[1] = -0.9549 y[1] (analytic) = 1.0966908330168557761954941777177 y[1] (numeric) = 1.0966908330168557763289234078827 absolute error = 1.3342923016493831932472474100631e-19 relative error = 1.2166530999250866911252425273799e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9625 Order of pole = 4.437 x[1] = -0.9548 y[1] (analytic) = 1.096920566628798043585129548074 y[1] (numeric) = 1.096920566628798043718913243947 absolute error = 1.3378369587296783695326622586602e-19 relative error = 1.2196297520806785270229996007782e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9624 Order of pole = 4.437 x[1] = -0.9547 y[1] (analytic) = 1.0971503724348254004223085384554 y[1] (numeric) = 1.0971503724348254005564469971482 absolute error = 1.3413845869281230450634655862563e-19 relative error = 1.2226077852494244292002598912364e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9623 Order of pole = 4.437 x[1] = -0.9546 y[1] (analytic) = 1.0973802504651904619746988887357 y[1] (numeric) = 1.0973802504651904621091924076404 absolute error = 1.3449351890466882647615503273090e-19 relative error = 1.2255872004955044423049974746620e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9622 Order of pole = 4.437 x[1] = -0.9545 y[1] (analytic) = 1.0976102007501616917026980081942 y[1] (numeric) = 1.0976102007501616918375468849832 absolute error = 1.3484887678902814407326306043563e-19 relative error = 1.2285679988839906847786379478685e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9621 Order of pole = 4.437 x[1] = -0.9544 y[1] (analytic) = 1.0978402233200234112231942548352 y[1] (numeric) = 1.0978402233200234113583987874619 absolute error = 1.3520453262667497375515626570098e-19 relative error = 1.2315501814808481902211353600170e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.962 Order of pole = 4.437 x[1] = -0.9543 y[1] (analytic) = 1.0980703182050758102806372352417 y[1] (numeric) = 1.0980703182050758104161977219403 absolute error = 1.3556048669868834618057502377798e-19 relative error = 1.2345337493529357496378513573608e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9619 Order of pole = 4.437 x[1] = -0.9542 y[1] (analytic) = 1.0983004854356349567254232531564 y[1] (numeric) = 1.0983004854356349568613399924428 absolute error = 1.3591673928644194559024373187182e-19 relative error = 1.2375187035680067545692532489408e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9618 Order of pole = 4.437 x[1] = -0.9541 y[1] (analytic) = 1.0985307250420328064996020407669 y[1] (numeric) = 1.0985307250420328066358753314385 absolute error = 1.3627329067160444961456994700832e-19 relative error = 1.2405050451947100411044489798301e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9617 Order of pole = 4.437 x[1] = -0.954 y[1] (analytic) = 1.0987610370546172136299109124551 y[1] (numeric) = 1.0987610370546172137665410535913 absolute error = 1.3663014113613986950889538028420e-19 relative error = 1.2434927753025907347795782792273e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9616 Order of pole = 4.437 x[1] = -0.9539 y[1] (analytic) = 1.0989914215037519402281424865677 y[1] (numeric) = 1.09899142150375194036512977753 absolute error = 1.3698729096230789081688159108600e-19 relative error = 1.2464818949620910963620805331406e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9615 Order of pole = 4.437 x[1] = -0.9538 y[1] (analytic) = 1.0992218784198166664988521265612 y[1] (numeric) = 1.0992218784198166666361968669939 absolute error = 1.3734474043266421446261408060946e-19 relative error = 1.2494724052445513685218612155936e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9614 Order of pole = 4.437 x[1] = -0.9537 y[1] (analytic) = 1.0994524078332070007544112586829 y[1] (numeric) = 1.099452407833207000892113748513 absolute error = 1.3770248983006089827200934110491e-19 relative error = 1.2524643072222106233903799982303e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9613 Order of pole = 4.437 x[1] = -0.9536 y[1] (analytic) = 1.0996830097743344894374127291563 y[1] (numeric) = 1.099683009774334489575473268594 absolute error = 1.3806053943764669892411027571602e-19 relative error = 1.2554576019682076110086849458878e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9612 Order of pole = 4.437 memory used=99.1MB, alloc=4.4MB, time=5.60 x[1] = -0.9535 y[1] (analytic) = 1.0999136842736266271504343696628 y[1] (numeric) = 1.0999136842736266272888532592017 absolute error = 1.3841888953886741433285626357236e-19 relative error = 1.2584522905565816086654184951604e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9611 Order of pole = 4.437 x[1] = -0.9534 y[1] (analytic) = 1.1001444313615268666931669457293 y[1] (numeric) = 1.1001444313615268668319444861468 absolute error = 1.3877754041746622645991500594216e-19 relative error = 1.2614483740622732711258222041865e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.961 Order of pole = 4.437 x[1] = -0.9533 y[1] (analytic) = 1.1003752510684946291069126684651 y[1] (numeric) = 1.1003752510684946292460491608226 absolute error = 1.3913649235748404455916415175295e-19 relative error = 1.2644458535611254817527685548614e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9609 Order of pole = 4.437 x[1] = -0.9532 y[1] (analytic) = 1.1006061434250053137264604559257 y[1] (numeric) = 1.1006061434250053138659562015689 absolute error = 1.3949574564325984885341156464710e-19 relative error = 1.2674447301298842045208493834149e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9608 Order of pole = 4.437 x[1] = -0.9531 y[1] (analytic) = 1.1008371084615503082393441362222 y[1] (numeric) = 1.1008371084615503083791994367816 absolute error = 1.3985530055943103464394395895789e-19 relative error = 1.2704450048461993369245518117920e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9607 Order of pole = 4.437 x[1] = -0.953 y[1] (analytic) = 1.1010681462086369987524897903456 y[1] (numeric) = 1.1010681462086369988927049477365 absolute error = 1.4021515739093375685349449857315e-19 relative error = 1.2734466787886255637815538505462e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9606 Order of pole = 4.437 x[1] = -0.9529 y[1] (analytic) = 1.1012992566967887798662584385266 y[1] (numeric) = 1.1012992566967887800068337549496 absolute error = 1.4057531642300327500322082059931e-19 relative error = 1.2764497530366232119321731439948e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9605 Order of pole = 4.437 x[1] = -0.9528 y[1] (analytic) = 1.1015304399565450647558902798134 y[1] (numeric) = 1.1015304399565450648968260577546 absolute error = 1.4093577794117429862428581505104e-19 relative error = 1.2794542286705591058360036302042e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9604 Order of pole = 4.437 x[1] = -0.9527 y[1] (analytic) = 1.1017616960184612952603567004172 y[1] (numeric) = 1.1017616960184612954016532426485 absolute error = 1.4129654223128133310463436247319e-19 relative error = 1.2824601067717074240667761919605e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9603 Order of pole = 4.437 x[1] = -0.9526 y[1] (analytic) = 1.1019930249131089519786262722454 y[1] (numeric) = 1.1019930249131089521202838818249 absolute error = 1.4165760957945902597156010345517e-19 relative error = 1.2854673884222505567064806802566e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9602 Order of pole = 4.437 x[1] = -0.9525 y[1] (analytic) = 1.1022244266710755643733509689242 y[1] (numeric) = 1.1022244266710755645153699491963 absolute error = 1.4201898027214251361065718742402e-19 relative error = 1.2884760747052799636397879989787e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9601 Order of pole = 4.437 x[1] = -0.9524 y[1] (analytic) = 1.1024559013229647208819788324939 y[1] (numeric) = 1.10245590132296472102435948709 absolute error = 1.4238065459606776842175282290565e-19 relative error = 1.2914861667047970337498122484106e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.96 Order of pole = 4.437 x[1] = -0.9523 y[1] (analytic) = 1.102687448899396079035299329856 y[1] (numeric) = 1.1026874488993960791780419626943 absolute error = 1.4274263283827194641241732762443e-19 relative error = 1.2944976655057139450162542359043e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9599 Order of pole = 4.437 x[1] = -0.9522 y[1] (analytic) = 1.102919069431005375583427643943 y[1] (numeric) = 1.1029190694310053757265325592291 absolute error = 1.4310491528609373522964925437322e-19 relative error = 1.2975105721938545255169689745750e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9598 Order of pole = 4.437 x[1] = -0.9521 y[1] (analytic) = 1.1031507629484444366292341504897 y[1] (numeric) = 1.1031507629484444367727016527169 absolute error = 1.4346750222717370263033404753030e-19 relative error = 1.3005248878559551153340011051889e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9597 Order of pole = 4.437 x[1] = -0.952 y[1] (analytic) = 1.1033825294823811877692253371937 y[1] (numeric) = 1.1033825294823811879130557311432 absolute error = 1.4383039394945464539107556542986e-19 relative error = 1.3035406135796654293651334925135e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9596 Order of pole = 4.437 x[1] = -0.9519 y[1] (analytic) = 1.1036143690634996642418824279662 y[1] (numeric) = 1.1036143690634996643860760187074 absolute error = 1.4419359074118193865800068551001e-19 relative error = 1.3065577504535494210419955652995e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9595 Order of pole = 4.437 x[1] = -0.9518 y[1] (analytic) = 1.1038462817225000210834639808998 y[1] (numeric) = 1.1038462817225000212280210737907 absolute error = 1.4455709289090388573713809226987e-19 relative error = 1.3095762995670861469557792887654e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9594 Order of pole = 4.437 x[1] = -0.9517 y[1] (analytic) = 1.1040782674900985432912787345064 y[1] (numeric) = 1.1040782674900985434361996351938 absolute error = 1.4492090068747206832597323256706e-19 relative error = 1.3125962620106706323916119799561e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=103.0MB, alloc=4.4MB, time=5.83 Real estimate of pole used Radius of convergence = 0.9593 Order of pole = 4.437 x[1] = -0.9516 y[1] (analytic) = 1.1043103263970276559944349827136 y[1] (numeric) = 1.1043103263970276561397199971336 absolute error = 1.4528501442004169718678230868119e-19 relative error = 1.3156176388756147377726364996587e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9592 Order of pole = 4.437 x[1] = -0.9515 y[1] (analytic) = 1.1045424584740359346320727650481 y[1] (numeric) = 1.1045424584740359347777221994262 absolute error = 1.4564943437807196326234906686040e-19 relative error = 1.3186404312541480260148506796746e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9591 Order of pole = 4.437 x[1] = -0.9514 y[1] (analytic) = 1.1047746637518881151390851643832 y[1] (numeric) = 1.1047746637518881152850993252345 absolute error = 1.4601416085132638923466902775869e-19 relative error = 1.3216646402394186307937591711735e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.959 Order of pole = 4.437 x[1] = -0.9513 y[1] (analytic) = 1.1050069422613651041393350105792 y[1] (numeric) = 1.105006942261365104285714204709 absolute error = 1.4637919412987318152724669526405e-19 relative error = 1.3246902669254941257238922286002e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9589 Order of pole = 4.437 x[1] = -0.9512 y[1] (analytic) = 1.1052392940332639891463732943063 y[1] (numeric) = 1.1052392940332639892931178288104 absolute error = 1.4674453450408558275159217171381e-19 relative error = 1.3277173124073623944522472741595e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9588 Order of pole = 4.437 x[1] = -0.9511 y[1] (analytic) = 1.1054717190983980487716656013051 y[1] (numeric) = 1.1054717190983980489187757835698 absolute error = 1.4711018226464222459852450039652e-19 relative error = 1.3307457777809325016667104202834e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9587 Order of pole = 4.437 x[1] = -0.951 y[1] (analytic) = 1.1057042174875967629403328833117 y[1] (numeric) = 1.1057042174875967630878090210142 absolute error = 1.4747613770252748117488995055098e-19 relative error = 1.3337756641430355650205164616826e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9586 Order of pole = 4.437 x[1] = -0.9509 y[1] (analytic) = 1.105936789231705823114412887853 y[1] (numeric) = 1.105936789231705823262255288962 absolute error = 1.4784240110903182278630435579604e-19 relative error = 1.3368069725914256279738071846086e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9585 Order of pole = 4.437 x[1] = -0.9508 y[1] (analytic) = 1.1061694343615871425236485751033 y[1] (numeric) = 1.1061694343615871426718575478791 absolute error = 1.4820897277575217016652951406062e-19 relative error = 1.3398397042247805335533491787997e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9584 Order of pole = 4.437 x[1] = -0.9507 y[1] (analytic) = 1.1064021529081188664038098559831 y[1] (numeric) = 1.1064021529081188665523857089777 absolute error = 1.4857585299459224915409455563583e-19 relative error = 1.3428738601427027990314736772667e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9583 Order of pole = 4.437 x[1] = -0.9506 y[1] (analytic) = 1.1066349449021953822425549916783 y[1] (numeric) = 1.1066349449021953823914980337361 absolute error = 1.4894304205776294581677408594116e-19 relative error = 1.3459094414457204915253022905854e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9582 Order of pole = 4.437 x[1] = -0.9505 y[1] (analytic) = 1.1068678103747273300328380007643 y[1] (numeric) = 1.1068678103747273301821485410221 absolute error = 1.4931054025778266202453581098775e-19 relative error = 1.3489464492352881045173238457084e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9581 Order of pole = 4.437 x[1] = -0.9504 y[1] (analytic) = 1.1071007493566416125338684261243 y[1] (numeric) = 1.1071007493566416126835467740118 absolute error = 1.4967834788747767147157125633611e-19 relative error = 1.3519848846137874352983888844955e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.958 Order of pole = 4.437 x[1] = -0.9503 y[1] (analytic) = 1.1073337618788814055396298198737 y[1] (numeric) = 1.1073337618788814056896762851137 absolute error = 1.5004646523998247614802409458464e-19 relative error = 1.3550247486845284633341897241872e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9579 Order of pole = 4.437 x[1] = -0.9502 y[1] (analytic) = 1.1075668479724061681549633105191 y[1] (numeric) = 1.1075668479724061683053782031278 absolute error = 1.5041489260874016326203150209330e-19 relative error = 1.3580660425517502295562953309125e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9578 Order of pole = 4.437 x[1] = -0.9501 y[1] (analytic) = 1.1078000076681916530792226226144 y[1] (numeric) = 1.1078000076681916532300062529019 absolute error = 1.5078363028750276261269487274372e-19 relative error = 1.3611087673206217165788116080397e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9577 Order of pole = 4.437 x[1] = -0.95 y[1] (analytic) = 1.1080332409972299168975069252078 y[1] (numeric) = 1.1080332409972299170486596037781 absolute error = 1.5115267857033160441459712506807e-19 relative error = 1.3641529240972427298417390537394e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9576 Order of pole = 4.437 x[1] = -0.9499 y[1] (analytic) = 1.1082665479905293303794778914178 y[1] (numeric) = 1.1082665479905293305309999291694 absolute error = 1.5152203775159767757448474904370e-19 relative error = 1.3671985139886447796821010965447e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=106.8MB, alloc=4.4MB, time=6.07 Real estimate of pole used Radius of convergence = 0.9575 Order of pole = 4.437 x[1] = -0.9498 y[1] (analytic) = 1.1084999286791145887857673575237 y[1] (numeric) = 1.1084999286791145889376590656497 absolute error = 1.5189170812598198842073365025380e-19 relative error = 1.3702455381027919643339177739630e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9574 Order of pole = 4.437 x[1] = -0.9497 y[1] (analytic) = 1.1087333830940267221819819760088 y[1] (numeric) = 1.1087333830940267223342436659973 absolute error = 1.5226168998847591988621876195716e-19 relative error = 1.3732939975485818538581007773171e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9573 Order of pole = 4.437 x[1] = -0.9496 y[1] (analytic) = 1.1089669112663231057603112630583 y[1] (numeric) = 1.1089669112663231059129432466927 absolute error = 1.5263198363438159114520830989497e-19 relative error = 1.3763438934358463750033472459802e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9572 Order of pole = 4.437 x[1] = -0.9495 y[1] (analytic) = 1.1092005132270774701687454470785 y[1] (numeric) = 1.1092005132270774703217480364378 absolute error = 1.5300258935931221770490453039272e-19 relative error = 1.3793952268753526969991110560169e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9571 Order of pole = 4.437 x[1] = -0.9494 y[1] (analytic) = 1.1094341890073799118479095308784 y[1] (numeric) = 1.1094341890073799120012830383376 absolute error = 1.5337350745919247195225355949239e-19 relative error = 1.3824479989788041182817317119534e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.957 Order of pole = 4.437 x[1] = -0.9493 y[1] (analytic) = 1.1096679386383369033755199862348 y[1] (numeric) = 1.109667938638336903529264724465 absolute error = 1.5374473823025884415664812947674e-19 relative error = 1.3855022108588409541548023159813e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9569 Order of pole = 4.437 x[1] = -0.9492 y[1] (analytic) = 1.1099017621510713038184705056482 y[1] (numeric) = 1.1099017621510713039725867876172 absolute error = 1.5411628196906000392914762922655e-19 relative error = 1.3885578636290414253848594563502e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9568 Order of pole = 4.437 x[1] = -0.9491 y[1] (analytic) = 1.1101356595767223690925532421895 y[1] (numeric) = 1.110135659576722369247041381162 absolute error = 1.5448813897245716213884100638508e-19 relative error = 1.3916149584039225477334792260283e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9567 Order of pole = 4.437 x[1] = -0.949 y[1] (analytic) = 1.1103696309464457623298219744371 y[1] (numeric) = 1.1103696309464457624846822839747 absolute error = 1.5486030953762443328697891229428e-19 relative error = 1.3946734962989410224268649539114e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9566 Order of pole = 4.437 x[1] = -0.9489 y[1] (analytic) = 1.1106036762914135642536036396082 y[1] (numeric) = 1.1106036762914135644088364335702 absolute error = 1.5523279396204919833950241511729e-19 relative error = 1.3977334784304941275640136039368e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9565 Order of pole = 4.437 x[1] = -0.9488 y[1] (analytic) = 1.1108377956428142835611646841026 y[1] (numeric) = 1.1108377956428142837167702766461 absolute error = 1.5560559254353246801859653247372e-19 relative error = 1.4007949059159206104645491724250e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9564 Order of pole = 4.437 x[1] = -0.9487 y[1] (analytic) = 1.1110719890318528673140386867934 y[1] (numeric) = 1.1110719890318528674700173923735 absolute error = 1.5597870558018924655389776228995e-19 relative error = 1.4038577798735015809573127908104e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9563 Order of pole = 4.437 x[1] = -0.9486 y[1] (analytic) = 1.1113062564897507113360217165245 y[1] (numeric) = 1.111306256489750711492373849895 absolute error = 1.5635213337044889589398571941027e-19 relative error = 1.4069221014224614056108006196615e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9562 Order of pole = 4.437 x[1] = -0.9485 y[1] (analytic) = 1.1115405980477456706188418914086 y[1] (numeric) = 1.1115405980477456707755677676217 absolute error = 1.5672587621305550037878991582657e-19 relative error = 1.4099878716829686029065420005068e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9561 Order of pole = 4.437 x[1] = -0.9484 y[1] (analytic) = 1.111775013737092069735509613652 y[1] (numeric) = 1.111775013737092069892609548059 absolute error = 1.5709993440706823187354365416885e-19 relative error = 1.4130550917761367393565117145047e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.956 Order of pole = 4.437 x[1] = -0.9483 y[1] (analytic) = 1.1120095035890607132613549597831 y[1] (numeric) = 1.112009503589060713418829268035 absolute error = 1.5747430825186171536491793735709e-19 relative error = 1.4161237628240253265656715813995e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9559 Order of pole = 4.437 x[1] = -0.9482 y[1] (analytic) = 1.1122440676349388962027587123079 y[1] (numeric) = 1.112244067634938896360607710355 absolute error = 1.5784899804712639501996923205028e-19 relative error = 1.4191938859496407192407380185207e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9558 Order of pole = 4.437 x[1] = -0.9481 y[1] (analytic) = 1.1124787059060304144335835249736 y[1] (numeric) = 1.1124787059060304145918075290664 absolute error = 1.5822400409286890070853585974303e-19 relative error = 1.4222654622769370141462735677887e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=110.6MB, alloc=4.4MB, time=6.31 Real estimate of pole used Radius of convergence = 0.9557 Order of pole = 4.437 x[1] = -0.948 y[1] (analytic) = 1.1127134184336555751393117199879 y[1] (numeric) = 1.1127134184336555752979110466773 absolute error = 1.5859932668941241498971872705660e-19 relative error = 1.4253384929308169500092017888068e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9556 Order of pole = 4.437 x[1] = -0.9479 y[1] (analytic) = 1.1129482052491512072688962217089 y[1] (numeric) = 1.1129482052491512074278711878463 absolute error = 1.5897496613739704056308304595138e-19 relative error = 1.4284129790371328083728463081400e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9555 Order of pole = 4.437 x[1] = -0.9478 y[1] (analytic) = 1.1131830663838706719943311374981 y[1] (numeric) = 1.1131830663838706721536820602359 absolute error = 1.5935092273778016818521863525566e-19 relative error = 1.4314889217226873154015962088106e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9554 Order of pole = 4.437 x[1] = -0.9477 y[1] (analytic) = 1.1134180018691838731779485026137 y[1] (numeric) = 1.1134180018691838733376756994055 absolute error = 1.5972719679183684505229733706201e-19 relative error = 1.4345663221152345446373013398842e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9553 Order of pole = 4.437 x[1] = -0.9476 y[1] (analytic) = 1.1136530117364772678474477122093 y[1] (numeric) = 1.1136530117364772680075515008104 absolute error = 1.6010378860116014364926702519098e-19 relative error = 1.4376451813434808207085025237805e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9552 Order of pole = 4.437 x[1] = -0.9475 y[1] (analytic) = 1.1138880960171538766786641697009 y[1] (numeric) = 1.1138880960171538768391448681685 absolute error = 1.6048069846766153106632262806468e-19 relative error = 1.4407255005370856239936030386149e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9551 Order of pole = 4.437 x[1] = -0.9474 y[1] (analytic) = 1.1141232547426332944860836869672 y[1] (numeric) = 1.1141232547426332946469416136608 absolute error = 1.6085792669357123878329553497261e-19 relative error = 1.4438072808266624962390891544783e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.955 Order of pole = 4.437 x[1] = -0.9473 y[1] (analytic) = 1.1143584879443517007211091780582 y[1] (numeric) = 1.1143584879443517008823446516396 absolute error = 1.6123547358143863292260370285088e-19 relative error = 1.4468905233437799471339089060828e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9549 Order of pole = 4.437 x[1] = -0.9472 y[1] (analytic) = 1.1145937956537618699780861943024 y[1] (numeric) = 1.1145937956537618701396995337365 absolute error = 1.6161333943413258497140573033699e-19 relative error = 1.4499752292209623618411196896466e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9548 Order of pole = 4.437 x[1] = -0.9471 y[1] (analytic) = 1.1148291779023331825080938549267 y[1] (numeric) = 1.1148291779023331826700853794815 absolute error = 1.6199152455484184297360311700794e-19 relative error = 1.4530613995916909094879166792716e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9547 Order of pole = 4.437 x[1] = -0.947 y[1] (analytic) = 1.1150646347215516347405077335308 y[1] (numeric) = 1.1150646347215516349028777627778 absolute error = 1.6237002924707540319233587836148e-19 relative error = 1.4561490355904044526151554673748e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9546 Order of pole = 4.437 x[1] = -0.9469 y[1] (analytic) = 1.115300166142919849812341266995 y[1] (numeric) = 1.1153001661429198499750901208097 absolute error = 1.6274885381466288224361764126249e-19 relative error = 1.4592381383525004575874837449789e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9545 Order of pole = 4.437 x[1] = -0.9468 y[1] (analytic) = 1.1155357721979570881053722596418 y[1] (numeric) = 1.1155357721979570882685002582035 absolute error = 1.6312799856175488970175730025046e-19 relative error = 1.4623287090143359059651982508527e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9544 Order of pole = 4.437 x[1] = -0.9467 y[1] (analytic) = 1.1157714529181992577910610617197 y[1] (numeric) = 1.1157714529181992579545685255125 absolute error = 1.6350746379282340117721527229267e-19 relative error = 1.4654207487132282068389446336117e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9543 Order of pole = 4.437 x[1] = -0.9466 y[1] (analytic) = 1.1160072083351989253832670075369 y[1] (numeric) = 1.1160072083351989255471542573496 absolute error = 1.6388724981266213186754334627357e-19 relative error = 1.4685142585874561101283792879605e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9542 Order of pole = 4.437 x[1] = -0.9465 y[1] (analytic) = 1.1162430384805253262987697048291 y[1] (numeric) = 1.1162430384805253264630370617554 absolute error = 1.6426735692638691058205808373656e-19 relative error = 1.4716092397762606208459136452692e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9541 Order of pole = 4.437 x[1] = -0.9464 y[1] (analytic) = 1.1164789433857643754256017732187 y[1] (numeric) = 1.1164789433857643755902495586581 absolute error = 1.6464778543943605424089868914234e-19 relative error = 1.4747056934198459143266628196424e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.954 Order of pole = 4.437 x[1] = -0.9463 y[1] (analytic) = 1.1167149230825186776991996358973 y[1] (numeric) = 1.1167149230825186778642281715549 absolute error = 1.6502853565757074284912123118093e-19 relative error = 1.4778036206593802524257219335524e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9539 Order of pole = 4.437 memory used=114.4MB, alloc=4.4MB, time=6.53 x[1] = -0.9462 y[1] (analytic) = 1.1169509776024075386863789749437 y[1] (numeric) = 1.1169509776024075388517885828306 absolute error = 1.6540960788687539494648206147499e-19 relative error = 1.4809030226369969006838948719830e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9538 Order of pole = 4.437 x[1] = -0.9461 y[1] (analytic) = 1.1171871069770669751771414669791 y[1] (numeric) = 1.1171871069770669753429324694128 absolute error = 1.6579100243375804353356424334238e-19 relative error = 1.4840039004957950464630016408547e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9537 Order of pole = 4.437 x[1] = -0.946 y[1] (analytic) = 1.1174233112381497257843194221581 y[1] (numeric) = 1.117423311238149725950492141763 absolute error = 1.6617271960495071247490177114933e-19 relative error = 1.4871062553798407180518919342988e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9536 Order of pole = 4.437 x[1] = -0.9459 y[1] (analytic) = 1.1176595904173252615510649557936 y[1] (numeric) = 1.1176595904173252617176197155011 absolute error = 1.6655475970750979337975733018387e-19 relative error = 1.4902100884341677047442939460953e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9535 Order of pole = 4.437 x[1] = -0.9458 y[1] (analytic) = 1.1178959445462797965661903282236 y[1] (numeric) = 1.1178959445462797967331274512725 absolute error = 1.6693712304881642296121031791559e-19 relative error = 1.4933154008047784778896288933186e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9534 Order of pole = 4.437 x[1] = -0.9457 y[1] (analytic) = 1.118132373656716298587366094843 y[1] (numeric) = 1.1181323736567162987546859047795 absolute error = 1.6731980993657686087421281998450e-19 relative error = 1.4964221936386451129179231549178e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9533 Order of pole = 4.437 x[1] = -0.9456 y[1] (analytic) = 1.118368877780354499672183714545 y[1] (numeric) = 1.1183688777803544998398865352238 absolute error = 1.6770282067882286803327220828175e-19 relative error = 1.4995304680837102123399513646299e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9532 Order of pole = 4.437 x[1] = -0.9455 y[1] (analytic) = 1.1186054569489309068170892711474 y[1] (numeric) = 1.1186054569489309069851754267314 absolute error = 1.6808615558391208541042000405038e-19 relative error = 1.5026402252888878297237452362592e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9531 Order of pole = 4.437 x[1] = -0.9454 y[1] (analytic) = 1.1188421111941988126041949687102 y[1] (numeric) = 1.1188421111941988127726647836708 absolute error = 1.6846981496052841331412762604824e-19 relative error = 1.5057514664040643946486043399744e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.953 Order of pole = 4.437 x[1] = -0.9453 y[1] (analytic) = 1.1190788405479283058559750679977 y[1] (numeric) = 1.1190788405479283060248288671154 absolute error = 1.6885379911768239114983062247982e-19 relative error = 1.5088641925800996386377464908774e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9529 Order of pole = 4.437 x[1] = -0.9452 y[1] (analytic) = 1.1193156450419062822978529376842 y[1] (numeric) = 1.1193156450419062824670910460489 absolute error = 1.6923810836471157766272396562236e-19 relative error = 1.5119784049688275220707368556788e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9528 Order of pole = 4.437 x[1] = -0.9451 y[1] (analytic) = 1.1195525247079364552286859002581 y[1] (numeric) = 1.1195525247079364553983086432694 absolute error = 1.6962274301128093166349196984581e-19 relative error = 1.5150941047230571620768363298877e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9527 Order of pole = 4.437 x[1] = -0.945 y[1] (analytic) = 1.1197894795778393661991545589429 y[1] (numeric) = 1.1197894795778393663691622623103 absolute error = 1.7000770336738319323763737705960e-19 relative error = 1.5182112929965737614104111864865e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9526 Order of pole = 4.437 x[1] = -0.9449 y[1] (analytic) = 1.1200265096834523956980632983206 y[1] (numeric) = 1.1200265096834523958684562880639 absolute error = 1.7039298974333926543907513851427e-19 relative error = 1.5213299709441395383095474476128e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9525 Order of pole = 4.437 x[1] = -0.9448 y[1] (analytic) = 1.1202636150566297738465586577199 y[1] (numeric) = 1.1202636150566297740173372601697 absolute error = 1.7077860244979859646865740834427e-19 relative error = 1.5244501397214946573390148833258e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9524 Order of pole = 4.437 x[1] = -0.9447 y[1] (analytic) = 1.1205007957292425911002722828139 y[1] (numeric) = 1.1205007957292425912714368246116 absolute error = 1.7116454179773956233829725226461e-19 relative error = 1.5275718004853581612187269960832e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9523 Order of pole = 4.437 x[1] = -0.9446 y[1] (analytic) = 1.120738051733178808959395167261 y[1] (numeric) = 1.1207380517331788091309459753594 absolute error = 1.7155080809846985002135956442849e-19 relative error = 1.5306949543934289036388448061058e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9522 Order of pole = 4.437 x[1] = -0.9445 y[1] (analytic) = 1.1209753831003432706866899026181 y[1] (numeric) = 1.1209753831003432708586273042817 absolute error = 1.7193740166362684108998867662044e-19 relative error = 1.5338196026043864830626737113674e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9521 Order of pole = 4.437 memory used=118.2MB, alloc=4.4MB, time=6.74 x[1] = -0.9444 y[1] (analytic) = 1.1212127898626577120334476611591 y[1] (numeric) = 1.1212127898626577122057719839643 absolute error = 1.7232432280517799584004313670129e-19 relative error = 1.5369457462778921775185041565118e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.952 Order of pole = 4.437 x[1] = -0.9443 y[1] (analytic) = 1.1214502720520607719733966426403 y[1] (numeric) = 1.1214502720520607721461082144757 absolute error = 1.7271157183542123790430912754049e-19 relative error = 1.5400733865745898803815483075759e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9519 Order of pole = 4.437 x[1] = -0.9442 y[1] (analytic) = 1.1216878297005080034445687224707 y[1] (numeric) = 1.1216878297005080036176678715377 absolute error = 1.7309914906698533935466499357068e-19 relative error = 1.5432025246561070371471263939877e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9518 Order of pole = 4.437 x[1] = -0.9441 y[1] (analytic) = 1.1219254628399718840991310451686 y[1] (numeric) = 1.1219254628399718842726180999814 absolute error = 1.7348705481283030629387033958130e-19 relative error = 1.5463331616850555831962578459194e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9517 Order of pole = 4.437 x[1] = -0.944 y[1] (analytic) = 1.1221631715024418270611893134157 y[1] (numeric) = 1.1221631715024418272350646028019 absolute error = 1.7387528938624776493765416543579e-19 relative error = 1.5494652988250328825548138236979e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9515 Order of pole = 4.437 x[1] = -0.9439 y[1] (analytic) = 1.1224009557199241916925695294562 y[1] (numeric) = 1.122400955719924191866833382557 absolute error = 1.7426385310086134818777750105234e-19 relative error = 1.5525989372406226676473892066335e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9514 Order of pole = 4.437 x[1] = -0.9438 y[1] (analytic) = 1.1226388155244422943665849520326 y[1] (numeric) = 1.1226388155244422945412376983032 absolute error = 1.7465274627062708269674700823457e-19 relative error = 1.5557340780973959800470535812969e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9513 Order of pole = 4.437 x[1] = -0.9437 y[1] (analytic) = 1.1228767509480364192497950384995 y[1] (numeric) = 1.1228767509480364194248370077093 absolute error = 1.7504196920983377642485701977875e-19 relative error = 1.5588707225619121122221422439869e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9512 Order of pole = 4.437 x[1] = -0.9436 y[1] (analytic) = 1.1231147620227638290917631482147 y[1] (numeric) = 1.1231147620227638292671946704478 absolute error = 1.7543152223310340669023849171988e-19 relative error = 1.5620088718017195502812497088650e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9511 Order of pole = 4.437 x[1] = -0.9435 y[1] (analytic) = 1.1233528487806987760228197897701 y[1] (numeric) = 1.1233528487806987761986411954255 absolute error = 1.7582140565539150871259435161452e-19 relative error = 1.5651485269853569177175896920102e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.951 Order of pole = 4.437 x[1] = -0.9434 y[1] (analytic) = 1.1235910112539325123598382010966 y[1] (numeric) = 1.1235910112539325125360498208886 absolute error = 1.7621161979198756465130173439456e-19 relative error = 1.5682896892823539201538870224533e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9509 Order of pole = 4.437 x[1] = -0.9433 y[1] (analytic) = 1.1238292494745733014200290579538 y[1] (numeric) = 1.1238292494745733015966312229124 absolute error = 1.7660216495851539313856260756761e-19 relative error = 1.5714323598632322910889684141088e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9508 Order of pole = 4.437 x[1] = -0.9432 y[1] (analytic) = 1.1240675634747464283427611128017 y[1] (numeric) = 1.1240675634747464285197541542726 absolute error = 1.7699304147093353930828529938741e-19 relative error = 1.5745765398995067386472205174129e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9507 Order of pole = 4.437 x[1] = -0.9431 y[1] (analytic) = 1.124305953286594210919414572541 y[1] (numeric) = 1.1243059532865942110967988221865 absolute error = 1.7738424964553566532138045707601e-19 relative error = 1.5777222305636858933320851564240e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9506 Order of pole = 4.437 x[1] = -0.943 y[1] (analytic) = 1.1245444189422760104312740301086 y[1] (numeric) = 1.1245444189422760106090498199075 absolute error = 1.7777578979895094138815597724978e-19 relative error = 1.5808694330292732567847631461339e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9505 Order of pole = 4.437 x[1] = -0.9429 y[1] (analytic) = 1.1247829604739682424954677714195 y[1] (numeric) = 1.1247829604739682426736354336676 absolute error = 1.7816766224814443728849646738699e-19 relative error = 1.5840181484707681515492995757863e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9504 Order of pole = 4.437 x[1] = -0.9428 y[1] (analytic) = 1.1250215779138643879189602856583 y[1] (numeric) = 1.1250215779138643880975201529687 absolute error = 1.7855986731041751439051381547877e-19 relative error = 1.5871683780636666718452249371004e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9503 Order of pole = 4.437 x[1] = -0.9427 y[1] (analytic) = 1.1252602712941750035606048134426 y[1] (numeric) = 1.125260271294175003739557218746 absolute error = 1.7895240530340821816835646492950e-19 relative error = 1.5903201229844626353489279714632e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9502 Order of pole = 4.437 x[1] = -0.9426 y[1] (analytic) = 1.1254990406471277332012627739076 y[1] (numeric) = 1.1254990406471277333806080504527 absolute error = 1.7934527654509167121986601332099e-19 relative error = 1.5934733844106485359849376073779e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=122.0MB, alloc=4.4MB, time=6.95 Real estimate of pole used Radius of convergence = 0.9501 Order of pole = 4.437 x[1] = -0.9425 y[1] (analytic) = 1.1257378860049673184219969182925 y[1] (numeric) = 1.1257378860049673186017353996463 absolute error = 1.7973848135378046678477077682889e-19 relative error = 1.5966281635207164977282928587446e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.95 Order of pole = 4.437 x[1] = -0.9424 y[1] (analytic) = 1.1259768073999556094903450641501 y[1] (numeric) = 1.1259768073999556096704770841982 absolute error = 1.8013202004812506276410698688348e-19 relative error = 1.5997844614941592294191810559131e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9499 Order of pole = 4.437 x[1] = -0.9423 y[1] (analytic) = 1.1262158048643715762546812708476 y[1] (numeric) = 1.1262158048643715764352071637947 absolute error = 1.8052589294711417624155931210174e-19 relative error = 1.6029422795114709805910262848739e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9498 Order of pole = 4.437 x[1] = -0.9422 y[1] (analytic) = 1.1264548784305113190466713235813 y[1] (numeric) = 1.1264548784305113192275914239514 absolute error = 1.8092010037007517850741342658768e-19 relative error = 1.6061016187541484983132114154623e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9497 Order of pole = 4.437 x[1] = -0.9421 y[1] (analytic) = 1.1266940281306880795918293996858 y[1] (numeric) = 1.1266940281306880797731440423225 absolute error = 1.8131464263667449058581437540490e-19 relative error = 1.6092624804046919850496186070326e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9496 Order of pole = 4.437 x[1] = -0.942 y[1] (analytic) = 1.1269332539972322519281827975893 y[1] (numeric) = 1.1269332539972322521098923176562 absolute error = 1.8170952006691797926602551937234e-19 relative error = 1.6124248656466060575341746897232e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9495 Order of pole = 4.437 x[1] = -0.9419 y[1] (analytic) = 1.1271725560624913933330516153392 y[1] (numeric) = 1.1271725560624913935151563483203 absolute error = 1.8210473298115135363838387432476e-19 relative error = 1.6155887756644007066645893311823e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9494 Order of pole = 4.437 x[1] = -0.9418 y[1] (analytic) = 1.1274119343588302352579502722046 y[1] (numeric) = 1.1274119343588302354404505539047 absolute error = 1.8250028170006056213564869461485e-19 relative error = 1.6187542116435922584154754124603e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9493 Order of pole = 4.437 x[1] = -0.9417 y[1] (analytic) = 1.1276513889186306942716177734503 y[1] (numeric) = 1.127651388918630694454513939995 absolute error = 1.8289616654467219008044118691859e-19 relative error = 1.6219211747707043357720425526968e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9492 Order of pole = 4.437 x[1] = -0.9416 y[1] (analytic) = 1.1278909197742918830111836249728 y[1] (numeric) = 1.1278909197742918831944760128092 absolute error = 1.8329238783635385773947427834090e-19 relative error = 1.6250896662332688216855562402542e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9491 Order of pole = 4.437 x[1] = -0.9415 y[1] (analytic) = 1.1281305269582301211414763110921 y[1] (numeric) = 1.128130526958230121325165256989 absolute error = 1.8368894589681461888527240240856e-19 relative error = 1.6282596872198268230517565480590e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.949 Order of pole = 4.437 x[1] = -0.9414 y[1] (analytic) = 1.1283702105028789463224812554012 y[1] (numeric) = 1.1283702105028789465065670964493 absolute error = 1.8408584104810535986608230778386e-19 relative error = 1.6314312389199296357134319331323e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9489 Order of pole = 4.437 x[1] = -0.9413 y[1] (analytic) = 1.1286099704406891251849551911934 y[1] (numeric) = 1.128609970440689125369438264806 absolute error = 1.8448307361261919918467693743918e-19 relative error = 1.6346043225241397104883451446038e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9488 Order of pole = 4.437 x[1] = -0.9412 y[1] (analytic) = 1.1288498068041286643142038746099 y[1] (numeric) = 1.128849806804128664499084518523 absolute error = 1.8488064391309188758675547060144e-19 relative error = 1.6377789392240316202237097909299e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9487 Order of pole = 4.437 x[1] = -0.9411 y[1] (analytic) = 1.1290897196256828212420300802825 y[1] (numeric) = 1.1290897196256828214273086325551 absolute error = 1.8527855227260220865964366600988e-19 relative error = 1.6409550902121930278784176455648e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9486 Order of pole = 4.437 x[1] = -0.941 y[1] (analytic) = 1.1293297089378541154468588258811 y[1] (numeric) = 1.1293297089378541156325356248956 absolute error = 1.8567679901457237994199969293327e-19 relative error = 1.6441327766822256556342183009824e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9485 Order of pole = 4.437 x[1] = -0.9409 y[1] (analytic) = 1.1295697747731623393620467786246 y[1] (numeric) = 1.1295697747731623395481221630873 absolute error = 1.8607538446276845454523168596627e-19 relative error = 1.6473119998287462550370543137012e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9484 Order of pole = 4.437 x[1] = -0.9408 y[1] (analytic) = 1.1298099171641445693923828034615 y[1] (numeric) = 1.1298099171641445695788571124028 absolute error = 1.8647430894130072328733431087244e-19 relative error = 1.6504927608473875781697565178440e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=125.8MB, alloc=4.5MB, time=7.18 Real estimate of pole used Radius of convergence = 0.9483 Order of pole = 4.437 x[1] = -0.9407 y[1] (analytic) = 1.1300501361433551769387866192888 y[1] (numeric) = 1.1300501361433551771256601920634 absolute error = 1.8687357277462411733985268166538e-19 relative error = 1.6536750609347993498573057217641e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9482 Order of pole = 4.437 x[1] = -0.9406 y[1] (analytic) = 1.1302904317433658394312125362411 y[1] (numeric) = 1.1302904317433658396184857125286 absolute error = 1.8727317628753861138868302372398e-19 relative error = 1.6568589012886492409058685413916e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9481 Order of pole = 4.437 x[1] = -0.9405 y[1] (analytic) = 1.1305308039967655513697652537575 y[1] (numeric) = 1.1305308039967655515574383735627 absolute error = 1.8767311980518962730942053402367e-19 relative error = 1.6600442831076238423768166652043e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.948 Order of pole = 4.437 x[1] = -0.9404 y[1] (analytic) = 1.1307712529361606353740347058122 y[1] (numeric) = 1.1307712529361606355621081094653 absolute error = 1.8807340365306843835796594753761e-19 relative error = 1.6632312075914296408969403891133e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9479 Order of pole = 4.437 x[1] = -0.9403 y[1] (analytic) = 1.131011778594174753240656946382 y[1] (numeric) = 1.131011778594174753429130974539 absolute error = 1.8847402815701257387710337852170e-19 relative error = 1.6664196759407939950060688050657e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9478 Order of pole = 4.437 x[1] = -0.9402 y[1] (analytic) = 1.1312523810034489170091080749202 y[1] (numeric) = 1.1312523810034489171979830685634 absolute error = 1.8887499364320622451976306674823e-19 relative error = 1.6696096893574661125433105748235e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9477 Order of pole = 4.437 x[1] = -0.9401 y[1] (analytic) = 1.1314930601966415000357382083063 y[1] (numeric) = 1.1314930601966415002250145087445 absolute error = 1.8927630043818064798968372179795e-19 relative error = 1.6728012490442180290731307701720e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9476 Order of pole = 4.437 x[1] = -0.94 y[1] (analytic) = 1.1317338162064282480760525124491 y[1] (numeric) = 1.1317338162064282482657304613179 absolute error = 1.8967794886881457530019022326234e-19 relative error = 1.6759943562048455873524808127461e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9475 Order of pole = 4.437 x[1] = -0.9399 y[1] (analytic) = 1.1319746490655022903752463134387 y[1] (numeric) = 1.1319746490655022905653262527011 absolute error = 1.9007993926233461755180350114915e-19 relative error = 1.6791890120441694178402001007521e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9474 Order of pole = 4.437 x[1] = -0.9398 y[1] (analytic) = 1.1322155588065741507670013148646 y[1] (numeric) = 1.1322155588065741509574835868109 absolute error = 1.9048227194631567322940048892856e-19 relative error = 1.6823852177680359202499094660946e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9473 Order of pole = 4.437 x[1] = -0.9397 y[1] (analytic) = 1.1324565454623717587805499546457 y[1] (numeric) = 1.1324565454623717589714349018944 absolute error = 1.9088494724868133601964311150712e-19 relative error = 1.6855829745833182461476181638068e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9472 Order of pole = 4.437 x[1] = -0.9396 y[1] (analytic) = 1.1326976090656404607560149414595 y[1] (numeric) = 1.1326976090656404609473029069572 absolute error = 1.9128796549770430314939634197435e-19 relative error = 1.6887822836979172825952676562278e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9471 Order of pole = 4.437 x[1] = -0.9395 y[1] (analytic) = 1.1329387496491430309680310175971 y[1] (numeric) = 1.1329387496491430311597223446191 absolute error = 1.9169132702200678424585643423682e-19 relative error = 1.6919831463207626368414370170758e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.947 Order of pole = 4.437 x[1] = -0.9394 y[1] (analytic) = 1.1331799672456596827576560018265 y[1] (numeric) = 1.1331799672456596829497510339771 absolute error = 1.9209503215056091071911151363771e-19 relative error = 1.6951855636618136220604363454304e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9469 Order of pole = 4.437 x[1] = -0.9393 y[1] (analytic) = 1.1334212618879880796725781726028 y[1] (numeric) = 1.1334212618879880798650772538155 absolute error = 1.9249908121268914566785778436108e-19 relative error = 1.6983895369320602441410161466755e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9468 Order of pole = 4.437 x[1] = -0.9392 y[1] (analytic) = 1.1336626336089433466156270587313 y[1] (numeric) = 1.1336626336089433468085305332694 absolute error = 1.9290347453806469430899569084087e-19 relative error = 1.7015950673435241895259222066521e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9467 Order of pole = 4.437 x[1] = -0.9391 y[1] (analytic) = 1.1339040824413580810015947113625 y[1] (numeric) = 1.1339040824413580811949029238192 absolute error = 1.9330821245671191493183145053855e-19 relative error = 1.7048021561092598141035270566503e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9466 Order of pole = 4.437 x[1] = -0.939 y[1] (analytic) = 1.1341456084180823639223745379774 y[1] (numeric) = 1.1341456084180823641160878332764 absolute error = 1.9371329529900673037761045732352e-19 relative error = 1.7080108044433551331527707004175e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=129.7MB, alloc=4.5MB, time=7.39 Real estimate of pole used Radius of convergence = 0.9465 Order of pole = 4.437 x[1] = -0.9389 y[1] (analytic) = 1.1343872115719837713204247858115 y[1] (numeric) = 1.1343872115719837715145435092072 absolute error = 1.9411872339567704004511013828898e-19 relative error = 1.7112210135609328123426448500943e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9464 Order of pole = 4.437 x[1] = -0.9388 y[1] (analytic) = 1.1346288919359473851705637689576 y[1] (numeric) = 1.1346288919359473853650882660354 absolute error = 1.9452449707780313242302093216680e-19 relative error = 1.7144327846781511597874564958976e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9463 Order of pole = 4.437 x[1] = -0.9387 y[1] (analytic) = 1.1348706495428758046701039401926 y[1] (numeric) = 1.1348706495428758048650345568694 absolute error = 1.9493061667681809814984514457039e-19 relative error = 1.7176461190122051191591082144736e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9462 Order of pole = 4.437 x[1] = -0.9386 y[1] (analytic) = 1.1351124844256891574373319153811 y[1] (numeric) = 1.1351124844256891576326689979056 absolute error = 1.9533708252450824360204452409797e-19 relative error = 1.7208610177813272638576342031280e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9461 Order of pole = 4.437 x[1] = -0.9385 y[1] (analytic) = 1.1353543966173251107183415651258 y[1] (numeric) = 1.1353543966173251109140854600788 absolute error = 1.9574389495301350501116849387244e-19 relative error = 1.7240774822047887922412326116208e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.946 Order of pole = 4.437 x[1] = -0.9384 y[1] (analytic) = 1.1355963861507388826022272951584 y[1] (numeric) = 1.1355963861507388827983783494532 absolute error = 1.9615105429482786311069606538191e-19 relative error = 1.7272955135029005239170363298871e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9459 Order of pole = 4.437 x[1] = -0.9383 y[1] (analytic) = 1.1358384530589032532446446437965 y[1] (numeric) = 1.1358384530589032534412032046793 absolute error = 1.9655856088279975831332555551928e-19 relative error = 1.7305151128970138970938659789225e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9458 Order of pole = 4.437 x[1] = -0.9382 y[1] (analytic) = 1.136080597374808576099745331629 y[1] (numeric) = 1.1360805973748085762967117466791 absolute error = 1.9696641505013250641944732350329e-19 relative error = 1.7337362816095219669982104431410e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9457 Order of pole = 4.437 x[1] = -0.9381 y[1] (analytic) = 1.1363228191314627891604939054405 y[1] (numeric) = 1.1363228191314627893578685225709 absolute error = 1.9737461713038471485753584190013e-19 relative error = 1.7369590208638604053546818758008e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9456 Order of pole = 4.437 x[1] = -0.938 y[1] (analytic) = 1.1365651183618914262073731252358 y[1] (numeric) = 1.1365651183618914264051562926933 absolute error = 1.9778316745747069945719851525692e-19 relative error = 1.7401833318845085009321937045771e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9455 Order of pole = 4.437 x[1] = -0.9379 y[1] (analytic) = 1.1368074950991376280654852500876 y[1] (numeric) = 1.1368074950991376282636773164532 absolute error = 1.9819206636566090175561976090943e-19 relative error = 1.7434092158969901611571117620665e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9454 Order of pole = 4.437 x[1] = -0.9378 y[1] (analytic) = 1.1370499493762621538700563853973 y[1] (numeric) = 1.1370499493762621540686576995869 absolute error = 1.9860131418958230683813996933884e-19 relative error = 1.7466366741278749147946302659207e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9453 Order of pole = 4.437 x[1] = -0.9377 y[1] (analytic) = 1.1372924812263433923403510610353 y[1] (numeric) = 1.1372924812263433925393619722995 absolute error = 1.9901091126421886171371006602948e-19 relative error = 1.7498657078047789156996259754439e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9452 Order of pole = 4.437 x[1] = -0.9376 y[1] (analytic) = 1.1375350906824773730620042167061 y[1] (numeric) = 1.137535090682477373261425074631 absolute error = 1.9942085792491189422596350312444e-19 relative error = 1.7530963181563659476382454558443e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9451 Order of pole = 4.437 x[1] = -0.9375 y[1] (analytic) = 1.1377777777777777777777777777778 y[1] (numeric) = 1.1377777777777777779776089322851 absolute error = 1.9983115450736053250064861729120e-19 relative error = 1.7563285064123484301814819879110e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.945 Order of pole = 4.437 x[1] = -0.9374 y[1] (analytic) = 1.1380205425453759516867490117088 y[1] (numeric) = 1.1380205425453759518869908130564 absolute error = 2.0024180134762212493016540009896e-19 relative error = 1.7595622738034884256720002696986e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9449 Order of pole = 4.437 x[1] = -0.9373 y[1] (analytic) = 1.1382633850184209147519378621108 y[1] (numeric) = 1.1382633850184209149525906608929 absolute error = 2.0065279878211266069595183887459e-19 relative error = 1.7627976215615986472654686678436e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9448 Order of pole = 4.437 x[1] = -0.9372 y[1] (analytic) = 1.1385063052300793730163804643976 y[1] (numeric) = 1.1385063052300793732174446115452 absolute error = 2.0106414714760719082946609945053e-19 relative error = 1.7660345509195434680476603894120e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9447 Order of pole = 4.437 memory used=133.5MB, alloc=4.5MB, time=7.61 x[1] = -0.9371 y[1] (analytic) = 1.1387493032135357299276560538914 y[1] (numeric) = 1.1387493032135357301291319006726 absolute error = 2.0147584678124024981251193744569e-19 relative error = 1.7692730631112399312285865606945e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9446 Order of pole = 4.437 x[1] = -0.937 y[1] (analytic) = 1.1389923790019920976708744841788 y[1] (numeric) = 1.1389923790019920978727623821993 absolute error = 2.0188789802050627771765584173494e-19 relative error = 1.7725131593716587614149258171218e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9445 Order of pole = 4.437 x[1] = -0.9369 y[1] (analytic) = 1.1392355326286683085101315804509 y[1] (numeric) = 1.1392355326286683087124318816541 absolute error = 2.0230030120326004288948553256598e-19 relative error = 1.7757548409368253769620166284747e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9444 Order of pole = 4.437 x[1] = -0.9368 y[1] (analytic) = 1.1394787641268019261384395594939 y[1] (numeric) = 1.1394787641268019263411526161616 absolute error = 2.0271305666771706516746055737719e-19 relative error = 1.7789981090438209034066802058141e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9443 Order of pole = 4.437 x[1] = -0.9367 y[1] (analytic) = 1.1397220735296482570361397549545 y[1] (numeric) = 1.139722073529648257239265919707 absolute error = 2.0312616475245403965110684976025e-19 relative error = 1.7822429649307831879821434610584e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9442 Order of pole = 4.437 x[1] = -0.9366 y[1] (analytic) = 1.1399654608704803618378048934522 y[1] (numeric) = 1.1399654608704803620413445192486 absolute error = 2.0353962579640926100830824119950e-19 relative error = 1.7854894098369078152163331168940e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9441 Order of pole = 4.437 x[1] = -0.9365 y[1] (analytic) = 1.1402089261825890667076381740808 y[1] (numeric) = 1.1402089261825890669115916142197 absolute error = 2.0395344013888304832744904120910e-19 relative error = 1.7887374450024491236148136937196e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.944 Order of pole = 4.437 x[1] = -0.9364 y[1] (analytic) = 1.1404524694992829747233764108081 y[1] (numeric) = 1.1404524694992829749277440189277 absolute error = 2.0436760811953817051416292928262e-19 relative error = 1.7919870716687212234296437316030e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9439 Order of pole = 4.437 x[1] = -0.9363 y[1] (analytic) = 1.1406960908538884772687045042632 y[1] (numeric) = 1.1406960908538884774734866343416 absolute error = 2.0478213007840027223344453167062e-19 relative error = 1.7952382910780990155154262387750e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9438 Order of pole = 4.437 x[1] = -0.9362 y[1] (analytic) = 1.1409397902797497654341885163862 y[1] (numeric) = 1.1409397902797497656393855227421 absolute error = 2.0519700635585830039788118741257e-19 relative error = 1.7984911044740192112738309939922e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9437 Order of pole = 4.437 x[1] = -0.9361 y[1] (analytic) = 1.1411835678102288414267346284085 y[1] (numeric) = 1.1411835678102288416323468657012 absolute error = 2.0561223729266493120276354127453e-19 relative error = 1.8017455131009813536878679681901e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9436 Order of pole = 4.437 x[1] = -0.936 y[1] (analytic) = 1.1414274234787055299875812696326 y[1] (numeric) = 1.1414274234787055301936090928625 absolute error = 2.0602782322993699770883473628506e-19 relative error = 1.8050015182045488394471927712040e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9435 Order of pole = 4.437 x[1] = -0.9359 y[1] (analytic) = 1.1416713573185774898188317114883 y[1] (numeric) = 1.1416713573185774900252754759975 absolute error = 2.0644376450915591797343911542267e-19 relative error = 1.8082591210313499421657266719732e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9434 Order of pole = 4.437 x[1] = -0.9358 y[1] (analytic) = 1.1419153693632602250185344283601 y[1] (numeric) = 1.1419153693632602252253944898323 absolute error = 2.0686006147216812373083248069218e-19 relative error = 1.8115183228290788366928753855703e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9433 Order of pole = 4.437 x[1] = -0.9357 y[1] (analytic) = 1.1421594596461870965243185336993 y[1] (numeric) = 1.1421594596461870967315952481605 absolute error = 2.0727671446118548962241709833669e-19 relative error = 1.8147791248464966245196324675949e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9432 Order of pole = 4.437 x[1] = -0.9356 y[1] (analytic) = 1.1424036282008093335655916069707 y[1] (numeric) = 1.1424036282008093337732853307895 absolute error = 2.0769372381878576297766578127082e-19 relative error = 1.8180415283334323602808548059775e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9431 Order of pole = 4.437 x[1] = -0.9355 y[1] (analytic) = 1.142647875060596045124307234018 y[1] (numeric) = 1.1426478750605960453324183239059 absolute error = 2.0811108988791299414650052399169e-19 relative error = 1.8213055345407840793549993520170e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.943 Order of pole = 4.437 x[1] = -0.9354 y[1] (analytic) = 1.1428922002590342314043095904793 y[1] (numeric) = 1.1428922002590342316128384034912 absolute error = 2.0852881301187796738389231123034e-19 relative error = 1.8245711447205198265626118865691e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9429 Order of pole = 4.437 x[1] = -0.9353 y[1] (analytic) = 1.1431366038296287953092624049383 y[1] (numeric) = 1.1431366038296287955182092984727 absolute error = 2.0894689353435863228744986945088e-19 relative error = 1.8278383601256786859648602736795e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=137.3MB, alloc=4.5MB, time=7.82 Real estimate of pole used Radius of convergence = 0.9428 Order of pole = 4.437 x[1] = -0.9352 y[1] (analytic) = 1.1433810858059025539291696455555 y[1] (numeric) = 1.1433810858059025541385349773549 absolute error = 2.0936533179940053578876627999114e-19 relative error = 1.8311071820103718117634063126462e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9427 Order of pole = 4.437 x[1] = -0.9351 y[1] (analytic) = 1.1436256462213962500354952809946 y[1] (numeric) = 1.143625646221396250245279409146 absolute error = 2.0978412815141725469929352416923e-19 relative error = 1.8343776116297834603029119604880e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9426 Order of pole = 4.437 x[1] = -0.935 y[1] (analytic) = 1.1438702851096685635848894735337 y[1] (numeric) = 1.1438702851096685637950927564689 absolute error = 2.1020328293519082881151618405981e-19 relative error = 1.8376496502401720231774773600969e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9425 Order of pole = 4.437 x[1] = -0.9349 y[1] (analytic) = 1.1441150025042961232315285693353 y[1] (numeric) = 1.1441150025042961234421513658312 absolute error = 2.1062279649587219455619667787347e-19 relative error = 1.8409232990988710614423097749714e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9424 Order of pole = 4.437 x[1] = -0.9348 y[1] (analytic) = 1.1443597984388735178480762579398 y[1] (numeric) = 1.1443597984388735180591189271188 absolute error = 2.1104266917898161921646556595701e-19 relative error = 1.8441985594642903409319241993573e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9423 Order of pole = 4.437 x[1] = -0.9347 y[1] (analytic) = 1.1446046729470133080552732801459 y[1] (numeric) = 1.1446046729470133082667361814763 absolute error = 2.1146290133040913569953162237418e-19 relative error = 1.8474754325959168686861780828777e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9422 Order of pole = 4.437 x[1] = -0.9346 y[1] (analytic) = 1.144849626062346037760163070549 y[1] (numeric) = 1.1448496260623460379720465638454 absolute error = 2.1188349329641497786678752782841e-19 relative error = 1.8507539197543159304854442813098e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9421 Order of pole = 4.437 x[1] = -0.9345 y[1] (analytic) = 1.1450946578185202457029607281199 y[1] (numeric) = 1.1450946578185202459152651735435 absolute error = 2.1230444542363001642308820235535e-19 relative error = 1.8540340222011321294962280200695e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.942 Order of pole = 4.437 x[1] = -0.9344 y[1] (analytic) = 1.1453397682492024770125727153312 y[1] (numeric) = 1.1453397682492024772252984733903 absolute error = 2.1272575805905619536597996074600e-19 relative error = 1.8573157411990904260285353342000e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9419 Order of pole = 4.437 x[1] = -0.9343 y[1] (analytic) = 1.1455849573880772947707746934647 y[1] (numeric) = 1.1455849573880772949839221250147 absolute error = 2.1314743155006696899565984006423e-19 relative error = 1.8605990780119971784063021282283e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9418 Order of pole = 4.437 x[1] = -0.9342 y[1] (analytic) = 1.1458302252688472915850549088719 y[1] (numeric) = 1.1458302252688472917986243751163 absolute error = 2.1356946624440773948644561689916e-19 relative error = 1.8638840339047411849521946811598e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9417 Order of pole = 4.437 x[1] = -0.9341 y[1] (analytic) = 1.1460755719252331011701305521044 y[1] (numeric) = 1.1460755719252331013841224145946 absolute error = 2.1399186249019629502053820214619e-19 relative error = 1.8671706101432947270880941061299e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9416 Order of pole = 4.437 x[1] = -0.934 y[1] (analytic) = 1.1463209973909734099381445189808 y[1] (numeric) = 1.1463209973909734101525591396167 absolute error = 2.1441462063592324848485927314309e-19 relative error = 1.8704588079947146135525789608201e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9415 Order of pole = 4.437 x[1] = -0.9339 y[1] (analytic) = 1.1465665016998249685975500098198 y[1] (numeric) = 1.1465665016998249688123877508502 absolute error = 2.1483774103045247673174817690372e-19 relative error = 1.8737486287271432257367218936905e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9414 Order of pole = 4.437 x[1] = -0.9338 y[1] (analytic) = 1.1468120848855626037606904102335 y[1] (numeric) = 1.1468120848855626039759516342565 absolute error = 2.1526122402302156040430331399424e-19 relative error = 1.8770400736098095641395179023678e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9413 Order of pole = 4.437 x[1] = -0.9337 y[1] (analytic) = 1.1470577469819792295600819040525 y[1] (numeric) = 1.1470577469819792297757669740158 absolute error = 2.1568506996324222432715439028827e-19 relative error = 1.8803331439130302959442634741789e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9412 Order of pole = 4.437 x[1] = -0.9336 y[1] (analytic) = 1.1473034880228858592734062761356 y[1] (numeric) = 1.1473034880228858594895155553367 absolute error = 2.1610927920110077846345310342185e-19 relative error = 1.8836278409082108037172075748229e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9411 Order of pole = 4.437 x[1] = -0.9335 y[1] (analytic) = 1.1475493080421116169572213700075 y[1] (numeric) = 1.1475493080421116171737552220944 absolute error = 2.1653385208695855943887101224971e-19 relative error = 1.8869241658678462352297971495442e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=141.1MB, alloc=4.5MB, time=8.04 Real estimate of pole used Radius of convergence = 0.941 Order of pole = 4.437 x[1] = -0.9334 y[1] (analytic) = 1.1477952070735037490893966724682 y[1] (numeric) = 1.1477952070735037493063554614398 absolute error = 2.1695878897155237263339452098360e-19 relative error = 1.8902221200655225544058415019008e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9409 Order of pole = 4.437 x[1] = -0.9333 y[1] (analytic) = 1.1480411851509276362202815045204 y[1] (numeric) = 1.1480411851509276364376655947264 absolute error = 2.1738409020599493484170809497599e-19 relative error = 1.8935217047759175933949216183285e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9408 Order of pole = 4.437 x[1] = -0.9332 y[1] (analytic) = 1.1482872423082668046326133051767 y[1] (numeric) = 1.1482872423082668048504230613185 absolute error = 2.1780975614177531750295801229985e-19 relative error = 1.8968229212748021057733722121739e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9407 Order of pole = 4.437 x[1] = -0.9331 y[1] (analytic) = 1.1485333785794229380101735019314 y[1] (numeric) = 1.1485333785794229382284092890622 absolute error = 2.1823578713075939050069014437246e-19 relative error = 1.9001257708390408208741659687248e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9406 Order of pole = 4.437 x[1] = -0.933 y[1] (analytic) = 1.1487795939983158891151984689066 y[1] (numeric) = 1.1487795939983158893338606524317 absolute error = 2.1866218352519026653375644988004e-19 relative error = 1.9034302547465934992470311829962e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9405 Order of pole = 4.437 x[1] = -0.9329 y[1] (analytic) = 1.1490258885988836914745530809228 y[1] (numeric) = 1.1490258885988836916936420266004 absolute error = 2.1908894567768874605898605918486e-19 relative error = 1.9067363742765159892501356946498e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9404 Order of pole = 4.437 x[1] = -0.9328 y[1] (analytic) = 1.1492722624150825710746743789884 y[1] (numeric) = 1.1492722624150825712941904529297 absolute error = 2.1951607394125376280641802124004e-19 relative error = 1.9100441307089612847746717394242e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9403 Order of pole = 4.437 x[1] = -0.9327 y[1] (analytic) = 1.1495187154808869580652928699527 y[1] (numeric) = 1.1495187154808869582852364386219 absolute error = 2.1994356866926282986789398180288e-19 relative error = 1.9133535253251805841036780538505e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9402 Order of pole = 4.437 x[1] = -0.9326 y[1] (analytic) = 1.1497652478302894984719389903286 y[1] (numeric) = 1.1497652478302894986923104205441 absolute error = 2.2037143021547248635981026042867e-19 relative error = 1.9166645594075243499064372898155e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9401 Order of pole = 4.437 x[1] = -0.9325 y[1] (analytic) = 1.1500118594973010659172422715609 y[1] (numeric) = 1.1500118594973010661380419304949 absolute error = 2.2079965893401874466082999434702e-19 relative error = 1.9199772342394433703697885177191e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.94 Order of pole = 4.437 x[1] = -0.9324 y[1] (analytic) = 1.1502585505159507733510307512882 y[1] (numeric) = 1.1502585505159507735722590064676 absolute error = 2.2122825517941753822535721987440e-19 relative error = 1.9232915511054898214676963215648e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9399 Order of pole = 4.437 x[1] = -0.9323 y[1] (analytic) = 1.1505053209202859847892381824322 y[1] (numeric) = 1.1505053209202859850108954017387 absolute error = 2.2165721930656516997357596650418e-19 relative error = 1.9266075112913183303704197163103e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9398 Order of pole = 4.437 x[1] = -0.9322 y[1] (analytic) = 1.1507521707443723270616265992406 y[1] (numeric) = 1.1507521707443723272837131509113 absolute error = 2.2208655167073876125885864524120e-19 relative error = 1.9299251160836870399946258472128e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9397 Order of pole = 4.437 x[1] = -0.9321 y[1] (analytic) = 1.1509991000222937015683318067057 y[1] (numeric) = 1.1509991000222937017908480593333 absolute error = 2.2251625262759670141334922111627e-19 relative error = 1.9332443667704586746957951627121e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9396 Order of pole = 4.437 x[1] = -0.932 y[1] (analytic) = 1.1512461087881522960452393670909 y[1] (numeric) = 1.1512461087881522962681856896241 absolute error = 2.2294632253317909787252787012906e-19 relative error = 1.9365652646406016071042664866298e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9395 Order of pole = 4.437 x[1] = -0.9319 y[1] (analytic) = 1.151493197076068596338198664611 y[1] (numeric) = 1.1514931970760685965615754263549 absolute error = 2.2337676174390822687956503313019e-19 relative error = 1.9398878109841909261062721521115e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9394 Order of pole = 4.437 x[1] = -0.9318 y[1] (analytic) = 1.1517403649201813981860826366341 y[1] (numeric) = 1.1517403649201813984098902072507 absolute error = 2.2380757061658898477027399336737e-19 relative error = 1.9432120070924095059713150988097e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9393 Order of pole = 4.437 x[1] = -0.9317 y[1] (analytic) = 1.1519876123546478190127007671051 y[1] (numeric) = 1.1519876123546478192369395166135 absolute error = 2.2423874950840933983947232059007e-19 relative error = 1.9465378542575490766272415763107e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=144.9MB, alloc=4.5MB, time=8.26 Real estimate of pole used Radius of convergence = 0.9392 Order of pole = 4.437 x[1] = -0.9316 y[1] (analytic) = 1.1522349394136433097275729452287 y[1] (numeric) = 1.1522349394136433099522432440056 absolute error = 2.2467029877694078478956374273541e-19 relative error = 1.9498653537730112950843648407342e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9391 Order of pole = 4.437 x[1] = -0.9315 y[1] (analytic) = 1.1524823461313616665355717997942 y[1] (numeric) = 1.1524823461313616667606740185744 absolute error = 2.2510221878013878976215322630846e-19 relative error = 1.9531945069333088180099969778035e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9389 Order of pole = 4.437 x[1] = -0.9314 y[1] (analytic) = 1.1527298325420150427554411268829 y[1] (numeric) = 1.1527298325420150429809756367592 absolute error = 2.2553450987634325595350926862620e-19 relative error = 1.9565253150340663754547477344847e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9388 Order of pole = 4.437 x[1] = -0.9313 y[1] (analytic) = 1.1529773986798339606471980360552 y[1] (numeric) = 1.1529773986798339608731652084795 absolute error = 2.2596717242427896981468862911898e-19 relative error = 1.9598577793720218457319509925400e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9387 Order of pole = 4.437 x[1] = -0.9312 y[1] (analytic) = 1.1532250445790673232484264474912 y[1] (numeric) = 1.1532250445790673234748266542742 absolute error = 2.2640020678305605783713995288054e-19 relative error = 1.9631919012450273314515812710274e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9386 Order of pole = 4.437 x[1] = -0.9311 y[1] (analytic) = 1.1534727702739824262194695799298 y[1] (numeric) = 1.153472770273982426446303193242 absolute error = 2.2683361331217044192460396763045e-19 relative error = 1.9665276819520502367100244009215e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9385 Order of pole = 4.437 x[1] = -0.931 y[1] (analytic) = 1.1537205757988649696975290766428 y[1] (numeric) = 1.1537205757988649699247964690143 absolute error = 2.2726739237150429535212916520434e-19 relative error = 1.9698651227931743454370682736168e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9384 Order of pole = 4.437 x[1] = -0.9309 y[1] (analytic) = 1.1539684611880190701596784240705 y[1] (numeric) = 1.1539684611880190703873799683918 absolute error = 2.2770154432132649931302311062189e-19 relative error = 1.9732042250696009009014813261277e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9383 Order of pole = 4.437 x[1] = -0.9308 y[1] (analytic) = 1.1542164264757672722947983251489 y[1] (numeric) = 1.1542164264757672725229343946712 absolute error = 2.2813606952229310005456075570228e-19 relative error = 1.9765449900836496863765481893027e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9382 Order of pole = 4.437 x[1] = -0.9307 y[1] (analytic) = 1.1544644716964505608844416967677 y[1] (numeric) = 1.1544644716964505611130126651031 absolute error = 2.2857096833544776660327237010640e-19 relative error = 1.9798874191387601069669336913436e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9381 Order of pole = 4.437 x[1] = -0.9306 y[1] (analytic) = 1.1547125968844283726926359682166 y[1] (numeric) = 1.1547125968844283729216422093388 absolute error = 2.2900624112222224908063494058697e-19 relative error = 1.9832315135394922725982481773595e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.938 Order of pole = 4.437 x[1] = -0.9305 y[1] (analytic) = 1.1549608020740786083646303649012 y[1] (numeric) = 1.1549608020740786085940722531456 absolute error = 2.2944188824443683760999212912622e-19 relative error = 1.9865772745915280821706888765939e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9379 Order of pole = 4.437 x[1] = -0.9304 y[1] (analytic) = 1.1552090872997976443345958690462 y[1] (numeric) = 1.1552090872997976445644737791105 absolute error = 2.2987791006430082181552912253797e-19 relative error = 1.9899247036016723088781338223492e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9378 Order of pole = 4.437 x[1] = -0.9303 y[1] (analytic) = 1.1554574525960003447422855565427 y[1] (numeric) = 1.1554574525960003449725998634871 absolute error = 2.3031430694441295091412995001231e-19 relative error = 1.9932738018778536866940666054945e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9377 Order of pole = 4.437 x[1] = -0.9302 y[1] (analytic) = 1.1557058979971200733586630165468 y[1] (numeric) = 1.1557058979971200735894140957946 absolute error = 2.3075107924776189440094609098769e-19 relative error = 1.9966245707291259980257120207895e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9376 Order of pole = 4.437 x[1] = -0.9301 y[1] (analytic) = 1.1559544235376087055205065678961 y[1] (numeric) = 1.1559544235376087057516947952338 absolute error = 2.3118822733772670332950644365267e-19 relative error = 1.9999770114656691625377644460878e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9375 Order of pole = 4.437 x[1] = -0.93 y[1] (analytic) = 1.1562030292519366400739969938721 y[1] (numeric) = 1.1562030292519366403056227454502 absolute error = 2.3162575157807727218719997430972e-19 relative error = 2.0033311253987903271470925778048e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9374 Order of pole = 4.437 x[1] = -0.9299 y[1] (analytic) = 1.1564517151745928113272965243156 y[1] (numeric) = 1.1564517151745928115593601766486 absolute error = 2.3206365233297480136696361978095e-19 relative error = 2.0066869138409249571898059318490e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9373 Order of pole = 4.437 memory used=148.7MB, alloc=4.5MB, time=8.47 x[1] = -0.9298 y[1] (analytic) = 1.1567004813400847010121268015784 y[1] (numeric) = 1.1567004813400847012446287315453 absolute error = 2.3250192996697226023600926900288e-19 relative error = 2.0100443781056379287620703075289e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9372 Order of pole = 4.437 x[1] = -0.9297 y[1] (analytic) = 1.1569493277829383502543535742891 y[1] (numeric) = 1.1569493277829383504872941591341 absolute error = 2.3294058484501485080242490594891e-19 relative error = 2.0134035195076246222360612027594e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9371 Order of pole = 4.437 x[1] = -0.9296 y[1] (analytic) = 1.1571982545376983715535858704056 y[1] (numeric) = 1.1571982545376983717869654877381 absolute error = 2.3337961733244047198048625403653e-19 relative error = 2.0167643393627120169524459622099e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.937 Order of pole = 4.437 x[1] = -0.9295 y[1] (analytic) = 1.1574472616389279607717974085335 y[1] (numeric) = 1.1574472616389279610056164363284 absolute error = 2.3381902779498018445551652222557e-19 relative error = 2.0201268389878597870907872358636e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9369 Order of pole = 4.437 x[1] = -0.9294 y[1] (analytic) = 1.1576963491212089091309780140034 y[1] (numeric) = 1.1576963491212089093652368306022 absolute error = 2.3425881659875867614913311509752e-19 relative error = 2.0234910197011613987192621237931e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9368 Order of pole = 4.437 x[1] = -0.9293 y[1] (analytic) = 1.1579455170191416152198228137245 y[1] (numeric) = 1.1579455170191416154545217978348 absolute error = 2.3469898411029472828572143332688e-19 relative error = 2.0268568828218452080250931838173e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9367 Order of pole = 4.437 x[1] = -0.9292 y[1] (analytic) = 1.1581947653673450970094669913565 y[1] (numeric) = 1.158194765367345097244606522053 absolute error = 2.3513953069650168206097715711841e-19 relative error = 2.0302244296702755607270892820730e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9366 Order of pole = 4.437 x[1] = -0.9291 y[1] (analytic) = 1.1584440942004570038782738918871 y[1] (numeric) = 1.1584440942004570041138543486118 absolute error = 2.3558045672468790591335967339091e-19 relative error = 2.0335936615679538926716960724388e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9365 Order of pole = 4.437 x[1] = -0.929 y[1] (analytic) = 1.158693503553133628645684272242 y[1] (numeric) = 1.1586935035531336288817060348045 absolute error = 2.3602176256255726339930057774449e-19 relative error = 2.0369645798375198316139576991718e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9364 Order of pole = 4.437 x[1] = -0.9289 y[1] (analytic) = 1.1589429934600499196151345021142 y[1] (numeric) = 1.1589429934600499198515979506924 absolute error = 2.3646344857820958167301245455474e-19 relative error = 2.0403371858027523001847931280745e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9363 Order of pole = 4.437 x[1] = -0.9288 y[1] (analytic) = 1.1591925639558994926260515267586 y[1] (numeric) = 1.1591925639558994928629570418988 absolute error = 2.3690551514014112057174441290091e-19 relative error = 2.0437114807885706200459923250035e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9362 Order of pole = 4.437 x[1] = -0.9287 y[1] (analytic) = 1.1594422150753946431149324110697 y[1] (numeric) = 1.159442215075394643352280373687 absolute error = 2.3734796261724504230733213245610e-19 relative error = 2.0470874661210356172343393165631e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9361 Order of pole = 4.437 x[1] = -0.9286 y[1] (analytic) = 1.1596919468532663581855162918395 y[1] (numeric) = 1.1596919468532663584233070832184 absolute error = 2.3779079137881188176489145195209e-19 relative error = 2.0504651431273507286962709863973e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.936 Order of pole = 4.437 x[1] = -0.9285 y[1] (analytic) = 1.1599417593242643286880565726795 y[1] (numeric) = 1.159941759324264328926290574474 absolute error = 2.3823400179453001740950581338116e-19 relative error = 2.0538445131358631100144822816211e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9359 Order of pole = 4.437 x[1] = -0.9284 y[1] (analytic) = 1.1601916525231569613077012036849 y[1] (numeric) = 1.1601916525231569615463787979194 absolute error = 2.3867759423448614280175915771718e-19 relative error = 2.0572255774760647443278903275967e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9358 Order of pole = 4.437 x[1] = -0.9283 y[1] (analytic) = 1.1604416264847313906619888955252 y[1] (numeric) = 1.1604416264847313909011104645944 absolute error = 2.3912156906916573872296715263094e-19 relative error = 2.0606083374785935524463717754895e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9357 Order of pole = 4.437 x[1] = -0.9282 y[1] (analytic) = 1.1606916812437934914074691252531 y[1] (numeric) = 1.1606916812437934916470350519225 absolute error = 2.3956592666945354591096091944414e-19 relative error = 2.0639927944752345041616895358232e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9356 Order of pole = 4.437 x[1] = -0.9281 y[1] (analytic) = 1.1609418168351678903554537987473 y[1] (numeric) = 1.160941816835167890595464466154 absolute error = 2.4001066740663403840727871541634e-19 relative error = 2.0673789497989207307560268825947e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9355 Order of pole = 4.437 memory used=152.5MB, alloc=4.5MB, time=8.68 x[1] = -0.928 y[1] (analytic) = 1.1611920332936979785969084423306 y[1] (numeric) = 1.161192033293697978837364233983 absolute error = 2.4045579165239189751662231839283e-19 relative error = 2.0707668047837346387095487464281e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9354 Order of pole = 4.437 x[1] = -0.9279 y[1] (analytic) = 1.1614423306542459236364908037403 y[1] (numeric) = 1.1614423306542459238773921035191 absolute error = 2.4090129977881248637943615386240e-19 relative error = 2.0741563607649090246084118517205e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9353 Order of pole = 4.437 x[1] = -0.9278 y[1] (analytic) = 1.1616927089516926815357447502758 y[1] (numeric) = 1.1616927089516926817770919424342 absolute error = 2.4134719215838232515846849958642e-19 relative error = 2.0775476190788281912546471917953e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9352 Order of pole = 4.437 x[1] = -0.9277 y[1] (analytic) = 1.1619431682209380090654573595964 y[1] (numeric) = 1.1619431682209380093072508287604 absolute error = 2.4179346916398956684017540016717e-19 relative error = 2.0809405810630290649793401777054e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9351 Order of pole = 4.437 x[1] = -0.9276 y[1] (analytic) = 1.1621937084969004758671871063069 y[1] (numeric) = 1.1621937084969004761094272374758 absolute error = 2.4224013116892447365182922322899e-19 relative error = 2.0843352480562023141605356405458e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.935 Order of pole = 4.437 x[1] = -0.9275 y[1] (analytic) = 1.1624443298145174766239710551362 y[1] (numeric) = 1.1624443298145174768666582336831 absolute error = 2.4268717854687989409519509029246e-19 relative error = 2.0877316213981934689472967139341e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9349 Order of pole = 4.437 x[1] = -0.9274 y[1] (analytic) = 1.1626950322087452432402189791919 y[1] (numeric) = 1.1626950322087452434833535908638 absolute error = 2.4313461167195174059763971893485e-19 relative error = 2.0911297024300040421913484727048e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9348 Order of pole = 4.437 x[1] = -0.9273 y[1] (analytic) = 1.1629458157145588570308023294595 y[1] (numeric) = 1.1629458157145588572743847603782 absolute error = 2.4358243091863946778153851845143e-19 relative error = 2.0945294924937926515877390558478e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9347 Order of pole = 4.437 x[1] = -0.9272 y[1] (analytic) = 1.1631966803669522609193459894095 y[1] (numeric) = 1.1631966803669522611633766260714 absolute error = 2.4403063666184655135284808896740e-19 relative error = 2.0979309929328761430259528562958e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9346 Order of pole = 4.437 x[1] = -0.9271 y[1] (analytic) = 1.1634476262009382716457307562767 y[1] (numeric) = 1.1634476262009382718902099855536 absolute error = 2.4447922927688096760971258380073e-19 relative error = 2.1013342050917307151529122173506e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9345 Order of pole = 4.437 x[1] = -0.927 y[1] (analytic) = 1.1636986532515485919828144982888 y[1] (numeric) = 1.1636986532515485922277427074282 absolute error = 2.4492820913945567357197370684782e-19 relative error = 2.1047391303159930451493059353183e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9344 Order of pole = 4.437 x[1] = -0.9269 y[1] (analytic) = 1.1639497615538338229623799448383 y[1] (numeric) = 1.163949761553833823207757521464 absolute error = 2.4537757662568908773245543085860e-19 relative error = 2.1081457699524614157206847303196e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9343 Order of pole = 4.437 x[1] = -0.9268 y[1] (analytic) = 1.1642009511428634761103170743202 y[1] (numeric) = 1.1642009511428634763561444064323 absolute error = 2.4582733211210557143089583869026e-19 relative error = 2.1115541253490968433047657122471e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9342 Order of pole = 4.437 x[1] = -0.9267 y[1] (analytic) = 1.1644522220537259856910480720927 y[1] (numeric) = 1.1644522220537259859373255480684 absolute error = 2.4627747597563591085139980798225e-19 relative error = 2.1149641978550242074963897364636e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9341 Order of pole = 4.437 x[1] = -0.9266 y[1] (analytic) = 1.1647035743215287209612028387646 y[1] (numeric) = 1.1647035743215287212079308473583 absolute error = 2.4672800859361779964428758018353e-19 relative error = 2.1183759888205333816915774140808e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.934 Order of pole = 4.437 x[1] = -0.9265 y[1] (analytic) = 1.164955007981397998432553036761 y[1] (numeric) = 1.1649550079813979986797319671048 absolute error = 2.4717893034379632217321557748999e-19 relative error = 2.1217894995970803649521314145246e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9339 Order of pole = 4.437 x[1] = -0.9264 y[1] (analytic) = 1.1652065230684790941442126708845 y[1] (numeric) = 1.1652065230684790943918429124889 absolute error = 2.4763024160432443738844715601881e-19 relative error = 2.1252047315372884150922345735911e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9338 Order of pole = 4.437 x[1] = -0.9263 y[1] (analytic) = 1.1654581196179362559441132063549 y[1] (numeric) = 1.1654581196179362561921951491086 absolute error = 2.4808194275376346332715231046149e-19 relative error = 2.1286216859949491829884951983268e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9337 Order of pole = 4.437 x[1] = -0.9262 y[1] (analytic) = 1.165709797664952715779761235589 y[1] (numeric) = 1.1657097976649527160282952697601 absolute error = 2.4853403417108356224161667452180e-19 relative error = 2.1320403643250238481148928408317e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=156.4MB, alloc=4.5MB, time=8.90 Real estimate of pole used Radius of convergence = 0.9336 Order of pole = 4.437 x[1] = -0.9261 y[1] (analytic) = 1.1659615572447307019982867127686 y[1] (numeric) = 1.1659615572447307022472732290042 absolute error = 2.4898651623566422635624149266265e-19 relative error = 2.1354607678836442553040796964926e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9335 Order of pole = 4.437 x[1] = -0.926 y[1] (analytic) = 1.1662133983924914516557897830377 y[1] (numeric) = 1.166213398392491451905229172365 absolute error = 2.4943938932729476425421757206064e-19 relative error = 2.1388828980281140527364946682027e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9334 Order of pole = 4.437 x[1] = -0.9259 y[1] (analytic) = 1.1664653211434752228359942409741 y[1] (numeric) = 1.1664653211434752230858868948002 absolute error = 2.4989265382617478789475755920280e-19 relative error = 2.1423067561169098311587490268259e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9333 Order of pole = 4.437 x[1] = -0.9258 y[1] (analytic) = 1.1667173255329413069782156607907 y[1] (numeric) = 1.1667173255329413072285619709036 absolute error = 2.5034631011291470026177222325981e-19 relative error = 2.1457323435096822643327444895132e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9332 Order of pole = 4.437 x[1] = -0.9257 y[1] (analytic) = 1.1669694115961680412146522485418 y[1] (numeric) = 1.1669694115961680414654526071103 absolute error = 2.5080035856853618364487776823864e-19 relative error = 2.1491596615672572507169864314916e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9331 Order of pole = 4.437 x[1] = -0.9256 y[1] (analytic) = 1.167221579368452820717006474438 y[1] (numeric) = 1.1672215793684528209682612740125 absolute error = 2.5125479957447268855362253795749e-19 relative error = 2.1525887116516370563815568436112e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.933 Order of pole = 4.437 x[1] = -0.9255 y[1] (analytic) = 1.1674738288851121110524455512096 y[1] (numeric) = 1.1674738288851121113041551847222 absolute error = 2.5170963351256992326582282210222e-19 relative error = 2.1560194951260014591582135472736e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9329 Order of pole = 4.437 x[1] = -0.9254 y[1] (analytic) = 1.1677261601814814605489088323023 y[1] (numeric) = 1.1677261601814814608010736930674 absolute error = 2.5216486076508634401089881801876e-19 relative error = 2.1594520133547088940270840803644e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9328 Order of pole = 4.437 x[1] = -0.9253 y[1] (analytic) = 1.1679785732929155126697702115451 y[1] (numeric) = 1.1679785732929155129223906932598 absolute error = 2.5262048171469364578910315147492e-19 relative error = 2.1628862677032975997414245724908e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9327 Order of pole = 4.437 x[1] = -0.9252 y[1] (analytic) = 1.1682310682547880183978636137892 y[1] (numeric) = 1.1682310682547880186509401105336 absolute error = 2.5307649674447725382753571039086e-19 relative error = 2.1663222595384867666919158351746e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9326 Order of pole = 4.437 x[1] = -0.9251 y[1] (analytic) = 1.1684836451024918486288796738893 y[1] (numeric) = 1.1684836451024918488824125801272 absolute error = 2.5353290623793681567383989849409e-19 relative error = 2.1697599902281776860119708026862e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9325 Order of pole = 4.437 x[1] = -0.925 y[1] (analytic) = 1.1687363038714390065741417092768 y[1] (numeric) = 1.1687363038714390068281314198558 absolute error = 2.5398971057898669392847677100614e-19 relative error = 2.1731994611414548999255293719213e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9324 Order of pole = 4.437 x[1] = -0.9249 y[1] (analytic) = 1.1689890445970606401727690992616 y[1] (numeric) = 1.1689890445970606404272160094135 absolute error = 2.5444691015195645961647487181806e-19 relative error = 2.1766406736485873533388186051279e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9323 Order of pole = 4.437 x[1] = -0.9248 y[1] (analytic) = 1.1692418673148070545132361920954 y[1] (numeric) = 1.169241867314807054768140697437 absolute error = 2.5490450534159138619955495116327e-19 relative error = 2.1800836291210295466775581773934e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9322 Order of pole = 4.437 x[1] = -0.9247 y[1] (analytic) = 1.1694947720601477242643348687357 y[1] (numeric) = 1.1694947720601477245196973652688 absolute error = 2.5536249653305294422953010455501e-19 relative error = 2.1835283289314226899710928715956e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9321 Order of pole = 4.437 x[1] = -0.9246 y[1] (analytic) = 1.1697477588685713061155489001587 y[1] (numeric) = 1.1697477588685713063713697842706 absolute error = 2.5582088411191929664388323772275e-19 relative error = 2.1869747744535958581849358470193e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.932 Order of pole = 4.437 x[1] = -0.9245 y[1] (analytic) = 1.1700008277755856512268482429951 y[1] (numeric) = 1.1700008277755856514831279114593 absolute error = 2.5627966846418579470442512846405e-19 relative error = 2.1904229670625671478032083340451e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9319 Order of pole = 4.437 x[1] = -0.9244 y[1] (analytic) = 1.1702539788167178176879114261913 y[1] (numeric) = 1.1702539788167178179446502761676 absolute error = 2.5673884997626547457993772472691e-19 relative error = 2.1938729081345448346624633362260e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=160.2MB, alloc=4.5MB, time=9.11 Real estimate of pole used Radius of convergence = 0.9318 Order of pole = 4.437 x[1] = -0.9243 y[1] (analytic) = 1.1705072120275140829867841893364 y[1] (numeric) = 1.1705072120275140832439826183714 absolute error = 2.5719842903498955457370868885844e-19 relative error = 2.1973245990469285330383828526969e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9317 Order of pole = 4.437 x[1] = -0.9242 y[1] (analytic) = 1.1707605274435399564879825412444 y[1] (numeric) = 1.170760527443539956745640947272 absolute error = 2.5765840602760793299686457080098e-19 relative error = 2.2007780411783103559868400682013e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9316 Order of pole = 4.437 x[1] = -0.9241 y[1] (analytic) = 1.1710139251003801919200484153365 y[1] (numeric) = 1.1710139251003801921781671966783 absolute error = 2.5811878134178968668841136809151e-19 relative error = 2.2042332359084760769408198950864e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9315 Order of pole = 4.437 x[1] = -0.924 y[1] (analytic) = 1.1712674050336387998725661063323 y[1] (numeric) = 1.171267405033638800131145661698 absolute error = 2.5857955536562357018289260782799e-19 relative error = 2.2076901846184062925646931914095e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9314 Order of pole = 4.437 x[1] = -0.9239 y[1] (analytic) = 1.1715209672789390603026476807323 y[1] (numeric) = 1.1715209672789390605616884092199 absolute error = 2.5904072848761851552657646531012e-19 relative error = 2.2111488886902775868673419218159e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9313 Order of pole = 4.437 x[1] = -0.9238 y[1] (analytic) = 1.1717746118719235350508955615568 y[1] (numeric) = 1.1717746118719235353103978626535 absolute error = 2.5950230109670413274308481584758e-19 relative error = 2.2146093495074636965756344731054e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9312 Order of pole = 4.437 x[1] = -0.9237 y[1] (analytic) = 1.1720283388482540803668504957955 y[1] (numeric) = 1.1720283388482540806268147693778 absolute error = 2.5996427358223121094937850025786e-19 relative error = 2.2180715684545366777697522843968e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9311 Order of pole = 4.437 x[1] = -0.9236 y[1] (analytic) = 1.1722821482436118594439331210221 y[1] (numeric) = 1.1722821482436118597043597673561 absolute error = 2.6042664633397222012301447085414e-19 relative error = 2.2215355469172680737818709025342e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.931 Order of pole = 4.437 x[1] = -0.9235 y[1] (analytic) = 1.1725360400936973549638873556352 y[1] (numeric) = 1.1725360400936973552247767753773 absolute error = 2.6088941974212181352159187325367e-19 relative error = 2.2250012862826300843597005268611e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9309 Order of pole = 4.437 x[1] = -0.9234 y[1] (analytic) = 1.1727900144342303816507338452046 y[1] (numeric) = 1.1727900144342303819120864394019 absolute error = 2.6135259419729733075530551012392e-19 relative error = 2.2284687879387967360963930637192e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9308 Order of pole = 4.437 x[1] = -0.9233 y[1] (analytic) = 1.1730440713009500988342417054259 y[1] (numeric) = 1.1730440713009500990960578755164 absolute error = 2.6181617009053930151352652603016e-19 relative error = 2.2319380532751450541283246700185e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9307 Order of pole = 4.437 x[1] = -0.9232 y[1] (analytic) = 1.1732982107296150230229268102208 y[1] (numeric) = 1.1732982107296150232852069580341 absolute error = 2.6228014781331194994633154785908e-19 relative error = 2.2354090836822562351022647269677e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9306 Order of pole = 4.437 x[1] = -0.9231 y[1] (analytic) = 1.1735524327560030404865848815629 y[1] (numeric) = 1.1735524327560030407493294093204 absolute error = 2.6274452775750369970190291287170e-19 relative error = 2.2388818805519168214134441495662e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9305 Order of pole = 4.437 x[1] = -0.923 y[1] (analytic) = 1.1738067374159114198483676456606 y[1] (numeric) = 1.173806737415911420111576955976 absolute error = 2.6320931031542767962072401628939e-19 relative error = 2.2423564452771198767160379047340e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9304 Order of pole = 4.437 x[1] = -0.9229 y[1] (analytic) = 1.1740611247451568246864103281875 y[1] (numeric) = 1.1740611247451568249500848240674 absolute error = 2.6367449587982223008749521244343e-19 relative error = 2.2458327792520661627075785810045e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9303 Order of pole = 4.437 x[1] = -0.9228 y[1] (analytic) = 1.174315594779575326145018769321 y[1] (numeric) = 1.1743155947795753264091588541649 absolute error = 2.6414008484385141004169710792476e-19 relative error = 2.2493108838721653171888198255287e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9302 Order of pole = 4.437 x[1] = -0.9227 y[1] (analytic) = 1.1745701475550224155554244474255 y[1] (numeric) = 1.1745701475550224158200305250266 absolute error = 2.6460607760110550464772949186062e-19 relative error = 2.2527907605340370334005704397439e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9301 Order of pole = 4.437 x[1] = -0.9226 y[1] (analytic) = 1.1748247831073730170661157083049 y[1] (numeric) = 1.1748247831073730173311881828505 absolute error = 2.6507247454560153362555555742266e-19 relative error = 2.2562724106355122406390219034481e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=164.0MB, alloc=4.5MB, time=9.33 Real estimate of pole used Radius of convergence = 0.93 Order of pole = 4.437 x[1] = -0.9225 y[1] (analytic) = 1.1750795014725215002827535050418 y[1] (numeric) = 1.1750795014725215005482927811136 absolute error = 2.6553927607178376024278247994041e-19 relative error = 2.2597558355756342861510940781978e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9299 Order of pole = 4.437 x[1] = -0.9224 y[1] (analytic) = 1.1753343026863816929176799615468 y[1] (numeric) = 1.1753343026863816931836864441213 absolute error = 2.6600648257452420096911083055928e-19 relative error = 2.2632410367546601183113258249151e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9298 Order of pole = 4.437 x[1] = -0.9223 y[1] (analytic) = 1.175589186784886893449028081052 y[1] (numeric) = 1.1755891867848868937155021755012 absolute error = 2.6647409444912313579408672024699e-19 relative error = 2.2667280155740614710818392573589e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9297 Order of pole = 4.437 x[1] = -0.9222 y[1] (analytic) = 1.1758441538039898837894409289056 y[1] (numeric) = 1.1758441538039898840563830409969 absolute error = 2.6694211209130961920909198712070e-19 relative error = 2.2702167734365260497569083426804e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9296 Order of pole = 4.437 x[1] = -0.9221 y[1] (analytic) = 1.1760992037796629419644086271534 y[1] (numeric) = 1.1760992037796629422318191630506 absolute error = 2.6741053589724199185450916054328e-19 relative error = 2.2737073117459587179936645526557e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9295 Order of pole = 4.437 x[1] = -0.922 y[1] (analytic) = 1.1763543367478978548002315065335 y[1] (numeric) = 1.176354336747897855068110872797 absolute error = 2.6787936626350839283299935822482e-19 relative error = 2.2771996319074826861304742643718e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9294 Order of pole = 4.437 x[1] = -0.9219 y[1] (analytic) = 1.1766095527447059306216177696563 y[1] (numeric) = 1.1766095527447059308899663732435 absolute error = 2.6834860358712727268983269766885e-19 relative error = 2.2806937353274407007945246071400e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9293 Order of pole = 4.437 x[1] = -0.9218 y[1] (analytic) = 1.1768648518061180119589240273012 y[1] (numeric) = 1.1768648518061180122277422755667 absolute error = 2.6881824826554790706121223072580e-19 relative error = 2.2841896234133962358001564532210e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9292 Order of pole = 4.437 x[1] = -0.9217 y[1] (analytic) = 1.1771202339681844882650470779232 y[1] (numeric) = 1.1771202339681844885343353786199 absolute error = 2.6928830069665091099153383976290e-19 relative error = 2.2876872975741346843394852535890e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9291 Order of pole = 4.437 x[1] = -0.9216 y[1] (analytic) = 1.177375699266975308641975308642 y[1] (numeric) = 1.1773756992669753089117340699207 absolute error = 2.6975876127874875392052596603452e-19 relative error = 2.2911867592196645524668524264209e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.929 Order of pole = 4.437 x[1] = -0.9215 y[1] (analytic) = 1.1776312477385799945770081041638 y[1] (numeric) = 1.1776312477385799948472377345744 absolute error = 2.7022963041058627534121447524269e-19 relative error = 2.2946880097612186538786520152965e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9289 Order of pole = 4.437 x[1] = -0.9214 y[1] (analytic) = 1.1778868794191076526886516582833 y[1] (numeric) = 1.1778868794191076529593525667747 absolute error = 2.7070090849134120112965940202036e-19 relative error = 2.2981910506112553059900793462206e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9288 Order of pole = 4.437 x[1] = -0.9213 y[1] (analytic) = 1.1781425943446869874821995908099 y[1] (numeric) = 1.1781425943446869877533721867305 absolute error = 2.7117259592062466054741175415123e-19 relative error = 2.3016958831834595273103504275539e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9287 Order of pole = 4.437 x[1] = -0.9212 y[1] (analytic) = 1.1783983925514663141150067809757 y[1] (numeric) = 1.1783983925514663143866514740742 absolute error = 2.7164469309848170391763999876662e-19 relative error = 2.3052025088927442361179428547495e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9286 Order of pole = 4.437 x[1] = -0.9211 y[1] (analytic) = 1.1786542740756135711714648366 y[1] (numeric) = 1.1786542740756135714435820370254 absolute error = 2.7211720042539182097587729653343e-19 relative error = 2.3087109291552514504374110024561e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9285 Order of pole = 4.437 x[1] = -0.921 y[1] (analytic) = 1.1789102389533163334476876265118 y[1] (numeric) = 1.1789102389533163337202777448141 absolute error = 2.7259011830226945989634199597340e-19 relative error = 2.3122211453883534893193303100647e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9284 Order of pole = 4.437 x[1] = -0.9209 y[1] (analytic) = 1.1791662872207818247459153119707 y[1] (numeric) = 1.1791662872207818250189787591011 absolute error = 2.7306344713046454699478534853647e-19 relative error = 2.3157331590106541754249274931458e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9283 Order of pole = 4.437 x[1] = -0.9208 y[1] (analytic) = 1.1794224189142369306786453210709 y[1] (numeric) = 1.1794224189142369309521825083826 absolute error = 2.7353718731176300710882185589330e-19 relative error = 2.3192469714419900389169555424595e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9282 Order of pole = 4.437 memory used=167.8MB, alloc=4.5MB, time=9.55 x[1] = -0.9207 y[1] (analytic) = 1.1796786340699282114824987183676 y[1] (numeric) = 1.179678634069928211756510057616 absolute error = 2.7401133924838728465669911411925e-19 relative error = 2.3227625841034315226583744043208e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9281 Order of pole = 4.437 x[1] = -0.9206 y[1] (analytic) = 1.1799349327241219148418304302293 y[1] (numeric) = 1.1799349327241219151163163335723 absolute error = 2.7448590334299686537546547501754e-19 relative error = 2.3262799984172841887204002710683e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.928 Order of pole = 4.437 x[1] = -0.9205 y[1] (analytic) = 1.1801913149131039887220917946904 y[1] (numeric) = 1.1801913149131039889970526746891 absolute error = 2.7496087999868879873949530277744e-19 relative error = 2.3297992158070899262014884482321e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9279 Order of pole = 4.437 x[1] = -0.9204 y[1] (analytic) = 1.1804477806731800942129539128633 y[1] (numeric) = 1.1804477806731800944883901824823 absolute error = 2.7543626961899822106033306448839e-19 relative error = 2.3333202376976281603588168057172e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9278 Order of pole = 4.437 x[1] = -0.9203 y[1] (analytic) = 1.1807043300406756183812002872559 y[1] (numeric) = 1.1807043300406756186571123598638 absolute error = 2.7591207260789887926881895573639e-19 relative error = 2.3368430655149170630538388639256e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9277 Order of pole = 4.437 x[1] = -0.9202 y[1] (analytic) = 1.1809609630519356871333972406422 y[1] (numeric) = 1.180960963051935687409785530012 absolute error = 2.7638828936980365538046022760033e-19 relative error = 2.3403677006862147645134776122309e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9276 Order of pole = 4.437 x[1] = -0.9201 y[1] (analytic) = 1.181217679743325178088350617442 y[1] (numeric) = 1.1812176797433251783652155377515 absolute error = 2.7686492030956509164501384884526e-19 relative error = 2.3438941446400205664085332066096e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9275 Order of pole = 4.437 x[1] = -0.92 y[1] (analytic) = 1.1814744801512287334593572778828 y[1] (numeric) = 1.1814744801512287337366992437153 absolute error = 2.7734196583247591638124760698360e-19 relative error = 2.3474223988060761562508797455092e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9274 Order of pole = 4.437 x[1] = -0.9199 y[1] (analytic) = 1.181731364312050772946259903544 y[1] (numeric) = 1.1817313643120507732240793298883 absolute error = 2.7781942634426957049784822414549e-19 relative error = 2.3509524646153668231110283782198e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9273 Order of pole = 4.437 x[1] = -0.9198 y[1] (analytic) = 1.1819883322622155066373136412186 y[1] (numeric) = 1.1819883322622155069156109434697 absolute error = 2.7829730225112073470144653837239e-19 relative error = 2.3544843435001226746576360581013e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9272 Order of pole = 4.437 x[1] = -0.9197 y[1] (analytic) = 1.1822453840381669479208731203732 y[1] (numeric) = 1.1822453840381669481996487143328 absolute error = 2.7877559395964585739273127802616e-19 relative error = 2.3580180368938198555205413140169e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9271 Order of pole = 4.437 x[1] = -0.9196 y[1] (analytic) = 1.1825025196763689264069083878404 y[1] (numeric) = 1.1825025196763689266861626897173 absolute error = 2.7925430187690368325162443649424e-19 relative error = 2.3615535462311817669789104772338e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.927 Order of pole = 4.437 x[1] = -0.9195 y[1] (analytic) = 1.1827597392133051008583583117406 y[1] (numeric) = 1.182759739213305101138091738151 absolute error = 2.7973342641039578251249273627409e-19 relative error = 2.3650908729481802879760798678820e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9269 Order of pole = 4.437 x[1] = -0.9194 y[1] (analytic) = 1.1830170426854789721323300150021 y[1] (numeric) = 1.1830170426854789724125429829701 absolute error = 2.8021296796806708093037115584123e-19 relative error = 2.3686300184820369974626815148158e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9268 Order of pole = 4.437 x[1] = -0.9193 y[1] (analytic) = 1.1832744301294138961311529072301 y[1] (numeric) = 1.1832744301294138964118458341884 absolute error = 2.8069292695830639043917597944870e-19 relative error = 2.3721709842712243980696420554008e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9267 Order of pole = 4.437 x[1] = -0.9192 y[1] (analytic) = 1.1835319015816530967632958920649 y[1] (numeric) = 1.1835319015816530970444691958549 absolute error = 2.8117330378994694050288631917632e-19 relative error = 2.3757137717554671411126465373626e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9266 Order of pole = 4.437 x[1] = -0.9191 y[1] (analytic) = 1.1837894570787596789141563355684 y[1] (numeric) = 1.1837894570787596791958104344406 absolute error = 2.8165409887226691016067455014985e-19 relative error = 2.3792583823757432529296609233817e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9265 Order of pole = 4.437 x[1] = -0.919 y[1] (analytic) = 1.1840470966573166414267293895882 y[1] (numeric) = 1.1840470966573166417088647022032 absolute error = 2.8213531261498996076696759388683e-19 relative error = 2.3828048175742853625531091806065e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9263 Order of pole = 4.437 x[1] = -0.9189 y[1] (analytic) = 1.1843048203539268900921662724649 y[1] (numeric) = 1.1843048203539268903747832178932 absolute error = 2.8261694542828576942742248120269e-19 relative error = 2.3863530787945819307183029216921e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=171.6MB, alloc=4.5MB, time=9.76 Real estimate of pole used Radius of convergence = 0.9262 Order of pole = 4.437 x[1] = -0.9188 y[1] (analytic) = 1.1845626282052132506502301178744 y[1] (numeric) = 1.1845626282052132509333291155972 absolute error = 2.8309899772277056313180112503075e-19 relative error = 2.3899031674813784802097236513558e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9261 Order of pole = 4.437 x[1] = -0.9187 y[1] (analytic) = 1.1848205202478184817996580110354 y[1] (numeric) = 1.1848205202478184820832394809449 absolute error = 2.8358146990950765358473073487812e-19 relative error = 2.3934550850806788275467597627795e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.926 Order of pole = 4.437 x[1] = -0.9186 y[1] (analytic) = 1.1850784965184052882184378399546 y[1] (numeric) = 1.1850784965184052885025022023546 absolute error = 2.8406436240000797273533780846044e-19 relative error = 2.3970088330397463160105025214843e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9259 Order of pole = 4.437 x[1] = -0.9185 y[1] (analytic) = 1.1853365570536563335940085978387 y[1] (numeric) = 1.1853365570536563338785562734449 absolute error = 2.8454767560623060900674514233536e-19 relative error = 2.4005644128071050500132073705637e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9258 Order of pole = 4.437 x[1] = -0.9184 y[1] (analytic) = 1.1855947018902742536633927812648 y[1] (numeric) = 1.1855947018902742539484241912054 absolute error = 2.8503140994058334422642281209311e-19 relative error = 2.4041218258325411308120289903921e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9257 Order of pole = 4.437 x[1] = -0.9183 y[1] (analytic) = 1.1858529310649816692632695371731 y[1] (numeric) = 1.185852931064981669548785102989 absolute error = 2.8551556581592319125838558386585e-19 relative error = 2.4076810735671038935686406481206e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9256 Order of pole = 4.437 x[1] = -0.9182 y[1] (analytic) = 1.1861112446145211993899972202297 y[1] (numeric) = 1.1861112446145211996759973638752 absolute error = 2.8600014364555693233823073259008e-19 relative error = 2.4112421574631071457563504774548e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9255 Order of pole = 4.437 x[1] = -0.9181 y[1] (analytic) = 1.1863696425756554742695940305961 y[1] (numeric) = 1.1863696425756554745560791744393 absolute error = 2.8648514384324165811201175860344e-19 relative error = 2.4148050789741304069163294373632e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9254 Order of pole = 4.437 x[1] = -0.918 y[1] (analytic) = 1.1866281249851671484376854106445 y[1] (numeric) = 1.1866281249851671487246559774677 absolute error = 2.8697056682318530737994501278149e-19 relative error = 2.4183698395550201497645678095127e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9253 Order of pole = 4.437 x[1] = -0.9179 y[1] (analytic) = 1.186886691879858913829426887667 y[1] (numeric) = 1.1868866918798589141168833006671 absolute error = 2.8745641300004720754594776152759e-19 relative error = 2.4219364406618910426511792083604e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9252 Order of pole = 4.437 x[1] = -0.9178 y[1] (analytic) = 1.1871453432965535128794110581449 y[1] (numeric) = 1.1871453432965535131673537409338 absolute error = 2.8794268278893861577400774652243e-19 relative error = 2.4255048837521271933736731949615e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9251 Order of pole = 4.437 x[1] = -0.9177 y[1] (analytic) = 1.1874040792720937516315674176748 y[1] (numeric) = 1.1874040792720937519199967942802 absolute error = 2.8842937660542326085238582022522e-19 relative error = 2.4290751702843833943458197056842e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.925 Order of pole = 4.437 x[1] = -0.9176 y[1] (analytic) = 1.1876628998433425128590637491838 y[1] (numeric) = 1.1876628998433425131479802440494 absolute error = 2.8891649486551788576665476669837e-19 relative error = 2.4326473017185863691237306301522e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9249 Order of pole = 4.437 x[1] = -0.9175 y[1] (analytic) = 1.1879218050471827691942177906139 y[1] (numeric) = 1.1879218050471827694836218285996 absolute error = 2.8940403798569279098257894840810e-19 relative error = 2.4362212795159360202907859988836e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9248 Order of pole = 4.437 x[1] = -0.9174 y[1] (analytic) = 1.1881807949205175962684279118117 y[1] (numeric) = 1.1881807949205175965583199181946 absolute error = 2.8989200638287237843984095323728e-19 relative error = 2.4397971051389066787030343702459e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9247 Order of pole = 4.437 x[1] = -0.9173 y[1] (analytic) = 1.1884398695002701858621315389254 y[1] (numeric) = 1.1884398695002701861525119393998 absolute error = 2.9038040047443569625762295204005e-19 relative error = 2.4433747800512483540966991385228e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9246 Order of pole = 4.437 x[1] = -0.9172 y[1] (analytic) = 1.1886990288233838590648000731858 y[1] (numeric) = 1.188699028823383859355669293864 absolute error = 2.9086922067821698415305201567292e-19 relative error = 2.4469543057179879870594246200862e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9245 Order of pole = 4.437 x[1] = -0.9171 y[1] (analytic) = 1.1889582729268220794449790595319 y[1] (numeric) = 1.1889582729268220797363375269444 absolute error = 2.9135846741250621957352018156042e-19 relative error = 2.4505356836054307023668979128866e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=175.4MB, alloc=4.5MB, time=9.98 Real estimate of pole used Radius of convergence = 0.9244 Order of pole = 4.437 x[1] = -0.917 y[1] (analytic) = 1.1892176018475684662303823691355 y[1] (numeric) = 1.1892176018475684665222305102316 absolute error = 2.9184814109604966454389160349766e-19 relative error = 2.4541189151811610636864846657354e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9243 Order of pole = 4.437 x[1] = -0.9169 y[1] (analytic) = 1.1894770156226268074980491684836 y[1] (numeric) = 1.1894770156226268077903874106317 absolute error = 2.9233824214805041322961066456309e-19 relative error = 2.4577040019140443296495190381402e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9242 Order of pole = 4.437 x[1] = -0.9168 y[1] (analytic) = 1.1897365142890210733745724562862 y[1] (numeric) = 1.1897365142890210736674012272744 absolute error = 2.9282877098816894021672648171556e-19 relative error = 2.4612909452742277112938902787888e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9241 Order of pole = 4.437 x[1] = -0.9167 y[1] (analytic) = 1.1899960978837954292464079581037 y[1] (numeric) = 1.1899960978837954295397276861402 absolute error = 2.9331972803652364950985078188614e-19 relative error = 2.4648797467331416308785705011583e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.924 Order of pole = 4.437 x[1] = -0.9166 y[1] (analytic) = 1.1902557664440142489802721772144 y[1] (numeric) = 1.1902557664440142492740832909281 absolute error = 2.9381111371369142424906768315027e-19 relative error = 2.4684704077635009820717303881502e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9239 Order of pole = 4.437 x[1] = -0.9165 y[1] (analytic) = 1.1905155200067621281536384088879 y[1] (numeric) = 1.1905155200067621284479413373286 absolute error = 2.9430292844070817714681547088495e-19 relative error = 2.4720629298393063915140917141404e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9238 Order of pole = 4.437 x[1] = -0.9164 y[1] (analytic) = 1.1907753586091438972953395338753 y[1] (numeric) = 1.1907753586091438975901347065143 absolute error = 2.9479517263906940164576201768305e-19 relative error = 2.4756573144358454817591677323755e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9237 Order of pole = 4.437 x[1] = -0.9163 y[1] (analytic) = 1.1910352822882846351362864155911 y[1] (numeric) = 1.1910352822882846354315742623218 absolute error = 2.9528784673073072379869705721670e-19 relative error = 2.4792535630296941355920446382540e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9236 Order of pole = 4.437 x[1] = -0.9162 y[1] (analytic) = 1.1912952910813296818703107341281 y[1] (numeric) = 1.1912952910813296821660916852662 absolute error = 2.9578095113810845487146608621868e-19 relative error = 2.4828516770987177617283594847094e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9235 Order of pole = 4.437 x[1] = -0.9161 y[1] (analytic) = 1.1915553850254446524251410989246 y[1] (numeric) = 1.1915553850254446527214155852087 absolute error = 2.9627448628408014466997223528951e-19 relative error = 2.4864516581220725618951320946630e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9234 Order of pole = 4.437 x[1] = -0.916 y[1] (analytic) = 1.1918155641578154497435212905932 y[1] (numeric) = 1.1918155641578154500402897431852 absolute error = 2.9676845259198513559227401834242e-19 relative error = 2.4900535075802067992951106873432e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9233 Order of pole = 4.437 x[1] = -0.9159 y[1] (analytic) = 1.1920758285156482780744794911162 y[1] (numeric) = 1.1920758285156482783717423416018 absolute error = 2.9726285048562511740680844217370e-19 relative error = 2.4936572269548620684562931101798e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9232 Order of pole = 4.437 x[1] = -0.9158 y[1] (analytic) = 1.1923361781361696562747573703188 y[1] (numeric) = 1.192336178136169656572515050708 absolute error = 2.9775768038926468275777053189605e-19 relative error = 2.4972628177290745664682877459851e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9231 Order of pole = 4.437 x[1] = -0.9157 y[1] (analytic) = 1.1925966130566264311204079052507 y[1] (numeric) = 1.1925966130566264314186608479783 absolute error = 2.9825294272763188339868190480237e-19 relative error = 2.5008702813871763656071803462235e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.923 Order of pole = 4.437 x[1] = -0.9156 y[1] (analytic) = 1.1928571333142857906285708178286 y[1] (numeric) = 1.1928571333142857909273194557545 absolute error = 2.9874863792591878715518260464110e-19 relative error = 2.5044796194147966873505752253628e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9229 Order of pole = 4.437 x[1] = -0.9155 y[1] (analytic) = 1.1931177389464352773894345248304 y[1] (numeric) = 1.1931177389464352776886792912402 absolute error = 2.9924476640978203561808199028663e-19 relative error = 2.5080908332988631777844814385933e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9228 Order of pole = 4.437 x[1] = -0.9154 y[1] (analytic) = 1.193378429990382801908393503076 y[1] (numeric) = 1.1933784299903828022081348316813 absolute error = 2.9974132860534340256770605738369e-19 relative error = 2.5117039245276031844037167556003e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9227 Order of pole = 4.437 x[1] = -0.9153 y[1] (analytic) = 1.1936392064834566559584099813829 y[1] (numeric) = 1.1936392064834566562586483063221 absolute error = 3.0023832493919035313058015873749e-19 relative error = 2.5153188945905450343075044365836e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=179.3MB, alloc=4.5MB, time=10.19 Real estimate of pole used Radius of convergence = 0.9226 Order of pole = 4.437 x[1] = -0.9152 y[1] (analytic) = 1.1939000684630055259425888796518 y[1] (numeric) = 1.1939000684630055262433246354902 absolute error = 3.0073575583837660366948767901687e-19 relative error = 2.5189357449785193137919400133493e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9225 Order of pole = 4.437 x[1] = -0.9151 y[1] (analytic) = 1.1941610159663985062669749242069 y[1] (numeric) = 1.1941610159663985065682085459373 absolute error = 3.0123362173042268240794681173909e-19 relative error = 2.5225544771836601493410074780428e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9224 Order of pole = 4.437 x[1] = -0.915 y[1] (analytic) = 1.194422049031025112723580877303 y[1] (numeric) = 1.1944220490310251130253128003463 absolute error = 3.0173192304331649079014918151861e-19 relative error = 2.5261750926994064900178264849691e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9223 Order of pole = 4.437 x[1] = -0.9149 y[1] (analytic) = 1.1946831676942952958836558275014 y[1] (numeric) = 1.1946831676942952961858864877069 absolute error = 3.0223066020551386557740565219059e-19 relative error = 2.5297975930205033912578143769497e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9222 Order of pole = 4.437 x[1] = -0.9148 y[1] (analytic) = 1.1949443719936394545012024964204 y[1] (numeric) = 1.1949443719936394548039323300664 absolute error = 3.0272983364593914168214626166974e-19 relative error = 2.5334219796430033000654490568053e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9221 Order of pole = 4.437 x[1] = -0.9147 y[1] (analytic) = 1.1952056619665084489267525261777 y[1] (numeric) = 1.1952056619665084492299819699717 absolute error = 3.0322944379398571574052282727904e-19 relative error = 2.5370482540642673416163209368357e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.922 Order of pole = 4.437 x[1] = -0.9146 y[1] (analytic) = 1.1954670376503736145314087206643 y[1] (numeric) = 1.1954670376503736148351382117438 absolute error = 3.0372949107951661042466437078709e-19 relative error = 2.5406764177829666072661644145911e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9219 Order of pole = 4.437 x[1] = -0.9145 y[1] (analytic) = 1.1957284990827267751411632226198 y[1] (numeric) = 1.1957284990827267754453931985527 absolute error = 3.0422997593286503949563712053107e-19 relative error = 2.5443064722990834439685615418062e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9218 Order of pole = 4.437 x[1] = -0.9144 y[1] (analytic) = 1.1959900463010802564815006173222 y[1] (numeric) = 1.1959900463010802567862315161071 absolute error = 3.0473089878483497359816245877877e-19 relative error = 2.5479384191139127451030127750980e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9217 Order of pole = 4.437 x[1] = -0.9143 y[1] (analytic) = 1.1962516793429668996322949625519 y[1] (numeric) = 1.1962516793429668999375272226186 absolute error = 3.0523226006670170679814779590414e-19 relative error = 2.5515722597300632427150719219171e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9216 Order of pole = 4.437 x[1] = -0.9142 y[1] (analytic) = 1.196513398245940074493009753355 y[1] (numeric) = 1.1965133982459400747987438135652 absolute error = 3.0573406021021242386408696901861e-19 relative error = 2.5552079956514588011702446232962e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9215 Order of pole = 4.437 x[1] = -0.9141 y[1] (analytic) = 1.1967752030475736932582098389977 y[1] (numeric) = 1.1967752030475736935644461386453 absolute error = 3.0623629964758676829338838142200e-19 relative error = 2.5588456283833397122233519461642e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9214 Order of pole = 4.437 x[1] = -0.914 y[1] (analytic) = 1.1970370937854622239033943183831 y[1] (numeric) = 1.1970370937854622242101332971947 absolute error = 3.0673897881151741108469072061496e-19 relative error = 2.5624851594322639915050628923886e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9213 Order of pole = 4.437 x[1] = -0.9139 y[1] (analytic) = 1.1972990704972207036811594490944 y[1] (numeric) = 1.1972990704972207039884015472296 absolute error = 3.0724209813517062025722771665531e-19 relative error = 2.5661265903061086764273018692865e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9212 Order of pole = 4.437 x[1] = -0.9138 y[1] (analytic) = 1.1975611332204847526277006141237 y[1] (numeric) = 1.1975611332204847529354462721759 absolute error = 3.0774565805218683111830502934787e-19 relative error = 2.5697699225140711255092394071056e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9211 Order of pole = 4.437 x[1] = -0.9137 y[1] (analytic) = 1.1978232819929105870796623992575 y[1] (numeric) = 1.1978232819929105873879120582542 absolute error = 3.0824965899668121727995398213552e-19 relative error = 2.5734151575666703191255766529214e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.921 Order of pole = 4.437 x[1] = -0.9136 y[1] (analytic) = 1.1980855168521750332013458430075 y[1] (numeric) = 1.1980855168521750335100999444107 absolute error = 3.0875410140324426242582849261370e-19 relative error = 2.5770622969757481616788364175428e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9209 Order of pole = 4.437 x[1] = -0.9135 y[1] (analytic) = 1.1983478378359755405222819299032 y[1] (numeric) = 1.1983478378359755408315409156102 absolute error = 3.0925898570694233282941318432548e-19 relative error = 2.5807113422544707851973758023559e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9208 Order of pole = 4.437 memory used=183.1MB, alloc=4.5MB, time=10.41 x[1] = -0.9134 y[1] (analytic) = 1.1986102449820301954851804069032 y[1] (numeric) = 1.1986102449820301957949447192466 absolute error = 3.0976431234331825062461230191494e-19 relative error = 2.5843622949173298543608376865822e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9207 Order of pole = 4.437 x[1] = -0.9133 y[1] (analytic) = 1.1988727383280777350042630116266 y[1] (numeric) = 1.198872738328077735314533093375 absolute error = 3.1027008174839186782979069182687e-19 relative error = 2.5880151564801438729547606121758e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9206 Order of pole = 4.437 x[1] = -0.9132 y[1] (analytic) = 1.1991353179118775600339902100674 y[1] (numeric) = 1.1991353179118775603447665044261 absolute error = 3.1077629435866064112633975354626e-19 relative error = 2.5916699284600594917560688635539e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9205 Order of pole = 4.437 x[1] = -0.9131 y[1] (analytic) = 1.1993979837712097491481905504206 y[1] (numeric) = 1.1993979837712097494594735010317 absolute error = 3.1128295061110020739284291187580e-19 relative error = 2.5953266123755528178511668025354e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9204 Order of pole = 4.437 x[1] = -0.913 y[1] (analytic) = 1.1996607359438750721296017486255 y[1] (numeric) = 1.1996607359438750724413917995687 absolute error = 3.1179005094316495999591680895876e-19 relative error = 2.5989852097464307253883637852694e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9203 Order of pole = 4.437 x[1] = -0.9129 y[1] (analytic) = 1.1999235744676950035698326302201 y[1] (numeric) = 1.1999235744676950038821302260129 absolute error = 3.1229759579278862583880606567251e-19 relative error = 2.6026457220938321677663582575703e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9202 Order of pole = 4.437 x[1] = -0.9128 y[1] (analytic) = 1.2001864993805117364797550620986 y[1] (numeric) = 1.200186499380511736792560647697 absolute error = 3.1280558559838484316881111565013e-19 relative error = 2.6063081509402294912605118979437e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9201 Order of pole = 4.437 x[1] = -0.9127 y[1] (analytic) = 1.2004495107201881959103350167677 y[1] (numeric) = 1.2004495107201881962236490375665 absolute error = 3.1331402079884774014463027153746e-19 relative error = 2.6099724978094297500886469536918e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.92 Order of pole = 4.437 x[1] = -0.9126 y[1] (analytic) = 1.200712608524608052583911920718 y[1] (numeric) = 1.2007126085246080528977348225516 absolute error = 3.1382290183355251416469884216681e-19 relative error = 2.6136387642265760229181021948364e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9199 Order of pole = 4.437 x[1] = -0.9125 y[1] (analytic) = 1.2009757928316757365359354475511 y[1] (numeric) = 1.2009757928316757368502676766935 absolute error = 3.1433222914235601195760978113023e-19 relative error = 2.6173069517181487308157851931922e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9198 Order of pole = 4.437 x[1] = -0.9124 y[1] (analytic) = 1.2012390636793164507671689255407 y[1] (numeric) = 1.2012390636793164510820109287063 absolute error = 3.1484200316559731043570201176952e-19 relative error = 2.6209770618119669566429609197734e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9197 Order of pole = 4.437 x[1] = -0.9123 y[1] (analytic) = 1.2015024211054761849063685383515 y[1] (numeric) = 1.2015024211054761852217207626956 absolute error = 3.1535222434409829831290424087248e-19 relative error = 2.6246490960371897658965189428223e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9196 Order of pole = 4.437 x[1] = -0.9122 y[1] (analytic) = 1.2017658651481217288834475066988 y[1] (numeric) = 1.2017658651481217291993103998179 absolute error = 3.1586289311916425848792374337933e-19 relative error = 2.6283230559243175289984638011183e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9195 Order of pole = 4.437 x[1] = -0.9121 y[1] (analytic) = 1.2020293958452406866131344477933 y[1] (numeric) = 1.2020293958452406869295084577259 absolute error = 3.1637400993258445119387127316511e-19 relative error = 2.6319989430051932450353754228638e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9194 Order of pole = 4.437 x[1] = -0.912 y[1] (analytic) = 1.202293013234841489689135118498 y[1] (numeric) = 1.2022930132348414900060206937246 absolute error = 3.1688557522663269791541493047766e-19 relative error = 2.6356767588130038669495887593521e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9193 Order of pole = 4.437 x[1] = -0.9119 y[1] (analytic) = 1.2025567173549534110888067572047 y[1] (numeric) = 1.2025567173549534114062043466487 absolute error = 3.1739758944406796607455749488165e-19 relative error = 2.6393565048822816281838441048135e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9192 Order of pole = 4.437 x[1] = -0.9118 y[1] (analytic) = 1.2028205082436265788883542485376 y[1] (numeric) = 1.2028205082436265792062643015658 absolute error = 3.1791005302813495448613341359139e-19 relative error = 2.6430381827489053707811618793021e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9191 Order of pole = 4.437 x[1] = -0.9117 y[1] (analytic) = 1.2030843859389319899885573440969 y[1] (numeric) = 1.2030843859389319903069803105195 absolute error = 3.1842296642256467958412331887459e-19 relative error = 2.6467217939501018749416979602504e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.919 Order of pole = 4.437 x[1] = -0.9116 y[1] (analytic) = 1.2033483504789615238510381815693 y[1] (numeric) = 1.2033483504789615241699745116409 absolute error = 3.1893633007157506241988563477941e-19 relative error = 2.6504073400244471900383379603653e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=186.9MB, alloc=4.5MB, time=10.62 Real estimate of pole used Radius of convergence = 0.9189 Order of pole = 4.437 x[1] = -0.9115 y[1] (analytic) = 1.2036124019018279562450783536628 y[1] (numeric) = 1.2036124019018279565645284980827 absolute error = 3.1945014441987151643340652278417e-19 relative error = 2.6540948225118679670927911648945e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9188 Order of pole = 4.437 x[1] = -0.9114 y[1] (analytic) = 1.2038765402456649730049947874554 y[1] (numeric) = 1.203876540245664973324959197368 absolute error = 3.1996440991264753599867110809705e-19 relative error = 2.6577842429536427927139471599397e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9187 Order of pole = 4.437 x[1] = -0.9113 y[1] (analytic) = 1.2041407655486271837980837038946 y[1] (numeric) = 1.2041407655486271841185628308902 absolute error = 3.2047912699558528574426062324717e-19 relative error = 2.6614756028924035245002605054604e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9186 Order of pole = 4.437 x[1] = -0.9112 y[1] (analytic) = 1.2044050778488901359031419363442 y[1] (numeric) = 1.2044050778488901362241362324591 absolute error = 3.2099429611485619065028180331351e-19 relative error = 2.6651689038721366279079311318815e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9185 Order of pole = 4.437 x[1] = -0.9111 y[1] (analytic) = 1.2046694771846503279995748962349 y[1] (numeric) = 1.204669477184650328321084813952 absolute error = 3.2150991771712152692273656763894e-19 relative error = 2.6688641474381845145866504678147e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9184 Order of pole = 4.437 x[1] = -0.911 y[1] (analytic) = 1.204933963594125223967100483058 y[1] (numeric) = 1.2049339635941252242891264753076 absolute error = 3.2202599224953301364644172617847e-19 relative error = 2.6725613351372468821846856383176e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9183 Order of pole = 4.437 x[1] = -0.9109 y[1] (analytic) = 1.2051985371155532666960582451241 y[1] (numeric) = 1.2051985371155532670186007652839 absolute error = 3.2254252015973340521761015473804e-19 relative error = 2.6762604685173820556250764083625e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9182 Order of pole = 4.437 x[1] = -0.9108 y[1] (analytic) = 1.2054631977871938919083331067063 y[1] (numeric) = 1.2054631977871938922313926086021 absolute error = 3.2305950189585708455720659227825e-19 relative error = 2.6799615491280083298547218847619e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9181 Order of pole = 4.437 x[1] = -0.9107 y[1] (analytic) = 1.205727945647327541988902986394 y[1] (numeric) = 1.2057279456473275423124799243005 absolute error = 3.2357693790653065710619292519099e-19 relative error = 2.6836645785199053140681363317188e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.918 Order of pole = 4.437 x[1] = -0.9106 y[1] (analytic) = 1.2059927807342556798280196407019 y[1] (numeric) = 1.2059927807342556801521144693428 absolute error = 3.2409482864087354560377953801097e-19 relative error = 2.6873695582452152774076558004303e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9179 Order of pole = 4.437 x[1] = -0.9105 y[1] (analytic) = 1.2062577030863008026740320762017 y[1] (numeric) = 1.2062577030863008029986452507502 absolute error = 3.2461317454849858564980102740376e-19 relative error = 2.6910764898574444961418796217825e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9178 Order of pole = 4.437 x[1] = -0.9104 y[1] (analytic) = 1.2065227127418064559968618826851 y[1] (numeric) = 1.2065227127418064563219938587646 absolute error = 3.2513197607951262205233629648184e-19 relative error = 2.6947853749114646023241331631426e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9177 Order of pole = 4.437 x[1] = -0.9103 y[1] (analytic) = 1.2067878097391372473621398491122 y[1] (numeric) = 1.2067878097391372476877910827967 absolute error = 3.2565123368451710596169476954574e-19 relative error = 2.6984962149635139339327406055753e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9176 Order of pole = 4.437 x[1] = -0.9102 y[1] (analytic) = 1.2070529941166788603160132333565 y[1] (numeric) = 1.2070529941166788606421841811711 absolute error = 3.2617094781460869279189219323294e-19 relative error = 2.7022090115711988864948988565022e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9175 Order of pole = 4.437 x[1] = -0.9101 y[1] (analytic) = 1.2073182659128380682806330660254 y[1] (numeric) = 1.2073182659128380686073241849468 absolute error = 3.2669111892137984093074121878856e-19 relative error = 2.7059237662934952661959460748804e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9174 Order of pole = 4.437 x[1] = -0.91 y[1] (analytic) = 1.2075836251660427484603308779133 y[1] (numeric) = 1.2075836251660427487875426253702 absolute error = 3.2721174745691941123968369175346e-19 relative error = 2.7096404806907496444758206514104e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9173 Order of pole = 4.437 x[1] = -0.9099 y[1] (analytic) = 1.2078490719147418957584942499318 y[1] (numeric) = 1.2078490719147418960862270838056 absolute error = 3.2773283387381326734449330980229e-19 relative error = 2.7133591563246807141145088550982e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9172 Order of pole = 4.437 x[1] = -0.9098 y[1] (analytic) = 1.2081146061974056367051505936603 y[1] (numeric) = 1.2081146061974056370334049722854 absolute error = 3.2825437862514487671797904676161e-19 relative error = 2.7170797947583806468082817296943e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=190.7MB, alloc=4.5MB, time=10.84 Real estimate of pole used Radius of convergence = 0.9171 Order of pole = 4.437 x[1] = -0.9097 y[1] (analytic) = 1.2083802280525252433952685799668 y[1] (numeric) = 1.2083802280525252437240449621313 absolute error = 3.2877638216449591255582148100105e-19 relative error = 2.7208023975563164522385241991227e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.917 Order of pole = 4.437 x[1] = -0.9096 y[1] (analytic) = 1.2086459375186131474377866424705 y[1] (numeric) = 1.2086459375186131477670854874165 absolute error = 3.2929884494594685644667590942395e-19 relative error = 2.7245269662843313386349617200006e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9169 Order of pole = 4.437 x[1] = -0.9095 y[1] (analytic) = 1.2089117346342029539153779919432 y[1] (numeric) = 1.2089117346342029542451997593673 absolute error = 3.2982176742407760183767787419295e-19 relative error = 2.7282535025096460748350922017314e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9168 Order of pole = 4.437 x[1] = -0.9094 y[1] (analytic) = 1.2091776194378494553549615870872 y[1] (numeric) = 1.2091776194378494556853067371412 absolute error = 3.3034515005396805829648847811551e-19 relative error = 2.7319820078008603538416333004521e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9167 Order of pole = 4.437 x[1] = -0.9093 y[1] (analytic) = 1.209443591968128645708968516478 y[1] (numeric) = 1.2094435919681286460398375097692 absolute error = 3.3086899329119875657101861628990e-19 relative error = 2.7357124837279541578797975823163e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9166 Order of pole = 4.437 x[1] = -0.9092 y[1] (analytic) = 1.2097096522636377343473732558164 y[1] (numeric) = 1.2097096522636377346787665534083 absolute error = 3.3139329759185145444797300617794e-19 relative error = 2.7394449318622891249562104442168e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9165 Order of pole = 4.437 x[1] = -0.9091 y[1] (analytic) = 1.2099758003629951600604992740085 y[1] (numeric) = 1.209975800362995160392417337421 absolute error = 3.3191806341250974341135665573324e-19 relative error = 2.7431793537766099169212880760949e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9164 Order of pole = 4.437 x[1] = -0.909 y[1] (analytic) = 1.2102420363048406050726084709681 y[1] (numeric) = 1.2102420363048406054050517621784 absolute error = 3.3244329121025965610208816957592e-19 relative error = 2.7469157510450455890368951484536e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9163 Order of pole = 4.437 x[1] = -0.9089 y[1] (analytic) = 1.2105083601278350090662839394314 y[1] (numeric) = 1.2105083601278350093992529208741 absolute error = 3.3296898144269027457986605647458e-19 relative error = 2.7506541252431109610511043115947e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9162 Order of pole = 4.437 x[1] = -0.9088 y[1] (analytic) = 1.2107747718706605832176155524697 y[1] (numeric) = 1.2107747718706605835511106870376 absolute error = 3.3349513456789433938843596757580e-19 relative error = 2.7543944779477079897818819994413e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9161 Order of pole = 4.437 x[1] = -0.9087 y[1] (analytic) = 1.2110412715720208242421978878011 y[1] (numeric) = 1.2110412715720208245762196388456 absolute error = 3.3402175104446885942540856391830e-19 relative error = 2.7581368107371271432115274405898e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.916 Order of pole = 4.437 x[1] = -0.9086 y[1] (analytic) = 1.2113078592706405284519500094216 y[1] (numeric) = 1.2113078592706405287864988407531 absolute error = 3.3454883133151572261777948378678e-19 relative error = 2.7618811251910487760936941924694e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9159 Order of pole = 4.437 x[1] = -0.9085 y[1] (analytic) = 1.2115745350052658058227666365086 y[1] (numeric) = 1.2115745350052658061578430123972 absolute error = 3.3507637588864230740430465540502e-19 relative error = 2.7656274228905445070748259311711e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9158 Order of pole = 4.437 x[1] = -0.9084 y[1] (analytic) = 1.2118412988146640940730102389926 y[1] (numeric) = 1.2118412988146640944086146241685 absolute error = 3.3560438517596209502588597834394e-19 relative error = 2.7693757054180785973318406496578e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9157 Order of pole = 4.437 x[1] = -0.9083 y[1] (analytic) = 1.2121081507376241727528536086441 y[1] (numeric) = 1.2121081507376241730889864682982 absolute error = 3.3613285965409528262512417783396e-19 relative error = 2.7731259743575093307278998406696e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9156 Order of pole = 4.437 x[1] = -0.9082 y[1] (analytic) = 1.2123750908129561773444824639885 y[1] (numeric) = 1.2123750908129561776811442637726 absolute error = 3.3666179978416939715619741992580e-19 relative error = 2.7768782312940903954881016677252e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9155 Order of pole = 4.437 x[1] = -0.9081 y[1] (analytic) = 1.2126421190794916133731676568314 y[1] (numeric) = 1.2126421190794916137103588628592 absolute error = 3.3719120602781991010622606214697e-19 relative error = 2.7806324778144722673969395581709e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9154 Order of pole = 4.437 x[1] = -0.908 y[1] (analytic) = 1.2129092355760833705292165576666 y[1] (numeric) = 1.2129092355760833708669376365137 absolute error = 3.3772107884719085302928570395589e-19 relative error = 2.7843887155067035945193700862629e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=194.5MB, alloc=4.5MB, time=11.05 Real estimate of pole used Radius of convergence = 0.9153 Order of pole = 4.437 x[1] = -0.9079 y[1] (analytic) = 1.2131764403416057368008132067261 y[1] (numeric) = 1.213176440341605737139064625431 absolute error = 3.3825141870493543389423249390856e-19 relative error = 2.7881469459602325834473364517926e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9152 Order of pole = 4.437 x[1] = -0.9078 y[1] (analytic) = 1.2134437334149544126177568269437 y[1] (numeric) = 1.2134437334149544129565390530079 absolute error = 3.3878222606421665424750644602842e-19 relative error = 2.7919071707659083870735963007744e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9151 Order of pole = 4.437 x[1] = -0.9077 y[1] (analytic) = 1.2137111148350465250061083046132 y[1] (numeric) = 1.2137111148350465253454218060019 absolute error = 3.3931350138870792719208031641351e-19 relative error = 2.7956693915159824938947050792240e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.915 Order of pole = 4.437 x[1] = -0.9076 y[1] (analytic) = 1.2139785846408206417537542530526 y[1] (numeric) = 1.2139785846408206420935994981952 absolute error = 3.3984524514259369618372339263260e-19 relative error = 2.7994336098041101188450085590678e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9149 Order of pole = 4.437 x[1] = -0.9075 y[1] (analytic) = 1.2142461428712367855868982841184 y[1] (numeric) = 1.214246142871236785927275741909 absolute error = 3.4037745779057005464575135295735e-19 relative error = 2.8031998272253515956635006267398e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9148 Order of pole = 4.437 x[1] = -0.9074 y[1] (analytic) = 1.2145137895652764483574891219643 y[1] (numeric) = 1.2145137895652764486983992617622 absolute error = 3.4091013979784536640343515995738e-19 relative error = 2.8069680453761737707954048800547e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9147 Order of pole = 4.437 x[1] = -0.9073 y[1] (analytic) = 1.214781524761942605241595202993 y[1] (numeric) = 1.2147815247619426055830384946231 absolute error = 3.4144329163014088693924376345370e-19 relative error = 2.8107382658544513988303410374943e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9146 Order of pole = 4.437 x[1] = -0.9072 y[1] (analytic) = 1.2150493485002597289487354155197 y[1] (numeric) = 1.2150493485002597292907123292734 absolute error = 3.4197691375369138547009720128906e-19 relative error = 2.8145104902594685394789396261176e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9145 Order of pole = 4.437 x[1] = -0.9071 y[1] (analytic) = 1.2153172608192738039421756422444 y[1] (numeric) = 1.2153172608192738042846866488797 absolute error = 3.4251100663524576784780850283672e-19 relative error = 2.8182847201919199560897708799062e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9144 Order of pole = 4.437 x[1] = -0.907 y[1] (analytic) = 1.2155852617580523406702007782177 y[1] (numeric) = 1.2155852617580523410132463489598 absolute error = 3.4304557074206770028389461963661e-19 relative error = 2.8220609572539125157084562494944e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9143 Order of pole = 4.437 x[1] = -0.9069 y[1] (analytic) = 1.2158533513556843898083719065849 y[1] (numeric) = 1.2158533513556843901519525131268 absolute error = 3.4358060654193623389993843002600e-19 relative error = 2.8258392030489665906808333969064e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9142 Order of pole = 4.437 x[1] = -0.9068 y[1] (analytic) = 1.2161215296512805565127783240055 y[1] (numeric) = 1.2161215296512805568568944385087 absolute error = 3.4411611450314643010468569012548e-19 relative error = 2.8296194591820174618020480251508e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9141 Order of pole = 4.437 x[1] = -0.9067 y[1] (analytic) = 1.2163897966839730146842941172628 y[1] (numeric) = 1.2163897966839730150289462123573 absolute error = 3.4465209509450998679906263205524e-19 relative error = 2.8334017272594167230134483722888e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.914 Order of pole = 4.437 x[1] = -0.9066 y[1] (analytic) = 1.2166581524929155212438490022113 y[1] (numeric) = 1.2166581524929155215890375509967 absolute error = 3.4518854878535586541030174179782e-19 relative error = 2.8371860088889336876491606829267e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9139 Order of pole = 4.437 x[1] = -0.9065 y[1] (analytic) = 1.2169265971172834304187231458526 y[1] (numeric) = 1.2169265971172834307644486218981 absolute error = 3.4572547604553091875636508369529e-19 relative error = 2.8409723056797567962342264569720e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9137 Order of pole = 4.437 x[1] = -0.9064 y[1] (analytic) = 1.2171951305962737080398757019808 y[1] (numeric) = 1.2171951305962737083861385793262 absolute error = 3.4626287734540051974185637617844e-19 relative error = 2.8447606192424950258361847659528e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9136 Order of pole = 4.437 x[1] = -0.9063 y[1] (analytic) = 1.2174637529691049458503168005043 y[1] (numeric) = 1.2174637529691049461971175536601 absolute error = 3.4680075315584919088661486397713e-19 relative error = 2.8485509511891793009719854212292e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9135 Order of pole = 4.437 x[1] = -0.9062 y[1] (analytic) = 1.2177324642750173758245327402229 y[1] (numeric) = 1.2177324642750173761718718441712 absolute error = 3.4733910394828123468818587575963e-19 relative error = 2.8523433031332639060721212760385e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9134 Order of pole = 4.437 memory used=198.3MB, alloc=4.5MB, time=11.26 x[1] = -0.9061 y[1] (analytic) = 1.2180012645532728844989741445249 y[1] (numeric) = 1.2180012645532728848468520747196 absolute error = 3.4787793019462136481936480290195e-19 relative error = 2.8561376766896278995038704445076e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9133 Order of pole = 4.437 x[1] = -0.906 y[1] (analytic) = 1.2182701538431550273136168491635 y[1] (numeric) = 1.2182701538431550276620340815309 absolute error = 3.4841723236731533816201308489783e-19 relative error = 2.8599340734745765291555417255520e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9132 Order of pole = 4.437 x[1] = -0.9059 y[1] (analytic) = 1.2185391321839690429646053009791 y[1] (numeric) = 1.2185391321839690433135623119184 absolute error = 3.4895701093933058767834663979554e-19 relative error = 2.8637324951058426495836190279554e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9131 Order of pole = 4.437 x[1] = -0.9058 y[1] (analytic) = 1.2188081996150418677679882561492 y[1] (numeric) = 1.2188081996150418681174855225334 absolute error = 3.4949726638415685612089903399083e-19 relative error = 2.8675329432025881407247031049094e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.913 Order of pole = 4.437 x[1] = -0.9057 y[1] (analytic) = 1.2190773561757221500345565762768 y[1] (numeric) = 1.2190773561757221503845945754526 absolute error = 3.5003799917580683058236354472428e-19 relative error = 2.8713354193854053281741514218711e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9129 Order of pole = 4.437 x[1] = -0.9056 y[1] (analytic) = 1.219346601905380264455792930365 y[1] (numeric) = 1.2193466019053802648063721401538 absolute error = 3.5057920978881677788652013072960e-19 relative error = 2.8751399252763184050333195008003e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9128 Order of pole = 4.437 x[1] = -0.9055 y[1] (analytic) = 1.2196159368434083265009432204752 y[1] (numeric) = 1.2196159368434083268520641191734 absolute error = 3.5112089869824718082145519166395e-19 relative error = 2.8789464624987848553273096066482e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9127 Order of pole = 4.437 x[1] = -0.9054 y[1] (analytic) = 1.2198853610292202068252195586269 y[1] (numeric) = 1.2198853610292202071768826250066 absolute error = 3.5166306637968337521628386522633e-19 relative error = 2.8827550326776968789951351684084e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9126 Order of pole = 4.437 x[1] = -0.9053 y[1] (analytic) = 1.220154874502251545689144632266 y[1] (numeric) = 1.2201548745022515460413503455752 absolute error = 3.5220571330923618786258648224194e-19 relative error = 2.8865656374393828184542118571084e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9125 Order of pole = 4.437 x[1] = -0.9052 y[1] (analytic) = 1.2204244773019597673890473054102 y[1] (numeric) = 1.2204244773019597677417961453737 absolute error = 3.5274883996354257528177267446393e-19 relative error = 2.8903782784116085867410887768188e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9124 Order of pole = 4.437 x[1] = -0.9051 y[1] (analytic) = 1.2206941694678240946987193123742 y[1] (numeric) = 1.220694169467824095052011759194 absolute error = 3.5329244681976626333958850742525e-19 relative error = 2.8941929572235790972303357620970e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9123 Order of pole = 4.437 x[1] = -0.905 y[1] (analytic) = 1.2209639510393455633222429107781 y[1] (numeric) = 1.2209639510393455636760794451337 absolute error = 3.5383653435559838770898389136720e-19 relative error = 2.8980096755059396949335053162702e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9122 Order of pole = 4.437 x[1] = -0.9049 y[1] (analytic) = 1.2212338220560470363579993703563 y[1] (numeric) = 1.2212338220560470367123804734055 absolute error = 3.5438110304925813518255940708373e-19 relative error = 2.9018284348907775893800902695966e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9121 Order of pole = 4.437 x[1] = -0.9048 y[1] (analytic) = 1.2215037825574732187738681839112 y[1] (numeric) = 1.2215037825574732191287943372907 absolute error = 3.5492615337949338583581357045738e-19 relative error = 2.9056492370116232890824007846389e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.912 Order of pole = 4.437 x[1] = -0.9047 y[1] (analytic) = 1.2217738325831906718936268965885 y[1] (numeric) = 1.2217738325831906722490985824141 absolute error = 3.5547168582558135604241344952800e-19 relative error = 2.9094720835034520375862868881379e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9119 Order of pole = 4.437 x[1] = -0.9046 y[1] (analytic) = 1.2220439721727878278945614594998 y[1] (numeric) = 1.2220439721727878282505791603672 absolute error = 3.5601770086732924234271344113715e-19 relative error = 2.9132969760026852511096352643012e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9118 Order of pole = 4.437 x[1] = -0.9045 y[1] (analytic) = 1.2223142013658750043162970235732 y[1] (numeric) = 1.2223142013658750046728612225583 absolute error = 3.5656419898507486616674891053190e-19 relative error = 2.9171239161471919577705716037158e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9117 Order of pole = 4.437 x[1] = -0.9044 y[1] (analytic) = 1.2225845202020844185808590993836 y[1] (numeric) = 1.2225845202020844189379702800433 absolute error = 3.5711118065968731941293329680000e-19 relative error = 2.9209529055762902384073023650728e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9116 Order of pole = 4.437 memory used=202.1MB, alloc=4.5MB, time=11.49 x[1] = -0.9043 y[1] (analytic) = 1.2228549287210702025239750185901 y[1] (numeric) = 1.2228549287210702028816336649627 absolute error = 3.5765864637256761088368918964737e-19 relative error = 2.9247839459307486689915323735536e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9115 Order of pole = 4.437 x[1] = -0.9042 y[1] (analytic) = 1.2231254269625084169376256425017 y[1] (numeric) = 1.2231254269625084172958322391073 absolute error = 3.5820659660564931357924578882564e-19 relative error = 2.9286170388527877646373972500801e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9114 Order of pole = 4.437 x[1] = -0.9041 y[1] (analytic) = 1.223396014966097066123857273189 y[1] (numeric) = 1.2233960149660970664826123050304 absolute error = 3.5875503184139921285083706647706e-19 relative error = 2.9324521859860814252078522396811e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9113 Order of pole = 4.437 x[1] = -0.904 y[1] (analytic) = 1.2236666927715561124598637324771 y[1] (numeric) = 1.2236666927715561128191676850399 absolute error = 3.5930395256281795541453686479192e-19 relative error = 2.9362893889757583825204615849779e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9112 Order of pole = 4.437 x[1] = -0.9039 y[1] (analytic) = 1.2239374604186274909743485840714 y[1] (numeric) = 1.2239374604186274913342019433249 absolute error = 3.5985335925344069922696907667582e-19 relative error = 2.9401286494684036491545351722534e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9111 Order of pole = 4.437 x[1] = -0.9038 y[1] (analytic) = 1.224208317947075123935177484008 y[1] (numeric) = 1.2242083179470751242955807364054 absolute error = 3.6040325239733776422413297560579e-19 relative error = 2.9439699691120599688615617627400e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.911 Order of pole = 4.437 x[1] = -0.9037 y[1] (analytic) = 1.2244792653966849354483306545605 y[1] (numeric) = 1.2244792653966849358092842870396 absolute error = 3.6095363247911528392458568252129e-19 relative error = 2.9478133495562292685808907106583e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9109 Order of pole = 4.437 x[1] = -0.9036 y[1] (analytic) = 1.2247503028072648660681654866932 y[1] (numeric) = 1.2247503028072648664296699866772 absolute error = 3.6150449998391585789822568245435e-19 relative error = 2.9516587924518741120626166621517e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9108 Order of pole = 4.437 x[1] = -0.9035 y[1] (analytic) = 1.2250214302186448874189992861188 y[1] (numeric) = 1.2250214302186448877810551415162 absolute error = 3.6205585539741920510192323165767e-19 relative error = 2.9555062994514191550996243256174e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9107 Order of pole = 4.437 x[1] = -0.9034 y[1] (analytic) = 1.2252926476706770168280221879914 y[1] (numeric) = 1.2252926476706770171906298871972 absolute error = 3.6260769920584281808324542724629e-19 relative error = 2.9593558722087526023707530040138e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9106 Order of pole = 4.437 x[1] = -0.9033 y[1] (analytic) = 1.2255639552032353319695502752623 y[1] (numeric) = 1.2255639552032353323327103071582 absolute error = 3.6316003189594261805352564583381e-19 relative error = 2.9632075123792276658970431835592e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9105 Order of pole = 4.437 x[1] = -0.9032 y[1] (analytic) = 1.2258353528562159855206289457188 y[1] (numeric) = 1.2258353528562159858843417996738 absolute error = 3.6371285395501361083152899532207e-19 relative error = 2.9670612216196640251130300808084e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9104 Order of pole = 4.437 x[1] = -0.9031 y[1] (analytic) = 1.2261068406695372198279965827421 y[1] (numeric) = 1.226106840669537220192262748613 absolute error = 3.6426616587089054365896736490179e-19 relative error = 2.9709170015883492885550516614298e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9103 Order of pole = 4.437 x[1] = -0.903 y[1] (analytic) = 1.2263784186831393815864185948401 y[1] (numeric) = 1.2263784186831393819512385629721 absolute error = 3.6481996813194856288911960244404e-19 relative error = 2.9747748539450404571685412590929e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9102 Order of pole = 4.437 x[1] = -0.9029 y[1] (analytic) = 1.2266500869369849365284018990457 y[1] (numeric) = 1.2266500869369849368937761602728 absolute error = 3.6537426122710387254981429581637e-19 relative error = 2.9786347803509653892362775417365e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9101 Order of pole = 4.437 x[1] = -0.9028 y[1] (analytic) = 1.2269218454710584841252999333143 y[1] (numeric) = 1.2269218454710584844912289789602 absolute error = 3.6592904564581439378203458524775e-19 relative error = 2.9824967824688242669295671951147e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.91 Order of pole = 4.437 x[1] = -0.9027 y[1] (analytic) = 1.2271936943253667722998182931113 y[1] (numeric) = 1.2271936943253667726663026149893 absolute error = 3.6648432187808042515540638769858e-19 relative error = 2.9863608619627910644843383199263e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9099 Order of pole = 4.437 x[1] = -0.9026 y[1] (analytic) = 1.2274656335399387121499310974441 y[1] (numeric) = 1.2274656335399387125169711878586 absolute error = 3.6704009041444530386183337127270e-19 relative error = 2.9902270204985150180041251690204e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9098 Order of pole = 4.437 x[1] = -0.9025 y[1] (analytic) = 1.2277376631548253926842181996762 y[1] (numeric) = 1.2277376631548253930518145514222 absolute error = 3.6759635174599606778854397804237e-19 relative error = 2.9940952597431220968919274851537e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=206.0MB, alloc=4.5MB, time=11.70 Real estimate of pole used Radius of convergence = 0.9097 Order of pole = 4.437 x[1] = -0.9024 y[1] (analytic) = 1.2280097832101000955686333685428 y[1] (numeric) = 1.2280097832101000959367864749072 absolute error = 3.6815310636436411847181775725073e-19 relative error = 2.9979655813652164769129303375470e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9096 Order of pole = 4.437 x[1] = -0.9023 y[1] (analytic) = 1.2282819937458583098847135748952 y[1] (numeric) = 1.2282819937458583102534239296569 absolute error = 3.6871035476172588493266023771551e-19 relative error = 3.0018379870348820148900729970637e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9095 Order of pole = 4.437 x[1] = -0.9022 y[1] (analytic) = 1.2285542948022177468992395298057 y[1] (numeric) = 1.2285542948022177472685076272365 absolute error = 3.6926809743080348839569753838728e-19 relative error = 3.0057124784236837250344580352180e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9094 Order of pole = 4.437 x[1] = -0.9021 y[1] (analytic) = 1.2288266864193183548453576297929 y[1] (numeric) = 1.2288266864193183552151839646577 absolute error = 3.6982633486486540789256388942296e-19 relative error = 3.0095890572046692569125944814137e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9093 Order of pole = 4.437 x[1] = -0.902 y[1] (analytic) = 1.2290991686373223337151734750567 y[1] (numeric) = 1.2290991686373223340855585426144 absolute error = 3.7038506755772714675105721282450e-19 relative error = 3.0134677250523703750524715258286e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9092 Order of pole = 4.437 x[1] = -0.9019 y[1] (analytic) = 1.2293717414964141500638271367609 y[1] (numeric) = 1.2293717414964141504347714327646 absolute error = 3.7094429600375189997133989167103e-19 relative error = 3.0173484836428044401904619122006e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9091 Order of pole = 4.437 x[1] = -0.9018 y[1] (analytic) = 1.2296444050368005518250603595549 y[1] (numeric) = 1.2296444050368005521965643802528 absolute error = 3.7150402069785122249046384024513e-19 relative error = 3.0212313346534758921610568254379e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.909 Order of pole = 4.437 x[1] = -0.9017 y[1] (analytic) = 1.229917159298710583138285895695 y[1] (numeric) = 1.2299171592987105835103501378305 absolute error = 3.7206424213548569833650097392652e-19 relative error = 3.0251162797633777344314367434851e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9089 Order of pole = 4.437 x[1] = -0.9016 y[1] (analytic) = 1.230190004322395599187169177304 y[1] (numeric) = 1.2301900043223955995597941381167 absolute error = 3.7262496081266561067356216760555e-19 relative error = 3.0290033206529930202828853912235e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9088 Order of pole = 4.437 x[1] = -0.9015 y[1] (analytic) = 1.2304629401481292810497325434992 y[1] (numeric) = 1.2304629401481292814229187207251 absolute error = 3.7318617722595161273898978455906e-19 relative error = 3.0328924590042963406410566063817e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9087 Order of pole = 4.437 x[1] = -0.9014 y[1] (analytic) = 1.2307359668162076505599922493172 y[1] (numeric) = 1.2307359668162076509337401411896 absolute error = 3.7374789187245539967401085424019e-19 relative error = 3.0367836965007553135571066034851e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9086 Order of pole = 4.437 x[1] = -0.9013 y[1] (analytic) = 1.2310090843669490851811384935814 y[1] (numeric) = 1.2310090843669490855554485988313 absolute error = 3.7431010524984038124913997726557e-19 relative error = 3.0406770348273320753417068017848e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9085 Order of pole = 4.437 x[1] = -0.9012 y[1] (analytic) = 1.2312822928406943328902687130775 y[1] (numeric) = 1.2312822928406943332651415309339 absolute error = 3.7487281785632235548562303904554e-19 relative error = 3.0445724756704847733539550668840e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9084 Order of pole = 4.437 x[1] = -0.9011 y[1] (analytic) = 1.2315555922778065270746844006403 y[1] (numeric) = 1.2315555922778065274501204308309 absolute error = 3.7543603019067018317421481999984e-19 relative error = 3.0484700207181690604472059034340e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9083 Order of pole = 4.437 x[1] = -0.901 y[1] (analytic) = 1.2318289827186712014397617150016 y[1] (numeric) = 1.2318289827186712018157614577538 absolute error = 3.7599974275220646329258560014082e-19 relative error = 3.0523696716598395910738428277991e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9082 Order of pole = 4.437 x[1] = -0.9009 y[1] (analytic) = 1.2321024642036963049284061605074 y[1] (numeric) = 1.2321024642036963053049701165482 absolute error = 3.7656395604080820932265386899150e-19 relative error = 3.0562714301864515190510188450052e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9081 Order of pole = 4.437 x[1] = -0.9008 y[1] (analytic) = 1.2323760367733122166521016250801 y[1] (numeric) = 1.232376036773312217029230295637 absolute error = 3.7712867055690752646914426834626e-19 relative error = 3.0601752979904619969893936535922e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.908 Order of pole = 4.437 x[1] = -0.9007 y[1] (analytic) = 1.2326497004679717608335640750852 y[1] (numeric) = 1.2326497004679717612112579618867 absolute error = 3.7769388680149228978067191527992e-19 relative error = 3.0640812767658316773868989051923e-17 % h = 0.0001 TOP MAIN SOLVE Loop memory used=209.8MB, alloc=4.5MB, time=11.91 Real estimate of pole used Radius of convergence = 0.9079 Order of pole = 4.437 x[1] = -0.9006 y[1] (analytic) = 1.2329234553281502217610102160531 y[1] (numeric) = 1.2329234553281502221392698213292 absolute error = 3.7825960527610682317465627607576e-19 relative error = 3.0679893682080262153895655527578e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9078 Order of pole = 4.437 x[1] = -0.9005 y[1] (analytic) = 1.2331973013943453587540514385092 y[1] (numeric) = 1.2331973013943453591328772649921 absolute error = 3.7882582648285257936736978837784e-19 relative error = 3.0718995740140177732214500323803e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9077 Order of pole = 4.437 x[1] = -0.9004 y[1] (analytic) = 1.2334712387070774211412233784836 y[1] (numeric) = 1.233471238707077421520615929408 absolute error = 3.7939255092438882071042845888595e-19 relative error = 3.0758118958822865262856987385657e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9076 Order of pole = 4.437 x[1] = -0.9003 y[1] (analytic) = 1.2337452673068891632491614325949 y[1] (numeric) = 1.2337452673068891636291212116988 absolute error = 3.7995977910393330093503369730695e-19 relative error = 3.0797263355128221709387929716821e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9075 Order of pole = 4.437 x[1] = -0.9002 y[1] (analytic) = 1.234019387234345859403432577944 y[1] (numeric) = 1.2340193872343458597839600894693 absolute error = 3.8052751152526294780527668406159e-19 relative error = 3.0836428946071254339400192590721e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9074 Order of pole = 4.437 x[1] = -0.9001 y[1] (analytic) = 1.2342935985300353189410338574016 y[1] (numeric) = 1.2342935985300353193221296060944 absolute error = 3.8109574869271454668181860942621e-19 relative error = 3.0875615748682095835782126780312e-17 % h = 0.0001 TOP MAIN SOLVE Loop Real estimate of pole used Radius of convergence = 0.9073 Order of pole = 4.437 x[1] = -0.9 y[1] (analytic) = 1.2345679012345679012345679012346 y[1] (numeric) = 1.2345679012345679016162323923458 absolute error = 3.8166449111118542499726216537025e-19 relative error = 3.0914823780006019424778235394990e-17 % h = 0.0001 Finished! Maximum Iterations Reached before Solution Completed! diff ( y , x , 1 ) = m1 * 2.0 / x / x / x ; Iterations = 1000 Total Elapsed Time = 11 Seconds Elapsed Time(since restart) = 11 Seconds Expected Time Remaining = 23 Seconds Optimized Time Remaining = 23 Seconds Time to Timeout = 14 Minutes 48 Seconds Percent Done = 33.37 % > quit memory used=211.2MB, alloc=4.5MB, time=11.99